Transcript

Desalination 285 (2012) 123–130

Contents lists available at SciVerse ScienceDirect

Desalination

j ourna l homepage: www.e lsev ie r .com/ locate /desa l

Cost optimization of a combined power and water desalination plant with exergetic,environment and reliability consideration

Seyed Reza Hosseini, Majid Amidpour ⁎, Seyed Ehsan ShakibFaculty of Mechanical Engineering—Energy Division, K.N. Toosi University of Technology, P.O. Box: 19395-1999, No. 15-19, Pardis Str., Mollasadra Ave., Vanak Sq., Tehran 1999 143344, Iran

⁎ Corresponding author. Tel.: +98 21 84063222; fax:E-mail address: [email protected] (M. Amidpour)

0011-9164/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.desal.2011.09.043

a b s t r a c t

a r t i c l e i n f o

Article history:Received 26 July 2011Received in revised form 23 September 2011Accepted 29 September 2011Available online 24 October 2011

Keywords:Power plantMulti stage flash desalinationMulti-objective optimizationThermoenvironomicExergy efficiencyReliability

The present study deals with the multi-objective optimization for designing a combined gas turbine andmulti stage flash desalination plant. In optimization approach, the exergetic, economic and environmental as-pects have been considered, simultaneously. In order to achieve the optimal design, Multi-objective geneticalgorithm (MOGA) is applied as a suitable optimization technique. The thermoenvironomic objective func-tion is obtained by integrating the environmental impacts and thermoeconomic objective. By applying theoptimization approach, this objective function is minimized, whereas system exergy efficiency is maximized.Moreover, equipment reliability using the state-space and the continuous Markov method is incorporated inoptimization results to improve the products' cost values. The optimization results show that the cost ofproducts and environmental cost impact are reduced by 13.4% and 53.4%, respectively, whereas a 14.8% in-crease happens in total exergy efficiency. Therefore, improvement in all objectives has been achieved usingthe optimization process, although the power and water productions have not changed much. Additionally,the sensitivity analysis shows the relationship between the fuel cost, pollution damage cost and the objectivefunctions.

+98 21 88674748..

rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Energy is the most important part of our life. The usage of energy isfound everywhere in a variety of applications [1]. Energy systems involvea large number and various types of interactions with systems outsidetheir physical boundaries. The designermust, therefore, facemany issues,whichdeal primarilywith the energetic, economic and environmental as-pects of the system. The “most efficient” configuration is not always theoptimal one in terms of cost, since the capital, labor, and energy costsplay a non-negligible role. A thermoeconomic analysis takes into accountboth fuel and capital costs, and allows determining the product's cost onthe basis of exergy criteria. This requires the determination of a functionalquantitative interdependence between equipment, operations costs andefficiency [2,3].

Large dual-purpose plants are built to reduce the cost of electricityproduction and freshwater. The dual purpose power desalination plantsmake use of thermal energy extracted or exhausted from power plantsin the form of low-pressure steam to provide heat input to thermal de-salinations, like multi-stage flash (MSF) or multi-effect distillation(MED) systems.

Numerous researchers, e.g. [1,4–8] have conducted exergy andthermoeconomic analyses and optimization for thermal systems.Using the optimization procedure with respect to thermodynamiclaws as well as thermoeconomics then becomes essential [1]. Ther-modynamic laws govern energy conversion processes, costs are in-volved in obtaining the final products (expenses for the purchase ofequipment and input energy resources, operation and maintenancecosts), and the effects of undesired fluxes to the ambient must beevaluated in order to answer environmental concerns. In fact, themain objective of a designer is to define the optimal plant configura-tion and operative conditions according to specified environmentalconstrains and to the user's requests. Therefore, an integrated designoptimization approach would be preferred to be able to deal with allthese aspects in real and complex energy systems. In order to incor-porate the emission assessment, ‘Environomic’ is proposed to denotethe combination of ‘Thermodynamic, Economic and Emissions’. Manystudies have performed environomic consideration of energy systems[1,9–13].

To increase competitiveness and market value of cogenerationsystems, it is important to analyze the influence of equipment reli-ability on the resulting cost of power and water. So reliability evalua-tion of hybrid system is very important to both utilities andcustomers. The reliability and economics of a cogeneration supplysystem have always been conflicting parameters. These parameterscan be dealt with by establishing quantitative links between them.Such links can best be established by using probabilistic criteria

Nomenclature

BR Brine circulatingc Unit cost of the exergy rateCC Combustion ChamberCO Carbon monoxideCom CompressorD DistillateĖ Exergy ratee Specific exergyGT Gas turbineHb Brine pool heightHJ Heat RejectionHR Heat RecoveryHRSG Heat recovery steam generatorMED Multi Effect EvaporationMOGA Multi objective genetic algorithmMSF Multi Stage FlashN Number of desalination stagesOMC Operating and Maintenance CostP Probability, Pressureppm Parts per millionsPR Performance ratio (the ratio between the mass of the

produced fresh water to that of the consumed steam)TBT Top Brine TemperatureTRR Total Revenue RequirementTur TurbineTN Temperature of rejected brineTpz Adiabatic temperature in the primary zone of combus-

tion chamber (K)Vv Vapor allowable velocityWnet Net power

Greek Lettersτ Residence time in the combustion zoneε Exergetic efficiencyφ Equivalent fuel–air coefficientηiT Gas turbine isentropic efficiencyηiC Compressor isentropic efficiency

Subscripts0 Environmental stateCC Combustion Chamberenv EnvironmentF FuelP Producttot Total

Fig. 1. Combined gas turbine cycle and desalination. (1,2: Air; 3, 7, 14: Power; 4, 6, 8:combustion products; 5: methane; 9: water; 10: steam; 11, 15: sea water; 12: distil-late; 13: brine).

124 S.R. Hosseini et al. / Desalination 285 (2012) 123–130

which consider the stochastic nature of component outages, customerdemands, etc. [14]. Many studies have performed reliability modelingof systems [15–20].

Our previous paper considered the effect of reliability analysis onthe cost of power and water, which is obtained by thermoeconomicanalysis [15]. This paper exhibits the multi objective optimization ofa combined gas turbine and multi stage flash-brine circulating desali-nation plant. The optimization algorithm is applied for minimizingthe total product cost and maximizing overall exergy efficiency ofthe dual-purpose plant. Note that the environmental equations ofpollutant gases are included in the cost of products. In addition,according to our previous paper, the equipment reliability consider-ation is incorporated in the optimization results. Finally, the resultsof base case and optimization design with and without reliability

consideration are compared and then the sensitivity of fuel cost andenvironmental damage cost on Pareto frontier of optimal solutionare presented.

2. Cogeneration cycle

Fig. 1 illustrates the schematic of the combined GT-MSF system for si-multaneous generation of the electric power and fresh water. Powergeneration cycle includes compressor, combustion chamber and gas tur-bine that have a nominal output power of 65 MW. Also, a heat recoverysteam boiler was used to produce saturated steam of distillation unit. Allparts of systems were modeled and simulated and energy and exergyequations were developed and applied to evaluate performance of com-bined system. Technical characteristics of the proposed plant are shownin Tables 1 and 2. The exergetic, thermoeconomic and reliability analyseswere fully described in our previous paper [15]. Following is a summaryof the thermoeconomic and reliability analysis of the hybrid plant.

3. Summary of thermoeconomic and reliability analysis

The cost balance equation of a component of an energy system iswritten as follows:

∑n

j¼1cj Ej

� �k;in

þ ZCIk þ ZOM

k ¼ ∑m

j¼1cjEj

� �k;out

ð1Þ

where cj is the unit cost of exergy ($/kJ) for the jth stream to/from thecomponent, Ėj is the exergy flow for the jth stream to/from the com-ponent (kW) and ZCI

k k and ZOMk ($/s) are the related cost of capital in-

vestment and operating and maintenance for the kth componentobtained using the economic model. The economic model is basedon the Total Revenue Requirement (TRR) method (which is basedon procedures adopted by the Electric Power Research Institute) [21].

An important method for reliability evaluation in continuous anddiscrete systems is Markov approach modeling. Consider the threecomponents as representing the gas turbine, the heat recovery

Table 3Reliability assumptions of the hybrid plant.

Component Failure per day Repair per day

GT 0.0033 0.03HRSG 0.002 0.19MSF 0.002 0.08

Table 1Specifications of the gas turbine power plant system.

Parameter Value

Ambient air temp. 25 °CRelative air humidity 60%Compression ratio 11Isentropic efficiency of compressor 86%Isentropic efficiency of turbine 87%Inlet turbine temp. 1100 °CHeat loss in combustion chamber 2%Pressure loss in combustion chamber 5%Inlet HRSG water temp. 25 °COutlet HRSG flue gas temp. 160 °CNet power output 65 MWThermal efficiency of power cycle 29.1%

125S.R. Hosseini et al. / Desalination 285 (2012) 123–130

steam generator and multi stage flash desalination which are compo-nents in series. To demonstrate the continuous Markov concepts, astate space diagram was applied to represent system state changes.A state is defined as a particular combination of component operationand failure. Satisfactory operation of combine system is defined asgenerating electricity and water. The failure rate and repair rate as-sumptions of the GT, HRSG, and MSF are shown in Table 3.

The product costs with reliability consideration can be obtainedusing the state probabilities as weights for every possible operatingstate [14,15]:

Ce ¼ ∑iPei Cei

ð2Þ

Cw ¼ ∑iPwi

Cwi: ð3Þ

Pei is the probability of the state in which the electricity is pro-duced andCei is the cost of electricity production in that state. This ex-pression is used for water production either. As was shown in [15],the effect of the inclusion of equipment reliability is to increase thewater cost due to unexpected equipment downtime resulting fromfailure and subsequent equipment repair.

Table 2Specifications of the MSF desalination system.

Parameter Value

Capacity 42,165 m3/dayNumber of effects 32Temperature of the inlet seawater 25 °CTemperature of the rejected brine 40 °CTop brine temperature 106 °CSalt composition of the inlet seawater 42,000 ppmSalt composition of the outlet brine 70,000 ppmOutside/inside diameters of the HR condenser tubes 34.9/31.6 mmOutside/inside diameters of the HJ condenser tubes 28.5/25.3 mmNumber of tubes in HR section 2403Number of tubes in HJ section 1653Brine velocity in the HR condenser tubes 2.37 m/sBrine velocity in the HJ condenser tubes 2.14 m/sPressure loss in the HR condenser tubes 1146 kPaPressure loss in the HJ condenser tubes 129 kPaTemperature of the inlet steam 143.6 °CTotal steam consumption 50.4 kg/sTotal feed seawater 1220 kg/sTotal cooling seawater 589 kg/sTotal brine outlet 732 kg/sDesalination length 132.2 mDesalination width 18 mDesalination height 5 mPerformance ratio 9.7Specific area 333 m2/(kg/s)Total head losses outlet the MSFa 127 mPumping power consumption 4.5 kW h/m3

a It is the sum of the following head losses: sea water supply to MSF, saline and cool-ing water rejected to sea, and distillate water transfer to storage tank.

4. Environmental consideration

The combustion in a gas turbine is an incomplete process. The ex-haust products mainly are carbon dioxide (CO2), water vapor (H2O),excess atmospheric oxygen (O2) and nitrogen (N2). Carbon dioxideand water vapor have not always been regarded as pollutants becausethey are the natural consequence of complete combustion of a hydro-carbon fuel. However, they both contribute to global warming andcan only be reduced by burning less fuel [22].

For a gas turbine engine burning a lean mixture of natural gas andair, the emissions of unburned hydrocarbons (UHC) and sulfur (SOx)are negligibly small and therefore most regulations for stationary gasturbines have been directed at oxides of nitrogen and carbon monox-ides. CO and NOx emissions are the pollutant emissions, and have aharmful effect on human health, as well as the environment [22].

A simple model, based on semi-analytical correlations [23], is addedhere to the thermoeconomic model to determine pollutant emissions,which are essential for the setup of an environmental objective function.The adiabatic flame temperature in the primary zone of the combustionchamber is derived from the expression by Gülder [24]:

Tpz ¼ Aσαexp β σ þ λð Þ2� �

πxθyψz ð4Þ

where π is a dimensionless pressure p/pref (p being the combustion pres-sure p2, and pref=101,325 Pa); θ is a dimensionless temperature T/Tref(T being the inlet temperature T2, and Tref=300 K); ψ is the H/C atomicratio (ψ=4, the fuel being pure methane); σ=φ for φb1 (φ being thefuel to air equivalence ratio) and σ=φ−0.7 for φN1. φ is equivalentfuel to air ratio that is considered equal to 0.64 in this work. Parametersdenoted as x, y, z,α, β, and λ can be found in Appendix A.

The adiabatic flame temperature is used in the semi-analyticalcorrelations proposed by Rizk and Mongia [23] to determine the pol-lutant emissions in grams per kilogram of fuel:

NOx ¼0:15E16τ0:5e −71100=Tpzð Þ

p0:053 Δp3=p3ð Þ0:5 ð5Þ

CO ¼ 0:179E9e 7800=Tpzð Þp23τ Δp3=p3ð Þ0:5 ð6Þ

where τ is the residence time in the combustion zone (τ is assumedconstant and is equal to 0.002 s); Tpz is the primary zone combustiontemperature; p2 is the combustor inlet pressure; Δp2=p2 is the non-dimensional pressure drop in the combustor (Δp2=p2=0.05). Notethat the primary zone temperature is used in the NOx correlation in-stead of the stoichiometric temperature, since the maximum attain-able temperature in premixed flames is Tpz, as pointed out byLefebvre [24].

5. Optimization approach

In order to achieve the optimal parameters, an optimization algo-rithm tool can be used. Although gradient descent methods are themost elegant and precise numerical methods to solve optimizationproblems, however, they have the possibility of being trapped at localoptimum depending on the initial guess of solution. In order to achievea good result, these methods require very good initial guesses for

Fig. 2. Basic concept of an evolutionary algorithm [1].

126 S.R. Hosseini et al. / Desalination 285 (2012) 123–130

parameters. Stochastic optimization method such as genetic algorithm(GA) that has been applied for this study seems to be a promising alter-native for solving this problem. The genetic algorithm (GA) is a popula-tion based optimization technique that searches the best solution of agiven problem based on the concepts of natural selection, geneticsand evolution [25]. The search is made starting from an initial popula-tion of individuals, often randomly generated. An individual is consid-ered a possible candidate solution for the optimization problem inhand. At each evolutionary step, individuals are evaluated using an ob-jective function [26]. Three types of operators do the evolution (i.e., thegeneration of a new population): breeding, mutation and selectionwhile selection includes killing a given proportion of the populationbased on probabilistic “survival of the fittest”. Killed individuals are su-perseded by children, which are created by breeding the remaining in-dividuals in the population. For each child produced, breeding firstrequires probabilistic selection of two parent individuals, getting morechance to choosefitter individuals.Mutation allows new areas of the re-sponse surface to be explored by random alterations of optimizationvariables. GA iteratively improved the set of tentative solutions by ap-plying the aforementioned stages to find a good solution.

5.1. Description of the multi-objective optimization algorithm

A multi-objective optimization problem requires the simultaneoussatisfaction of a number of different and often conflicting objectives.When it is tried to optimize several objectives simultaneously, the searchspace also becomes partially ordered. To gain the optimal solution, therewill be a set of optimal trade-offs between the objectives. Hence, the op-timum solution for multi objective optimization is not necessarilyunique. In a typicalmulti objective optimization problem, the interactionof multiple objectives yields a set of efficient or non-dominated solu-tions, known as Pareto-optimal solutions, which give a decision makermore flexibility in the selection of a suitable alternative [27].

There are several ways to approach a multi objective optimizationproblem, that all of them focus on the approximation of the Pareto-optimal solutions. For multi objective optimization, evolutionary al-gorithms have been widely used because of their natural propertiessuited for these types of problems. So, in this paper multi objectivegenetic algorithm (MOGA) was applied for finding optimal solution.The flow chart of the GA is shown in Fig. 2. A detailed introductionto evolutionary computation is presented in [28–32].

5.2. Objective functions

The three objective functions of the multi-criteria optimizationproblem are the total exergetic efficiency (to be maximized), the totalcost rate of products (to beminimized) and the “environmental impact”(to be minimized). In this research the cost of pollution damage is as-sumed to be added directly to the expenditures that must be paid forproduction of system products. Therefore, the environmental objectivefunction is addedwith thermoeconomic one to form a unique objectiveknown as thermoenvironomic objective in this work. Themathematicalformulation of objective functions is as the following.

Exergetic εoverall ¼EP

EF¼ E12 þ E13 þ E15−E11 þ W net−W pumps

E fuel þ E1

ð7Þ

Economic C Ptot¼ C F þ∑

kZ k þ C env ð8Þ

Environmental C env ¼ CCOmCO þ CNOxmNOx

ð9Þ

A single pollutant can be considered in such an “environmental im-pact” objective according to its degree of harmfulness. If more than onepollution source is taken into account, their degrees of harmfulness can

be introduced as relativeweights of each pollutantmeasure. Theweight-ing criterion may also derive from economic considerations, when theunit damage cost of each pollutant is available. In particular, links maynot exist between the environmental impact and economic objectives(e.g., taxes on pollutant emissions are not imposed in many countries,or, if they are imposed, they are often based on the installed powerand the relationship with the emission rate is not direct). Furthermore,using unit damage costs toweigh the contribution of each pollutant con-sidered in the environmental impact objective function does not affectthe flexibility of taking into account pollution costs in the economic ob-jective. In other words, the minimization of the environmental impactremains a distinct objective from the minimization of system total costeven if pollution costs themselves are already included in the economicobjective, as suggested in environomics. As a final remark, note thatwhen the only pollutant considered is CO2 production, which is directlyproportional to fuel consumption, and in turn depends on the exergeticefficiency, the environmental objective does not compete with the ener-getic one (exergetic efficiency). In this case, the surface of the Paretofront degenerates to the curve of the optimal solutions of the two-objective (energetic and economic) optimization problem [9].

In Eq. (9) the associated cost of the environmental impact is con-sidered to be a part of expenditures that should be paid for produc-tion of the system products. Values for the external environmentalcosts (damage cost) are taken from [33]. (CNOx and CCO are equal to4.98 $/kgNOx and 1.68 $/kgCO, respectively).

5.3. Decision variables

In thermal system design and optimization, it is convenient toidentify two types of independent variables. These variables are deci-sion variables and parameters. The decision variables may be variedin optimization process. However, the parameters remain fixed in agiven application. All other variables are dependent variables. Theirvalues are calculated from independent variables using thermody-namic relations.

The selected decision variables in this work are:

The compressor pressure ratio 8≤P2=P1≤15 ð10Þ

The turbine inlet temperature 900≤T4≤1300 -C ð11Þ

Isentropic efficiency of the turbine 0:75≤ηiT≤0:9 ð12Þ

Isentropic efficiency of the compressor 0:75≤ηiC≤0:9 ð13Þ

Number of desalination stages 24≤N≤37 ð14Þ

Temperature of rejected brine 30≤TN≤50 -C ð15Þ

Table 4Tuning parameters in MOGA optimization program.

Tuning parameters Value

Population size 400Maximum no. of generations 700Minimum function tolerance 1e-5Probability of crossover (%) 80Probability of mutation (%) 1Number of crossover point 2Selection process TournamentTournament size 2

127S.R. Hosseini et al. / Desalination 285 (2012) 123–130

Top brine temperature 100≤TBT≤120 -C ð16Þ

Inlet steam pressure 300≤P10≤800 kPa: ð17Þ

5.4. Constraints

The following process limitations are considered in the cogenera-tion plant:

Outlet HRSG flue gas temp: T7N160 -C ð18Þ

Brine mass flow rate per stage width 200bVbb350 kg=ms ð19Þ

Brine velocity in condenser tubes Vtubeb3ms

ð20Þ

Brine pool height Hbb0:5 ð21Þ

The vapor allowable velocity Vvmax¼ 8

ms

ð22Þ

Temperature difference perstages ΔTstage≥2 -C: ð23Þ

In addition, it was decided to have the specified production ofpower and water in the optimization approach:

Net power production 64:5≤Wnet≤65:5 MW ð24Þ

Desalination capacity 40;000≤D≤43;000m3=day: ð25Þ

Since the amount of power and water production does not changemuch, so it is assumed that the failure and repair rates of componentsremain constant.

4850

4900

4950

5000

5050

5100

5150

5200

5250

5300

30.4 30.6 30.8 31

Tot

al p

rodu

cts

cost

rat

e ($

/hr)

Total exergy

Non reliability

With reliability

Fig. 3. Pareto frontier: best trade off v

6. Results

As it was mentioned, multi-objective optimization was performedfor finding minimum total cost rate and maximum overall exergeticefficiency of the cogeneration system. The tuning parameters of theoptimization program are presented in Table 4.

Fig. 3 is the Pareto optimum frontier in multi-objective optimiza-tion. Selection of the final solution among optimum points that existon Pareto front needs a process of decision-making. This process ismostly carried out based on engineering experiences and importanceof each objective for decision makers. In fact, in multi-objective opti-mization, all point located on the Pareto front are potentially an opti-mum solution. The selection of the final optimum point amongavailable solutions depends on importance of each objective for de-signers. The selected optimum in this paper is according the authors'preferences and it might be different in another cases and conditions.Moreover, for each optimum solution on Pareto frontier, it is possibleto define a weighting coefficient for each objective.

According to Fig. 3, it could be observed that, by applying the reli-ability analysis the Pareto front moves to different cost points. Inother words, the total product cost is increased for constant exergyefficiency (As noted, the effect of the inclusion of equipment reliabil-ity is to increase the production costs due to unexpected equipmentdowntime resulting from failure and subsequent equipment repair).In this paper, it is supposed that the total exergy efficiency is notless than 31% that this limitation is the designer's criterion for select-ing the optimal point. Thus according to Fig. 3 the selected optimumpoint is chosen for the system with reliability consideration.

The amount of objective functions is shown in Fig. 4. As it can beseen, by applying the optimization approach, the cost of productsand environmental cost impact are reduced by 13.4% and 53.4%, re-spectively, despite a 14.8% increase that happened in total exergy ef-ficiency. Therefore, improvement in all objectives has been achieved,although the power and water productions have not changed much.

Moreover, it should be noted that according to our model, the envi-ronmental cost impact is directly considered in expenditure that mustbe allocated to the production of the system products. Therefore,the total cost rate of system product (thermoenvironomic objective=thermoeconomic objective+environomic objective) after optimizationwill be 5174 $/h.

Fig. 5 illustrates the amount of exergy destruction of the systemcomponents for the base case design and optimization approach. Ascan be seen, by using Genetic algorithm the value of exergy destruc-tion of each part is decreased. Note that the maximum and minimum

Selected Optimal Point

31.2 31.4 31.6 31.8

efficiency (%)

alues for the objective functions.

27

31

57714995

384

179

0

1000

2000

3000

4000

5000

6000

7000

25

26

27

28

29

30

31

32

33

Base case Optimization

Tot

al p

rodu

cts

cost

rat

e ($

/hr)

Tot

al e

xerg

y ef

fici

ency

(%

)

Total exergy efficiency Environomic objective

Thermoeconomic objective

Fig. 4. Objective functions values for the base case design and optimization.

4,85

7

75,9

52

5,56

9

25,6

28 32,3

24

4,45

0

61,2

09

4,15

7

20,6

16 28,4

32

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

Com CC Tur HRSG MSF

Exe

rgy

dest

ruct

ion

(kw

)

Base case

Optimization

Fig. 5. Exergy destruction of the system for the base case design and optimization.

Table 6Specification of the gas turbine andMSF-BR desalination plant at the base case and finalselected optimum solution.

Parameters Unit Base case Optimization

Power plant

128 S.R. Hosseini et al. / Desalination 285 (2012) 123–130

values of exergy destruction rate are related to combustion chamberand compressor, respectively.

The amount of decision variables, thermoeconomic parametersand specification of gas turbine and desalination plant for base caseand optimal designs are shown in Tables 5 and 6.

As can be seen, the total capital investment of desalination plantreduces by 17% although a slight increase happens in the stage

Table 5Decision variables and economic parameters values at the base case and final selectedoptimum solution of the cogeneration system.

Parameters Unit Base case Optimization

Decision variablesP2/P1 – 11 14.9Tinlet tur. °C 100 1255ηiT % 87 89ηiC % 86 84N – 32 37TN °C 40 41TBT °C 106 118P10 kPa 400 525

Economic parametersCost of electricity with reliability $/kWh 0.0378 0.0344Cost of water with reliability $/m3 1.886 1.655Cost of electricity without reliability $/kWh 0.0363 0.0333Cost of water without reliability $/m3 1.772 1.555Total capital investment of power plant $ 61,573,000 52,985,000Total capital investment of desalination $ 54,123,000 44,878,000Fuel cost of power plant in first year $ 20,402,000 17,784,000Fuel cost of desalination plant in first year $ 89,914,000 71,818,000O and M cost of power plant in first year $ 4,607,600 3,965,000O and M cost of desalination in first year $ 80,337 66,614

Net power Mw 65 64.6Thermal efficiency of power cycle % 29.1 33.2Outlet HRSG flue gas temp. °C 160 °C 160 °CAir rate m3/s 213.2 160.8Ambient air temp. °C 25 25Relative air humidity % 60 60NOx emission kg/h 1.9 3.9CO emission kg/h 223 95.3

DesalinationDesalination capacity m3/day 42,165 40,179Number of tubes in HR section – 2403 1947Number of tubes in HJ section – 1653 1298Brine velocity in the HR condenser tubes m/s 2.37 2.42Brine velocity in the HJ condenser tubes m/s 2.14 2.08Pressure loss in the HR condenser tubes kPa 1146 1324Pressure loss in the HJ condenser tubes kPa 129 119Temperature of the inlet Steam °C 143.6 153.7Total steam consumption kg/s 50.4 42.2Total feed seawater kg/s 1220 1163Total cooling seawater kg/s 589 216Total brine outlet kg/s 732 697Desalination length m 132.2 129.6Desalination height m 5 4.7Performance ratio – 9.7 11Specific area m2/(kg/s) 333 328Pumping power consumption kW h/m3 4.5 4.3

Table A.1Constants for equations (A.1)–(A.3) [22].

Constants 0.3≤φ≤1.0 1.0≤φ≤1.6

0.92≤θ≤2.0 2.0≤θ≤3.2 0.92≤θ≤2.0 2.0≤θ≤3.2

A 2361.7644 2315.7520 916.8261 1246.1778α 0.1157 −0.0493 0.2885 0.3819β −0.9489 −1.1141 0.1456 0.3479λ −1.0976 −1.1807 −3.2771 −2.0365a1 0.0143 0.0106 0.0311 0.0361b1 −0.0553 −0.0450 −0.0780 −0.0850c1 0.0526 0.0482 0.0497 0.0517a2 0.3955 0.5688 0.0254 0.0097b2 −0.4417 −0.5500 0.2602 0.5020c2 0.1410 0.1319 −0.1318 −0.2471a3 0.0052 0.0108 0.0042 0.0170b3 −0.1289 −0.1291 −0.1781 −0.1894c3 0.0827 0.0848 0.0980 0.1037

129S.R. Hosseini et al. / Desalination 285 (2012) 123–130

numbers. Decreasing the capital investment of desalination is becauseof reducing the number of condenser tubes and the specific heattransfer area. On the other hand, by using the optimization approachthe performance ratio and specific electricity consumption of the MSFplant are improved although a slight decrease happens in the desali-nation capacity. Table 6 also indicates that the process of optimizationleads to 14% increases in the thermal power efficiency and 8.2% re-duction in the cost of electricity. Note that, by the optimization ap-proach, the CO generation is decreased inasmuch as the NOx

emission is increased (fold double), because it is more harmful ascan be seen from the cost for its emission.

7. Sensitivity analysis

The purpose of a sensitivity analysis is to study the impacts of im-portant parameters on hybrid plant performance. This analysis whichis performed based on changes in a related parameter as well as someother modeling parameters help us to predict the results while somemodifications are necessary in modeling.

Fig. 6 shows the sensitivity of the Pareto optimal Frontier to the spe-cific fuel cost (which increases by 50%) and specific environment dam-age cost (which increases by 50%) of the system. This figure shows thatthe Pareto Frontier shifts upward since the specific fuel cost increases.Further, at the constant exergy efficiency by increasing the fuel cost,the total cost rate of product increases since the fuel price plays a sig-nificant role in this objective function. As can be seen, by increasingthe specific environment cost, the Pareto Frontier shifts a little upward.It means that in comparison with the fuel cost, the pollution damagecost has a slight influence on the total product cost rate.

8. Conclusion

In this paper, multi-objective optimization for designing a combinedgas turbine andmulti stageflash desalination plantwas investigated. Theproposedmethod covered exergetic, economical, environmental and re-liability aspects of the system design and the component selection. Forthe optimization procedure, evolutionary algorithm (i.e. genetic algo-rithm) was utilized for multi-objective optimization of the cogenerationplant. Moreover, the needs to quantify the environmental impacts leadto the introduction of pollution-related costs in our economic objectivefunction. The thermoeconomic model was developed based on theexergy and economics analysis. The new environmental costing functionwas merged in thermoeconomic objective and a new thermoenviro-nomic function was obtained. By applying genetic algorithm, this objec-tive function was minimized, whereas system exergy efficiency wasmaximized. Furthermore, equipment reliability using the state-spaceand the continuous Markov method was incorporated in optimizationresults to improve the product cost values.

5000

5500

6000

6500

7000

30.6 30.8 31

Tot

al c

ost r

ate

of p

rodu

cts

($/h

r)

Total exergy

c-Fuel=3.7 $/Gjc_Nox=4.98 $/kgc_CO=1.68 $/kg

c-Fuel=c_Nox=c_CO=

Fig. 6. Sensitivity of Pareto optimum solution to th

It was mentioned that multi criteria optimization approach, whichis a general form of single objective optimization, enables us to con-sider various and ever competitive objectives. The optimization re-sults showed that by applying the reliability analysis, the Paretofront approaches to different cost points. It means that the total costof product increases for specified exergy efficiency. So, introductionof reliability leads to the higher product costs due to reduced plantuptime. In addition, the process of optimization leads to 53.4% and13.4% reduction in the environmental cost impact and the cost rateof system product, respectively. Moreover, the total exergy efficiencywas increased by 14.8%, whereas the power and water productionswould not change much (electricity production being less than0.76% and for water production being less than 5.1%). Eventually, sen-sitivity analysis was shown that in comparison with the fuel cost, theenvironment damage cost has a little influence on the total productcost rate.

Appendix A. (Adiabatic flame temperature constants)

Following are the constants of the adiabatic flame temperatureequation:x, y and z are quadratic functions of σ in accordance withthe following equations [24]:

x ¼ a1 þ b1σ þ c1σ2 ðA:1Þ

y ¼ a2 þ b2σ þ c2σ2 ðA:2Þ

z ¼ a3 þ b3σ þ c3σ2: ðA:3Þ

The constants in equations (A.1)–(A.3) are given in Table A.1.

31.2 31.4 31.6 efficiency (%)

5.55 $/Gj4.98 $/kg

1.68 $/kg

c-Fuel=3.7 $/Gjc_Nox=7.47 $/kgc_CO=2.52 $/kg

e specific fuel cost and pollution damage cost.

130 S.R. Hosseini et al. / Desalination 285 (2012) 123–130

References

[1] P. Ahmadi, A. Almasi, M. Shahriyari, I. Dincer, Multi-objective optimization of acombined heat and power (CHP) system for heating purpose in a paper millusing evolutionary algorithm, Energy Research 12 (35) (2011).

[2] Y. Sanjay, O. Singh, B.N. Prasad, Energy and exergy analysis of steam cooled reheatgas–steam combined cycle, Appl. Therm. Eng. 27 (2007) 2779–2790.

[3] Z. Chao, W. Yan, Exergy cost analysis of a coal fired power plant based on struc-tural theory of thermoeconomics, Energy Convers. Manage. 47 (2006) 817–843.

[4] A. Rovira, C. Sánchez, M.Muñoz, M. Valdés, M.D. Durán, Thermoeconomic optimisa-tion of heat recovery steam generators of combined cycle gas turbine power plantsconsidering off-design operation, Energy Convers. Manage. 52 (2011) 1840–1849.

[5] M.H. Khoshgoftar Manesh, M. Amidpour, Multi-objective thermoeconomic opti-mization of coupling MSF desalination with PWR nuclear power plant throughevolutionary algorithms, Desalination 249 (2009) 1332–1344.

[6] J. Uche, L. Serra, A. Valero, Thermoeconomic optimization of a dual-purposepower and desalination plant, Desalination 136 (2001) 147–158.

[7] K. Ansari, H. Sayyaadi, M. Amidpour, A comprehensive approach in optimizationof a dual nuclear power and desalination system, Desalination 269 (2011) 25–34.

[8] H. Sayyaadi, A. Saffari, Thermoeconomic optimization of multi effect distillationdesalination systems, Appl. Energy 87 (2010) 1122–1133.

[9] A. Lazzareto, A. Toffolo, Energy, economy and environment as objectives in multi-criterion optimization of thermal systems design, Energy 29 (2004) 1139–1157.

[10] Q.L. Chen, et al., Environmental-exergoeconomic strategies for modelling and op-timization of energy systems, Comput. Aided Chem. Eng. 15 (2003) 754–759.

[11] C.A. Frangopoulos, Introduction to environomics, Symposium on Thermodynam-ics and the Design, Analysis and Improvement of Energy Systems, AES, 25, ASMEPress, 1991, pp. 49–54.

[12] P. Ahmadi, I. Dincer, Thermodynamic and exergoenvironmental analyses, andmulti-objective optimization of a gas turbine power plant, Appl. Therm. Eng. 31(2011) 2529–2540.

[13] A. Molyneaux, G. Leyland, D. Favrat, Environomic multi-objective optimisation ofa district heating network considering centralized and decentralized heat pumps,Energy 35 (2010) 751–758.

[14] A.M. El-Nashar, Optimal design of a cogeneration plant for power and desalinationtaking equipment reliability into consideration, Desalination 229 (2008) 21–32.

[15] S.R. Hosseini, M. Amidpour, A. Behbahaninia, Thermoeconomic analysis with reli-ability consideration of a combined power and multi stage flash desalinationplant, Desalination 278 (2011) 424–433.

[16] G. Koeppel, G. Andersson, Reliability modelling of multi-carrier energy systems,Energy 34 (2008) 235–244.

[17] G. Koeppel, G. Andersson, The influence of combined power, gas and thermal net-works on the reliability of supply, Sixth World Energy System Conference, Torino,Italy, July 10–12 2006.

[18] M.R. Haghifam, M. Manbachi, Reliability and availability modeling of combinedheat and power (CHP) systems, Electr. Power Energy Syst 33 (2010) 385–393.

[19] T.F. Hassett, D.L. Dietrich, F. Szidarovszky, Time-varying failure rates in the avail-ability and reliability analysis of repairable systems, IEEE Trans. Reliab. 44 (1)(Mar. 1995) 155–160.

[20] C.A. Frangopoulos, G.G. Dimopoulos, Effect of reliability considerations on the optimalsynthesis, design and operation of a cogeneration system, Energy 29 (2004) 309–329.

[21] TR-100281 Technical Assessment Guide (TAGTM), 3, Electric Power Research In-stitute, California, 1991 (Revision 6).

[22] A.H. Lefebvre, Gas Turbine Combustion, Taylor & Francis, Philadelphia, 1999.[23] N.K. Rizk, H.C. Mongia, Semianalytical correlations for NOx, CO and UHC emis-

sions, Eng. Gas Turbines Power 115 (1993) 9–612.[24] Ö.L. Gülder, Flame temperature estimation of conventional and future jet fuels,

Eng. Gas Turbines Power 108 (1986) 80–376.[25] J.H. Holland, Adaptation in Natural and Artificial Systems, The University of

Michigan Press, Michigan, 1975.[26] H. Modares, M.B. NaghibiSistani, Solving nonlinear optimal control problems

using a hybrid IPSO–SQP algorithm, Eng. Appl. Artif. Intel. 24 (2011) 476–484.[27] N. Nedjah, L. dos Santos Coelho, L. deMacedo deMourelle, Multi- Objective Swarm

Intelligent Systems, Springer, Chennia, 2010.[28] K. Christoph, F. Cziesla, G. Tsatsaronis, Optimization of combined cycle power

plants using evolutionary algorithms, Chem. Eng. Process. 46 (2007) 1151–1159.[29] T. Bäck, D. Fogel, Z. Michalewicz, Evolutionary Computation 1 — Basic Algorithms

and Operators, Evolutionary Computation 2 — Advanced Algorithms and Opera-tors, Institute of physics publishing, Bristol, Philadelphia, 2000.

[30] F. Rothlauf, Representations for Genetic and Evolutionary Algorithms, Springer,Berlin, 2006.

[31] C.A. Coello, G.B. Lamont, D.A. Van Veldhuizen, Evolutionary Algorithms for Solv-ing Multi-Objective Problems, Springer, New York, 2007.

[32] M. Pelikan, H. Bayesian, Optimization Algorithm Toward a New Generation ofEvolutionary Algorithms, Springer, Berlin, 2005.

[33] A. Frangopoulos, D.E. Keramioti, Multi-criteria evaluation of energy systems withsustainability considerations, Entropy 12 (2010) 1006–1020.


Recommended