UCHE - Thermoeconomic Analysis and Simulation of a Combined Power and Desalination Plant

Universidad de Zaragoza

Ph. D. Thesis

Francisco Javier Uche Marcuello

Departamento de Ingeniería Mecánica

THERMOECONOMIC ANALYSIS AND SIMULATION OF A COMBINED POWER

AND DESALINATION PLANT

THERMOECONOMIC ANALYSIS AND SIMULATION OF A COMBINED POWERAND DESALINATION PLANT

Departamento de Ingeniería Mecánica

Universidad de Zaragoza

Ph. D. Tesis

Francisco Javier Uche Marcuello

Zaragoza, Mars 2000

D. Antonio Valero Capilla, Catedrático del Departamento de Ingeniería Mecánicade la Universidad de Zaragoza, y D. Luis Serra De Renobales, Profesor Titular delÁrea de Máquinas y Motores Térmicos de la Universidad de Zaragoza

CERTIFICAN

que la memoria titulada

Thermoeconomic Analysis and Simulation of a Com-bined Power and Desalination Plant

presentada por el Ingeniero IndustrialD. Francisco Javier Uche Marcuello para optar al grado de Doctor en el programa deOptimización Energética del Departamento de Ingeniería Mecánica, ha sido realiza-da bajo su dirección.

Zaragoza, 20 de Marzo de 2000

Fdo: Antonio Valero Capilla Fdo: Luis Serra de Renobales

a Sonia

Agradecimientos

Quiero agradecer especialmente la realización de esta tesis doctoral a mis padres Luisy Pilar, y a mi hermano José Luis por su paciencia y ánimos para realizarla, a pesar deno entender a veces muy claramente la finalidad de la misma.

Por supuesto, Natalia es la que más me ha tenido que aguantar y animar en los malosmomentos que a veces he tenido. Además, ella ha tenido siempre un interés especialpara que yo la realizara.

Los directores de mi tesis, Antonio y Luis, han estado siempre a mi lado disponiblespara cualquier duda o sugerencia en su realización. Nuestras reuniones periódicas hanservido para enriquecerme personalmente. Esta tesis también ha servido para estable-cer una relación especial de amistad y confianza con Luis, que para mí es fundamentalen el trabajo diario.

También quiero agradecer al personal de la Central Térmica Teruel (ENDESA) por suflexibilidad de horarios, que me ha permitido desarrollar gran parte de mi tesis docto-ral durante mi estancia en Andorra. Y a mis compañeros de piso durante dicha estan-cia, que me dejaron trabajar en todo momento sin impedimento alguno.

Finalmente, quiero agradecer a Rosa y a Morris su ayuda en la edición. Y a esa granfamilia que es CIRCE, y al gran ambiente que existe dentro de ella.

Acknowledgements

The financial support provided by ICWES (International Center for Water and EnergySystems, United Arab Emirates) is gratefully acknowledged. Sincere appreciation isexpressed to D. M. K. Al-Gobaisi, Director of ICWES, for his continued support andencouragement during the course of this thesis. The discussions that the author andmy directors had with him and Ali El-Nashar and Asghar Husain were very helpful.Thanks are also extended to Hanif Sultan and John Nynam who provided the technicalinformation essential to the design of my simulator.

Thermoeconomic analysis and simulation of a combined power and desalination plant

La desalación de aguas de mar o salobres es una de las formas más utilizadas paradotar con la calidad suficiente a la población de los recursos hídricos necesarios parasu manutención y desarrollo. En un sector industrial en constante crecimiento, ya queel consumo humano per cápita sigue aumentando constantemente con el incrementodel nivel de vida, a pesar de las campañas buscando el ahorro y la racionalidad en elconsumo, sobre todo en la agricultura intensiva.

España es país que cuenta con un claro déficit de agua en las zonas costeras delLevante y Sur, así como en los dos archipiélagos principales (Baleares y Canarias),dichas zonas coinciden con ser las más turísticas del país, lo que significa que lademanda se multiplica en verano. Sin tener en cuenta la posibilidad de efectuar tras-vases de otras cuencas hidrográficas no deficitarias, el problema está siendo resueltoprincipalmente por plantas de Osmosis Inversa, plantas cuyas dimensiones y produc-ción se adecuan mucho mejor a las necesidades de los diferentes tamaños de losnúcleos ó asentamientos estables de población. El coste del agua producida siguesiendo muy alto en comparación con la obtención por medios naturales, pero sinembargo es menor que otros métodos de desalación.

Sin embargo, la situación de España no es extrapolable a las zonas con verdaderosproblemas de escasez de agua: los países desérticos del Golfo Pérsico. Su escasísimapluviometría, sus elevadas temperaturas durante todo el año y la casi nula imper-meabilidad de sus suelos disparan su consumo de agua. Son además países de relati-vamente reciente creación, por lo que la demanda de energía eléctrica también debeser resuelta. La instalación de grandes plantas de cogeneración permite a la vez resol-ver los dos problemas, con la utilización de los inmensos recursos petrolíferos y gasde la zona. Las plantas duales de generación de potencia acopladas con las unidadesde desalación por destilación flash multietapa producen el 80% del agua desalada enel mundo. Pero ello no significa que sea el método más eficiente de producir esos dosproductos necesarios para toda sociedad.

El análisis termoeconómico permite conocer el funcionamiento interno de dichasplantas de generación de electricidad y agua dulce, las posibilidades de ahorro queofrece este modo combinado de producción. Es esencial realizar dicho análisis de

Resumen

Resumen

12


forma conjunta, cosa que normalmente no se hace en este tipo de instalaciones: cadaplanta es gestionada independientemente.

Esta Tesis Doctoral desarrolla el análisis termoeconómico completo de la planta decogeneración más grande que actualmente existe (en cuanto a la producción de aguapor unidad desaladora), que consta de una planta con una turbina de vapor para lageneración de electricidad y una desaladora por destilación flash de un único efectopor cada una de sus etapas. Es una tesis eminentemente práctica, es decir, trata deaplicar las metodologías que la Termoeconomía actualmente está aplicando a otrossistemas tales como plantas de potencia a un sistema muy complejo en el cual losprocesos químicos también son importantes en el balance de la instalación, no sólolos procesos mecánicos y térmicos.

El análisis termoeconómico comprende cuatro partes principales que se detallan acontinuación:

• En primer lugar, el análisis de costes permite conocer los costes físicos de los flu-jos más importantes de las dos plantas, así como los costes finales de producciónde agua y energía, teniendo en cuenta los costes de operación y de adquisición ymantenimiento de los equipos de la planta. Dicho análisis se basa en la creaciónde un modelo termoeconómico que representa de una forma funcional los proce-sos que ocurren dentro de la planta de potencia y de agua. Los resultados obteni-dos son comparados con métodos tradicionales de contabilidad de costes que sehan usado para asignar costes a los productos industriales.

• Después, el análisis desarrolla el diagnóstico de la planta combinada, es decir,analiza los efectos provocados por una o varias ineficiencias simuladas dentro dela planta. Para ello, se ha construido un simulador de los dos procesos a partir deun modelo matemático y datos reales de una planta de cogeneración, que permiteconocer los estados termodinámicos de referencia y con la ineficiencia con unaprecisión suficiente para nuestro análisis. Dichos efectos se traducen a un consu-mo adicional de fuel, incremento en la irreversibilidad de los diferentes procesosy una menor eficiencia en los mismos, además de ayudar a conocer las relacionesde los diferentes componentes de una instalación. En este análisis se demuestraque la planta de potencia los parámetros guía de funcionamiento de cada compo-nente son locales, es decir, una variación de ellos no significa prácticamente alresto de componentes del sistema. Sin embargo, en la unidad MSF todos elemen-tos principales están interconectados a través de los flujos principales que circu-lan por los destiladores, y por lo tanto los fallos ó mejoras sufridas en elfuncionamiento de la planta afectan a toda ella, no sólo al equipo en el que estánocurriendo.

• La tercera parte del análisis termodinámico es la optimización de la planta de po-tencia a partir de la optimización local de sus componentes. En la planta destila-dora de agua la optimización local no es posible al no estar sus componentes

Resumen

Thermoeconomic analysis and simulation of a combined power and desalination plant 13

termodinámicamente aislados, como ya se vió en la diagnosis de la planta. Estametodología es muy valida para el diseño de nuevas plantas o la readaptación deplantas existentes hacia un mayor ahorro en las mismas.

• Finalmente, un nuevo apartado conteniendo los conceptos de coste, precio y bene-ficio obtenidos se desarrolla brevemente, para aclarar errores que normalmente secometen en la contabilización de los costes de una instalación.

La Tesis Doctoral también incluye dos partes introductorias, la primera contiene lasituación en los países con escasez de agua y los métodos de desalación más comunesutilizados actualmente. La segunda parte introductoria incluye el estado actual de lateoría termoeconómica necesaria para el análisis termoeconómico de la planta.


Desalination is the most important source of drinking water in arid zones, especiallyin the Gulf Area. Desalination consumes a lot of energy and, unfortunately, mostlyfrom oil or natural gas. Co-generation plants providing freshwater and electricity areused in the arid areas. The combination of steam turbine plants and MSF (Multi-stageFlash) units is one of the most common schemes to meet water and energyrequirements, providing almost 80% of all desalinated water in the world.

A dual-purpose plant is a very complex system. Its behaviour is difficult to model,especially when all the available configurations of both sub-systems are considered.Usually plant performance is analysed separately, neglecting component interactionsand possible savings from the combined systems.

Thermoeconomic analysis techniques are the most convenient tools to analyze thesesystems, because they can:

• Calculate the costs of the flows and products of a plant based on physical criteria(Second Law of Thermodynamics).

• Assess alternatives to save energy.

• Optimize operations.

• Locally optimize subsystems.

• Perform energy audits and assess the fuel impact of malfunctions (operationdiagnosis)

This Ph. D. Thesis develops the complete thermoeconomic analysis applied in anexisting steam power plant and MSF desalination unit, including cost analysis,diagnosis and local optimization of the plant. Cost analysis provides the physicalcosts of the main flows of the dual plant depending on operating conditions. Specialemphasis was made on the interactions between the plant components of bothsubsystems: new concepts such as induced or intrinsic malfunction, dysfunction orthe malfunction matrix were included. The results demonstrate the effect of differentconditions or inefficiencies in terms of water and energy costs and additional fuelconsumption during an inefficiency. Operation recommendations were also included

Abstract

Abstract

16


in the analysis. Local optimization of the dual plant locates the optimum point foreach operating condition and is a very powerful tool for the design analysis.

Thermoeconomic analysis was developed using a validated model (simulator) of theplant to determine the thermodynamic reference state at design conditions for anyload point, ambient condition, operating mode etc. Plant data from a dual-plant in theGulf were used to adapt the mathematical models. The simulator also obtained thethermodynamic state of the plant when an inefficiency is estimated in the plantdiagnosis.


CHAPTER 1

Introduction

Water scarcity will soon be a serious problem, especially considering the rapidlyincreasing world population and water consumption per capita. Fortunately, part ofthis problem may be alleviated by desalting seawater, although this process consumesa lot of energy and may be difficult to use in non-developed countries. This Ph. D.Thesis contributes to searching for a way to reduce the energy required by desaltingplants and provides tools to improve desalination technology.

Several studies and international organizations focus on energy and others on water,but there seems to be a marked lack of attention on combined water and energy issues.The interaction between water production and energy is the main topic in this thesis.The main objective is to determine the validity of the thermoeconomic analysis invery complex systems like a dual-purpose power and desalination plant.

This thesis considers the behavior of one of the most developed systems for providingwater within the following framework:

• Increasing human consumption and its consequences.

• Water quality and the uses derived from its quality.

• The world water crisis is mostly focused on water stressed areas. In these areasthe water problem may also be solved by using desalting plants.

• The interactions among the methods required to provide energy to desalt water.

• The reasons for studying the steam turbine power plant + Multi-Stage Flash(MSF) desalination unit from thermodynamic point of view.

• How Thermoeconomic techniques as the most useful to study complex systems.

The final section of this chapter includes the structure of this Ph. D. Thesis.

Introduction

18


1.1 Water requirements

According to Al-Gobaisi (1999), all life depends on water and all terrestrial species,including humans, depend on fresh or non-saline water. Although the oceansrepresent the largest water reservoir on earth (covering three-quarters of its surface),it contains a high concentration of dissolved salts (more than the 3% of its weight).This makes it unsuitable for humans, industry and even irrigation. Less than 3% ofthe earth's water is non-saline, and the vast majority of it is locked up in glaciers andice sheets. Water is moved around the earth in global cycles (evaporation-cloudformation-rain-percolation), but only when it is non-saline and in the liquid state, canit be used by humans. Human development and indeed civilization requires a reliablesupply of even greater volumes of fresh water for drinking, cooking, washing andsanitation. Furthermore, industry consumes on average 200 tons of water per ton ofmanufactured product (Al-Gobaisi, 1997). Water also makes up more than half of thehuman body. An average adult drinks about 2.5 liters of water per day and needs0.75 liters a day just to stay alive. According to the World Health Organization, about150 liters of water are needed per day for a satisfactory hygienic life (Al-Gobaisi,1999). But in the South more than 1,500 million people do not have drinking water(Intermón, 1998).

The imbalance between the available water resources and demand is clear, especiallyin arid areas like the Arabian Gulf or Northern Africa. Human water consumption percapita in this region is very high (including domestic, agricultural and industrial uses)ranging from 300 to 1,500 liters per day. Rapidly rising incomes in some countries,with the resultant increase of living standards, and water losses in the network haveled to even higher per capita water consumption. Intensive agriculture under aridconditions increases this demand. The available water resources from perennialsurface water, renewable ground water and reclaimed wastewater are insufficient tomeet the demand. Overexploitation of ground-water decreases ground-water levelsand deteriorates water quality, including salt-water intrusion. On the basis of the pastexperiences in arid zones, renewable freshwater resources of 1,000 cubic meters percapita per year have been considered the limit for a chronic water scarcity that willimpede development and harm human health. In terms of resources deficiency, waterstress is defined as an annual renewable resource less than 1,000 cubic meters percapita per year. All the countries of the Arabian World suffer from water stress(Al-Gobaisi, 1999).

1.2 Water quality and uses

Water use depends on its quality. The salinity of average seawater is 34,800 ppm,although it may vary between oceans. For example, the total dissolved solids (TDS)in Arabian Gulf seawater is between 43,000 and 50,000 ppm, while the Atlantic

World water resources and demand


Ocean has an average TDS of 36,000 ppm, and 33,600 ppm for the Pacific Oceanwater (Abu Qdais, 1999).

The highest limit for human consumption is 1,000 ppm (Spiegler and El-Sayed,1994), although the maximum permissible salt concentration in drinking waterdepends on the type of salt, the total daily water consumption and the climate (e.g., ifthe climate is hot and the salt is mainly sodium chloride, excess salt can even bebeneficial to the human body). On average humans consume 2-8 liters per day. Thus,salt-water rejection for drinking water does not present a serious economic problemin the future, if compared with the water demand for agricultural or industrialpurposes.

The purity of water for industry strongly depends on the use. Sometimes brackishwater (water with less than 5,000 ppm) is enough for industrial purposes, butultrapure water is needed for specific processes like cooling power generation plants.The amount of water for industry is several times human water consumption whichis why we need more research on saving water in industrial processes and reusingwaste water.

Non-natural irrigation (that is, not provided by rainfall) consumes the most amount ofthe world's water. For example, in China agriculture uses up 87% of the total waterdemand. In arid areas irrigation consumes enormous amounts of water. Desalinationprocesses are so expensive that they are not feasibly introduced to irrigate land.However, brackish waters with a moderate salinity (about 2,000 ppm) are acceptablefor some crops. The tolerance limits of each plant must be examined as a function ofthe soil, climate, saltwater composition, irrigation method and additional treatments(fertilizers).

1.3 World water resources and demand

Seawater desalination is most common in the countries bordering the Persian-Arabian gulf, the north of Africa and the Canary islands, the Caribbean islands, thePacific region (Australia, Japan, Korea and China), and the south and east of Spain, aswell as various locations in the American south-west and Florida. The following is abrief explanation of water demand and disposal in these areas in order to introducethe reader to the world’s water scarcity problem.

1.3.1 Gulf Region

The annual per capita annual water resources of countries in the Gulf region (UnitedArab Emirates, Saudi Arabia, Bahrain, Oman, Qatar and Kuwait. Iran and Iraq areexcluded in the study) are very scarce. The fast growing population and increasing

Introduction

20


per capita water demand (over 500 l per capita per day, Abdel-Jawad and Al-Tabtabaei, 1999) to meet the huge socio-economic developments since the 70s haverecently magnified the problem. These countries are characterized by scanty rainfalland high evaporation and consumption which leads to deficits in their water budget.All these factors classify these countries as arid to semi-arid because of their limitedconventional water resources and generally absent reliable surface water.

Arabian Gulf seawater is quite different from other oceans:

• The Arabian Gulf is roughly rectangular, surrounded by Iraq and Kuwait on thenorthwest, Saudi Arabia, Qatar, United Arab Emirates (UAE) and Oman on thewest and south and by Iran on the east. The Gulf is approximately 100 Km longand 300 Km wide, with a surface area of 2.39

×

10

5

Km

2

. Average water depth is35 meters, so its volume is 8.63

×

10

3

Km

3

. Water circulates very slowly betweenthe Arabian Gulf and the Gulf of Oman via the Strait of Hormuz: the averageresidence time of water is 2-5 years.

• The Gulf Region has an arid sub-tropical climate with very limited annual rainfall.Water temperature varies seasonally from 18 ºC to 33 ºC. Therefore, evaporation isvery high most of the year, exceeding the total river runoff by approximately afactor of 10. The effect of the river runoff, temperature and evaporation explain thegradually increasing salinity (from 36,300 to 50,000 ppm).

• The Gulf ecosystem is seriously endangered and it is located in a region withpolitical conflicts (two major wars in the last 15 years). It is also the largest oilroute in the world; 20% of the total world production of oil passes through theGulf. The serious environmental impact of large desalination units should beconsidered.

Water stores are gradually depleting since it is extracted faster than refilled:approximately 17,000 million cubic meters are used per year and 3,000 million cubicmeters recharged, and 4,000 million cubic meters are available from surface water. Thetotal current water demand is about 20,000 Mm

3

/y, with non renewable resourcessatisfying approx. 75% with the rest supplied by renewable conventional sources,desalination plants and recycled wastewater. Table 1.1 shows the ground waterresources and the amount of renewable water resources in 1994 per year in the GulfCountries.

Table 1.1 informs that the water stress in the Gulf countries is one of the mainproblems that needs to be solved. Water withdrawal or water demand is shown intable 1.2. The total demand is divided in domestic, agricultural and industrial uses.



Desalination is a means of augmenting fresh water resources to remove or at leastreduce water stress. The number of desalination plants in the Gulf Council Countries(GCC) states increases daily. Table 1.3 summarizes the production and capacity ofthe Middle East countries.

TABLE 1.1

Ground water disposal and renewable water resources in the Gulf Countries in 1994 (Alawadhi,1999).

Country Population (millions)

Ground water resources (Mm

3

/y)

Renewable water resources (Mm

3

/y)

ConventionalNon conventional

Desalination Wastewater

Saudi Arabia 18.18 14,430 4,550 874 217

UAE 2.15 1,000 490 385 110

Kuwait 1.62 114 161 514 83

Qatar 0.53 185 50 108 25

Bahrain 0.55 190 90 75 32

Oman 2.05 728 1,929 39 25

Total 25.08 16,647 7,270 1,995 492

TABLE 1.2

Water demand for the Gulf Countries in 1990 (ESCWA, 1994).

CountryTotal demand

(Mm

3

/y)

Withdrawal in various sectors (Mm

3

/y)

Domestic Agricultural Industrial

Saudi Arabia 16,300 1,508 14,600 192

UAE 1,490 513 950 27

Kuwait 383 295 80 8

Qatar 194 76 109 9

Bahrain 223 86 120 17

Oman 1,236 81 1,150 5

Total 19,826 2,559 17,009 258

Introduction

22


Water production in Gulf countries represented the majority of the worldwidecapacity. Table 1.4 shows representative values of freshwater produced in differentprocesses. As seen in the table, large-scale Multi-stage Flash (MSF) plants installedin the Gulf produce the maximum quantity of freshwater and are the mostcompetitive with more than 20,000 m

3

/d. Desalted seawater per capita per day is veryhigh in some countries such as UAE and Qatar: 1.2 and 1.7 cubic meters per personand day.

Gulf countries actually recycle no more than 35% of their total treated wastewater,which contributes about 2.2% to the total water supply. Treated seawater is currentlyused mainly for landscaping, fodder crop irrigation and some very specific industrialuses. There are a total of 105 sewage water treatment plants in the Gulf countries with

TABLE 1.3

Total installed capacity and production in the seawater desalination plant of the Gulf Area in year1994 (Alawadi, 1999; Al-Gobaisi, 1999).

Country Total capacity (m

3

/d) Total production (Mm

3

/y)

Saudi Arabia 4,179,882 874.2

UAE 2,066.340 385

Kuwait 1,409,000 514

Qatar 295,000 108

Bahrain 220,571 75

Oman 105,000 39

Total 8,275,793 1,995

TABLE 1.4

Contracted capacity of freshwater production from seawater and all waters with the existingprocess. The total capacity is 12.8 million cubic meters per day and 21 million cubic meters perday, respectively. Data collected in 1996 (Alawadhi, 1999).

Seawater All waters

World Gulf World Gulf

% MSF 77.3 64.8 47.6 39.5

% RO 13.3 4.7 38.6 10.9

% ED — — 5.2 1.0

% VC 4.6 1.5 4.3 1.0

% ME 4.6 0.7 4.3 0.5

Total 100 71.7 100 52.9



a total capacity of about 2 Mm

3

/d. There is no doubt that this water source is

underused due to the lack of wastewater plants. More of these plants are needed make

better use of this water source and minimize the serious impact on the environment as

a result of its uncontrolled and unsafe disposal. Salt intrusion, ground water quality

and the saline interface between sea and ground water are some of the problems that

could be avoided with these plants.

1.3.2 Pacific Region and India

The Pacific Region is diverse in terms of desalination. Japan and Korea have

developed their own desalination technology which competes on the world market.

Australia and China also have their own technology and the rest of countries import

plants from overseas. Here we will consider the first two categories.

Table 1.5 shows the water resources in these four countries. Water resource per capita

is one of the fundamental indexes of water abundance. However, they only express

part of the potential availability since in some cases the transportation cost is too

high. Australia, for example, has the highest water value per capita because it has a

small population with rather little and irregular precipitation, and high evaporation.

Japan has the most precipitation but also the largest population. In China water

availability is irregular due to the climate and population distribution. Korea has the

least water per capita despite of a lot of precipitation.

Agricultural use occupies the largest portion in the region, whereas the consumption

for living is dependent of the area (standard of living, life-style and climate determine

the water consumption). Industrial water consumption is increased by industrial

development but can be decreased by efforts such as recycling. Table 1.6 summarizes

the fresh water consumption in the four countries.

TABLE 1.5

Natural resources in the pacific region in the year 1998 (Goto et al., 1999).

Country Precipitation (mm/y)

Population (millions)

Available water (Mm

3

/y)Water per capita

(m

3

/y)

Australia 465 18.1 100 5,520

China 648 1,224 2,813 2,340

Japan 1,714 125.6 422 3,360

Korea 1,274 46.4 69.7 1,500

Introduction

24


Desalination in the Pacific region is not as important as in the Gulf region. Table 1.7explains the capacity, process, use and feed water of the desalination plants in thePacific area.

In conclusion, water shortage will increase with the development of industry and animproved standard of living in the coming century, especially in the more populatedareas like China.

There are more than 200,000 villages in India with inadequate drinking water, out ofwhich about 50,000 suffer from brackishness problems affecting a population ofabout 60 million. Approximately one third of these villages are acutely affected bysalinity levels above 4,000 ppm. Villages with an average population of about 500 to1,500 are mostly separated either by mountainous terrain or long stretches of barrenland and can be broadly categorized into inland and coastal. Provision of safedrinking water to the villages inland has been given high priority in recent years, with

TABLE 1.6

Water use trends in the Pacific region (Goto et al., 1999).

Country (year) Total (Mm

3

/y) % Agriculture % Living % Industry

Australia (1995) 18,600 82.17 10,35 7.47

China — 87 11 2

Japan (1995) 90,700 58.7 17.2 14.8

Korea (1996) 23,668 62.85 26.23 10.91

TABLE 1.7

Desalination installations in the Pacific region. Data from 1998 (Goto et al., 1999).

CountryCapacity

(m

3

/d)Process Use Feed water

Australia 84,00064% RO18% VC12% MSF + ME

45% Industry33% Power gen.15% Municipal

70% brackish18% wastewater10% seawater

China 182,00085% RO15% MSF + ME

55% Industry40% Power gen. 5% Living

50% brackish20% pure water30% river, wastewater

Japan 129,885

88% RO6.5% ED3.5% MSF1.8% ME

53% Industry47% Water supply systems

Seawater and brackish mainly

Korea 180,000> 90% RORest ED

100% Industry including power generation

Pure > brackish >wastewater > river water



hundreds of small Reverse Osmosis and Electrodialysis (RO/ED) plants (10-30 m

3

/d)installed in the affected villages. Only two Multi-Effect Distillation (MED) plants ofmore than 10,000 m

3

/d were installed to supply process water in their industrialcomplex by seawater desalination (Prabhakar et al., 1997).

1.3.3 North Africa

In this region, water resources seem to be limited in time and space, unequallydistributed and remote with respect to centers suffering from a continuous increase indemand. The annual renewable water resources in this region are shown in table 1.8(Al-Gobaisi, 1997).

Water extracted from the ground is very high in some of these countries, as seen intable 1.9.

TABLE 1.8

Water disposal in the African region in 1995.

CountryAnnual renewable water resources

Total (Mm

3

/y) Per capita (m

3

/y)

Algeria 14.8 528

Egypt 58.1 923

Libya — —

Morocco 30.0 1,110

Tunisia 3.9 443

TABLE 1.9

Water withdrawal in North African countries. Data collected in 1990 for Algeria and Tunisia; forEgypt and Morocco data from 1992 (Al-Gobaisi, 1997).

CountryAnnual withdrawal

% water resources Per capita (m

3

/y) % Agriculture % Industrial % Living

Algeria 30 180 60 15 25

Egypt 97 956 85 9 6

Libya — — — — —

Morocco 36 427 92 3 5

Tunisia 78 381 89 3 9

Introduction

26


In the future, desalination should be the alternative saving solution when themobilization of non-conventional water resources is impossible or very costly(essentially in coastal zones). In this regard, five North African countries (Morocco,Algeria, Tunisia, Libya and Egypt) requested in 1989 technical assistance from theInternational Agency of Atomic Energy (IAAE) to study the feasibility ofdesalination using nuclear power. The aim was to reuse the treated water inwastewater plants and provide an important resource to agriculture.

There is little information about desalination plants in Northern Africa, although thewater production there is almost negligible with respect to the Middle East Countries.Desalination in Egypt is the most important in the region, but the total capacitycontracted is now reported to be 95,000 m

3

/d (Hassan and Florido, 1999). The MSFdesalination technology switched to reverse osmosis for large plants over 5,000 m

3

/din the last few years The proportion is 55% for the RO plants, 40% for the MSF plantsand the rest in Vapor Compression (VC). Libya has two MSF plants of 24,000 and10,000 m

3

/d (VA Tech, 1999), and in the south of Tunisia there are two brackish ROplants with a capacity of 12,000 m

3

/d (Cadagua, 1999). Morocco has only one ROplant with an installed capacity of more than 1,000 m

3

/d: the Laayoune SeawaterReverse Osmosis (SWRO) plant produces 7,000 m

3

/d of freshwater (NOPW, 1996).

1.3.4 US experience and the Caribbean Islands

California, Texas and Florida, the three states considered as the most arid and coastalareas of the country, will account for more than 45% percent of the nation’s totalpopulation growth between now and 2025. They are already experiencing the highestoverall water deficit and droughts are also very common. As the population willcontinue growing in these areas, progressive approaches to meet water demands willbe necessary (Ponce and Jankel, 1999).

The total water use in the US has fallen since the 80’s since water is now used moreefficiently. Table 1.10 shows the total water consumption and the use by each sector.

Thermal technologies were used in the early years of desalination prior todevelopment of RO, beginning in the 60’s with two MSF plants in SouthernCalifornia and Florida. After that experience, RO technology has been successfullyintroduced in several plants. The use of desalination plants is steadily growing in the

TABLE 1.10

Water use in the U.S. in 1995 (Gleick, 1998).

Total use (Mm

3

/y) % Public % Irrigation % Thermo-industrial

552,1 10.9 39.2 49.9



US. The desalination growth rated based on increased contracted capacity was thehighest in the world from 1996-1997, with about 120,000 m

3

/d of new freshwater.This implies a rate of growth between 10-20% per year, with a total installed capacityof more than 900,000 m

3

/d. (Wangnick, 1998). Much of the potable supplies utilizebrackish water.

Many of the island nations of the world are in warm sunny environments and havetwo significant items in common: beautiful beaches and a pernicious lack of potablewater. Major economic growth is inhibited since the island’s population cannotenhance its agriculture and stimulate the tourist trade without a suitable andconsistent supply of useable water. The Caribbean sea is a good example. In Antigua,about 50% of the total drinking water requirements are supplied by a SWRO plant of9,500 m

3

/d which substitutes an old MED plant (Barendsen and Moch, 1999). Otherexamples are a 10,000 m

3

/d SWRO plant in Nassau (Bahamas) (Andrews andShumway, 1999), a SWRO plant in Curaçao producing 9,000 m

3

/d and the VirginIslands with 9 MED units and a combined production of 30,000 m

3

/d (Elovic andWillocks, 1999).

1.3.5 Mediterranean area and Europe

Desalination in Spain started in the early 70’s in places with little water and near thecoast. Here it was the only way to supplement natural water resources needed fordomestic uses in highly populated isolated territories. The current and futuredevelopment of the tourism industry is assured by the seawater desalination plants inthose areas.

The total capacity of Spanish desalination plants is now above 600,000 m

3

/d, and newprojects for another 400,000 m

3

/d for urban uses are being developed and should bein operation in two years. Table 1.11 shows the seawater desalinated in Spain in 1998.

The desalination industry is located in dry Spain, that is, the southern part of thecountry: Balearic Islands, Canary Islands, Ceuta and the Costa del Sol. Three MSFplants were installed in Ceuta (1) and Las Palmas (2) in the 70’s, and small vaporcompression units (VC) were the water supply in public delivery systems and private

TABLE 1.11

Desalinated water in Spain during the year 1998 (Torres and Medina, 1999).

Total (Mm

3

/y) % Urban & Tourism % Agriculture % Industry

Seawater 95.3 94.4 5.6 —

Brackish 126.57 20.4 47.6 32.0

Introduction

28


tourist resorts in the 80’s. Since then, reverse osmosis process (RO) is being used inbig plants. Table 1.12 resumes the biggest desalination plants in Spain.

The use of wastewater in agriculture irrigation, landscape improvement, leisure needsand aquifer recharge is another way to supply the increasing water demand in Spain.

The Republic of Cyprus is an island at the eastern end of the Mediterranean Seaplagued by draught and water shortages in recent years. Seawater desalination hasbeen the main solution. It has two little MSF plants, a MED plant and a RO plant witha capacity of 20,000 m

3

/d (Echaniz et al., 1997). A new RO plant with a capacity of40,000 m

3

/d will be built by the year 2000.

Desalination in the rest of Mediterranean countries is less important. There are smallold MSF plants and VC units in the south of Italy to cover the local demand (Ophirand Gendel, 1999; Italimpianti, 1999). Greece, Turkey, Jordan, Israel and Lebanon(VA Tech, 1999) also have small desalination RO plants.

Germany and Austria have several desalination plants to recycle wastewater orproduce pure water for industrial processes including power generation (VA Tech,1999). They do not produce drinking water.

Humanity has developed non-conventional sources of potable water in order toremove or at least reduce water stress. Seawater desalination is the most important ofthe non-conventional ways of producing water and several processes have beendeveloped in the last few years to produce fresh water for human consumption. Yetdesalinated water makes up only one part in a thousand of the fresh water usedworldwide. Desalination costs several times more than conventional means and istherefore mostly used in developed countries with water scarcity (i.e. Arab countries).

TABLE 1.12

Some of the RO desalination plants installed in Spain (Cadagua, 1999; Sánchez et al., 1997;Fayas and Novoa, 1997; Torres et al., 1999; AECYR, 1999).

Plant Location Capacity (m

3

/d) Feed water

Son Tugores Mallorca 35,000 Brackish

Maspalomas Las Palmas 35,000 Brackish/Sea

Marbella

a

a. Not in operation

Málaga 56,000 Sea

Bahía de Palma Mallorca 42,000 Sea

Arrecife Lanzarote 32,500 Sea

Las Palmas III Las Palmas 38,000 Sea

Alicante

a

Alicante 50,000 Sea

Desalination and energy


1.4 Desalination and energy

Desalination is highly energy intensive and should not be considered in isolationfrom energy. The power requirements of seawater desalination plants is alsoincreasing. There is a theoretical minimum power needed to desalt water but muchmore power is required in practice (El-Sayed and Silver, 1980). Unfortunately, mostof the energy used is obtained from oil and natural gas. The Arab World desalinatesusing their large fossil fuel reserves. Consequently, the specific consumption of adesalination process must be accounted in fuel not electrical consumption as usuallygiven when measuring plant efficiency. Table 1.13 shows the primary energy or fuelconsumed in most desalination methods in the world. Note that the specificconsumption has strongly decreased as desalting technology has developed.

As seen in the previous table, thermal distillation consumes more than other methodsand more or less recovers (in the worst case) 80% of the latent heat of boiling water atatmospheric conditions (about 2,257 kJ/kg). In the previous table, specificconsumption strongly depends on way the required energy is obtained (converting theprimary energy from the fossil fuels into thermal or electrical energy to supply theplant). Up until recently power plant technology has developed separately from thetechnology used to desalt sea or brackish water. However, when the co-generationconcept is applied to combine the two processes, the consumption of the desalinationprocess can be reduced more than 50%. Including combined cycles in new MSF/MED plants considerably reduces consumption and also provides electricity in areaswith energy demand. Co-generation fuels could be substituted by biomass or refusefuels (Tadros and Tadros, 1997). The energy-water interaction should be investigatedfurther and improved in order to provide water to water stressed areas at minimumcost.

Desalination is almost entirely powered by the combustion of fossil fuels. Their finitesupply is rapidly being depleted and they also pollute the air and contribute to globalclimate change. Assuming that all desalinated water in the world (total installedcapacity of 13 Mm

3

/d) is produced at an average fuel consumption of 200 kJ/kg, and

TABLE 1.13

Specific consumption of desalination processes. Data obtained from several sources (Fisia-Italimpianti, 1999; I.D.E., 1999).

Process MSF MED VC

a

a. Electrical energy produced in a conventional power plant at 30% efficiency.

RO

a

Specific consumption (kJfuel/kgwater)

400-500200-300b

b. Desalination process in a co-generation plant.

350-400200-250b 100-200

70-9030-50c

c. Including energy recovery system in the RO process.

Introduction

30 Thermoeconomic analysis and simulation of a combined power and desalination plant

that the current annual global consumption of oil is 25 billion barrels (rising 2% perannum, Al-Gobaisi, 1997), 0.17% of world oil consumption is consumed indesalination. To underline how important energy is in desalination, if all the waterconsumed in the world came from desalination plants (remember that it is actuallyonly one part in a thousand, Al-Gobaisi, 1999) the required oil would surpass thecurrent yearly oil consumption.

The development of renewable-driven desalination is still severely impeded (if notstopped) by the pressure from contemporary economic factors and political inertia. Ifour technology continues along the present unsustainable path, not only it is essentialto have an orderly transition in the energy used for desalination (from fossil fuels torenewable resources) but the whole industry needs to gear itself towards enhancedefficiency, waste minimization and less environmental impact (Menéndez, 1997). Inshort, the philosophy of industrial ecology needs to be applied for desalination. Theconcept of industrial ecology considers an industrial system together with itssurrounding systems. This systems view of industrial operations seeks to optimize thetotal materials cycle from raw material to manufactured material, from component toproduct and waste to ultimate disposal. Energy, resources and capital are the factorsthat have to be optimized.

1.5 Why a MSF and power plant?

The demand for electricity increases every day in arid and warm areas where airconditioning is used to improve living standards. A dual-purpose plant is one of thebest solutions to supply water and energy demands (although is not the most efficientmethod to produce fresh water, see table 1.13). As the nuclear or coal power plantsare not very common in the Gulf Area, the more abundant fossil fuels like natural gasor fuel oil are consumed in new co-generation plants. Solar powered desalination isan insignificant proportion because of the costs of using renewable energy are verydependent on the scale of the infrastructure.

Several power generation configurations can be coupled with a desalination unit:steam turbine plants, gas turbine plants, combined cycle power plant (gas turbine,heat recovery steam generator and steam turbine). Some desalination processes onlyrequire electrical power (not exhaust gas or steam) and co-generation is not possible.In those cases, desalination and power generation can be studied separately althoughthe way of producing electricity is the same.

This thesis aims to demonstrate the scope of Thermoeconomic Analysis when appliedto a very complex system. One of the most important configurations of dual-purposedesalination plants is the multi-stage flash desalination unit (MSF) coupled with asteam turbine power plant fuelled by natural gas (fuel is also available in exceptionalconditions and startups). This type of configuration is used in a plant containing the

Why a MSF and power plant?


largest single desalination units in the world, in the United Arab Emirates (UAE).MSF units provide almost 77% of all desalinated seawater and nearly 82% of thatproduction is from the Gulf Area (Alawadhi, 1999). MSF plants with unit capacity upto the unit studied here are likely to dominate the scene in the Gulf countries for atleast another 10 years. The other predominant method of obtaining freshwater,reverse osmosis (RO), is not in favor due to the high salinity and temperatures of Gulfseawater. MSF desalination is energy intensive and inefficient especially if the steamturbine plant does not include a reheater in the boiler. It is therefore a good exampleto study from the thermodynamic point of view, following the Second Lawperspective. The conventional energy analysis methods based on the First Law ofThermodynamics are implicitly compared here.

The reason for studying an MSF plant is not only its dominant position in the worlddesalination market. In terms of energy consumption, MSF is the worst desalinationprocess (see table 1.13). However, from a thermodynamic point of view it offersmany more possibilities to reduce energy consumption in the process. The minimumpower requirement (or thermodynamic limit) to desalt water is consumed in rejectingthe difference of the equilibrium vapor pressure between saltwater and freshwater(this difference depends on the process temperature). All practical processes arenon-ideal, performed by imperfect devices, and are accompanied by auxiliary non-ideal processes. So, the minimum power requirement is higher for all desalinationprocesses. In RO or VC processes, the power requirement is electrical energyproduced in external power plants. Reducing the energy consumption of the processis only possible in the desalination process. But when a thermal desalination plantlike a MSF unit is combined with a power plant, MSF technology can be oriented toimprove the thermal efficiency of vertical tube evaporators (VTE) that allow the useof low temperature heat sources such as turbine reject steam (Sephton, 1999; Sephtonand Salomon, 1997), normally rejected to the environment (through the steam cyclecondenser). In the limit, the cooling tower of a conventional power plant can besubstituted by a low-temperature MSF unit to highly improve the efficiency of thesteam cycle. Thermoeconomic analysis connects the Second Law of Thermodynamicand Economics and is especially recommended for these two combined processes.

This is the first time an in depth thermoeconomic study has been made of adesalination plant, a system combining thermal and chemical processes. Interestinglythe first thermoeconomic ideas were applied to desalination processes in the sixtiesand early seventies (Evans, 1962; Tribus et al., 1960; Tribus and Evans, 1963;El-Sayed and Aplenc, 1970; El-Sayed and Evans, 1970), but were most developed inthe eighties and nineties when Thermoeconomics was applied in power plants.Several exergy analyses of MSF plants have already been made (Hamed et al., 1999;Darwish, Al-Najem and Al-Ahmad, 1993; Al-Sulaiman and Ismail, 1995; El-Nashar,1993), and the optimization of thermal desalting systems has also been considered(El-Sayed, 1996). In this Ph. D. Thesis, thermoeconomic techniques previouslyapplied only to power plants were successfully used for a combined power generation

Introduction


and desalination process. Chemical exergy was successfully introduced in a mostcomplex installation, in the global exergy balance. Furthermore, no thermodynamicanalysis has been done for a dual-purpose plant with two different products: waterand electricity. The interactions between the two processes were analyzed in thisPh. D. Thesis. New methodologies are introduced in this complex system, allowing abetter understanding of the real relationships between the plant equipment.

1.6 Thermoeconomic analysis

A dual-purpose plant is a very complex system that is difficult to analyze, especiallywhen all the available configurations of both sub-systems are considered. Usually theplants are analyzed separately, neglecting component interactions and the energysavings possible from the combined analysis. When two different products areobtained in a co-generation plant, it is very difficult to quantify the real cost of eachproduct and redistribute the costs over the rest of upstream flows inside the dual-purpose plant by applying conventional energy analysis techniques based on the FirstLaw of Thermodynamics.

Thermoeconomic analysis techniques are the most convenient tools to analyze thesesystems, because they can:

• Calculate the costs of the flows and products of a plant based on physical criteria(Second Law of Thermodynamics).

• Assess alternatives for energy savings.

• Optimize operation.

• Locally optimize subsystems.

• Perform energy audits and assess fuel impact of malfunctions (operationdiagnosis)

Thermoeconomic analysis uses the First and Second law of Thermodynamics incombination with economic data and introduces new concepts such as Fuel-Product,productive structure, exergy savings, cost of irreversibilities, additional fuelconsumption, malfunction and others. The degradation mechanisms of the energyquality in each component require a comprehensive approach that encompassesresources, generation of products, specific unit consumption and cost, plant/systemmalfunction, impact on fuel consumption, etc. A better understanding of the actualplant performance increases the potential for improvements in operation and/ordesign.

When applied to analyze an existing dual plant, thermoeconomic analysis requires avalidated model (simulator) of the plant to determine the thermodynamic referencestate at design conditions for any load point, ambient conditions, operating mode, etc.Data from a dual plant in Abu Dhabi were used to adapt the models to reproduce the

Ph. D. Thesis development


states of the plant (therefore, the data obtained by the simulator are consideredmeasured data). As in this case, the data acquisition, processing and storage system isnot operative to be used in the thermoeconomic analysis. The simulator can obtain thethermodynamic state of the plant when an inefficiency is detected or estimated.

1.7 Ph. D. Thesis development

The structure of the Ph. D. Thesis is summarized as follows. First, world waterresources and demand are reviewed, especially for the Gulf area. Water quality anduses are also included to inform the non-specialist readers. A brief description is thenmade of the most important desalination methods (Chapter 2). When the desalinationunit follows a thermal principle it is usually coupled with a power generation plant.

In Chapters 3 and 4 the mathematical models applied to the power and desalinationplant are developed. The results are compared and readapted with operational datafrom the data acquisition system of the plant. The mathematical model was validatedas a tool that widely reproduces the real state of the plant under different operatingconditions, as if the results were real plant data. An interactive steady-state simulatorwas made that can be used on a personal computer to help obtain output data.

The simulator (Chapter 5) supplied the main part of this Ph. D. Thesis: the completethermoeconomic analysis of a dual-purpose power and desalination plant (Chapter 7).After explaining the fundamental concepts of Thermoeconomics (Chapter 6), the firststep was to build the thermoeconomic model. The most convenient productivestructure was chosen for the power and desalination plant. The thermodynamicoperation and economic costs of every flowstream of the plant were calculated andanalyzed. Those costs allow cost assessment of the plant products based on physicalcriteria. Then, the thermoeconomic diagnosis was applied. The steady-state diagnosisof the dual-purpose plant helped us obtain a more cost-effective operation and a betterunderstanding of plant performance. The mathematical model was applied for a givenoperating condition characterized by operational data (previously validated andprocessed) to quantitatively analyze the following steps:

• Comparison with a reference case (target) with the same operating conditions.

• Identification of inefficiencies, and the performance degradation of sub-systemsor components. These inefficiencies were simulated.

• Evaluation of the causes of cost generation and component inefficiencies.

• Assessment of the extra-operating cost due to malfunctions with respect to themost feasible operation and the cost impact of appropriate maintenance actions.The previous cost analysis is therefore essential to perform the diagnosis of thesystem.

Introduction


• Operation recommendations for the plant managers, taking into account theexperience from the analysis (assessment of alternatives).

A new method is introduced to develop the thermoeconomic diagnosis, including thematrix formulation and some new concepts like induced and intrinsic malfunction,and dysfunction.

Once the diagnosis was completed, a global optimization of the plant was performedfrom locally optimizing the system units. The local optimization of a unit consists infinding the minimum cost of the product of each component. The thermoeconomicmodel was also used in this process.

Finally, the idea of maximum benefit in water and electricity production wasanalyzed using practical examples. The contribution of the price policy applied in thefinal benefit is considered by separating the methods of assessing product price andcost.

The last chapter (Chapter 8) contains the conclusions of the Ph. D. Thesis and futurelines of research.


CHAPTER 2

Desalination processes

In chapter 1, the great problem of water scarcity and desalination as the way to solveit is remarked. Desalination is the process that convert brackish or seawater in waterfor human consumption, there are several processes technologically developedproviding water in arid areas.

This chapter includes a general review of desalination methods, in order to have anoverall perspective of the state of the art in desalination technology. The importanceof the MSF with respect to the other methods is also argued in this chapter.

The most reliable techniques of seawater desalination are rated into three categoriesdepending on the principle applied:

• Processes involving a change of phase: Freezing or distillation.

• Processes using membranes: Reverse osmosis or electrodialysis.

• Processes acting on chemical bonds: Ion exchange.

Among the processes above, distillation and reverse osmosis processes show highperformances in seawater desalination; thus they are the most marketable in theworld. Next, we develop the following processes in detail:

• Multi-Stage Flash (MSF).

• Multi-Effect Distillation (MED).

• Reverse Osmosis (RO).

• Vapor Compression (VC).

We also mentioned the other techniques, which have not been developed in the fieldof desalination due to problems generally, related to energy consumption and/or to thehigh investments required. These techniques are:



• Solar Distillation.• Freezing.• Electrodialysis.• Ion Exchange.

2.1 Phase change processes: distillation and freezing

More than 85% of the world’s desalted water is obtained by distillation. Desalinationby distillation involves boiling water seawater to release water vapor and dissolvedgasses, leaving behind the salts (which are only volatile above 300 ºC). Pure water iscollected by condensing the vapor inside or on the outside of tubes which may bearranged horizontally or vertically depending on the installation. Every distillationsystem must also be ventilated to extract air and non-condensable gases in theseawater, and a vacuum pump or steam ejector is required when the evaporator-condenser system is at lower than atmospheric pressure.

2.1.1 Multi-stage flash process (MSF)

Multi-Stage Flash is the most widely used evaporation process (Wangnick, 1998).It is especially common wherever the temperature, salt content, biological activity orpollution level of raw water is high, as in the Middle East. MSF also be used if thedesalination plant is coupled to a power station or if waste heat is present (e.g. fromgas turbine effluents). In general, MSF plants are more common because they aresimple and robust, although their specific consumption may be higher than othermethods (12-24 kWh/m

3

).

Flash evaporation takes place when a fluid is heated to a certain temperature andevaporates both above and below the atmospheric pressure: under gradual decreasingpressure, flashing by pressure reduction is called flash evaporation. In multi-stageflash plants seawater (pumped through heat exchanger tubes installed in the variousevaporator stages) is heated to a certain temperature. Final heating is performed bysteam in a final heater. The hot seawater then goes into flash chambers where thepressure is maintained below the equilibrium pressure corresponding to thetemperature at which the brine enters. Part of the brine flashes into vapor and afterpassing a demister, it condenses outside the tubes while heating the seawater flowingthrough the tubes. The multi-flash distillation unit contains cells assembled in series,at a different pressure. The water produced in each stage is collected in a troughmounted below the tube bundle which collects the fresh water end product. Thesewidely used units perform recycle brine (50% to 70% of the brine quantity within thelast stage is collected and discharged through the seawater feeding pipe of the unit) inorder to reduce the quantity of the make-up seawater needed to produce fresh water.The concentrated seawater is also removed from the last stage by a pump or bygravity. Figure 2.1 shows a general scheme of a conventional MSF unit.

Phase change processes: distillation and freezing


37

FIGURE 2.1

General outlay of MSF distillation with brine recycling.



Seawater with 40,000 to 50,000 ppm dissolved solids is converted into distillate andfresh water with a few ppm of solids. An MSF type plant operates between twotemperatures: the top brine temperature (brine heater outlet temperature, or TBT) andthe last stage temperature. The top brine temperature depends on:

a) Available steam quality.

b) Scale prevention technique.

c) Brine concentration and nature of dissolved salts

The last stage temperature depends on:

a) Cooling water inlet temperature.

b) Absolute pressure maintained in the last stage by the ejector system.

In practice, MSF plants are designed for various gain outputs ratios (GOR, tons offresh water produced per tons of steam supplied to the brine heater). In practice, aG.O.R of 12:1 being the upper limit. Obviously, the production rate is a directfunction of the flashing brine flow and the flash range (brine top temperature-laststage temperature). Also, in theory, the actual number of stages is not important for agiven ratio.

However, the number of stages determines the total exchange area required for heatrecuperation. More stages will decrease the total exchange area required therebylimiting the maximum number of stages per plant. In practice, however, stage numberincreases at increasing gain ratios but also depends on the plant’s capacity. Thenumber of stages is generally about 20 and sized to keep the temperature differenceconstant between stages (the temperature difference is estimated to be about 3 ºC).

2.1.2 Multi-effect distillation (MED)

Contrary to MSF, in Multi-Effect Distillation (MED) evaporation takes place onsurfaces, by exchanging the latent heat through the heat transfer surface betweencondensing vapor on one side and evaporating brine on the other. The MED plantalso has several stages, each with a heat exchanger tube bundle (see fig. 2.2).Seawater is sprayed onto the tubes and the condensing heating steam inside thetubes evaporates part of the seawater on the outside. The steam produced is used asheating steam in the next stage, where it condenses inside the tubes. The condensateis the water product. Obviously the boiling temperatures (and pressures) in thedifferent evaporators cannot be the same. The specific consumption depends on thesteam conditions supplied to the first stage, but is usually lower than in MSF(10-15 kWh/m

3

).



39

FIGURE 2.2

Flow diagram of Multi-Effect Distillation (MED) with thermal vapor compression (TVC).



FIGURE 2.3

MED process with vertical tube evaporators (VTE).



41

The first stage is heated by external steam from a heat recovery system or aback-pressure steam turbine. But in most cases, MED plants are equipped withthermal vapor compressors for better efficiency. A steam ejector driven by medium-pressure steam removes a part of the steam produced in the last stage and compressesit to use as the heating steam. The steam produced in the last stage is condensed onthe outside of exchanger tubes in a separate condenser, which is cooled by incomingseawater. Part of the heated seawater is then used as feedwater. Product water andconcentrated seawater are then pumped out from the last stage of the evaporator.

Most MED plants have horizontal evaporators. Vertical tube evaporators (VTE) arealso available: In vertical tube evaporation, salt water falls in a thin film throughvertical tubes in a large chamber (figure 2.3). As it falls, it is heated by steam thatcondenses on the outer surface of the tubes. This heat exchange converts some of thesalt water in the tubes into steam and some of the steam around the tubes into freshwater (condensate).

Steam generated inside the tubes in the first chamber flows to the second chamber,and condenses on the tubes there. The process is repeated in several chambers and issometimes called “multiple-effect falling-film” distillation, because each bundle oftubes is an “effect”, and because a thin film of water falls down the inside surface ofthe tubes. Vertical tube evaporators are most cost-effective in large plants requiringhigh efficiency. They have an improvement over older systems since less heat transfersurface is required and the water need only be circulated once.

2.1.3 Vapor compression (VC)

Thermocompression (TVC) or vapor compression distillation (VC) involves boiling aliquid (seawater in this case) on one side of the heat transfer surface, and directing thecompressed vapor to the other side of the heat transfer surface to be condensed (seeflow diagram, figure 2.4).

In the specific design described here as an example, a single-stage VTE type seawateris boiled inside a bank of enhanced surface tubes. The generated vapor then passesthrough a mist separator to remove any entrained salt-water droplets. In a verticaltube evaporator, the pure vapor enters the compressor at 101,5 ºC and 1 psig for acompressed steam temperature of 106 ºC and 3.6 psig (the pressure is thereforeincreased 0.18 bar). The compressor is a centrifugal, single-stage type designed forhigh-volumetric flows. This higher-energy compressed steam is discharged into theevaporator onto the outside of the enhanced surface tubes, where it condenses andprovide its latent heat energy to the boiling seawater inside the tubes.

Note that the process is very efficient thermodynamically, because most of the shaftwork required by the compressor is used to avoid the boiling point elevation ofseaweater (BPE). Additional vapor is generated and the process continues. Thevapor, which condenses on the outside of the tubes, is collected, and drawn off by



the distillate pump and pumped through a three-stream heat exchanger. The excessfeed water, called blowdown, which is concentrated, is also pumped through thesame heat exchanger. The distillate and blowdown are cooled therein whilepreheating the incoming feedwater. This heat exchanger helps to minimize energyconsumption of the system, in a VC system the specific electric consumption islower than 10 kWh/m

3

.

FIGURE 2.4

Flow diagram of a vapor compression system with vertical tube evaporators (VTE).



43

Distilled water is made by condensing above atmospheric pressure at 106 ºC. A smallamount of make-up heat is required for continuous operation to replace the heat lostto radiation and venting and the portion not reclaimed in the three-stream heatexchanger. Electric immersion heaters, a steam coil, or heat recovery exchangers torecover waste heat from engine jacket water or exhaust gas when available canprovide this make-up heat. The distillate must be sterilized to meet Health Servicerequirements and may also be chlorinated for storage purposes.

2.1.4 Solar distillation

Solar stills use can be an ideal source of fresh water for drinking and agriculture inarid, isolated zones. Solar energy has a definite advantage over fossil energy, forsmall stand-alone units in rural and isolated areas (India). However, solar distillationis not widely used since installation costs are high and only a few liters can beproduced per day, per square meter of pan area in the stills. Of course any economicor energetic comparison should not be considered.

Several different configurations can be used to recycle the recuperated heat from thevapor condensation in solar stills. But we will only consider the conventional solarstill (figure 2.5). The sun heats salt water in a black pan covered with a sloping glassroof. Water vapor rises to the glass where it condenses, forming a film which runs offinto a collecting trough and is stored. The water does not boil but vaporizes slowlythrough a layer of water-saturated air and reaches the cooler glass by convection. Therate of evaporation is primarily controlled by the intensity of the incoming solarradiation which creates both temperature and water vapor concentration differencesbetween the water and glass surface. Additional solar radiation can be obtained usinglenses, mirrors and other focusing devices, but also heat losses increase when thetemperature inside the solar still change. Finally, wind velocity has a negative effecton the cooling of the heating surface.

The principle of the thermal energy extraction from a solar pond or other methodscould be used as the energy source for seawater desalination processes. For example,the use of parabolic trough collectors (PTC) could make competitive the use of solarenergy for desalination processes (MSF, García and Gómez, 1999; MED, García,Palmero and Gómez, 1999), depending on conventional energy costs, the solarcollectors cost and the climatic conditions that determine the attainable fresh waterproduction per m

2

of solar collector (the PTC collectors provide on average 10 m

3

offresh water per m

2

of solar collector), and the solar fraction SF that determines thepercentage of the day in which the desalination plant consumes solar energy.



FIGURE 2.5

Diagram model of a solar still.

2.1.5 Freezing process

This process, also based on phase change, is independent of the water salt content.Seawater is cooled and the ice is collected (ice crystals are essentially salt free). Iceformation is analogous to distillation in this respect since salt-free vapor is producedwhile the liquid may have a high salt concentration. The ice is melted to obtain freshwater (the fusion temperature is less than that of salts contained in the ice).

The freezing process is different from distillation since the latter is carried out wellabove ambient temperature and the equipment is designed for minimal heat losses.In freezing methods, the system must be protected against heat gains or

cold losses

,and ice needs to be transported and purified, which is somewhat more complex thanhandling fluids alone. Although the low operating temperature of freezing processesgreatly reduces scale and corrosion problems, refrigeration technology may beadapted. So that water is the first or secondary refrigerant. This secondary refrigerantsystem could be mixed or separated from water by a heat transfer surface.

Freezing methods are not widely used in the desalination industry, and to calculatetheir power consumption, we still have to rely on experiments in relatively small andmedium-sized plants and extrapolation to larger plants.

Solar energy

Glass

Vapor

Distilled water Distilled waterInsulation

Salt water

Condensed vapor

Processes using membranes


45

2.2 Processes using membranes

2.2.1 Reverse osmosis

Osmosis is a physical process which occurs naturally in animals and plants(figure 2.6). Osmotic pressure is measured using a recipient divided into 2compartments by a semi-impermeable membrane. Saline solution is poured into onehalf and freshwater into the other. Part of the fresh water will flow through themembrane into the saline solution. The excess height at the saline solution over thefresh water is a measure of the osmotic pressure of the solution.

If external pressure greater than osmotic pressure is applied to the saline solution, thewater will flow through the membrane in the other direction, leaving behind a morehighly concentrated salt solution. This process is called reverse osmosis (RO). Theosmotic pressure of a solution is directly proportional to the solute concentration, andthe permeated water flow is proportional to the difference between the appliedpressure and the osmotic pressure of the concentrated solution.

RO can be used to demineralize brackish water with 1-10 gr/l salinity. It is also usedfor seawater desalination and has lower energy consumption, investment cost, spacerequirements and maintenance than other processes. However, RO seawater plants inthe Gulf Area need an intensive water pre-treatment process with a lower productquality, and are not often used.

In RO desalination (figure 2.7) seawater is pretreated to avoid membrane fouling.It then passes through filter cartridges (a safety device) and is sent by a high-pressurepump through the membrane modules (permeators). Because of the high pressure,pure water permeates through the membranes and the seawater is concentrated. Thewater product flows directly from the permeators into a storage tank, and theconcentrated seawater (at high pressure) is sent via an energy recovery system backinto the sea. The four main parts of the RO installation are:

Preliminary treatment unit

The treatment has the following steps:

•

Chlorination

: To reduce bacteriological and organic loads found in raw water.

•

Filtration on a sand bed

: To reduce raw water turbidity.

•

Acidification

: Acid is added to clarified raw water to lower its pH and limit theformation of calcareous deposits.

•

Inhibition by polyphosphates

: Polyphosphates delay the formation of precipitatessuch as calcium and barium sulfate.

•

Dechlorination

: To remove the residual chlorine from the pre-treatment.



FIGURE 2.6

Reverse osmosis process.

Processes using membranes


47

FIGURE 2.7

Reverse osmosis (RO) desalination with Pelton turbine.



•

Cartridge filtering

: To catch the particles obtained by oxidation of dissolved ions(Fe++) in raw water.

Note that distillation methods only need a light chlorination process and some scaleinhibitors (addition of polyphosphates). Sometimes acid is added to prevent thescaling problem.

High-pressure pumping system

This stage is the least problematic and normally involves centrifugal pumps.

RO modules

The main modules used for RO seawater desalination are made out of hollow fibersand spiral fibers provided by several manufacturers. The spiral-wound and hollowfiber designs were developed to contain the high-pressure fluid in the lowest possiblevolume for a given membrane surface.

In spiral-wound elements membranes and backing are wound similar to a jelly rollaround a central perforated tube which collects the product. Saline water flowsthrough separate channels in one direction; the membrane elements are typically30-120 cm long and 10-30 cm in diameter. They can be mounted in series with anti-telescoping devices between adjacent elements to form modules. Separate modulescan readily be connected in series or in parallel.

The hollow fiber units have a very large number of hollow fibers, thinner than humanair, with their ends potted in epoxy resin, are held in a pressure vessel. Pressurizedsaline water circulates on the outside of the fibers while the hyperfiltrate flows withinthe fibers toward the open ends of the fibers held in position by the epoxy resin.Desalted water emerging from millions of open fiber ends is collected there. Thehollow fibers are made by methods similar to those developed in the textile fiberindustry. These units pack more membrane surface per unit volume than spiral-wound unit and are extensively used for seawater RO.

The brine energy recovery system

In the last years, investigators have tried to reduce the energy requirements(6-8 kWh/m

3

) of RO seawater desalination using two main devices:

•

Pelton turbines

: The high-pressure concentrate from membranes pushes on thePelton blades to provoke a pair in a common shaft. Energy recovery for RO plantsresults in energy savings of 40% (Calder, 1999).

•

Pressure exchangers (PE)

: The PE unit uses the principle of positivedisplacement to pressurize low-pressure raw seawater by direct contact with theconcentrate stream from a seawater membrane system. A cylindrical rotor withlongitudinal ducts parallel to its rotational axis is used to transfer the pressure

Processes acting on chemical bounds


49

energy from the concentrate stream to the feed stream. The energy recovery withPE is in the range of 50-65% (Hauge and Ludvigsen, 1999).

2.2.2 Electrodialysis (ED)

This process is used to demineralize brackish water by making different ionsmigrate through selective membranes in electric field made by the dirct difference ofvoltage potential between two electrodes connected at the boundaries of themembranes.

Whenever salt water is flowing in a cell, the cations are attracted by the anode and theanions by the cathode. If not constrained, these ions discharge on the electrodes ofopposite sign. In return, if a set of selective and permeable membranes is placedbetween the electrodes, salt concentration decreases in some compartments of the cellwhere water is desalinated, while this concentration increases in the othercompartments where salt water becomes even more concentrated. This process(shown in fig. 2.8) is suitable for desalinating brackish waters with an average saltcontent between 1 to 3 g/l with a very low power consumption (about 1 kWh/m

3

) anda salt rejection of 75% (data obtained from De Armas, Torrent and Von Gottberg,1999). Above this it becomes more costly than competitive processes (its energyconsumption for seawater desalination is much higher).

2.3 Processes acting on chemical bounds

2.3.1 Ion exchange

Ion-exchanging resins are insoluble substances. In contact with a solution, theyexchange some ions with the dissolved salt.

Two types of resins can be used: anionic resins that substitute water anions byOH-- ions (hydroxil permutation); and cationic resins substitute cations by H+ ions(acidic permutation).

Ion exchange demineralization provides high purity water if the salt concentrationdoes not exceed 1 g/l. It is often used for water preparation of boilers from water ofstreams or aquifers, characterized by their low salt content, and for softening waterwith excessive calcium and magnesium. Resins must be regenerated regularly withchemical reagents to substitute its original ions and those fixed by the resin.The resins and chemicals must be substituted regularly, which raises the cost andmakes it unpractical for seawater desalination.



FIGURE 2.8

Electrodialysis process.

Summary


51

2.4 Summary

A general review of desalination technology has been written in this chapter. Thereview includes the principle of operation, description of the necessary installation,advantages/disadvantages, characteristic parameters (including specific consumption)and application range of each desalination method that is now available indesalination market.

MSF is not only the most dominant process in desalination. It offers the possibility tobe connected to several heat sources: steam turbines, gas turbines, solar storage,combined cycles. So, it allows applying techniques oriented to produce the MSFproduct with the lowest cost. This Ph. D. Thesis develops one of those techniques,based on 2

nd

Law of Thermodynamics.


CHAPTER 3

MSF desalinationsteady-state model

The daily world production of drinkable water from Multi-Stage Flash plants (MSF)far exceeds that of other desalination methods. This is particularly the case wherepower generation is linked to water production to use the process steam.

In this chapter I will describe a mathematical model used in the SIMTAW program, tosimulate a MSF plant under different operating conditions.

MSF plant design data were included in the mathematical model, which is notoriented for design analysis. Several operating variables can be modified by the userto observe changes in plant behavior, such as consumed steam, inlet watertemperature, water mass flow rates, TBT value, fouling factors and more variablesexplained below. The inverse calculation procedure option can evaluate the foulingfactor of the stages instead of the distillate temperature profile.

This model provides information to perform the exergy and thermoeconomic analysisof the whole dual-purpose plant, i.e. power generation plant and MSF plant, in orderto analyze plant efficiency and cost savings.

The structure of this section is as follows:

• First, brief descriptions of the physical processes in a MSF plant.

• Second, an explanation of the mathematical model, including the equations usedto solve the model.

• Third, a description of the solution algorithm of the system of model equations.

• Finally an explanation of the simulation options and the design data.

MSF desalination steady-state model

54


3.1 Process description

Many multi-stage flash plant arrangements and operational techniques are available.Each evaporator is usually described by defining the three main plant characteristics:the flashing flow system, the chemical treatment and the tube configuration. The MSFPlant studied here is a brine recirculation flow, high-temperature (HT) antiscaletreatment, and cross tube configuration, the most typical of the MSF plant types. Ithas six 20-stage condensing lines which deliver up to 14,400 m

3

/h of water with asteam turbine cycle to provide electrical power.

The plant has a single effect MSF evaporator with recycled brine (see figure 3.1).Recycled brine plants contain three main sections from left to right: the

‘heat inputsection’

(or brine heater), the

‘heat recovery section’

, and the

‘heat rejection section’

.The recovery and rejection sections both have a series of stages. Each stage has aflash chamber and a heat exchanger/condenser, where vapor (flashed off in the flashchamber) is condensed. The flash chamber is separated from the condenser by ademister, where entrained brine droplets are removed from the flashing vapor, and adistillate trough catches the condensate from the condenser above.

FIGURE 3.1

Schematic diagram of a single effect MSF evaporator with recycled brine.

A brief description of the MSF desalination flow process follows (see figure 3.1). Theplant feed, SR, is allowed to pass through the heat rejection section, which rejects theexcess thermal energy from the plant and cools the product and brine to the lowestpossible temperature when it comes from the last recovery section stage.

At the output of the first (warmest) rejection stage the feed stream splits into two parts,reject seawater CW (which is returned back to the sea) and a make up stream F (whichis then combined with the recycle stream). The combined stream R passes through theheat exchangers of the recovery section, where its temperature increases as it proceedstowards the heat input section of the plant. In the brine heater, the brine temperature israised from T

F,1

to a maximum value T

B,o

(

=

Top Brine Temperature TBT)

Process description


55

approximately equal to the saturation temperature at the system pressure. If theseawater temperature is lower than 25 ºC, the temper system takes part of the coolingreject seawater, so that the distiller feed temperature is at least the above mentionedtemperature.

The brine then enters the first heat recovery stage where it is flashed by reducing thepressure in a throttling valve. As the brine was already at its saturation temperaturefor a higher pressure, superheated water vapor is generated in the throttling process.This vapor passes through a wire mesh (demister), to remove any entrained brinedroplets before condensing onto a heat exchanger where cold brine passes throughand recovers the latent heat (as shown in figure 3.2). The condensed vapor drips ontoa distillate tray.

The process is repeated all the way down the plant as both brine and distillate enterthe next stage at a lower pressure. The concentrated brine is divided into two parts asit leaves the plant, the blowdown BD, which is pumped back to the sea, and a recyclestream R, which returns to the recovery section.

From a mathematical point of view, the once-through design (with no reject section),and the recycle design can be represented by the same model if the zero value is set tothe mass flow rates of the recycle R and the reject seawater CW streams.Furthermore, there is no distinction between heat recovery and heat rejection sectionsin the once-through plant.

FIGURE 3.2

Cross-section of a stage in a typical MSF plant.

For the recycled brine plants, the mass flow rates of the recycled brine and coolingwater loops are typically 10 times greater than the distillate production rate. The latteris, in turn, approximately an order of magnitude greater than the steam supply massflow rate.

Tube bundle

Distillated

Flash boxFlashing brine

Vapor

Demister

Roof


56


MSF plant operation can be better analyzed by temperature profiles and sorting outthe main parameters. The temperature profiles of a recycled brine plant are illustratedin figure 3.3. The first obvious parameter is the temperature range,

∆

T

,

which is thedifference between the top temperature (T

B,o

) of the incoming feed and coolingwater, i.e. seawater, T

sea

. Another important parameter is the temperature rise in thebrine heater, (= T

B,o

– T

F,1

).

FIGURE 3.3

Temperature profile of a recycle brine MSF plant.

A non-uniform temperature difference is assumed over the entire flash range, but thisdoes not imply a different design for each stage. This means that the interstagetemperature differences will vary slightly down the plant and may vary significantlybetween stages of different designs. Specifically, the interstage temperaturedifferences in the recovery and reject sections may differ considerably.

The total temperature drop in each stage may have a number of causes, including:

a) Interstage temperature difference (

δ

T): the drop temperature of all fluids at eachstage. As a first assumption, all the fluids of an MSF plant have the sameinterstage temperature difference.

b) Condenser terminal difference (

δ

T

C

): the temperature difference between therecycled brine flow being heated inside the evaporator tubes (being heated) andthe flashed vapor temperature at each stage. This value strongly depends on theheat exchanger type (design, material, fouling effect, etc.). A high heat transfercoefficient value means a lower

δ

T

C

value.

c) Demister pressure losses (

δ

T

P

): the frictional pressure loss when the vapor ispassed through the demister, to remove any entrained brine droplets, results in afurther decrease in saturation temperature. The resulting saturation temperaturedrop can be estimated either using the Clausius-Clayperon relationship or thesteam tables.

Brineheater Heat recovery

Heat rejection

Blowdown + distillate

Feedwater Tsea

Make-up

CoolingrejectDistillate

Flashing brine

Brine recirculation

TF1

TS TBo

Mathematical model of MSF unit


57

d) Condenser pressure losses: vapor undergoes a frictional pressure loss in thecondenser tube bundle as when passing through the demisters.

e) Boiling point elevation (BPE): Non-volatile solutes (i.e. sodium chloride)dissolved in water, raise its boiling point. The size of this raise may be predictedby considering the equilibrium between the solution and the water vapor, whosevalue is a function of the brine temperature and salinity. The BPE value is mostoften less than 1 ºC.

f) Non equilibrium allowance (NEA): When the flashing brine stream enters astage, it undergoes a pressure reduction. If this brine had an infinite residencetime in the stage, the whole lot would cool down to the saturation temperaturecorresponding to the flash chamber pressure and a maximum amount of distillatewould flashed off.

The energy consumption of an MSF plant is usually expressed in terms of theperformance ratio PR, sometimes also called Gained Output Ratio, GOR definedpreviously. PR is commonly defined as kg of distillate per kg of dry saturated heatingsteam condensed in the brine heater without condensate subcooling. MSF plantsnormally have a PR value of 8 in the nominal case. The cleaning ball system is notnormally installed in MSF plants but helps to avoid fouling in heat exchanger tubes,so the PR is also increased.

Another measure of the energy consumption in MSF plants is sometimes expressedas the energy input to the brine heater per unit mass of distillate produced, oftencalled the specific energy consumption (NC). This can be converted into aperformance ratio, as defined above, by providing the steam condensing temperaturein the brine heater.

A large flash range as possible is desirable. Since the performance ratio improves asflash range increases, either for a fixed performance ratio (the operational efficiencyincreases due to a reduction in the required heat transfer surface area) or for aconstant surface area. The recycled ratio is also reduced as the flash range increases,which results in a larger temperature rise in the heat input section for a fixed heatinput, and a larger logarithmic mean temperature differences in the recovery section,with the corresponding reduction in the required heat transfer surface area.

Seawater temperature limits the lowest temperature value in the plant. The only wayto increase flash range is by raising the top temperature. This is limited by the onsetof calcium sulphate scaling, and the increasing costs of additional stages.

3.2 Mathematical model of MSF unit

Several models of a single effect MSF plant are available (Barba, Liuzzo andTagliaferri, 1973; Darwish and Arazzini, 1989; Itahara and Stiel, 1968; Beamer andWilde, 1971; Coleman, 1971; Al Owais, Nijhawan and Budhijara, 1989; Helal,


58


Medani and Soliman, 1986; Al-Mutaz, 1989; Alhumaizi, 1997; Hayakawa, Satori andKonishi, 1973; Glueck and Bradshaw, 1970; Rautenbach and Buchel, 1979; Husain etal., 1993; Husain et al., 1994; Falcetta and Sciuba, 1997). In the SIMTAW modelpresented here, the energy and mass balances are applied to each stage of the MSFplant and guidelines and nomenclature following Helal et al. (1986), although all of itwith significant modifications.

Apart from assumptions considered in the next two sections, the followingassumptions were introduced in the SIMTAW model:

a) The product leaving any stage is salt free (distillate concentration = 0 ppm). Nomist is entrained with the flashing vapor.

b) No subcooling of condensate leaving the brine heater is considered. Furthermore,inlet steam to the brine heater is assumed to be saturated vapor, even though itcan be slightly superheated, i.e., desuperheater model in the brine heater was notconsidered.

c) There is no interstage model in SIMTAW. So, the effect of the flashing brine levelper stage is not taken into account.

Hence the mathematical equations —i.e., mass, energy and heat transfer equations—for a single stage (figure 3.4) and brine heater model (figure 3.5) are basically asfollows:

3.2.1 Stage model

Referring to figure 3.4, the following equations can be written for stage number j atsteady state.

FIGURE 3.4

A general stage in a MSF plant.

R

TF,j

CR

Dj–1

TD,j–1

Bj–1

TB,j–1

CB,j–1

R

TF,j+1

CR

Dj

TD,j

Bj, flow rate

TB,j, temperature

CB,j, concentration

jth Stage

Flashing brine

Distillate

Cooling brine



59

Enthalpy balance on flashing brine:

B

j–1

Hb

j–1

= B

j

Hb

j

+ (B

j–1

– B

j

) Hv

j

(3.1)

where B

j

is the flashing brine flowstream in jth flash chamber (stage j), Hb

j

is theflashing brine enthalpy, which is a function of temperature and concentration. Thisproperty is calculated as a saturated liquid, Hv

j

is the saturated vapor enthalpy ofwater in jth stage.

Total material balance (water + salt):

B

j–1

+ D

j–1

= B

j

+ D

j

(3.2)

where D

j

is the distillate in the jth stage.

Salt balance:

B

j–1

C

B,j–1

= B

j

C

B,j

(3.3)

where C

B,j

is the salt concentration in the jth stage.

Overall enthalpy balance:

R CP

R,j

(T

F,j

– T

F,j+1

) = D

j

CP

D,j–1

(T

D,j–1

– T*)

+ B

j–1

CP

B,j–1

(T

B,j–1

– T*) – D

j

CP

D,j

(T

D,j

– T*)

– B

j

CP

B,j

(T

B,j

– T*) (3.4)

where R is the recycled brine mass flow rate. In the Recovery Section, R depends onthe required distillate and seawater temperature, but in the Reject Section the valuecorresponds to feed water supply (SR). CP

R,j

is the heat capacity of cooling brine,passing through the heat exchanger tubes, this property is a function of temperatureand concentration. Although cooling brine is under high pressure, (to allowcirculation inside the tubes), this property is calculated as if cooling brine weresaturated liquid. CP

D,j

is the heat capacity of distillate, in this case, it is considered tobe saturated liquid water; CP

B,j

is the heat capacity of flashing brine, which isassumed to be saturated liquid at flash chamber pressure in each stage. This propertyis calculated in a similar way to the cooling brine. T* is the temperature reference(273.15 K); T

F,j

is the cooling brine temperature in the jth stage; T

D,j

is the distillatetemperature in the jth stage, and T

B.j

is the flashing brine temperature in the jth stage.


60


Heat transfer equation (condenser):

(3.5)

where Aj is the total evaporator/condenser heat exchange area; Uj is the overall heattransfer coefficient of the evaporator in each stage. Its value depends on the variousheat transfer resistance in the plant. The overall heat transfer coefficient is then:

(3.6)

where Rbi is the inside tube heat transfer resistance, given by

(3.7)

where OD and ID are the outside and inside tube diameters respectively and hi is theconvective heat transfer coefficient for fully-developed turbulent flow inside a tube.Assuming a small temperature difference between the wall surface and the bulk of thefluid,

(3.8)

where E is the ‘Enhancement factor’ (for smooth tubes this is 1.0, but is much greaterfor enhanced tubes); Re is the Reynolds number of the tube flow, Pr is the Prandtlnumber of the tube flow.

Rw is the tube wall resistance, given by

(3.9)

where dlm is the logarithmic mean diameter of the tube, defined as:

(3.10)

kw is the thermal conductivity of the wall and t is the wall thickness. Note that thetube wall resistance can be reduced, by either reducing the wall thickness orincreasing the thermal conductivity of the wall.

TD j, TF j 1+,–

TD j, TF j,–----------------------------------

Uj Aj⋅R CPR j,⋅-----------------------

exp=

Uj1

Rbi Rw Rc Rf+ + +----------------------------------------------=

Rbi1

hbi------- OD

ID---------⋅=

hbi E 0.023k

ID------ Re

0.8Pr

0.4⋅⋅=

Rwt OD⋅

kw dlm⋅-------------------=

dlmOD ID–

ODID---------ln

---------------------=



Rc is the resistance from the condensate film on the vapor-side, given by

(3.11)

where hc is the condensing film heat transfer coefficient obtained from the well-known Nusselt equation:

(3.12)

where k is the condensate thermal conductivity; ρ is the condensate density; λfg is thelatent heat of evaporation; n represents the number of tubes in a vertical row; µ refersto the condensate viscosity; ∆Tfm is the temperature difference across the film(=Ts--Tw) where Ts and Tw are the saturated vapor and outside wall temperatures; g isthe acceleration due to gravity.

The condensate properties are usually evaluated at the film temperature Tfm given by

Tfm = Ts – 0.5 (Ts – Tw) (3.13)

Rf is the overall fouling resistance, which includes the inside and outside foulingresistance and the non-condensable gas resistance. It is usually provided by the heatexchanger designer and depends on the material and acid treatment applied to bothsides of the tube walls and the cleaning ball system.

Distillate and flashing brine temperatures correlation:

(3.14)

where BPE is the boiling point elevation of brine with respect to pure water. Asexplained below, it is a function of brine temperature and concentration; NEArepresents the non equilibrium allowance, which is the temperature drop due to thenon infinite residence time of flashing brine in the flash chamber. PL refers to thepressure losses and includes demister and condenser pressure losses.

Rc1hc-----=

hc 0.729 =k

3 ρ2g λ fg

n µ OD ∆Tfm---------------------------------

0.25

TB j, TD j, BPE NEA PL+ + +=



3.2.2 Brine Heater Model

Brine heater performance (figure 3.5) can be described by the following equations:

FIGURE 3.5 Heat input section.

Mass and salt balance (brine):

, and (3.15)

where Bo is the mass flow in the Brine Heater outlet; CB,o is the salt concentration inthe Brine Heater outlet; CR is the salt concentration in recovery section.

Overall enthalpy balance:

(3.16)

where TB,o is the brine temperature in the Brine Heater outlet; CPH is the mean heatcapacity of brine flowing inside the brine heater; mST is the steam mass flow rate tothe brine heater leaving the power generation plant; λST is the latent heat of steam tothe brine heater.

Heat transfer equation in the brine heater evaporator:

(3.17)

where AH is the total heat exchange area of the brine heater; UH is the overall heattransfer coefficient of the brine heater. It contains the same terms (explained insection 3.2.1), as the overall heat transfer coefficient of the evaporator in the jth stage;TS is the saturation temperature of the vapor entering to the brine heater.

Heat recovery section

Saturated steam

Saturated liquid

Brine heaterStage 1

BoTB,oCB,o

RTF,1CR

mST

TS

B0 R= CB o, CR=

R CPH TB o, TF 1,–( ) mST λST=

TS TF 1,–

TS TB o,–-----------------------

UH AH⋅R CPH⋅--------------------

exp=



3.2.3 Mixer and splitter model

This model takes into account the MSF Plant configuration and the model proposedby Helal et al. (1986). In the SIMTAW model the mixing process is considered afterthe last stage of the reject section. As a result this last stage is considered anotherdistillation stage with exactly the same model as the other MSF stages. For thisreason, the SIMTAW model contains an explicit mixer and splitter model, completelyseparate from the desalination stages (see figure 3.6) which can be modeled with theequations below. Note that even though it does not exactly reflect the real physicalconditions in the plant, the results are accurate enough.

Mass balance (salt + water) on mixer:

(3.18)

where BN is the flashing brine flow in the last stage of the reject section; BD is theblowdown mass flow rate.

FIGURE 3.6 Mixing and splitting points in the MSF desalination plant.

Mass balance on mixer:

R = F + BN – BD (3.19)

Enthalpy balance on mixer:

R · HbR = (BN – BD) HbN + F · HbDR (3.20)

where HbN, HbR, HbDR are respectively the enthalpy of brine leaving the rejectsection, recycle stream and deaerator.

BN BD–( ) CB N, F CF+ R CR=

18 19 20 SRSeawater inlet

D, Distillate

F, Make-up

Deareator

CWReject seawaterBD

Blowdown

R, Recycle brine

Rejection section



Mass balance on reject seawater splitter:

CW = SR – F (3.21)

where SR is the inlet seawater into the reject section. The temper water is neglectedhere.

3.3 Auxiliary equations

Correlations of various properties used to solve the MSF SIMTAW model areincluded in this section. Most of thermodynamic and transport properties of purewater and steam are calculated with the same correlations used in the steam powerplant model, described in Chapter 4. Correlations for calculating the brine andseawater properties in the SIMTAW model are described below, but most propertiescan be found in technical handbooks (Fabuss and Korosi, 1968; Hömig, 1978). Thecorrelations used in the simulator are accepted here because results that they gave arereasonable when other mathematical models have been developed (Helal et al.,1986).

3.3.1 Density

The expression for the brine density ρb (lb/ft3) given here is valid for the range of0-26% Cb concentration and 40-300 ºF temperature. Pure water density wascalculated (Mothershed, 1966) from the equation below with Cb = 0.

(3.22)

Another correlation can be found in Chen et al. (1973).

3.3.2 Viscosity

Tabulated and interpolated data (Lewis and Randal, 1961) for a given concentrationCb and temperature Tb are extrapolated between the range 0 < Cb < 20%,0 ºC < Tb < 120 ºC, to obtain brine viscosity µb (N·s/m2). Other correlations can befound in Leyendekkers (1979); Isdale, Spence and Tudhope (1971).

ρb 62.707172= 49.364088+ Cb 0.43955304– 102–

Tb⋅

0.032554667– Cb Tb 0.46076921– 104–

Tb2⋅

0.63240299+ 104–

Cb Tb2⋅

Auxiliary equations


(3.23)

3.3.3 Thermal conductivity

Tabulated data (Lewis and Randal, 1961) are used, interpolating with threeconcentrations Cb (0%, 10%, 20% weight) at different temperatures Tb (up to120 ºC). As we can see in the formula, brine thermal conductivity kb (W/mK) is closeto pure water conductivity (brine is about 2% less than pure water).

(3.24)

Yusufova et al. (1978) also provides a correlation for thermal conductivity of brine.

3.3.4 Heat capacity

Specific water heat capacity CPd is the equation (3.26). The correlation of brinespecific heat (BTU/lb ºF) is obtained (Helal et. al, 1986) by applying a factordependent upon the solid concentrations and temperature to the heat capacity of purewater CPd at the desired temperature (Bromley et al., 1970):

(3.25)

where

(3.26)

where Tb is the brine temperature (50 ºF < Tb < 200 ºF); Cb the percentage of saltconcentration.

3.3.5 Enthalpy

For a given concentration Cb, integration of the heat capacity from the referencetemperature T* = 273.15 K gives the specific enthalpy (BTU/lb) of brine solution Hbat Tb:

µb 1.745 2.5Cb+( ) 103–

5.26 4Cb+( ) 105–

Tb–=

9 107–

Tb2

8 109–

Tb3

3 1011–

Tb4⋅+⋅–⋅+

kb 0.569118 0.00184086 Tb 7.289 106–

Tb2⋅–+( ) 1 0.2 Cb–( )=

CPb 1.0 Cb 0.011311 0.0000146 Tb–( )– CPd=

CPd 1.0011833 6.1666652 105–

T 1.3999989 107–

T2⋅+⋅–=

1.3333336 109–

T3⋅+



(3.27)

where

a = 1 – Cb · 0.011311

a1 = a · 1.0011833

3.3.6 Vapor pressure

The following equation (Antoine correlation) describes how the vapor pressure ps ofsaturated steam is dependant on temperature T (using the water coefficients, Reid,Prausnitz and Sherwood, 1977):

(3.28)

Equation (3.28) is used until 441 K. Above this temperature (and the critical point),the Harlacher & Braun vapor-pressure correlation is used, with the coefficientsproposed by Reid et al. (1977).

(3.29)

Equation (3.29) needs an iteration algorithm, for example a Newton-Raphsonmethod. SI units must be used. No correlation is used to calculate the vapor pressureof brine solutions.

Hb a1 Tb T*–( ) a2 Tb T*–( ) a3 Tb T*–( )3+ +=

a4 Tb T*–( )4a5 Tb T*–( )5

+ +

a21.1473561 10

5–⋅ 6.1666652 105–

a⋅ ⋅–2

-----------------------------------------------------------------------------------------------=

a31.3999989 10

7–⋅ 7.0669983 1010–

a⋅ ⋅–3

-------------------------------------------------------------------------------------------------=

a41.3333336 10

9–⋅ 1.6043987 1012–

a⋅ ⋅–4

-------------------------------------------------------------------------------------------------=

a51.5296 10

14–⋅5

----------------------------------=

psln 23.196452= 3816.44T 46.13–-----------------------–

psln 60.228852= 68695T

---------------– 5.115– T 7.875+ 103–⋅

ps

T2

------ln

Auxiliary equations


3.3.7 Boiling point elevation

Data from Stoughton and Lietzke (1965) were correlated (Friedrich and Hafford,1971) to represent the boiling point rise BPE (ºF) as a function of temperature TK and

salt concentration C:

(3.30)

where TK = (Tb + 460)/1.8 (K); C = (19.819 Cb)/(1 – Cb).

Brandoni, del Re, and Di Giacomo (1985) include correlations for BPE and otherseawater properties.

3.3.8 Non-equilibrium allowance

Burns and Roe correlation (Omar, 1981) reported the following empirical equationfor the non-equilibrium allowance (NEA), expressed as temperature loss (ºF):

(3.31)

where Hj is the height of brine pool in each stage (in.); is the flash down perstage (TB,j–1 – TB,j), expressed in ºF; ωj the chamber load per unit width (lb·h/ft).

3.3.9 Demister and other losses

Omar (1981) suggests the following empirical equation to calculate the temperatureloss due to the pressure drop in the demister and condenser tubes.

(3.32)

where ∆TL is expressed in ºF, and TD,j is the distillate temperature (ºF) in stage j.

BPE 565.757Tk

------------------- 9.81559– 1.54739 TKln+=

337.178TK

------------------- 6.41981– 0.922753 TKln+

C–

32.681TK

---------------- 0.55368– 0.079022 TK C2

ln+

+

C

266919.6

TK2

---------------------- 379.669TK

-------------------– 0.334169+-----------------------------------------------------------------------------

1.8⋅

NEA 352( ) Hj( )1.1 ∆TB j,( ) 0.25– ωj 103–⋅( )

0.5TD j,( ) 2.5–

=

∆TB j,

∆TL 1.885 0.0263TD j,–( )exp=



3.4 Solution algorithm

MSF can be classified as a steady-state and lumped parameter model (Husain, 1999).A wide variety of iterative solution procedures for solving non-linear algebraicequations exist in the literature. In such procedures the equations are usually split intogroups and then ordered by carefully choosing the iteration variables so that the largesystem of equations is decomposed into simpler subsystems.

The methods usually applied to solve the multistage countercurrent separationproblems encompassing large systems of non-linear equations are:

a) Stage by stage calculations, i.e., iterative methods,

b) Global methods, e.g. Newton and quasi-Newton methods,

c) Linear methods (Helal et al., 1986),

d) Other mathematical procedures, such as relaxation methods or a combination ofseveral methods.

The procedure to simulate a MSF plant with the SIMTAW model is a global one, i.e.,the Powell hybrid method (Powell, 1964), which was also used to solve the powerplant model in Chapter 4. The subroutines implemented for this method are availablein internet (UTK and ORNL, 1999).

FIGURE 3.7 Solution algorithm of a MSF desalination plant model.

Solution algorithm


Figure 3.7 shows how the Powell hybrid model is applied to solve the MSF model.First, the variable array is built with the initial values included in SIMTAW, takinginto account the chosen program options. Then, the Jacobian matrix is calculatedusing the differences of the array function, which contains the equations that performthe MSF model, included in the above sections. Finally, the variable array is updatedby multiplying the Jacobian and the array function. If the values do not vary withrespect to the latest iteration (that is, they are lower than the specified tolerance), theprocess is finished, or new updates are made until a new value of the Jacobian matrixis needed. The condition leading to a new calculation of the Jacobian matrix dependson the convergence of the iterations. Usually the Jacobian matrix is calculated whenthe variable array is updated five times.

The criteria for convergence applied in SIMTAW has been imposed by the Powellmethod (Powell, 1964). The simulation is completed when the relative error betweentwo consecutive iterations satisfies the specified tolerance:

(3.33)

where

is the calculated value of the variable j in the iteration m; is the calculatedvalue of the variable j in the iteration m–1; x is the variable array, containing thedependent variables needed to perform the MSF plant simulation. The variable arraycontains the following terms:

• Flashing brine temperature in each stage (TB,j).

• Cooling brine temperature in each stage (TF,j).

• Distillate temperature in each stage (TD,j) (it is not a variable in the inverseproblem, see Section 3.6.3).

• Flashing brine concentration in each stage (CB,j).

• Flashing brine flow rate in each stage (Bj).

• Distillate flow rate in each stage (Dj).

• Top brine temperature (TB,o). In the TBT option this variable is not considered(see Chapter 5).

• Recovery section concentration (CR).

• Deaerator temperature (TDR).

max∆xj

xjm--------

103–≤

∆xj xjm

xjm 1–

–=

xjm

xjm 1–



3.5 Simulation cases

The MSF brine recycle flowchart (figure 3.1) has 7 (NRC + NRJ) + 13 degrees offreedom as demonstrated by the number of independent equations and unknowns.

The following variables are defined for an existing plant:

• Number of recovery stages NRC (=17 in our case).

• Number of rejection stages NRJ (3 stages).

The following five variables (design data) are fixed for each stage (assuming thenumber and arrangement of tubes):

a) heat transfer area of evaporators Aj,

b) tube length Lj,

c) stage width wj,

d) outside diameter ODj; and

e) inside diameter IDj (or tube thickness t).

The four brine heater variables (AH, LH, ODH, and IDH) are also known. The definedvariables mentioned above sum up to 5 · (NRC + NRJ) + 6 specifications. Thus, if thefouling factor is also fixed in every different stage as well as the brine heater, this willresult in (NRC + NRJ+1) more specifications. Furthermore, if the brine levels in thedifferent stages are defined (NRC + NRJ variables), then the total number ofspecifications is

(3.34)

The above specifications limit the degrees of freedom to only 6; obtained bysubtracting 7 (NRC + NRJ) + 7 from 7 (NRC + NRJ) + 13. Since the feedtemperature Tsea and concentration Csea will be known, only four remainingvariables will have to be specified to solve the problem.

Different combinations of variables can be chosen to simulate the MSF plant,depending on the objective of the simulation study. Each set (different case) has fourspecifications. For example, three cases are explained below:

a) The first is called performance calculation. In this case the following operatingvariables are specified: R, CW, F, TS, Tsea, Csea; distillate production, steam

5 NRC NRJ+( ) 6+ NRC NRJ 1+ +( ) NRC NRJ+( )+ +

7 NRC NRJ+( ) 7+=

Simulation cases


consumption and Top Brine Temperature are solved. This case is most useful forsensitivity analysis studies, it is the simulation case implemented in SIMTAW.Two new simulation options, explained in Section 3.5.1 and 3.5.2, were alsoincluded in the SIMTAW program: TBT option and the inverse problem option,where the fouling factors were obtained by substituting in the distillatetemperature profile.

b) In the second case, the operating parameters F, CW, Tsea, Csea, TB,o and the plantcapacity DN are specified; steam consumption, steam temperature and recyclebrine are solved. This case may be used to investigate the possibility ofmaintaining a specified plant capacity when the feed temperature is modified.This case it is not considered in the SIMTAW program because the recycle brineis determined by the MSF plant (design curves).

c) In the third case, the parameters F, Csea, CW/R, mST and Tsea are specified. Thebehavior of the whole plant is analyzed when a specified amount of steam issupplied to the desalination plant by a coupled power plant. This case is notincluded in the SIMTAW program, taking into account the control implementedin the combined power and MSF plant.

3.5.1 TBT control

The MSF Plant has a TBT control (from 84 to 112 ºC), to avoid the tube scaling,which was included in the simulator option with a fixed TBT value. The rest of thevariables can be affected by this option, e.g., distillate output is close to the initialvalue, due to the TBT/distillate correspondence (initial curves).

This option reduces the number of equations. The equation governing heat transfer inthe heater is rejected because the TBT is not a constraint in this equation. This is theonly equation removed from the MSF plant model. As a result, a new system ofequations is obtained.

3.5.2 Inverse problem

This problem involves calculating the global heat transfer coefficient, U, and thefouling factor of all distillation stages of the MSF plant. In this simulation option thedistillation temperature profile is a user variable. As a consequence, the resultsobtained in the brine heater are less accurate than in other simulation modes.

The heat transfer equations used to calculate the distillate temperature in each stageof the recovery and reject section are omitted, when solving the inverse problembecause the user should provide the distillate profile. The other equations included inthe MSF model remain unchanged.



Taking into account the four possibilities in the simulation of the MSF process (TBTcontrol, inverse problem, both or none options), there are four mathematical modelsimplemented in SIMTAW.

3.6 Initial data and simulation

Internal parameters of the MSF plant were calculated in the simulation model, usingsome design curves provided by the manufacturers (Fisia-Italimpianti, 1996):

• Top Brine Temperature (TBT) as a function of seawater temperature (SWT infigure 3.8) and distillate D.

• Recycle brine R as a function of seawater temperature Tsea and distillate D(figure 3.9).

• Feedwater (make-up F) as a function of distillate D and seawater concentration(figure 3.10).

• Seawater to reject section as a function of distillate D and seawater temperatureTsea (≡ SWT) (figure 3.11).

FIGURE 3.8 Correspondence between the Top Brine Temperature and distillate output.

80

85

90

95

100

105

110

115

1200 1400 1600 1800 2000 2200 2400Distillate output (T/h)

Top

Brin

e T

empe

ratu

re (

º C

)

SWT 25º C

SWT 32º C

SWT 28º C

65 %

100 % 125 %

TBT 112 º C

TBT 84 ºC

Initial data and simulation


FIGURE 3.9 Brine recirculation as a function of the distillate output.

FIGURE 3.10 Make-up feed water as a function of the distillate output.

FIGURE 3.11 Seawater to reject section as a function of the distillate output.

16000

16500

17000

17500

18000

18500

19000

19500

20000

1000 1200 1400 1600 1800 2000 2200 2400Distillate output (T/h)

Brin

e re

circ

ulat

ion

(T/h

)

SWT 25º C

SWT 28º C

SWT 32º C

65 %

100 %

125 %

4500

5000

5500

6000

6500

7000

7500

8000

8500

1200 1400 1600 1800 2000 2200 2400

Distillate output (t/h)

Mak

e-up

feed

(t/h

)

Sea water inlet TDS: 45,000

14000

14500

15000

15500

16000

16500

17000

17500

18000

1000 1200 1400 1600 1800 2000 2200 2400

Distillate output (T/h)

Sea

Wat

er to

Rej

ect (

T/h

)

65 %100 %

125 %

SWT 25º C

SWT 28º C

SWT 32º C



These curves contain the limits and the feasible operation ranges in the MSF plant.But those graphics also could be correlated by using the real data obtained from theplant managers in 1997 (WED, 1997). Figures 3.12 to 3.15 show how the correlationshave been made using regression lines in a range of 2 ºC of seawater temperature.This possibility is available in SIMTAW with the option ‘Sim. with real data’.

FIGURE 3.12 Top brine temperature depending on the seawater temperature and distillate production. Data collected during the year 1997.

FIGURE 3.13 Recycle brine flow as a function of the seawater temperature and production. Real data collected in the MSF distillers during 1997.

Therefore, only three input parameters are needed to run the program (note that themodel has only 6 degrees of freedom): distillate or Top Brine Temperature, seawatertemperature and concentration (the seawater salinity concentration Csea in ArabianGulf area is 45,000 TDS). Steam to brine heater conditions is also requested bySIMTAW, and the temper system takes into account the seawater intake temperatureand flow rate.

88

92

96

100

104

108

112

1350 1550 1750 1950 2150 2350D (T/h)

TB

T (

ºC) TBT 26ºC

TBT 28ºC

TBT 30ºC

TBT 32ºC

TBT 34ºC

TBT 36ºC

17500

18000

18500

19000

19500

20000

1350 1550 1750 1950 2150 2350D (T/h)

R (

T/h

) R 26ºC

R 28ºC

R 30ºC

R 32ºC

R 34ºC

R 36ºC

Initial data and simulation


FIGURE 3.14 Make-up feed flow obtained for each range of seawater temperature when real data are computed. Average data of 1997.

FIGURE 3.15 Seawater to reject flow correlations for different seawater temperatures entering the MSF plant. Data collected during the year 1997.

3.6.1 Fouling effect

Design curves account for the fouling inside and outside of the tubes, without acleaning ball system. Although the fouling values are very difficult to evaluate, theyare input data in the program.

The cleaning ball system can reduce the design fouling factor by five (Barthelmes andBolmer, 1996), depending on the tube material. Overall heat transfer coefficient of

3600

4600

5600

6600

1350 1550 1750 1950 2150 2350D (T/h)

F (

T/h

)

F 26ºC

F 28ºC

F 30ºC

F 32ºC

F 34ºC

F 36ºC

17300

17500

17700

17900

1350 1550 1750 1950 2150 2350D (T/h)

SR

(T

/h)

SR 26ºC

SR 28ºC

SR 30ºC

SR 32ºC

SR 34ºC

SR 36ºC



the evaporator is increased from ≈2,500 to ≈3,500 W/m2·K, then the PerformanceRatio and the steam consumption are also improved.

3.7 Summary

Thermoeconomic analysis of a system requires knowledge of thermodynamic statesof the system under different operating conditions and circumstances of the plant.If the data acquisition system of the plant does not provide those data or the system isnot an existing plant, the state of the system could be obtained by using amathematical model describing system behavior.

Energy and mass balance, and heat transfer equations compose the mathematicalmodel of the MSF process, so it is not necessary to apply additional equations toobtain a reasonable agreement in the model results. Correlations providingthermodynamic properties of seawater are essential for accurate results. The model issolved using conventional methods and software. Mathematical method differs formthe original if some important parameters of the plant are introduced. Thus, the stateof the plant could be achieved below different perspectives. Finally, the model hasbeen adjusted as much as possible, in order to respond the design but also the realbehavior of the MSF plant.

When the thermodynamic state of the MSF plant is obtained, the state of the steampower plant is also demanded if the thermoeconomic analysis is going to beperformed. It will be obtained by using equations described in Chapter 4.

TABLE 3.1 Fouling factors of the heat sections in MSF Plants.

Tube material Fouling factor (m2 K/W)

Cooper alloys 0.00005

Titanium or Stainless Steels 0.00003

Without On-Load Cleaning System 0.00020


CHAPTER 4

Steam power plantsteady-state model

In this chapter the mathematical model of the power generation system of a dual-purpose plant is described, which is implemented in the SIMTAW program (thesimulator included in Chapter 5). This model can perform both a conventional energyanalysis and a thermoeconomic analysis of a power plant. Thermophysical properties,such as temperature, pressure, viscosity, specific enthalpy, specific exergy, and so on,are calculated for the most significant mass and energy flow streams, together withoperating parameters of different plant units, e.g., isoentropic efficiencies, heattransfer coefficients, etc. Different operating scenarios can be simulated by varyingthe input data and the simulation options to analyze plant behavior and theinteractions among equipment.

Power plants produce both electricity and process steam used in the MSF plant toproduce desalted water from seawater. The co-generation concept considers thevarying demands for power generation and process steam in the production ofdrinking water. Continuous water production is required throughout the year, whereasthe generation of electricity will be higher in summer than in winter.

In the first part of this Chapter I will describe the power plant. Later, the mathematicalmodel together with the most significant formulae and the solution algorithm of thesystem of equations are explained. Finally, the model solution is given in the thirdsection. The operating modes of the co-generation plant lead to different models thatare also described in the last section of this chapter.

Steam power plant steady-state model

78


4.1 Model description

The power generation plant is a co-generation plant providing both electrical powerand the steam required by the seawater desalination plant (MSF plant). The selectedpower plant had six turbojets, each of them at the co-generation design pointproduced 122 MW of electricity and 198 MJ/s of process heat to provide 57,600 m

3

of drinking water per day. A maximum of 6

×

146 MW can be delivered in generatorterminals in pure condensing mode.

Extraction/condensing turbines in each unit operated under constant pressure (that is,pressure at the high-pressure (HP) turbine inlet is always constant). Each of theturbines has two sections, a single flow HP section and a single flow low-pressure(LP) section. Steam extraction outlets for the seawater desalination plant andextraction points for the feedwater heaters (points 3,4,5,6 and 8 in figure 4.1) areavailable on both turbine sections.

Steam flow is an important variable determining the behavior of the power plant. Ifthere is no steam supply for the MSF plant, the steam flows through the LP sectionand is returned (via a damper and bypass line).

FIGURE 4.1

Schematic diagram of the power generation plant. Main significant flows are numbered for later descriptions and equations.

Main HP steam flows from the steam generator —point 1 in figure 4.1— through thesteam supply lines to the main steam emergency and control valves, which areflange-mounted onto the lower section of the HP outer casing. The steam from thevalve casings to the valve chests welded onto the HP inner casing is supplied by the

Model description


79

lower section, and via bypass lines between the valve and turbine casing in the uppersection.

Afterward, the steam enters the valve chests which house the nozzle segments. It thenflows via the control wheel of the HP rotor into the impulse chamber of the turbinecasing. The steam expands through the reaction blading and enters the exhaust steamchamber of the HP section. The steam required for the seawater desalination plant isextracted via the extraction outlets in the lower exhaust section —point 6 infigure 4.1—.

A certain percentage of the steam flows through the exhaust nozzles in the upperexhaust section and then through the downstream damper and bypass line to the LPsection. It then flows into the LP reaction blading via the steam inlet nozzles and,after expansion, enters the condenser at the exhaust nozzles.

The simple design of the high-pressure casing is based on a single shell constructionwith perfect rotational symmetry. All the components of the HP section are securedso that concentric alignment and unrestricted movement is maintained under alloperating conditions.

First and second HP turbine extractions —points 3 and 4 in figure 4.1— are fed to theHP heaters. The first HP extraction goes to the vacuum system of the MSF plant, andis condensed in the condenser. The third HP extraction —point no. 5— feeds thedeaerator; and finally a smaller quantity of the lowest extraction is sent to the first LPheater (the main part is sent to the desalination plant).

The LP section is a standard single-flow design with an upstream inlet section.Depending on the operating mode of the turbojet, the steam is directed to the firstblade carrier via a vertically mounted inlet steam nozzle —point no. 7— and led tothe second blade carrier via a bypass, when the amount of steam to the LP turbine islarge enough. The automatically controlled water injection system in the uppersection of the casing provides the cooling required in specific operating modes. Arupture disc is fitted in the outer casing as a safeguard against over pressure. LPextraction —point no. 8— feeds the second LP heater.

The Power Generation Plant also contains a live steam reduction pressure station, toextract the steam flow to desalination in case of turbine system failure. As seen infigure 4.1, E1 and E2 are the live steam extractions to the two connected desalinationunits. The reduction pressure station mixes the live steam with water feed from thefeed pump (S1 to S4 in figure 4.1), to reach the optimum pressure for the

MSF

plant.When the turbine does not work, a new extraction E3 is needed to feed the vacuumsystem of the MSF units, and a fourth one, called E4 in figure 4.1, feeds the deaerator,where it is mixed with the condensate returned to the MSF units. In this way, thesteam cycle is closed, via the HP feed flow to the boiler.


80


4.2 Mathematical model

4.2.1 Steam turbines

Simulation of admission properties (Salisbury, 1974) is based on the determination ofthe mass flow coefficient, which was defined according to the Cooke’s model(Cotton, 1993; Spencer, Cotton and Cannon, 1974) and the Stodola’s Ellipse model(Stodola, 1927; Cooke, 1985). The mass flow coefficient

φ

is defined as:

or (4.1)

where m is the mass flow rate (kg/s), p is the pressure (bar), T is the temperature (K)and v is the specific volume (m

3

/kg). The mass flow coefficient under operatingconditions can be calculated as a function of the design parameters (subscript d).Thus, the admission values can be solved:

(4.2)

where is the pressure ratio at each turbine section (see figure 4.2):

FIGURE 4.2

Schematic diagram of a turbine section.

The admission properties of the steam turbine are evaluated using a model in whichthe mass flow coefficient is a function of the pressure ratio in each turbine section,and is a characteristic value for each type of turbine. This model cannot be applied tothe first section, due to the fixed pressure mode which controls the steam turbineoperation. Therefore,

φ mp

T---------------= φ m

pv---

--------=

φ mp

T---------------

md

pd

Td

----------

----------1 rpd

2–

1 rp2

–---------------------= =

rpp0

pi-----=

p0

T0

Ti

pimi

Mathematical model


81

(4.3)

Values of the constant K are obtained using the turbine admission properties for thedesign conditions supplied by the manufacturer. For example, the value of K

4

for the4

th

section of the high-pressure turbine can be obtained as follows:

(4.4)

where the subscript ‘4d’ refers to the steam properties at the 3

rd

extraction of the highpressure turbine, taken from a performance data case (ABB, 1996b).

The

efficiency model is also based on the mass flow coefficient. A correlation wasproposed to obtain the isoentropic efficiency of a turbine section as a function of thiscoefficient. The design mass flow coefficients were used to solve this correlation forthe different operation loads of the plant. Polynomial formulae were obtained foreach section of the turbine. The formula corresponding to the 2

nd

section of the high-pressure turbine is a linear function of the mass flow coefficient

φ

2d

, obtained fromthe pressure, temperature and flow of the performance data cases in the 2

nd

section ofthe high-pressure turbine:

(4.5)

FIGURE 4.3

Isoentropic and real expansion of the steam in a turbine section.

Finally, the thermodynamic properties of the steam at each turbine section arecalculated as follows (see figure 4.3):

(4.6)

φ K 1 rp2

–⋅=

φ4d

m4d

p4d

T4d

------------

------------- K4 1 rp4d2

–⋅= =

η2 f φ2d( ) 0.013985 φ2d 0.1002+⋅= =

h

s

h1p1

p2

h2h2s

η i

hi hi 1+–

hi hi l s,+–-------------------------=


82


where h

i

is the enthalpy of the inlet section, h

i+1

is the enthalpy of the outlet section,and h

i+1,s

is the enthalpy of the outlet section in an isoentropic process.

The steam pressure in the lowest section of the high-pressure turbine was a fixedvalue, due to the pressure control applied to the desalination units. Hence, HP and LPturbines can be considered two different pieces of equipment.

4.2.2 HP heat exchangers

HP heat exchangers have desuperheating, condensation, and subcooling sections(ABB, 1996c). Thus, feed water is heated by exchanging the maximum quantity ofheat with the steam bled from the HP extractions.

The model of the HP heat exchangers is based on a correlation of the terminaltemperature differences (TTD) for the different existing loads, see figure 4.4. Theoverall heat balances are used to calculate the amount of extracted steam from the HPturbine. The overall heat transfer coefficient in each section cannot be used becauseof the lack of design data, except for the heat transfer coefficient in the condensingzone, which is a design data that varies with the requested load. Moreover, it isassumed that the condensate is a saturated liquid, even though some sub-cooling mayoccur.

FIGURE 4.4

TTD differences in an HP heater.

Numerical correlations proposed by Erbes (Erbes and Gay, 1989) were used to solvethe terminal temperature differences TTD (inlet/outlet) in HP heaters:

(4.7)

L

T

TTDi

TTDo

Condensation section

Desuperheating section Subcooling section

∆Ti

∆Td----------

mmd-------

xTTd------

yppd-----

z

⋅ ⋅=

Mathematical model


83

where

∆

T

i

is the inlet TTD in an HP exchanger (usually called Drain CoolingAdvantage (DCA)), and m, T and P are the feedwater properties at the HP inlet. The dsubscript refers to the design conditions. The x, y and z exponents were obtainedfrom the heat balances for different loads supplied by the manufacturer (ABB,1996b). Typical x, y and z values are shown in table 4.1:

The outlet TTD (

∆

T

o

) (or simply called TTD) correlation contains more factors.Thus, the mass flow rate and steam pressure of the turbine extraction are also needed,in order to model the correct behavior in all cases. Typical values for the fivecoefficients needed in a HP heater are shown in table 4.2.

(4.8)

The Erbes and Gay model (Erbes and Gay, 1989) also provides the pressure losses inthe feed waterside of the HP heat exchangers:

(4.9)

4.2.3 LP heat exchangers

LP heat exchangers in the Steam Power Plant only have a condensation and asubcooling section (ABB, 1996c). Usually the steam flow is saturated vapor orcontains a humidity fraction. Thus the feedwater is heated by extracting the maximumquantity of steam heat from the LP extraction and the lowest HP extraction.

TABLE 4.1

Typical x, y and z coefficient values for the inlet TTD’s in an HP heater.

x y z

0.64 –0.29 0.52

TABLE 4.2 Typical x, y, z, a and b coefficient values for the outlet TTD’s in an HP heater.

x y z A b

–2.395 4.407 –0.713 0.584 0

∆T0

∆Td----------

mmd-------

xTTd------

yppd-----

zmex

mex d,-------------

apex

pex d,------------

d

⋅ ⋅ ⋅ ⋅=

∆p∆pd---------

mmd-------

1.8 TTd------

p

pd-----

1–

=



Correlations similar to those used in the HP heaters to calculate the TTD’s (seefigure 4.5) and the pressure losses were also used to model the LP heater behavior.The exponent values were also obtained from the heat balances for different loadssupplied by the manufacturer (ABB, 1996b), they are shown in tables 4.3 and 4.4.

FIGURE 4.5 TTD differences in an LP heater.

4.2.4 Deaerator

A whole plant energy balance is included when modeling the deaerator and feedwatertank behavior (ABB, 1996c). Feedwater from the LP heaters, condensate from thedesalination units and cooled drain from the HP heaters enter the feedwater tank, butthe operating pressure is controlled by the 3rd HP extraction.

The mass flow leaving the extraction must be correlated to assure some saturatedliquid is entering the feed pump. Several parameters were included to calculate the3rd HP extraction mass flow rate, to cover the operating range designed by themanufacturer (ABB, 1996b). The proposed correlation is:

TABLE 4.3 Typical x, y and z coefficient values for the inlet TTD’s in an LP heater.

x y z

0.43 –0.02 0.10

TABLE 4.4 Typical x, y, z, a and b coefficient values for the outlet TTD’s in a LP heater.

x y z z b

–0.04 18.97 –0.12 1.11 4.33

L

T

TTDo

TTDi

Subcoolingsection

Condensationsection

Mathematical model


(4.10)

where m1 is the live steam mass flow rate generated in the boiler; T5 and P5 are theadmission properties leaving the 3rd section, m1,des is the difference between m1 anddesalination mass flow rate mdes, m1,LS is the difference between m1 and Live Steamextraction sent to the reducing pressure station mLS, and m1,LS,des m1 minusdesalination and live steam (to the reduction pressure station). The last three variableshave a strong influence on the rest of the plant process units, which is why they wereincluded in the above-proposed correlation. Table 4.5 shows the coefficientscalculated in the last correlation.

4.2.5 Condenser

A global energy balance was applied to develop the condenser model. Three streamsenter the vapor side of the condenser: (i) exhaust steam from the low-pressureturbine, (ii) condensate from the MSF vacuum system and (iii) discharge from theejectors. The maximum cooling seawater flow rate is at the seawater temperature.The condensate presumably discharges at the saturation temperature (ABB, 1996d).

4.2.6 Boiler

A model was used including the heat balance of the waterside of the boiler tosimulate performance of the boiler (figure 4.1). The energy needed to heat thefeedwater leaving the high-pressure heater No. 1 to the fixed conditions of the steamleaving the boiler was used to calculate the natural gas consumption of the boiler(LHV of natural gas is 8026 kcal/Nm3). Boiler efficiency was introduced using thedesign data provided by the contractors (ABB, 1996a) for different operatingconditions. Pressure losses on the waterside of the boiler were computed using thefollowing equation:

(4.11)

TABLE 4.5 x, y, z, a, b and c coefficient values in deaerator.

x y z a b c

Deaerator 0.121 1.091 1.905 0.206 2.588 –0.211

mex 3,mex 3d,----------------

m1

m1d---------

xT5

T5d--------

yp5

p5d--------

zmdes

mdes d,---------------

amLS

mLS d,--------------

bm1 LS des,,

m1 LS des d,,,----------------------------

c

⋅ ⋅ ⋅ ⋅ ⋅=

∆P∆Pd---------

mmd-------

0.463TTd------

0.436–pd

p-----

3.917–

=



A more detailed model could calculate the intermediate properties inside the boiler(the boiler in study has two economizers and three superheaters, and a non reheatprocess inside the boiler). A detailed boiler model clearly surpasses the scope of thisPh. D. Thesis and is not necessary to perform a thermoeconomic analysis of a wholeplant.

4.2.7 Valves

Pressure losses in valves were calculated using the BBC Thermal kit correlations(BBC, 1979):

(4.12)

where p is the pressure of the flow entering the valve; Z is the pressure drop

coefficient (constant value); DV, is the main stop valve seat diameter (m) Sa = ,

the sonic area (m2), with v, specific volume (m3/kg), α, sonic velocity (m/s), and m

the mass flow inside the inside the valve.

4.2.7.1 Turbine control valves

The inlet of the HP turbine has four control valves with some pressure losses (about4-5 bars). The main steam mass flow in the boiler is equally divided into four parts,each flowing through one of the valves. The pressure drop coefficient value (Z) wastaken to be 0.38.

4.2.7.2 Boiler outlet stop valve

The security valve fixed at the boiler outlet had a pressure drop coefficient Z of 2.31.

4.2.7.3 Boiler inlet control valve

This valve, used to control the pressure entering the boiler, had a pressure dropcoefficient Z of 1.30.

4.2.8 Pipes

Significant pressure losses occur in the pipelines, e.g., pipes to the deaerator,extraction pipes or pipes to the boiler. These are calculated by applying thecorrelation proposed by Erbes and Gay (1989):

∆pp

------- ZSa

DV2

----------- 2

=

m vα---

Mathematical model


(4.13)

The value of the a coefficient depends on the type of pipe and operating conditions.Table 4.6 lists the values of the applied a coefficient.

4.2.9 Pumps

The pump model is based on the efficiency versus mass flow rate curves provided bythe power plant manufacturers (ABB, 1996f). Energy consumption is derived fromthe energy balance applied to the pump, when the conditions of the water enteringand leaving the pump are known.

The thermodynamic properties of the water at the inlet/outlet of the feedwater andcondenser pump can be calculated using the isoentropic efficiency (see figure 4.6):

(4.14)

TABLE 4.6 Values of the a coefficient for each pipe of the power model.

Pipe description a

1st HP extraction 1.95

2nd HP extraction 1.95

3rd HP extraction (to deaerator) 1.95

4th HP extraction 1.8

LP extraction 1.95

Waterside of LPH No. 2 1.5


LPH2 to deaerator 1.5

Feed pump to HPH No. 2 1.8



LPH No. 1 to Boiler 1.85

1st HP extraction 1.95

∆p∆pd---------

mmd-------

a TTd------

p

pd-----

1–

⋅ ⋅=

η i

hi 1 s,+ hi–

hi 1+ hi–--------------------------=



where hi is the enthalpy of the inlet water, hi+1 is the enthalpy of the outlet water, andhi+1,s is the outlet water enthalpy in an isoentropic pumping process.

FIGURE 4.6 Isoentropic and real compression process in a pump.

4.2.10 Gland and seal steam system

All steam flow leakages are considered and accounted for in the heat balancecalculations. Gland steam system of the power plant is described in figure 4.7.

FIGURE 4.7 Gland and seal steam system.

Martin’s formula (Martin, 1919) for steam leakage through labyrinth seals was usedto calculate the leakage flows for representative designs with normal runningclearances (figure 4.8):

(4.15)

(4.16)

h

s

h1

h2h2s

p1

p2

Ejector

Live steam

HP LP

m1 m2+ Kd

pt pl–( ) pt

273.15 Tt+----------------------------=

m2 K ′dp1 p2–( )p1

273.15 T1+-----------------------------=

Mathematical model


where Kd and are constants, obtained from the design data (ABB, 1996b), and1, 2 and t subscripts refer to the first and second seal in a leakage and the steamconditions inside the turbine.

FIGURE 4.8 Leakage flows and seals of a steam turbine.

The valve connecting the high and low pressure lines of the gland steam system (seefigure 4.7) is only opened in the condensing operation mode, i.e. when the turbine isworking without desalination flow and only producing electricity, due to the highamount of steam lost in the HP leakage.

Finally, the energy balances in the high and low pressure lines of the gland steamsystem are used, to evaluate the properties of the steam flowing to the ejector.

Table 4.7 shows the Kd and values obtained for the four parts of the turbineinteracting with the gland and seal steam system.

4.2.11 Generator

Generator losses were accounted for in the model to more precisely calculate theplant’s output power, using manufacturer design data (ABB, 1996e). Generatorefficiency is therefore included in equation (4.17) as a function of the output powerin MW:

ηgen (%) = (0.941 + 9.701 · 10–4 · MW + 7.071 · 10–6 · MW2

+ 1.771 · 10–8 · MW3) · 100 (4.17)

TABLE 4.7 Kd and Kd’ constants of the gland and seal steam system.

Kd Kd’

HP Turbine. Inlet 0.02 1.392

HP Turbine. Outlet 0.83 1.448

LP Turbine. Inlet 1.4288 2.962

LP Turbine. Outlet 1.4288 2.962

K ′d

shaft

mt

turbine

pt, Ttp1p2

m2 m1

K ′d



The excitation system was also included, using plant performance data. Theexcitation system losses (ESL) are calculated by a formula that depends on the outputpower in kW:

ESL = 0.00152 * kW – 5.01645 (4.18)

Therefore, the simulator can calculate the electrical and net output power produced inthe power plant.

4.3 Auxiliary equations

The thermodynamic and transport properties in a steam power plant simulationinvolve pure water and steam.

4.3.1 Thermodynamic properties

The thermodynamic properties of water can be calculated by a group of functionsusing equations from the IFC-1967 formulae for industrial applications. Thoseformulae was accepted in the Sixth International Conference about Water Properties(1967). Since then, they have become the standard for ASME, JSME, etc. (also seeASME, 1967; JSME, 1968).

Detailed numerical methods used to solve the inverse functions can be found in Pina(1979).

4.3.2 Transport properties

Specific heat at constant pressure was obtained by numerical integrating the enthalpyfunction. Formulae used to calculate the thermal conductivity and dynamic viscositywere taken from Sangers and Watson (1986) and Yata and Minamiyama (1979).Vargaftik (1978) covers the entire range of the properties, and numerical interpolationmethods were used to complete them at the proper conditions.

4.4 Solution algorithm

The mathematical model of the power plant is also a set of non-linear algebraicequations. There are a wide variety of iterative procedures to solve this kind ofproblem; splitting the equations into subgroups and then solving each subsystem tocreate an iteration loop. Our model was not portioned into subsystems.

The power plant model is solved using the Powell hybrid method (Powell, 1964), alsoused by SIMTAW simulator to solve the MSF plant model. It is a derivation of the

Solution algorithm


Newton method supported by an iterative technique where non-linear terms, such asvariable products and properties, are set to constant values from the latest iteration.The Powell hybrid method is applied to the whole set of equations. It requires aconsiderable programming effort and computer storage. Despite this, a global methodprovides the best solution. Solving the whole system sequentially (where it isdecomposed in a set of subsystems), or linearally (where some variables areconsidered a linear combinations of others), does not provide a better convergence ofthe whole system of equations.

The Powell hybrid method calculates the Jacobian by a forward-difference formula,and uses a relaxation technique to update the values in a new iteration, i.e. theJacobian does not need to be calculated in each iteration. The applied solutionalgorithm is available in the Subroutine HYBRID, in the NETLIB mathematicallibraries (UTK and ORNL, 1999). The user should provide a subroutine containingthe model functions, which are, in turn, the functions needed in the subroutineHYBRID to calculate the Jacobian applying the forward-difference approximation.

In the power plant, the number of equations is much higher than the systemdeveloped to solve the desalination unit: the variable array, (with the dependantvariables needed for the power plant simulation) includes the following termscorresponding to the main flowstreams of the model:

• Admission properties (m, p, h, T, η, K, φ) in each section of the HP and LP tur-bine.

• Gland and seal steam system properties (m, h, T).

• HP and LP heaters properties (mex, p, h, T).

• Condenser and deaerator values (m, X, p, h, T).

• Boiler parameters (m, p, h, T).

• Pressure losses in pipes and heat exchangers (∆p).

Live Steam properties are kept constant to take into account the plant operationstrategy (sliding pressure control is avoided). The applied convergence criterion wasthe same as in the SIMTAW model to solve the MSF plant: the relative error of eachvariable included in the variable array between two consecutive iterations must belower than the specified tolerance. Usually, this value is set to 10-3 but it could beconsiderably reduced:

(4.19)

where

(4.20)

max∆xj

xjm

--------

103–≤

∆xj xjm

xjm 1–

–=



represents the calculated value of the variable j in the iteration m.

is the calculated value of the variable j in the iteration m-1.

The solution algorithm adopted to solve the mathematical model by using the Powellhybrid method is shown in figure 4.9.

FIGURE 4.9 Algorithm to solve the power plant model using the Powell hybrid method.

4.5 Operating modes and mathematical models

A wide variety of operating modes are available in the power plant, depending on theamount of required steam for the MSF desalination units, (either via the live steamreduction pressure station or via the fourth extraction of the HP turbine). Moreover, ifit is not necessary to produce electricity, the system live steam-deaerator-boiler canbe used to obtain the required steam for one or two desalination units.

The operating modes of the steam power plant are as follows:

a) Extraction mode. The most common operation mode where the plant produceselectricity and also supplies steam to the MSF unit.

b) Parallel mode: When the power output is less than 75 MW, the live steam reduc-tion pressure station supplies steam with enough pressure to the MSF unit.

c) Condensing mode: In this case no distilled water is produced and the plant oper-ates as a conventional steam power plant (the power output is maximum).

xjm

xjm 1–

Operating modes and mathematical models


d) Desalination mode: The opposite of the condensing mode. The plant only pro-duces distilled water and the steam turbine does not work. Thus the boiler pro-vides the required steam to the MSF units via the steam reduction pressurestation.

e) Twin desalination mode: Here the boiler is in full load operation and producessteam for two MSF desalination units. This mode is unusual and the steam tur-bine plant does not operate either.

f) Twin extraction mode: Similar to the extraction mode, but the boiler also pro-vides steam for a second MSF desalination unit using a portion of the live steamderived from the live steam reduction pressure station.

Three different mathematical models were implemented to simulate all the differentoperating modes included in the boiler performance data (ABB, 1996a).

The models included in the power plant simulation program were the following:

(i) Normal Turbine Load Model (NTL MODEL): Mass flow entering the LP turbineis between 3-125 kg/s; then the Stodola’s model is applied to simulate the LPturbine. The amount of steam required via the live steam reducting pressurestation is not important if the mass flow to LP turbine is more than thespecified lower limit. This model is more complex, and has the maximumnumber of equations.

(ii) Low Turbine Load Model (LTL MODEL): Mass flow entering the LP turbine isless than the lower limit imposed previously. The Stodola´s model cannot beapplied to the LP turbine, there is a compressor action at high exhaustpressures and low loads, illustrated by the stream lines in figure 4.10:

FIGURE 4.10 Last stage of LP turbine acting as a compressor.



This model determines entry conditions at the condenser. A parametric modelbased on the thermal balances is then used to solve the admission properties inthe LP turbine. Thus, the number of equations in the LTL model is reducedwhen the LP values are solved differently. However, the model has a poorstability because negative mass flows could appear during the iteration processand the program must be aborted.

(iii)Non Turbine Working Model (NTW MODEL): The Power Plant is only used tosupply steam to the MSF desalination units, and the HP and LP turbines areoff. Therefore, the power plant scheme is reduced to a very simple model,composed of the boiler, live steam reduction pressure station and deaerator.HP heaters are bypassed, and pressure losses are neglected. This final schemeis shown in figure 4.11:

FIGURE 4.11 Power plant scheme in the NTW Model. Some flowstreams are renumbered with respect fig. 4.1.

The third model is the simplest one used to describe the power plant as the number ofequations is considerably reduced.

Operating conditions should be classified in one of the three simulation modelsoutlined above (see table 4.8). Performance data cases included in the Design Data ofthe Boiler (ABB, 1996a) are:

1. MSL1 (Minimum stable load at 20% boiler MCR)

Load at which the boiler is still able to operate continuously with rated steamproperties, without the bypass system in operation and without extraction heatflow to desalination and pressure reduction station.

Operating modes and mathematical models


2. MSL2 (Minimum stable load)

Load corresponding to unit operation at 45 MW and with combined heat flow of145 Gcal/h from parallel operation of turbine extraction and live steam reducingpressure station (118.66 and 26.34 Gcal/h respectively).

3. MSL3 (Minimum stable load with two distillers)

The turbine is at minimum stable load and the extraction heat flow is 145 Gcal/hplus 150 Gcal/h through HP pressure reduction station.

4. MSL4 (Winter operation)

The turbine is at minimum stable load with an extraction heat flow of 170 Gcal/hto desalination unit.

5. PL65

The turbine generator load is 65 MW and the extraction heat flow is 145 Gcal/h.

6. PL85

The turbine generator is at 85 MW and an extraction heat flow of 145 Gcal/h.

7. PL115

The turbine generator at 115 MW and an extraction heat flow of 145 Gcal/h.

8. MCR (Maximum Continuous Rating)

The turbine generator at rated steam parameters with a power output of 115 MWand an extraction heat flow of 170 Gcal/h.

9. VWO

Turbine swallowing capacity (all control valves open) with extraction heat flowof 170 Gcal/h.

10. MR (Maximum Rating)

The turbine generator at rated steam parameters, nominal control valve spindleposition and no extraction heat flow to desalination.

11. Boiler MCR

Maximum continuous rating of boiler to be 10% above the requirement of unitMCR test mentioned in item 8.

12. Boiler peak load (COC)

Boiler peak load at least 5% more than boiler MCR. The extraction heat flow is170 Gcal/h to desalination and 50.8 Gcal/h to live steam reduction pressurestation.



13. ODOB (One desalination and one boiler only)

170 Gcal/h extracted through the HP reduction pressure station (a desalinationunit), turbine is not in use.

14. TDOB (Two desalination and one boiler only)

340 Gcal/h extracted through the HP reduction pressure station (two desalinationunits), turbine is not in use.

Table 4.8 shows the type of model applied to simulate each operating mode in theperformance data:

4.6 Summary

The thermodynamic states of the co-generation plant with the steam turbine plant andthe MSF unit are now permissible thanks to the mathematical models described in theprevious and this chapter. The mathematical model of the steam turbine plant is insome cases very unstable, especially when the operating conditions provoke thedeviation of the steam to the MSF unit and LP turbine is forced to work in unexpectedconditions.

TABLE 4.8 Operating mode and mathematical model corresponding to the performance data cases.

Performance data case Mathematical Model Operating mode

MSL1 LTLa

a. Live steam temperature is 460 ºC.

Condensing

MSL2 LTL Parallel

MSL3 LTL Twin Extraction

MSL4 LTL Extraction

PL65 NTL Extraction

PL85 NTL Extraction

PL115 NTL Extraction

MCR NTL Extraction

VWO NTL Extraction

MR NTL Condensing

MCR NTL Extraction

COC NTL Twin Extraction

ODOB NTW Desalination

TDOB NTW Twin Desalination

Summary


The set of equations composing the mathematical model depending on the operationmode of the plant is solved with a global method in which the variables aresimultaneously calculated.

These two chapters contain the mathematical models introduced in the simulator,which is the tool that allows the use of the model’s results in the thermoeconomicanalysis of the dual-purpose plant.


CHAPTER 5

Simulator

Mathematical models used to simulate a dual-purpose plant are quite complex (seeChapters 3 and 4), so a solid basis is needed to solve them. Despite this, the SIMTAWprogram has been built in such way that only a few input data are essential to simulatethe power and desalination plants in order to analyze plant performance. Hence, nohighly qualified background is needed to use the program, although we onlyrecommend its use to obtain a correct understanding of the results to technicians andplant managers that have an in depth knowledge of the dual plant.

Simulation of the thermodynamic processes in a dual-purpose plant is the first step todevelop the Thermoeconomic Analysis of the Plant. Thermodynamic properties of theflowstreams in the plant are needed to apply the exergy balance, and to calculate theexergy costs of these flows. In this way, the complete analysis of the irreversibilitiesand malfunctions can be done, and the causes that generate these faults can bedetected.

SIMTAW is the thermoeconomic software that can provide these results. It is theresult of a complex project with several model developments of different complexity.A Visual Basic coded program is the user friendly interface. SIMTAW was builtfollowing those stages:

1. To solve the mathematical models using an Equation Solver. In this case the EESprogram was used (Klein and Alvarado, 1999). Mathematical models weresolved in blocks, then the whole model was connected. Relationships betweenvariables, and independent blocks of equations were found, then the mathemati-cal model was translated to a high-level programming language such as Fortran.

Simulator


2. The dual-plant was simulated with a Fortran coded program (Microsoft Corpora-tion, 1997). This program has several files including the design data, steam andbrine properties, subroutines to initialize and calculate the variables, subroutinesto solve the system of equations, and the algorithm which controls the wholeprogram.

3. The Dynamic Link Libraries, usually named ‘DLL’s’, are the interface betweenthe Fortran and Visual Basic programs. Seven ‘DLL’s’ were built to develop fourmathematical models included in the MSF Plant and three Power Plant models -all these mathematical models correspond to the operating modes explained inthe previous chapters-.

4. Finally, a Visual Basic coded program (Microsoft Corporation, 1997) was builtto make the program more user friendly. This program is described in the follow-ing section.

The first section of the chapter describes how to use the simulator when thethermoeconomic state of the MSF or the steam power plant is requested. But inChapters 3 and 4 the accuracy of the mathematical models is not analyzed. Modelvalidation is therefore included in this section, when the data flowsheets obtainedfrom plant designers are compared with the results given by the simulator. In general,simulator calculates the properties of the main flowstreams of the dual-plant, theassociated error in the calculations is very low.

5.1 SIMTAW structure

SIMTAW is the program that simulates the two processes involved in a well-knowndual-purpose plant: the MSF and the Power Generation units. SIMTAW has a user-friendly interface that (through a set of more than 20 windows) allows the user toproceed by clicking the specified buttons. SIMTAW is built in Visual Basic 5.0, a newversion only useful for 32 bits, and requires at least Windows’95. A user guideexplaining how to manage the program has been implemented (Villalon, 1995), andincludes a very strict control over the input data introduction in order to avoidinconsistencies in the mathematical models.

The two processes can be simulated independently and are driven by two differentwindows. The window that manages the MSF simulation is shown in figure 5.1,containing the MSF unit scheme, and seven text boxes and control buttons. In the textboxes, the user must introduce an allowed value for the following variables:

1. Distillate mass flow rate (1,200-2,400 T/h) or Top Brine Temperature (84-112 ºC)in the MSF plant.

2. Seawater to reject temperature (25-36 ºC).

SIMTAW structure


101

3. Seawater concentration at the seawater inlet (40,000-50,000 TDS).

4. Steam to brine heater temperature (80-150 ºC).

5. Steam to brine heater pressure (0.8-3.0 bar).

6. Sea water temperature (18-36 ºC)

7. Seawater inlet flow (12,000-20,500 T/h).

FIGURE 5.1

SIMTAW MSF process window.

After these values are correctly introduced, the user must choose the

TBT control

option—clicking the corresponding box—, to fix the Top Brine Temperature valueduring the simulation. The

inverse problem

option also calculates the fouling factor ineach stage. The third option, called

Sim. With real data

, includes a correlation withreal data of the main mass flow rates of the MSF unit collected during the year 1997(WED, 1997).

The window that manages the power plant (figure 5.2) contains the plant scheme andfour text boxes where the user introduces input variables needed to perform the powerplant simulation:

Simulator


1. Generator output (including generator losses, 50-147 MW).

2. Live Steam extractions to the reduction station

1

(0-340 Gcal/h).

3. Steam mass flow rate to the desalination units (0-189 kg/s).

4. Condenser pressure (0.02-0.14 bar).

Then, the user must choose one of the six operating modes in the dual-plant,depending on the power and steam demanded to the MSF unit(s), the operationmodes are (see section 4.6 relating the operating and mathematical models of theprocess):

• Extraction mode.

• Parallel mode.

• Condensing mode.

• Desalination mode.

• Twin desalination mode.

• Twin extraction mode.

The four input variables must be consistent with the selected operating mode, anywaythe program will inform you which variable is out of the range specified for eachoperating mode.

The simulation results of both processes are also presented in several windows, andare resumed here:

• Relevant parameters corresponding to the whole plant and to differentcomponents (fuel consumption, performance ratio, plant efficiency, specificconsumption, steam consumption, etc).

• Thermophysical properties of the mass flowstreams considered in the simulation(the flowstreams are numbered in figures 5.1 and 5.2 respectively). In the powerplant process the values of the gland steam leakage system are also available (seesection 4.3.10 for specifications). The properties are:

–

Temperature.

–

Pressure.

–

Mass flow rate.

–

Steam quality.

–

Specific enthalpy.

–

Specific entropy.

1. Taking into account for the two extraction units (E1, E2) —see figure 4.1— with the same thermodynamicproperties.

SIMTAW structure


103

FIGURE 5.2

SIMTAW power plant window.

–

Specific exergy (thermal, mechanical and chemical contributions).

–

Dynamic viscosity.

–

Thermal conductivity.

–

Specific heat.

–

Density.

• Some charts of different variables plotted by using a graphic server in SIMTAW:temperature profiles in the MSF stages, distillation per stage, expansion line ofthe steam turbine.

• The exergy costs of the main components of the power plant and water are shownin a window, if the fuel cost is introduced (in dollars per unit of energy) theexergoeconomic costs are also included.

All these results can be saved in a text file than can be accessed by conventionalapplications (MS Office). The file also includes the input values and some interestingdesign values introduced in the simulator (tube characteristics and fouling factor in

Simulator


distillers in the MSF plant, for example), and the exergy cost of the products of eachcomponent, following the productive structure that will be explained in Chapter 7.

5.2 Model validation

The simulator should predict the most important values of the main flowstreams ofthe power and desalination plant with an accuracy that allows reproducing theoperating conditions of the plant without using a data flowsheet for each situation.The accuracy of the simulator is tested with the data flowsheets provided by the plantmanagers, also called model validation of the simulator. Furthermore, when the dataacquisition system of a plant is not enough to provide the data necessary for thediagnosis of the plant, a good simulator could substitute the acquisition system.

The model validation is separately applied to the power and desalination plant, notethat the way to calculate the thermodynamic properties in the design flowsheets isunknown, therefore an indeterminate error is structurally included in the comparativeanalysis (or model validation).

Only a few values calculated in the simulator are also available in the data acquisitionsystem of the power plant (this does not means that there are more signals than thesystem can measure, but that the recording system is limited by the plant managers):temperature and pressure of some turbine extractions, live steam conditions andfeedwater temperature in some heaters. Furthermore, the live steam properties are notmaintained under operating conditions, and the data collected is every four hours.Consequently, no adjustment has been made to the simulator in order to achieve amore realistic set of values of the main flowstreams of the power plant.

The data acquisition system of the MSF plant only provides a few data of the maincontrolling variables of the process every four hours (temperatures and flow ratesentering and leaving the heater, recovery and reject section, and the internalparameters mentioned above). Therefore no comparison is included between the realdata and the results obtained when the simulator operates with the ‘

Sim. with realdata

’ option, that is, using the correlated internal parameters based on realexperience.

5.2.1 Power plant

Most of the performance data cases are simulated and compared with the dataprovided by the plant contractors (ABB, 1996b). The first table of each comparativestudy shows (in different rows) the inputs of the simulation (output power W, steam toMSF unit Md, condenser pressure Pc and Live steam extraction LS); note that theoutput power is not exactly the same as that proposed by the contractors. This is

Model validation


105

because the input power value inserted in the simulator window is only a first step tocalculate the main steam flow to the boiler. Therefore, the output results try to find outthe minimum difference in both live steam mass flow and the final output power foreach performance case. The feed pump consumption is also included in this table(W FP). The third row shows the relative error observed in the input process.

The second table shows in its first part the pressure p, temperature T and mass flowrate m of the main flowstreams of the power plant. The second part includes thevalues ( , and ) obtained by the simulator. Finally, the third part introducesthe relative error of each property of the flowstreams (

ε

p,

ε

T,

ε

m). Each flow isnumbered according to the scheme followed in figure 5.2. The meaning of eachperformance data case is described in section 4.6. Only the values that are providedby the contractors have been compared in the table.

Analyzing the model results, when the steam to LP turbine is not close to zero, that is,in performance data cases which represent partial or full load in extraction or twinextraction mode (MCR, MR, VWO, COC, PL115, PL85 performance data cases), thehighest relative error is detected in the LP extraction (< 3% in any case), but theabsolute difference between the simulator and data flowsheet is minimum.

However, when the NTW mathematical model is applied, i.e. a minimum amount ofsteam passes through the LP turbine (this situation correspond to MSL3 and MSL4cases, the last one is the most usual in winter operation in the Gulf Area, when thewater demand is always high but the energy consumption decrease to the 30% of theplant capacity), the relative error could reach to a 10% in the LP extraction and thesteam derived to the condenser, although in those limit cases the absolute differencedetected is very low. It is clear that the mathematical model applied when the steamto LP turbine is close to zero (NTW model) is more unstable than othermathematical models applied when some amount of steam passes through the LPturbine (LTW model).

p ′ T ′ m ′

Simulator


5.2.1.1 MCR case

TABLE 5.1

Input variables for the MCR (maximum continous rating, producing both electricity and water)case.

W (MW) W FP (kW) Md (kg/s) Pc (bar) LS (Gcal/h)

Design 122 2308 89.68 0.072 0

Simulation 122.75 2262.4 89.68 0.072 0

Rel. error (%) 0.611 –2.016 0.000 0.000 0.000

TABLE 5.2

Model validation for the MCR case.

No. p (bar) T (ºC) m (kg/s) p

'

(bar) T

'

(ºC) m

'

(kg/s)

ε

p (%)

ε

T (%)

ε

m (%)

1 93 535 156.187 93 535 156.09 0.00 0.00 0.06

3 28.46 365.4 10.839 28.39 363.5 10.8 0.25 0.52 0.36

4 14.79 282.1 8.303 14.73 278.1 8.24 0.41 1.42 0.76

5 7.235 203.2 10.989 7.213 198.6 10.94 0.30 2.26 0.45

6 2.76 130.7 3.321 2.76 130.7 3.32 0.00 0.00 0.03

8 0.482 80.4 2.278 0.482 80.4 2.21 0.00 0.00 2.99

9 0.072 39.5 29.631 0.072 39.5 29.75 0.00 0.00 –0.40

11 39.6 36.545 39.8 36.59 –0.51 –0.12

12 41 36.545 41.2 36.59 –0.49 –0.12

24 5.599 5.53 1.23

14 78.2 36.545 78.2 36.59 0.00 –0.12

23 84.2 3.321 84.4 3.32 –0.24 0.03

15 128.2 36.545 128.3 36.59 –0.08 –0.12

16 162.9 156.355 162.8 156.25 0.06 0.07

18 164.8 156.187 164.7 156.09 0.06 0.06

22 168.8 19.142 168.7 19.04 0.06 0.53

19 194.6 156.187 194.4 156.09 0.10 0.06

21 198.6 10.839 198.4 10.8 0.10 0.36

20 230.1 156.187 230 156.09 0.04 0.06

30 27.18 10.839 27.106 10.8 0.27 0.36

31 14.12 8.303 14.08 8.24 0.28 0.76

32 6.655 10.989 6.634 10.94 0.32 0.45

33 2.677 3.321 2.677 3.32 0.00 0.03

34 0.467 2.278 0.467 2.21 0.00 2.99

Model validation


107

5.2.1.2 MR case

TABLE 5.3

Input variables for the MR (maximum rating, producing only electricity) performance case.


Design 146.693 2,274 0 0,135 0

Simulation 146.73 2,331.4 0 0.135 0

Rel. error (%) –0.025 –2.524 0.000 0.000 0.000

TABLE 5.4

Model validation for the MR case.


'

(bar) T

'

(ºC) m

'

(kg/s)

ε

p (%)

ε

T (%)

ε

m (%)

1 93 535 156.187 93 535 156.2 0.00 0.00 –0.01

3 30.58 374.5 9.254 30.52 374 9.22 0.20 0.13 0.37

4 17.7 302.8 5.492 17.61 298.6 5.49 0.51 1.39 0.04

5 11.23 248.9 6.012 11.17 243.3 5.92 0.53 2.25 1.53

6 8.232 218.8 13.291 8.232 213.6 13.35 0.00 2.38 –0.44

8 1.913 118.8 11.778 1.916 118.9 11.65 –0.16 –0.08 1.09

9 0.135 51.9 110.043 0.135 51.8 110.26 0.00 0.19 –0.20

11 52 135.429 52 135.58 0.00 –0.11

12 53.6 135.429 53.5 135.58 0.19 –0.11

24 25.069 25 0.28

14 108 135.429 107.6 135.58 0.37 –0.11

23 118 13.291 117.8 13.35 0.17 –0.44

15 162.4 135.429 162.3 135.58 0.06 –0.11

16 184.5 156.187 184.2 156.2 0.16 –0.01

18 186.6 156.187 186.3 156.2 0.16 –0.01

22 190.6 14.476 190.2 14.7 0.21 –1.55

19 205.3 156.187 205.1 156.2 0.10 -0.01

21 209.3 9.254 209 9.22 0.14 0.37

20 235 156.187 234.8 156.2 0.09 -0.01

30 29.71 9.254 29.62 9.22 0.30 0.37

31 17.45 5.492 17.349 5.49 0.58 0.04

32 11.11 6.012 11.038 5.92 0.65 1.53

33 7.676 13.291 7.674 13.35 0.03 -0.44

34 1.799 11.778 1.78 11.65 1.06 1.09

Simulator


5.2.1.3 PL115 case

TABLE 5.5

Input variables for the PL115 performance case (partial load with 115 MW of electricity and aheat extraction to MSF of 145 Gcal/h).


Design 122 2162 75.96 0.065 0

Simulation 122.12 2063.1 75.96 0.065 0

Rel. Error (%) –0.098 4.574 0.000 0.000 0.000

TABLE 5.6

Model validation for the PL115 performance data case.


'

(bar) T

'

(ºC) m

'

(kg/s)

ε

p (%)

ε

T (%)

ε

m (%)

1

93 535 148.923 93 535 148.11 0.00 0.00 0.55

3

26.99 360.5 10.252 26.791 358.4 10.17 0.74 0.58 0.80

4

13.97 277.4 8.03 13.848 273.2 8.07 0.87 1.51 –0.50

5

6.749 198 10.897 6.705 193.3 10.59 0.65 2.37 2.82

6

2.39 126 3.317 2.39 126 3.29 0.00 0.00 0.81

8

0.588 85.4 3.237 0.587 85.4 3.13 0.17 0.00 3.31

9

0.065 37.5 36.083 0.065 37.7 35.75 0.00 –0.53 0.92

11

37.6 43.949 37.7 43.48 –0.27 1.07

12

38.8 43.949 37.7 43.48 2.84 1.07

24

6.553 6.51 0.66

14

82.2 43.949 82.2 43.48 0.00 1.07

23

88.7 3.317 88.9 3.29 –0.23 0.81

15

123.2 43.949 123.4 43.48 –0.16 1.07

16

159.7 149.087 158.9 148.27 0.50 0.55

18

161.6 148.923 160.6 148.11 0.62 0.55

22

165.5 18.282 164.5 18.24 0.60 0.23

19

191.9 148.923 191.4 148.11 0.26 0.55

21

195.8 10.252 195.3 10.17 0.26 0.80

20

227.3 148.923 226.9 148.11 0.18 0.55

30

25.79 10.252 25.598 10.17 0.74 0.80

31

13.32 8.03 13.188 8.07 0.99 –0.50

32

6.141 10.897 6.135 10.59 0.10 2.82

33

2.295 3.317 2.299 3.29 –0.17 0.81

34

0.563 3.237 0.562 3.13 0.18 3.31

Model validation


109

5.2.1.4 PL85 case

TABLE 5.7

Input variables for the PL85 performance case (partial load with 85 MW of electricity and 145Gcal/h of extraction heat flow).


Design 91 1,649 75.62 0.055 0

Simulation 91.24 1,540.4 75.62 0.05 0

Rel. error (%) –0.264 6.586 0.000 0.000 0.000

TABLE 5.8

Model validation for the PL85 performance case.


'

(bar) T

'

(ºC) m' (kg/s) εp (%) εT (%) εm (%)

1 93 535 117.391 93 535 117.03 0.00 0.00 0.31

3 21.15 340.7 7.331 21.064 340.4 7.29 0.41 0.09 0.56

4 11.1 261.7 5.719 11.036 259.2 5 .83 0.58 0.96 –1.94

5 5.56 187.7 7.875 5.538 184.6 7.68 0.40 1.65 2.48

6 2.39 126 2.21 2.39 126 2.18 0.00 0.00 1.36

8 0.261 66 0.993 0.262 66.1 0.95 –0.38 –0.15 4.33

9 0.055 34.6 16.478 0.055 34.6 16.63 0.00 0.00 –0.92

11 34.6 20.993 34.7 20.76 –0.29 1.11

12 37 20.993 37.1 20.76 –0.27 1.11

24 3.203 3.12 2.59

14 65 20.993 65 20.76 0.00 1.11

23 69.7 2.21 70.1 2.18 -0.57 1.36

15 124.4 20.993 124.5 20.76 -0.08 1.11

16 153.2 117.539 152.5 117.18 0.46 0.31

18 155 117.391 154.1 117.03 0.58 0.31

22 158.5 13.051 157.6 13.12 0.57 -0.53

19 182.4 117.391 182.3 117.03 0.05 0.31

21 185.9 7.331 185.8 7.29 0.05 0.56

20 215 117.391 215 117.03 0.00 0.31

30 20.39 7.331 20.31 7.29 0.39 0.56

31 10.7 5.719 10.62 5.83 0.75 –1.94

32 5.186 7.875 5.185 7.68 0.02 2.48

33 2.348 2.21 2.347 2.18 0.04 1.36

34 0.257 0.993 0.258 0.95 –0.39 4.33

Simulator


5.2.1.5 MSL2 case

TABLE 5.9 MSL2 performance case (minimum stable load with 45 MW of electricity and a combined heatextraction flow of 145 Gcal/h). Main input data.


Design 51 1,305 60.4 0.048 26.34

Simulation 51.57 1,250.7 60.4 0.048 26.34

Rel. error (%) –1.118 4.161 0.000 0.000 0.000

TABLE 5.10 Model validation for the MSL2 performance case.

No. p (bar) T (ºC) m (kg/s) p' (bar) T' (ºC) m' (kg/s) εp (%) εT (%) εm (%)

1 93 535 86.5 93 535 86.49 0.00 0.00 0.01

3 13.75 324.9 4.477 13.714 322.9 4.49 0.26 0.62 –0.29

4 7.442 251.2 3.355 7.411 247.4 3.38 0.42 1.51 –0.75

5 4.074 186.8 4.971 4.061 182.6 4.89 0.32 2.25 1.63

6 2.39 137.9 0.454 2.39 135.8 0.46 0.00 1.52 –1.32

8 0.054 34.4 0 0.055 34.7 0 –1.85 –0.87 0.00

9 0.048 80 1.751 0.048 80 1.75 0.00 0.00 0.06

11 32.4 3.466 32.2 3.55 0.62 –2.42

12 46.9 3.466 47.4 3.52 –1.07 –1.56

24 0.454 0.46 –1.32

14 47.3 3.466 47.7 3.52 –0.85 –1.56

23 49.6 0.454 50.2 0.46 –1.21 –1.32

15 125.7 3.466 125.7 3.52 0.00 –1.56

16 142.4 90.218 142 90.19 0.28 0.03

18 144.3 86.5 143.7 86.49 0.42 0.01

22 147.4 7.832 146.7 7.87 0.47 –0.49

19 166.4 86.5 166.1 86.49 0.18 0.01

21 169.5 4.477 169.2 4.49 0.18 –0.29

20 194.5 86.5 194.4 86.49 0.05 0.01

30 13.32 4.477 13.288 4.49 0.24 –0.29

31 7.235 3.355 7.206 3.38 0.40 –0.75

32 3.871 4.971 3.864 4.89 0.18 1.63

33 2.388 0.454 2.387 0.46 0.04 –1.32

34 0.108 0 0.055a

a. Note that the simulator does not suppose a pressure loss in the 5th extraction if any vapor is extracted.

0 49.07 0.00

Model validation


5.2.1.6 MSL3 case

TABLE 5.11 Input data of the MSL3 performance case (minimum stable load with two extractions of 150 and145 Gcal/h to MSF units).


Design 72.44 2,975 75.13 0.048 150

Simulation 73.6 3,122.2 75.2 0.048 150

Rel. error (%) –1.601 –4.948 –0.093 0.000 0.000

TABLE 5.12 Model validation for the MSL3 performance case.


1 93 535 163 93 535 163.1 0.00 0.00 –0.06

3 18.22 333 9.851 18.176 329.8 9.94 0.24 0.96 –0.90

4 9.344 252.4 7.883 9.314 247.4 7.69 0.32 1.98 2.45

5 4.891 179.6 10.272 4.687 174.6 10.02 4.17 2.78 2.45

6 2.39 126 0.461 2.39 126 0.5 0.00 0.00 –8.46

8 0.054 34.3 0 0.055 34.7 0 –1.85 –1.17 0.00

9 0.048 80 1.727 0.048 80 1.91 0.00 0.00 –10.60

11 32.4 3.462 32.2 3.75 0.62 –8.32

12 47 3.462 46.4 3.72 1.28 –7.45

24 0.461 0.5 –8.46

14 47.3 3.462 46.7 3.72 1.27 –7.45

23 49.6 0.461 49.3 0.5 0.60 –8.46

15 125.7 3.462 125.7 3.72 0.00 –7.45

16 142.8 183.567 142 183.61 0.56 –0.02

18 144.6 163 144.2 163.1 0.28 –0.06

22 148.7 17.514 148.4 17.63 0.20 –0.66

19 171.6 163 171.3 163.1 0.17 –0.06

21 175.6 9.851 175.5 9.94 0.06 –0.90

20 204 163 204.1 163.1 –0.05 –0.06

30 16.6 9.851 16.62 9.94 –0.12 –0.90

31 8.465 7.663 8.505 7.69 –0.47 –0.35

32 3.907 10.272 4.026 10.02 –3.05 2.45

33 2.388 0.461 2.387 0.5 0.04 –8.46

34 0.108 0 0.055a

a. The same argumentation of the MSL2 case.

0 49.07 0.00

Simulator


5.2.1.7 MSL4 case

TABLE 5.13 Input data of the MSL4 performance case (minimum stable load with the maximum heat flowextraction to MSF unit: 170 Gcal/h).


Design 75.52 1,543 88.63 0.021 0

Simulation 76.36 1,501.5 88.63 0.021 0

Rel. error (%) –1.112 2.690 0.000 0.000 0.000

TABLE 5.14 MSL4 performance case. Model validation.


1 93 535 109.5 93 535 109.64 0.00 0.00 –0.13

3 19.87 340.3 6.537 19.821 338.1 6.55 0.25 0.65 –0.20

4 10.58 262.9 4.956 10.534 258.9 5.04 0.43 1.52 –1.69

5 5.514 192.5 6.789 5.495 188.1 6.68 0.34 2.29 1.61

6 2.76 130.7 0.424 2.76 131.1 0.45 0.00 –0.31 –6.13

8 0.025 20.9 0 0.024 20.5 0 4.00 1.91 0.00

9 0.021 80 1.004 0.021 79.8 1.14 0.00 0.25 –13.55

11 18.3 2.743 18.3 2.92 0.00 –6.45

12 36.7 2.743 36.6 2.92 0.27 –6.45

24 0.424 0.45 –6.13

14 37.1 2.736 36.9 2.9 0.54 –5.99

23 39.2 0.424 39.1 0.45 0.26 –6.13

15 130.5 2.736 130.5 2.9 0.00 –5.99

16 153.6 109.649 153 109.79 0.39 –0.13

18 155.3 109.5 154.7 109.64 0.39 –0.13

22 158.8 11.493 158.2 11.58 0.38 –0.76

19 180.8 109.5 180.7 109.64 0.06 –0.13

21 184.2 6.537 184.1 6.55 0.05 –0.20

20 212.2 109.5 212.2 109.6 0.00 –0.09

30 19.23 6.537 19.176 6.55 0.28 –0.20

31 10.26 4.956 10.207 5.04 0.52 –1.69

32 5.233 6.789 5.22 6.68 0.25 1.61

33 2.759 0.424 2.758 0.45 0.04 –6.13

34 0.063 0 0.024a

a. No pressure losses are associated to the final extraction

0 61.90 0.00

Model validation


5.2.1.8 ODOB case

TABLE 5.15 Main input data of the ODOB case (one desalination-one boiler).


Design 0 ? 88.45 0 170

Simulation 0 1,222.6 88.45 0 170

Rel. error (%) 0.000 ? 0.000 0.000 0.000

TABLE 5.16 Model validation of the ODOB case.


1 93 535 70.383 93 535 70.38 0.00 0.00 0.00

3 0 0 0 0 0 0

4 0 0 0 0 0 0

5 0 0 0 0 0 0

6 0 0 0 0 0 0

8 0 0 0 0 0 0

9 0 0 0 0 0 0

11 0 0 0 0

12 0 0 0 0

24 0 0

14 0 0 0 0

23 0 0 0 0

15 0 0 0 0

16 138.9 93.841 138.9 94.94 0.00 –1.17

18 140.7 70.383 140.5 70.38 0.14 0.00

22 0 0 0 0

19 140.7 70.383 140.5 70.38 0.14 0.00

21 0 0 0 0

20 140.7 70.383 140.5 70.38 0.14 0.00

30 0 0 0 0

31 0 0 0 0

32 0 0 0 0

33 0 0 0 0

34 0 0 0 0

Simulator


5.2.1.9 TDOB case

TABLE 5.17 Main input data of the TDOB case (two desalination-one boiler).


Design 0 ? 140.766 0 340

Simulation 0 764.8 140.76 0 340

Rel. error (%) 0.000 ? 0.004 0.000 0.000

TABLE 5.18 Model validation data for the TDOB case.


1 93 535 140.766 93 535 140.76 0.00 0.00 0.00

3 0 0 0 0 0 0

4 0 0 0 0 0 0

5 0 0 0 0 0 0

6 0 0 0 0 0 0

8 0 0 0 0 0 0

9 0 0 0 0 0 0

11 0 0 0 0

12 0 0 0 0

24 0 0

14 0 0 0 0

23 0 0 0 0

15 0 0 0 0

16 138.9 187.682 138.9 187.38 0.00 0.16

18 140.8 140.766 139.7 140.76 0.78 0.00

22 0 0 0 0

19 140.8 140.766 139.7 140.76 0.78 0.00

21 0 0 0 0

20 140.8 140.766 139.7 140.76 0.78 0.00

30 0 0 0 0

31 0 0 0 0

32 0 0 0 0

33 0 0 0 0

34 0 0 0 0

Model validation


5.2.1.10 VWO case

TABLE 5.19 Main input data of the VWO performance case (maximum capacity of the steam turbine with andextraction heat flow of 170 Gcal/h to MSF).


Design 126.587 2,412 89.69 0.074 0

Simulation 126.78 2,425.9 89.68 0.074 0

Rel. error (%) –0.152 –0.576 0.011 0.000 0.000

TABLE 5.20 Model validation data for the VWO case.


1 93 535 161.038 93 535 160.21 0.00 0.00 0.51

3 29.36 368.1 11.317 29.158 365.4 11.17 0.69 0.73 1.30

4 15.23 284.3 8.665 15.11 279.6 8.59 0.79 1.65 0.87

5 7.419 204.7 11.473 7.368 199.5 11.33 0.69 2.54 1.25

6 2.759 130.7 3.485 2.76 130.7 3.44 –0.04 0.00 1.29

8 0.533 82.9 2.623 0.528 82.7 2.4 0.94 0.24 8.50

9 0.074 40 32.64 0.074 40.1 32.44 0.00 –0.25 0.61

11 40.1 40.064 40.1 39.63 0.00 1.08

12 41.3 40.064 42.2 39.6 –2.18 1.16

24 6.109 5.85 4.24

14 80.4 40.064 80.3 39.6 0.12 1.16

23 86.6 3.485 86.8 3.44 –0.23 1.29

15 128 40.064 128.1 39.6 –0.08 1.16

16 163.8 161.209 163.5 160.38 0.18 0.51

18 165.7 161.038 165.5 160.21 0.12 0.51

22 169.7 19.982 169.5 19.76 0.12 1.11

19 195.8 161.038 195.6 160.21 0.10 0.51

21 199.9 11.317 199.6 11.17 0.15 1.30

20 231.8 161.038 231.4 160.21 0.17 0.51

30 28.01 11.317 27.817 11.17 0.69 1.30

31 14.53 8.665 14.41 8.59 0.83 0.87

32 6.8 11.473 6.758 11.33 0.62 1.25

33 2.667 3.485 2.671 3.44 –0.15 1.29

34 0.515 2.623 0.512 2.4 0.58 8.50

Simulator


5.2.1.11 COC case

TABLE 5.21 Input data of the COC performance case (boiler peak load at least 5% more than the MCR case).


Design 124.41 3,103 89.72 0.072 50.8

Simulation 124.65 3,350 89.72 0.072 50.8

Rel. error (%) –0.193 –7.960 0.000 0.000 0.000

TABLE 5.22 Model validation data for the COC case.


1 93 535 180.556 93 535 179.58 0.00 0.00 0.54

3 29.02 366.9 12.704 28.77 363.7 12.6 0.86 0.87 0.82

4 14.93 282.3 9.723 14.786 277 9.7 0.96 1.88 0.24

5 7.219 202.2 12.96 7.17 196.8 12.55 0.68 2.67 3.16

6 2.76 130.7 3.314 2.76 130.7 3.29 0.00 0.00 0.72

8 0.479 80.3 2.258 0.471 79.9 2.17 1.67 0.50 3.90

9 0.072 39.5 29.449 0.072 39.5 29.14 0.00 0.00 1.05

11 39.6 36.335 39.6 35.92 0.00 1.14

12 41 36.335 40.7 35.92 0.73 1.14

24 5.572 5.46 2.01

14 78.1 36.335 77.7 35.92 0.51 1.14

23 84 3.314 83.9 3.29 0.12 0.72

15 128.2 36.335 128.3 35.92 –0.08 1.14

16 161.4 187.942 160.3 186.94 0.68 0.53

18 163.5 180.556 162.8 179.58 0.43 0.54

22 167.7 22.427 167 22.3 0.42 0.57

19 193.8 180.556 193.3 179.58 0.26 0.54

21 198 12.704 197.5 12.6 0.25 0.82

20 230 180.556 229.6 179.58 0.17 0.54

30 27.28 12.704 27.06 12.6 0.81 0.82

31 14.02 9.723 13.888 9.7 0.94 0.24

32 6.398 12.96 6.415 12.55 –0.27 3.16

33 2.677 3.314 2.678 3.29 –0.04 0.72

34 0.464 2.258 0.457 2.17 1.51 3.90

Model validation


5.2.2 MSF Plant

Distiller design data in the most characteristic operating conditions have beenprovided by the plant manufacturers (Italimpianti, 1997). Only a few cases containthe temperature profile of the three flows inside each stage of the distiller. Theycorrespond to the guarantied conditions of the contractors:

• Nominal production in summer (normal-temperature operation in summer,NTOS): 1,900 T/h of freshwater produced (or a TBT of 100 ºC) and a seawatertemperature of 32 ºC.

• Maximum production in summer (high-temperature operation in summer,HTOS): distillation of 2,258 T/h (112 ºC TBT) with a seawater entering at 32 ºC.

• Minimum production in summer (low-temperature operation in summer, LTOS):distillation of 1,232 T/h (84 ºC TBT), seawater enters at 32 ºC.

• Maximum production in winter (high-temperature operation in winter, HTOW):distillation of 2,400 T/h (112 ºC TBT) with a seawater entering at 18 ºC. Seawaterto reject section enters at 25 ºC by using the temper system by the way ofdeviating a quantity of cooling seawater rejected to the sea.

The first table of each comparative study shows some inputs of design data andsimulation in the first and second rows respectively (seawater intake flow SW andtemperature Tsea). Some other inputs (steam to heater conditions, seawater intaketemperature) needed for the simulator are not included because they must be the samequantity as the proposed design value. The distillate produced in the two cases ismaintained in the same quantity too. Other operating parameters that are obtained inthe simulation are also compared in the table: seawater to reject and recycle brineflows (SR and R), Top Brine Temperature (TBT), Performance Ratio (PR) and steamconsumption (mST). The third row shows the relative error observed in the table, thehighest error is in the steam consumed. This error can be due to the absence of adesuperheater before the brine heater in the mathematical model applied to the MSFdistillers, and the error introduced when the steam properties (the latent heat ofvaporization) below two different perspectives are calculated.

The second table shows in its first part the chamber pressure p, temperature profile(cooling brine TF, distillate TD and flashing brine TB) and distillate flow rate (D) ofeach stage of the MSF plant. The second part includes the values ( , , , and ) obtained by the simulator. Finally, the third part introduces the relative errorof the stage values (εp, εTF, εTD, εTB, εD). Each stage is numbered according to thescheme followed in figure 5.1.

p ′ TF ′ TD ′ TB ′D ′

Simulator


In Gulf Area the water demand in summer is the 100% of the plant capacity, andcovers the 80% in winter. So, the most realistic performance data cases are (in thisorder) HTOS and HTOW. The error analysis is going to be underlined in these twocases.

The main error source in HTOS case is detected in the pressure of the reject stagesand the last stage of the recovery section (a maximum of 9% of relative error). Thecontractors for absolute pressure of the MSF chambers give an accuracy of twodecimals, therefore the error associated to the numeric presentation could beimportant. The correlation to calculate the absolute pressure of a flash chamber alsoshould improve the error detected in those values.

The distillate produced in the first stages of the recovery section has a maximumrelative error of 5%. This error is due to the correlations for calculating both brine andsteam properties and the global heat transfer coefficient of each condenser. Thetemperatures of the three main flows of each distiller do not exceed in any case arelative error of 1.5%.

Model validation


5.2.2.1 NTOS case

TABLE 5.23 Input data and performance parameters of the NTOS case (normal-temperature operation insummer).

SW (T/h) SR (T/h) R (T/h) TBT (ºC) mST (T/h) PR Tsea (ºC)

Design 19,900 17,700 19,650 100 239.6 8 32

Simulator 19,965 17,396.8 19,584.5 100.4 247.9 7.85 32

Rel. Error (%) –0.33 1.71 0.33 –0.40 –3.46 1.88 0.00

TABLE 5.24 Model validation of the NTOS performance case.

Stage p(bar)

TF(ºC)

TD(ºC)

TB(ºC)

D(T/h)

p’(bar)

TF’(ºC)

TD’(ºC)

TB’(ºC)

D’(T/h)

εP(%)

εTF(%)

εTD(%)

εTB(%)

εD(%)

1 0.87 93.1 95.7 96.7 109 0.883 93.3 96.2 97.1 114.2 –1.49 –0.21 –0.52 –0.41 –4.77

2 0.77 90 92.5 93.5 219 0.781 89.9 92.9 93.8 226.3 –1.43 0.11 –0.43 –0.32 –3.33

3 0.68 86.7 89.3 90.2 328 0.688 86.6 89.5 90.4 338.9 –1.18 0.12 –0.22 –0.22 –3.32

4 0.59 83.5 86 86.9 437 0.605 83.3 86.2 87.1 449.4 –2.54 0.24 –0.23 –0.23 –2.84

5 0.52 80.1 82.7 83.6 545 0.531 80 82.8 83.7 557.9 –2.12 0.12 –0.12 –0.12 –2.37

6 0.46 76.8 79.4 80.3 652 0.465 76.7 79.5 80.5 664.3 –1.09 0.13 –0.13 –0.25 –1.89

7 0.4 73.5 76.1 77 757 0.407 73.4 76.3 77.2 768.7 –1.75 0.14 –0.26 –0.26 –1.55

8 0.35 70.2 72.8 73.8 861 0.355 70.2 73 74 871 –1.43 0.00 –0.27 –0.27 –1.16

9 0.3 67 69.5 70.5 963 0.309 67 69.8 70.8 971.4 –3.00 0.00 –0.43 –0.43 –0.87

10 0.26 63.7 66.3 67.3 1064 0.269 63.8 66.6 67.6 1069.7 –3.46 –0.16 –0.45 –0.45 –0.54

11 0.22 60.4 63 64 1160 0.234 60.6 63.5 64.5 1165.9 –6.36 –0.33 –0.79 –0.78 –0.51

12 0.19 57.3 59.9 60.9 1255 0.203 57.5 60.4 61.4 1260.4 –6.84 –0.35 –0.83 –0.82 –0.43

13 0.17 54.2 56.8 57.8 1347 0.175 54.4 57.3 58.3 1352.6 –2.94 –0.37 –0.88 –0.87 –0.42

14 0.14 51.1 53.7 54.8 1437 0.152 51.4 54.2 55.3 1442.6 –8.57 –0.59 –0.93 –0.91 –0.39

15 0.12 48 50.7 51.8 1527 0.131 48.4 51.2 52.3 1530.3 –9.17 –0.83 –0.99 –0.97 –0.22

16 0.105 45 47.7 48.8 1614 0.113 45.4 48.3 49.4 1615.4 –7.62 –0.89 –1.26 –1.23 –0.09

17 0.09 42.1 44.7 45.9 1698 0.097 42.5 45.4 46.6 1698 –7.78 –0.95 –1.57 –1.53 0.00

18 0.08 39.5 42.5 43.7 1761 0.086 39.6 43 44.4 1763.5 –7.50 –0.25 –1.18 –1.60 –0.14

19 0.07 37.1 40.2 41.5 1826 0.076 37.1 40.6 42.1 1829.7 –8.57 0.00 –1.00 –1.45 –0.20

20 0.06 34.7 37.9 39.2 1896 0.067 34.6 38.2 39.7 1896.2 –11.67 0.29 –0.79 –1.28 –0.01

Simulator


5.2.2.2 HTOS case

TABLE 5.25 Input data and performance parameters of the HTOS case (high-temperature operation insummer).


Design 19,900 17,700 19,850 112 294.1 8 32

Simulator 19,975 17,509.1 19,850 112.3 301.3 7.86 32

Rel. Error (%) –0.38 1.08 0.00 –0.27 –2.45 1.75 0.00

TABLE 5.26 Model validation of the HTOS performance case.

Stage p(bar)

TF(ºC)

TD(ºC)

TB(ºC)

D(T/h)

p’(bar)

TF’(ºC)

TD’(ºC)

TB’(ºC)

D’(T/h)

εP(%)

εTF(%)

εTD(%)

εTB(%)

εD(%)

1 1.3 103.8 107.2 108.2 131 1.311 103.9 107.4 108.4 138.5 –0.85 –0.10 –0.19 –0.18 –5.73

2 1.14 100.2 103.5 104.5 261 1.147 100 103.5 104.5 274.1 –0.61 0.20 0.00 0.00 –5.02

3 1 96.4 99.7 100.7 390 0.997 96.2 99.5 100.5 409.9 0.30 0.21 0.20 0.20 –5.10

4 0.87 92.7 95.9 96.9 521 0.865 92.2 95.6 96.6 542.8 0.57 0.54 0.31 0.31 –4.18

5 0.75 88.8 92 93 649 0.748 88.3 91.7 92.7 672.9 0.27 0.56 0.33 0.32 –3.68

6 0.65 85 88.2 89.2 776 0.646 84.5 87.9 88.8 800.3 0.62 0.59 0.34 0.45 –3.13

7 0.56 81.1 84.4 85.3 902 0.556 80.6 84 85 924.9 0.71 0.62 0.47 0.35 –2.54

8 0.48 77.2 80.5 81.5 1025 0.478 76.8 80.2 81.2 1047 0.42 0.52 0.37 0.37 –2.15

9 0.41 73.4 76.7 77.7 1146 0.41 73 76.4 77.4 1166.3 0.00 0.54 0.39 0.39 –1.77

10 0.35 69.6 72.9 73.9 1266 0.35 69.3 72.7 73.7 1283.3 0.00 0.43 0.27 0.27 –1.37

11 0.3 65.8 69 70 1381 0.299 65.6 69 70 1397.6 0.33 0.30 0.00 0.00 –1.20

12 0.25 62 65.4 66.4 1493 0.254 61.9 65.3 66.3 1509.7 –1.60 0.16 0.15 0.15 –1.12

13 0.21 58.4 61.7 62.7 1603 0.215 58.3 61.7 62.7 1619.1 –2.38 0.17 0.00 0.00 –1.00

14 0.18 54.7 58.1 59.1 1711 0.182 54.7 58.1 59.2 1725.8 –1.11 0.00 0.00 –0.17 –0.86

15 0.15 51.1 54.5 55.5 1817 0.154 51.1 54.6 55.7 1829.7 –2.67 0.00 –0.18 –0.36 –0.70

16 0.12 47.5 50.9 52 1920 0.13 47.6 51.1 52.2 1930.7 –8.33 –0.21 –0.39 –0.38 –0.56

17 0.1 44 47.4 48.5 2021 0.109 44.2 47.6 48.9 2028.6 –9.00 –0.45 –0.42 –0.82 –0.38

18 0.09 40.5 44.6 45.9 2096 0.095 40.9 44.9 46.2 2104.2 –5.56 –0.99 –0.67 –0.65 –0.39

19 0.08 38.1 41.9 43.2 2173 0.083 38 42.2 43.6 2180.7 –3.75 0.26 –0.72 –0.93 –0.35

20 0.07 35.1 39.2 40.5 2258 0.071 35 39.3 40.8 2257.9 –1.43 0.28 –0.26 –0.74 0.00

Model validation


5.2.2.3 LTOS case

TABLE 5.27 Some input data and performance parameters of the LTOS case (low-temperature operation insummer).


Design 17,000 14,800 16,450 84 148.1 8.1 32

Simulator 17,000 14,900.2 16,476.9 84.6 150.5 8.14 32

Rel. Error (%) –0.00 –0.68 –0.16 –0.71 –1.62 –0.49 0.00

TABLE 5.28 Model validation. LTOS performance case in MSF distillers.

Stage p(bar)

TF(ºC)

TD(ºC)

TB(ºC)

D(T/h)

p’(bar)

TF’(ºC)

TD’(ºC)

TB’(ºC)

D’(T/h)

εP(%)

εTF(%)

εTD(%)

εTB(%)

εD(%)

1 0.475 78.7 80.48 81.4 72 0.495 79.2 81.1 81.9 73.9 –4.21 –0.64 –0.77 –0.61 –2.64

2 0.428 76.2 77.97 78.9 143 0.445 76.6 78.5 79.3 146.6 –3.97 –0.52 –0.68 –0.51 –2.52

3 0.385 73.6 75.37 76.3 215 0.399 74 75.8 76.7 219.7 –3.64 –0.54 –0.57 –0.52 –2.19

4 0.345 71 72.79 73.7 286 0.357 71.3 73.2 74.1 291.5 –3.48 –0.42 –0.56 –0.54 –1.92

5 0.309 68.4 70.21 71.1 356 0.32 68.7 70.6 71.5 362.2 –3.56 –0.44 –0.56 –0.56 –1.74

6 0.277 65.9 67.65 68 426 0.286 66.2 68 68.9 431.6 –3.25 –0.46 –0.52 –1.32 –1.31

7 0.247 63.3 65.08 66 494 0.255 63.6 65.4 66.3 499.7 –3.24 –0.47 –0.49 –0.45 –1.15

8 0.22 60.7 62.53 63.5 562 0.228 61.1 62.9 63.8 566.6 –3.64 –0.66 –0.59 –0.47 –0.82

9 0.196 58.2 60.01 61 629 0.203 58.6 60.4 61.3 632.1 –3.57 –0.69 –0.65 –0.49 –0.49

10 0.175 55.7 57.49 58.4 695 0.181 56.1 57.9 58.9 696.3 –3.43 –0.72 –0.71 –0.86 –0.19

11 0.154 53.2 54.9 55.8 756 0.161 53.6 55.5 56.4 759.2 –4.55 –0.75 –1.09 –1.08 –0.42

12 0.138 50.8 52.56 53.3 816 0.143 51.2 53.1 54.1 820.7 –3.62 –0.79 –1.03 –1.50 –0.58

13 0.123 48.5 50.23 51.2 876 0.127 48.9 50.7 51.7 880.8 –3.25 –0.82 –0.94 –0.98 –0.55

14 0.109 46.1 47.91 48.9 934 0.113 46.5 48.3 49.4 939.7 –3.67 –0.87 –0.81 –1.02 –0.61

15 0.098 43.9 45.64 46.6 992 0.101 44.2 46 47.2 996.1 –3.06 –0.68 –0.79 –1.29 –0.41

16 0.087 41.6 43.36 44.4 1048 0.09 42 43.7 45 1051.2 –3.45 –0.96 –0.78 –1.35 –0.31

17 0.077 39.3 41.11 42.2 1104 0.08 39.8 41.5 42.8 1104.3 –3.90 –1.27 –0.95 –1.42 –0.03

18 0.071 37.1 39.44 40.5 1145 0.072 37.6 39.7 41.1 1146.9 –1.41 –1.35 –0.66 –1.48 –0.17

19 0.064 35.8 37.71 38.8 1187 0.066 35.8 37.9 39.4 1189.5 –3.13 0.00 –0.50 –1.55 –0.21

20 0.058 33.9 35.94 37.1 1232 0.059 33.9 36 37.7 1231.9 –1.72 0.00 –0.17 –1.62 0.01

Simulator


5.2.2.4 HTOW case

TABLE 5.29 Some input data and performance parameters of the HTOW case (high-temperature operation inwinter).


Design 11,231.5 16,400 19,850 112 313.3 8 18

Simulator 11,231 17,000 19,850 111.4 320.6 7.84 18

Rel. Error (%) 0.00 –3.66 0.00 0.54 –2.33 2.00 0.00

TABLE 5.30 Model validation of HTOW case of the MSF plant.

Stage p(bar)

TF(ºC)

TD(ºC)

TB(ºC)

D(T/h)

p’(bar)

TF’(ºC)

TD’(ºC)

TB’(ºC)

D’(T/h)

εP(%)

εTF(%)

εTD(%)

εTB(%)

εD(%)

1 1.28 103.2 106.8 107.9 142 1.258 102.4 106.2 107.1 148.5 1.72 0.78 0.56 0.74 –4.58

2 1.12 99.3 102.8 103.8 284 1.088 98.2 102 103 294.1 2.86 1.11 0.78 0.77 –3.56

3 0.97 95.2 98.7 99.7 424 0.935 94.1 97.8 98.7 439.6 3.61 1.16 0.91 1.00 –3.68

4 0.83 91 94.5 95.5 565 0.801 89.8 93.5 94.5 581.9 3.49 1.32 1.06 1.05 –2.99

5 0.71 86.9 90.3 91.3 703 0.684 85.7 89.4 90.3 721 3.66 1.38 1.00 1.10 –2.56

6 0.6 82.7 86.2 87.2 840 0.583 81.5 85.2 86.1 857.1 2.83 1.45 1.16 1.26 –2.04

7 0.51 78.5 82 83 975 0.495 77.4 81.1 82 990.1 2.94 1.40 1.10 1.20 –1.55

8 0.43 74.3 77.8 78.8 1107 0.42 73.3 77 78 1120.3 2.33 1.35 1.03 1.02 –1.20

9 0.36 70.1 73.7 74.7 1237 0.354 69.2 73 73.9 1247.5 1.67 1.28 0.95 1.07 –0.85

10 0.3 66 69.6 70.6 1365 0.298 65.2 69 69.9 1371.7 0.67 1.21 0.86 0.99 –0.49

11 0.25 61.8 65.4 66.4 1487 0.25 61.3 65 66 1493.1 0.00 0.81 0.61 0.60 –0.41

12 0.21 57.8 61.4 62.5 1605 0.21 57.3 61.1 62.1 1611.8 0.00 0.87 0.49 0.64 –0.42

13 0.17 53.9 57.5 58.6 1721 0.175 53.4 57.2 58.2 1727.5 –2.94 0.93 0.52 0.68 –0.38

14 0.14 50 53.6 54.8 1833 0.146 49.6 53.4 54.4 1840 –4.29 0.80 0.37 0.73 –0.38

15 0.12 46.2 49.8 51.1 1943 0.121 45.8 49.6 50.7 1949.2 –0.83 0.87 0.40 0.78 –0.32

16 0.1 42.4 46.1 47.4 2049 0.1 42.1 45.9 47.1 2055 0.00 0.71 0.43 0.63 –0.29

17 0.08 38.7 42.3 43.8 2150 0.083 38.5 42.2 43.5 2157 –3.75 0.52 0.24 0.68 –0.33

18 0.07 35.2 39.5 41.1 2229 0.071 34.9 39.4 40.7 2236.8 –1.43 0.85 0.25 0.97 –0.35

19 0.06 32.3 36.5 38.2 2310 0.06 31.7 36.4 37.9 2317.9 0.00 1.86 0.27 0.79 –0.34

20 0.05 28.8 33.6 35.2 2400 0.051 28.4 33.3 34.9 2400 –2.00 1.39 0.89 0.85 0.00


CHAPTER 6

Thermoeconomics

Fundamentals, applications of thermoeconomic diagnosisand optimization of complex energy systems

As the human population grows, our finite world is becoming smaller and naturalresources are more and more scarce. We must conserve them in order to survive andThermoeconomics plays a key role in this endeavor. We should find out how energyand resources degrade, which systems work better, how to improve designs to reduceconsumption and prevent residues from damaging the environment. Thermoeco-nomics and its application to engineering energy systems can help to answer thesequestions.

The production process of a complex energy system (e.g., a dual-purpose power anddesalination plant) can be analyzed in terms of its economic profitability andefficiency with respect to resource consumption.

An economic analysis can calculate the cost of fuel, investment, operation andmaintenance for the whole plant but provides no means to evaluate the singleprocesses taking place in the subsystems nor how to distribute the costs among them.

On the other hand, a thermodynamic analysis calculates the efficiencies of thesubsystems and locates and quantifies the irreversibilities but cannot evaluate theirsignificance in terms of the overall production process.

Thermoeconomic analysis combines economic and thermodynamic analysis byapplying the concept of cost (originally an economic property) to exergy (an energeticproperty). Most analysts agree that exergy is the most adequate thermodynamicproperty to associate with cost since it contains information from the second law ofthermodynamics and accounts for energy quality (Tsatsaronis, 1987, 1998; Gaggioliand El-Sayed, 1987; Moran, 1990). Exergetic efficiency compares a real process to areversible one, (i.e. an ideal process of the same type). An exergy analysis locates and

Thermoeconomics


quantifies irreversibilities in a process. Exergy based thermoeconomic methods arealso referred to as “exergoeconomics” (Tsatsaronis and Winhold, 1985).

In his seminal book,

The Entropy Law and the Economic Process

, NicholasGeorgescu-Roegen (1971) pointed out that “…the science of thermodynamics beganas physics of economic value and, basically, can still be regarded as such. TheEntropy Law itself emerges as the most economic in nature of all natural laws… theeconomic process and the Entropy Law is only an aspect of a more general fact,namely, that this law is the basis of the economy of life at all levels…”.

Hence, the physical magnitude connecting physics (thermodynamics) and economicsis entropy generation or, more specifically, irreversibility. This represents the “useful”or available energy lost or destroyed (exergy destruction) in all physical processes.All real processes in a plant are non-reversible and, as a consequence, some exergy isdestroyed and some natural resources are consumed and lost forever, which createscost. All natural resources have an economic cost: the more irreversible a process, themore natural resources are consumed (higher energetic cost) and the higher therequired investment (higher thermoeconomic cost). If we can measure thisthermodynamic cost by identifying, locating and quantifying the causes ofinefficiencies in real processes, we can provide an objective economic basis using thecost concept.

Thus, thermoeconomics assesses the cost of consumed resources, money and systemirreversibilities in terms of the overall production process. Consumed resource costinvolves resources destroyed by inefficiencies and helps to point out how resourcesmay be used more effectively to save energy. Money costs express the economiceffect of inefficiencies and are used to improve the cost effectiveness of productionprocesses.

Assessing the cost of the various streams and processes in a plant helps to understandthe process of cost formation, from the input resource(s) to the final product(s). Thisprocess can solve problems in complex energy systems that cannot normally besolved using conventional energy analysis based on the First Law of Thermo-dynamics (mass and energy balances only), for instance:

1. Rational price assessment of plant products based on physical criteria.

2. Optimization of specific component variables to minimize final product costs andsave resource energy, i.e., global and local optimization.

3. Detection of inefficiencies and calculation of their economic effects in operatingplants, i.e., plant operation thermoeconomic diagnosis.

4. Evaluation of various design alternatives or operation decisions and profitabilitymaximization.

5. Energy audits.


125

Specific examples of these applications will be given here and applied to a real dual-purpose power and desalination plant. Many reports also provide specific informationabout thermoeconomic applications (Lozano and Valero, 1993; Tsatsaronis, 1994;Lozano, Valero and Serra, 1996; Valero et al., 1994; Bejan, Tsatsaronis and Moran1997, Valero and Lozano, 1997; Valero, Correas and Serra, 1999; Lozano et al., 1994;Frangopoulos, 1987; Von Spakovsky and Evans, 1993; El-Sayed and Tribus, 1983;El-Sayed, 1988; Pisa, 1997).

Thermoeconomic methods can generally be subdivided into two categories(Tsatsaronis, 1987), those based on cost accounting (e.g. Exergetic Cost Theory,Lozano et al., 1993; Average-Cost-Approach, Bejan et al., 1997; Last-In-First-OutApproach; Lazzareto and Tsatsaronis, 1997) and those based on optimizationtechniques (e.g. Thermoeconomic Functional Analysis, Frangopoulos, 1987;Engineering Functional Analysis, von Spakovsky and Evans, 1993; IntelligentFunctional Approach, Frangopoulos, 1990). Cost accounting methods help todetermine actual product cost and provide a rational basis for pricing, whileoptimization methods are used to find the optimum design or operating conditions.

Unfortunately, there are almost as many nomenclatures as theories. This causesconfusion, complicates method comparison and impedes the development ofThermoeconomics in general (Tsatsaronis, 1994). The Structural Theory ofThermoeconomics (Valero, Serra and Torres, 1992; Valero, Serra and Lozano, 1993)provides a general mathematical formulation using a linear model whichencompasses all thermoeconomic methodologies. The most systematic andwidespread methodologies (see above) use exergy to linearly apportion costs whentwo or more coproducts appear, and their results can be reproduced using theStructural Theory (Erlach, 1998; Erlach, Serra and Valero, 1999). For this reason, allconcepts and procedures explained here are based on the general and commonmathematical formalism of the Structural Theory.

This chapter on the fundamentals of thermoeconomics is divided into three parts.First the basic concepts needed to perform and understand the thermoeconomicanalysis of complex energy systems are presented. Special attention has been paid toexplaining the thermoeconomic cost concept. Once the average and marginal costsare defined, in the second part their meaning, relationship and calculation proceduresare fully explained with examples. Finally, the third part describes some applicationsof thermoeconomic analysis as applied to operation diagnosis and optimization ofcomplex energy systems.

Thermoeconomics


6.1 Basic concepts

All thermoeconomic theories use costs based on the Second Law of thermodynamicswhen solving engineering problems. In this section, the cost concept is explainedtogether with all the new basic concepts, including fuel, product and thermoeconomicmodels needed to perform a thermoeconomic analysis of a plant.

FIGURE 6.1

Physical structure of the co-generation plant.

6.1.1 The concept of cost

The cost of a flow in a plant represents the external resources that have to be suppliedto the overall system to produce this flow. Thermoeconomic analysis distinguishesbetween exergetic costs and monetary costs.

The

exergetic cost

of a mass and/or energy flow is the units of exergy used to produceit, e.g. the exergetic cost of the net power is the exergy provided by the natural gas togenerate the electrical power delivered to the net by the cogeneration plant (see figure6.1). These costs are a measure of the thermodynamic efficiency of the productionprocess generating these flows. The

unit exergetic cost

of a mass and/or energy flowrepresents the amount of resources required to obtain one unit. Thus, if the unitexergetic cost of the electricity is three, three units of plant exergy resources (naturalgas in the case of the cogeneration plant) are consumed to obtain one exergy unit ofelectrical power.

The

monetary cost

takes into account the economic cost of the consumed fuel (i.e., itsmarket price) as well as the cost of the installation and the operation of the plant anddefines the amount of money consumed to generate a mass and/or energy flow. Thesecosts are a measure of the economic efficiency of a process. Similarly, the

unit

HRSG

Compressor

Combustor

7AirGasesNatural gasWorkWater/Steam

1

2 3

40

5 6

8

2

Turbine

1

3

4

Basic concepts


127

monetary cost

(also called

unit exergoeconomic cost

or

unit thermoeconomic cost

) of amass and/or energy flow is the amount of monetary units required to obtain one unit.

We can further distinguish between

average costs

, which are ratios and express theaverage amount of resources per unit of product, and

marginal costs

, which are aderivation and indicate the additional resources required to generate one more unit ofthe product under specified conditions. Mathematically they are defined as:

unit average cost (6.1)

unit marginal cost (6.2)

The average costs are only known after production, when we know how manyresources were used and the production obtained. The average cost is not predictive.Knowing the average unit cost of a product does not provide the cost of a productionprocess P +

∆

P. Thermoeconomic cost accounting theories calculate average costsand use them as a basis for a rational price assessment, under physical criteria, of theinternal flows and the products of the plant.

Marginal costs can be used to calculate additional fuel consumption when theoperating conditions are modified. Thermoeconomic optimization methods(Frangopoulos, 1997, 1990; Von Spakovsky and Evans, 1993) are based on marginalcosts when solving optimization problems.

The relationship between average and marginal costs will be analyzed in more detailin section 6.3.1.

6.1.2 Fuel, product and unit exergetic consumption

A productive purpose, a certain good or service to be produced, can be defined forevery plant. In order to generate this product, some resources have to be supplied tothe plant and are consumed in the process. For example, in the co-generation plant,natural gas is supplied to the plant to generate electric power and process steam.

A productive purpose expressing component function in an overall productionprocess can be defined for each component. The productive purpose of a componentmeasured in terms of exergy is called

product

. To create this product, another exergyflow(s) is consumed. The flow of exergy which is consumed in the component duringthe generation of its product is called

fuel (s)

.

k* B0

Bi------=

kB

Bo

iconditions

* = ∂∂

)

Thermoeconomics


Real process exergy is destroyed in any process. That is, part of the fuel exergy isdestroyed during product generation. Using the definitions of fuel and product, theexergy balance for a component can be formulated as:

F = P + I (6.3)

Therefore, the fuel required to generate a certain amount of a product depends on theamount of irreversibility (exergy destroyed).

The fuel exergy required to generate one exergy unit of product is defined as unitexergetic consumption k:

(6.4)

It is a measure of the thermodynamic efficiency of the process and equals one forreversible processes and is greater than one for all real processes. The moreirreversible a process, the higher the value of the unit exergetic consumption.Combining equation (6.4) with the exergy balance on a fuel/product basis (Equation6.3), the unit exergetic consumption

k

can also be formulated as:

(6.5)

The reciprocal of the unit exergy consumption is defined as the exergetic efficiency

η

.It is equal to one for reversible processes and is less than one for all real processes.

(6.6)

Fuel and product definitions for some typical components in a dual-purpose powerand desalination plant are shown in table 6.1. The fuel-product definition for thecomponents of the cogeneration plant (figure 6.1) are shown in table 6.2.

k FP---=

k 1 IP---+=

η PF--- 1 I

F---–= =

Basic concepts


129

TABLE 6.1

Fuel and product definitions for typical dual-purpose power and desalination plant units.

Component Fuel Product

BoilerNatural gasB

1

Exergy difference between the generated steam flow and the entering water flowB

3

– B

2

PumpWork to drive pump/compressorW

Exergy supplied to the working fluidB

2

– B

1

Turbine without extraction

Exergy removed from working fluid during the expansionB

1

– B

2

Generated work

W

Turbine with extraction

Exergy removed from working fluid during the expansion

B

1

– B

2

– B

3

Generated work

W

GeneratorMechanical work

W

mech

Electric Work

W

el

Heat exchanger/brine heater

Exergy removed from the hot flow

B

3

– B

4

Exergy supplied to the cold flow

B

2

– B

1

MSF stage

Exergy removed from the flashing brine (B

1

– B

2

) minus exergy provided to the cooling brine (B

4

– B

3

)

Distilled water in the stageD

B3

B2water

fuel

B1

steam

B2

W

B1

W

B2

B1

B2

W

B3

B1

Wmech Wel

B3hot stream

B1cold

B2

B4

stream

B4

B2

B3

B1

D

Thermoeconomics


6.1.3 Physical and thermoeconomic plant models

A plant is analyzed using a physical model with a group of equations to describe thephysical behavior of the components. It calculates parameters such as temperatures,pressures, efficiencies, power generated etc. to describe the physical state of the plant.Depending on the analysis, a decision has to be taken on the detail required i.e.,which flows and components are to be considered. The components for the analysisdo not necessarily correspond to physical units. Various parts of the installation canbe combined into one component and physical units can be further disaggregated. Itis important to chose an appropriate aggregation level that properly defines thebehavior of each component and its purpose in the overall production process. Thephysical structure (see figure 6.1) depicts the components, mass and connectingenergy flows considered in the physical model.

The minimum physical data required in a thermoeconomic analysis are temperatures,pressures, mass flow rates and compositions of all mass flows together with the heatand power rates of the energy flows considered. Usually all this information is fullyor partially obtained from the physical model of the plant. But it is not strictlyindispensable if all the required data are measured plant data, collected directly fromthe plant data acquisition system.

FIGURE 6.2

Productive structure of the cogeneration plant.

Nevertheless, when pricing all mass and energy flows in the thermoeconomicanalysis, it is absolutely necessary to define a thermoeconomic model of the plantwhich considers the productive purpose of the components, i.e. the definitions offuels and products and the distribution of the resources throughout the plant. Theproductive model can be graphically depicted by the productive structure diagram(figure 6.2).

HRSG

Turbine

Compressor

Combustor

F2 = B5 = WCp

F3 = B3 – B4

F4 = B4 P4 = B7 = Bheat

W net = B 6P3

P2 = B2 – B0

P1 = B3 – B2

F1 = B1

b1

b2

j1Pj1 = B3

Basic concepts


131

In this scheme, the flows (lines connecting the equipment) are the fuel and theproduct of each subsystem. Each “real“ piece of equipment in the plant has an outletflow (product) and an inlet flow (fuel). The capital cost of the units is also consideredas an external plant resource and is represented as inlet flows coming directly fromthe environment (not considered in figure 6.2). Since the fuel of a process unit can bethe product of another and the product of a process unit can be the fuel of severalsubsystems, two types of fictitious devices are introduced: junctions (rhombs) andbranching points or branches (circles). In a junction, the products of two or morecomponents are joined to form the fuel of another component. In a branching point,an exergy flow (fuel or product in the productive structure –see figure 6.2-) isdistributed between two or more components. Sometimes the productive structurecan be simplified (with the same results) by merging the junctions and branches in anew fictitious component called junction-branching point. Figure 6.5 in section 6.3.1shows a similar productive structure as figure 6.2, where the junction j1 and thebranching point b1 have been merged in a junction-branching point. For the sake ofsimplicity, the explanation of the fundamentals of thermoeconomics will be madeusing the productive structure depicted in figure 6.2.

The productive structure is a graphical representation of resource distributionthroughout the plant. Thus, its flows are fictitious and are not necessarily physicalflows. While each plant has only one physical structure to describe the physicalrelations between the components, various productive structures can be defined

TABLE 6.2

Fuels and Products of the components of the co-generation plant.

No Subsystem Fuel ProductTechnical

production coefficients

1 Combustor F

1 = B1 P1 = B3 – B2 kcb = F1/P1

2 Compressor F2 = B5 = Wcp P2 = B2 – B0 kcp = F2/P2

3 Turbine F3 = B3 – B4 P3 = B5 + B6 = Wcp + Wnet kgt = F3/P3

4 HRSG F4 = B4 P4 = B7 = Bheat kHRSG = F4/P4

5 JunctionP1 = B3 – B2

P2 = B2 – B0Pj1 = B3

r1 = P1/Pj1

r2 = P2/Pj1

6 Branching 1 Pj1 = B3F3 = B3 – B4

F4 = B4

7 Branching 2 P3 = B5 + B6 = Wcp + WnetF2 = B5 = Wcp

B6 = Wnet

Thermoeconomics


depending on the fuel and product definitions as well as decisions on how the plantresources are distributed among the components.

Thus, the thermoeconomic model (mathematical representation of the productivestructure) is a set of mathematical functions called characteristic equations, whichexpress each inlet flow as a mathematical function of the outlet flows for all theproductive structure components and a set of internal parameters xl:

Bi = gi (xl, Bj) i = 1,…, m–s (6.7)

where the index i refers to the input flows of the component l, the index j refers to theoutput flows of the component l, and m is the number of flows considered in theproductive structure. Every flow is an input flow of a component and an output flowof another component or the environment. For the flows interacting with theenvironment, we define:

Bm–s+1 = ωi i = 1,…, s (6.8)

where s is the number of system outputs, and ωi is the total system product, i.e., anexternal variable which determines the total product. The characteristic equations forthe system in figure 6.2, are shown in table 6.3:

TABLE 6.3 Characteristic equationsa of the cogeneration plant.

a. Variables in these characteristic equations are from the Exergetic Cost Theory, corresponding to the PF repre-sentation (Torres, 1991, Valero and Torres, 1990). Note that the Exergetic Cost Theory is a particular case(Serra, 1994) of the Structural Theory which is the thermoeconomic mathematical formalism presented inthis Ph. D. Thesis.

No Component Entry Outlet Equation

1 Combustor F1 P1 F1 = gF1 (x1, P1) = kcb P1

2 Compressor F2 = Wcp P2 F2 = gF2 (x2, P2) = kcp P2

3 Turbine F3 P3 = Wgt F3 = gF3 (x3, P3) = kgt P3

4 HRSG F4 P4 = Bheat = ω4F4 = gF4 (x4, P4) = kHRSG P4 = kHRSG ω4

= kHRSG Bheat

5 Junction 1 P1, P2 Pj1P1 = gP1 (x5, Pj1) = r1 Pj1 = r1 (F3 + F4)

P2 = gP2 (x5, Pj1) = r2 Pj1 = r2 (F3 + F4)

6 Branching 1 Pj1 F3, F4 Pj1 = gPj1 (x6, F3, F4) = (F3 + F4)

7 Branching 2 P3 F2, WnetP3 = gP3 (x7, F2, ω3) = F2 + ω3

= Wcp + Wnet

Basic concepts


The inlet and outlet flows of the productive structure units are extensive magnitudes,which are the product of a quantity (usually mass flow rate) and a quality (specificmagnitude). The magnitudes applied by most thermoeconomic methodologies areexergy (Tsatsaronis, 1987), negentropy (Frangopoulos, 1983) and money. Othermagnitudes, like enthalpy or entropy, can also be used.

The internal variables appearing in the thermoeconomic model depend on thebehavior of the subsystem and they are presumably independent of mass flow rates.This implies that relations like efficiencies or pressure and temperature ratios —which are mainly independent of the quantity of the exiting flows— can be used asinternal parameters.

Note, that the main objective of the productive structure, and hence of thethermoeconomic model, consists on sorting the thermodynamic magnitudes relatedto the physical mass and energy flow-streams connecting the plant subsystems, in adifferent way that the equations modeling the physical plant behavior do, in order toexplicitly determine for each subsystem its energy conversion efficiency.

It is important take in mind that, as it was already explained, thermoeconomicsconnects thermodynamics, which is a phenomenological (black box analysis)science, with economics. That is, by sorting the thermodynamic properties of thephysical mass and energy flow-streams of a plant, which in turn provide the energyconversion efficiency of each subsystem, thermoeconomics analyzes the degradationprocess of energy quality through an installation, i.e., thermoeconomics evaluates theprocess of cost formation.

Depending on the analysis scope each subsystem can be identified with a separatepiece of equipment, a part of a device, several process units or even the whole plant.Sometimes the objective consists on analyzing a plant in a deep detail. In this case itis advisable, if possible, to identify each subsystem with a separate physical process(heat transfer, pressure increase or decrease and chemical mixture or reaction) inorder to locate and quantify, separately if possible, each thermal, mechanical andchemical irreversibility occurring in the plant. If the objective consists on analyzing amacro-system composed of several plants, probably in this case the more convenientapproach is consider each separate plant as a subsystem.

Thus, thermoeconomics always performs a systemic analysis, no matter howcomplex the system is, basically oriented to locate and quantify the energyconversion efficiency. It is out of the scope of thermoeconomics to model thebehavior of the components, which is made by the mathematical equations of thephysical model.

Even though (it is out of the scope of thermoeconomics simulate the behavior of thesubsystems), it is very important build the thermoeconomic model with physicalmeaning. This is the reason, as already explained, of defining different

Thermoeconomics


thermoeconomic models for the same plant. Depending on the aggregation level andon the nature of the thermoeconomic equations the model will content physicalinformation about the actual system behavior with different accuracy degrees. Theobtained results from a very rough thermoeconomic model, without any physicalsensitivity related with the actual behavior of the plant, probably will be useless.

The more extended thermoeconomic methodologies use linear equations in theirthermoeconomic models, because they present practical (the model is simpler and forthis reason much more powerful when applied to very complex energy systems) andconceptual advantages, as it will be explained before. Moreover, in many real plants itis possible to find an aggregation level where the system and subsystems linearlybehave with accuracy enough, under an engineering point of view (Valero, Torres andLerch, 1999; Martínez, Serra and Valero, 2000). This is also the case of the dualpower and desalination plant analyzed in this work, as it is proved in next chapter.

Thus, if the characteristic equations are first grade homogeneous functions withrespect to the subset B, of independent variables (as linear equations do), that is:

λ Bi = gi (λ B1,… λ Bj, xl) λ∈ℜ (6.9)

Euler’s Theorem states that the homogeneous function of first order verify:

l1,…,ls in Sl (6.10)

or using the marginal consumption notation,

(6.11a)

i = 1,...,m l = 1,...,n. (6.11b)

This property means that the input of a component varies at the same rate as itsoutputs. Note that this property does not imply that the function must be linear. Forinstance, a Cobb-Douglas function z = a xα y(1–α), is also a homogeneous first orderfunction.

κij are the technical production coefficients and represent the portion of the i-thcomponent production:

(6.12a)

Bg

BB

g

BB

g

BBi

i

ll

i

ll

i

ll

s

s= ∂

∂

+ ∂∂

+ + ∂∂

1

1

2

2...

κ iji

j

g

B= ∂

∂

B Bi ij j

j Sl

=∈

∑κ

κ iji

j

gB

= ∂∂

Basic concepts


The sum of κij coefficients of a unit is the unit exergy consumption of that unit:

(6.12b)

In thermoeconomics there are three types of characteristic equations, which arelinear:

1. Those connecting each fuel of a component to its corresponding product:

Fi = κij Pj as for instance F1 = gF1 (x1, P1) = kcb P1 (6.13a)

There is one such equation for each component’s fuel. These types of equationsare generated in the pieces of equipment and they inform about:

– the productive function of each component, i.e., its production (product)

– what the component needs (fuel) to develop its productive purpose, and

– the thermodynamic efficiency of the process in the component

2. Structural equations model how the resources consumed by the plant are distrib-uted through the plant components. They show how the process units are con-nected from a productive point of view. Structural equations are characteristicequations to describe the productive model of junctions and branches, e.g.:

P1 = gP1 (x 5, Pj1) = r1 Pj1 = r1 (F3+F4) (6.13b)

3. When the capital cost of the equipment is also considered in the analysis, a thirdtype of characteristic equation is required; costing equations. These equations arevery often not linear, but in the case of these equations this is a minor problem,because they can be linearized for different operation intervals. They relate theinvestment cost of the component with thermodynamic variables and its product.They express the amount of resources needed to build, install, maintain (etc.) acomponent. For example, a costing equation proposed by El-Sayed (1996), seesection 7.3.3.1 for details:

(6.13c)

The diagram of the productive structure is also called a Fuel/Product diagram (Torreset al., 1999) because in most cases the lines connecting the pieces of equipmentrepresent the fuels and products of the different units. Thus, the characteristicequations (see table 6.3) using the Fuel–Product notation can also be written as:

i = 0,1,…, n (6.14)

k

F

P

F

Pj iji

n ii

n

j

j

j

= = ==

=∑∑

κ0

0

Z Q T T Pn t t= ⋅ ⋅ ⋅ ⋅ ⋅− − −0 02 10 0 75 0 5 0 1. . . .∆ ∆ ∆

P B Bi i ij

j

n

= +=∑0

1

Thermoeconomics


This equation shows how the production of a process unit is used as fuel by anotherunit or as a part of the total plant production. In the above expression, Bij is theproduction portion of the i-th component that fuels the j-th component, and Bi0represents the production portion of the component i leading to the final plant product(the subscript 0 refers to the environment, which is considered another process unitinteracting with the plant).

Equation (6.14) can be expressed in terms of the unit exergetic consumptions as:

i = 0,1,…, n (6.15)

In matrix notation it can also be expressed as:

(6.16)

where Ps is a (n×1) vector whose elements contain the contribution to the finalproduction of the system Pi0 obtained in each component, and ⟨KP⟩ is a (n×n) matrix,whose elements are the unit exergy consumption κij. This expression helps to relatethe production of each component as a function of the final production and the unitconsumption of each component:

where (6.17)

In the same way, we can express the irreversibility of each component as:

where (6.18)

while the total resources of the system may be obtained as:

(6.19)

where , is a (n×1) vector whose elements contain the unitconsumption of the system-input resources.

6.2 Calculating thermoeconomic costs

Once the thermoeconomic model has been defined and the characteristic equationscorresponding to the productive structure of the system are known, the costs of allflows in the productive structure can be easily calculated.

There are two different types of thermoeconomic costs: average costs and marginalcosts (equations 6.1 and 6.2). It is important to note that (as discussed below) the

P B Pi i ij j

j

n

= +=∑0

1

κ

P P KP P= +s

P P P= s P U KP≡ −

−

D

1

I I P= s I K U P≡ −( )D D

FTt

e s= κ P P

κt e κ01 … κ0n, ,( )≡

Calculating thermoeconomic costs


average and marginal costs coincide when the characteristic equations of thethermoeconomic model are first grade homogeneous functions.

This result is very important since both costs can be calculated using the sameprocedure. Marginal costs are a derivative (see equation 6.2) and can be calculated byapplying the chain rule of the mathematical derivation. Similarly, average costs canalso be obtained from the rules of the mathematical derivation applied to thethermoeconomic model when the characteristic equations are first gradehomogeneous functions.

According to the previous premises, the cost of the plant resources can be defined as:

(6.20)

where e, is the number of system inputs, and k*0,i is the unit cost of the –i– external

resource.

Each flow, as a component input, is a function (defined by the characteristic equation) of aset of internal variables, x, external variables ω and the output flows of the component.The cost of the plant resources is then a function of each flow, the set of internalvariables of each component and the final product of the plant B0 = B0 (Bi, x, ω),according the relations (6.7) and (6.8).

When calculating the variation of the resources consumed in the plant concerning aflow, the chain rule can be applied:

i = 1,…, e (6.21a)

i = e + 1,…, m (6.21b)

The expression represents the marginal costs which evaluate the additional

consumption of the resources, when an additional unit of the flow –i– is produced,under the conditions that the internal variables, x, do not vary throughout this process.

We can denote these marginal costs as , and the marginal consumption

of flow –i– to produce the flow –j–, then we can rewrite the previous expressions, as:

i = 1,…, e (6.22a)

B k Bii

e

i0 01

==∑ ,

*

∂∂

=BB

ki

i0

0,*

∂B0

∂Bi---------

∂B0

∂Bj---------

∂gj

∂Bi--------

j 1=

m

∑=

∂B0

∂Bi---------

ki* κ ij

∂gi

∂Bj---------=

k ki i*

,*= 0

Thermoeconomics


i = e + 1,…, m (6.22b)

Note that the unit exergetic cost of each fuel entering the plant is unity because thereis no energy quality degradation nor exergy destruction at the very beginning of theproductive process. Hence, the amount of exergy consumed to obtain each plant’sfuel is its own exergy content and therefore its unit exergetic cost equals one.

It can easily be proved that the cost of each flow of the productive structure usingthe Fuel/Product notation is:

(6.23)

And the exergetic cost of the product of each component is the same as the cost of theresources needed to obtain it, hence:

i = 1,…, n (6.24)

This cost equation can also be expressed in terms of the unit exergetic consumptions:

i = 1,…, n (6.25)

which can be used to obtain the unit exergetic cost of the flows appearing in theproductive structure diagram as a function of the unit exergetic consumption of eachprocess unit.

Then, if the characteristic equations and the marginal consumptions for eachcomponent are known, the marginal cost k* for each flow can be obtained by solvingthe system of linear equations (6.25).

Example 1

For the example of a co-generation plant (figure 6.2), equations 6.21a, 6.21b can bewritten as:

ki* κ ji k j

*

j 1=j i≠

m

∑=

Pij*

P k Bij P i ij*

,*=

P F k Bi i P j jij

n* *

,*= =

=∑

0

k kP i i ji P jj

n

,*

,*= +

=∑κ κ0

1

kBFF1

1

1

* = ∂∂

kBF

BP

PF

kF P2 3

1

2

1

3

3

2

* *= ∂∂

= ∂∂

∂∂

=

kBF

BP

P

FkF

j

jPj3 1

1

3

1

1

1

3

* *= ∂∂

= ∂∂

∂∂

=



The thermoeconomic model (characteristic equations) of an energy system containsthe mathematical dependence between the resources consumed and plant flows(products and internal flows). It is therefore possible to define a set of linear equationsto calculate the costs of every flow of the plant's productive structure. Note that theseequations show the process of cost formation on the productive structure.

The proposed procedure to calculate the marginal cost of all the flows of a plant isgeneral and valid for any thermoeconomic formulation that uses equationsconnecting inlet and outlet flows of each component.

Just as k* was defined as a marginal cost when production is modified, we can alsoobtain the marginal cost when the internal variables x are modified. Similarly,applying the chain rule, we get:

(6.26)

This equation expresses the effect on additional resource consumption when aninternal parameter xi is modified and is the basis for the thermoeconomic diagnosis(explained in detail below).

To determine the physical model of the system, a set of equations must be definedwhich relate the internal and external variables to the thermodynamic laws: mass,energy and entropy balances.

kBF

BP

P

FkF

j

jPj4 1

1

4

1

1

1

4

* *= ∂∂

= ∂∂

∂∂

=

kBP

BF

FP

k kP F cb1 1

1

1

1

1

1

1

* *= ∂∂

= ∂∂

∂∂

=

kBP

BF

FP

k kP F cp2 2

1

2

1

2

2

2

* *= ∂∂

= ∂∂

∂∂

=

kBP

BF

FP

k kP F gt3 3

1

3

1

3

3

3

* *= ∂∂

= ∂∂

∂∂

=

kBP

BF

FP

k kP F HRSG4 4

1

4

1

4

4

4

* *= ∂∂

= ∂∂

∂∂

=

kBP

BP

PP

BP

PP

k r k rPj j j

P Pj1 2 1

1

1

1

2

2

1

1

1

1

12 1

* * *= ∂∂

= ∂∂

∂∂

+ ∂∂

∂∂

= +

kB

WBP

PW

kWnet net

Pnet

* *= ∂∂

= ∂∂

∂∂

=1 1

3

33

∂∂

=∂∂=

∑Bx

kg

xij

j

ij

m0

1

*

Thermoeconomics


The most developed thermoeconomic optimization methodologies (Frangopoulos,1987, 1990; Von Spakovsky et al., 1993), use the Lagrange multipliers optimizationmethod to calculate the marginal costs defined in the previous section. It can easily beproved (Serra, 1994; Reini, 1994) that the Lagrange multipliers are the marginal costsdefined in equation (6.2), i.e:

i = 1,..., m (6.27)

This multiplier represents the variation of the objective function B0 concerning thestate variable Bi.

6.2.1 Marginal and average thermoeconomic costs

Now, we will show that the marginal and average costs coincide when thecharacteristic equations of the system are first grade homogeneous functionsconcerning the extensive magnitude B. This is a very important result since themarginal and average costs can be calculated using the same procedure. This unifiesaccounting and optimization theories in a common mathematical formulation. Themost important advantage is that variables and costs with different conceptualsignificance can be compared and better understood. Thus, the Exergetic Cost Theory(Valero, Lozano and Muñoz, 1986a), a cost accounting methodology which providesaverage costs, and Thermoeconomic Functional Analysis (Frangopoulos, 1983,1987), an optimization methodology which provides marginal costs, are particularcases of the Structural Theory. As a result of the integration of different approaches,some useful thermoeconomic applications have been developed, e. g. diagnosisoperation and thermoeconomic optimization using the same mathematical formalism.

As an illustration, consider a generic component or subsystem with several inlet andoutlet flows. For the sake of simplicity we will use a general subsystem with two inletflows and two outlet flows (figure 6.3).

FIGURE 6.3 Generic component scheme.

λ ii

BB

= ∂∂

0

B3

B4

B13

B24

B1

B2

B23B1

4



The characteristic equations that describe component behavior are:

B1 = k13 B3 + κ14 B4 (6.28)

B2 = k23 B3 + κ24 B4 (6.29)

These equations provide the amount of inlet resources (B1, B2) consumed to obtaineach one of the outlet flows (B3, B4). This idea is easily understood if the componentis made up of two subsystems. The equations modeling each subsystem are:

B13 = κ13 B3 (6.30a)

B14 = κ14 B4 (6.30b)

B23 = κ23 B3 (6.31a)

B24 = κ24 B4 (6.31b)

Equations (6.30a, 6.31a) represent the resources needed to produce B3 and Equations(6.30b, 6.31b) are the resources consumed to produce B4. The total amount ofresources required to obtain B3 is thus:

B13 + B23= κ13 B3 + κ23 B3 (6.32)

and to obtain B4:

B14 + B24 = κ14 B4 + κ24 B4 (6.33)

According to Equation (6.1) the average cost of the outlet flows are:

(6.34a)

(6.34b)

And the marginal cost of the outlet flows are:

(6.35a)

(6.35b)

considering that the value of the marginal cost of the input flows (B1, B2) is equal toone. Since equations (6.34) are the same as equations (6.35), the average andmarginal costs of B3 and B4 coincide. Both kinds of costs coincide because theequations modeling the component are homogeneous functions of first orderconcerning the extensive magnitudes characterizing the outlet flows.

k3* κ13 B3 κ23 B3+

B3-------------------------------------- κ13 κ23+= =

k4* κ14 B4 κ24 B4+

B4-------------------------------------- κ14 κ24+= =

kgB

kgB

k k k31

31

2

32 13 23

* * *= ∂∂

+ ∂∂

= +

kgB

kgB

k k k41

41

2

42 14 24

* * *= ∂∂

+ ∂∂

= +

Thermoeconomics


In this proof, the cost of the inlet flows was unity. This is equivalent to consideringthat the subsystem was at the beginning of the productive process. The generalmathematical formulation of the cost generated in a component is the same for eachone and is not dependent on the position in the productive process. Thus, the resultsobtained are general.

The average and marginal costs coincide because the equations modeling thecomponents are first grade homogeneous functions concerning the extensivemagnitude characterizing the outlet flows. The mass is the property determiningwhether a magnitude is extensive or not. If all equations modeling a system are firstgrade homogeneous functions concerning the mass, a simple substitution cantransform those equations in homogeneous functions with respect to any extensiveproperty. Thus, the marginal and average costs coincide if all equations modeling thebehavior of the system are first grade homogeneous functions concerning the massflow rate.

6.2.2 Economic resources and thermoeconomic costs

Thermoeconomic cost calculation considering the component capital cost Z, issimilar to the above method but should be explained in more detail. The capital costof each component Z can be considered an external flow of plant resources from theenvironment to the component (see figure 6.4). This will represent the monetary unitsper second needed to compensate the depreciation, maintenance cost and so on, of thecomponent.

FIGURE 6.4 Economic resources scheme.

According to marginal cost analysis, Z represents an environmental resource and canbe handled in the same mathematical way as energy resources. The amount ofresources consumed when manufacturing a device are, in fact, resources consumed toobtain the plant products. Some authors (Brodyansky et al., 1993; Le Goff, 1979)have developed methodologies to evaluate the total amount of resources consumedwhen building a process unit. Then the marginal unit cost ∂Z/∂B, can be considered amarginal consumption κZj.

Bj

BhBix1

Z1 = Z1 (B1, Bj, Bh)

B0

Economic resources

Thermoeconomic applications to thermoeconomic operation diagnosis and the optimization of


For the component depicted in figure 6.4 the characteristic equations are:

Bi = f (Bj, κij) (6.36a)

Z j = Z (Bj, κZj) (6.36b)

And the cost of the product is:

If Zj is proportional to the production of the unit, or in other words its characteristicfunction is first order homogeneous, the marginal cost is equal to the average cost.But, unfortunately Zj is a non-linear function of the production in most cases.

6.3 Thermoeconomic applications to thermoeconomic operation diagnosis and the optimization of complex energy systems

Having defined the tools needed for a thermoeconomic analysis of a complex system,some applications to thermoeconomic diagnosis and optimization can be presented.The methodology is presented together with a simple application.

6.3.1 Operation thermoeconomic diagnosis

Diagnosis is the art of discovering and understanding signs of malfunction andquantifying their effects. In the case of Thermoeconomics, the effect of a malfunctionis quantified in terms of additional resources consumed to obtain the sameproduction, both in quality and in quantity.

The main problem in energy system diagnosis can be summarized in the followingquestion: Where, how and which part of the consumed resources can be saved bykeeping the quantity and quality of the final products constant? To answer thesequestions, we need:

• Procedures that accurately determine the state of the plant.

• A theory to provide the concepts and tools to understand and explain the causesof this state.

The methodology presented in this paper applies Structural Theory to provide thetools to investigate the causes of the irreversibilities and the cost formation process.

kBB

kZ

Bkj

i

ji

j

ji ij Zj

* * *= ∂∂

+∂∂

= +κ κ

Thermoeconomics


In order to clarify the explanation of the proposed method we use a simple example (amore complex one can be found in Lerch, Royo and Serra, 1999), the co-generationplant depicted in figure 6.1, whose design and operational exergy flow values areshown in table 6.4. The plant has a co-generation gas turbine cycle and uses theturbine outlet gases as thermal energy in a heat recovery steam generator thatproduces steam (flow #7) together with the electric energy produced in the turbo-generator (flow #6).

6.3.1.1 Technical exergy saving

Once the exergy flows have been supplied by an appropriate performance test or amodel simulator, the irreversibilities in each productive unit can be obtained from theexergy balance. But not all exergy losses can be saved in practice. In fact, thepotential exergy saving is limited by technical and/or economic constraints. It alsodepends on the decision level that limits the actions to be undertaken. In contrast toconventional thermodynamic analysis, Thermoeconomics assumes a referencesituation of the plant operating under design conditions. From this perspective, in theplant of figure 6.1, we see that only 133 kW, of the 7.06 MW of total irreversibilitiescan be saved with respect to design conditions.

Therefore, the additional fuel consumption can be expressed as the differencebetween the resource consumption of the operating plant and the resourceconsumption for a reference or design condition with the same production objectives:

(6.37a)

and it can be broken up into the sum of the irreversibilities of each component:

(6.37b)

However, even though the methods based on Second Law Analysis (Kotas, 1985) andTechnical Exergy Saving are useful to quantify the additional fuel consumption, theyfail when trying to identify the real causes of the additional resources consumption.

TABLE 6.4 Design and operation exergy flow values of the cogeneration plant (figure 6.1).

Flow (kW) 1 2 3 4 5 6 7 8

Design 11781 2704 9614 3831 2977 2500 2355 388

Operation 11914 2758 9753 3887 3056 2500 2355 424

∆F F FT T T= − 0

∆ ∆ ∆F I I I IT T j jj

n

jj

n

= = −

=

= =∑ ∑0

1 1



6.3.1.2 Impact on resources consumption

The Fuel/Product diagram of the cogeneration plant is shown in figure 6.2. Thisdiagram can be simplified by merging junction 1 and branching point 1 in a newfictitious component called junction–branching point (see figure 6.5). This newproductive structure is slightly different than figure 6.2, and is more compact.

The characteristic equations of this new productive structure are obtained as in theprevious section applying equation (6.15)

FIGURE 6.5 Fuel / Product diagram and fuel and product exergy flows (kW) in design conditions for the co-generation plant shown in figure 6.1.

For the sake of simplicity we did not consider thermal and mechanical exergies asseparate entities. Two auxiliary variables also appear r1 = (B3 – B2)/B3 and r2 = B3/B2,

which correspond to the part of the fuel of the turbine and HRSG coming from thecombustor and the compressor respectively. Flow #8, produced in part in thecombustor and in the compressor, also leaves the system as a residue. Only a part of

F0 F1 F2 F3 F4 Total

P0 0 11781 0 0 0 11781

P1 0 0 0 4156 2474 6631

P2 0 0 0 1627 968 2595

P3 2500 0 2977 0 0 5477

P4 2355 0 0 0 0 2355

Total 4855 11781 2977 5783 3443

P P KP P= +s

1

3-2

2

3-4

4-8

6

5

18

74

3

2

Thermoeconomics


the entering gases to the turbine: B3 – B8 are used as a fuel of other components of the

system. Therefore, only a part of the combustor’s and compressor’s product is used asa fuel for other components (useful product). Accordingly, figure 6.5 shows the chosendisaggregation scheme of the system and the Fuel/Product values for the designconditions.

In order to bring together the problem of the impact of resources consumption withthermoeconomic diagnosis we need to know the increase of the unit exergyconsumption of each component of the plant. A performance test or a simulatorprovides the real values of the unit consumptions which are then compared with thedesign values.

The values of the unit exergetic consumption increase are found as: ∆κij = κij (x) – κij(x0). Table 6.6 shows the ∆κij values for the plant in figure 6.1.

Equation (6.19) is used to obtain the increment of the total resources of an operatingplant regarding the reference conditions:

(6.38)

TABLE 6.5 Fuel/Product definition corresponding to figure 6.5

No. Component Fuel Product Residue

1 Combustor B1 B3 – B2

2 Compressor B5 B2

3 Turbine B3 – B4 B6

4 HRSG B4 – B8 B7 B8

TABLE 6.6 Increase of unit consumption. (100 ∆κij).

∆κe 0.4006 0.0000 0.0000 0.0000

0.0000 0.0000 –0.1667 0.3857

0.0000 0.0000 0.1593 0.4636

0.0000 1.1147 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000

∆k 0.4006 1.1147 -0.0074 0.8493

∆ KP

∆ ∆ ∆FTt

et

e= +κ κP P0



The increase of the component production from equation (6.16) may be expressed interms of the unit exergy consumption as:

(6.39)

hence, applying equation (6.17), we obtain:

(6.40)

If we want to analyze the fuel impact due to an increment of the exergy unitconsumption of the components, equation (6.38) could be written as:

(6.41)

If no change in the total production of the plant is assumed, then:

(6.42a)

or in scalar format:

(6.42b)

Using the above equation, the additional resource consumption ∆FT (also called FuelImpact; Reini, 1994) can be expressed as the sum of the contributions of eachcomponent.

The variation of the exergetic unit consumption of each component increases itsresources consumption and its irreversibilities in a quantity , which we call,malfunction. Consequently, this implies an additional consumption of externalresources given by , which is also named the malfunction cost.Therefore, the total fuel impact can be written as the sum of the fuel impact ormalfunction cost of each component, as shown in equation (6.42b).

The proposed method provides the exact values of the additional resourceconsumption of each component malfunction for any operational state. Othermethods, such as the Theory of Perturbations (Lozano et al., 1996), only provide anapproximate predictive value, based on marginal costs (Lagrange multipliers) whichis valid for an operating state close to the reference conditions.

∆ ∆ ∆ ∆P P KP P KP P= + +s0

∆P P| ⟩ ∆Ps ∆ KP⟨ ⟩ P0+

=

∆ ∆ ∆ ∆FTt

et

Pt

P s= + +κ κ κP KP P P0 0* *

∆ ∆ ∆FTt

et

P= +

κ κ * KP P0

∆ ∆F k PT jj

n

ji ii

n

=

==

∑∑ P,*

0

0

1

κ

∆κ ji iP0

k Pj ji iP,* ∆κ 0

Thermoeconomics


FIGURE 6.6 Fuel impact and technical saving.

Figure 6.6 compares the fuel impact and the increase of irreversibilities or thetechnical exergy saving of each component and also compares (first column) themalfunction and the fuel impact for each component. Three malfunctions in the plantare shown in the combustor, the compressor and the HRSG. The largestirreversibilities increase is in the combustor, but the largest fuel impact is in thecompressor. The question that arises is: What causes the irreversibilities increase andthe fuel impact, and how are they related?

6.3.1.3 Malfunction and dysfunction analysis

We have shown that there is no direct relationship between the increase of theirreversibilities and fuel impact. The more advanced the production process is, thegreater the cost of the irreversibility malfunction and, as a consequence, the greaterits fuel impact.

Furthermore, the degradation of a component will force other components to adapttheir behavior in order to maintain their production conditions and modify theirirreversibilities. Figure 6.7 shows how an increase of the unit consumption of acomponent will not only increase the irreversibilities on it but also the irreversibilitiesof the previous component.

FIGURE 6.7 Malfunction and fuel impact.

0

20

40

60

80

Combustor Compressor Turbine HRSG

Fuel Impact

Malfunction

Technical Saving

∆F1

F1P1 F2

P2

I2

∆I2∆F2∆P1

I1

∆I1



The irreversibility increase of a generic system’s component is given by:

∆I = ∆KD P0 + (KD – UD) ∆P (6.43)

From the above expression, we can distinguish two types of irreversibilities:

Endogenous irreversibility or malfunction produced by an increase of the unitconsumption of the component itself:

Exogenous irreversibility or dysfunction induced in the component by themalfunction of other subsystems, which forces it to consume more local resources toobtain the additional production required by the other components:

The malfunction only affects the behavior of the components; the dysfunction is aresult of how the components adapt themselves to maintain the total production.

Now we will consider the causes and effects of the irreversibilities systems andintroduce a new method to compute the fuel impact of a malfunction and its effect. Inother words, how to compute the dysfunction on the rest of the system components.

If we substitute ∆P from equation (6.40) then the irreversibility increase of eachcomponent, equation (6.43) is written in terms of the unit consumption as:

(6.44)

or in scalar format:

i = 1,…, n (6.45)

The first part of the previous expression corresponds to the component malfunction,and the last part to the dysfunction. If we denote:

(6.46)

DFij represents the part of i–th component dysfunction generated by component –j–,where φih are the coefficients of the irreversibility matrix operator for the actualoperation values. The above expression shows how a malfunction Pj ∆κhj, on the j-thcomponent, generates a dysfunction on the i–th component proportional to the φihcoefficients, which represent the weight of the malfunction effect. The coefficient φih

M F P k Pi i i jij

n

i= =

=∑0 0

0

∆ ∆κ

DF k Pi i i= −( )1 ∆

∆ ∆ ∆I K I KP P= +

D

0

∆ ∆ ∆I P Pi i jij

n

ih hj jj h

n

= += =∑ ∑κ φ κ

1

0

1,

DF Pij ihh

n

hj j==∑ φ κ

1

0∆

I| ⟩

Thermoeconomics


does not depend on the malfunction amount, but only on the unit consumption of thecomponents in the operating state. Therefore, the dysfunction cannot be corrected byitself but decreases the malfunction which generated it.

The technical exergy saving of component –i–, equation (6.45) can be written as thesum of its malfunction and the dysfunction generated by other components of thesystem:

i = 1,…, n (6.47)

The graph in figure 6.8 describes the cause of the irreversibilities increase in the gasturbine cycle (of the example) as the sum of the malfunctions and the dysfunctiongenerated by the rest of the components

FIGURE 6.8 Analysis of the irreversibility causes (kW).

Fuel impact and dysfunction

For a specified constant quality and quantity of total production, the fuel impact(6.42b) could be written as the sum of the malfunctions and dysfunctions of all theplant components:

(6.48)

If we rearrange the previous expression, grouping by component production, weobtain:

∆I MF DFi i ijj

n

= +=∑

1

0

20

40

60

80

∆I1 ∆I2 ∆I3 ∆I4

HRSG

TurbineCompressor

CombustorMalfunction

∆ ∆F I MF DFT ii

n

i ijj

n

i

n

= = +

= ==∑ ∑∑

1 11



(6.49)

Therefore, the fuel impact or the malfunction cost of each component is given by thesum of the malfunction and the dysfunction:

i = 1,…, n (6.50)

If we compare the previous equations with the fuel impact equation (6.42b), we find arelationship between the unit cost of production and the irreversibility dysfunctioncoefficients, given by:

j = 1,…, n (6.51)

The above expression is an alternative method to compute the unit cost of the productas the sum of the contribution of the irreversibilities of each component. Table 6.7shows the irreversibility matrix operator coefficients and unit cost of the componentproduct for an operating gas turbine plant.

A graph of the fuel impact for each component is shown in figure 6.9. Note that thedysfunction becomes even greater than its own malfunction as the production processproceeds. The cost of the malfunction in the compressor and HRSG includes thedysfunction generated, for the most part, in the combustor.

The sum of the dysfunctions generated by a component:

i = 1,…, n (6.52a)

could be written as: (6.52b)

TABLE 6.7 Irreversibility matrix and unit cost of product.

0.7807 1.0469 0.9037 1.2586

0.0000 0.2422 0.0723 0.1007

0.0000 0.0988 0.0853 0.0411

0.0000 0.0000 0.0000 0.4704

1.7807 2.3880 2.0614 2.8708

∆ ∆ ∆F k PT i jh hij h

n

i

n

i= +

==∑∑ φ κ, 11

0

MF MF DFi i hih

n* = +

=∑

1

kP j iji

n

,* = +

=∑1

1

φ

I| ⟩

kP*

DI DFi jij

n

==∑

1

DI k Pi P j ji ij

n

= −

=∑ ,

* 1 0

1

∆κ

Thermoeconomics


FIGURE 6.9 Analysis of fuel impact (kW).

Therefore, the dysfunction generated by a component (as with the fuel impact)

depends on the malfunction and the position of the component in the productive

process, which is, in turn, characterized by the unit cost of the resources required by

the component.

The relationship between irreversibility increase and fuel impact can be represented

by a double input table (see table 6.8). The dysfunction table containing the DFij

elements can be computed in a compact matrix form using the expression:

TABLE 6.8 Malfunction and dysfunction table in (kW).

Combustor Compressor Turbine HRSG DF Malfunction Total

∆I1 0.000 26.140 2.004 18.520 46.664 26.562 73.226

∆I2 0.000 2.092 2.113 2.644 6.849 28.925 35.774

∆I3 0.000 2.467 0.862 1.079 4.408 –0.408 4.000

∆I4 0.000 0.000 0.000 0.000 0.000 20.000 20.000

DI 0.000 30.699 4.979 22.243 57.921

Malfunction 26.562 28.925 –0.408 20.000 75.079

Total 26.562 59.624 4.571 42.243 133.000

0

20

40

60

80

Combustor Compressor Turbine HRSG

∆I4∆I3

∆I2∆I1

MF

DF I KP P[ ] = ∆ D0



Each cell represents the DFij dysfunction. The DI column represents the sum of thedysfunctions generated by each component, and the DF row is the sum of thedysfunctions generated in each component. The total sum by columns represents theFuel Impact of each component, and the total sum by rows is the irreversibilityincrease. The methodology proposed in this section is summarized in the tablementioned above. It is a powerful tool to find the causes and effects of variations fromthe design conditions of a plant and to study, classify and assign the role of eachsystem unit.

6.3.1.4 Intrinsic and induced malfunctions

Using the above method we can identify and quantify malfunction effects. Forexample, we found three malfunctions in the gas turbine cycle (figure 6.1): one eachin the combustor, compressor and HRSG. But, What are the causes of themalfunctions? In fact, the actual operation values shown in table 6.4 correspond to a1% decrease in compressor isoentropic efficiency. This means that HRSG andcombustor efficiencies can be changed by varying compressor efficiency.

How do we approach this problem? The relationship between operation andefficiency of the components could be analyzed using a simulator. If all the pantcomponents were isolated, the efficiencies of those components would beindependent variables (Lozano et al., 1996). So we will assume that there is anoperating parameter xr affecting the efficiency of the i-th component of the plant andthus, in most cases, also indirectly affecting the efficiencies of the other plant processunits.

Once the relationship between unit exergy consumption and the operating parametersis known, the above methodology can be applied to distinguish the effect of anoperating parameter on the internal economy of a component, i.e. its malfunction andthe cost of its malfunction.

Plant operating parameters could be classified according to their effect on theefficiency of the components of the system:

Local variables: They mainly affect the behavior of the component related to thevariable, e.g, the isoentropic efficiency of a turbine. From a practical point of view, avariable is considered local and therefore related to a subsystem. The total fuel impactdue to its perturbation is basically located in this component.

Global and/or zonal variables: This is the case when an operating parameter cannotbe associated with a specific component. We must identify them as operating setpoints, environmental parameters and the production load or fuel quality.

In this thesis we will focus our analysis on local variables and how they affectadditional fuel consumption and the other plant components. This analysis is, in fact,the next step in the thermoeconomic diagnosis.

Thermoeconomics


Unfortunately the problem of locating causality of losses in a structure is rather morecomplex than locating malfunctions and dysfunctions.

When a plant unit deteriorates (when its behavior is degraded) its physical variablesare modified, its efficiency is decreased and its unit exergy consumption increases.

The unit exergy consumption increase of each component, due to the variation of anoperating parameter xr, is:

Therefore, it will be possible to approximate the malfunction of a component as thesum of the contributions of each operating parameter:

(6.53)

According to the classification of operating parameters, the intrinsic malfunction isthat part of the component malfunction due to the degradation/improvement of thecomponent itself, which is, in turn, due to variation of local operating parameters:

(6.54)

A system malfunction or improvement does not only have consequences upstream(by trying to see the variation in consumption of used resources) but alsodownstream. Clearly the degradation or improvement of a system’s flow entryconditions will affect its efficiency to a greater or lesser extent. This will modify theproduction and affect the next component.

Not only are there dysfunctions when there is an intrinsic malfunction. There are alsoinduced malfunctions, that can decisively affect the system's behavior. For example,using the throttle valve in a power plant can destroy a small additional amount ofexergy but the downstream effects on turbine efficiencies can be quite serious.

Thus, the difference between total component malfunction and intrinsic malfunctionis called induced malfunction. It is due to the degradation of other plant componentswhich provoke a variation in the unit consumption of that component:

(6.55)

This phenomenon is not foreseen in classic linear thermoeconomic theory. Theaverage cost obtained from the most rigorous disaggregation analysis can neverpredict induced malfunctions and dysfunctions will only be predicted in cases wherethe hypothesis of linearity and continuity holds.

∆ ∆κ κ κijr

ij r ijx= + −( ) ( )x x0 0

MF Pi jir

ij

n

r

≅=∑∑ ∆κ 0

1

MF PiL

jir

ij

n

r Li

≡=∈∑∑ ∆κ 0

1

MF MF MFiG

i iL= −



Malfunction matrix

It is important to know the fuel impact associated with the variation of each physicalparameter when a malfunction occurs.

The fuel impact of an operating parameter on the whole plant can be calculated usingthe simulator but the latter does not provide information about the effects on otherplant components. A deterioration in a component (intrinsic malfunction) can modifythe efficiencies of other plant components.

Information about interactions among different plant components can be obtainedwith the methodology presented here. It is basically contained in the so calledmalfunction matrix, or ⟨∆KP⟩ matrix. This matrix can relate any operating parameterwith all the possible malfunctions. Note that the overall impact on resources (fuelimpact) can be written as:

(6.56)

Where the first term is the fuel impact associated with the intrinsic malfunction andthe last term is the fuel impact associated with the induced malfunctions and ∆κij areelements of the ∆ ⟨KP⟩ matrix. The ∆ ⟨KP⟩ matrix has been built for each parameter(see Chapter 7) in a variational analysis.

In a real power plant, the most general case is when several plant components suffersimultaneous efficiency deviations. The total fuel impact can be calculated from the∆ ⟨KP⟩ matrix associated with each physical parameter and its causes can beexplained and quantified component by component.

This operation is completely new in Thermoeconomics or in any energy analysistechnique. Thus, the malfunction matrix has a very important engineering applicationand also introduces new theoretical ideas in Thermoeconomics (see Chapter 7).

6.3.2 Thermoeconomic optimization

Here we describe strategies for optimizing complex systems as proposed by Lozanoet al. (1996). They are based on sequential optimization from component tocomponent using the Thermoeconomic Isolation Principle (Evans, 1980).

A component of a thermal system is thermoeconomically isolated from the rest of thesystem if the product of the component and the unit cost of its resources (internalproduct and/or external resources) are constant and known quantities. If a unit of athermal system is thermoeconomically isolated, the unit may be optimized by itself(without considering the modifications of other variables of the rest of the system)and the optimun solution obtained for the unit coincides with the optimum solutionfor the whole system.

∆ ∆ ∆F k P k PT P j jir

ij

n

r LP j ji

ri

j

n

r Li i

≡ +=∈ =∉∑∑ ∑∑,

*,

*κ κ0

0

0

0

Thermoeconomics


Of course, TI (Thermoeconomic Isolation) is an ideal condition which cannot beachieved in most of the real systems: Pj and k*

P,i change when design variables ofother components change, due to feedback. But the more constant Pj and k*

P,i are, thecloser to TI conditions and the fewer iteration loops needed to achieve the optimalsolution for the whole system. Thus, the goal is not to achieve TI but to approach it asmuch as possible in order to obtain maximum advantages, which include:

1. Improvements and optimal design of individual units in highly interdependentcomplex systems are greatly facilitated, as well as of whole systems.

2. The designers can be specialized and their efforts concentrated on designing thevariables of single units, while resting assured that these efforts yield optimumdesign and/or improve the overall system.

3. The convergence of the solution is faster.

To optimize individual units, the objective function of the cost of product of thecomponent –j– could be defined as:

(6.57)

where the unit cost of the input resources and the production Pj are known andconstant.

In real world optimization problems, the design free variables do not necessarilycoincide with the technical production coefficients. In practice there will be afunction of the actual design free variables which can be named –x–.

We say that a free variable x is a local variable of a subsystem –j– when theproduction coefficients κij of this subsystem only depend on x. When a designvariable is attached to several subsystems, the previous expression must be extendedto all concerned subsystems.

To determine whether a design free variable is local or not and which components areinvolved, the cost resource impact of the design variables to each component can becomputed:

(6.58)

Minκ

κ ij kP i,*

i 0=

n

∑

Pj

kP i,*

∆C0 j,x

kP i,* ∂κ ij

∂x---------

∂κZP j,

∂x--------------+

i 0=

n

∑

P ∆x=



and the ratio calculated:

(6.59)

If this ratio is equal (or close) to 1, the design variable is local for component –j–, if itis equal (or close) to zero, the design variable is independent of the referred jcomponent. In other cases the design variable involves several components.

These ideas could be used to design a strategy for global optimization problems:

1. Determine which variables are local and which are regional (involve several com-ponents)

2. Determine a sequence for local optimization of each component

3. Take an initial value of the design variables

4. Calculate technical production coefficients and unit product cost

5. Find optimum values for local variables

6. Find optimum values for global variables

7. Iterate from (3) to convergence when design variables or unit product cost do notvary in the next iteration. In each iteration the unit cost of total product mustdecrease.

ε jx ∆ C0 j,

x

∆ C0 i,x

i 1=

n

∑-------------------------=


CHAPTER 7

Thermoeconomic analysis ofa dual-purpose power anddesalination plant

The basic concepts and fundamentals of Thermoeconomics were explained inChapter 6 and will now be applied to a dual-purpose power and desalination plant; themost important contribution of this Ph. D. Thesis. During the 60’s and early 70’sEvans (1962), Tribus (Tribus et al., 1960; Tribus and Evans, 1963) and El-Sayed (El-Sayed and Aplenc, 1970; El-Sayed and Evans, 1970) laid down the seminal ideas ofThermoeconomics and applied them to the desalination processes. Tribus firstproposed the term ‘

Thermoeconomics

’. Since then, Thermoeconomic techniques havebeen developed and applied mostly to power plants. This thesis represents the mostcomplete and rigorous thermoeconomic analysis ever made on a complex energysystem and more specifically on a dual-purpose power and desalination plant. Itencompasses the whole range between an energy audit based on a detailed costanalysis, up to a thermoeconomic optimization, via a thermoeconomic diagnosis ofseveral plant component failures.

The first section of this chapter includes the resolution of the thermoeconomic modelfor the power and desalination plant. The steps to build and solve the thermoeconomicmodel are described in detail.

The second section contains an in depth cost analysis of the most significant operatingmodes governing the power and desalination plant (including operational andinvestment capital costs) in order to quantify the efficiency of each operation mode.This is used to calculate the physical (and therefore more realistic) value of theresources consumed to produce every flowstream inside the plant, which is the key toan energy audit. An inefficient process can be located and quantified in terms of fuelplant consumption. Eight different operating modes were considered in the dual-purpose plant, covering the whole range of the diverse combinations:

Thermoeconomic analysis of a dual-purpose power and desalination plant

160


• In the first case, the plant only produced electricity. The second case was theopposite: the plant was like a pure distillation unit, producing only desaltedwater.

• The third to sixth cases studied the effect of partial load operation on theefficiency of the installation, starting from maximum production to the minimumload of water and electricity demand.

• The seventh and eighth cases considered the effect of the cleaning ball system onthe MSF evaporators. In both cases, some live steam was throttled in the HPreduction station corresponding to the maximum load of extracting live steam toa second MSF unit.

Non-operating costs were added to the calculated exergy costs. We compared ourthermoeconomic method with other indirect methods that calculate product costs asthe accounting of expenses in plant exploitation: fuel, maintenance, amortization,etc., divided by the total plant production.

The third section of this chapter describes a complete thermoeconomic diagnosis ofthe inefficiencies in the units of the power and desalination plant. Not only was theadditional fuel consumption due to the inefficiency calculated (impact on fuelanalysis), but also the effect on the behavior of other plant units. This effect wasseparated in different contributions over the rest of devices: malfunctions (inducedand intrinsic malfunctions) and dysfunctions. Four different loads in the power plantwere considered and two distillate productions in the MSF plant. These examplesencompass the most significant operating conditions. Each study considered fiveinefficiencies corresponding to five components of the power plant and threeinefficiencies in the MSF plant.

The fourth section applies the thermoeconomic technique based on localoptimization. The local optimization of energy systems is very valuable to find theoptimum operating conditions. The plant can be optimized by minimizing the cost ofthe product of each unit, starting from real operating conditions.

The fifth section analyzes the concepts of price and cost. They were distinguished inorder to obtain the maximum benefit in plant exploitation.

Finally, the last section contains the conclusions and some ‘

operation recommenda-

tions

’ from the thermoeconomic analysis. These are very useful to guide managers insaving energy and achieving a more cost-effective operation of a dual-purpose plantoperation.

Thermoeconomic model


161

7.1 Thermoeconomic model

A thermoeconomic model mathematically represents the productive structure of aplant. This structure is a graphical representation of the resource distribution. Itsflows describe the

productive relationship

among components based on the physicalstructure, although they are not forced to coincide with the existing physical flows ofthe plant.

The thermoeconomic model should logically be defined after the physical structure(section 7.1.2). Then the productive structure is built (section 7.1.3) along with thesystem of characteristic equations that mathematically describe the productivestructure of the plant (section 7.1.4). Before considering the complex thermoeco-nomic model of the dual plant, a very simple thermoeconomic model of a co-generation system is included in section 7.1.1. It is a simple example of how to builda thermoeconomic model and calculate the cost of live steam, water and electricity.These can be compared with other methodologies that only account for the cost of thefinal products (water and electricity) with external information or othersimplifications (see section 7.2.5).

7.1.1 A simple co-generation system

A steam generator (boiler), a steam turbine and the MSF plant can represent a verysimple dual-purpose desalination plant. Auxiliary non-producer elements like heaters,pumps or condensers are not included in the scheme. The productive structure infigure 7.1 can be built using the F-P definitions in table 7.1. The availability of thesteam generated in the boiler is sent to the two productive units (steam turbine andMSF desalination unit). The fuel and product definition and the characteristic andexergy cost equations of every component of the system are included in table 7.1.

FIGURE 7.1

Productive structure of the simple co-generation system.

AB1

B2

B1 – B2

C1

W

D

1

3

2

Boiler

MSF unit

Steam turbine


162


The results of the model (table 7.2) were obtained under maximum continuous rating(MCR). The cost of fuel cf was 2.23

×

10

–6

$/kJ, and the cost of water and electricitywas also expressed in the most commercial units.

The values are very similar to the results of the thermoeconomic model explainedbelow. This simple model can easily calculate the cost of the two main products usingthermoeconomic principles. The only requirement is to introduce the quality of thesteam derived to the MSF unit (from the simulator or an owner’s data sheet).

7.1.2 Physical structure

The physical structure of a plant is similar to a set of subsystems or units linkedamong themselves and to the environment by another set of matter, heat, and workthat express plant behavior more or less accurately, or, in general:

energy system = subsystems or units + matter and/or energy flows

(7.1)

TABLE 7.1

Fuel, product, characteristic equation and exergy cost balance in the simple co-generation system.

Fuel Product Ch. Equation Cost equation

1 Boiler C

1

B

1

C

1

= k

1

B

1

k

1

*

= k

1

cf

A Branching k

A

*

= k

1

*

2 Turbine B

1

– B

2

W B

1

– B

2

= k

2

W k

2

*

= k

2

k

A

*

3 MSF B

2

D B

2

= k

3

D k

3

*

= k

3

k

A

*

TABLE 7.2

Results of the simple co-generation system model, MCR case.

Fuel or product (kW) Unit consumption Exergy cost

C

1

= 455,000 k

1

= 2.244 k

1

*

= 2.244

B

1

= 202,800 k

2

= 1.293k

2

*

= 2.902 (= 0.0233 ($/kWh)B

2

= 45,000 k

3

= 6.553

W = 122,000k

3

*

=14.7 (=151.4 kJ/kg, 0.3377 $/m

3

)D = 6,867



163

The relationship between the flows and subsystems can be set up in a matrixformulation (Lozano and Valero, 1993; Valero et al., 1993), that describes thebalances of matter, energy and exergy in a very compact form.

The more detailed the definition of the physical structure, the better the possibilitiesof analyzing the installation. However, a more detailed physical structure impliesincreasing both the number of measurements to be taken in a performance test(temperatures, pressures, mass flow rates…) and the complexity of calculations. Thegoal is to find an optimum level of aggregation, i.e. level of detailed description in thephysical structure corresponding to the depth of analysis.

The physical structure of the power plant analyzed thermoeconomically is verysimilar to the mathematical model in the simulator (chapter 5). The thermophysicalproperties of the main flowstreams calculated in a simulation can be used asreasonable initial values for a thermoeconomic analysis in an operating condition.Only the gland steam leakage flow is neglected, which is not significant. Figure 7.2shows the physical structure of the power plant. If the power plant is working inparallel or twin-extraction mode (that is, the reducing pressure extraction is working),the pressure reduction station is included in the physical model. Table 7.3 describesthe nomenclature adopted in the previous figure.

FIGURE 7.2

Physical structure of the power plant considered for the thermoeconomic model.


164


TABLE 7.3

Description of components appearing in figure 7.2.

Component no. Initials Description

1 CP Condenser Pump

2 LPH2 Low Pressure Heater No. 2

3 LPH1 Low Pressure Heater No. 1

4 DRT Deaerator

5 FP Feed Pump

6 HPH2 High Pressure Heater No. 2

7 HPH1 High Pressure Heater No. 1

8 VEX4 4

th

extraction valve

9 VEX3 3

rd

extraction valve

10 VEXD Extraction valve to deaerator

11 VEX2 2

nd

extraction valve

12 VEX1 1

st

extraction valve

13 VF Feed valve

14 BOI Boiler

15 VB Boiler valve

16 VST Stop valve

17 BHP Brine heater pump

18 HPT1 High pressure turbine (1

st

section)


nd

section)


rd

section)


th

section)

22 LPT1 High pressure turbine (1

st

section)

23 LPT2 High pressure turbine (2

nd

section)

24 CND Condenser

25 GEN Generator

26 MSF Desalination unit (multistage flash)

27 VS1 1

st

Reducing pressure valve (steam)

28 VS2 2

nd

Reducing pressure valve (vac.)

29 VS3 3

rd

Reducing pressure valve (FP)



165

However, the physical model considered for the thermoeconomic analysis of theMSF unit (figure 7.3) differs from the mathematical model implemented in thesimulator. The physical model treats the recovery and reject sections as a uniquecomponent. If these sections are divided into stages, a huge productive structure isgenerated in the plant. Since the functionality of each stage is identical, thispossibility of plant dissagregation is not considered. Consequently, the input/outputvalues of the recovery and reject sections in the simulator can be used as the basis ofthe analysis (their operating data are also available). The pump system of thedistillation unit is also considered. Exit conditions of these pumps are calculated inthe thermoeconomic model with their characteristic charts.

FIGURE 7.3

Physical structure of the MSF plant considered for the thermoeconomic analysis.

Table 7.4 further describes the meaning of figure 7.3.

TABLE 7.4

Components description from figure 7.3. Note that component no. 1 is not described in physical model but is included in other schemes.

Component no. Initials Description

2 BH Brine heater

3 RP Recycle brine pump

4 BDP Blowdown pump

5 RCS Recovery section

6 MIX Mixer

7 RJS Reject section

8 SWP Seawater pump

9 DP Distillate pump

10 MXT Mixer (temper water)

11 TP Tempering pump


166


7.1.3 Productive structure

A plant is more than a set of flows and units. Each unit has a particular productivefunction which contributes to final production. We will clearly indicate which flow orcombination of flows constitute the product of the unit (P), which ones are theresources or fuel consumed (F) and which flows are the losses (L), i.e. those thatleave the unit and plant and are not subsequently used.

The productive structure contains the mathematical definition of the function of eachcomponent. The production objective (product) and the resources needed (fuel) todevelop its function are defined for each device, which is equivalent to definingefficiency. The productive structure also includes the distribution of consumedresources in the different units and how plant products are obtained.

The best F-P-L definition to represent unit productive function is obtained bysimultaneously examining their own energy transformation. Using the F-P-Ldefinition and the data from the design and operation, it is possible to carry out theenergy and exergy analysis of the plant.

The productive structure can be explained in a diagram with squares representingphysical plant units (productive and dissipative physical processes), and circles andrhombuses that are not physical components of the plant. The lines connecting thedifferent productive units are exergy resources (fuels and products). The inlet arrowsgoing into squares are the fuels of the corresponding components and outlet arrowsrepresent products. The circles are branching points where the exergy resource isdistributed to other components. In every junction (rhombus), a significant exergyresource is obtained by the addition of others of the same nature but different origin.

To apply an on-line thermoeconomic analysis (as presented in Chapter 7) to the dualplant, the thermoeconomic model should be disaggregated to a deep enough decisionlevel to make use of the most important data provided by the data acquisition system.The data acquisition system of the plant is clearly insufficient to provide the datarequired by the productive structure defined in section 7.1 for the power anddesalination plant. For this reason all required data were provided by the modelpresented in chapters 3 to 5, as if they were measured data provided by the plantacquisition system.

7.1.3.1 Steam power plant

Depending on the analysis, a productive structure can be designed in different detailor

aggregation levels

. For instance, in a thermoeconomic analysis of a power plant,the MSF plant is considered a single plant unit in the productive structure.The minimum aggregation level is considered for the MSF plant in the productivestructure of the power plant. The F-P definition used for the power plant follows thetrend adopted in conventional steam power plants. The difference between thermal,



167

mechanical and chemical exergy was not considered in the power and desalinationplant when the productive structure of the system was built. However, a loweraggregation level was used in the thermoeconomic analysis of the MSF unit withseveral plant units. The F-P-L definition of the steam power plant components ispresented in figure 7.4, where B is the exergy flow of a stream (its mass flow rate mmultiplied by its specific exergy b), W is the work consumed or generated in acomponent, DB is the exergy flow of fresh water leaving the MSF, S is the entropyflow of a stream (mass flow m multiplied by the specific entropy s). Exergy losses (L)are considered but do not explicitly appear in the productive structure.

FIGURE 7.4

F-P description in steam power plant.

The fuel and product of each device is defined depending on the functionality of thecomponent (Frangopoulos, 1990). Thus, the heater is a component installed to heatfeedwater (B

4

– B

1

) in a Rankine cycle, with extracted steam supplied by the turbine,which is condensed inside the heater (B

2

– B

5

). If the heater has a drain from anotherheater, the fuel also incorporates its exergy flow (B

3

). The job of a steam turbine is toproduce work (W) by exhausting the steam from a boiler (B

1

– B

2

). A pump has theinverse functionality: it uses work (W) as the fuel to increase the pressure of a fluid(B

2

– B

1

). A generator is an energy converter, therefore, the fuel is the primary(mechanical) energy (W

1

) and the product is secondary (electrical) (W

2

). A valve is a



dissipative component. It undergoes exergy losses when the fuel (B2) passes throughthe valve (B1). The fuel and product in a boiler are very clear. A boiler uses primaryenergy like natural gas (Bgas) to boil and superheat the feedwater in a steam cycle(B2 -- B1). The deaerator is a heater with a mixing process of several flows. Theproduct is the heating of the colder streams ((m1 + m2) b3 – m1 b1 – m2 b2) and thefuel is the heat released by hotter streams (m4 b4 + m5 b5 – (m4 + m5) b3).

The condenser is a dissipative unit which condensates the steam coming from thesteam turbines to produce liquid water. The heat released (Q) has a low temperatureand is thus rejected to the atmosphere without any further application. From athermodynamic point of view, the condenser function allows the working fluid(water) to reach the physical conditions to perform a new thermodynamic cycle. Forthis reason, several authors (Frangopoulos, 1983; Von Spakovsky, 1986; Benelmir,1989) propose negentropy as the condenser product. The negentropy is athermodynamic function (Frangopoulos, 1983) with exergy or energy dimensions butwith entropy reduction of water/steam in the condenser. The water/steam entropy isincreased in other plant components. As a result, their negentropy consumption isprimarily produced in the condenser. The amount of negentropy consumed in acomponent is proportional to its entropy increase. In summary, the exergy losses ofthe different flows entering the condenser are the fuel of the device (B1 + B2 + B3 –B4). The negentropy produced is the condenser product (T0 (S4 – S3 – S2 – S1)).Finally, the MSF is treated as a component whose main purpose is to producefreshwater (DB) using different flows of steam and electricity (B1 + B2 – B3 + W). Asthe steam (B3) is condensed in the heater of the distillation unit, some negentropy isgenerated in this process (S) which is a secondary product of the MSF (auxiliaryproduct or byproduct).

From the point of view of the diagnosis, the selected productive structure isindependent of the final results (Valero et al., 1999). The maximum aggregation levelprovides the product and fuel formation cost of each component in the steam plant.Although it is complicated to construct a productive structure with a maximumaggregation level, it provides the best information to understand the behavior of theindividual components of a power plant.

The productive structure is made up of components with exergy added to the workingfluid of the power plant (steam/water). In this case, the components of the exergyaddition are the boiler, heaters, deaerator and pumps. The amount of exergy suppliedto the working fluid is added in a junction and then redistributed (using branchingpoints) to the components where the exergy is removed from the working fluid to bemixed with another flow or used as fuel of a component. The components of exergyremoval in the steam cycle with co-generation are the turbine sections, the condenser,the MSF unit and the pressure losses in tubes. Finally, a junction is settled to pick upthe work produced in the turbine sections and, after passing the generator, isredistributed to the components that need the electrical consumption as fuel (pump or



MSF unit). Only two streams leave the plant: distillate flow (DB) and net outputpower, and one stream enters (the exergy flow of fuel).

Different productive structures were defined for each operating mode becausedifferent plant units depend on it. For instance, the F-P formulation applied to theproductive structure generated for the more realistic mode, generating power andfresh water (extraction mode, see figure 7.5) does not use the live steam reducingpressure station.

FIGURE 7.5 Productive structure of the power plant in extraction mode.

When the power plant is working in condensing mode (only electricity is produced),brine heater pump and MSF components must be removed, and consequently, the J3junction. Figure 7.6 shows the small changes needed to perform the productivestructure of the condensing mode.

When the power plant is working in extraction mode at low loads, the low-pressureturbine is acting as a compressor. As a result, the condenser and 2nd section of thelow-pressure turbine are treated as a component with two fuels: work needed to movethe turbine and the exergy flow lost in the condenser. Figure 7.7 shows the changesapplied to this operating mode with respect to the first structure (figure 7.5).



FIGURE 7.6 Changes applied to extraction mode productive structure (figure 7.5) when the plant operates in condensing mode.

When the power production is less than a minimum (the outlet pressure of the fourthsection of the high-pressure turbine is very low), the reduction pressure station isautomatically opened to maintain steam conditions to the MSF heater (this is theparallel mode). The productive structure in figure 7.7 includes the reduction pressurevalve. Figure 7.8 shows the additional structure added to figure 7.5, which is alsovalid for the twin extraction mode.

FIGURE 7.7 Productive structure corresponding to extraction mode with low energy production in a dual-purpose plant. Changes with respect to figure 7.5.

Finally, in desalination or twin desalination mode (steam power plant not working),the productive structure is quite simple because only six components need to beconsidered to perform the productive structure (see figure 7.9), i.e., those operating inthis mode.

Steam to MSF

Vacuum

BHP

MSF

17

26

J3



FIGURE 7.8 Productive structure of the steam power plant in parallel and twin extraction mode. Changes with respect to figure 7.5.

FIGURE 7.9 Productive structure of the steam power plant in desalination or twin desalination mode.

7.1.3.2 MSF unit

The F-P-L definition of the MSF components is the first step in building theproductive structure, depending on the aggregation level used to solve thethermoeconomic model. In this case, recovery and reject sections are considered onecomponent, independently of the number of their stages. This case could beconsidered an intermediate aggregation level, following the physical model



previously defined in figure 7.3. Figure 7.10 resumes the F-P-L definition applied tothe MSF plant units. For more information of brine exergy calculation see Annex 2.

The recovery and reject sections are complex devices. Their products are very clear:the distillate produced (DB or DB2 – DB1) in each distiller. The resources consumedare the exergy released by the flashing brine, which is partially recovered by thecooling brine ((B1 – B2) – (F2 – F1)), and the steam consumed to hold the distillersbelow atmospheric pressure (vacuum). Distillate from the recovery section (DB1) isalso a fuel component of the reject section. The brine heater gives the final heating tothe brine (B4 – B3) by condensing vapor bled from the turbine (B1 – B2). The mixerdevice produces an outlet stream (B3) by merging two or more inlet streams(B1 + B2).

FIGURE 7.10 F-P definition in the MSF unit.



Some other interpretations of the F-P definitions were considered to select theappropriate productive structure. The objective was to obtain the exact value of theexergy cost of the final product (whose value is independent of the productivestructure) and the F-P definition. But the exergy cost of the intermediate flowstreamsis obviously different when the fuel and product definition of each component and/orthe aggregation level is changed. The most important point is to find out the physicalsense of the flowstreams in the productive structure, in order to explain and study theexergy cost of each flow. Several productive structures were studied in this thesis.

• One possibility is to consider that the exergy recovered in the cooling brine(F2 -- F1) is a component of the product of these components. The fuel of thesesections is the exergy released by the flashing brine (B1 – B2) and the product isthe two effects obtained in the sections (F2 – F1) + DB. This results of thisdefinition are similar to the final F-P definition chosen but it contradicts thefunctionality of the components.

• The heated cooling brine could be considered a subproduct of the recovery andreject sections while maintaining the fuel as in the previous case. The high valueof the subproduct (F2 – F1), (several times the value of distilled water in thesesections) gives nonsense values for the calculated exergy costs.

• Consider a zero exergy cost of the MSF plant residues (fourth proposition of theexergy cost theory, Valero et al., 1986a). The cost of the rejected coolingseawater and blowdown is not charged over the rest of the MSF plantflowstreams. This avoids introducing the fictitious device in the productivestructure of the distillation plant. This consideration is a price allocation becausethe residues are final products external to the system and have zero cost.

• The distilled water in the recovery section may not be considered a fuel of thereject section. The product of the reject section should only be the quantity ofdistilled water produced in that section, not the total amount of freshwaterproduced. This scenario only varies the cost of reject section.

• The system recovery-reject section could be considered a component, in order toavoid the effect of recycling flows in the MSF plant and the modeling of afictitious mixer in the final stage of the distillation plant. This is a higheraggregation level than adopted in this thesis.

• It would not be adequate to consider the chemical exergy of the distillate leavingthe reject section as the final product of the MSF plant. Its low value wouldimply huge exergy operating costs of the rest of the flowstreams inside thedistillers. Furthermore, the analysis of a thermal inefficiency in a distiller cannotbe performed with the F-P definition adopted in this hypothetical assumption.The chemical exergy of freshwater only depends on salt concentration and doesnot vary under thermal inefficiency. The only consequence of a thermalinefficiency is a thermal exergy variation.



The formation of the productive structure of the MSF unit is not easily explained withthe F-P definition considered in the thermoeconomic model (several junctions areneeded to obtain component fuel and product). As the flows circulating by the MSFunit are pumped, the main flows of the plant are added to a junction in which theexergy added by the pump is incorporated to the flow. The most significant branchingpoints of the MSF plant redistribute their product as a fuel for some components ofthe MSF unit. The first one is the cooling brine heated in the brine heater, the secondbranching has the cooling seawater to reject. But the most amazing situation of thisstructure is the non-physical component or fictitious device (FD). It was included atthe beginning of the structure to account for residue costs (blowdown and rejectcooling seawater) in the thermoeconomic model. The cost of steam to brine heater(considered to be the main fuel of the plant) is overcharged by the effect of the twouseless flows sent to sea. The exergy costs of the blowdown and discharged coolingbrine are used and conveniently incorporated into the rest of the internal costs and thefinal product of the MSF unit.

Figure 7.11 shows the productive structure of the MSF plant corresponding to the F-Pdefinition explained above (figure 7.10), the number of junctions and branches are aresult of the F-P definition adopted for the recovery and reject sections. The operatingmodes of the power plant do not affect the productive structure of the desalinationunit, unless the condensing mode is selected (in this case there is no freshwaterproduction).

FIGURE 7.11 Productive structure of the MSF unit.



7.1.4 Thermoeconomic model

The thermoeconomic model is the mathematical representation of the productivestructure. It consists of a group "characteristic equations" which express (for allcomponents in the productive structure) each inlet flow as a function of the outletflows and a set of internal parameters, i.e.:

Unit j: Fi = κij · Pj (7.2)

Junction j: Fi = rij · Pj (7.3)

Branching point j: Fj = ∑ Pi (7.4)

where κ is the technical production coefficient of the unit and r is a structuralparameter in the junctions or exergy ratio. Equation (7.2) provides information about:

• the productive function of each commoponent, i.e. its production (P),

• what the component needs (F) to develop its productive purpose, and

• the thermodynamic efficiency (κ) of the process taking place in the component.

The structural equations (7.3) and (7.4) contain the distribution of the resourcesconsumed by the plant components, i.e. how the components are interconnected froma productive viewpoint.

The Thermoeconomic model of the steam power plant (extraction mode) has one 7.2-type equation for each fuel entering a component (57 equations in total), fourequations for the four junctions and four equations derived from the four branchingpoints in the productive structure (figure 7.5). There are 19 characteristic equations inthe MSF unit model and seven and three equations corresponding to the junctions andbranching points.

The characteristic equations (equations 7.2–7.4) can easily be written using theproductive structure diagram. The subscript numbers of the fuel and productscorrespond to the flow diagram of Chapter 4 (power plant scheme) and Chapter 3(diagram of the MSF plant). Table 7.5 includes the equations that describe thethermoeconomic model of the steam power plant.



TABLE 7.5 Exergy flows and characteristic equations of components in the steam power plant (extraction mode).

Dev. Exergy Flows Characteristic equation(s)

CPPCP = m12 (b12–b11)

FSCP = m12 T0 (s12–s11)

WCP = kBCP * PCP

FSCP = kSCP * PCP

LPH2

PLPH2 = m12 (b14–b12)

FB1LPH2 = m34 (b34–b25)+ mci (bci–b25)

FB2LPH2 = m33 (b23–b25)

FSLPH2 = T0 {m12 (s14–s12) – m34 (s34–s25)

– m33 (s33–s25)– mci (sci–s25)}

FB1LPH2 = kB1LPH2 * PLPH2

FB2LPH2 = kB2LPH2 * PLPH2

FSLPH2 = kSLPH2 * PLPH2

LPH1

PLPH1 = m12 (b15–b14)

FBLPH1 = m33 (b33–b23)

FSLPH1 = T0 {m12 (s15–s14)– m33 (s33–s23)}

FBLPH1 = kBLPH1 * PLPH1

FSLPH1 = kSLPH1 * PLPH1

DRT

PDRT = m12 (b16–b15)+ mdes (b16–brdes)

FB1DRT = m32 (b32–b16)

FB2DRT = (m30 + m31) (b22–b16)

FSDRT = T0 {m20 s16 –(m30 + m31) s22 –m12 s15

– m32 s32 – mdes srdes}

FB1DRT = kB1DRT * PDRT

FB2DRT = kB2DRT * PDRT

FSDRT = kSDRT * PDRT

FPPFP = m20 (b17–b16)

FSCP = m20 T0 (s17–s16)

WFP = kBFP * PFP

FSFP = kSFP * PFP

HPH2

PHPH2 = m20 (b19–b17)

FB1HPH2 = m31 (b31–b22)

FB2HPH2 = m30 (b21–b22)

FSHPH2 = T0 {m20 (s19–s17)–m31 (s31–s22)

– m30 (s21–s22)}

FB1HPH2 = kB1HPH2 *PHPH2

FB2HPH2 = kB2HPH2 * PHPH2

FSHPH2 = kSHPH2 * PHPH2

HPH1

PHPH1 = m20 (b20–b19)

FBHPH1 = m30 (b30–b21)

FSHPH1 = T0 {m20 (s20–s19)–m30 (s30–s21)}

FBHPH1 = kBHPH1 * PHPH1

FSHPH1 = kSHPH1 * PHPH1

VEX4

PVEX4 = m34 (b34–b25) + mci (bci–b25)

FBVEX4 = m34 (b8–b25) + mci (bci–b25)

FSVEX4 = T0 m34 (s34–s8)

FBVEX4 = kBVEX4 * PVEX4

FSVEX4 = kSVEX4 * PVEX4

VEX3

PVEX3 = m33 (b33–b23)

FBVEX3 = m33 (b6–b23)

FSVEX3 = T0 m33 (s33–s6)



VEXD

PVEXD = m32 (b32–b16)

FBVEXD = m32 (b5–b16)

FSVEXD = T0 m32 (s32–s5)

FBVEXD = kBVEXD * PVEXD

FSVEXD = kSVEXD * PVEXD



VEX2

PVEX2 = m31 (b31–b22)

FBVEX2 = m31 (b4–b22)

FSVEX2 = T0 m31 (s31–s4)



VEX1

PVEX1 = m30 (b30–b21)

FBVEX1 = m30 (b3–b21)

FSVEX1 = T0 m30 (s30–s3)



VF

PVF = m12 (b28–b11) + (m20–m12) (b28–b16)

FBVF = m12 (b20–b11) + (m20–m12) (b20–b16)

FSVF = T0 m20 (s28–s20)

FBVF = kBVF * PVF

FSVF = kSVF * PVF

BOIPBOI = m20 (b29–b28)

FSBOI = T0 m20 (s29–s28)

C1 = kBBOI * PBOI

FSBOI = kSBOI * PBOI

VB

PVB = m12 (b1–b11) + (m20–m12) (b1–b16)

FBVB = m12 (b29–b11) + (m20–m12) (b29–b16)

FSVB = T0 m20 (s1–s29)

FBVB = kBVB * PVB

FSVB = kSVB * PVB

VST

PVST = m12 (b1’–b11) + (m20–m12) (b1’–b16)

FBVST = PVB

FSVB = T0 m20 (s1’–s1)

FBVST = kBVST * PVST

FSVST = kSVST * PVST

BHPPBHP = mdes (brdes–bdes)

FSBHP = T0 mdes (srdes–sdes)

WBHP = kBBHP * PBHP

FSBHP = kSBHP * PBHP

HPT1FBHPT1 = m20 (b1’–b3)

FSHPT1 = T0 m20 (s3–s1’)

FBHPT1 = kBHPT1 * WHPT1

FSHPT1 = kSHPT1 * WHPT1

HPT2FBHPT2 = (m20–m30–mva) (b3–b4)

FSHPT2 = T0 (m20–m30–mva) (s4–s3)



HPT3FBHPT3 = (m20–m30–mva–m31) (b4–b5)

FSHPT3 = T0 (m20–m30–mva–m31) (s5–s4)



HPT4FBHPT4 = (m20–m30–mva–m31–m32) (b5–b6)

FSHPT4 = T0 (m20–m30–mva–m31–m32) (s6–s5)



LPT1FBLPT1 = (m9 + m34) (b6–b8)

FSLPT1 = T0 (m9 + m34) (s8–s6)

FBLPT1 = kBLPT1 * WLPT1

FSLPT1 = kSLPT1 * WLPT1

LPT2FBLPT2 = m9 (b8–b9)

FSLPT2 = T0 m9 (s9–s8)

FBLPT2 = kBLPT2 * WLPT2

FSLPT2 = kSLPT2 * WLPT2

CND

PCND = T0 {m9 s9 + (m34 + m33 + mci) s25

+ mva sva –m12 s11}

FBCND = m9 b9 + (m34 + m33 + mci) b25

+ mva bva – m12 b11

FBCND = kBCND * PCND





The physical model of the thermoeconomic analysis differs from the mathematicalmodel presented in Chapter 3. Figure 7.12 shows the exergy flows considered in thethermoeconomic model of the MSF plant (which also appear in the characteristicequations in table 7.6). We used the flow nomenclature adopted in Chapter 3.

FIGURE 7.12 Physical model considered in the thermoeconomic analysis of the MSF plant.

GENWT = WHPT1 + WHPT2 + WHPT3

+ WHPT4 + WLPT1 + WLPT2WT = kGEN * PGEN

MSF

FB1MSF = mdes (b6–bdes)

FB2MSF = mva (b3–bva)

FSMSF = T0 {mdes (sdes–s6)+ mva (sva–s3)}

WMSF = kB3MSF * PD

FB1MSF = kB1MSF * PD

FB2MSF = kB2MSF * PD

FSMSF = kSMSF * PD

A FBJ3 = mdes (b6–b16)

PVST = FBVEX4 + FBVEX3 + FBVEX2 + FBVEX1

+ FBVEXD + FB2LPH2 + FB2DRT + FB2HPH2

+ FBHPT1 + FBHPT2 + FBHPT3 + FBHPT4

+ FBLPT1 + FBLPT2 + FBJ3 + FBCND+FB2MSF

B PDRT = m12 (b16–b15) + mdes (b16–brdes)

C PGEN = WTN + WFP + WCP +WMSF +WBHP

J1

FVF = rFP * PFP + rLPH2 * PLPH2 + rLPH1

* PLPH1 + rDRTj1* m12 (b16–b15)+ rCP * PCP + rHPH2 * PHPH2 + rHPH1 * PHPH1

J2 FVB = rVF * PVF + rBOI * PBOI

J3FB1MSF = rJ3 * FBJ3 + rDRTj3* mdes

(b16–brdes) + rBHP * PBHP

J4

WT = rHPT1 * WHPT1 + rHPT2 * WHPT2

+ rHPT3 * WHPT3 + rHPT4 * WHPT4

+ rLPT1 * WLPT1 + rLPT2 * WLPT2





TABLE 7.6 Exergy flows and characteristic equations for the components of the MSF plant.

Devices Exergy flows Characteristic equation(s)

FD

PFD = mdes (b6 – bdes) ≡ FB1MSF

F1FD = PFD

F2FD = BD b10

F3FD = CW b13

F1FD = k1FD * PFD

F2FD = k2FD * PFD

F3FD = k3FD * PFD

BHPBH = R (b4 – b3)

FBH = PFDPBH = kBH * PBH

RP PRP = R (b7 – b8) WRP = kRP * PRP

BDP PBDP = BD (b10 – b8) WBDP = kBDP * PBDP

RCS

PRCS = Drcs b5

F1RCS = R b4 – (R – Drcs) b6 – R (b3 – b7)

F2RCS ≡ 0.5 FB2MSF

F3RCS = 0.5 mvent b15

F1RCS = k1RCS * PRCS



MIX

PMIX = R b8

F1MIX = (R – D – BD) b9

F2MIX = F b13

F1MIX = k1MIX * PMIX

F2MIX = k2MIX * PMIX

RJS

PRJS = D b11

F1RJS = (R – Drcs) b6 – (R – D) b9 + Drcs b5

– SR (b13 – b17)

F2RJS = 0.5 FB2MSF

F3RJS = 0.5 mvent b15

F1RJS = k1RJS * PRJS



SWP PSWP = SW (b15 – b16) WSWP = kSWP * PSWP

DP PDP = D (b12 – b11) WDP = kDP * PDP

MXT

PMXT = SR b17

F1MXT = TP b14

F2MXT = (SW – mvent) b15

F1MXT = k1MXT * PMXT

F2MXT = k2MXT * PMXT

TP PTP = TP (b14 – b13) WTP = kTP * PTP

JA

PJA = F2FD

F1JA = PBDP

F2JA = BD b8

PJA = r1JA * F1JA + r2JA * F2JA



7.2 Cost analysis

Thermoeconomic analysis combines the First and Second Law of Thermodynamicsalong with monetary cost balances at the system component level. It helps tounderstand the process of cost formation, minimize overall product costs and assesscosts of the different products obtained in the processes. The cost accounting methodcan calculate costs using rough data from an energy system control room (pressures,temperatures, mass flow rates, electrical production, fuel consumption, excess ofoxygen etc. and the economic data).

The costs of all significant mass and energy flowstreams is a very powerful andinteresting piece of information about the amount of resources used to obtain each

JB

PJB = R b4 – R (b3 – b7)

F1JB = PBH

F2JB = PRP

F3JB = PMIX

PJB = r1JB * F1JB + r2JB * F2JB

+ r3JB * F3JB

CF1JD = (R – Drcs) b6 – (R – D) b8 – SR (b13 – b17)

F1JI = SR (b13 – b17)

PJB = F2JA + F1JD + F1RCS + F1JI

+ F1MIX

JDPJD = F1RJS

F2JD = PRCSPJD = r1JD * F1JD + r2JD * F2JD

E F1JK = TP b13 PJI = F3FD + F1JK + F2MIX

JG

PJG = SR b15

F1JG = PSWP

F2JG = SR b16

PJG = r1JG * F1JG + r2JG * F2JG

H PJG = F3RCS + F3RJS + F2MXT

JIPJI = SR b13

F2JI = PMXTPJI = r1JI * F1JI + r2JI * F2JI

JJ

PJJ = PD = D b12

F1JJ = PRJS

F2JJ = PDP

PJJ = r1JJ* F1JJ + r2JJ * F2JJ

JKPJK = F1MXT

F2JK = PTPPJK = r1JK * F1JK + r2JK * F2JK

TABLE 7.6 Exergy flows and characteristic equations for the components of the MSF plant.

Devices Exergy flows Characteristic equation(s)

Cost analysis


significant mass and energy flowstream. Knowing the costs of the mass and energyflowstreams is the key to thermoeconomic analysis. The first consequence is priceassessment of the products based on physical criteria.

7.2.1 Exergy costs allocation

Valero et al. (1986a) present the fundamental problem of cost allocation as follows:Given a system whose limits have been defined and a level of aggregation thatspecifies the subsystems which constitute it, how to obtain the cost of all the flows thatbecome interrelated in this structure.

The origin of every cost lies in the irreversibility of the processes. This is acornerstone in thermoeconomics. But how do we link the variation in the localirreversibility (∆Ii) to the increase of resources consumed (∆FT)?

Two factors are added to consider the economic: market prices (cf), which are notnecessarily linked to the exergy of the processed resources and depreciation, andmaintenance costs of the productive process (Z). The thermoeconomic cost of a flowcan be calculated after the second factor is introduced (section 7.2.3). The exergycosts calculated in this section only take into account the fuel consumed to produceeach flowstream.

Valero et al (1986a) also propose a rational procedure to determine the cost of allmass and energy flowstreams based on four propositions presented in the ‘Theoryof exergetic cost’. Consider a plant with n units and m flows with known exergyflows. The set of balances of exergy costs (P1 proposition) of the n units provides asystem of n equations. The number of flows will be higher than the number ofunits, and (m – n) auxiliary equations will be needed to determine flow cost. Serra(1994) demonstrated that the rest of the required equations are obtained from theproductive structure of the plant through the F-P-L definition of its units and thesubsequent application of the Theory of exergetic cost.

The Structural Theory of Thermoeconomics (Valero et. al, 1993) based on the rules ofmathematical derivation provides exactly the same system of cost equations.Consequently, this theory can calculate flow cost of the above four propositions bysimply applying the chain rule of derivatives to the characteristic equations of thethermoeconomic model (as explained in Chapter 6). The system of equationsproviding the exergy costs of the steam power plant (cost of the flows appearing inthe productive structure depicted in figure 7.5) is shown in table 7.7. Note thatnegentropy is included in the cost equation of each component as a second fuel. Thenegentropy generated in the condenser must be allocated to the rest of the plantcomponents as a function of their entropy increase.



TABLE 7.7 System of equations providing the unit exergy costs of the steam power plant (extraction mode).

Device Exergy cost balance

CP = kBCP + kSCP

LPH2 = kB1LPH2 + kB2LPH2 + kSLPH2

LPH1 = kBLPH1 + kSLPH1

DRT = kB1DRT + kB2DRT + kSDRT

FP = kBFP + kSFP

HPH2 = kB1HPH2 + kB2HPH2 + kSHPH2

HPH1 = kBHPH1 + kSHPH1

VEX4 = kBVEX4 + kSVEX4


VEXD = kBVEXD + kSVEXD



VF = kBVF + kSVF

BOI = kBBOI + kSBOI

VB = kBVB + kSVB

VST = kBVST + kSVST

BHP = kBBHP + kSBHP

HPT1 = kBHPT1 + kSHPT1




kCP* kCPw

* kCPs*

kLPH2* kVEX4

* kLPH2v* kLPH2s

*

kLPH1* kVEX3

* kLPH1s*

kDRT* kVEXD

* kDRTv* kDRTs

*

kFP* kFPw

* kFPs*

kHPH2* kVEX2

* kHPH2v* kHPH2s

*

kHPH1* kVEX1

* kHPH1s*

kVEX4* kVEX4v

* kVEX4s*

kVEX3* kVEX3v

* kVEX3s*

kVEXD* kVEXDv

* kVEXDs*

kVEX2* kVEX2v

* kVEX2s*

kVEX1* kVEX1v

* kVEX1s*

kVF* kJ1

* kVFs*

kBOI* kFUEL

* kBOIs*

kVB* kJ2

* kVBs*

kVST* kVB

* kVSTs*

kBHP* kBHPw

* kBHPs*

kHPT1* kHPT1v

* kHPT1s*

kHPT2* kHPT2v

* kHPT2s*

kHPT3* kHPT3v

* kHPT3s*

kHPT4* kHPT4v

* kHPT4s*

Cost analysis


In the system of equations providing the exergy costs of the MSF plant (table 7.8), thenegentropy does not appear, although the brine heater is acting as a plant condenser.The negentropy decreases energy waste in the condenser and improves the powerplant efficiency.

LPT1 = kBLPT1 + kSLPT1

LPT2 = kBLPT2 + kSLPT2

CND = kBCND

GEN = kBGEN

MSF = kB3MSF + kB1MSF + kB2MSF + kSMSF

J1 = rFP + rLPH2 + rLPH1 + rDRTj1 + rHPH2

+ rHPH1 + rCP

J2 = rVF + rBOI

J3 = rDRTj3 + rVA + rBHP

J4 = rHPT1 + rHPT2 + rHPT3 + rHPT4 + rLPT1

+ rLPT2

A

= = = = = = =

= = = = = = =

= =

B = = = =

C = =

D

= = = = = = =

= = = = = = =

= = = = = = =

= = =

TABLE 7.7 System of equations providing the unit exergy costs of the steam power plant (extraction mode).

Device Exergy cost balance

kLPT1* kLPT1v

* kLPT1s*

kLPT2* kLPT2v

* kLPT2s*

kCND* kCNDv

*

kGEN* kJ4

*

kMSF* kMSFw

* kJ3* kMSFv

* kMSFs*

kJ1* kFP

* kLPH2* kLPH1

* kDRTJ1* kHPH2

*

kHPH1* kCP

*

kJ2* kVF

* kBOI*

kJ3* kDRTJ3

* kJ3v* kBHP

*

kJ4* kHPT1

* kHPT2* kHPT3

* kHPT4* kLPT1

*

kLPT2*

kVST* kLPH2v

* kDRTv* kHPH2v

* kVEX4v* kVEX3v

* kVEX2v* kVEX1v

*

kHPT1v* kHPT2v

* kHPT3v* kHPT4v

* kLPT1v* kHPT2v

* kCNDv*

kMSFv* kJ3v

*

kGEN* kFPw

* kCPw* kMSFw

* kBHPw*

kDRT* kDRTJ1

* kDRTJ3*

kCND* kCPs

* kLPH1s* kLPH2s

* kDRTs* kFPs

* kHPH1s* kHPH2s

*

kVEX4s* kVEX3s

* kVEXDs* kVEX2s

* kVEX1s* kVFs

* kBOIs*

kVBs* kVSTs

* kBHPs* kHPT1s

* kHPT2s* kHPT3s

* kHPT4s*

kLPT1s* kLPT2s

* kMSFs*



TABLE 7.8 System of equations providing the exergy costs of the MSF plant (figure 7.11).

Components Exergy cost equations

FD = k1FD + k2FD + k3FD

BH = kBH

RP = kRP

BDP = kBDP

RCS = k1RCS + k2RCS + k3RCS

MIX = k1MIX + k2MIX

RJS = k1RJS + k2RJS + k3RJS

SWP = kSWP

DP = kDP

MXT = k1MXT + k2MXT

TP = kTP

JA = r1JA + r2JA

JB = r1JB + r2JB + r3JB

JD = r1JD + r2JD

JG = r1JG + r2JG

JI = r1JI + r2JI

JJ = r1JJ + r2JJ

Jk = r1JK + r2JK

C = = = = =

E = = =

F = = =

kFD* kST

* kJA* kFDf 3

*

kBH* kFD

*

kRP* kW

*

kBDP* kW

*

kRCS* kRCSf 1

* kVA* kRCSf 3

*

kMIX* kMIXf 1

* kMIXf 2*

kRJS* kJD

* kVA* kRCSf 3

*

kSWP* kW

*

kDP* kW

*

kMXT* kJK

* kMXTf 2*

kTP* kW

*

kJA* kBDP

* kJAf 2*

kJB* kBH

* kRP* kMIX

*

kJD* kJDf 1

* kRCS*

kJG* kSWP

* kSW*

kJI* kJIf 1

* kMXT*

kJJ* kRJS

* kDP*

kJK* kJKf 1

* kTP*

kJB* kJAf 2

* kJDf 1* kRCSf 1

* kJIf 1* kMIXf 1

*

kJI* kMIXf 2

* kFDf 3* kJKf 1

*

kJG* kRCSf 3

* kRJSf 3* kMXTf 2

*

Cost analysis


7.2.2 Exergy cost analysis

We calculated the exergy costs for the productive structure in figure 7.5 and analyzedthem under eight different operating conditions with equations in table 7.7. They areexpressed in energy units and represent the amount of resources (usually natural gas)consumed to obtain each significant mass and energy flowstream. These onlyrepresent the operation costs (they do not include the cost of each plant device) interms of energy.

The thermodynamic properties of the mass and energy flowstreams (figures 7.2and 7.3) were obtained by the simulator. The main features of each case are shown intable 7.9. Most of them correspond to a performance data case of the power plant,already described in Chapter 4.

Most case studies corresponded to the limited operating conditions. The operatingmode in each study was as follows:

Case 1 The plant was only working as a full load power plant with no distilledwater production (condensing mode).

Case 2 The opposite of case 1. The plant was working as a pure distillationunit, producing only fresh water (desalination mode).

Case 3 The nominal case: the plant was working at full load producing themaximum distilled water and maximum power (extraction mode).

Case 4 The more usual operating conditions in winter (parallel mode).

TABLE 7.9 Case studies of the exergy cost analysis (PTC: Performance Test Case of the dual plant; Gc: Natural gas consumed; CBS: Cleaning Ball System was used).

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

PTC MR ODOB MCR MSL4 PL85 — MSL3 —

W (kW) 146,693 — 122,000 75,440 91,000 53,500 76,500 71,000

mls (kg/s) 156.187 70.38 156.187 109.5 117.39 70.0 170.0 160.0

Gc (Nm3/h) 43,090 22,780 43,460 31,560 33,650 20,850 49,340 49,390

LS (GCal/h) 0.0 150.0 0.0 0.0 0.0 0.0 150.0 150.0

mdes (kg/s) 0.0 88.5 89.68 88.63 75.62 41.7 83.0 73.5

Pc (bar) 0.135 — 0.072 0.021 0.055 0.048 0.048 0.048

D (T/h) — 2,418.0 2,418.0 2,418.0 2,060.0 1,216.3 2,260.5 2,309.5

TBT (º C) — 112.0 112.0 112.0 100.0 84.0 112.0 112.0

SW (º C) — 25.0 25.0 25.0 25.0 32.0 32.0 32.0

CBS NO NO NO NO NO NO NO YES



Case 5 Partial load operating conditions (extraction mode).

Case 6 Minimum load operating conditions (parallel mode).

Cases 7&8 The effect of the cleaning ball system was analyzed. In both cases somelive steam was throttled in the reducing pressure station: the maximumload extracting live steam to a second MSF unit (twin extraction mode).

The exergy and exergoeconomic costs of the most significant mass and energy

flowstreams (live steam generated in the boiler , steam to MSF vacuum system

, steam to MSF brine heater , electric power and distilled water

) appear in tables 7.10 and 7.11 respectively. No other energy analysis based on

the First Law of Thermodynamics can provide this information, i.e., the amount

(exergy or $) of the fuel plant consumed to obtain a flow.

The unit costs in this section (the cost per unit exergy of the considered flow) onlyrefer to the operating costs since they do not take into account the capital costinvestment of the plant units.

Afgan, Darwish and Carvalho (1999) quantified the primary energy or fuel needed toproduce 1 kg of freshwater in a single purpose MSF desalination plant (case 2 in ouranalysis) and a dual purpose MSF desalination plant (case 3). These values (445 kJand 225.7 kJ respectively) are based on an energy analysis of the dual-plant productsand are quantitatively similar.

Both tables provide the same information expressed in different units. The calculatedcosts are operating costs, discounting investment capital costs. The exergoeconomiccosts c* were obtained by considering the natural gas market price (cf) of 2.35 ($/MBTU).

TABLE 7.10 Exergy (kW fuel/kW product) unit costs k* of most significant flows of the dual plant.

k* Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

2.733 2.371 2.604 2.590 2.576 2.572 2.677 2.559

2.842 3.147 2.657 2.620 2.616 2.611 2.714 2.600

— 3.871 2.693 2.644 2.667 2.650 3.650 3.615

3.286 — 2.938 2.955 2.938 3.149 3.042 2.935

a

a. Exergy of water measured in a more realistic unit: (kJ fuel/kg water), therefore is included the exergy of water leaving the MSFunit (bD, in kJ/kg).

— 416.511 221.67 224.99 227.67 261.02 549.48 526.38

bD (kJ/kg) — 10.35 10.35 10.35 9.81 11.62 13.29 12.98

kBOI*

kVST*

kMSF*

kGEN*

kD*

kBOI*

kVST*

kMSF*

kGEN*

kD*

kD*

Cost analysis


These values only contain the irreversibilities, the destruction of exergy or usefulenergy in the productive process. The live steam cost is always lower because it isgenerated at the very beginning of the production process. The irreversibilities duringnatural gas combustion and heat transfer inside the boiler increase the cost of thissteam.

Flowstreams further down the productive process were more costly. All processes inthe plant were irreversible (see table 7.12) and the total exergy destroyedcontinuously increased throughout the productive process. The amount of exergyrequired to obtain a flow (exergy cost) also increased. For this reason, the finalproducts had the highest costs.

The effect of irreversibilities in the cost generation process is clearly shown bycomparing studies 7 and 8. The cleaning ball system directly decreases distilled watercost by decreasing the irreversibility in the MSF plant (see table 7.12) and increasingefficiency (table 7.14). This benefit in the MSF plant also affects the power plant. Theamount of steam needed in the MSF plant brine heater decreases (see table 7.9),increasing the steam mass flow rate expanded in the LP turbine and the electricalpower produced. Modifying the operating conditions of the MSF affects the electricalcost.

Irreversibilities (table 7.12) may have different costs. For example, boilerirreversibilities (IBOI) are much higher than MSF plant irreversibilities (IMSF), but livesteam cost is lower than distilled water cost.

TABLE 7.11 Exergoeconomic (monetary) unit costs ($/GJ) of most significant flows of a dual power and desalination plant. Cost of water c*D is expressed in $/m3, and electricity cost of is also expressed in $/kW·h (c*GEN*).

c* Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

6.087 5.281 5.799 5.770 5.738 5.728 5.964 5.699

6.331 7.010 5.913 5.835 5.827 5.816 6.046 5.792

— 8.621 5.997 5.888 5.940 5.902 8.130 8.052

7.319 — 6.543 6.583 6.545 7.014 6.775 6.537

0.0263 — 0.0235 0.0237 0.0235 0.0252 0.0244 0.0235

— 0.9277 0.4937 0.5011 0.5071 0.5814 1.223 1.172

cBOI*

cVST*

cMSF*

cGEN*

cGEN**

cD*



The reasons for the impressive cost of distilled water are:

• The large amount of exergy destruction (irreversibility) in the MSF plant,considering the high fuel value of the MSF unit (steam exhausted in brine heaterand ejectors, electrical consumption) and the low value of the product(freshwater exergy flow). The energy and exergetic cost balance must be fulfilled(Valero, Muñoz and Lozano, 1986c).

TABLE 7.12 Irreversibilities (exergy destruction, kW) in the different components of the dual plant. MSF unit is considered a component.

I Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

ICP 89.26 58.44 13.93 16.53 13.84 4.94 7.94 16.52

ILPH2 2,125.1 — 277.6 38.40 118.0 148.8 26.34 42.77

ILPH1 1,687.8 — 363.0 80.85 279.0 268.2 28.97 219.7

IDRT 306.0 655.5 990.4 544.1 1,362.4 638.7 821.1 2,317.7

IFP 265.0 — 212.3 124.7 123.4 229.5 601.9 549.8

IHPH2 243.2 — 505.4 274.1 329.7 77.61 454.3 566.6

IHPH1 513.8 — 688.7 368.2 430.6 204.2 661.9 737.6

IBOI 265,908.9 — 268,206.6 195,921.1 208,749.0 130,195.6 306,254.9 306,605.8

IVST 89.62 — 1,157.2 394.8 493.7 105.0 423.0 442.7

IHPT1 2,206.0 — 2,254.8 4,870.4 4,379.7 5,983.7 4,734.6 4,698.4

IHPT2 250.5 — 637.2 451.1 489.8 112.8 467.1 479.8

IHPT3 303.5 — 813.9 508.4 595.6 240.1 512.8 539.4

IHPT4 955.4 — 2,369.5 1,097.1 1,464.0 583.0 912.5 1,054.3

ILPT1 4,265.0 — 1,888.0 470.0 945.6 1,097.2 131.0 1,139.1

ILPT2 9,598.9 — — — — 732.3 — 230.1

ICND 37,816.7 — — — — 3,260.5 — 1,769.3

IGEN 2,041.7 — — — — 1,372.9 — 1,489.5

IVS1 — 38,198.1 — — — — 33,892.9 35,451.4

IVS2 — 314.4 — — — — — —

IVS3 — 1,750.2 — — — — — —

ITOT-PP 329,734.2 185,880.0 292,042.4 206,923.9 226,061.2 145,255.9 351,501.1 358,339.3

ITOT-MSF — 67,482.6 67,014.5 66,954.5 56,843.2 35,350.0 117,924.4 106,596.9

Cost analysis


• The low distillate exergy flow is due to the low freshwater temperature leavingthe MSF unit (see the last row in table 7.10. The different values stem from thedifferent distilled water temperatures in different operating conditions (whichstrongly depends on the seawater temperature entering the desalination unit).The contribution of chemical and mechanical exergy to the global exergy flow ofseawater flows is minimum. Consequently, the final exergy cost is very low butthe intermediate flows inside the distiller can be extremely high (the flashingbrine, cooling brine, etc). The relationship between the inlet/outlet exergy flowswhich determine the exergy unit consumption k in the characteristic equationsthat model MSF thermoeconomics, is quite elevated in this example. The exergyunit consumption k propagates the exergy cost of the final product increasing thecost of water from the exergetic point of view.

• The resources consumed in the MSF units are not primary energy. The electricityand steam produced to the distiller were produced in the power plant and the costof the fuels of the MSF do not have a unit exergy cost. Only primary energy hasan exergy cost equal to one (as natural gas entering the boiler).

Another important result was the significantly higher water cost when the live steamwas throttled through the HP reduction station (cases 2, 7 and 8). This has a physicalexplanation related with energy quality degradation. When the live steam expandsthrough a throttle valve, its energy content remains stable while its exergy decreases(pressure is dramatically reduced in the reduction pressure station). The exergydestruction in the pressure reduction station correspond to IVS1, IVS2 and IVS3(table 7.12).

Regarding component efficiencies, the more efficient a process the lower costgenerated. Consider, for example, turbine efficiencies (table 7.13).

TABLE 7.13 Isoentropic efficiencies of pumps and turbine sections of the power plant.

η (%) Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

HPT1 0.733 — 0.719 0.546 0.581 0.430 0.558 0.560

HPT2 0.939 — 0.949 0.913 0.919 0.885 0.921 0.922

HPT3 0.978 — 0.950 0.950 0.950 0.978 0.950 0.950

HPT4 0.968 — 0.938 0.941 0.939 0.947 0.940 0.938

HPT5 0.812 — 0.847 0.865 0.857 0.857 0.864 0.864

LPT1 0.873 — 0.752 < 0 0.820 0.815 0.070 0.802

LPT2 0.738 — 0.729 < 0 0.737 0.746 < 0 0.756

FP 0.861 0.807 0.861 0.855 0.870 0.692 0.735 0.737

CP 0.778 — 0.773 0.113 0.627 0.588 0.077 0.377



The live steam generated in the boiler is expanded in the HP turbines, before beingextracted to the brine heater of the MSF plant. For this reason, the difference betweenthe cost of steam to brine heater and the cost of live steam for the analyzed cases isdirectly related to the HP turbines efficiencies. Thus, the higher the HP turbineefficiency, the lower the cost difference in brine heater and live steam.

A similar result is obtained for the cost difference between live steam and powergenerated. In the analysis, the low-pressure turbine efficiencies also influenced theobserved differences.

Table 7.14 contains global efficiency parameters for the whole plant and for thepower and MSF plants. As in the device analysis, the more efficient the globalprocess, the lower the cost of the final product. For example, in cases 7 and 8 thecleaning ball system clearly increases the exergy efficiency of the MSF plant and thewhole plant. The distilled water and power cost decrease as a result. The exergeticefficiency we obtained for the MSF plant is similar to other estimate (Hamedet. al, 1999).

Finally, product costs of different plant components were also calculated (seetable 7.15).

The steam leaving the boiler has a lower exergy cost since the fuel plant exergy onlydegraded in the boiler tubes (the combustion and heat transfer process is non-ideal).As the steam passes through the turbine section, its energy quality graduallydegrades: the exergy cost increases from the first to the last turbine section. Theexergy cost of the electricity is a weighted sum of the exergy costs of the turbinesections. The inefficiencies of the pumps increase the exergy cost of the electricity.

TABLE 7.14 Product and fuel (kW), and exergetic efficiency (%) values for the power and MSF plants. Note: The efficiency of the boiler is not included in the final efficiency.

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

PPP 144,260.4 64,712.9 186,024.8 140,244.6 144,096.3 87,113.3 191,289.9 184,994.0

PMSF — 6,951.78 6,951.78 6,951.78 5,613.4 3,925.9 8,344.9 8,326.9

FPP 473,994.6 250,592.9 478,067.2 347,168.5 370,157.5 229,369.2 542,791.0 543,333.3

FMSF — 74,434.4 73,966.4 73,906.3 62,456.6 39,275.9 126,269.3 114,923.8

ηPP 30.4 0.0 38.9 40.4 38.9 36.7 35.2 34.0

ηMSF — 9.3 9.4 9.4 9.0 10.0 6.6 7.2

ηTOT 30.4 2.7 24.9 21.1 23.6 21.3 13.5 14.4

Cost analysis


The energy quality of the steam extracted for the heaters is degraded in this heating

process. Although the live steam is the cheapest in desalination mode (case 2), the

exergy cost of the steam to the MSF unit has a higher cost than the steam provided

when the plant is producing electricity. The reduction pressure station is more

inefficient than the set of components turbine-heaters-condenser.

7.2.3 Thermoeconomic costs

The thermoeconomic cost of a flow has two parts, one from the monetary cost of the

fuel (natural gas) exergy needed to produce this flow, i.e., its exergoeconomic cost

(Valero, Muñoz and Lozano, 1986b) and the other from the rest of the costs generated

in the productive process (capital, maintenance, etc).

TABLE 7.15 Unit exergy costs k* (kW/kW) of component products in the steam power plant coupled with a MSF unit.

k* Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

4.942 — 3.957 20.67 4.960 3.396 16.45 8.020

3.851 — 3.476 8.106 3.465 3.664 5.363 3.824

3.389 — 3.177 3.592 3.230 3.249 3.393 3.400

3.040 4.306 3.021 2.944 3.283 3.280 3.059 3.473

3.764 3.151 3.282 3.272 3.223 4.077 3.771 3.560

2.992 — 2.850 2.793 2.796 2.729 2.926 2.822

3.034 — 2.853 2.796 2.797 2.789 2.930 2.813

2.733 2.371 2.604 2.590 2.576 2.572 2.677 2.559

2.842 — 2.657 2.620 2.616 2.611 2.714 2.600

3.001 — 2.794 2.988 2.925 3.261 3.074 2.926

2.881 — 2.739 2.706 2.701 2.648 2.807 2.686

2.910 — 2.778 2.735 2.735 2.706 2.841 2.719

3.282 — 3.029 2.935 2.951 2.952 3.049 2.918

3.373 — 3.533 10.434 3.191 3.350 15.711 4.164

3.858 — 3.660 — 3.577 3.505 — 3.506

— 3.851 — — — — — 4.591

— 3.017 — — — — — —

— 3.527 — — — — — —

kCP*

kLPH2*

kLPH1*

kDRT*

kFP*

kHPH2*

kHPH1*

kBOI*

kVST*

kHPT1*

kHPT2*

kHPT3*

kHPT4*

kLPT1*

kLPT2*

kVS1*

kVS2*

kVS3*



The balance of thermoeconomic costs for any individual unit has one more term thanthe exergy cost balances (tables 7.7 and 7.8). The term Z/ϕ represents the contributionof the non-energetic production factors (investment capital costs). The balance ofthermoeconomic cost ($/s) is expressed in equation 7.5:

cf F + Z/ϕ = cp P (7.5)

where cf and cp are the unit thermoeconomic costs ($/kJ) of the fuel (F) and product(P) respectively. As the term Z is usually calculated in US dollars ($) it must bedivided by a temporary factor, called amortization factor (ϕ). The amortization factortakes into account the economic life period of the plant and is also called the capitalcost of an installation (see section 7.2.3.2 for more information on capital costs).

7.2.3.1 Investment costs

According to Bejan et al. (1997), an investment cost is a one-time cost, in contrast tofuel costs and O&M costs which are continuous or repetitive in nature. Investmentcosts are treated differently than fuel and O&M expenses in an economic analysis.Some concepts are necessary to understand these costs:

• Fixed capital investment, the total system capital cost assuming a zero-timedesign and construction period, i.e., the capital to purchase the land, build all thenecessary facilities and purchase and install the required machinery andequipment.

• Total capital investment, the sum of the fixed-capital investment and otheroutlays, i.e., startup costs, working capital, costs of licensing, research anddevelopment, and allowance for funds used during construction.

• Direct costs, the costs of all permanent equipment, materials, labor and otherresources involved in the fabrication, erection, and installation of the permanentfacilities.

• Indirect costs, not a permanent part of the facilities but required for the orderlycompletion of the project: engineering and supervision, construction costs,contingencies. The fixed capital investment is the sum of direct and indirect costs.

In our case, purchased-equipment costs provided by the plant managers are quitedifferent from other studies (El-Sayed, 1996; Boehm, 1987; Frangopoulos, 1991;Lozano et al., 1996). This is due to the magnitude of the components considered inthe dual plant. Several authors propose costing equations for most of the componentsused in our analysis, but the main parameters used in the proposed correlations areoutside the specified range (our power plant and desalination units were very large).Other costs not included in the capital costs of the components (but that alsoconstitute a part of the direct costs of the fixed-capital investment) include thepurchased-equipment installation, piping, instrumentation and controls, electricalequipment and materials, land, civil and structural work and service facilities.

Cost analysis


El-Sayed (1996) calculates the cost (in thousands of dollars, k$) of the maincomponents of the equipment used in a MSF and steam power plant using thefollowing equation:

Z = ca A, (7.6)

where the area A is calculated using an exponential formula as a function of fourparameters, i.e.:

(7.7)

These parameters are shown in table 7.16.

Boehm (1987) introduces the size effect of the units into a simple cost equation thatonly depends on a variable, S. Thus, a complete tabulation of data for a particularpiece of equipment could contain reference cost and size (Zr and Sr), and the factor mresponsible for the economies of scale.

Z = Zr (S/Sr)m (7.8)

In the cost equation, Boehm normally uses a range of 0.5-1.0. Sometimes m is greaterthan 1.0 (boilers, heaters…), which produces unexpected results. Table 7.17 includesthe main parameters of the above mentioned equation.

Finally, the more accurate equations, in comparison with the cost estimation providedby the plant managers, are those proposed by Frangopoulos (1991). They are usuallya correlation with three or four main parameters and correction factors depending onthe device (see table 7.18).

TABLE 7.16 Costing equation parameters for an MSF and power plant (El-Sayed, 1996). Units: ca k$/ft2,A ft2, M lb/s, Q kW, Pi, Pe psia, Ti R, ∆T F, ∆P, dP psi, e = η/1– η. Subscripts: i, inlet; e, exit; t,tube; s, shell; m, mean (LTMD).

Component ca k x1 x2 x3 x4 n1 n2 n3 n4

Steam turbine 50 0.45 M Ti/Pi Pe e 1 0.05 –0.75 0.9

Feed pump 3 0.0025 M ∆P e — 1 0.55 1.05 —

C.W. pump 3 0.0063 M ∆P e — 1 0.1 0.7 —

Economizer 0.015 310 Q ∆Tm dPt dPs 1 –1 –0.16 –0.12

Boiler 0.015 340 Q ∆Tm dPt dPs 1 –1 –0.33 –0.26

Superheater 0.015 310 Q ∆Tm dPt dPs 1 –1 –0.15 –0.14

Heater 0.02 3.3 Q ∆Tt dPt dPs 1 –0.7 –0.08 –0.04

MSF 0.02 10 Q ∆Tn ∆Tt dPt 1 –0.75 –0.5 –0.1

A k x1n1

x2n2

x3n3

x4n4

=



TABLE 7.17 Component parameters in Boehm (1987) equations.

Component Zr S Sr m

Pump 47 M 10 0.03

Steam turbine 25 W 1000 0.68

Heater 21 A 100 0.71

Condenser 3 Q 10 0.55

Boiler 340 M 12 0.67

TABLE 7.18 Costing equations proposed by Frangopoulos (1991).

Component Cost equation

Boiler 20.1552224 * exp (0.0014110546 * P1) * exp (0.7718795 * ln (M1)) * FAR * FAN * FAT

Steam Turbine 5240.378 * exp (0.569323 * ln (FB1 * (F2T + F2P))) * FBN * FBT

Condenser 1.11 * A * 426.2632633 * exp (–0.4556513 * ln (A)) * FCR * FCPW * FCP * FCB

Pump 1969.2325 * exp (0.4838546 * ln (7.279088e – 5 * M1 * 0.018 * (P2–P1) * FDN

Heatera

a. From Chemical Engineering (Corripio, Chrien and Evans, 1982). P1, T1 and M1 are the inlet conditions, T2, P2 the exit conditions,A area, η and η1 efficiency and First principle efficiency, TTD terminal temperature difference, ∆Ps, ∆Pt pressure losses in tubes andshell.

Exp (8.202 + 0.01506 * ln (A) + 0.06811 * (ln (A))2) * FD * FP * FM

Factor Correction factor

FAR FAR = 1.0 + ((1–∆Pr)/(1–∆P))8

FAN FAN = 1.0 + ((1 – η1r)/(1– η1))7

FAT FAT = 1.0 + 5 * exp ((T1 – 1100)/18.75)

FB1 FB1 = 0.0003929119 * η * M1

F2T F2T = 0.55 * (T1 – T2 – T2 * ln (T1/T2))

F2P F2P = 0.1102109 * T2 * ln (P1/P2)

FBN FBN = 1 + ((1 – ηr)/(1 – η))3

FBT FBT = 1.0 + 5 * exp ((T1 – 1100)/18.75)

FCR FCR = (P3 * ((1/∆Ps) – 1)/14.7)–0.11

FCPW FCPW = (∆Pt/14.7)–0.38

FCP FCP = 0.93 + 2.6380952 e–4 * P2 + 1.352381 e–6 * P22

FCB FCB = exp (0.10/(TTD–5))

FDN FDN = 1 + ((1 – 0.8)/(1 – η))3

FD FD = exp (–0.7844 + 0.083 * LN (A))

FP FP = 0.8955 + 0.04981 * LN (A)

FM FM = 1.4144 + 0.23296 * LN (A)

Cost analysis


Lozano et al. (1996) also propose a set of equations for a wide range of values toobtain a reasonable equipment cost (see table 7.19):

Purchase cost provided by the plant managers is much more complete than theindividual components. It includes the price breakdown per section of each unit, andthe direct costs of the installation. Table 7.20 includes a list with the percentages ofeach unit or subsystem with respect the total purchase cost (direct cost) of a powerand desalination plant. Land cost is neglected in the Gulf Area.

The price breakdown in table 7.20 does not contain the cost of each component in theproductive structure. As a result, the thermoeconomic cost can only be calculated forthe final products in the power and desalination plant, knowing the exergy cost of theelectricity and distillate, the economic investment cost and the thermoeconomic costof the products. The thermoeconomic cost can be expressed in units of money perunit of time ($/s), or units of money per unit of product: $/kW·h or $/m3. All cost datamust have the same reference year as a basis for calculations. This is done with anappropriate cost index, an inflation indicator from technical journals (e.g. ChemicalEngineering) that corrects the cost of equipment. We did not apply the cost indexsince the purchase costs of our installation were updated in 1997.

TABLE 7.19 Cost equations proposed by Lozano et al. (1996). η exergetic efficiency, B exergy flow of product, S negentropy, vw velocity of tubes , W power, e eficiency of the condenser (= T0 (s2–s1)/(h2–h1)).

Component Cost equation

Boiler 740 * exp ((P1–28)/150) * (1 + 5 * exp ((T1–866)/10.42)) * (1 + ((0.45–0.405)/(0.45–η))7) * B0.8

St. Turbine 3000 * (1 + 5 * exp ((T1–866)/10.42)) * (1 + ((1–0.953)/(1–η))3) * W0.7

Condenser (1/(T0 * e)) (217 * (0.247 + 1/(3.24 * vw0.8)) * ln (1/(1–e)) + 138) * (1/(1–η)) * S

Pump 378 * (1 + ((1–0.808)/(1–η))3) * B0.71



TABLE 7.20 Price breakdown per section in a dual-purpose plant.

Component system Portion

Steam Turbine Plant 12,25

HP heater, LP heater, feedwater storage tank with deaerator, cold condensate storage tank

1,13

Steam generating plant 13,15

HP feeding system 0,12

LP feeding system 0,30

Boiling feed pump sets with hydraulic coupling 1,66

Generator complete with air cooling and excitation systems 2,63

Others: Transformers, busbars, switchboards, cabling and cable laying, rectifiers, batteries, electrical control equipment, instrumentation and control, service water and drainage system.

14,08

Total for the steam power plant 45,32

MSF unit: Evaporator shell and tube bundles 20,38

Brine heater 1,06

Deaerator 0,04

Vacuum system 0,63

Cooling water recircul. pump set including isolating, non-return valves 0,29

2 Brine recirculating pump sets, complete 0,87

Blow down pump set, complete 0,22

2 Distillate pump units 0,22

2 Brine heater condensate pump sets, complete 0,07

Others: Protective coating, make-up water strainers, cranes, seawater, brine recirculation, blowdown and distillate pipeline, HP, MP and LP reducing stations, antiscaling, antifoaming and sodiumsulfite systems, on-load tube cleaning system, lighting system, instrumentation and control, switchgear, switchboards, transformer.

9,01

Total for the desalination unit 32,79

General services: Circulating water and seawater supply system, seawater cleaning plant, fuel oil and gas system, power transformers, bus duct systems, cables, lighting and power outlets, earthing system, common instrumentation and control, water treatment, lifts, buildings, fire fighting systems, chemicals and chlorination system, town water storage, DPS system, chemical storage.

21,89

Total for the dual plant 100

Cost analysis


7.2.3.2 Capital costs

The average capital cost for the system was assumed to be 3.47×10–9 $/s·$. It wascalculated based on 8% capital recovery per calendar year (8,000 hours operation ayear) and 15% allowance for the fixed part of O&M (El-Sayed, 1996). The averagecapital cost takes into account the effect of inflation: price increases associated withincrease in available currency and credit without a proportional increase in availablegoods and services of the same quality. This cost also includes the effect of escalation(resource depletion, increased demand and technological advances); and depreciation(decrease in equipment value due to physical deterioration, technological advancesand replacement). Some assumptions were made to assess the average capital cost.For example, land costs and total capital investment were placed at the beginning ofthe design and construction period so that the end of this period is considered thebeginning of commercial operation (economic-life period).

7.2.4 Thermoeconomic cost analysis

The exergy and economic costs of a system provide the real plant operating costs.Tables 7.21 and 7.22 show the thermoeconomic cost in the eight cases (see table 7.9for details).

El-Sayed (1996) proposes the following costs for the products of a typical dual-purpose power and desalination plant:

• Electricity: 0.045 $/kW·h.

• Water: 1.3 $/m3.

TABLE 7.21 Thermoeconomic costs of distilled water and electricity of the analyzed dual-purpose plant.

Cost ($/s) Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

Electricity 1.5798 0.5068 1.3046 1.0030 1.1019 0.8818 1.0248 0.9706

Water 0.3571 0.9798 0.6885 0.6935 0.6471 0.5534 1.1251 1.1088

TABLE 7.22 Thermoeconomic cost of electricity ($/kW·h) and water ($/m3) for the cases studied in the exergetic cost analysis.

Cost Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8

Electricity 0.0388 0 0.0385 0.0479 0.0436 0.0593 0.0482 0.0492

Water 0 1.5026 1.0558 1.0635 1.1648 1.6871 1.8456 1.7802



The results of the thermoeconomic analysis were very close to the values given by El-Sayed, especially in the most representative cases (in hours of operation per year,cases 3, 4 and 5). Note that the thermoeconomic cost was not zero in case 1 for waternor for electricity in case 2 (see table 7.21) despite the lack of production. This wasdue to the effect of amortization of the purchase costs in the first table. The effect onquantity production is clear in table 7.22 (the cost of electricity per unit of energy isreduced in case 1 and is lower than other costs, although this is the worst case if weanalyze exergy costs). In Case 6 (with partial load) the investment costs overchargethe cost per unit of production. The use of the reduction pressure station to producefreshwater is not recommended even with a high freshwater demand (see cases 2, 7and 8 in table 7.22). Case 3 is the most interesting case to maintain the best operationmode.

7.2.5 Cost allocation: Indirect methods

Some cost allocation methods allocate the total cost of owning and operating theplant among two products, without having to split the total cost in two products(direct methods). Other methods allocate the main factory costs (e.g. manpower,material, fuel and capital depreciation) among the two products (indirect methods).Some criterion is usually needed to help in cost allocation. For example, the exergycost method is an indirect method that allocates the cost of producing the twoproducts in terms of fuel consumption.

Although cost allocation methods are a rational basis for pricing the two products, thecost is the amount of resources needed to obtain these products. The price imposed ona product is independent of the efficiency of the formation process of that product.

7.2.5.1 WEA method

The method proposed by El-Nashar (1999) and the Water and Electricity Departmentof the UAE (WEA method) is indirect and allocates all cost components among waterand electricity according to functional considerations. The annual cost for a co-generation plant can usually be separated into three cost components: fixed capitalcharges, fuel costs and O&M costs. Each one can be separated into costs forelectricity production, costs for heat production and common costs to both products.The methods differ in how they separate annual costs into the three components andin allocating common costs between electricity and heat.

The total costs are divided into five cost departments: fuel, personnel, maintenancecontracts, spares and consumables and depreciation of fixed capital. Personnel costsare divided among those directly involved in the co-generation plant (such asoperation and maintenance work), or those that serve several plants. The cost of fuelconsumed by the steam turbines is split between electricity and water since the steamderived to the MSF unit has the potential to generate a certain amount of electrical

Cost analysis


power if allowed to expand through a hypothetical condensing turbine. Since thissteam is used for desalination instead of additional power generation, the fuelconsumed for this amount of non-produced electrical power should be charged towater. The amount of additional power (WCT) which could have been generated bythis hypothetical turbine (in our case is the low pressure turbine) may be expressedas:

WCT = Q ηB ηCT (7.9)

where Q is the amount of heat supplied to the hypothetical steam turbine, ηB is theefficiency of boiler and ηCT is the thermal efficiency of the condensing steam turbinecycle. The fuel consumption Gc could be allocated to electricity and water accordingto the following equations, taking into account the power generated in the real steamturbine (WST):

Gce = Gc WST /(WST + WCT) (7.10)

Gcw = Gc WCT /(WCT + WCT) (7.11)

The fuel allocation problem could also be solved using the difference in output powerproduced when the amount of fuel consumed is the same in both cases. The MR (nodesalination) and MCR (co-generation) cases are a good example. The totalpersonnel cost consists of directly assessable costs (e.g. operating and maintenancestaff) and indirect or common service personnel. The directly assessable portions arecharged to either electricity or water, depending on the case. The cost of commonservice personnel is allocated to electricity and water according to the ratio of thecapital cost of the plant and equipment associated with electricity production anddesalination. Maintenance contracts for specialized maintenance work is priced andelectricity and water are finally allocated. Depreciation of capital cost betweenelectricity and water is allocated according to the function of the equipment inoperation. The depreciation cost is allocated to electricity in the steam turbine powerplant and water in the desalination plant. Depreciation costs of common equipmentand facilities are allocated according to the capital cost of equipment related toelectricity and water, as done for the common personnel costs.

The WEA method is widely used in the UAE to allocate the cost of producing waterand electricity in co-generation plants (starting from the yearly electrical and waterproduction) and the cumulative number of operating hours of power and desalinationplants. Those data are confidential and cannot be presented here. Other characteristicsinclude:

• Average yearly cost (with a wide range of operating modes) of the co-generationplants (with several configurations of dual plants) operating in the country. It isnot valid for calculating an instantaneous cost of water and electricity.

• Applied fuel and capital costs (which are unknown).



Compared with exergy cost methodology, the trend of water and electricity costs isthe following:

• The WEA method tends to overvalue electricity and undervalue water bycharging all the capital and O&M costs of the steam turbine (except fuel) toelectricity.

• The WEA costing methodology only allocates fuel cost to steam turbines.

• The WEA method suffers from a certain degree of arbitrariness with regard tothe efficiency of a hypothetical condensing steam turbine. The assumptionscould cause fluctuations in the resulting cost of electricity and water. Thedifference in production between operating modes could partially avoid thisproblem (see next section).

• The exergy/thermoeconomic method charges each product of a multi-productunit to the appropriate portion of capital and O&M costs involved in operatingthe unit.

• The exergy/thermoeconomic method is based on a solid accounting andthermodynamics. Therefore, it will be used in our studies.

As a result of the above, El-Nashar (1993; 1999) developed a model based on exergyanalysis to predict the final costs of the two products. Other authors propose costredistribution using the exergy analysis of the dual-purpose plant (Evans, Crellin andTribus, 1980; Breidenbach, Rautenbach and Tusel, 1997; Slesarenko and Shtim,1986). The energy efficiency of the dual-purpose plant is also used to allocate thefuels to power and desalination and the relevant specific fuel costs for powergeneration and water production (Saeed, 1992).

7.2.5.2 Fuel cost of water in dual plants

Fuel energy for desalting depends on fuel allocation rules between the power anddesalted water produced in a dual-purpose plant (Darwish, Yousef and Al-Najem,1997). Kronenberg and Dvornikov (1999) argues that the steam cost of desaltingshould be calculated by defining the heat rate difference between the power plantcoupled and uncoupled to the desalination plant (also called the Lost KilowattsMethod, see Gaggioli and El-Sayed, 1987; El-Saie and El-Saie, 1989). This heat ratedifference is defined by the Fuel Cost of Water (FCW) in a dual-purpose installation.

The fuel cost of water largely depends on the overall efficiency of the power plant,and is calculated as:

(7.12)FCW $ m3⁄( )

W1 W2–( ) HR1 cf

Qf D----------------------------------------------=

Cost analysis


where W1 and W2 are the electric power output of the uncoupled and coupled plant(kW), HR1 is the heat rate of the uncoupled power plant (the inverse of the efficiency,kJ/kW·h), cf is the fuel cost ($/kg), Qf is the heat value of fuel (kJ/kg) and D is thewater production (m3/h).

Fuel cost of water can be calculated in the dual-purpose plant. For instance, the FCWof the MCR case was calculated using natural gas with a high heating value(HHV = 9,500 kcal/m3), a density of 0.75 kg/m3 and an energy cost of 2.23×10–6 $/kJ(applied in the cost analysis). The gas consumption in the MR case (the uncoupledpower plant in our case) was 43,500 Nm3/h. The final values to be introduced informula (7.12) for our example are also introduced after the FCW value:

FCW = 0.271 $/m3

W1 = 146,700 kW

W2 = 122,000 kW

HR1 = 43,500 · (9,500 · 4.1868)/146,700 = 11,794 ·1 kJ/kW·h

cf = 2.23 ·10–6 (9,500 · 4.1868)/0.75 = 0.1182 $/kg

Q = (9,500 · 4.1868)/0.75 = 53,032.8 kJ/kg

D = 2,400 m3/h

Note that the exergy analysis and the lost kilowatts method are similar (see section7.1.1 for the exergy analysis of the simple co-generation plant), although the latteruses the energy analysis to calculate the cost of fuel consumed in the co-generationplant. The resulting cost of water is very similar in both methods.

If the FCW is compared with the exergoeconomic cost of case 3 in table 7.11 (i.e., theexergoeconomic cost of the MCR case), the FCW is more or less 55% of thethermoeconomic cost (0.493 $/m3). The difference is mainly due to several factors:

The exergoeconomic cost also includes the cost of electricity needed to pump theMSF flows and the steam derived to the vacuum system of the distillers.

The FCW assumes a constant efficiency in the power plant (the heat rate of the plantin condensing mode). The overall efficiency of the dual-purpose plant is lower whenthe plant is only generating electricity (see table 7.14 for the exergetic efficiency ofthe whole plant). Therefore, the amount of additional electricity generated in thecondensing mode is not a valid index to calculate the fuel cost in co-generation mode,with a higher efficiency.



7.3 Thermoeconomic diagnosis

Diagnosis is the identification of something that is not working properly.Thermoeconomic diagnosis is the only operation analysis based on the Second Law.It uses the exergy balance of an installation to allocate and calculate irreversibilitiesin the production process and identify the equipment affecting overall efficiency. Inpractice, however, this useful information is not sufficient since some irreversibilitiescannot be avoided. The technical possibilities for saving energy are always lower thanthe theoretical limit of thermodynamic energy losses. Moreover, the local exergysavings in different units or processes are not equivalent. The same localirreversibility decrease in two different components generally produces differentvariations in the total energy consumption.

The final objective of Thermoeconomic diagnosis is to describe how malfunctionsaffect additional resource consumption (see Chapter 6 for a review ofThermoeconomic theory and its applications). In this section, we analyze a power anddesalination plant according to the principles outlined in the previous chapter. Theentire diagnosis is presented using the Structural Theory of Thermoeconomics(Valero et al., 1993). It provides information about component fuel consumptionduring equipment degradation (inefficiency), how each component increases fuelconsumption and how a component's inefficiency affects the behavior of other plantunits.

We will only consider the direct problem of thermoeconomic diagnosis (Valero,Torres and Lerch, 1999), where inefficiencies are quantified in terms of irreversibilityincrease, while distinguishing between efficiency deterioration (intrinsic and inducedmalfunctions) and component dysfunction (generated by the malfunction). Theinefficiencies were previously simulated and the causes of the behavior deviationprovoked by this inefficiency are not searched here.

The inverse problem is to identify and quantify malfunctions (the origin of newirreversibilities). Classical thermoeconomic analysis does not elucidate the cause ofirreversibilities, although an effort is made to detect and stop malfunctions. Theinverse problem finds the cause of the deviation between two states of the plant(actual and reference conditions). It requires a data acquisition system (for thereference conditions), a simulator (to provide the reference state for the sameoperating conditions) and conventional methods of the thermoeconomic diagnosis(the direct problem). One of the main difficulties with the inverse problem isrecognizing and separating effects not intimately related with the inefficiencies of theplant components, such as load variation, set points or ambient conditions.

The impact on fuel predicted by the simulator is exactly the same as that calculatedby the Structural Theory of Thermoeconomics. This plant diagnosis reproduces thedeviation of the physical values when one or more inefficiencies are detected.

Thermoeconomic diagnosis


Although the simulator calculates the thermodynamic state of the dual plant withreasonable accuracy under different operating conditions, it might not be able torespond as well to unexpected non-linear inefficiencies. The diagnosis involves asensitivity analysis of the mathematical model of the dual-purpose plant (simulator)with respect to a parameter (in this case, one or several inefficiencies in a componentof the system). The simulator could be avoided in the diagnosis if the data acquisitionsystem of the dual plant were available.

We will first summarize the different inefficiencies, loads and operating modessimulated in the plant diagnosis. Then, the ‘direct problem’ of diagnosing one orseveral inefficiencies is analyzed for a defined load (corresponding to an operatingmode) in the power and/or desalination plant. The analysis involves a new technique(see Chapter 6, Torres et al., 1999) based on Structural Theory and SymbolicThermoeconomics to provide a huge quantity of information, including:

1. The irreversibility generated in each component.

2. The exergetic cost of each component's product.

3. The intrinsic malfunction in each component (i.e. the efficiency decrease of acomponent due to its own inefficiency).

4. The induced malfunction in each component (i.e. the efficiency decrease of acomponent due to inefficiencies in other components).

5. The dysfunction induced in the component due to the malfunction orinefficiency of other subsystems, which forces it to consume more localresources to attain the additional production required by the other components.

6. The fuel impact or malfunction cost of each component due to an inefficiency,and the total impact on fuel.

7. A compact and easy to understand malfunction matrix containing the cost ofinefficiencies and the effect of a component inefficiency on all othercomponents.

7.3.1 Thermoeconomic diagnosis of a power and desalination plant: case studies

System operating parameters can be classified according to their effect on componentefficiency:

• Local variables, which mainly affect the behavior of the component related tothe variable (e.g. the isoentropic efficiency of a turbine).

• Global or zonal variables, where the operating parameter cannot be associatedwith a specific component (e.g. live steam conditions of a steam power plant).



A variable is considered local if the total impact on fuel associated with a subsystemis basically located in this component.

We simulated the device inefficiencies and considered the different simulation data asplant data under different conditions (including inefficiencies). All the analyzedinefficiencies were associated with local plant variables and were chosen in terms oftheir effect on energy:

• Degradation of the isoentropic efficiency of the high-pressure turbine (1st section,HPT1, and 4th section HPT4).

• Degradation of the isoentropic efficiency of the low-pressure turbine (1st section,LPT1).

• Heat transfer problems in HP heaters were analyzed by varying the TerminalTemperature Difference TTD (temperature difference between the saturationtemperature of the steam extracted from the turbine and feedwater leaving theheater). Only the HP heater no. 1 (HPH1) was treated.

• By varying the feed pump isoentropic efficiency, operating inefficiencies weresimulated in the feed pump.

The effect of a global variable such as live steam temperature can be studied if thesimulator supports a non-fixed condition in the live steam leaving the boiler. In thecase of the MSF unit, the analyzed inefficiencies refer to fouling at different stages:

• brine heater,

• recovery section, and

• reject section

Neither the MSF pumping process nor the brine level in each flash chamber werediagnosed since they were not simulated in the mathematical model. The analysiscould be performed with respect to thermal problems inside the distillers, vaporconditions to the brine heater or the TBT/distillate.

As we will see in later sections, fouling in distillers was considered a global variableif it affected other distillers.

The effect of these eight inefficiencies was measured on:

• the behavior of the rest of the plant devices (intrinsic/induced malfunction anddysfunction analysis),

• additional fuel plant consumption (impact on fuel),

• the thermoeconomic cost of electricity and distilled water,

• the irreversibility increase of each unit.

Thermoeconomic analysis should cover as much of the maximum range of electricityand water production as possible so that intermediate demands can be predicted from



acquired experience. Four loads were considered under the most usual operatingsituations:

• Full load in condensing mode (no extraction to MSF unit): 140 MW of powergenerated.

• Full load in extraction mode (electricity and water production): 122 MW ofoutput power (89.68 kg/s of steam extracted to the desalination unit).

• Partial load in extraction mode at 90 MW output power (60 kg/s steam extractedto the MSF unit).

• Parallel mode (the reduction pressure station is opened to maintain the pressureto the MSF unit): 60 MW of output power (50 kg/s extraction to desalination).

The first situation is a high-electricity demand when the distiller has been stopped forrepair, the two intermediate productions are the most common and the fourth istypical in winter.

Two freshwater productions were analyzed under the following specific conditions:

• 1,900 T/h distillate with 32 ºC seawater (the nominal production under Gulfseawater conditions in spring or autumn).

• 2,400 T/h distillate with 25 ºC feedwater to the reject section (the maximumwinter production). Seawater can be less than 25 ºC (the minimum temperatureoperation for the reject section), so the temper system uses a part of the rejectcooling brine and stay secure in the last stage of the reject section.

Loads and inefficiencies may be combined in many ways. We analyzed all of thesepossibilities but only present two: an inefficiency in the fourth section of the high-pressure turbine and an inefficiency in the MSF unit (with the cleaning ball system inthe heater) at a prefixed load. These examples represent a local and global variable intwo separate systems. We subsequently considered the ‘upstream’ effect of fouling inthe recovery section of the MSF plant on the steam power plant. Finally, the mostgeneral situation was analyzed when several inefficiencies in the power ordesalination plant occurred together. The rest of the combinations (i.e. the analysis ofthe individual inefficiencies presented above) are presented in Annex 1 for a 122 MWload in the power plant and the NTOS case of the MSF plant, including figures andmatrices calculated in the analysis of each inefficiency. The effect of the load in theabove inefficiencies is summarized in section 7.3.4.

7.3.2 Analysis of individual inefficiencies

7.3.2.1 Inefficiency in the fourth section of the high-pressure turbine

As defined by Royo (1994), an intrinsic malfunction in a steam turbine is expressedas the damage in the steam expansion process and energy transmission to the shaft



due to several factors including erosion, fractures, ruptures, sediments, surface finish,friction, steam path, seals and diaphragm deterioration, control valve and heat losses.An inefficiency can also be an induced malfunction due to the variation of externalfactors apart from component damage. These external factors include changes inadmission temperature, exhaust pressure or extraction mass flows of a steam turbine(Zaleta, 1997).

We simulated that the fourth section of the high-pressure turbine underwent behaviordegradation and, as a result, the isoentropic efficiency decreased by 10% (at 122 MWtotal output power). The three upstream turbine sections are insensitive to andincapable of responding to this inefficiency and the vapor conditions entering theinefficient section were maintained with respect to the design condition. A lowerisoentropic efficiency means that the outlet steam vapor conditions have a higherenthalpy, if the exhaust pressure of the high-pressure turbine is controlled by the MSFsystem. Thus, the first induced malfunction in the MSF unit was due to the variationof external factors; the steam conditions entering the MSF plant were changed by aninefficiency (or intrinsic malfunction) in the fourth section of the high-pressureturbine.

The output power of this section was also considerably lower because of thereduction in the enthalpy drop. The three sections of the high-pressure turbinemaintained their power production. The steam pressure entering the low-pressureturbine was maintained and the exhaust pressure must be the same as in the design(we assumed that the ambient conditions remained unchanged and constantcondenser pressure). Therefore, the efficiency of the low-pressure turbine should notvary considerably and the two sections of the low-pressure turbine do not produceadditional power to maintain the final production.

Consequently, additional live steam was needed to maintain final production. Thethree sections of the high-pressure turbine and the two sections of the low-pressureturbine provided the extra power not supplied by the inefficient section. Theadditional live steam affected the whole system, but the latter generally readapts tomaintain design values: design feedwater system values were maintained byincreasing the extraction mass flows. Pump consumption increased in proportion tothe additional mass flow required by the boiler. As a result, no significant inducedmalfunctions were provoked by the inefficiency in the high-pressure turbine.

The total impact on the fuel was 6.035 MW, but 6.015 MW in the inefficientcomponent. Thus, the effect of the inefficiency could be considered local to thecomponent with the intrinsic malfunction. Next we considered the contribution ofeach component.

The physical consequences of inefficiencies will be reviewed using the symbolicdiagnosis notation of this Ph. D. Thesis (see Chapter 6 for nomenclature). The samemethodology was used for each example. First the target conditions and the



inefficient situations were simulated (see Chapter 5). The design and inefficientsituation include the most significant flowstreams, which are the basis of thethermoeconomic analysis. Following the F-P definitions adopted for thethermoeconomic model (section 7.1), the fuel and product table was prepared.table 7.23 corresponds to the design and table 7.24 to the inefficient condition. Theunit exergy consumption κ of each component is very easy to calculate using the F-Ptables (by dividing the fuels entering the plant by their product). Then the reference⟨KP⟩ matrix (table 7.25) and the ⟨KP⟩ matrix (table 7.26) are made for the inefficientmode. If these two matrices are subtracted, we obtain the ∆ ⟨KP⟩ matrix with the unitexergy consumption increase of each component (table 7.27). The ∆ ⟨KP⟩ matrix isthe basis for calculating the endogenous irreversibility or malfunction. If the twomatrices are multiplied, we obtain the irreversibility matrix |I⟩ (table 7.28) with theirreversibility increase (or dysfunction coefficients) of each component. The firstfactor is the diagonal matrix KD–UD, where KD is the array containing the sum (bycolumns) of the ⟨KP⟩ matrix and UD is the unitary matrix. The second factor is theinverse of the unitary matrix minus the ⟨KP⟩ matrix, i.e., (UD–KP)–1. The unit exergycost of a product is the column sum of the dysfunction coefficients in the |I⟩ matrixplus one (table 7.28). Finally, the dysfunction matrix [DF] needed to build themalfunction and dysfunction table is calculated by multiplying the |I⟩ matrix by∆ ⟨KP⟩ P, where P is the array containing the product of each component. Thus, theirreversibility increase in each unit is connected to the increase in unit exergyconsumption of each component. The malfunction of each component MF is theproduct ∆ ⟨KP⟩ P and is located at the end of the table. The column sum is the fuelimpact of a component, i.e., the additional fuel plant consumption provoked by theconsidered unit and the row sum is the irreversibility increase of a component (seetable 7.29).

After having explained the most relevant matrices to analyze a plant inefficiency(table 7.29), we will now consider the results and explain the values using physicalreasons. Figure 7.13 shows the impact on fuel analysis from the malfunction/dysfunction table (included in table 7.29) and figure 7.14 includes the irreversibilityincrease of each component of the power plant.

The intrinsic malfunction is the easiest to explain. When the fourth section of thehigh-pressure turbine was working at 10% less isoentropic efficiency than normal, theoutput power (P in the F-P table 7.24) decreased but the section's steam conditionswere maintained. The irreversibility increased (the turbine section increased itsirreversibility to 3,270 kW, table 7.29), and the resources required to produce thesame output power increased as well as the unit exergy consumption of thecomponent ∆k (∆k = 0.2144, see table 7.27). Multiplying by the product in thissection (19.23 MW), the malfunction was 4.12 MW (see table 7.29). The fuel impactdue to the inefficient component was 6.01 MW (see also the table 7.29).



FIG

UR

E 7

.13

Impa

ct o

n fu

el a

naly

sis

whe

n th

e ef

ficie

ncy

of th

e H

PT4

is d

ecre

ased

10%

.

FIG

UR

E 7

.14

Irrev

ersi

bilit

y in

crea

se a

naly

sis

with

the

inef

ficie

ncy

in th

e H

PT4

.



TAB

LE

7.2

3 F

-P d

iagr

am in

des

ign,

out

put p

ower

of 1

22 M

W .



TAB

LE

7.2

4 F

-P v

alue

s w

ith in

effic

ienc

y in

HP

T4 (1

0% lo

wer

effi

cien

cy).



TAB

LE

7.2

5 K

P m

atrix

in d

esig

n (1

22 M

W).



TAB

LE

7.2

6 K

P m

atrix

with

inef

ficie

ncy

in H

PT4

(10%

).



TAB

LE

7.2

7 V

aria

tion

de K

P w

ith in

effic

ienc

y in

HP

T4.



TAB

LE

7.2

8 Ir

reve

rsib

ility

mat

rix I

with

an

inef

ficie

ncy

in H

PT4

.



TAB

LE

7.2

9 D

ysfu

nctio

n/m

alfu

nctio

n m

atrix

with

inef

ficie

ncy

in H

PT4

(10%

isoe

ntro

pic

eff.)

.



TAB

LE

7.3

0 M

alfu

nctio

n m

atrix

with

inef

ficie

ncy

in H

PT4

(1%

isoe

ntro

pic

eff.

is v

arie

d).



As mentioned, the inefficiency also affected MSF unit behavior. This inducedmalfunction was expected because the steam leaving the HPT4 section is consumedin the MSF unit. Since the MSF product (exergy flow of distilled water) is constant,the variation of the steam conditions entering the MSF unit directly affects itsbehavior (we assumed that the condensate returned to the deaerator maintains itsproperties independent of inlet conditions). A higher enthalpy in the exhaust vapor ofthe high-pressure turbine should imply a higher specific consumption per freshwaterunit produced, as seen in the variation of the unit exergy consumption (∆k = 0.075,see the corresponding value in table 7.27). But the thermoeconomic model gives animportant function to the MSF unit: the negentropy generated in the MSF heater. Theinefficiency in the fourth section of the high-pressure turbine generated a highernegentropy in the MSF unit (the entropy of exhaust vapor from the turbine increaseswith a lower isoentropic efficiency). This negentropy is a secondary product of theMSF unit. Its increase implies a decrease in unit exergy consumption of thecomponent (the ∆k variation due to negentropy generation is –0.154, see table 7.27).Balancing the two terms, the increase in unit exergy consumption in the MSF wasnegative, provoking –537 kW induced malfunction. In conclusion, the value of theinduced malfunction in this component was due to the thermoeconomic model. It didnot correspond to the expected response to an intrinsic malfunction in the fourthsection of the high-pressure turbine. In other words, the negentropy generated in theMSF unit reduced the cost of water because the negentropy generated in the MSF unitreduced the cost of the condenser.

The physical analysis of the inefficiency did not detect any more inducedmalfunctions in the system, although two components had a higher inducedmalfunction than the accuracy of the simulator: the boiler (–128 kW) and the firstsection of the HPT (–331 kW). These values are the consequence of a very highcomponent product since unit exergy consumption increase was almost zero in bothcases. This consumption varied only slightly because the steam needed to produce therequired power increased with the simulated inefficiency.

The irreversibility increase in each component (table 7.29) was calculated bysubtracting the fuel-product differences in tables 7.23 and 7.24, or by adding the unitmalfunction to the unit dysfunction generated by the malfunction of the rest of unitsin the system. In our example, the boiler dysfunction was the highest, mainly due tothe malfunctions in HPT1, HPT4 and MSF (see table 7.29), the most important onesdetected in this case. The dysfunction generated in the condenser was also important,but the cause was again the three components undergoing the malfunction. Boiler andcondenser production increased by about 3 MW (this additional production wasrequired by the rest of components to maintain the final production of the steampower plant with the inefficiency simulated in the fourth section of the HPT). In theproductive structure (figure 7.5), the two products generated by these twocomponents (the availability of the steam generated in the boiler and the negentropygenerated in the steam cycle) were easily apportioned to the rest of the plant



components. Figure 7.13 shows the irreversibility increase analysis of thisinefficiency.

Some explanations are required regarding the malfunction and dysfunction values ofthe non-physical components of our thermoeconomic model. A junction is a non-physical device and is fictitious in the productive structure. Its function, similar to thatof branching points, is structural, i.e. junctions and branches show how the resourcesare distributed among the plant devices. The malfunction and the dysfunctiongenerated in a junction must be zero: in equation (6.45) the unit exergy consumptionincrease in a junction is zero and the dysfunction coefficients φ responsible for thedysfunction generated by other components are also zero (remember that thedysfunction coefficients φ only depend on the unit exergy consumption k of thecomponent in operating conditions). However, a junction can generate a dysfunctionin other system components (see equation 6.46). The value of the dysfunctionstrongly depends on the dysfunction coefficients φ of each component where thedysfunction is generated. For example, the unit exergy consumption k of junction J4varies with a change in the unit exergy consumption of its exergy ratios r (theelectricity produced in the turbine sections). All the boiler φ coefficients were non-negative (the dysfunction generated by the junction in the boiler was not zero, –445kW). The junction usually generates dysfunctions due to the variation in the fuels(i.e., the product of the units that enter the junction) but the components that havenon-zero values in all their φ coefficients also suffer from the junction dysfunction.These special components are the boiler and condenser, which are interrelated withthe rest of components in the productive structure of the power plant (see figure 7.5).

The impact on fuel analysis is similar to the previous analysis, but here the impact onfuel consumption is the sum of the malfunction and the dysfunction generated byeach component in all others (see figure 7.14). Logically, the dysfunctions generatedby HPT1, HPT4 and MSF in the boiler and the condenser were the most important.

One of the most useful applications of the thermoeconomic diagnosis is themalfunction matrix. It provides information about the malfunction associated witheach component during an inefficiency. It is a very valuable tool to predict systembehavior without using the simulator (recall that the same results were obtained usingeither the diagnosis or simulator). We want to predict the additional fuel consumptionwith an inefficiency and maintain the equations that model the physical behavior ofthe plant in the simulator (performing each individual analysis for an operatingcondition). At least two premises are required to create the malfunction matrix:

The response of the system must be proportional to the degree of inefficiency (impacton fuel, associated malfunctions, etc.). To calculate the fuel impact of a knowninefficiency, the corresponding malfunction matrix need only be multiplied ordivided, depending on the ratio of the real inefficiency and the inefficiency defined inthe malfunction matrix.



To predict the effect of several malfunctions, the inefficient components must be localto their subsystems. The total impact on fuel can then be calculated as the sum of themalfunction matrices associated with the individual inefficiencies.

The second assumption is not necessary here because we only analyzed an individualinefficiency. The first premise could be checked by analyzing the graphic impact onfuel analysis versus the degree of inefficiency applied. In this case, the isoentropicefficiency of the fourth section of HPT was varied from –10% to +10% with respectto the design efficiency (around 85%). Figure 7.15 shows how the linearity of thesensitivity analysis varies while the plant load is kept constant (122 MW of outputpower in extraction mode and 2,400 T/h freshwater production).

FIGURE 7.15 Additional fuel consumption when varying the isoentropic efficiency in HPT4.

Plant behavior was linear when we varied this inefficiency (figure 7.15). Themalfunction matrix in table 7.30 is very useful to calculate the malfunctionsassociated with each inefficiency (by summing the columns and multiplying eachcomponent by its product). The high unit exergy consumption of the condenser pumpwas the result of the mathematical model (as were the high values of the low-pressureheater no. 2). In these two cases, the low product values minimized the previouslymentioned effect in the malfunction analysis. The MSF components of this matrixwere very high but the low exergy value of its product (freshwater) induced a lowmalfunction. All sections of the high-pressure turbine were affected by theinefficiency but, as expected, the fourth section had the highest value. The values ofthe first section of the high and low-pressure turbine were also considerable sincethey had to readapt their products to maintain final production.

The effect of the inefficiency can be quantified as the total cost (including capital costof devices) of electricity and water, which is especially illustrative for plantmanagers. Electricity increases 0.000033 $/kWh per 1% variation in efficiency(figure 7.16) or a yearly savings of 35,200 $/y.

Inc. fuel consumption

-6000

-4000

-2000

0

2000

4000

6000

-10 -8 -6 -4 -2 0 2 4 6 8 10

% eff. in HT4

kW



FIGURE 7.16 Unit electricity cost when the isoentropic HPT4 efficiency is modified.

Surprisingly, the effect on the cost of water was even greater –in absolute terms- thanfor electricity (0.00047 $/m3 per 1% inefficiency, or almost 10,000 $/y; figure 7.17),although the relative cost of electricity varied more. This is because the apparentlylocal inefficiency changes the steam conditions sent to MSF unit, which implies anadditional cost, mainly due to the high exergetic cost associated with water (seetable 7.28).

FIGURE 7.17 Unit distilled water cost when the isoentropic HPT4 efficiency is modified.

The main conclusions of our analysis of an inefficiency in the final section of thehigh-pressure turbine are:

• The isoentropic efficiency only affected the behavior of the inefficientcomponent and provoked a small malfunction in the MSF plant by changingexhaust vapor conditions leaving the HPT.

Electricity cost

0,0373

0,0375

0,0377

0,0379

0,0381

0,0383

-10 -8 -6 -4 -2 0 2 4 6 8 10

% eff. in HT4

$/kWh

Water cost

1,266

1,270

1,274

1,278

-10 -8 -6 -4 -2 0 2 4 6 8 10

% eff. in HT4

$/m3



• The steam power plant could not readapt its behavior to maintain the finalproduction. Additional live steam was required to produce the electricitydemanded, consuming more fuel (6,035 kW). The dysfunction analysis wasuseful to observe how the components that provide the energy quality to thesteam cycle (boiler and condenser) have to increase their productions that aredistributed to the rest of plant components, producing the additional power notsupplied by the inefficient section of the turbine.

• The effect of this inefficiency was quite significant and represented an additionalwater and electricity cost of 0.00047 $/m3 and 0.000033 $/kWh respectively, perunit of efficiency (or 45,200 $/y in both products). The nature of the inefficiencyshould be studied carefully, taking into account several factors including repairtime, personnel costs and the price of the components if they need to be replacedto avoid extra natural gas consumption.

• The sensitivity analysis applied in a reasonable range revealed a linear responseby the simulator mathematical model. Thus, the malfunction matrix can substitutenew simulations with this inefficiency and predict its effect on a real plant.

• The value of the induced MSF unit malfunction demonstrates that plantdiagnosis strongly depends on the thermoeconomic model. Sometimes thephysical consequences of an inefficiency cannot be translated into a table ofexpected values for fuel impact or irreversibility increase of a process orcomponent.

7.3.2.2 Using the cleaning ball system in the brine heater

The fouling resistance Rf (for definition see section 3.2.1) involves three resistances:

• Resistance due to fouling or scale inside the tube.

• Resistance due to fouling outside the tube.

• Resistance due to the accumulation of non-condensable gases in the vapor.

The cleaning ball system can only reduce tube fouling or scale in a heat exchanger,one of the main causes of performance loss in MSF plants in the high-temperaturesections. In general, fouling occurs when deposits are laid down on the heat transfersurfaces (Hanbury, Hodgkiess and Morris, 1993). These deposits can be due to scalefrom the reverse solubility of salts in the brine, dirt from corrosion products orbiological growths on the surface. The latter only occurs in the rejection section andcan be controlled by feed chlorination. The scale type depends on the brine chemistry,plant conditions, chemical additives to the feed and the type of cleaning. In general,calcium carbonate and calcium sulfate are the most common forms of scale.



TAB

LE

7.3

1 F

-P v

alue

s (d

esig

n) fo

r the

MS

F pl

ant.

Nom

inal

pro

duct

ion

in s

umm

er.



TAB

LE

7.3

2 F

-P v

alue

s w

ithou

t fou

ling

in h

eate

r. N

omin

al p

rodu

ctio

n, 3

2 ºC

sea

wat

er.



TAB

LE

7.3

3 K

P m

atrix

in d

esig

n.



TAB

LE

7.3

4 K

P m

atrix

with

out f

oulin

g in

hea

ter.

NTO

S d

ata

case

.



TAB

LE

7.3

5 V

aria

tion

of th

e K

P m

atrix

with

out f

oulin

g in

hea

ter.

NTO

S c

ase.



TAB

LE

7.3

6 I

rrev

ersi

bilit

y m

atrix

with

out f

oulin

g in

hea

ter.

1,90

0 T/

h an

d 32

ºC

sea

wat

er te

mp.



TAB

LE

7.3

7 M

alfu

nctio

n/dy

sfun

ctio

n m

atrix

with

out f

oulin

g in

hea

ter.

NTO

S c

ase.



TAB

LE

7.3

8 M

alfu

nctio

n m

atrix

var

ying

foul

ing

in h

eate

r 0,0

0001

m2

K/W

in N

TOS

cas

e.



The fouling effect in the MSF plant was simulated, quantified and analyzed for thebrine heater. The cleaning ball system was assumed to be working at maximum andfouling in brine heater was set to zero (fouling factor in heater at design conditionswas 0.00025 m2·K/W), although this is impossible in practice since outside foulingand non-condensable gas phenomena cannot be avoided. The reference case had thesame operating conditions without the cleaning ball system. For this reason, mostmalfunctions associated with the cleaning ball system are negative (they should becalled ‘benefunctions’), i.e., they save fuel. The malfunction analysis was performedat 1,900 T/h water production with 32 ºC seawater (the first of the two examples).Water production was constant although but this does not imply a constant productexergy flow.

To explain how fouling in the brine heater affects MSF behavior, first the recyclebrine, seawater to reject and make-up flows (R, SR, F) were maintained at designedlevels. The condensation temperature of the steam provided by the steam power plantalso remained constant. A lower fouling inside the brine heater improved the overallheat transfer coefficient, which implied that:

• The interstage temperature difference in the heater was reduced, i.e. the coolingbrine temperatures entering (TF,1) and leaving (TBT = TB,O) the heater wereincreased.

• The temperature rise of the cooling brine in the heater was also increased.

A higher Top Brine Temperature (TBT) implies a higher flash range ∆T and morefreshwater production. The temperature profile of the recovery and reject section isaltered if the temperatures entering and leaving the recovery section are increased. Ifthe final production is to be maintained, R, SR and F must be decreased. But even theTBT and TF,1 reach higher than design temperatures (and therefore the temperaturesprofile in recovery and reject sections). Brine fouling is a global variable in the MSFunit since it affects the rest of the system.

About 1,411 kW of fuel was saved with the benefunction in different plantcomponents (not only in the heater). Less steam was consumed, affecting thebehavior of the steam power plant when less steam is required for this extraction, asin the next example.

Inefficiency was diagnosed using the symbolic notation explained in Chapter 6. Thesimulator in Chapter 5 was used to obtain the F and P values for the referenceconditions and inefficient situation. Following the productive structure of the MSFunit (see figure 7.11) with 1,900 T/h water production, the F and P values areincluded in tables 7.31 and 7.32 respectively, using the nomenclature in table 7.4 forthe components. In this case, the matrix was 18×18 (11 components and 7 junctions)whereas the matrix was 30×30 (26 components and 4 junctions) in the power plantanalysis. The ∆ ⟨KP⟩ matrix (table 7.35) was built by subtracting the ⟨KP⟩ referencematrix (table 7.33) and the ⟨KP⟩ matrix (table 7.34) corresponding to an inefficient



operation. The latter were obtained by dividing the F-P tables. The irreversibilitymatrix |I⟩ (table 7.36) contains the irreversibility and unit exergy costs of eachcomponent. Finally, the dysfunction table (table 7.37) contains the dysfunctioncoefficients φ and the malfunction array MF. The column sum is the fuel impact of acomponent and the row sum is the irreversibility increase of a component. Figure7.18 shows the impact on fuel analysis in the malfunction/dysfunction table. Figure7.19 includes the irreversibility increase of each component of the power plant.

Having obtained the dysfunction matrix (which provides information about the stateof a given plant with an inefficiency), we analyzed the malfunctions in thedesalination plant components. The physical variations in the MSF plant with thebenefunction were translated into malfunctions. The first important conclusion is thatthe malfunction generated in the brine heater was not the highest. The malfunctioninduced in other components was more important than the intrinsic malfunctionprovoked by heater inefficiency. Therefore, each malfunction should be analyzedseparately.

The intrinsic malfunction is quite easy to explain. Using the cleaning ball system inthe heater improves the heat transfer process in the tubes. This reduces the thermalirreversibility, assuming that the mechanical and chemical irreversibility ismaintained. The irreversibility was reduced by 865 kW in this component (see table7.37), increasing its exergetic efficiency. The reference unit exergy consumption wasreduced with respect to the inefficient condition (respectively 1.096 and 1.075 intables 7.33 or 7.34), or the change in unit exergy consumption ∆k decreased withrespect to the reference state. The decrease of the unit exergy consumption (–0.02) isincluded in the ∆ ⟨KP⟩ matrix (table 7.35). The product of the heater is the coolingbrine heated to the TBT (42,021 kW), then the intrinsic malfunction of –875 kW. Theimpact on fuel saved in this component was 2,419.6 kW (both values are intable 7.37).

The induced malfunction in the recovery section was positive (203 kW) and theirreversibility increase was 247 kW in the process (see both values in table 7.37).Consequently, the variation in unit energy consumption in this component with heaterfouling was positive (∆k = 0.025, see table 7.35), i.e. the process was more inefficientin this section. Assuming that the distillate quantity and quality is maintained, anuncontrolled TBT increases due to the effect of the cleaning ball system in the brineheater. Although cooling brine was also increased, the temperature rise was lowerthan the TBT (because of the two effects of fouling in the brine heater). Thus, theamount of energy needed to produce the distillate in the recovery section was higherthan in the design situation. The efficiency of the component decreased and provokedan additional fuel consumption of 494 kW.



FIG

UR

E 7

.18

Impa

ct o

n fu

el a

naly

sis

whe

n th

e fo

ulin

g in

BH

is n

egle

cted

.

FIG

UR

E 7

.19

Irrev

ersi

bilit

y in

crea

se in

the

MS

F w

ith B

H=0

. N

TOS

cas

e.



On the other hand, the temperature profile in the reject section remained almostunchanged because the effect of the heater fouling is far away from the reject section.A higher TBT also implies lower recycled brine R flowing toward the reject section tomaintain final production. This flow is the main contribution of the reject section toproduce distilled water, which was maintained constant (the reject section product ispractically the final product of the MSF unit). Less energy was needed to producefreshwater. The efficiency was increased and the variation of the unit exergyconsumption and irreversibility generated were reduced in the inefficient case (∆k = –0.013, ∆I = –91 kW, resulting in a negative malfunction of 91 kW (see tables 7.35 and7.37) and 725 kW in fuel savings.

The induced malfunction associated with the mixer was quite substantial (-- 942 kW).The make-up F and recirculation R flows were decreased by the cleaning ball systemin the heater under constant final production of freshwater. The mechanical andthermal irreversibility of the mixing process is logically reduced if the two flowsentering the mixing chamber are reduced. The unit exergy consumption of theprocess or the irreversibility increase was reduced (∆k = -- 0.0159, ∆I = –912 kW, seetables 7.35 and 7.37) and 1,360 kW (table 7.37) of fuel was saved.

The fictitious device is a non-physical component intercalated at the beginning of theproductive structure of the MSF unit (see figure 7.11). It charges the exergy costs ofthe distiller flows with the plant residues: brine blowdown and reject coolingseawater. There is no physical explanation for malfunction of this device but thethermoeconomic model suggests two causes:

• The exergy flow of the residues is higher (the fuel of this unit). The specificenergy or mass flow rate of one of the two streams must be increased by aninefficiency in the MSF unit.

• The steam to the brine heater decreases (here the unit product corresponds to thefuel of the brine heater).

The second cause provoked a positive malfunction of 938 kW in the FD and1,222 kW of extra fuel consumption (table 7.37). The same MSF residues are sent outto sea at a higher cost to the distiller when less fuel is consumed to produce water.

The amount of irreversibility in each component is the sum of its own malfunctionplus the dysfunctions generated by the malfunction of other components. Only thefictitious device had a considerable dysfunction value (–764 kW), generated bymalfunctions in the brine heater, recovery and reject sections, mixer and severaljunctions (see table 7.37). As above (tables 7.31 and 7.32), the product of thefictitious device decreased more than 700 kW to readapt the use of the cleaning ballsystem in the brine heater under constant freshwater production. The dysfunctiondepends on the φ coefficients of the component. Since the fictitious device is at thebeginning of the productive structure, most of its φ coefficients were non-zero values.In conclusion, dysfunction analysis is clearly unrelated to the physical behavior of the



plant, i.e., the MSF components do not vary production to maintain the final distillatedue to the malfunctions.

The impact on fuel analysis was similar to the previous analysis. In this case, theimpact on fuel consumption was the sum of the malfunction and dysfunctiongenerated by each component on others (table 7.37). As expected, the dysfunctiongenerated by the brine heater, recovery and reject section and the mixer are important.

Note that the malfunction/dysfunction analysis considers an unchanged final product.This is quite easy when the product is electricity, since the simulator can control thepower output. However, the exergy flow of freshwater as the final product has twoterms: the mass flow and the specific exergy of water leaving the distiller unit(quantity * quality, see Structural Theory, Valero et al., 1993). The mass flow must becontrolled in the simulator but the specific distillate exergy is a function of thedistiller temperature. The latter temperature depends on the operating conditions ofthe MSF unit: seawater temperature and concentration, fouling in each section, etc. Inour example, the water temperature leaving the distillate pump did not vary with thebrine heater fouling. If the temperature changed, the impact on fuel associated withthe change in total production is k*∆P, where k* is the exergy cost of the product and∆P is the variation of the total production (the value is shown in the right-bottomcorner of the DF/MF table). The impact on fuel associated with the variation of thefinal product can be more important than the impact on fuel associated with thevariation of the unit exergy consumption ∆k in each component (the total contributiondue to both variations is also shown at the end of the DF/MF table).

Having explained the most important results of MSF plant diagnosis without heaterfouling, we can consider one of the most useful applications. Figure 7.20 can be usedto study the linearity of the simulator (and a real plant, since the simulator wasvalidated using data collected from a physical plant) to validate the malfunctionmatrix. Changing the design fouling factor in the brine heater (25×10–5 m2·K/W)gradually to zero saves fuel when the plant was operating to produce the samequantity of water as in the example.

The model was reasonably linear when heater fouling was varied, at least for nominalproduction conditions in summer. However, at maximum operation, some internalflows like the recirculation flow R, make-up F or seawater to reject SR reached amaximum and the effect of the cleaning ball system was lower than expected for thatload.

Table 7.38 shows the malfunction matrix associated with each component when thefouling factor in the brine heater was changed by 0.00001 m2 K/W. The mostimportant terms of the matrix are associated with the above mentioned components:fictitious device, brine heater, recovery and reject sections and the mixer. These valuescan also be explained by analyzing the malfunctions associated with this inefficiency.As expected, pumps were not affected by brine heater fouling. The impact on fuel due



to changes in brine heater fouling can be calculated by multiplying the components ofthe malfunction matrix by the product of each component and their unit exergy cost(obtained from the irreversibility matrix). Sometimes the malfunction matrix hascomponents with high values, but the low product or low exergy cost associated withthis component results in a lower impact on fuel.

FIGURE 7.20 Impact on fuel analysis when the fouling in heater is varied.

Knowing the monetary cost of fresh water as a function of an inefficiency helps plantmanagers take decisions on using the cleaning ball system, depending on thecompromise between consumption, operating costs and energy saved. Note that thecost of water decreased when heater fouling was decreased (figure 7.21).

FIGURE 7.21 Monetary cost of distillate when the fouling in heater is varied.

In the nominal case, 0.00045 $/m3 was saved when fouling was decreased by10--5 m2·K/W (or 7,650 $/y). Although the effect of the cleaning ball system was verydifficult to translate into a constant fouling variation, the system reduced the fouling

Inc. fuel consumption-3000

-2500

-2000

-1500

-1000

-500

0

0 5 10 15 20 25fouling*10-5 in BH

kW

Water cost

1,460

1,465

1,470

1,475

0 5 10 15 20 25

fouling*10-5 in BH

$/m3



factor several times over (see section 3.6.1) when the cleaning system wasperiodically connected (for example in a four-hour cycle). At maximum production,the cost decreases due to the effect of purchase costs and because the increase inexergy cost is lower than in the nominal case (remember that the internal flows reacha maximum during maximum winter production).

The sensitivity analysis of the monetary cost and fuel impact takes into account thatthe exergy costs k* of the steam to the brine heater and the electricity for the MSFpumps are different from unity (unit exergy cost of steam to heater and vacuum systemwas 2.55 and 2.5 respectively and exergy cost of electricity was 2.85). So, the real costof producing water and the consequences of an inefficiency can be dealt with correctly.

In summary, using the cleaning ball system in the heater had the followingconsequences:

• It changed the temperature profiles of the cooling, flashing brine and distillate inthe MSF unit. As the brine heater is settled at the beginning of the process, thetemperatures of the recycle brine before and after the heater were affected. Asthose temperatures enter and leave the recovery section, the whole system wasinfluenced by this inefficiency.

• As a consequence of the last point, the induced malfunctions in the rest ofcomponents were higher than the intrinsic malfunction in the heater, taking intoaccount the dimensions of each component. However, the dysfunction analysisdid not provide any interesting information on how the components readaptedtheir production to maintain the final production of freshwater. The non-physicalcomponents cannot be explained from a physical viewpoint.

• The model was linear under changes in heater fouling. So, the malfunctionmatrix can be used to predict the fuel saved with the cleaning ball system orcomponent malfunctions.

• The cleaning ball system in heater increased the TBT of the unit. This implies alower consumption to produce the same amount of freshwater, but also provokesscale formation due to the high-operation temperatures. Consequently, thecleaning ball system should be continuously maintained in the heater to keep thefouling factor low. If the system is not operating, scale formation will reduce theeffectiveness of the condenser and the whole MSF unit.

7.3.2.3 The effect of recovery section fouling on steam power plant behavior

An inefficiency in a power plant or desalination unit will provoke additional fuelconsumption. The analysis was performed separately for both plants. But if aninefficiency in the MSF unit provokes an increase/decrease in steam consumption bythe brine heater, how does the steam power plant readapt?. If the electricity and waterproduction are kept constant, the inefficiency in the MSF unit is an inlet parameterthat seriously affects power plant behavior. This parameter is the amount of steam



diverted to the MSF unit. Our analysis considered an inefficiency detected‘downstream’ and the MSF unit can induce the malfunctions; an inefficiency detecteddownstream should also be quantified upstream. So, we considered the ‘co-lateral’effects of a co-generation plant with this example.

In this example, electricity production was held at 122 MW in MCR operatingconditions. The fouling in the recovery section was reduced to zero by the cleaningball system and the live steam leaving the boiler was maintained. The first physicalconsequence (the effects of the cleaning ball system in the recovery section areexplained in section 6 of Annex 1) of an inefficiency was a reduction in steamconsumption from 89.1 to 71.1 kg/s (corresponding to a freshwater production of2,400 T/h, the maximum distillated in a MSF unit). Extraction to the MSF unit is atthe end of the high-pressure turbine, so the latter was not affected by the differentuses of the exhaust steam from this turbine. If the steam leaving the high-pressureturbine is not diverted to the MSF unit when some of it is saved with the cleaning ballsystem, an extra quantity of steam goes to the low-pressure turbine. Although thefinal section of the turbine has to maintain the exhaust pressure (we maintain theexternal parameters of the plant), at least the efficiency of the first section of the low-pressure turbine is improved with a higher entering mass flow rate (remember that thelow-pressure turbine is designed to work in condensing mode, that is, when no steamis derived to the MSF unit).

But the electricity production increases since the amount of steam and the efficiencyof the low-pressure turbine have been improved. To maintain the final production, theamount of steam leaving the boiler must decrease from 156.1 to 146.6 kg/s. Theredistribution of the flows inside the steam cycle was similar to the previous analysis;the low-pressure turbine produces the electricity that the high-pressure turbinecannot. This produces a negative impact when more steam is forced to flow in thelow-pressure cycle (that is, passing through the condenser and not through the MSFheater). The feedwater system cools and additional fuel is required to reach the setpoint conditions of live steam in the boiler. Finally, the steam conditions leaving thehigh-pressure turbine are slightly varied (recall that the exhaust pressure is controlledby the MSF unit).

Tables 7.39 and 7.40 show the F-P values for the steam power plant in design andoperation (when the inefficiency occurs in the recovery section of the MSF unit). The⟨KP⟩ matrix is shown in tables 7.41 and 7.42 for the design and inefficient case,respectively. The ∆ ⟨KP⟩ matrix is the key to analyze the system with this inefficiency(table 7.43). Table 7.44 contains the |I⟩ matrix and the exergy cost array. Thedysfunction matrix [DF] including the malfunction array MF is shown in table 7.45.Figures 7.22 and 7.23 include the impact on fuel analysis and irreversibility increase.



TAB

LE

7.3

9 F

-P v

alue

s in

des

ign,

122

MW

out

put p

ower

.



TAB

LE

7.4

0 F

-P v

alue

s w

ithou

t fou

ling

in re

cove

ry s

ectio

n. M

CR

cas

e.



TAB

LE

7.4

1 K

P m

atrix

in d

esig

n. M

CR

cas

e.



TAB

LE

7.4

2 K

P m

atrix

with

out f

oulin

g in

reco

very

sec

tion.

MC

R c

ase.



TAB

LE

7.4

3 V

aria

tion

of K

P w

ithou

t fou

ling

in re

cove

ry s

ectio

n. M

CR

cas

e.



TAB

LE

7.4

4 I

rrev

ersi

bilit

y m

atrix

with

out f

oulin

g in

reco

very

sec

tion

(MC

R c

ase)

.



TAB

LE

7.4

5 M

alfu

nctio

n/dy

sfun

ctio

n m

atrix

with

out f

oulin

g in

reco

very

sec

tion

(MC

R c

ase)

.



TAB

LE

7.4

6 M

alfu

nctio

n m

atrix

whe

n th

e fo

ulin

g in

reco

very

is v

arie

d 0,

0000

1 m

2·K

/W in

MC

R c

ase.



FIG

UR

E 7

.22

Impa

ct o

n fu

el a

naly

sis

with

out f

oulin

g in

RC

S, M

CR

cas

e.

FIG

UR

E 7

.23

Irrev

ersi

bilit

y in

crea

se a

naly

sis

of s

ectio

n 7.

4.2.

3.



The first analysis compared the fuel impact associated with the whole plant (a fuelsavings of 24.00 MW), with the fuel saved in the MSF1 unit (26.47 MW). This meansthat the steam power plant is forced to work under less-efficient operating conditions.We will now explain the most significant values in the malfunction array of table7.45, relating the physical consequences to the matrix values.

The deaerator component mixes and preheats the feedwater from the condenser.Irreversibility in the mixing process is lower because the mass flows entering thedeaerator are lower during operation (where the live steam mass flow rate is reducedto maintain the final production) than in the design. Thermal irreversibility was lowerbecause the cold flow entering the mixer was increased and its irreversibility wasreduced by 828 kW (see table 7.45). The efficiency of the component should therebyincrease, i.e., the variation of the unit exergy consumption was negative in thecomponent (∆k = –0.085, see the ∆ ⟨KP⟩ table 7.43), implying an inducedmalfunction of –682 kW.

The feedwater temperature entering the boiler was reduced because the low-pressurecycle increased its contribution to the whole system. The boiler consumed additionalresources to reach the set point of the steam turbine (93 bar, 535 ºC). The increasedexergy unit consumption in the boiler was ∆k = 0.004, and the malfunction associatedwith the component was finally 858 kW (see tables 7.45 and 7.43 respectively), withan associated fuel impact of 576 kW.

The first section of the high-pressure turbine had a 1,320 kW induced malfunction asa consequence of the mathematical model. The efficiency of the Curtis blade wascorrelated as a function of the live steam from the boiler under different operatingconditions, as in this case this amount has been decreased considerably, theisoentropic efficiency in the section decreases (and consequently the exergy andentropy properties of steam leaving the section). Consequently, ∆ ⟨KP⟩ in table 7.43was positive (∆k = 0.0267) with a 1,320 kW malfunction and a 1,954 kW fuel impact.

Surprisingly, the fourth section of the high-pressure turbine had a decreasedisoentropic efficiency but a negative induced malfunction (–484 kW, see table 7.45)and 1,500 kW fuel was saved. This abnormal behavior is explained by the exhaustpressure of the high-pressure turbine which decreased with the amount of live steam,allowing the output power (produced in the section) to increase. Since the product ofthis component is the output power (according to the thermoeconomic model), theunit exergy consumption was lower during the inefficiency, resulting in a ∆k value of–0.025 (see table 7.43 with the ∆ ⟨KP⟩ components).

1. In this case the MSF unit is the component inserted in the structure productive of the steam power plant.Exergy product of the MSF unit is kept constant.



As mentioned above, the efficiency of the first section of the low-pressure turbineincreased because the amount of entering steam increases considerably and its∆ ⟨KP⟩ component was negative (∆k = –0.319, table 7.43). The irreversibility of theprocess was reduced by 1,965 kW, with a –2,177 kW induced malfunction and 2,970kW fuel savings.

The malfunction associated with the MSF was positive, although the fuel impactsaved was very high in this component. The dysfunction generated by this componentachieved the desired fuel savings (a large negative value). The reason for the 12,491kW induced malfunction (table 7.45, which coincides with the irreversibility increaseof the process in this case) was the drastic reduction in negentropy (which wasintroduced in the thermoeconomic model of the steam cycles to account for the heatrejected in the condenser). This negentropy is a subproduct in the productivestructure. The unit exergy consumption of the unit increased (∆k = 1.837, table 7.43).

The most important dysfunctions in the boiler and condenser were caused by thecomponents with the most important malfunctions (figure 7.24). The boiler andcondenser suffered dysfunctions of 1,620 kW and 752 kW from the deaerator;1,812 kW and –1,215 kW from the first section of the high pressure turbine,-- 1,391 kW and 404 kW from the fourth section of this turbine and –24.55 MW and--13.68 MW from the MSF unit, respectively. The final product in the boiler wasreduced by more than 10 MW to maintain the total production at a lower steamconsumption (total boiler dysfunction, –22.65 MW). The condenser also increasedproduction by 16 MW (total condenser dysfunction, –13.71 MW). The high φcoefficients promote high dysfunction since they are related to the position of thecomponents in the productive structure of the system.

Following the methodology in Chapter 6 for the diagnosis of complex systems, theDI array is the column sum of the dysfunctions. The values of the main componentsare described in the previous paragraph (2.43 MW for the deaerator, 634 kW for theHPT1, and –38.9 MW for the MSF unit!). The impact on fuel associated with eachcomponent (table 7.45) was obtained by adding the malfunction array MF. This is theadditional fuel consumed due to the change in the operation of each unit with respectto the operating conditions and no inefficiency.

Having obtained the most relevant results in the inefficiency analysis, the malfunctionmatrix can be used as a predictive tool to diagnose the effects of the inefficiency.Figure 7.24 shows the total impact on fuel associated with the inefficiency variationin the recovery section (the effect of fouling in the recovery section when fouling isvaried). Here the malfunction matrix did not exactly predict the malfunctions becausethe response of the mathematical model was not perfectly linear when varying thesteam to the MSF unit (under maximum production, some internal flows of thedistiller are forced to keep a constant value). However, the MSF model behavedlinearly at nominal production.



FIGURE 7.24 Impact on fuel depending on fouling in recovery section.

Since the model responded in a non-linear way to the efficiency, the most rigorousdiagnosis should separate simulate each case (avoiding the malfunction matrix). Themalfunction matrix in table 7.46 provides the ‘linearized’ malfunction induced ineach component when the fouling in the recovery section is changed by0.00001 m2·K/W. The condenser pump and low-pressure heater coefficients wereagain high (as are the brine heater and feed pump values), although the low productdid not induce an important malfunction. As expected, the MSF coefficients were thehighest and the HPT1 and HPT4 were also elevated.

FIGURE 7.25 Monetary cost of electricity depending on the fouling in recovery section.

The ‘monetary diagnosis’ (figures 7.25 and 7.26) involves the cost of electricity andwater as a function of recovery section fouling during maximum production in winter(which was the load requested in the example). The cost of electricity increased a bit(4×10–6 $/kW·h) when the fouling was decreased. The malfunction analysis proved


-24000

-18000

-12000

-6000

0

0 3 6 9 12 15

kW

Electricity cost

0,03788

0,03790

0,03792

0,03794

0,03796

0 3 6 9 12 15

fouling*10-5 in RCS

$/kW·h



that the steam power plant decreases its global efficiency with an inefficiency in therecovery section of the MSF unit (as explained at the beginning of this section).

Water cost followed the expected results, 0.0057 $/m3 was saved with a 0.00001 m2

K/W decrease in recovery section fouling (see figure 7.26) or 120,000 $/y.

FIGURE 7.26 Cost in $ per cubic meter of water when recovery section fouling is varied.

In summary:

• The results of the inefficiency diagnosis imply that fouling in the recoverysection considerably reduces the amount of steam needed to produce freshwater.The cost of water was drastically reduced (see figure 7.26) when the cleaningball system operates in the recovery section of the MSF distillers. But areduction in the derived steam did not imply improved plant performance (forthis particular case, the electricity cost was even higher).

• A consequence of this example is that the co-generation plant should operate atan optimum ratio between the steam to MSF and the live steam produced in theboiler. The installation of the cleaning ball system in the MSF distillers shouldbe taken into account in the design in the co-generation plant, because theoptimum point of the performance in the dual plant is seriously affected by theuse of this system.

• An inefficiency in the MSF unit provokes induced malfunctions in severalcomponents of the steam power plant (boiler, deaerator, some turbinesections…). Therefore, this type of inefficiency detected ‘downstream’ has amore global effect than an inefficiency local to a component in the steam powerplant.

Water cost

0,95

0,97

0,99

1,01

1,03

1,05

0 3 6 9 12 15

$/m3



7.3.3 Analysis of several inefficiencies

7.3.3.1 Analysis of several simultaneous inefficiencies in the steam power plant

We will now consider the combined effect of several simultaneous inefficiencies indifferent components and the effect of induced malfunctions. This exercise reinforcesthe concept of local and intrinsic malfunctions. We simulated the physical effect ofthese inefficiencies (changing main flowstreams) and describe related malfunctions,dysfunctions, and additional fuel consumption in the steam power plant (the directproblem).

The analyzed inefficiencies were:

• TTD in high-pressure heater no. 1 increases 5 ºC

• Isoentropic efficiency of the feed pump decreases 10%.

• Isoentropic efficiency of the first section of the high-pressure turbinedecreases 5%.

• Isoentropic efficiency of the first section of the low-pressure turbine decreases15%.

• Isoentropic efficiency of the fourth section of the high-pressure turbinedecreases 10%.

If the TTD of the HPH1 increases, the feedwater leaves the heater at a lowertemperature and the turbine extraction temperature increases. If the heater does notneed to preheat the feedwater the same amount, the extraction mass flow should bereduced. The boiler is also affected because feedwater enters the economizers at alower-than-design temperature.

The mechanical irreversibility of the feed pump increases if the isoentropic efficiencyis lower than expected. The pump responds by consuming more power and thefeedwater temperature increases.

The exhaust conditions of the high and low-pressure turbine are more or lessmaintained with the MSF unit and ambient conditions. When the isoentropicefficiency of several sections of the steam turbine decreases, the steam conditions arenot significantly affected by inefficiencies in other sections. The output power in eachinefficient section is not enough to maintain final production but other sections cannotproduce this extra power since their efficiency was maintained constant. Thus,although the system demands more live steam, the efficiency of the boiler does notnecessarily decrease.



TAB

LE

7.4

7 F

-P v

alue

s in

des

ign,

122

MW

out

put p

ower

.



TAB

LE

7.4

8 F

-P v

alue

s w

ith in

effic

ienc

ies

in fi

ve c

ompo

nent

s (M

CR

cas

e).



TAB

LE

7.4

9 K

P m

atrix

in d

esig

n (M

CR

Cas

e).



TAB

LE

7.5

0 K

P m

atrix

with

sev

eral

inef

ficie

ncie

s in

MC

R c

ase.



TAB

LE

7.5

1 V

aria

tion

of K

P m

atrix

with

sev

eral

inef

ficie

ncie

s in

MC

R c

ase.



TAB

LE

7.5

2 Ir

reve

rsib

ility

mat

rix w

ith fi

ve in

effic

ienc

ies

in p

ower

pla

nt (M

CR

cas

e).



TAB

LE

7.5

3 M

alfu

nctio

n/dy

sfun

ctio

n m

atrix

with

five

inef

ficie

ncie

s in

MC

R c

ase.



FIG

UR

E 7

.28

Irrev

ersi

bilit

y in

crea

se in

sec

tion

7.3.

3.1.

FIG

UR

E 7

.27

Impa

ct o

n fu

el a

naly

sis

in s

ectio

n 7.

3.3.

1.


CHAPTER 8

Synthesis, contributions and perspectives

8.1 Synthesis

This Ph. D. Thesis brings together three topics that have never been thoroughlyinterrelated.

• Desalination processes.

Water scarcity is a serious problem for humanity now and in the future. Waterresources are being depleted by excessive consumption and polluted by humandevelopment. Fortunately, the problem can be solved by desalting seawater orreusing wastewater. Chapter 1 describes the current situation in arid countries andhow to solve some water shortages. Chapter 2 summarizes the most commonmethods to produce freshwater for human consumption.

• Energy consumed in desalination.

The detailed description of desalination processes in Chapter 2 including theconsumption and energy producing process in desalination. It is very energyintensive and should not be isolated from energy production processes.Desalination designers normally present the energy consumption of differentdesalination processes in terms of electrical consumption (kW·h/m

3

) even if theyconsume thermal energy. The current trend is to separate the two processes. Theexistence of big companies that only produce electricity or only water widens thegap between desalination and energy communities. This thesis demonstrates thatenergy and water suppliers interact in a co-generation installation to provide bothproducts and that both systems should not be analyzed separately.


324


• Thermoeconomic analysis of the most common desalting and power installations.

We used thermoeconomic techniques normally applied to power plants. In thisway, we took advantage of everything that thermoeconomics provides to obtainan in depth knowledge of a very complex system. The energy supplier was alsoanalyzed since the desalting plant is coupled with the power plant. We analyzedone of the most common processes used in arid regions with important waterscarcity problems: multi-stage flash desalting plants that use fossil fuels to alsoproduce electricity with the help of a conventional power plant. Thethermoeconomic analysis was also applied to a steam power plant providingsteam to the MSF unit.

The main contribution of the thesis is contained in Chapter 7. The thermoeconomicanalysis of the dual plant included cost analysis, diagnosis, and optimization. Theresults of the different thermoeconomic techniques applied in each case are asfollows:

1. The cost analysis is very useful to find the enormous possibilities of energysavings under different configurations of the co-generation plant. A detailedanalysis of the internal costs pin-points the component responsible forirreversibilities. New processes can also be combined to produce minimum waterand electricity costs.

2. Plant diagnosis helps to elucidate component interaction. The differentrelationships and effects of component inefficiencies on other subsystems can besuccessfully quantified by considering both plants together. The interaction canalso be separated by varying component efficiency (malfunction) and thesubsequent additional component production (dysfunction). This thesis includesone example of a thermodynamically isolated (power plant) and non-isolated(MSF unit) system. However, the diagnosis cannot be used as a predictive tool inthe control systems because the theory cannot yet recognize the origin of theinefficiencies.

3. Local optimization optimizes the operating conditions by calculating theminimum product cost of each plant unit. It is very valuable to design new co-generation plants or to readapt existing ones.

4. Product cost and price must be calculated from their origin. Cost is the resourcesconsumed to produce something and price is the value obtained when this productis sold. Benefit is the difference between both concepts. Once the price is known,the cost must be minimized to obtain the maximum benefit (plant operatingconditions of the plant can be changed intentionally depending on demand andprice).

Main contributions


325

8.2 Main contributions

This Ph. D. Thesis applies the most recent thermoeconomic techniques (normallyonly applied to power generation systems) to a power and desalination plant. Themain contributions of the thesis are listed here:

8.2.1 Simulator of a dual-purpose power and desalination plant

A simulator was used to provide the thermodynamic states of desalination and powergeneration process. Thermal desalination processes have been simulated by chemicalengineers (Jernqvist, Jernqvist and Aly, 1999; Ettouney and El-Dessouky, 1999), butthe steam producing system is not considered. The two processes were separatelyintroduced in the simulator to independently analyze each process. A combined statecan be modelled by introducing the same quantity of steam sent to the MSF unit. Thesimulator was validated using performance data cases and real operating data for thedual-plant with a MSF unit and a steam power plant. It can model the effect ofinefficiencies in the two systems for diagnosis.

The mathematical model applied under different operating modes accuratelyreproduces (for engineering purposes) the real state of the plant, despite the scarcityof data for each operating mode. The most difficult case is when the amount of steamentering the low-pressure turbine is so low that the system has to consumemechanical energy to move the blades. In this case, the input conditions of themathematical model have to be continuously restricted in order to preserve thestability of the model. The mathematical models of the MSF and steam turbine powerplant were solved using a solution algorithm that simultaneously handles the wholeset of model equations. The packages containing the sequential scheme to solve theflowsheeting of a plant are discarded here, although this threatens model stabilityunder different operating conditions.

8.2.2 State of the art in Thermoeconomics

An effort was made in Chapter 6 to review and summarize Thermoeconomicmethodologies. The Structural Theory was finally adopted to explain the concepts,procedures and applications of these techniques, including the matrix formulationand new terms like induced malfunction, intrinsic malfunction and dysfunction. Thethermoeconomic analysis of the dual plant was based on this theory and its latestimprovements.


326


8.2.3 F-P definition for a MSF unit

The F-P definition of the thermoeconomic analysis of the MSF unit (see section7.1.3.2) highlights the cost of water production in the recovery and reject section,taking into account the thermodynamic processes in the plant. Several F-P definitionssolved the model but none gave appropriate costs of device functionality nor for themain flow degradation in the MSF plant.

8.2.4 Cost analysis of a dual-plant

A detailed cost analysis of the power and desalination plant was carried out underdifferent operating modes (see section 7.2). The physical (or formation) costs of themain components were calculated. Exergy operating costs are available for eachcomponent as well as the thermoeconomic costs of water and electricity. These lattercosts were successfully compared with other methodologies (EL-Nashar, 1999;Kronenberg et al., 1999) that do not use the thermoeconomic model and providemuch less information.

8.2.5 Diagnosis of a complex system

The thermoeconomic diagnosis in section 7.3 was based on Structural Theory andSymbolic Thermoeconomics (Torres et al., 1999). This is the first time that amalfunction/dysfunction analysis is applied to a complex energy system (26components and 4 junctions for the power plant and 11 components and 7 junctionsfor the MSF plant). Usually the matrix formulation is only used to study simplersystems like the gas turbine co-generation plant in Chapter 6. The malfunction/dysfunction table provides a lot of information that should be carefully analyzedwhen an inefficiency is simulated in the plant (exergy costs, impact on fuel,irreversibility increase in each component...). The relationships between componentsare rapidly found with in terms of efficiency variation (intrinsic or inducedmalfunction) or additional production (dysfunction). This method does not find thenature of the malfunction. Whether it is intrinsic or induced depends on userknowledge.

The symbolic notation and Structural Theory also helps to formulate the malfunctionmatrix to find the quantity of additional resources consumed due to an inefficiency(without using the simulator). This matrix is used when the system responds linearlyto the applied inefficiencies. If the inefficiency is local to the component, individualmatrices of different inefficiencies may be added to make one large malfunctionmatrix with the same effect.

To date, most analyzed systems demonstrate additivity of diagnosis: severalinefficiencies can be disaggregated. However, the MSF did not fulfil this requirement

Perspectives


327

in the diagnosis of complex systems. As seen above, this fulfilment strongly dependson the physical structure of the system.

8.2.6 Local optimization of the steam power plant

Local optimization of the main components of the steam power plant also provides aglobal minimum final cost of electricity and water. Global optimization of the steampower plant (based on local optimization, see section 7.5) has never been applied to aset of 14 free-design variables that govern plant behavior. Local optimization can beapplied to the steam power plant because it is thermodynamically isolated, i.e. localperturbations only affect one component (demonstrated in the diagnosis of the steampower plant).

8.2.7 Cost, price and benefit

Finally, a new methodology is included to assign product cost, price and benefit usingexamples to demonstrate that cost and price are independent. The main objective ofan investment is to obtain maximum benefit, which does not always imply minimumcost.

8.3 Perspectives

8.3.1 Improving existing plants. Process integration

One of the immediate consequences of this work is to increase the ways existingplants may reduce energy consumption. After analyzing one of the most developedmethods to produce freshwater and electricity, some areas were found lacking. Oursuggestions include:

• Promoting the simulation of both processes (water and energy production)integrated in specific simulators.

• Applying our methodology to other desalination processes. Our objective was tofind the most efficient process at the lowest energy consumption, the best way toproduce both energy and water and not contribute to fossil fuel depletion, airpollution and climate change. The importance of hybrid configurations, i.e. theintegration of other processes to produce energy (wind, solar, tides, even nuclear)and water (MSF/RO or MED/RO units, heat absorption pumps) will possibly bethe trend in the next decades. 'Building-block’ software will be required tothermoeconomically analyze any process producing water or electricity.

• Thermoeconomics only considers the costs of operation, installation andmaintenance, but processes also involve other costs that should be taken into


328


account including environmental (pollution, brine discharges...), costs ofproducing materials, biological costs, building costs, etc. All these are lessdeveloped than the costs evaluated in the thermoeconomic analysis. Sincethermoeconomic techniques can consider any type of costs, they should beintroduced in the global theory when they are more or less available.

8.3.2 Improvements in thermoeconomic diagnosis

Cost analysis provides a lot of information about how processes degrade and theenergy quality of fluids in a plant. It is very useful to quantify the efficiency of plantprocesses. Diagnosis is directly oriented to an on-line implementation in the controlsystem. In this regard, a big effort is needed to improve thermoeconomic techniquesrelated to plant diagnosis (the ‘

inverse problem

’) when the data acquisition system(DAS) finds deviations from the target conditions for each operating mode and load.The diagnosis should detect the inefficiency from the data collected by the DAS totake corrective actions. New communication technologies (Internet) allow remotecontrol of the on-line implementation of system diagnosis, so plant managers can alsosee the benefits of the implementation. The on-line system can also be installedhigher up in the control system, i.e. it can be used for all units. The units respond as awhole unit when a deviation is detected. Regarding maximizing benefit, the higherlevel of hierarchy can help decide the most profitable configuration and thepossibility of connecting the hybrid systems installed in the plants for additionalwater or energy in peak or low-demand periods.

Some previous steps may be needed to solve the inverse problem of thethermoeconomic diagnosis:

• Analyze the problem of ‘noise’ provoked by the real boundary conditions in aninstallation: set points, ambient conditions, fuel quality, different loads andoperating modes. We should consider the way to isolate the system from theseboundary conditions or their effects. Once the problem is solved, the diagnosisfinds the real causes of the deviations.

• Thermoeconomics should be used to investigate the development of newtechniques to study component interdependence during induced malfunctions in acomplex system. The non-additivity of the diagnosis in these interrelated systemsopens an interesting new line of investigation.

• Clarifying the application and interpretation of dysfunctions generated in/by plantcomponents. We could consider performing the analysis under a constant finalproduction (of the complex system), depending on the finality of the analysis.

Perspectives


329

8.3.3 Integrating attitudes

Thermoeconomic analysis provides enormous amounts of information about plantfunctioning and possible savings. This information should be clearly integrated in avertical structure, i.e. a different kind of information should go to each level in theplant staff hierarchy. For example, if we divide the organization of the plant in threelevels, we have:

Operator level

The information derived from the diagnosis is the most important at this level. Thephysical and economic effects of the inefficiencies and the control strategies (securityversus economy) are the main issues for operators.

Technician level

This field includes optimizing existing systems and investigating and developingmore efficient systems, and new control systems to handle inefficiencies.

Managers level

Cost analysis must be the main tool used by the plant managers since they managethe whole plant (assuming there are many units per plant). Cost, price and benefitmust be clearly differentiated at this level.

Training seminars are necessary for all levels to inform staff about the“thermoeconomic culture” and its benefits for humanity.

8.3.4 Sustainable desalination

Desalination is one of the most promising means of producing drinkable water with alow impact on the environment. The tendency of the desalination scientificcommunity is to reduce energy consumption and substitute primary energy sourcesby renewable sources on a large scale. This tendency should be followed in all areasthat influence our future. A more global analysis, like the Life Cycle Analysis (LCA),including additional aspects (residues, product use, materials, etc) is also necessary toprovide an overall perspective of desalination processes.

Research on desalination using solar energy for existing or new methods, should beencouraged. As solar technology develops, the cost of producing water (on a largescale) will decrease as will the strong dependence on energy.

Promoting the installation of simple devices to provide water in acceptable conditionsat a very low (or zero) cost in non-developed/isolated areas (Africa, India), is another


330


means of redistributing world resources and promoting a more equal development inthe world community.

8.3.5 Promote energy and water interactions

Water and energy are both limited resources, vital to the quality of the human life.The rapidly growing human population increases the demand for these resourcesevery day. Several international organizations are dedicated to energy and severalothers to water, but there is a marked lack of attention to combined water and energyissues.

This Ph. D. Thesis demonstrates that energy and water cannot be studied separately.A multi-disciplinary group of water and energy specialists has been formed(International Study Group for Water and Energy Systems (ISGWES), settled at theUniversity of Zaragoza) to promote the interchange of ideas, scientific knowledgeand sustainable development of water and energy systems. Some of the investigationlines commented above will be promoted by ISGWES.


ANNEX 1


The thermoeconomic diagnosis of the dual plant in section 7.3 considered severalinefficiencies described at the beginning of the chapter. Each inefficiency requiresmany tables and figures, all of which are included in this annex. Thus, this annex isan overall view of the effects provoked by one or more inefficiencies in the powerand desalination plant.

The following individual inefficiencies (described but not analyzed in section 7.3)were applied:

• Inefficiency in the HPH1: variation in terminal temperature difference of heater.

• Inefficiency in the feed pump: reduced efficiency.

• Inefficiency in the high-pressure turbine: efficiency analysis in the first section.

• Inefficiency in the low-pressure turbine: efficiency variation in first section.

• Inefficiency in the recovery section: effect of reduced fouling in MSF.

• Inefficiency in the reject section: effect of the fouling factor.

The analysis was performed under different operating conditions but is onlypresented for one load, the MCR case for the power plant and NTOS performancecase for the MSF unit. The effect of the different loads in the two systems issummarized in sections 7.3.4 and 7.3.5.


332


A1.1 Effect of an inefficiency in the high-pressure heater

no.1 (HPH1)

The TTD of the HPH1 was varied to analyze the effect on the steam power plant.The heater TTD is the difference between the temperature of saturated vaporextracted from the turbine and the feedwater leaving the heater. Since the conditionsof the steam extracted in the turbine are maintained, a higher TTD implies a poorerheat transfer inside the heater tubes. The feedwater therefore leaves the heater at alower temperature than expected. Consequently, the extraction mass flow to thisheater decreases and the boiler produces less live steam. Although the live steamneeded for the electricity demand is reduced, the boiler heats the feedwater from alower temperature and natural gas consumption increases. An excessive change inheater TTD may also sharply vary the levels inside the heater, leading to dangerousproblems or even drains in the heaters. The consequences are very difficult toevaluate with conventional component analysis since the model does not incorporatethe security system layout of the power plants.

The mathematical explanation of varying TTD involves the malfunction anddysfunction matrices detailed in section 7.3. Tables A1.1 and A1.2 include the

F

-

P

definition of the steam power plant in design and operation with an inefficiency inthe HPH1: the TTD increases 5 ºC. The output power used was 122 MW, but otherexamples were at 60, 90 and 140 MW, corresponding to the parallel mode,extraction mode with partial load and condensing mode, respectively (section 7.3.4).These are the most important operating modes (the most operating hours per year) inthe power and desalination plant. Tables A1.3 and A1.4 include the

⟨

KP

⟩

tablescorresponding to the design and inefficient operation, and table A1.5 is the

∆

⟨

KP

⟩

matrix. Table A1.6 contains the

φ

coefficients of the irreversibility matrix

|

I

⟩

withexergy cost of components. Finally, table A1.7 is the malfunction/dysfunction tablebuilt using table A1.6. Table A1.8 is the malfunction matrix when we vary the TTDof the HPH1 1 ºC. Figures A1.1 and A1.2 show the impact on fuel analysis and theirreversibility increase per component.

The highest malfunctions in table A1.7 corresponded to the boiler, HPH1 (theinefficient component) and HPT1. The rest of the components were within simulatoraccuracy (< 100 kW). Varying the heater TTD only affected the componentsinteracting with the heater. This inefficiency did not induce malfunctions in othercomponents.

Effect of an inefficiency in the high-pressure heater no.1 (HPH1)


333

TAB

LE

A1.

1 F

-P v

alue

s in

des

ign

(MC

R c

ase)

.


334


TAB

LE

A1.

2 F

-P v

alue

s in

ope

ratio

n w

ith 5

º C

TTD

resp

ect t

o de

sign

.



335

TAB

LE

A1.

3 K

P m

atrix

in d

esig

n (M

CR

cas

e).


336


TAB

LE

A1.

4 K

P m

atrix

with

inef

ficie

ncy

in H

PH

1 (M

CR

cas

e).



337

TAB

LE

A1.

5 V

aria

tion

of K

P m

atrix

whe

n TT

D in

the

HP

H1

is 5

ºC

hig

her t

han

the

expe

cted

.


338


TAB

LE

A1.

6 Ir

reve

rsib

ility

mat

rix w

ith th

e in

effic

ienc

y in

HP

H1.



339

TAB

LE

A1.

7 M

alfu

nctio

n/D

ysfu

nctio

n m

atrix

whe

n th

e TT

D in

HP

H1

is 5

º C

hig

her.


340


TAB

LE

A1.

8 M

alfu

nctio

n m

atrix

whe

n TT

D in

HP

H1

is v

arie

d 1

ºC



341

FIG

UR

E A

1.2

Irrev

ersi

bilit

y an

alys

is w

hen

the

TTD

in H

PH

1 is

incr

ease

d 5

ºC.

FIG

UR

E A

1.1

Impa

ct o

n fu

el a

naly

sis

with

an

inef

ficie

ncy

in H

PH

1.


342


In the simulated intrinsic malfunction, increasing the TTD of the HPH1 by 5 ºC(which could be interpreted as a problem in the heat transfer mechanism of theheater), decreases more than expected the feedwater temperature leaving the heater.The extraction flow to this heater also decreases (to meet the energy balance of theheater). In any case, the inefficiency increases the irreversibility in the heater(

∆

I = 16.5 kW, see table A1.7) when the temperature difference in the water tubesincreases. The first effect (a lower heating process in the heater) is more importantthan the second (a lower extraction flow). Unit exergy consumption varied by

∆

k = 0.020 (see table A1.5). The result of the inefficiency was a 223.6 kW intrinsicmalfunction (or an associated 272 kW impact on fuel).

The effect induced in the boiler is clear: if the feedwater leaves the heater at a lowertemperature, the boiler consumes additional fuel to maintain the live steamconditions (which are fixed in the simulator and the real plant). The

∆

⟨

KP

⟩

component, i.e. the variation of component unit exergy consumption (table A1.5)was

∆

k = 0.005. As the boiler product was very high (the heat transferred to thefeedwater was about 210 MW), the malfunction was 1,179 kW with an associated830 kW impact on fuel. The total impact on fuel associated with this inefficiencywas 1,048 kW. In this case, the malfunction induced in the boiler was moreimportant than the intrinsic malfunction in the heater.

The amount of steam flowing in HPT1 was lower than in design, although this effectdisappears when HPH1 extraction was reduced. The steam flowing through thesecond section of the HPH is maintained. The energy production in this section ismaintained, but the efficiency in this section is lightly decreased (the efficiency ofthe Curtis blade is higher as the live steam flow grows), then the variation of the unitexergy consumption of the section is

∆

k = 0.0026, then we have a little malfunctioninduced in this section of 130 kW, and an impact on fuel associated of 209 kW.

The dysfunctions due to the HPH1 inefficiency emphasizes the results of otherinefficiencies in the steam power plant: only the boiler and the condenser sufferdysfunctions generated by component malfunctions (HPH1, boiler or HPT1). Thedysfunction generated in the boiler was positive. The

φ

coefficients were positive butnegative for the condenser, provoking a negative dysfunction. The junction J2produced a –393 kW dysfunction in the boiler associated with its exergy unitconsumption variation. This variation is explained by the productive structure of thesteam power plant (see figure 7.5): feedwater heated in the boiler in one of the inletsof that junction.

The power plant model varied linearly to a one degree change in the heater TTDwhen comparing the amount of fuel saved. Figure A1.3 shows this effect forelectricity production in the extraction mode of the example (122 MW). The effect isnon-linear when TTD is negative and close to zero (the design TTD for thisoperating condition is –1.7 ºC). The analysis could be performed avoiding this range



343

of temperature differences since the impact on fuel associated with the whole plantcan be less than 200 kW and the mathematical model cannot diagnose theinefficiency with less than 100 kW accuracy.

FIGURE A1.3

Impact on fuel associated with a variation in the TTD of HPH1. 122 MW power plant production.

In any case, the observed trend could be used to apply the malfunction matrix to thisinefficiency. Some matrix components had large values. The condenser pump andlow-pressure heater No.2 were high due to the behavior of the mathematical modelat the condenser exit area (see section 4, mathematical model of the power plant).The feed pump and deaerator also had considerable values due to the decrease infeed water flow in the high-pressure zone (provoked by the HPH1 inefficiency).

FIGURE A1.4

Cost of electricity when varying TTD in HPH1 (MCR performance case).

The effect on the cost of electricity and water was not as important as the impact onfuel associated with the inefficiency in the turbine section. It implied an additional0.000009 $/kW·h in electricity and 0.00017 $/m

3

in freshwater per degree Celsius inthe TTD of the HPH1. This could save 9,600 $ and 3,570 $ if the plant were


-1200

-800

-400

0

400

800

1200

-5 -4 -3 -2 -1 0 1 2 3 4 5

TTD (º C) in HPH1

kW

Electricity cost

0,03775

0,03780

0,03785

0,03790

-5 -4 -3 -2 -1 0 1 2 3 4 5TTD (º C) in HPH1

$/kwh


344


operating yearlong at these loads. Figures A1.4 and A1.5 refer to this assumption,emphasizing the linearity of the model (except from –2 to 0 ºC).

FIGURE A1.5

Cost of water when varying TTD in the first HPH (MCR performance case).

In summary:

• the heater TTD affects heater behavior and components receiving feedwaterheated by the inefficient heater (the boiler). The inefficiency did not result onlylocal to its component, and the associated malfunctions were higher in othercomponents than the intrinsic one. The rest of the components were notconsiderably affected compared to an inefficiency in the steam turbine sections.

• The impact on fuel associated with the additional cost of water or energy due tothe inefficiency was not important when compared with other inefficiencies (thetotal saving of 14,000 $/y in both products could be obtained by decreasing theTTD of the HPH1 by 1 ºC). This only refers to the range where the modelresponds linearly to TTD variation (the variational analysis was assumed to belinear). If the TTD is abnormally high, an excess heater level or excessiveheating in the economizers can lead to extreme induced malfunctions that cannot be calculated in the diagnosis (Valero, Torres and Lerch, 1999). Therefore,heater TTD should be carefully controlled. A by-pass in one of the HPHs is avery good example of heater inefficiency, but it is very difficult to simulate. Themodel needs to be modified considerably to consider this inefficiency.

• The results of the HPH1 inefficiency could be extrapolated to HPH2, taking intoaccount the amount of heat transferred in the two heaters (usually the HPH2 usesless steam to heat the feedwater). The effect on the boiler should also bereduced.

Water cost

1,2710

1,2715

1,2720

1,2725

1,2730

-5 -4 -3 -2 -1 0 1 2 3 4 5TTD (º C) in HPH1

$/m3

Effect of feed pump isoentropic efficiency


345

A1.2 Effect of feed pump isoentropic efficiency

The feed pump pressurizes the feedwater before it enters the boiler. An inefficiencyinside the pump mechanism (assuming that the pump can supply the specifiedpressure) only slightly increases feedwater temperature since the temperature rise inpumping a liquid is also low. Therefore, this inefficiency should not induceimportant malfunctions in other components. The most important consequence isthe significant increase in feed pump power consumption. Additional live steam isrequired to maintain the net output power.

If the feed pump is coupled with an auxiliary turbine providing energy, aninefficiency should affect other components because an abnormally functioningauxiliary turbine would redistribute the flows in the steam/water cycle of the powerplant.

Feed pump behavior can be studied considering an isoentropic efficiency, a variablethat appears in our mathematical model. Pump efficiency decreased 12% withrespect to its characteristic curve at 122 MW (MCR performance case). Theinefficiency was also analyzed under different operating conditions (seesection 7.3.4). Tables A1.9 and A1.10 show the

F-P

values for design and operatingconditions. The

⟨

KP

⟩

matrices are written dividing fuels and the product of eachcomponent (tables A1.11 and A1.12). After these matrices are built, the

∆

⟨

KP

⟩

matrix and irreversibility matrix

I

are immediately processed, containing the unitexergy costs of the components (tables A1.13 and A1.14). The malfunction/dysfunction matrix with the dysfunction coefficients is included in table A1.15. Themalfunction matrix with the extra consumption when the pump isoentropicefficiency increases 1% is finally included (table A1.16). Figures A1.6 and A1.7show the impact on fuel and the irreversibility increase in all components for thissimulated inefficiency.

We will now explain the physical analysis using results from the inefficiencydiagnosis. The malfunction array demonstrates that the feed pump does not induceany malfunction in the rest of the components. Only the boiler and the inefficientcomponent have a malfunction greater than 30 kW. The mechanical irreversibilityincreases when the pump has serious problems to reach the demanded pressure.These internal frictions also increase the temperature of the pressurized feedwaterleaving the pump. So, the thermal irreversibility also appears in the inefficiency andthe final reversibility increase was

∆

I = 475 kW (see table A1.15). The unit exergyconsumption increase was obvious (

∆

k = 0.200, see table A1.13). The intrinsicmalfunction was therefore 409 kW, and the impact on fuel associated with theinefficiency is 608 kW (the total impact on fuel taking for the whole system is750 kW).


346


TAB

LE

A1.

9 F

-P d

esig

n va

lues

.



347

TAB

LE

A1.

10 F

-P v

alue

s w

ith in

effic

ienc

y in

FP

: -12

% in

its

effic

icie

ncy.


348


TAB

LE

A1.

11 K

P m

atrix

in d

esig

n (M

CR

cas

e).



349

TAB

LE

A1.

12 K

P m

atrix

whe

n th

e in

effic

ienc

y in

FP

is d

etec

ted.


350


TAB

LE

A1.

13 V

aria

tion

of th

e K

P m

atrix

whe

n th

e FP

is w

orki

ng im

prop

erly.



351

TAB

LE

A1.

14 Ir

reve

rsib

ility

mat

rix w

ith -1

2% in

the

FP e

ffici

ency

.


352


TAB

LE

A1.

15 D

ysfu

nctio

n ta

ble

and

mal

func

tion

arra

y w

hen

the

FP is

wor

king

with

12%

low

er e

ffici

ency

.



353

TAB

LE

A1.

16 M

alfu

nctio

n m

atrix

whe

n th

e ef

ficie

ncy

of th

e FP

var

ies

1%.


354


FIG

UR

E A

1.6

Impa

ct o

n fu

el a

naly

sis

whe

n a

inef

ficie

ncy

in F

P is

det

ecte

d.

FIG

UR

E A

1.7

Irrev

ersi

bilit

y an

alys

is w

ith th

e irr

ever

sibi

lity

in F

P.



The malfunction induced in the boiler was mainly due to the large amount ofproduct it generates (210 MW), since its efficiency and unit exergy consumption arenot varied (the ∆k component is close to zero, see the ∆ ⟨KP⟩ matrix in table A1.13).This provokes a malfunction of –80 kW and an impact on fuel of only –69 kW.

The irreversibility analysis shows that the dysfunctions associated with the boilerand condenser were the highest (754 and –472 kW respectively) and were generatedby the feed pump. The weight coefficients φij (see table A1.14) were quite high in therows corresponding to boiler and condenser (the unit consumption was changed inthis case because the final products of these components had to increase 370 and550 kW respectively to maintain the net output power). In these rows, the pumpinefficiency dysfunction was provoked by varying the unit exergy consumption ofcomponents more related to other components (i.e., the boiler and the condenser).

Since the feed pump does not induce malfunctions and the model reacts linearly tovariations in pump efficiency, the malfunction matrix is an exact tool to quantifyadditional fuel consumption for this inefficiency. Figure A1.8 demonstrates thislinear behavior at the extraction mode load (122 MW).

FIGURE A1.8 Effect of feed pump efficiency on fuel consumption. Variational study in the MCR performance case.

The cost of electricity and water as a function of feed pump inefficiency was veryclear and linear (see figures A1.9 and A1.10). We can save 0.000003 $/kW·h and0.00006 $/m3 in electricity and freshwater production with a 1% increase in pumpefficiency. The relative effect on electricity (the effect per unit produced) issupposedly greater than the effect on water. For a constant yearly production, a 1%isoentropic efficiency implies a savings of 3,530 $/y in electricity and 1,260 $/y inwater.


-600

-400

-200

0

200

400

600

800

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

% eff. in FP

kW



FIGURE A1.9 Effect of pump inefficiency on electricity cost (MCR performance case).

FIGURE A1.10 Water cost when the efficiency of the feed pump is varied.

The main results of the inefficiency analysis were:

• As expected, the effect of the feed pump inefficiency was only local. Theincrease in feedwater temperature leaving the pump was almost insignificant.The additional electrical consumption of the pump did not change the steamcycle behavior. The additional fuel supplied the extra electrical consumption ofthe feed pump. The effect of this inefficiency is not as important as inefficienciesin other components, such as the steam turbine sections (less than 5,000 $/y inthe combined production of water and electricity).

• The feed pump is not strategic in a power plant. Its effects need only beconsidered if an inefficiency stops the plant because of a broken pumpcomponent (i.e. the linearity of the variational analysis is not valid).

• The product of the steam power plant must be the net output power. The effect ofthis inefficiency is not clearly noted in the system if gross output power ismaintained.

Electricity cost

0,03776

0,03778

0,03780

0,03782

0,03784

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

% eff. in FP

$/kWh

Water cost

1,2710

1,2715

1,2720

1,2725

1,2730

-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

% eff. in FP

$/m3

Effect of an inefficiency in the first section of the high-pressure turbine (HPT1)


A1.3 Effect of an inefficiency in the first section of thehigh-pressure turbine (HPT1)

The physical effects of an inefficiency in a turbine section are described in section7.3.2.1 as intrinsic malfunctions (steam path degradation, etc). HPT1 contains thegoverning section which is also affected by the control valves. Although the steampower plant always works at constant pressure, an intrinsic malfunction in the Curtisblade or wheels induces malfunctions downstream (see section 7.3.2.1). This variessteam conditions downstream because the steam conditions exiting HPT1 arechanged, even though the HPT exhaust pressure remains constant. As this steampasses through the rest of turbine sections, they should also be affected, althoughtheir isoentropic efficiencies remain almost constant due to a constant pressure ratio.Conditions of low-pressure steam are slightly varied as the HPT exhaust values aresent to the MSF unit. The exhaust pressure remains constant by definition. Thesystem can only respond to the inefficiency by producing additional live steam tomaintain output power. This extra steam is proportionally spread over the steamcycle so no new induced malfunctions (in pre-heaters or pumps) arise. The non-inefficient turbine sections produce the power that the inefficient section cannotproduce.

HPT1 efficiency was varied to observe its effect on other plant components andadditional consumption. We considered a production of 122 MW in extraction modewith a 5% decrease in isoentropic efficiency. The diagnosis was also developed at asimilar degree of inefficiency for 60 MW (parallel mode), 90 MW (extraction mode)and 140 MW (condensing mode).

Tables A1.17-A1.24 show, step by step, the methodology applied in the previoussections. Tables A1.17 and A1.18 are the F-P definition tables of the design andinefficient situation, tables A1.19 and A1.20 are the ⟨KP⟩ matrices. The ∆ ⟨KP⟩matrix and the irreversibility matrix are depicted in tables A1.21 and A1.22, and the[DF] matrix and the malfunction matrix are shown in tables A1.23 and A1.24.Figures A1.11 and A1.12 show the impact on fuel and irreversibility increaseanalysis of the inefficiency.

An inefficiency in an component producing an important part of the final productshould have important consequences. Other components have to readapt the turbinesection to maintain electricity production and improve their efficiency (turbinesections) or consume more resources (boiler). A inefficiency diagnosis will explainthese ideas.



TAB

LE

A1.

17 F

-P v

alue

s w

ithou

t any

inef

ficie

ncy.

MC

R c

ase.



TAB

LE

A1.

18 F

-P v

alue

s w

hen

the

HP

T1 d

ecre

ases

5%

its

effic

ienc

y (M

CR

cas

e).



TAB

LE

A1.

19 K

P m

atrix

in d

esig

n (M

CR

cas

e).



TAB

LE

A1.

20 K

P m

atrix

whe

n th

e in

effic

ienc

y in

HP

T1 is

5%

in it

s ef

ficie

ncy.



TAB

LE

A1.

21 V

aria

tion

of th

e K

P w

ith th

e in

effic

ienc

y in

HP

T1 (M

CR

cas

e).



TAB

LE

A1.

22 Ir

reve

rsib

ility

mat

rix w

ith th

e in

effic

ienc

y in

HP

T1 (M

CR

cas

e).



TAB

LE

A1.

23 D

ysfu

nctio

n/m

alfu

nctio

n ta

ble

whe

n th

e ef

ficie

ncy

of th

e H

PT1

is d

ecre

ased

5%

.



TAB

LE

A1.

24 M

alfu

nctio

n m

atrix

whe

n th

e ef

ficie

ncy

of th

e H

PT1

is v

arie

d 1%

.



FIG

UR

E A

1.11

Impa

ct o

n fu

el a

naly

sis

whe

n th

e H

PT1

effic

ienc

y is

5%

less

than

the

expe

cted

.

FIG

UR

E A

1.12

Irrev

ersi

bilit

y an

alys

is w

ith th

e in

effic

ienc

y in

HP

T1.



The malfunctions of this inefficiency will be analyzed using table A1.23. Thecomponents with a malfunction that surpasses a non-negligible quantity are theinefficient component (HPT1), the boiler and the MSF unit. First we will explain theinefficient component. If the isoentropic efficiency of a turbine section decreases,the expansion line is moved away from the reversible process. The irreversibility inthe section increases by 1,667 kW. Since the turbine exhaust has a higher enthalpy(see the h-s diagram), the output power strongly decreases with respect to the designsituation (2,220 kW). This means that unit exergy consumption increases and theproduct decreases. The ∆ ⟨KP⟩ component of HPT1 was ∆k = 0.039 (see tableA1.21). The intrinsic malfunction was 1,948 kW, and the impact on fuel due to theinefficiency was 2,825 kW. Since the total impact on fuel in the plant was 3,732 kW,this parameter could be considered local to the system.

However, the malfunction associated with the MSF unit is negative(MF = --280 kW), if we assume that the water produced and the condensate returnedto the deaerator are constant. The is because the end point of the expansion line islocated in HPT. Steam leaving HPT has a higher enthalpy but also a higher entropy.The energy needed by the MSF unit also increases, decreasing efficiency. Thegenerated negentropy in the MSF unit is considered a secondary product of thecomponent and is beneficial (see section 7.3.2.1), so the final variation of the unitexergy consumption is negative (∆k = –0.041).

The malfunction associated with the boiler is also negative. As its product exergyflow is huge, the induced malfunction is –242 kW, although its unit exergyconsumption did not change very much (∆k = –0.0011, see table A1.21). The reasonis the increased feedwater temperature entering the boiler due to the additionalsteam required by the steam power plant to maintain the electricity production in theinefficient situation. The additional fuel consumed is not used for the sametemperature rise in the boiler with respect to the design conditions. The impact onfuel associated with the boiler is –175 kW, but the irreversibility in the componentincreases 3,341 kW. The last assumption is a consequence of the dysfunctionanalysis explained below.

The dysfunction analysis is quite similar to when other components sufferinefficiencies. Once again, the two components suffering from the dysfunctionsgenerated by the components with an inefficiency are the boiler and the condenser.In both components the highest dysfunction is provoked by the inefficientcomponent (2,616 kW for the boiler and –1,795 kW for the condenser), that is, thecomponent with the intrinsic and greatest malfunction. The sum of the dysfunctionsgenerated by the other components is the irreversibility increase associated witheach component. For example, the total dysfunction generated in the boiler is3,583 kW and its production is increased by 1,790 kW to maintain the finalproduction of the power plant.



Figure A1.13 shows the linearity of the model when the isoentropic efficiency isvaried from –5 to +5 %, in extraction mode under MCR (122 MW), in this figure thetotal impact on fuel associated to this inefficiency is analyzed.

FIGURE A1.13 Model linearity with respect to an inefficiency in HPT1.

The model behaved more of less linearly to variations of the inefficiency using thesimulator. Thus, the malfunction matrix can be used to predict the impact on fuel.Since the inefficiency does not provoke any important induced malfunctions in othercomponents, the malfunction matrix could also be used when several inefficienciesare occurring in different components.

FIGURE A1.14 Cost of electricity depending on the degree of inefficiency applied to HPT1 (MCR case).

The cost of electricity and water as a function of the isoentropic efficiency of HPT1illustrates its effect (see figures A1.14 and A1.15). A 1% decrease in the isoentropicefficiency in HTP1 means an additional cost of 0.00004 $/kW·h (44,900 $/y) inelectricity and 0.0005 $/m3 in water (11,800 $/y). Clearly the inefficiency should be


-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

-5 -4 -3 -2 -1 0 1 2 3 4 5

% eff. in HPT1

kW

Electricity cost

0,0375

0,0376

0,0377

0,0378

0,0379

0,0380

0,0381

-5 -4 -3 -2 -1 0 1 2 3 4 5

% eff. in HPT1

$/kWh

Effect of inefficiency in the first section of the low-pressure turbine (LPT1)


corrected to avoid additional costs, because the first section is responsible for a highpercentage of the total electricity produced in the steam power plant.

FIGURE A1.15 Cost of water when the isoentropic efficiency is varied from –5% to 5% with respect to design efficiency (MCR case).

The most important results derived from the analysis of this inefficiency include:

• HPT1 is very important in terms of additional fuel consumption and cost ofwater and electricity (more than 55,000 $/y savings in the two products when theinefficiency is improved by only 1%).

• The steam conditions exiting HPT1 also affect (to a lesser degree) some othercomponents receiving that steam, i.e. the MSF unit. In any case, the inefficiencycould be considered local to the turbine section.

• The HPT1 inefficiency should be avoided, even if the turbine needs repair toprevent against inefficiencies or failures, since the savings would be quicklyrecovered.

A1.4 Effect of inefficiency in the first section of the low-pressure turbine (LPT1)

The low-pressure turbine has only two sections in the power plant configuration.Unless the plant is working at condensing mode, the amount of steam sent to thisturbine is very low. Thus, an inefficiency in this section should have less effect thanother inefficiencies in the turbine sections. The induced malfunctions should bedetected in the second section of the low-pressure turbine. The degradation processcould be accelerated if the last section of the low-pressure turbine has to work as acompressor when the amount of steam diverted to this section is so low that thesteam cannot overcome the mechanical losses of the turbine. But this section also

Water cost

1,268

1,269

1,270

1,271

1,272

1,273

1,274

1,275

-5 -4 -3 -2 -1 0 1 2 3 4 5

% eff. in HPT1

$/m3



suffers from induced malfunctions form HPT (according to the definition of inducedand intrinsic malfunctions by Royo (1994) for a steam turbine). The amount ofsteam to the MSF unit gives the pressure of the steam leaving the high-pressureturbine. Some part of this steam is also introduced in the low-pressure turbine.Finally, the atmospheric conditions control the exhaust pressure of the turbinemaking the behavior of this section strongly dependent the ambient temperature.

This inefficiency analysis was performed for the MCR case (122 MW powerproduction with an extraction to the MSF unit of 89.68 kg/s). The physical effects ofthese inefficiencies were translated into malfunctions and additional fuelconsumption. The isoentropic efficiency of this section was 15% lower than thedesign efficiency (about the 76%).

Tables A1.25 and A1.26 show the F-P values of the simulation corresponding to thedesign and inefficient cases. If we apply the analysis for other operating modes(condensing or parallel mode, or 140 and 60 MW of output power, respectively), theproductive structure changes (see section 7.1), and the F-P definitions and the rest ofmatrices are different than in these examples. Tables A1.27 and A1.28 include the⟨KP⟩ matrices dividing the fuels and products of each component. Table A1.29 is the∆ ⟨KP⟩ matrix composed by the subtraction of the two last matrices, and table A1.30is the irreversibility matrix |I⟩ . Finally, table A1.31 is the dysfunction/malfunctiontable, and table A1.32 is the malfunction matrix associated with the inefficiency inLPT1. Figures A1.16 and A1.17 include the impact on fuel and the increase ofirreversibility.

An inefficiency in LPT1 is less important than in HPT1 in a co-generation plant. TheHPT does not detect an inefficiency. The conditions of the steam downstream theinefficient component do vary but the exhaust pressure is controlled by the externaltemperature and does not vary, although the exhausted vapor to the condenser canvary its humidity. Some other turbine sections have to readapt their production toproduce the electricity required, as their efficiencies do not vary when some amountof extra live steam is demanded to the boiler.

In the malfunction array of this inefficiency, the inefficient component (LPT1) andthe first section of the high-pressure turbine have a higher malfunction than theminimum accuracy of the simulator. The physical interpretation of thesemalfunctions will be connected. The irreversibility of the steam expansion increasesin the inefficient component of LTP1 (∆I = 2,062 kW, see table A1.31), when theisoentropic efficiency decreases. The electricity production of the componentreduces by 1,230 kW, and its variation of unit exergy consumption is ∆k = 0.522(see table A1.29). The last assumptions result in an intrinsic malfunction (that is, themalfunction created in the inefficient component of a system) of 3,408 kW. The totalmalfunction associated with the whole plant is 3,260 kW. Clearly this inefficiencydoes not provoke any induced malfunctions in the rest of the plant components.



TAB

LE

A1.

25 F

-P v

alue

s in

des

ign

(MC

R c

ase)

.



TAB

LE

A1.

26 F

-P v

alue

s w

ith th

e in

effic

ienc

y in

LP

T1, M

CR

cas

e.



TAB

LE

A1.

27 K

P m

atrix

in d

esig

n, M

CR

cas

e.



TAB

LE

A1.

28 K

P m

atrix

whe

n th

e ef

ficie

ncy

in th

e LP

T1 is

dec

reas

ed 1

5%, M

CR

cas

e.



TAB

LE

A1.

29 V

aria

tion

of th

e K

P m

atrix

with

an

inef

ficie

ncy

in L

PT1

, MC

R c

ase.



TAB

LE

A1.

30 I

rrev

ersi

bilit

y m

atrix

with

the

effic

ienc

y of

the

LPT1

dec

reas

ed 1

5%, M

CR

cas

e.



TAB

LE

A1.

31 D

ysfu

nctio

n/m

alfu

nctio

n ta

ble

for a

n in

effic

ienc

y in

the

LPT1

(15%

), M

CR

cas

e.



TAB

LE

A1.

32 M

alfu

nctio

n m

atrix

whe

n th

e ef

ficie

ncy

of th

e LP

T1 is

var

ied

1%, M

CR

cas

e.



FIG

UR

E A

1.16

Impa

ct o

n fu

el a

naly

sis,

sec

tion

A1.

4.

FIG

UR

E A

1.17

Irrev

ersi

bilit

y an

alys

is in

sec

tion

A1.

4.



HPT1 has a negative malfunction of 215 kW and ∆k = –0.004 (see table A1.29).This negative value is explained in the mathematical model of the steam turbine. Theamount of steam entering the Curtis blade is higher than expected and the sectionoperates more efficiently when the steam leaving this section is slightly increased.The total impact on fuel associated with this effect was –281 kW.

The dysfunction analysis applied to this inefficiency is very illustrative. Only theboiler and condenser suffer dysfunctions generated by the components withmalfunctions: HPT1 and LTP1. In both cases these components have to readaptproduction by 1,470 and 2,430 kW respectively, to maintain the additionalproduction required by the first section of the low-pressure turbine. Since these twocomponents redistribute their products over the rest of the components, their φijcoefficients are not zero. If there is a ∆kij coefficient whose value is not zero, thedysfunction generated by the last component in the first two components issignificant. The rest of components do not have any important dysfunction worthmentioning in our analysis.

Figure A1.18 shows the effect of varying the efficiency in this turbine section aroundthe design point. The efficiency was varied from –15 to +15% with respect to thispoint. Since the model was linear with respect to the inefficiency, the malfunctionmatrix (table A1.32) can be used to quantify the additional fuel consumption bymultiplying this matrix by the product and the unit exergy cost of every component.With this inefficiency there were no induced malfunctions (isolated component),making the malfunction matrix an exact guide to predict the increment on fuelconsumption.

FIGURE A1.18 Effect on the fuel consumption when the degree of inefficiency in the LPT1 is varied from the design point (MCR case).

The monetary cost (including the capital cost and device maintenance) of water andelectricity is one of the consequences of the diagnosis of the plant with respect to ancomponent inefficiency. Figures A1.19 and A1.20 show how the cost in electricity


-4000

-2000

0

2000

4000

-15 -12 -9 -6 -3 0 3 6 9 12 15

% eff. in LPT1

kW



increases 0.000015 $/kWh and the water increases 0.00006 $/m3 when the LTP1isoentropic efficiency decreases by 1%. In a year, at 122 MW and 2,400 T/h,15,000 $ and 1,280 $ are saved in electricity and water costs.

FIGURE A1.19 Cost of electricity for inefficiencies in LPT1 (MCR case).

FIGURE A1.20 Water cost per cubic meter for inefficiencies in LPT1. 122 MW in extraction mode (MCR case).

This section demonstrated that:

• The behavior of LPT1 is linear when its efficiency is varied within allowablelimits. It does not induce any significant malfunctions in other plant components,following the trend in other examples.

• As predicted in the first paragraph of this section, the cost of water andelectricity were not affected as much as by inefficiencies in HPT (only 16,300 $/y are saved in both products if the isoentropic efficiency is improved 1%).Therefore, the effect of an inefficiency in the turbine is proportional to theamount of steam entering the turbine section.

Electricity cost

0,0375

0,0377

0,0379

0,0381

-15 -12 -9 -6 -3 0 3 6 9 12 15

% eff. in LPT1

$/kWh

Water cost

1,2705

1,2710

1,2715

1,2720

1,2725

1,2730

-15 -12 -9 -6 -3 0 3 6 9 12 15

% eff. in LPT1

$/m3



• The most dangerous problem associated with inefficiencies in LPT is the steamquality when the efficiency is increased. Low quality steam can damage thewheels of the condensing turbine. The variational analysis can also be brokenwhen the inefficiency provokes a non-linear system response.

A1.5 Effect of the cleaning ball system in the recovery section

The recovery section is the most important component of the MSF unit. Therefore,the cleaning ball system inside the distiller tubes could provoke several malfunctionsin other plant components. In this section we analyze the fouling reduction effect.

The benefits of reducing fouling in the reject section can be translated into thephysical response of the MSF unit. First, an analysis was done keeping the controlparameters constant (SR, R, F). If the fouling is decreased in the recovery section,heat transfer inside the tubes is increased and the inter-stage temperature differencebetween the vapor and cooling brine decreases. This raises the temperature ofcooling brine and decreases the flashing brine and released vapor. But the coolingbrine goes to the brine heater since it is hotter than in design. Finally, the coolingbrine flow enters the recovery section at a higher temperature than expected. In thefinal stages of the recovery section, both distillate and flashing temperatures arereduced by the effect of the fouling inside the recovery tubes. The flash range of thedistillers is increased in the two limits and the distillate produced in the MSF unit ishigher than in design. The control parameters of the MSF unit (seawater to rejectSR, recycle brine R or make-up feed F) must be reduced if the distillate product is tobe maintained (although the distillate temperature leaving the unit could be reduced)and, indirectly, the amount of steam consumed in the heater. The diagnosismathematically explains the physical effects.

Tables A1.33 and A1.34 show the F-P definition matrices following the productivestructure in section 7.1. Then, the ⟨KP⟩ matrices from the last two matrices (tablesA1.35 and A1.36) are shown. The ∆ ⟨KP⟩ matrix (table A1.37) is obtained bysubtracting tables A1.35 and A1.36. The irreversibility matrix |I⟩ (table A1.38) andthe malfunction/dysfunction table is shown in table A1.39. The example analyzedproduced 1.900 T/h with 32 ºC seawater (nominal-temperature operation of the MSFdistillers in summer). Figures A1.21 and A1.22 show the impact on fuel analysis andthe increase of the irreversibility in the MSF components.

Effect of the cleaning ball system in the recovery section


TAB

LE

A1.

33 F

-P v

alue

s in

des

ign,

NTO

S c

ase.



TAB

LE

A1.

34 F

-P v

alue

s w

ith fo

ulin

g in

RC

S=0

, NTO

S c

ase.



TAB

LE

A1.

35 K

P m

atrix

in d

esig

n, N

TOS

cas

e.



TAB

LE

A1.

36 K

P m

atrix

with

an

inef

ficie

ncy

in R

CS

, NTO

S c

ase.



FIG

UR

E A

1.21

Impa

ct o

n fu

el a

naly

sis

in s

ectio

n A

1.5.

FIG

UR

E A

1.22

Irrev

ersi

bilit

y in

crea

se in

sec

tion

A1.

5.



In the malfunction analysis, only the inefficient component has an intrinsicmalfunction of –1,570 kW. This low value can be explained physically. The foulingreduction inside the recovery tubes improves the heat transfer coefficient in thosestages, reducing the thermal irreversibility (∆I = –2,132 kW, see table A1.39) andalso the flows recirculating in the recovery section in order to maintain finalproduction. This means that the variation of the unit exergy consumption is∆k = --0.194, see table A1.37. The impact on fuel associated with the inefficientcomponent is –4,279 kW.

The brine heater has an induced malfunction of –626 kW. The brine entering theheater has a higher temperature due to improved heat transmission in the recoverysection, but the temperature entering the distiller is reduced by 0.3 ºC. The brineheater needs less steam to heat the cooling brine, considering that the recycle brineflow is also reduced to maintain distillate production. This means that theirreversibility generated in the heater is also reduced by ∆I = –1,131 kW, andtherefore the variation of the unit exergy consumption (the ∆ ⟨KP⟩ coefficient is∆k = –0.0149, see table A1.37).

The inefficiency in the recovery induces a –540 kW malfunction in the rejectsection. The distillate flow leaving the section depends on the temperature of theflashing brine and distillate entering the plant (both temperatures decrease 2.6 ºC)and the recycle brine to the distiller (which is reduced 263 T/h). The energy requiredto produce the distillate is lower than the design value and the irreversibilitygenerated in this section (∆I = –554 kW, see table A1.39). The unit exergyconsumption of the reject is reduced because the amount of resources to distillatethe freshwater is lower (∆k = –0.079, see table A1.37). As the distillate is producedat a considerable exergy cost (see the last row of table A1.38 for the exergy cost ofeach component), 5,408 kW of fuel was saved with this induced malfunction.

The component suffering the highest malfunction is the fictitious device (FD),included in the productive structure to quantify the flows sent to sea: blowdown andreject cooling seawater. The malfunction associated with this component (7,850 kW,see table A1.39) can only be explained by the thermoeconomic model. Its product(the fuel consumed in the MSF unit to produce freshwater, i.e. the steam comingfrom the steam power plant) is obviously decreased with the use of the cleaning ballsystem. The exergy flow of the steam to the MSF unit decreases 9,250 kW. Theincrease in unit exergy consumption is ∆k = 0.170 and the impact on fuel associatedwith this component is 13,249 kW. It is clearly not convenient to use non-physicalcomponents in the productive structure of the system because their associatedmalfunctions and dysfunctions are quite difficult to explain physically.



TAB

LE

A1.

37 V

aria

tion

of th

e K

P m

atrix

whe

n th

e fo

ulin

g in

RC

S is

neg

lect

ed.



TAB

LE

A1.

38 I

rrev

ersi

bilit

y m

atrix

with

out f

oulin

g in

RC

S.



TAB

LE

A1.

39 D

ysfu

nctio

n/m

alfu

nctio

n ta

ble

with

out f

oulin

g in

RC

S, N

TOS

cas

e.



The mixer is also a non-physical device in the last stage of the reject section. Itmodels the mixing process between the make-up feed and the brine flashing in thelast stage of the reject section. It has a negative induced malfunction of 765 kW dueto the reduction of irreversibility generated (∆I = –735 kW, see table A1.39) in themixing process (the two mixed flows are reduced in quantity and energy). Theefficiency of the process is therefore improved, with a unit exergy consumptionvariation of ∆k = –0.013 (see table A1.37). The impact on fuel associated with the‘benefunction’ in the mixer is –996 kW.

Now the dysfunction analysis will be introduced. Components suffering a importantmalfunction clearly induce a large dysfunction in the rest of components. Forexample, the main dysfunctions in the fictitious device are generated by itself(5,016 kW), the heater (–1,226 kW), the recovery section (–2,534 kW), the mixer(--212 kW) and the reject section (–3,022 kW). The value of the dysfunction isproportional to the malfunction in each component. The dysfunction in a componentdue to the junctions of the productive structure must be distributed to thecomponents supplying the junction. The total dysfunctions generated by eachcomponent were 5,398 kW for the FD, –1,263 kW for the heater, –2,708 kW for therecovery section, –230 kW for the mixer and finally –4,867 kW for the rejectsection. The temperature profile change in the distillers provokes differences in theexergy of products leaving each component to readapt the final production ofdistilled water.

The previous analysis kept the final product of the system constant (distillate water).As mentioned in previous sections, the simulator can maintain the mass flow rate inthe distiller but it cannot maintain the exergy of this flow. As in this case, thetemperature of distillate leaving the MSF unit is reduced by 1.3 ºC. The impact onfuel associated with the variation of the final product is an astonishing –4,337 kW!This value is similar to the total impact on fuel associated with the unit exergyconsumption variation inside the MSF unit (–5,336 kW).

The variational analysis of this inefficiency involves the linear behavior of themodel, as in the figure A1.23, where the total impact on fuel saved (including thefinal product variation) with decreased fouling is depicted from the design value tototal absence. In this section we analyzed nominal production (1,900 T/h) with 32 ºCseawater and the typical exergy costs of electricity and steam obtained in the powerplant analysis.

The inefficiency diagnosis can also be quantified in monetary terms. The cost ofwater depending on fouling helps plant managers develop a maintenance plan tooperate under the best conditions. In this case (see figure A1.24) the cost of a cubicmeter of water decreased 0.0069 $ when the fouling in this section decreased0.00001 m2·K/W. This value is very high (115,000 $ a year) and implies that thecleaning ball system should always operate in the recovery section.



FIGURE A1.23 Effect on fuel consumption when the fouling in recovery section is gradually decreased. 1,900 T/h and 32º C seawater.

FIGURE A1.24 Cost of a cubic meter of water depending on the fouling in the recovery section.

The malfunction matrix (table A1.40) of the MSF unit with this inefficiency is agood tool to calculate the effect on natural gas. The malfunction matrix can be usedbecause the model is linear with respect to the fouling in recovery. But the inducedmalfunctions produced by this inefficiency imply that the malfunction matrix canonly be used for individual malfunctions.


-24000

-20000

-16000

-12000

-8000

-4000

0

0 3 6 9 12 15

fouling*10-5 in RC

kW

Water cost

1,36

1,39

1,42

1,45

1,48

0 3 6 9 12 15

fouling*10-5 in RC

$/m3



TAB

LE

A1.

40 M

alfu

nctio

n m

atrix

whe

n th

e fo

ulin

g in

RC

S is

var

ied

0.00

001

m2 K

/W.

Effect of reject section fouling


Summarizing the results:

• The change of the temperature profile by the fouling in the main flows of theMSF plant is responsible for the induced malfunctions in the distillers. Thus,each malfunction should be dealt individually. The values of the inducedmalfunctions surpass the intrinsic malfunction because the flows leaving andentering the recovery section also pass through the reject or brine heater. Thedysfunctions generated in the different components are also very important.

• The increased heat transfer increases the production rate per stage in the distiller.This reduces the amount of resources to produce the same distillate. Since thecleaning ball system obviously saves fuel (115,000 $/y), it should operatecontinuously.

• A large part of fuel saved with this inefficiency is due to the lower temperatureof the distillate leaving the plant. But, in fact, the distillate temperature is nowirrelevant (unless this energy is used by another process). So, this effect shouldnot be considered during the analysis, although that temperature has a directrelationship with the other distiller temperatures.

A1.6 Effect of reject section fouling

Usually the cleaning ball system is not installed in the reject section since itsseawater operating temperatures do not produce any scaling problems. But thebiological activity of seawater intake can lead to dangerous bio-fouling in thissection. The effect of installing a cleaning ball system here is similar to the recoverysection. It reduces the interstage difference because the distillate temperaturedecreases and the cooling brine is heated to a higher temperature. Since the seawatertemperature is imposed by the environment, the distillate temperature is forced todecrease when the heat transfer coefficient of each stage is increased, because thefouling inside the tubes is neglected. In this case, the flash range of the plant ∆T ishigher because the lower limit of this range is decreased. A higher flash rangeimplies a higher distillation per stage. If the control parameters of the plant aremaintained, it can only produce additional freshwater with the help of the cleaningball system. A lower recycle (R), seawater to reject (SR) and make-up feed (F) floware needed to maintain the distillate production.

As the brine heater is so far from the reject section, the temperature profiles of thecooling brine entering and leaving the heater do not vary considerably. Theperformance indexes or steam consumption of the plant are not expected to greatlyimprove.

This system should not be used for several reasons based on thermoeconomiccriteria. The example is the same as in previous sections: a water production of



1.900 T/h with 32 ºC seawater and a fouling factor reduced to zero. Tables A1.41and A1.42 show the F-P definition applied to the design and inefficient case, tablesA1.43 and A1.44 are the ∆ ⟨KP⟩ matrix made by using the previous tables, tableA1.45 is the ∆ ⟨KP⟩ matrix and table A1.46 is the irreversibility matrix I containingthe dysfunction coefficients and the exergy cost array. The dysfunction/malfunctionmatrix [DF]/MF is the table that resumes the final results of the thermoeconomicdiagnosis applied to this inefficiency (table A1.47). The impact on fuel and theincrease of irreversibility per component are shown in figures A1.25 and A1.26respectively.

Although the reject section has three stages, the effect of fouling should be identicalto the effect observed in the recovery section (17 stages). In this case, thetemperature of cooling brine entering the distiller is given by the ambientconditions. The flashing and distillate temperatures would try to reach the coolingtemperature flowing inside the tubes if the heat transfer were an ideal process. Thesymbolic formulation of thermoeconomics will give us the effects provoked by thisinefficiency in the MSF unit.

The most significant malfunctions are yet again located in the fictitious device,heater, recovery and reject sections and the mixer. The inefficient componentanalysis considers the cleaning ball system installed in the reject section.Suprisingly, the associated malfunction with no fouling in the reject is positive(49 kW). The ∆ ⟨KP⟩ component corresponding to its exergy unit consumption is∆k = 0.007 (see table A1.45). But this result is provoked by the assumptions adoptedin the thermoeconomic model of the reject section. The part of the unit exergyconsumption corresponding to the efficiency of the process (or the heat transferimprovement) is logically lower than the design situation (∆k1 = –0.024). But thesteam and brine needed for maintaining the vacuum inside the chambers is more orless independent from the distillate produced (i.e. is a constant value). As theproduct of the reject section decreases (the distillate temperature leaves the sectionat a lower temperature), the unit exergy consumption due to the vacuum system is∆k2 = 0.031. Clearly the general services of the MSF unit are not affected by anintrinsic inefficiency but they have to consider product variation in order to accountfor its contribution to the final cost of water.

The brine heater is located on the other side of the MSF plant. The effect of theinefficiency in the reject section also affects this component because the recycledbrine heated in the brine heater comes from the reject section. The recycle brineflowing in the recovery section is reduced by 195 T/h and the cooling brine heatingis reduced by 227 kW. The temperature difference in the first stage of the recoverysection is improved by 0.1 ºC. So, heater efficiency decreases and the variation ofthe unit exergy consumption is positive (∆k = 0.0044, see table A1.45). Themalfunction is MF = 185 kW and an irreversibility increase in the heater of∆I = 468 kW (see table A1.47).



TAB

LE

A1.

41 F

-P v

alue

s in

des

ign,

NTO

S c

ase.



TAB

LE

A1.

42 F

-P v

alue

s w

hen

the

foul

ing

in R

JS=0

, NTO

S c

ase.



TAB

LE

A1.

43 K

P m

atrix

in d

esig

n, N

TOS

cas

e.



TAB

LE

A1.

44 K

P m

atrix

with

the

inef

ficie

ncy

in R

JS, N

TOS

cas

e.



TAB

LE

A1.

45 V

aria

tion

of th

e K

P m

atrix

whe

n th

e in

effic

ienc

y in

RJS

is d

etec

ted.



TAB

LE

A1.

46 Ir

reve

rsib

ility

mat

rix c

orre

spon

ding

to re

ject

foul

ing

in R

JS, N

TOS

cas

e.



TAB

LE

A1.

47 D

ysfu

nctio

n/m

alfu

nctio

n ta

ble

whe

n th

e fo

ulin

g in

RJS

=0.



FIG

UR

E A

1.25

Impa

ct o

n fu

el a

naly

sis,

sec

tion

A1.

6.

FIG

UR

E A

1.26

Incr

ease

of i

rrev

ersi

bilit

y in

sec

tion

A1.

6.



As seen for the brine heater, the cleaning ball system in the reject section induces anunexpected 1,800 kW positive malfunction in the recovery section. This result willbe described analytically. The temperature of water leaving the distiller is reducedby 1.7 ºC (remember that the cleaning ball system in the reject decreases thedistillate profile in the reject section and, therefore, in the last section of the recoverydistiller). In general, since the heat transfer coefficient is higher at hightemperatures, the thermal irreversibility increases in the recovery section(∆I = 2,079 kW, see table A1.47). As the product of the section decreases, thevariation of the unit exergy consumption is positive (∆k = 0.223, see table A1.45).The impact on fuel associated with this induced malfunction is 4,248 kW.

The malfunction associated with the fictitious device is –788 kW. Two fuels enterthis component in the productive structure of the MSF unit, one is the exergy of theblowdown leaving the recovery section. This exergy is reduced because thetemperature of the flashing brine decreases 1.8 ºC when leaving the reject section.So, the unit exergy consumption of the component is lower than in design(∆k = --0.017, see table A1.47). As demonstrated, a lower temperature of theblowdown rejected to the sea at least implies a lower cost in the water production.

Finally, the mixer has an induced malfunction of 1,208 kW, with a very clearphysical explanation. The temperatures of the make-up and flashing brine toblowdown are similar in the reference case but these temperatures are separated withthe cleaning ball system in the reject section. The irreversibility generated in themixing process is higher although those two flows are reduced to maintain the finalproduction in the MSF plant (∆I = 1,191 kW, see table A1.47). The variation of theunit exergy consumption in the idealized component was ∆k = 0.0204 (see tableA1.45). The additional fuel necessary for this component provoked by the cleaningball system in RJS was 1,868 kW.

In the dysfunction analysis, only the fictitious device had an important dysfunctiongenerated by the inefficient components (total dysfunction was 3,283 kW). Thiscomponent reduces its product by only 64 kW, however the final reduction in thedistillate exergy flow is 482 kW.

Although the plant diagnosis suggests that the MSF unit is working at a poorerefficiency (the impact on fuel associated with the unit exergy consumption variationwas 6,394 kW), this analysis considered a constant total production. Thetemperature of the distillate leaving the MSF unit is 1.8 ºC lower than expected indesign. This means that total production is not constant and the last term in equation(6.41) cannot be neglected. The impact on fuel associated with this variation iscalculated by multiplying the total product variation by the exergy unit cost of theproduct. In this case 6,768 kW of fuel were saved (in the case of the power plant, theterm of the product variation can usually be neglected because it is normally lessthan 20 kW). The total amount of fuel saved with this inefficiency is 374 kW, by



combining the two effects. Therefore, the cleaning ball system also benefits the MSFunit, as well as the heater and recovery section.

Figure A1.26 shows the effect of fouling in the reject section when we graduallydecrease to zero the design value (0.000018 m2 K/W). If the thermoeconomic modelis linear with respect the variational analysis of the fouling, the malfunction matrixcould be used to predict the impact on fuel associated with the desired variation ofthe fouling of this component (if known).

If the model responds linearly, the total cost of water (includes capital andmaintenance costs) must also increase linearly depending on the degree ofinefficiency (see figure A1.27). Each cubic meter of water increases 0.00012 $ whenthe fouling factor in the reject distiller increases 0.00001 m2 K/W. Yearly freshwaterproduction would involve an additional cost of 2,000 $ with this small variation inreject fouling.

FIGURE A1.27 Effect on fuel consumption when the fouling in reject is varied. Nominal-temperature operation in summer (NTOS, i.e., 1,900 T/h and 32 ºC seawater temperature).

The linearity of the model with respect to fouling variation is shown in figure A1.28.The malfunction matrix (table A1.48) can be used to predict the impact on fuelconsumed with the inefficiency. But the induced malfunctions provoked bytemperature variation in the rest of components implies that the analysis for severalinefficiencies has different results than the individual analysis of those inefficiencies.So, the malfunction matrix can only be used to predict specific inefficiencies.Important errors may arise if it is used for several inefficiencies.

The most important results derived from the analysis of the fouling in recoverysection are :

• Fouling increases the flash range of the plant and, therefore, the distillateproduction if the same control parameters of the plant are maintained. Inputconditions must be relaxed to maintain the final production of freshwater.


-500

-400

-300

-200

-100

0

0 3 6 9 12 15 18

fouling*10-5 in RJ

kW

Summary


FIGURE A1.28 Variation of the water cost when fouling in the reject section is decreased from the design value to zero.

• The inefficiency negatively affects the rest of the MSF components (see themalfunctions induced in other components in table A1.47). Furthermore, thebenefit is due to the lower temperature of the freshwater produced, although theplant is not working more efficiently (the impact on fuel associated with the unitexergy consumption variation is positive). The cost of water is not reduced verymuch with the cleaning ball system.

• The cleaning ball system is not recommended for the reject section. It is verydifficult to install there (it is an open circuit in which some of the cooling brine isrejected to the sea), and the low temperatures do not provoke serious scalingproblems in this section. Feed chlorination is a simpler solution to avoid possiblebiological fouling (which depends on seawater intake conditions).

A1.7 Summary

Thermoeconomic diagnosis of the dual-purpose plant for the inefficiencies insection 7.3 was completed in this annex for the most representative load in thepower and desalination plant. The symbolic formulation of the Structural Theory ofThermoeconomics provides a lot of information and explains the physicalconsequences expected with the inefficiency.

Inefficiencies studied in steam power plant are local to the components suffering theinefficiency, but in the desalination plant the main units of the system are connectedby the cooling brine, flashing brine and distillate, where any inefficiency is easilydistributed over the rest of the plant components.

Water cost

1,471

1,472

1,473

1,474

0 3 6 9 12 15 18

fouling*10-5 in RJ

$/m3



TAB

LE

A1.

48 M

alfu

nctio

n m

atrix

whe

n th

e fo

ulin

g in

RJS

is v

arie

d 0.

0000

1 m

2 K/W

.


ANNEX 2

Thermodynamic propertiesof seawater

Below are the models and correlations of the thermodynamic properties needed tosimulate the MSF desalination plant, except for the properties previously describedby the auxiliary equations (Chapter 3).

A2.1 Specific enthalpy h of superheated or saturated vapor

We used equations from Badr, Probert and O’Callaghan (1990), from formulationsby Keenan and Keyes (1955, 1969) and conveniently expressed for computercalculation (Schnakel, 1958). The temperature and pressure range was valid belowthe critical point.

Units: International System

where

h F 101.31558 F0p

101325.0----------------------

B0

2------

p101325.0T--------------------------

2+

+=

B6– B0 B2 B3 B0 B7p

101325.0T--------------------------

2

+–

+

B B0 1B0 p

101325T2------------------------ B2 B3–

B0 p

101325T----------------------

2

+ B4 B5–( )+

–

Thermodynamic properties of seawater

410


B

0

= 1.89 – B

1

B

2

= 82.546

B

4

= 0.21828 T

B

6

= B

0

B

3

– 2 F

0

(B

2

– B

3

)

B

7

= 2 F

0

(B

4

– B

5

) – B

0

B

5

F = 1804036.3 + 1472.265 T + 0.37789824 T

2

+ 47845.137 ln T.

A2.2 Specific entropy of superheated or saturated vapor

Term ß was added to those in section A2.1. The specific entropy s of superheatedvapor was:

s = 1472.626 ln T – 461.4874 ln p + 0.7557174 T + 3830.4065

–

where

B12641.62

T------------------- 10

80870 T2⁄=

B3162470

T------------------=

B5126970

T------------------=

F0 1.89 B1372420

T2------------------ 2+

–=

47845.076T

------------------------- 101.31344 β–

β 1T--- B0 F0–( ) p

101325------------------

B0

2------

p101325T----------------------

2B6

12---

B0 p

101325T----------------------

2

+ +

=

B0 B4 B5–( ) 2B7–

Specific volume of superheated or saturated vapor


411

A2.3 Specific volume of superheated or saturated vapor

Using B from section A2.1, the specific volume v of pure water was:

A2.4 Latent heat vaporization of water as a function of

boiling temperature

Below the atmospheric boiling point (373.15 K), latent heat of vaporization

λ

s

was(SI units):

where h was solved in section A2.1 and p

s

in section 3.3.6.

The Fish & Lielmezs correlation (Reid, Prausnitz and Sherwood, 1977) was used inthe range 373.15 < T < 450 K:

where

The Carruth & Kobayashi correlation (Reid et al., 1977) was used for450 < T < 647.3 K:

vT

pB= ⋅ +

−1 00035 10

461539 4533..

λ s sh T p T T= ( ) − −( ), ( ) . .4 186 273 15

λs 6051.1583ℵ ℵ 0.35298

+

1 ℵ 0.13856+-------------------------------

T=

ℵ 1.3615467647.3 T–

T-----------------------

=

λs 2115173.3 1 T647.3-------------–

0.3541125343.9 1 T

647.3-------------–

0.456+=


412


A2.5 Seawater exergy

A2.5.1 Theory

Mass flow and five parameter measurements characterize the different stages ofseawater: pressure, temperature, altitude, velocity and composition (Zaleta, Ranzand Valero, 1998). The exergy method associates each parameter with its exergeticcomponent: mechanical, thermal, potential, kinetic and chemical, respectively.These components help to quantify some quality and quantity aspects of seawater.The information provided by the exergy method also clarifies concepts related to theseawater availability.

Ambient reference

The first step in developing the analytic exergy methodology is to establish theambient reference (AR) for seawater comparison. The AR must be relativelyabundant with respect to the rest of the systems or subsystems. The thermodynamicequilibrium conditions of AR must resemble a closed system; therefore, the systembrought to AR conditions will undergo a series of physical-chemical changes.Authors sometimes call this the ‘dead state’, because it is a zero exergy state(although its energy is different than zero).

AR may be chosen in different ways to establish thermodynamic equilibrium.Ahrendts (1980) proposes an approximation of the “dead” ambient of Earth if itwere thermodynamically isolated from the rest of the universe. When we imposerestrictions on the method (excluding HNO3 formation and its products), theresulting AR composition is very similar to the real physical ambient. Liquid AR ismainly seawater with more than 99% of the system's total mass. On the other hand,Szargut (1980) proposes an AR that is more similar to the real physical ambient innature and independent of the process or system under consideration. This is moreconvenient to exegetically analyze systems classified as natural resources.

We used the AR proposed by Szargut to analyze seawater. The AR in the liquidphase corresponded to seawater composition at main ambient temperature and sealevel atmospheric pressure. The seawater composition for the AR proposed bySzargut (1989) is shown in the next table.

Seawater exergy


TABLE A2.1 Liquid phase composition of Reference Ambient (Szargut, 1989; Morris, and Szargut, 1986).

Chemical element Molality (mol/kg)

Ag (s) 2.7 × 10–9

As (s) 2.1 × 10–8

Au (s) 5.8 × 10–11

B (s) 3.4 × 10–4

Ba (s) 1.4 × 10–7

Bi (s) 1.0 × 10–10

Br2 (l) 8.7 × 10–4

Ca (s) 9.6 × 10–3

Cd (s) 6.9 × 10–11

Cl2 (g) 0.5657

Co (s) 6.8 × 10–9

Cs (s) 2.3 × 10–9

Cu (s) 7.3 × 10–10

F2 (g) 3.87 × 10–5

Hg (l) 3.4 × 10–10

I2 (s) 5.2 × 10–7

K (s) 1.04 × 10–2

Li (s) 2.5 × 10–5

Mg (s) 4.96 × 10–2

Mn (s) 7.5 × 10–9

Mo (s) 1.1 × 10–7

Na (s) 0.474

Ni (s) 1.2 × 10–7

P (s) 4.9 × 10–7

Pb (s) 4.2 × 10–11

Rb (s) 1.42 × 10–6

S (s) 1.17 × 10–2

Se (s) 1.2 × 10–9

Sr (s) 8.7 × 10–5

W (s) 5.6 × 10–10

Zn (s) 1.7 × 10–8



Seawater availability: exergy function

The availability of a renewable resource can be understood as ‘how accessible is it’.In order to be used, a resource must be changed chemically and physically to therequired conditions (e.g., for human consumption, water must be extracted from ariver or sea, be purified and sent to end users).

The analogy between the availability of a natural resource and exergy helps relateeach resource parameter with its exergy components. As the exergy method isconditioned by a Stable Reference Environment (SRE) —dead state conditions—the SRE proposed by Szargut (1980) is the most convenient (the most similar to thereal physical environment of Earth).

In the case of seawater, the exergy method is useful to quantify the ‘availability’ of asea, with respect to the defined SRE. By applying the exergy model (Gaggioli, 1980)in terms of temperature, pressure, height, velocity and composition, and assumingseawater is an incompressible liquid and dilute substance, the specific exergy can beused in terms of its components for each seawater property (thermal, mechanical,chemical, kinetic and potential components, respectively):

(A2.1)

According to equation (A2.1), the thermal exergy component depends on the heatcapacity of the aqueous solution and its absolute temperature Ta. The mechanicalexergy component is calculated from the specific volume of the solution (seawater)and the pressure difference between the sea and the SRE. The specific heating valueCPH2O and the specific volume vH2O of the solution can be calculated withoutserious error if it is considered pure water (Perry and Chilton, 1984). We used thecorrelations described in Chapter 4. The potential exergy component requires thealtitude z above sea level (almost negligible in a MSF plant). It is used to calculatethe maximum mechanical work obtained from a waterfall, such as a hydroelectricstation. The kinetic exergy component is of relatively little exergetic importance incomparison with other exergetic components (taking into account the low velocity caof brine inside the tubes or in the flash chambers). Its mean velocity must becalculated, which depends on flow and operation conditions. The chemical exergycomponent is the most complex to calculate. It may be broken down into thefollowing components: (i) the chemical exergy of the water, (ii) the chemical exergyof the dissolved inorganic substances, (iii) the chemical exergy of the organicsubstances.

ba r, CPH2O Ta Tr Tr LnTa

Tr-----–– vH2O Pa Pr–( )+=

xi r, µi a, µi r,–( ) 12--- ca

2cr

2–( ) g za zr–( )+

i∑+

Seawater exergy


i) The chemical exergy of pure water in the sea. This component provides informa-tion about the thermodynamic degradation process; pure water availability underdifferent conditions such as pollution (the presence of substances other than purewater like salts, organic material, etc.). The magnitude of the exergetic compo-nent µ can be calculated from its activity as a pure substance in a solution equa-tion (equation A2.2):

(A2.2)

where xH2O is the molar fraction of pure water in seawater, and aH2O, aH2O,r canbe estimated from measuring coligative properties, such as osmotic pressure, π.In the case of seawater, the osmotic pressure of a diluted solution with respect toits pure solvent is typically calculated using equation A2.3,

and (A2.3)

where π is obtained by measuring the Electrical Conductivity (EC) of seawaterand considering that the osmotic pressure is a function of the salt concentration(binary) in solution (without any serious errors, as in the case of a very dilutedsubstance, such as seawater).

πH2O = 0.36 EC (A2.4)

where π is the osmotic pressure (atmospheres) and EC the electrical conductivityin dS/m (1 dS/m = 640 ppm, Medina (2000)) of ionized electrolytic componentsin a solution.

ii) The chemical exergy of the dissolved inorganic substance is determined by thewell-known procedure for an electrolytic solution (equation A2.5):

(A2.5)

where the activity for each chemical substance i in the sea and in the SRE can beexpressed in terms of the activity coefficient, γ, and its molality, m:

ai = γi mi (A2.6)

The activity coefficient, γ, of each of the electrolytic species is determined usingthe equation obtained by Debye-Hückel (equation A2.7).

bq H2O, xH2O µH2O µH2O r,–( ) xH2O RTr LnaH2O

aH2O r,---------------

= =

πH2O

RTr

v--------- Ln aH2O( )–= πH2O r,

RTr

v--------- Ln aH2O r,( )–=

bq i, xi µi µi r,–( ) xi RTr Lnai

ai r,-------

= =



(A2.7)

where A, B are constants depending on the solvent and temperature, zi is the ionic

charge, di is the ionic diameter of specie i and I is the ionic dissolution force,

. For diluted solutions (seawater is a good example), this equation can

be expressed as:

(A2.8)

The activity coefficient of non-electrolytic inorganic substances is always γ =1.

iii) The chemical exergy of organic substances. It is difficult to determine the pre-sence of organic substances in seawater due to the diversity of species involved(including biological organisms). However, organic substances are not present inthe Szargut (1980) definition of SRE, but are purified naturally in rivers. Thismeans that the oxygen (from photosynthesis or atmospheric) dissolved in wateroxidizes the organic substances. This process may be slow or fast depending onthe substance. One way to quantify the exergetic content of an organic substanceis by proposing a single organic molecule to represent the “organic substancemean”.

For practical sea analysis, our representative substance was a fat molecule, as shownin equation A2.9. This enabled us to calculate the order of magnitude of the exergyorganic component to be determined qualitatively.

(A2.9)

The laboratory measurement of Chemical Oxygen Demand (COD, mg. of O2/lt ofseawater consumed in the reaction is estimated) was used to obtain the amount ofmoles of mean organic substance per liter of water. The exergy of the organicsubstance was obtained from the definition of exergy reaction in the standard state,according to the expression in equation A2.10.

(A2.10)

where , so and are well known for industrial substances.

Log γi( )Azi I

1 2⁄

1 Bdi+ I1 2⁄-----------------------------–=

I mi zi2

i∑=

Log γi( ) Azi I1 2⁄[ ]–=

C39 H80 O31152

--------- O2 39 CO2 40 H2O+↔+

bo ∆hf

oT

os

o– xj µ j

o∑–=

∆hfo µ j

o

Seawater exergy


A2.5.2 Practice: Brine exergy as a function of temperature, pressure and salt concentration

Brine exergy only includes thermal, chemical and mechanical terms (kinetic andpotential terms are neglected, see equation A2.1). Although it is impossible to knowthe chemical analysis of seawater entering the MSF unit, the chemical term onlyconsiders seawater concentration due to sodium chloride.

This means that the chemical energy of the organic compounds is not consideredand the contribution of inorganic substances is only calculated for Na+ and Cl– ions.Chemical exergy of pure water depends on the osmotic pressure difference withrespect to reference seawater. The AR used was 0 ºC and 45,000 TDS (averageseawater concentration in the Arabian Gulf). The results were similar to otherstudies (Zaleta et al., 1998). For more detailed information about how to calculatethese terms, see Barner and Scheuerman (1978), Newman (1980) and Marín andTurégano (1985).


ANNEX 3

Technical data

This annex includes the most important design and constructive values provided bythe contractors. Most of those values are introduced in the simulator, but they cannotbe changed unless requested by the author.

A3.1 MSF plant

MSF: Guarantee figures (112 ºC TBT, 25 ºC SWT)

Seawater temperature (T

sea

) 25 (ºC)

Distillate production per hour (D) 2,400 (T/h)

Distillate temperature at pump suction 38 (ºC)

Distillate density at production temperature 994 (kg/m

3

)

Discharge pressure at distillate pump 3.5 (bar)

Distillate purity expressed as TDS 10 (ppm)

pH value of distillate before caustic soda injection 5.5-6.0

Fe content in distillate 0.05 (ppm)

Cu content in distillate 0.05 (ppm)

Vapor velocity at the smallest path in last stage 14 (m/s)

Technical data

420


Performance ratio (PR) not less than 8

Quantity of heating steam at reducing valve before brine heater (m

ST

) 313.400 (kg/h)

Steam pressure at heater inlet 1.8 (bar)

Steam temperature at heater inlet 120 (ºC)

Heater condensate temperature at pump suction 117 (ºC)

Net specific heat consumption (NC) 290.75 (kJ/t distillate)

Total specific heat consumption 295 (kJ/kg distillate)

Specific electric power consumption 4.0 (kWh/kg dist. x 10

–3

)

O

2

content in heater condensate (at 20 ºC) 0.03 (ppm)

Fe content in heater condensate 0.04 (ppm)

Cu content in heater condensate 0.04 (ppm)

Conductivity of heater condensate 5 (µs/cm)

Temperature of ejector condensate 40 (ºC)

PH of ejector condensate 5.5-6.0

T.D.S in brine blow down 71,000 (ppm, máx.)

T.D.S in recirculated brine in the heater tubes 62,000 (ppm)

Temperature of the sea water outlet from heat rejection section 36 (ºC)

Sea water velocity inside tubes of heat rejection section 2.0 (m/s)

Brine velocity inside tubes of heat recovery section 2.1 (m/s)

Brine velocity inside tubes of brine heater 2.1 (m/s)

Pressure inside the heater space 1.8 (bar)

Brine pressure after the heater 1.9 (bar)

Brine temperature in first stage (TBT) 108 (ºC)

Brine temperature in last stage 35.5 (ºC)

Vapor temperature in first stage 106.5 (ºC)

Vapor temperature in last stage 34.5 (ºC)

Absolute pressure in first stage 1.305 (bar)

Absolute pressure in last stage 0.055 (bar)

MSF plant


421

Evaporators

Temperature of make-up feed entering deaerator 36 (ºC)

Temperature of make-up feed leaving deaerator 36 (ºC)

Absolute pressure in deaerator space 0.05 (bar)

O

2

content in feed make-up leaving deaerator (without sulphite inj.) 0.03 (ppm)

O

2

content in feed make-up leaving deaerator (with sulphite inject.) 0.04 (ppm)

Specific chemical consumption (antiscale with sponge ball cleaning) 12 (kg/kg dist. x 10

–6

)

Specific chemical consumption (antiscale without sponge ball clean.) 27.2 (kg/kg dist. x 10

–6

)

Heat losses due to radiation, venting or other losses 5 x 10

7

(kJ/h)

GENERAL

Recovery section: heat exchange surface 110,200 (m

2

)

Reject section: heat exchange surface 15,150 (m

2

)

Brine heater: heat exchange surface 10,272 (m

2

)

Recovery section: Fouling factor (design) 0.00015 (m

2

K/W)

Reject section: Fouling factor (design) 0.00018 (m

2

K/W)

Brine heater: Fouling factor (design) 0.00025 (m

2

K/W)

Recovery section: Heat transfer coefficient (design) 2,673 (W/m

2

K)

Reject section: Heat transfer coefficient (design) 2,211 (W/m

2

K)

Brine heater: Heat transfer coefficient (design) 2,147 (W/m

2

K)

Demisters: Total area 640 (m

2

)

Total width 19 (m)

Total length 87 (m)

Total height 17 (m)

Total weight-empty 3,000,000 (kg)

Tube Pitch (pattern: triangular) 1.25

Technical data

422


BRINE HEATER

Number of tubes 3060 (2 passes)

Tube internal diameter 33 (mm)

Tube thickness 1.2 (mm)

Tube effective length 15.1 (m)

Tube material CuNi 66/30 2 Fe 2 Mn

Tube conductivity 28.0 (W/m K)

RECOVERY SECTION: Stages 1-2

Number of tubes 3060




Tube material CuNi 70/30 ASTM B107







Tube material CuNi 90/10 ASTM B111







Tube material Titanium B338Gr2


MSF plant


423

REJECT SECTION: Stages 18-20


Tube internal diameter 33.6 (mm.)

Tube thickness 0.7

Tube effective length 19.2

Tube material Titanium B338Gr2


EFFECTIVE STAGE LENGTHS AND WIDTHS FOR BRINE FLOW

Stage no. Length (m) Width (m)

1 3.800 19.000

2 3.800 19.000

3 3.800 19.000

4 3.800 19.000

5 3.800 19.000

6 4.000 19.000

7 4.000 19.000

8 4.000 19.000

9 4.200 19.000

10 4.200 19.000

11 4.400 17.500

12 4.400 17.500

13 4.500 17.500

14 4.500 17.500

15 4.800 17.500

16 4.800 17.500

17 4.000 17.500

18 4.800 17.500

19 4.300 17.500

20 5.100 17.500

Technical data

424


DEMISTERS

Stage no. Area (m

2

) Height (m)

1 26.89 2.8

2 22.00 2.8

3 22.00 2.8

4 22.00 2.8

5 22.00 2.8

6 25.75 2.8

7 25.75 2.8

8 25.75 2.8

9 29.50 2.8

10 29.50 2.8

11 33.30 2.8

12 33.30 2.8

13 35.20 2.8

14 35.20 2.8

15 40.80 2.8

16 40.80 2.8

17 40.80 2.8

18 35.10 2.8

19 38.80 2.8

20 52.33 2.8

MSF plant


425

BRINE ORIFICES (112 ºC TBT, 25 ºC SW)

Stage no. Height (mm) Width (mm) Area (m

3

)

1 77 16.134 19.000

2 80 16.134 19.000

3 83 16.134 19.000

4 87 16.134 19.000

5 91 16.134 19.000

6 95 16.134 19.000

7 99 16.134 19.000

8 104 16.134 19.000

9 108 16.134 19.000

10 113 16.134 19.000

11 131 14.420 17.500

12 137 14.420 17.500

13 144 14.420 17.500

14 150 14.420 17.500

15 156 14.420 17.500

16 163 14.420 17.500

17 169 14.420 17.500

18 175 14.420 17.500

19 182 14.420 17.500

20 200 14.420 17.500

Technical data

426


A3.2 Power Plant

Boiler

GENERAL

Length x width x height (furnace) 9.825 x 10.875 x 19.9 (m)

Length x width x height (steel structure) 23.0 x 15.5 x 45.5 (m)

Total weight of boiler unit 3,500 (T)

Shipping volume of largest item 120 (m

3

)

Total gross weight of the largest item to be shipped 80 (T)

Weight of the largest item to be dismantled during maintenance 15 (T)

ECONOMIZERS

Effective heating surface (ECO 1/ ECO 2) 10,890/4,390 (m

2

)

Number of stages in line (ECO 1/ ECO 2) 7/3

Number of parallel streams (ECO 1/ ECO 2) 1/1

Location (ECO 1/ ECO 2) 3

rd

/3

rd

-2

nd

pass

Design pressure 129 (bar)

Design temperature (ECO 1/ ECO 2) 260/355 (ºC)

Effective height of one stage 1,555 (mm)

Pitch across the gas flow (ECO 1/ ECO 2) 65/75 (mm)

Pitch parallel to the gas flow 75/110 (mm)

Power Plant


427

AIR WATER HEATER

Number of heaters per boiler 2

Design pressure (airside) 1,300 (mm WG)

Design pressure (waterside) 129 (bar)

Design temperature (airside) 250 (º C)

Design temperature (waterside) 260 (º C)

Design air throughput 463,740 (Nm

3

/h)

Design water throughput 211 (t/h)

Effective surface heating 20,920 (m

2

)

Fouling factor considered (air/water side) 5/2 %

STEAM WATER DRUM

Type 48 (m

3

)

Water content 24 (m

3

/h)

Steam space rating 470 (m

3

/m

3

·h)


Design temperature 330 (º C)

Total length 14,000 (mm)

Shell length 12,800 (mm)

Shell thickness 82 (mm)

Technical data

428


WALL HEATING SURFACES

Combustion chamber

Nominal height 19.9 (m)

Nominal width 10.875 (m)

Nominal depth 9.825 (m)

Volume 2.123 (m

3

)

Total effective heat absorbing surface of the combustion chamber 1,454 (m

2

)

Total length 14,000 (mm)

Shell length 12,800 (mm)

Shell thickness 82 (mm)

Heat input (natural gas at MCR, 40º C air temperature) 422.22

×

10

6

(kcal/h)

Evaporators

Total effective heat absorbing surface 2,740 (m

2

)


Design temperature 375 (ºC)

Maximum local heat flux 290,000 (kcal/m

2

·h)

Evaporator headers

Number 40


Design temperature 330 (ºC)

Power Plant


429

SUPERHEATERS

Number of stages in line 3

Number of parallel streams 2

Number of spray attemperators 4


Design temperature (máx.) (SH1/SH2/SH3) 580/590/590 (ºC)

Effective heating surface (SH1/SH2/SH3) 3,090/860/360 (m

2

)

Number of elements over the width (SH1/SH2/SH3) 144/72/72

SPRAY ATTEMPERATORS

Number 2

Design steam flow (inlet/outlet) (AT1/AT2) 270-295/295-310 (t/h)

Calculated spray water flow (AT1/AT2) 27/18 (t/h)

Design spray water flow (AT1/AT2) 41/27 (t/h)


Design temperature (AT1/AT2) 500/550 (ºC)

DOWNCOMERS

Number 2

Outside diameter 508 (mm)

Wall thickness 16 (mm)

Technical data

430


Condensing Plant

Condensate Pumps

Condenser surface (between tube sheets and related to steam side) 6,725 (m

2

)

Condenser vacuum at MCR 0.072 (bar abs)

Specific condenser surface demand at MCR 67.5 (m

2

·h/t)

Condenser hotwell useful capacity 25 (m

3

)

Circulating water velocity within tube bundle 2.2 (m/s)

Associated hydraulic loss of CW 0.37 (bar)

Basic heat transfer coefficient at MCR 2,732 (kcal/m

2

·h·K)

Applied cleanliness factor 90 %

Associated maximum temperature difference 6.7 (ºC)

Thermal conductivity 14 (kcal/m·h·K)

Number of tubes per total cond. for one turbine 7124

Number of pumps 2 + 2

Specific gravity of fluid (MCR) 992.5 (kg/m

3

)

Suction pressure (MCR) 0.071 (bar)

Suction temperature (MCR) 39.2 (ºC)

Discharge pressure (MCR) 18 (bar abs.)

Discharge temperature (MCR) 39.2 (ºC)

Flow at discharge nozzle (MCR) 2 x 131 (T/h)

Overall efficiency according to DIN 1944 of equiv. (MCR) 71.6 %

Pump speed 1485 (l/min)

Critical speeds of pump and motor unit > 1800 (rpm)

Nameplate rating (MCR) 130 (kW)

Power Plant


431

HP1 Heater

HP2 Heater

Overall dimensions of feed heater 1,300 x 8,600 (mm)

Main steam flow (feedwater side, MCR) 562.9 (t/h)

Inlet pressure (feedwater side, MCR) 119.05 (bar)

Inlet/outlet temperature (feedwater side, MCR) 194.6/230.1 (ºC)

Heating steam flow 39.0 (t/h)

Pressure incl. vacuum if appl. 27.2 (bar)

Temperature (heating side, MCR) 369 (ºC)


Overall heat transfer coefficient (condensing zone) 3,280 (kcal/m

2

·h·K)

LMTD (condensing zone) 11.6 (ºC)

Heat transfer surface (desuperheating section) 65.3 (m

2

)

Heat transfer surface (condensing section) 531.6 (m

2

)

Heat transfer surface (condensate cooling section) 64.4 (m

2

)

Velocity of main condensate or feed water inside tubes 1.54 (m/s)


Main steam flow (feedwater side, MCR) 562.3 (t/h)





Temperature (heating side, MCR) 282 (ºC)



2

·h·K)


Heat transfer surface (desuperheating section) 37.8 (m

2

)


2

)


2

)


Technical data

432


LP1 Heater

LP2 Heater


Main steam flow (feedwater side MCR) 131.6 (t/h)





Temperature (heating side, MCR) 129.7 (ºC)



2

·h·K)



2

)


2

)



Main steam flow (feedwater side MCR) 131.6 (t/h)





Temperature (heating side, MCR) 79.7 (ºC)



2

·h·K)



2

)


2

)



Nomenclature

Abbreviatures/ Symbols/Acronyms

a Cost parameter, activity, or constant of Cobb-Douglass equation.

A Exchange area of the evaporator/condenser or constant of Debye-Hückel equation.

AR Reference Ambient.

AT Atemperator.

b Specific exergy.

B Flashing brine flow in j-th flash chamber, exergy flow, constant of Debye-Hückel equation, or constant for calculating vapor enthalpy.

BD Brine Blowdown.

BDP Blowdown Pump.

BH Brine Heater.

BHP Brine Heater Pump.

BOI Boiler.

BPE Boiling Point Elevation of brine with respect the pure water.

c Velocity.

C Salt concentration, or total monetary cost.

c* Exergoeconomic cost.

ca Cost per unit of area.

CBS Cleaning Ball System.

cf Fuel cost.

CND Condenser.

COC Boiler Peak Load.

COD Chemical Oxygen Demand.

CP Condensate Pump or Heat Capacity.

cp Product cost.

CW Cooling rejected Water.

d Ionic diameter.

D Distillate flow.

Nomenclature

434


DAS Data Acquisition System.

DB Exergy flow of distillate.

DCA Drain Cooling Advantage.

DF Dysfunction generated in a component.

DI Dysfunction generated by a component.

DLL Dynamic Link Library.

DP Distillate Pump.

DRT Deaerator.

DV Main stop valve seat diameter.

e Condenser efficiency.

E Enhancement factor.

EC Electrical Conductivity.

ECO Economizer.

ED Electrodyalisis.

EDS European Desalination Society.

EES Engineering Equation Solver.

ESL Excitation System Losses.

f Generic function.

F Fuel, Make-up feed or constant for calculating vapor enthalpy.

FCW Fuel Cost of Water.

FD Fictitious Device.

FP Feed Pump.

g Acceleration due to gravity, or characteristic equation.

Gc Gas consumption.

GCC Gulf Council Countries.

GEN Generator.

GOR Gain Output Ratio.

h Heat transfer coefficient or enthalpy.

H Height.

Hb Flashing brine (seawater) enthalpy.

HHV High Heating Value.

HT High-Temperature.

HP High-Pressure.

HPH High-Pressure Heater.

HPT High-Pressure Turbine.

HR Heat Rate of a power plant.

HRSG Heat Recovery Steam Generator.

HTOS High-Temperature Operation in Summer.

HTOW High-Temperature Operation in Winter.

Hv Saturated vapor enthalpy of water.

Nomenclature


I Irreversibility or Ionic dissolution force.

IAAE International Agency of Atomic Energy.

ID Inside Diameter.

IDA International Desalination Association.

k Thermal conductivity or unit exergy consumption.

K Constant for mass flow coefficient or gland steam system.

k* Exergy unit cost.

L Length or Exergy Losses.

LP Low-Pressure.

LPH Low-Pressure Heater.

LPT Low-Pressure Turbine.

LS Live Steam Extraction.

LTL Low Turbine Load.

LTMD Logarithmic Temperature Mean Difference.

LTOS Low-Temperature Operation in Summer.

m Mass flow or molality.

MCR Maximum Continuous Rating.

Md Steam flow to MSF unit.

MED Multi-Effect Distillation.

MF Malfunction of a component.

MF* Malfunction cost (impact on fuel).

MFl Intrinsic malfunction.

MFg Induced malfunction.

MIX Mixer.

MR Maximum Rating.

MSL Minimum Stable Load.

MSF Multistage Flash.

MXT Mixer Temper water.

n number of tubes in a vertical row.

NC Net energy Consumption.

NEA Non Equilibrium Allowance.

NRC Number of Recovery Stages.

NRJ Number of Reject Stages.

NTL Normal Turbine Load.

NTOS Nominal-Temperature Operation in Summer.

NTW Non Turbine Working.

OD Outside Diameter.

ODOB One Desalination One Boiler.

O&M Operating and Maintenance

p Pressure.

Nomenclature

436


P Product.

Pc Condenser pressure.

Pr Prandtl number.

PE Pressure Exchanger.

PL Pressure losses, or Partial Load.

PR Performance Ratio.

PTC Performance Test Case or Parabolic Trough Collector.

Q Heat flow.

Qf Heat value of fuel.

r Exergy ratio.

R Thermal resistance or recycle brine.

RCS Recovery Section.

Re Reynolds number.

RJS Reject Section.

RO Reverse Osmosis.

rp Pressure ratio in a turbine section.

RP Recycle Pump.

s Specific entropy.

S Entropy flow or size.

Sa Sonic area.

SF Solar Factor.

SH Superheater.

SR Seawater to Reject section flow.

SRE Stable Reference Environment

SW Seawater feed flow.

SWP Seawater Pump.

SWRO Seawater Reverse Osmosis.

t Thickness.

T Temperature.

T* Temperature reference, 273.15 K.

TBT Top Brine Temperature.

TDOB Two Desalination One Boiler.

TDS Total Dissolved Solids.

To Ambient Temperature.

TP Temper water Pump (also TPP).

TTD Terminal Temperature Difference.

TVC Thermal Vapor Compression.

UAE United Arab Emirates.

U Overall heat transfer coefficient.

US, USA United States of America.

Nomenclature


VC Vapor Compression.

VEX Extraction valve (pressure loss simulation).

VF Feed valve.

vw Tube velocity.

VS Reducing pressure station valve.

VST Stop valve.

VTE Vertical Tube Evaporator.

VWO Valve Wide Open.

x

Variable or molar fraction.

X Steam quality.

w Width.

W Power.

z Ionic charge.

Z Pressure drop coefficient or Capital Cost of a component.

Greeks

α

Sonic velocity or constant of Cobb-Douglass equation.

β

Constant for calculating vapor entropy.

γ

Activity coefficient.

δ

Interstage (temperature) difference.

∆

Difference, increment, variation (or loss).

ε

Relative error or ratio.

η

Efficiency.

κ

Technical production coefficient.

λ

Latent heat, real number or Lagrange multiplier.

µ

Viscosity or chemical exergy component.

ν

Specific volume.

π

Osmotic pressure.

ρ

Density.

φ

Mass flow coefficient of a turbine section, or dysfunction coefficient.

Constant for calculating latent heat of vapor.

ϕ

Amortization factor.

ϖ

Chamber load or total final product.

Arrays/Matrices

B

Exergy flows set.

[DF]

Dysfunction matrix.

DF

Array of dysfunctions generated in the components.

DI

Array of dysfunctions generated by the components.

∆

F

T

Impact on fuel array.

ℵ

Nomenclature

438


κ

e

Unit exergy consumption array of the system input resources.

K

D

Diagonal matrix of the unit exergy consumption.

⟨

KP

⟩

Unit exergy consumption matrix.

MF

Malfunction array.

I

Irreversibility array.

|

I

⟩

Irreversibility matrix operator.

P

Product array.

P

S

Final product array.

|

P

⟩

Product matrix operator.

U

D

Unitary matrix.

Subscripts

a Absolute.

b Exergy flow or brine.

B Brine.

bi Brine inside the tubes.

c Condensate.

C Condenser.

ci Steam to Ejector from leakage system.

CT Condensing Turbine.

d Distillate, design.

D Distillate.

des Low-Pressure Steam to MSF unit.

DR Deaerator.

e Exit or electricity.

es Interstage.

ex Extraction.

f Fouling, formation or fuel relative.

F Cooling brine.

fg Evaporation.

fm Film.

gen Generator.

H Brine Heater.

H

2

O Pure water.

i Inlet, i-section or array index.

j j-Stage, index, variable or specie.

K Kelvin.

L Loss.

ls Live Steam Flow.

LS Live Steam Extraction from reduction pressure station.

Nomenclature


lm Logaritmic mean.

m Mean.

msf MSF plant.

N Last stage of MSF unit.

NRC Last stage of recovery section.

o Outlet.

P Demister pressure losses, or product.

q Chemical.

r Reference.

rcs Recovery section (exit).

rdes Condensate returned from the MSF unit (heater), after passing brine heater pump.

s Isoentropic, shell or entropy flow.

S Saturated.

sea Seawater.

ST Steam or Steam Turbine.

t Turbine or tube.

T Total.

va Steam to vacuum system of MSF unit (condensate returning to condenser).

vent Venting system.

w Wall or water.

Z Capital cost.

0 To the environment.

Superscripts

a, b, c, x, y, z Exponents for calculations of TTDs in heaters or deaerator, pressure losses or gland steam system.

L Local.

G Induced.

m m-Iteration or scaling factor.

n1, n2, n3, n4 Exponents for capital costing equation.

´ Extraction mass flow rate.

o Standard state.

r Operating parameter.

t Transpose (matrix notation).

–1 Inverse (matrix notation).

0 Reference or design (matrix notation).


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FIGURE 2.1 General outlay of MSF distillation with brine recycling ....................................................

37

FIGURE 2.2 Flow diagram of Multi-Effect Distillation (MED) with thermal vapor compression (TVC)

39

FIGURE 2.3 MED process with vertical tube evaporators (VTE) ..........................................................

40

FIGURE 2.4 Flow diagram of a vapor compression system with vertical tube evaporators (VTE) .......

42

FIGURE 2.5 Diagram model of a solar still ............................................................................................

44

FIGURE 2.6 Reverse osmosis process.....................................................................................................

46

FIGURE 2.7 Reverse osmosis (RO) desalination with Pelton turbine ....................................................

47

FIGURE 2.8 Electrodialysis process........................................................................................................

50

FIGURE 3.1 Schematic diagram of a single effect MSF evaporator with recycled brine .......................

54

FIGURE 3.2 Cross-section of a stage in a typical MSF plant .................................................................

55

FIGURE 3.3 Temperature profile of a recycle brine MSF plant .............................................................

56

FIGURE 3.4 A general stage in a MSF plant...........................................................................................

58

FIGURE 3.5 Heat input section ...............................................................................................................

62

FIGURE 3.6 Mixing and splitting points in the MSF desalination plant.................................................

63

FIGURE 3.7 Solution algorithm of a MSF desalination plant model ......................................................

68

FIGURE 3.8 Correspondence between the Top Brine Temperature and distillate output.......................

72

FIGURE 3.9 Brine recirculation as a function of the distillate output.....................................................

73

FIGURE 3.10 Make-up feed water as a function of the distillate output ..................................................

73

FIGURE 3.11 Seawater to reject section as a function of the distillate output..........................................

73

FIGURE 3.12 Top brine temperature depending on the seawater temperature and distillateproduction. Data collected during the year 1997 ................................................................

74

FIGURE 3.13 Recycle brine flow as a function of the seawater temperature and production.Real data collected in the MSF distillers during 1997........................................................

74

FIGURE 3.14 Make-up feed flow obtained for each range of seawater temperature when realdata are computed. Average data of 1997 ..........................................................................

75

FIGURE 3.15 Seawater to reject flow correlations for different seawater temperatures enteringthe MSF plant. Data collected during the year 1997 ..........................................................

75

List of figures

List of figures

458


FIGURE 4.1 Schematic diagram of the power generation plant. Main significant flows arenumbered for later descriptions and equations ...................................................................

78

FIGURE 4.2 Schematic diagram of a turbine section ..............................................................................

80

FIGURE 4.3 Isoentropic and real expansion of the steam in a turbine section........................................

81

FIGURE 4.4 TTD differences in an HP heater ........................................................................................

82

FIGURE 4.5 TTD differences in an LP heater.........................................................................................

84

FIGURE 4.6 Isoentropic and real compression process in a pump..........................................................

88

FIGURE 4.7 Gland and seal steam system ..............................................................................................

88

FIGURE 4.8 Leakage flows and seals of a steam turbine ........................................................................

89

FIGURE 4.9 Algorithm to solve the power plant model using the Powell hybrid method .....................

92

FIGURE 4.10 Last stage of LP turbine acting as a compressor .................................................................

93

FIGURE 4.11 Power plant scheme in the NTW Model. Some flowstreams are renumberedwith respect fig. 4.1.............................................................................................................

94

FIGURE 5.1 SIMTAW MSF process window ........................................................................................

101

FIGURE 5.2 SIMTAW power plant window ..........................................................................................

103

FIGURE 6.1 Physical structure of the co-generation plant ......................................................................

126

FIGURE 6.2 Productive structure of the cogeneration plant ...................................................................

130

FIGURE 6.3 Generic component scheme ................................................................................................

140

FIGURE 6.4 Economic resources scheme ...............................................................................................

142

FIGURE 6.5 Fuel / Product diagram and fuel and product exergy flows (kW) in designconditions for the co-generation plant shown in figure 6.1 ................................................

145

FIGURE 6.6 Fuel impact and technical saving ........................................................................................

148

FIGURE 6.7 Malfunction and fuel impact ...............................................................................................

166

FIGURE 6.8 Analysis of the irreversibility causes (kW).........................................................................

150

FIGURE 6.9 Analysis of fuel impact (kW)..............................................................................................

152

FIGURE 7.1 Productive structure of the simple co-generation system ...................................................

161

FIGURE 7.2 Physical structure of the power plant considered for the thermoeconomic model .............

163

FIGURE 7.3 Physical structure of the MSF plant considered for the thermoeconomic analysis ............

165

FIGURE 7.4 F-P description in steam power plant..................................................................................

167

FIGURE 7.5 Productive structure of the power plant in extraction mode ...............................................

169

FIGURE 7.6 Changes applied to extraction mode productive structure (figure 7.5) whenthe plant operates in condensing mode ...............................................................................

170

List of figures


FIGURE 7.7 Productive structure corresponding to extraction mode with low energy productionin a dual-purpose plant. Changes with respect to figure 7.5...............................................

170

FIGURE 7.8 Productive structure of the steam power plant in parallel and twin extraction mode.Changes with respect to figure 7.5 .....................................................................................

171

FIGURE 7.9 Productive structure of the steam power plant in desalination or twin desalination mode

171

FIGURE 7.10 F-P definition in the MSF unit............................................................................................

172

FIGURE 7.11 Productive structure of the MSF unit..................................................................................

174

FIGURE 7.12 Physical model considered in the thermoeconomic analysis of the MSF plant .................

178

FIGURE 7.13 Impact on fuel analysis when the efficiency of the HPT4 is decreased 10% .....................

208

FIGURE 7.14 Irreversibility increase analysis with the inefficiency in the HPT4....................................

208

FIGURE 7.15 Additional fuel consumption when varying the isoentropic efficiency in HPT4 ...............

219

FIGURE 7.16 Unit electricity cost when the isoentropic HPT4 efficiency is modified ............................

220

FIGURE 7.17 Unit distilled water cost when the isoentropic HPT4 efficiency is modified .....................

220

FIGURE 7.18 Impact on fuel analysis when the fouling in BH is neglected ........................................

232

FIGURE 7.19 Irreversibility increase in the MSF with BH = 0. NTOS case ........................................

232

FIGURE 7.20 Impact on fuel analysis when the fouling in heater is varied .............................................

235

FIGURE 7.21 Monetary cost of distillate when the fouling in heater is varied.........................................

235

FIGURE 7.22 Impact on fuel analysis without fouling in RCS. MCR case ..........................................

246

FIGURE 7.23 Irreversibility increase analysis of section 7.3.2.3 ..........................................................

246

FIGURE 7.24 Impact on fuel depending on fouling in recovery section ..................................................

249

FIGURE 7.25 Monetary cost of electricity depending on the fouling in recovery section .......................

249

FIGURE 7.26 Cost in $ per cubic meter of water when recovery section fouling is varied......................

250

FIGURE 7.27 Impact on fuel analysis in section 7.3.2.4 .......................................................................

259

FIGURE 7.28 Irreversibility increase in section 7.3.2.4............................................................................

259

FIGURE 7.29 Additional fuel consumption due to inefficiencies in several componentsof the power plant ...............................................................................................................

264

FIGURE 7.30 Electricity cost with five inefficiencies in the power plant ................................................

264

FIGURE 7.31 Water cost under different degrees of inefficiency in five components .........................

265

FIGURE 7.32 Impact on fuel analysis without fouling in distillers .........................................................

274

FIGURE 7.33 Increase of irreversibility when fouling is neglected in MSF plant ................................

274

FIGURE 7.34 Impact on fuel due to several inefficiencies in the MSF plant.Unit exergy cost of steam and electricity is 2.55 and 2.85 respectively.............................

277

FIGURE 7.35 Water cost when the fouling in three distillers is varied ....................................................

279

FIGURE 7.36 Malfunctions with an inefficiency of 5 ºC in the TTD of HPH1 heater undervarying loads in the steam power plant ..............................................................................

280

List of figures

460


FIGURE 7.37 Malfunctions generated when the FP is working with an isoentropic efficiency12% lower than the expected under four different loads in the steam power plant ............

281

FIGURE 7.38 Malfunctions generated by an inefficiency of 5% in the isoentropic efficiencyof the HPT1 under varying loads in the steam power plant................................................

281

FIGURE 7.39 Malfunctions generated in the fourth section of the HPT under a 10% decreasein its isoentropic efficiency .................................................................................................

282

FIGURE 7.40 Malfunctions in LPT1 under varying loads in the steam power plant and a 15%decrease in isoentropic efficiency .......................................................................................

282

FIGURE 7.41 Malfunctions provoked by the fouling reduction in heater at different loads.....................

283

FIGURE 7.42 Malfunctions generated in the MSF plant at different loads with no foulingin the recovery section ........................................................................................................

283

FIGURE 7.43 Malfunctions generated in the MSF plant when the fouling in reject sectionis neglected for the two analyzed loads ..............................................................................

284

FIGURE 7.44 Impact on fuel in the MSF plant when the fouling is neglected in the three distillers.Three loads at 32 ºC seawater are included ........................................................................

284

FIGURE 7.45 Physical model applied to the thermoeconomic optimization ............................................

297

FIGURE 7.46 Productive structure of the thermoeconomic model applied to the thermoeconomic optimization ............................................................................................

297

FIGURE 7.47 Optimization algorithm to find the minimum cost of the plant using local optimization...

304

FIGURE 7.48 Speed of convergence of the local variables that are efficiencies.......................................

305

FIGURE 7.49 Evolution of the local variables that are TTD in heaters ....................................................

305

FIGURE 7.50 Minimization of the global cost of the system....................................................................

306

FIGURE 7.51 Sensitivity analysis of the energetic efficiency of the boiler aroundthe optimum point (

η

1

= 0.8608) ........................................................................................

309

FIGURE 7.52 Sensitivity analysis of the efficiency of the first section of the high-pressureturbine around the optimum point (

η

2

= 0.924)..................................................................

309

FIGURE 7.53 Exergy cost of water (k* of steam and electricity entering the MSF is the unity),and distillate temperature at different loads at 32 ºC seawater ...........................................

315

FIGURE A1.1 Impact on fuel analysis with an inefficiency in HPH1 ................................................... 341

FIGURE A1.2 Irreversibility analysis when the TTD in HPH1 is increased 5 ºC .................................. 341

FIGURE A1.3 Impact on fuel associated with a variation in the TTD of HPH1.122 MW power plant production ........................................................................................ 343

FIGURE A1.4 Cost of electricity when varying TTD in HPH1 (MCR performance case)........................ 343

FIGURE A1.5 Cost of water when varying TTD in the first HPH (MCR performance case) ................... 344

FIGURE A1.6 Impact on fuel analysis when a inefficiency in F in detected ......................................... 354

FIGURE A1.7 Irreversibility analysis with the irreversibility in FP ...................................................... 354

List of figures


FIGURE A1.8 Effect of feed pump efficiency on fuel consumption. Variational study in theMCR performance case ...................................................................................................... 355

FIGURE A1.9 Effect of pump inefficiency on electricity cost (MCR performance case) ......................... 356

FIGURE A1.10 Water cost when the efficiency of the feed pump is varied................................................ 356

FIGURE A1.11 Impact on fuel analysis when the HPT1 efficiency is 5% less than the expected .......... 366

FIGURE A1.12 Irreversibility analysis with the inefficiency in HPT1 .................................................... 366

FIGURE A1.13 Model linearity with respect to an inefficiency in HPT1 ................................................... 368

FIGURE A1.14 Cost of electricity depending on the degree of inefficiency applied to HPT1 (MCR case) 368

FIGURE A1.15 Cost of water when the isoentropic efficiency is varied from –5% to 5% withrespect to design efficiency (MCR case) ............................................................................ 369

FIGURE A1.16 Impact on fuel analysis, section A1.4 ............................................................................. 379

FIGURE A1.17 Irreversibility analysis in section A1.4 ........................................................................... 379

FIGURE A1.18 Effect on the fuel consumption when the degree of inefficiency in the LPTis varied from the design point (MCR case) ....................................................................... 380

FIGURE A1.19 Cost of electricity for inefficiencies in LPT1 (MCR case) ................................................. 381

FIGURE A1.20 Water cost per cubic meter for inefficiencies in LPT1. 122 MW in extractionmode (MCR case) ............................................................................................................... 381

FIGURE A1.21 Impact on fuel analysis in section A1.5 .......................................................................... 387

FIGURE A1.22 Irreversibility increase in section A1.5 ........................................................................... 387

FIGURE A1.23 Effect on fuel consumption when the fouling in recovery section isgradually decreased. 1,900 T/h and 32º C seawater ........................................................... 393

FIGURE A1.24 Cost of a cubic meter of water depending on the fouling in the recovery section ............. 393

FIGURE A1.25 Impact on fuel analysis, section A1.6 ............................................................................. 404

FIGURE A1.26 Increase of irreversibility in section A1.6 ....................................................................... 404

FIGURE A1.27 Effect on fuel consumption when the fouling in reject is varied. Nominal-temperatureoperation in summer (NTOS, i.e., 1,900 T/h and 32 ºC seawater temperature) ................. 406

FIGURE A1.28 Variation of the water cost when fouling in the reject section is decreased fromthe design value to zero ...................................................................................................... 407


TABLE 1.1 Ground water disposal and renewable water resources in the Gulf Countries in 1994(Alawadhi, 1999) ..............................................................................................................

21

TABLE 1.2 Water demand for the Gulf Countries in 1990 (ESCWA, 1994)......................................

21

TABLE 1.3 Total installed capacity and production in the seawater desalination plant of theGulf Area in year 1994 (Alawadi, 1999; Al-Gobaisi, 1999) ............................................

22

TABLE 1.4 Contracted capacity of freshwater production from seawater and all waters with theexisting process. The total capacity is 12.8 million cubic meters per day and 21 millioncubic meters per day, respectively. Data collected in 1996 (Alawadhi, 1999) ................

23

TABLE 1.5 Natural resources in the pacific region in the year 1998 (Goto et al., 1999)....................

23

TABLE 1.6 Water use trends in the Pacific region (Goto et al., 1999)................................................

24

TABLE 1.7 Desalination installations in the Pacific region. Data from 1998 (Goto et al., 1999).......

24

TABLE 1.8 Water disposal in the African region in 1995...................................................................

25

TABLE 1.9 Water withdrawal in North African countries. Data collected in 1990 for Algeriaand Tunisia; for Egypt and Morocco data from 1992 (Al-Gobaisi, 1997) .......................

25

TABLE 1.10 Water use in the U.S. in 1995 (Gleick, 1998)...................................................................

26

TABLE 1.11 Desalinated water in Spain during the year 1998 (Torres and Medina, 1999) .............

27

TABLE 1.12 Some of the RO desalination plants installed in Spain (Cadagua, 1999; Sánchezet al., 1997; Fayas and Novoa, 1997; Torres et al., 1999; AECYR, 1999) ......................

28

TABLE 1.13 Specific consumption of the thermal desalination processes. Data obtained fromseveral sources (Fisia-Italimpianti, 1999; I.D.E., 1999)...................................................

29

TABLE 3.1 Fouling factors of the heat reject section in MSF Plants ..................................................

76

TABLE 4.1 Typical x, y, and z coefficient values for the inlet TTD’s in an HP heater ......................

83

TABLE 4.2 Typical x, y, z, a, and b coefficient values for the outlet TTD’s in an HP heater ............

83

TABLE 4.3 Typical x, y, and z coefficient values for the inlet TTD’s in an LP heater ......................

84

TABLE 4.4 Typical x, y, z, a, and b coefficient values for the outlet TTD’s in a LP heater ...............

84

TABLE 4.5 x, y, z, a, b, and c coefficient values in deaerator .............................................................

85

TABLE 4.6 Values of the a coefficient for each pipe of the power model ..........................................

87

List of tables

List of tables

464


TABLE 4.7 Kd and Kd’ constants of the gland and seal steam system ...............................................

89

TABLE 4.8 Operating mode and mathematical model corresponding to the performancedata cases ..........................................................................................................................

96

TABLE 5.1 Input variables for the MCR (maximum continous rating, producing both electricityand water) case..................................................................................................................

106

TABLE 5.2 Model validation for the MCR case..................................................................................

106

TABLE 5.3 Input variables for the MR (maximum rating, producing only electricity)performance case ..............................................................................................................

107

TABLE 5.4 Model validation for the MR case ....................................................................................

107

TABLE 5.5 Input variables for the PL115 performance case (partial load with 115 MWof electricity and a heat extraction to MSF of 145 Gcal/h) ..............................................

108

TABLE 5.6 Model validation for the PL115 performance data case ...................................................

108

TABLE 5.7 Input variables for the PL85 performance case (partial load with 85 MWof electricity and 145 Gcal/h of extraction heat flow) ......................................................

109

TABLE 5.8 Model validation for the PL85 performance case.............................................................

109

TABLE 5.9 MSL2 performance case (minimum stable load with 45 MW of electricityand a combined heat extraction flow of 145 Gcal/h). Main input data ............................

110

TABLE 5.10 Model validation for the MSL2 performance case ...........................................................

110

TABLE 5.11 Input data of the MSL3 performance case (minimum stable load with twoextractions of 150 and 145 Gcal/h to MSF units) .............................................................

111

TABLE 5.12 Model validation for the MSL3 performance case ...........................................................

111

TABLE 5.13 Input data of the MSL4 performance case (minimum stable load with the maximumheat flow extraction to MSF unit: 170 Gcal/h) .................................................................

112

TABLE 5.14 MSL4 performance case. Model validation......................................................................

112

TABLE 5.15 Main input data of the ODOB case (one desalination-one boiler) ...................................

113

TABLE 5.16 Model validation of the ODOB case.................................................................................

113

TABLE 5.17 Main input data of the TDOB case (two desalination-one boiler)....................................

114

TABLE 5.18 Model validation data for the TDOB case ........................................................................

114

TABLE 5.19 Main input data of the VWO performance case (maximum capacity of the steamturbine with and extraction heat flow of 170 Gcal/h to MSF) ..........................................

115

TABLE 5.20 Model validation data for the VWO case .........................................................................

115

TABLE 5.21 Input data of the COC performance case (boiler peak load at least 5% more thanthe MCR case) ..................................................................................................................

116

TABLE 5.22 Model validation data for the COC case...........................................................................

116

List of tables


TABLE 5.23 Input data and performance parameters of the NTOS case (normal-temperatureoperation in summer)........................................................................................................

119

TABLE 5.24 Model validation of the NTOS performance case ............................................................

119

TABLE 5.25 Input data and performance parameters of the HTOS case (high-temperatureoperation in summer)........................................................................................................

120

TABLE 5.26 Model validation of the HTOS performance case ............................................................

120

TABLE 5.27 Some input data and performance parameters of the LTOS case (low-temperatureoperation in summer)........................................................................................................

121

TABLE 5.28 Model validation. LTOS performance case in MSF distillers ..........................................

121

TABLE 5.29 Some input data and performance parameters of the HTOW case (high-temperatureoperation in winter) ..........................................................................................................

122

TABLE 5.30 Model validation of HTOW case of the MSF plant .........................................................

122

TABLE 6.1 Fuel and product definitions for typical dual-purpose power and desalinationplant units .....................................................................................................................

129

TABLE 6.2 Fuels and Products of the components of the co-generation plant ...................................

131

TABLE 6.3 Characteristic equations of the cogeneration plant...........................................................

132

TABLE 6.4 Design and operation exergy flow values of the cogeneration plant (figure 6.1) ............

144

TABLE 6.5 Fuel/Product definition corresponding to figure 6.5 ........................................................

146

TABLE 6.6 Increase of unit consumption. (100

∆

κ

ij

) ......................................................................... 1

46

TABLE 6.7 Irreversibility matrix and unit cost of product..................................................................

151

TABLE 6.8 Malfunction and dysfunction table in (kW) .....................................................................

152

TABLE 7.1 Fuel, product, characteristic equation and exergy cost balance in the simpleco-generation system ........................................................................................................

162

TABLE 7.2 Results of the simple co-generation system model, MCR case........................................

162

TABLE 7.3 Description of components appearing in figure 7.2 .........................................................

164

TABLE 7.4 Components description from figure 7.3. Note that component no. 1 is not describedin physical model but is included in other schemes .........................................................

165

TABLE 7.5 Exergy flows and characteristic equations of components in the steam power plant(extraction mode)..............................................................................................................

176

TABLE 7.6 Exergy flows and characteristic equations for the components of the MSF plant ...........

179

TABLE 7.7 System of equations providing the exergy cost of the steam power plant(extraction mode)..............................................................................................................

182

TABLE 7.8 System of equations providing the exergy costs of the MSF plant (figure 7.11) .............

184

List of tables

466


TABLE 7.9 Case studies of the exergy cost analysis (PTC: Performance Test Case of the dualplant; Gc: Natural gas consumed; CBS: Cleaning Ball System was used) ......................

185

TABLE 7.10 Exergy (kW fuel/kW product) unit costs k* of most significant flows of the dual plant .

186

TABLE 7.11 Exergoeconomic (monetary) unit costs ($/GJ) of most significant flows of a dualpower and desalination plant. Cost of water c*

D

is expressed in $/m

3

, and electricitycost of is also expressed in $/kW·h (c*

GEN*

) ...................................................................

187

TABLE 7.12 Irreversibilities (exergy destruction, kW) in the different components of the dualplant. MSF unit is considered a component......................................................................

188

TABLE 7.13 Isoentropic efficiencies of pumps and turbine sections of the power plant ......................

189

TABLE 7.14 Product and fuel (kW), and exergy efficiency (%) values for the power andMS plants. Note: The efficiency of the boiler is not included in the final efficiency.......

190

TABLE 7.15 Unit exergy costs k* (kW/kW) of component products in the steam power plantcoupled with a MSF unit...................................................................................................

191

TABLE 7.16 Costing equation parameters for an MSF and power plant (El-Sayed, 1996).Units: ca k$/ft

2

, A ft

2

, M lb/s, Q kW, P

i

, P

e

psia, T

i

R,

∆

T F,

∆

P, dP psi, e =

η

/1–

η

.Subscripts: i, inlet; e, exit; t, tube; s, shell; m, mean (LTMD) ........................................

193

TABLE 7.17 Component parameters in Boehm (1987) equations.........................................................

194

TABLE 7.18 Costing equations proposed by Frangopoulos (1991) ......................................................

194

TABLE 7.19 Cost equations proposed by Lozano et al. (1996).

η

exergetic efficiency, B exergyflow of product, S negentropy, vw velocity of tubes , W power, e eficiency of thecondenser (= T

0

(s

2

– s

1

)/(h

2

– h

1

)) ...................................................................................

195

TABLE 7.20 Price breakdown per section in a dual-purpose plant .......................................................

196

TABLE 7.21 Thermoeconomic costs of distilled water and electricity of the analyzeddual-purpose plant.............................................................................................................

197

TABLE 7.22 Thermoeconomic cost of electricity ($/kW·h) and water ($/m

3

) for the casesstudied in the exergetic cost analysis ................................................................................

197

TABLE 7.23 F-P diagram in design, output power of 122 MW ........................................................... 209

TABLE 7.24 F-P values with inefficiency in HPT4 (10% lower efficiency) .................................... 210

TABLE 7.25 KP matrix in design (122 MW) ....................................................................................... 211

TABLE 7.26 KP matrix with inefficiency in HPT4 (10%) ................................................................... 212

TABLE 7.27 Variation de KP with inefficiency in HPT4...................................................................... 213

TABLE 7.28 Irreversibility matrix I with an inefficiency in HPT4 ...................................................... 214

TABLE 7.29 Dysfunction/malfunction matrix with inefficiency in HPT4 (10% isoentropic eff.) ....... 215

TABLE 7.30 Malfunction matrix with inefficiency in HPT4 (1% isoentropic eff. is varied) ........... 216

TABLE 7.31 F-P values (design) for the MSF plant. Nominal production in summer. .................... 222

TABLE 7.32 F-P values without fouling in heater. Nominal production, 32 ºC seawater ................ 223

List of tables


TABLE 7.33 KP matrix in design ...................................................................................................... 224

TABLE 7.34 KP matrix without fouling in heater. NTOS data case .................................................... 225

TABLE 7.35 Variation of the KP matrix without fouling in heater. NTOS case .............................. 226

TABLE 7.36 Irreversibility matrix without fouling in heater. 1,900 T/h and 32 ºC seawater temp ..... 227

TABLE 7.37 Malfunction/dysfunction matrix without fouling in heater. NTOS case ..................... 228

TABLE 7.38 Malfunction matrix varying fouling in heater 0.00001 m2 K/W in NTOS case .......... 229

TABLE 7.39 F-P values in design, 122 MW output power .................................................................. 238

TABLE 7.40 F-P values without fouling in recovery section. MCR case ............................................ 239

TABLE 7.41 KP matrix in design. MCR case ...................................................................................... 240

TABLE 7.42 KP matrix without fouling in recovery section. MCR case ............................................ 241

TABLE 7.43 Variation of KP without fouling in recovery section. MCR case .................................... 242

TABLE 7.44 Irreversibility matrix without fouling in recovery section (MCR case) .......................... 243

TABLE 7.45 Malfunction/dysfunction matrix without fouling in recovery section (MCR case) ......... 244

TABLE 7.46 Malfunction matrix when the fouling in recovery is varied 0.00001 m2 K/Win MCR case ................................................................................................................. 245

TABLE 7.47 F-P values in design, 122 MW output power ............................................................... 252

TABLE 7.48 F-P values with inefficiencies in five components (MCR case) ................................... 253

TABLE 7.49 KP matrix in design (MCR Case) ............................................................................... 254

TABLE 7.50 KP matrix with several inefficiencies in MCR case ..................................................... 255

TABLE 7.51 Variation of KP matrix with several inefficiencies in MCR case ................................. 256

TABLE 7.52 Irreversibility matrix with five inefficiencies in power plant (MCR case ............................ 257

TABLE 7.53 Malfunction/dysfunction matrix with five inefficiencies in MCR case ............................... 258

TABLE 7.54 Comparison of individual inefficiencies and combined inefficiencies in thepower plant. The first five columns are individual inefficiencies, the sixth isthe sum of the five inefficiencies and the seventh is the malfunctions generatedwith the five combined inefficiencies. MCR conditions .................................................. 261

TABLE 7.55 Intrinsic and induced malfunctions (MF) and impact on fuel (MF*) of the powerplant. 122 MW load .......................................................................................................... 262

TABLE 7.56 The first column represents the X-axis in charts, corresponding to the inefficiencyassociated with each component ...................................................................................... 263

TABLE 7.57 F-P values in design, nominal production with 32 ºC seawater ...................................... 267

TABLE 7.58 F-P values without fouling in heater, recovery and reject section. NTOS case ............. 268

TABLE 7.59 KP matrix in design (NTOS case) ............................................................................... 269

TABLE 7.60 KP matrix with three inefficiencies in distillers (NTOS case) ...................................... 270

List of tables


TABLE 7.61 Variation of KP when the fouling in distillers is zero (NTOS case). ........................... 271

TABLE 7.62 Irreversibility matrix with three inefficiencies in distillers. NTOS case ...................... 272

TABLE 7.63 Malfunction/dysfunction matrix when fouling in distillers is zero (NTOS case). ...... 273

TABLE 7.64 Correspondence between the X-label and fouling ............................................................ 276

TABLE 7.65 Comparison between the sum of individual inefficiencies and three combinedinefficiencies in the MSF unit. The first three columns are individual inefficiencies,the fourth is the sum of the three inefficiencies and the fifth is the malfunctionsgenerated with the three combined inefficiencies. Nominal production with 32 ºCseawater (NTOS case) ...................................................................................................... 277

TABLE 7.66 Intrinsic (MFl) and induced (MFg) malfunctions of the MSF plant and their costs(impact on fuel, MF*) under nominal production (32 ºC seawater temperature)............. 278

TABLE 7.67 Impact on fuel associated with the inefficiencies in the power plant in extractionmode (MCR case) ............................................................................................................. 285

TABLE 7.68 Cost variation associated with the inefficiencies in the power plant in co-generationmode (MCR) ..................................................................................................................... 286

TABLE 7.69 Impact on fuel associated with the inefficiencies in the MSF plant (isolated fromthe power plant). 32 ºC Seawater...................................................................................... 286

TABLE 7.70 Additional cost associated with the inefficiencies in the MSF plant (isolated fromthe power plant). 32 ºC Seawater (NTOS case)................................................................ 287

TABLE 7.71 Impact on fuel associated with the inefficiencies in the MSF plant (coupled withthe power plant) ................................................................................................................ 287

TABLE 7.72 Additional cost associated with the inefficiencies in the MSF plant (coupled withthe power plant) ................................................................................................................ 287

TABLE 7.73 Intrinsic and induced malfunctions at 122 MW ............................................................... 290

TABLE 7.74 Intrinsic and induced malfunctions at 140 MW ............................................................... 291

TABLE 7.75 Intrinsic and induced malfunctions at 90 MW ................................................................. 292

TABLE 7.76 Intrinsic and induced malfunctions at 60 MW ................................................................. 293

TABLE 7.77 Intrinsic and induced malfunctions at 1,900 T/h ............................................................. 294

TABLE 7.78 Intrinsic and induced malfunctions at 2,400 T/h .......................................................... 295

TABLE 7.79 Resources and products in the productive structure of the thermoeconomic model.The superscript (´) is extraction mass flow rate, mdes is the steam flow to MSF unit(89.7 kg/s), D is the distilled water mass flow (2000 T/h) and bw is the exergy ofwater leaving the MSF plant (7 kJ/kg·K).......................................................................... 298

TABLE 7.80 Equations of the thermoeconomic model applied in the local optimization..................... 299

TABLE 7.81 Values of parameter a in the capital cost equation of a heater ......................................... 303

TABLE 7.82 Results of the local variables in the optimization process ............................................. 304

TABLE 7.83 Main physical variables after the optimization process .................................................... 306

List of tables


TABLE 7.84 Results for the optimization of the dual-purpose plant in the MCR performancecase. Exergy flows are described in figure 7.45. c is the cost (10–6 $/kJ), with afuel cost cf of 2×10–6 $/kJ and includes the capital cost factor kZ (kZ = ϕ·Z/P);Z (106 $) is the capital cost of the component .................................................................. 307

TABLE 7.85 Different configurations in a dual power plant with 6 co-generation units, appliedto two different power and water demands ...................................................................... 311

TABLE 7.86 Price for water and electricity depending on the policy applied ...................................... 312

TABLE 7.87 Benefit obtained in the two examples with five different price policies seeprevious table) .................................................................................................................. 312

TABLE A1.1 F-P values in design (MCR case) ................................................................................ 333

TABLE A1.2 F-P values in operation with 5 ºC TTD respect to design ............................................. 334

TABLE A1.3 KP matrix in design (MCR case) ................................................................................ 335

TABLE A1.4 KP matrix with inefficiency in HPH1 (MCR case) ...................................................... 336

TABLE A1.5 Variation of KP matrix when TTD in the HPH1 is 5 ºC higher than the expected ........ 337

TABLE A1.6 Irreversibility matrix with the inefficiency in HPH1 .................................................... 338

TABLE A1.7 Malfunction/Dysfunction matrix when the TTD in HPH1 is 5 ºC higher....................... 339

TABLE A1.8 Malfunction matrix when TTD in HPH1 is varied 1 ºC ................................................ 340

TABLE A1.9 F-P design values ........................................................................................................ 346

TABLE A1.10 F-P values with inefficiency in FP: –12% in its efficiciency ........................................... 347

TABLE A1.11 KP matrix in design (MCR case) ............................................................................. 348

TABLE A1.12 KP matrix when the inefficiency in FP is detected ...................................................... 349

TABLE A1.13 Variation of the KP matrix when the FP is working improperly.................................... 350

TABLE A1.14 Irreversibility matrix with –12% in the FP efficiency .................................................. 351

TABLE A1.15 Dysfunction table and malfunction array when the FP is working with 12%lower efficiency ......................................................................................................... 352

TABLE A1.16 Malfunction matrix when the efficiency of the FP varies 1% ............................................ 353

TABLE A1.17 F-P values without any inefficiency. MCR case ......................................................... 358

TABLE A1.18 F-P values when the HPT1 decreases 5% its efficiency (MCR case) ............................ 359

TABLE A1.19 KP matrix in design (MCR case) ..................................................................................... 360

TABLE A1.20 KP matrix when the inefficiency in HPT1 is 5% in its efficiency ................................. 361

TABLE A1.21 Variation of the KP with the inefficiency in HPT1 (MCR case) ................................... 362

TABLE A1.22 Irreversibility matrix with the inefficiency in HPT1 (MCR case) ................................. 363

TABLE A1.23 Dysfunction/malfunction table when the efficiency of the HPT1 is decreased 5% ........ 364

List of tables


TABLE A1.24 Malfunction matrix when the efficiency of the HPT1 is varied 1% ................................ 365

TABLE A1.25 F-P values in design (MCR case) ..................................................................................... 371

TABLE A1.26 F-P values with the inefficiency in LPT1, MCR case ..................................................... 372

TABLE A1.27 KP matrix in design, MCR case ....................................................................................... 373

TABLE A1.28 KP matrix when the efficiency in the LPT1 is decreased 15%, MCR case ..................... 374

TABLE A1.29 Variation of the KP matrix with an inefficiency in LPT1, MCR case ............................. 375

TABLE A1.30 Irreversibility matrix with the efficiency of the LPT1 decreased 15%, MCR case ......... 376

TABLE A1.31 Dysfunction/malfunction table for an inefficiency in the LPT1 (15%), MCR case ......... 377

TABLE A1.32 Malfunction matrix when the efficiency of the LPT1 is varied 1%, MCR case .............. 378

TABLE A1.33 F-P values in design, NTOS case ..................................................................................... 383

TABLE A1.34 F-P values with fouling in RCS=0, NTOS case .............................................................. 384

TABLE A1.35 KP matrix in design, NTOS case ..................................................................................... 385

TABLE A1.36 KP matrix with an inefficiency in RCS, NTOS case ....................................................... 386

TABLE A1.37 Variation of the KP matrix when the fouling in RCS is neglected .................................. 389

TABLE A1.38 Irreversibility matrix without fouling in RCS .................................................................. 390

TABLE A1.39 Dysfunction/malfunction table without fouling in RCS, NTOS case .............................. 391

TABLE A1.40 Malfunction matrix when the fouling in RCS is varied 0.00001 m2 K/W ...................... 394

TABLE A1.41 F-P values in design, NTOS case ..................................................................................... 397

TABLE A1.42 F-P values when the fouling in RJS = 0, NTOS case ...................................................... 398

TABLE A1.43 KP matrix in design, NTOS case ..................................................................................... 399

TABLE A1.44 KP matrix with the inefficiency in RJS, NTOS case ....................................................... 400

TABLE A1.45 Variation of the KP matrix when the inefficiency in RJS is detected ............................. 401

TABLE A1.46 Irreversibility matrix corresponding to reject fouling in RJS, NTOS case ...................... 402

TABLE A1.47 Dysfunction/malfunction table when the fouling in RJS = 0 ........................................... 403

TABLE A1.48 Malfunction matrix when the fouling in RJS is varied 0.00001 m2 K/W ..................... 408

TABLE A2.1 Liquid phase composition of Reference Ambient (Szargut, 1989; Morris, andSzargut, 1986) ................................................................................................................... 413


Resumen ..................................................................................................................................................... 11

Abstract ..................................................................................................................................................... 15

CHAPTER 1. Introduction

..................................................................................................................... 17

1.1 Water requirements ................................................................................................................. 18

1.2 Water quality and uses ............................................................................................................ 18

1.3 World water resources and demand ........................................................................................ 19

1.3.1 Gulf Region ................................................................................................................. 19

1.3.2 Pacific Region and India ............................................................................................. 23

1.3.3 North Africa ................................................................................................................. 25

1.3.4 US experience and the Caribbean Islands ................................................................... 26

1.3.5 Mediterranean area and Europe ................................................................................... 27

1.4 Desalination and energy .......................................................................................................... 29

1.5 Why a MSF and power plant? ................................................................................................. 30

1.6 Thermoeconomic analysis ....................................................................................................... 32

1.7 Ph. D. Thesis development ...................................................................................................... 33

CHAPTER 2. Desalination processes

..................................................................................................... 35

2.1 Phase change processes: distillation and freezing ................................................................... 36

2.1.1 Multi-stage flash process (MSF) ................................................................................. 36

2.1.2 Multi-effect distillation (MED) ................................................................................... 38

2.1.3 Vapor compression (VC) ............................................................................................. 41

2.1.4 Solar distillation ........................................................................................................... 43

2.1.5 Freezing process .......................................................................................................... 44

2.2 Processes using membranes .................................................................................................... 45

2.2.1 Reverse osmosis .......................................................................................................... 45

2.2.2 Electrodialysis (ED) .................................................................................................... 49

2.3 Processes acting on chemical bounds ...................................................................................... 49

2.3.1 Ion exchange ................................................................................................................ 49

2.4 Summary ................................................................................................................................. 51

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CHAPTER 3. MSF desalination steady-state model

............................................................................ 53

3.1 Process description ..................................................................................................................... 543.2 Mathematical model of MSF unit ............................................................................................... 57

3.2.1 Stage model .................................................................................................................... 583.2.2 Brine Heater Model ........................................................................................................ 623.2.3 Mixer and splitter model ................................................................................................. 63

3.3 Auxiliary equations ..................................................................................................................... 643.3.1 Density ............................................................................................................................ 643.3.2 Viscosity ......................................................................................................................... 643.3.3 Thermal conductivity ...................................................................................................... 653.3.4 Heat capacity .................................................................................................................. 653.3.5 Enthalpy .......................................................................................................................... 653.3.6 Vapor pressure ................................................................................................................ 663.3.7 Boiling point elevation ................................................................................................... 673.3.8 Non-equilibrium allowance ............................................................................................ 673.3.9 Demister and other losses ............................................................................................... 67

3.4 Solution algorithm ...................................................................................................................... 683.5 Simulation cases ......................................................................................................................... 70

3.5.1 TBT control .................................................................................................................... 713.5.2 Inverse problem .............................................................................................................. 71

3.6 Initial data and simulation .......................................................................................................... 723.6.1 Fouling effect .................................................................................................................. 75

3.7 Summary ..................................................................................................................................... 76

CHAPTER 4. Steam power plant steady-state model

.......................................................................... 77

4.1 Model description ....................................................................................................................... 784.2 Mathematical model ................................................................................................................... 80

4.2.1 Steam turbines ................................................................................................................ 804.2.2 HP heat exchangers ......................................................................................................... 824.2.3 LP heat exchangers ......................................................................................................... 834.2.4 Deaerator ......................................................................................................................... 844.2.5 Condenser ....................................................................................................................... 854.2.6 Boiler .............................................................................................................................. 854.2.7 Valves ............................................................................................................................. 86

4.2.7.1 Turbine control valves ...................................................................................... 864.2.7.2 Boiler outlet stop valve ..................................................................................... 864.2.7.3 Boiler inlet control valve .................................................................................. 86

4.2.8 Pipes ................................................................................................................................ 864.2.9 Pumps ............................................................................................................................. 874.2.10 Gland and seal steam system .......................................................................................... 884.2.11 Generator ........................................................................................................................ 89

4.3 Auxiliary equations ..................................................................................................................... 904.3.1 Thermodynamic properties ............................................................................................. 904.3.2 Transport properties ........................................................................................................ 90

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4.4 Solution algorithm ...................................................................................................................... 904.5 Operating modes and mathematical models ............................................................................... 92

4.6 Summary ..................................................................................................................................... 96

CHAPTER 5. Simulator

.......................................................................................................................... 99

5.1 SIMTAW structure ..................................................................................................................... 100

5.2 Model validation ......................................................................................................................... 1045.2.1 Power plant ..................................................................................................................... 104

5.2.1.1 MCR case .......................................................................................................... 1065.2.1.2 MR case ............................................................................................................ 1075.2.1.3 PL115 case ........................................................................................................ 1085.2.1.4 PL85 case .......................................................................................................... 1095.2.1.5 MSL2 case ......................................................................................................... 1105.2.1.6 MSL3 case ........................................................................................................ 1115.2.1.7 MSL4 case ........................................................................................................ 1125.2.1.8 ODOB case ....................................................................................................... 1135.2.1.9 TDOB case ........................................................................................................ 1145.2.1.10 VWO case ......................................................................................................... 1155.2.1.11 COC case .......................................................................................................... 116

5.2.2 MSF Plant ....................................................................................................................... 1175.2.2.1 NTOS case ........................................................................................................ 1195.2.2.2 HTOS case ........................................................................................................ 1205.2.2.3 LTOS case ........................................................................................................ 1215.2.2.4 HTOW case ...................................................................................................... 122

CHAPTER 6. Thermoeconomics. Fundamentals, applications of thermoeconomic diagnosisand optimization of complex energy systems

.................................................................... 123

6.1 Basic concepts ............................................................................................................................ 1266.1.1 The concept of cost ......................................................................................................... 1266.1.2 Fuel, product and unit exergetic consumption ................................................................ 1276.1.3 Physical and thermoeconomic plant models ................................................................... 130

6.2 Calculating thermoeconomic costs ............................................................................................. 1366.2.1 Marginal and average thermoeconomic costs ................................................................. 1406.2.2 Economic resources and thermoeconomic costs ............................................................ 142

6.3 Thermoeconomic applications to thermoeconomic operation diagnosis andthe optimization of complex energy systems .............................................................................. 1436.3.1 Operation thermoeconomic diagnosis ............................................................................ 143

6.3.1.1 Technical exergy saving ................................................................................... 1446.3.1.2 Impact on resources consumption .................................................................... 1456.3.1.3 Malfunction and dysfunction analysis .............................................................. 1486.3.1.4 Intrinsic and induced malfunctions ................................................................... 153

6.3.2 Thermoeconomic optimization ....................................................................................... 155

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CHAPTER 7. Thermoeconomic analysis of a dual-purpose power and desalination plant

............. 159

7.1 Thermoeconomic model ............................................................................................................. 1617.1.1 A simple co-generation system ....................................................................................... 1617.1.2 Physical structure ......................................................................................................... 1627.1.3 Productive structure ........................................................................................................ 166

7.1.3.1 Steam power plant ............................................................................................ 1667.1.3.2 MSF unit ........................................................................................................... 171

7.1.4 Thermoeconomic model ................................................................................................. 1757.2 Cost analysis ............................................................................................................................... 180

7.2.1 Exergy costs allocation ................................................................................................... 1817.2.2 Exergy cost analysis ....................................................................................................... 1857.2.3 Thermoeconomic costs ................................................................................................... 191

7.2.3.1 Investment costs ............................................................................................... 1927.2.3.2 Capital costs ...................................................................................................... 197

7.2.4 Thermoeconomic cost analysis ....................................................................................... 1977.2.5 Cost allocation: Indirect methods ................................................................................... 198

7.2.5.1 WEA method .................................................................................................... 1987.2.5.2 Fuel cost of water in dual plants ....................................................................... 200

7.3 Thermoeconomic diagnosis ........................................................................................................ 2027.3.1 Thermoeconomic diagnosis of a power and desalination plant: case studies .............. 2037.3.2 Analysis of individual inefficiencies .............................................................................. 205

7.3.2.1 Inefficiency in the fourth section of the high-pressure turbine ......................... 2057.3.2.2 Using the cleaning ball system in the brine heater ........................................... 2217.3.2.3 The effect of recovery section fouling on steam power plant behavior ............ 236

7.3.3 Analysis of several inefficiencies ................................................................................... 2517.3.3.1 Analysis of several simultaneous inefficiencies in the steam power plant ....... 2517.3.3.2 Analysis of several inefficiencies in the MSF plant ......................................... 265

7.3.4 Thermoeconomic diagnosis and load influence in the dual plant ................................... 2797.3.4.1 Effect of inefficiencies in the power plant for different loads .......................... 2807.3.4.2 Effect of MSF unit inefficiencies under different loads ................................... 283

7.3.5 Summary of applying thermoeconomic diagnosis to power and desalination plants .. 2857.4 Thermoeconomic optimization ................................................................................................... 288

7.4.1 Introduction ..................................................................................................................... 2887.4.2 Thermoeconomic isolation ............................................................................................. 2887.4.3 Physical model ................................................................................................................ 2967.4.4 Thermoeconomic model ................................................................................................. 2967.4.5 Local and global variables .............................................................................................. 2997.4.6 Local optimization of subsystems .................................................................................. 3017.4.7 Local optimization results ............................................................................................... 303

7.5 Economic analysis. Cost, price and benefit ................................................................................ 3097.5.1 Case study ....................................................................................................................... 311

7.6 Conclusions and operation recommendations ............................................................................ 3137.6.1 Cost analysis ................................................................................................................... 313

7.6.1.1 Results .............................................................................................................. 3137.6.1.2 Conclusions and operation recommendations .................................................. 316

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7.6.2 Thermoeconomic diagnosis ............................................................................................ 3177.6.2.1 Results .............................................................................................................. 3177.6.2.2 Conclusions and final considerations ............................................................... 318

7.6.3 Local optimization .......................................................................................................... 3217.6.4 Operating management ................................................................................................... 322

CHAPTER 8. Synthesis, contributions and perspectives

..................................................................... 323

8.1 Synthesis ..................................................................................................................................... 323

8.2 Main contributions ..................................................................................................................... 3258.2.1 Simulator of a dual-purpose power and desalination plant ............................................ 3258.2.2 State of the art in Thermoeconomics .............................................................................. 3258.2.3 F-P definition for a MSF unit ......................................................................................... 3268.2.4 Cost analysis of a dual-plant ........................................................................................... 3268.2.5 Diagnosis of a complex system ...................................................................................... 3268.2.6 Local optimization of the steam power plant ................................................................. 3278.2.7 Cost, price and benefit .................................................................................................... 327

8.3 Perspectives ................................................................................................................................ 3278.3.1 Improving existing plants. Process integration .............................................................. 3278.3.2 Improvements in thermoeconomic diagnosis ................................................................. 3288.3.3 Integrating attitudes ........................................................................................................ 3298.3.4 Sustainable desalination ................................................................................................. 3298.3.5 Promote energy and water interactions .......................................................................... 330

ANNEX 1. Thermoeconomic diagnosis

.................................................................................................. 331

A1.1 Effect of an inefficiency in the high-pressure heater no.1 (HPH1) ............................................ 332

A1.2 Effect of feed pump isoentropic efficiency ................................................................................ 345

A1.3 Effect of an inefficiency in the first section of the high-pressure turbine (HPT1) ..................... 357

A1.4 Effect of inefficiency in the first section of the low-pressure turbine (LPT1) ........................... 369

A1.5 Effect of the cleaning ball system in the recovery section ......................................................... 382

A1.6 Effect of reject section fouling ................................................................................................... 395

A1.7 Summary .................................................................................................................................... 407

ANNEX 2. Thermodynamic properties of seawater

............................................................................. 409

A2.1 Specific enthalpy h of superheated or saturated vapor ............................................................ 419

A2.2 Specific entropy of superheated or saturated vapor ................................................................ 410

A2.3 Specific volume of superheated or saturated vapor ................................................................. 411

A2.4 Latent heat vaporisation of water as a function of boiling temperature .................................. 411

A2.5 Seawater exergy ......................................................................................................................... 412A2.5.1 Theory ............................................................................................................................. 430A2.5.2 Practice: Brine exergy as a function of temperature, pressure and salt concentration 417

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ANNEX 3. Technical data

....................................................................................................................... 419

A3.1 MSF plant ................................................................................................................................ 419A3.2 Power Plant .............................................................................................................................. 426

NOMENCLATURE ........................................................................................................................................ 433

REFERENCES ................................................................................................................................................ 441

LIST OF FIGURES.......................................................................................................................................... 457

LIST OF TABLES .......................................................................................................................................... 463

Documents

UCHE - Thermoeconomic Analysis and Simulation of a Combined Power and Desalination Plant