Energy 28 (2003) 457–477www.elsevier.com/locate/energy

Cost analysis of energy conversion systems via a novelresource-based quantifier

Enrico Sciubba∗

Dept. of Mechanical and Aeronautical Engineering, University of Roma 1 “La Sapienza”y, Via Eudossiana 1800184 Roma, Italy

Received 5 October 2001

Abstract

The paper presents a new formalism for the costing of production chains, with special emphasis onenergy conversion systems. From a mathematical point of view, this method can be described as a standardLeontiev-type input-output technique, in the formulation commonly adopted by most costing theories,including Thermoeconomics. Any complex production chain can be decomposed into modules, to eachone of which mass and energy balances are applied. The resulting flow diagram is then examined froman exergetic point of view, and a cost analysis is performed. The costing paradigm is the novel featurehere: rather than monetary units, a resource-based quantifier, called “extended exergy”, is employed. It isargued that both labour and financial costs can be properly linked to an equivalent resource consumptionthrough a back-to-resource accounting procedure that expresses the total exergy consumption required to“generate” one man-hour of work or one monetary unit of currency circulation. Environmental remediationcosts are similarly taken into account by computing the equivalent cumulative exergy expenditures requiredto achieve zero impact. It is argued, and discussed on the basis of an example of application to a cogener-ation plant, that the new technique, called Extended Exergy Accounting (EEA), is a substantial improvementwith respect to current engineering economic techniques, including Thermoeconomics. It is shown thatEEA calculates the real, resource-based “value” of a commodity (which is not necessarily equal to itsmonetary cost) thus enabling Analysts and Energy Planners to perform a more complete and meaningfulassessment of an Engineering Complex System. The decisive advantage of EEA consists in its being entirelyand uniformly resource-based: in this respect, it owes some of its structural formalism both to the economictheory of production of commodities, which it extends by accounting for the unavoidable energy dissipationin the productive chain, and to resource-oriented economics. It must be acknowledged as well that EEAfollows a path originally proposed by Szargut in his “Cumulative Exergy Consumption” method, which itextends by providing a rational and uniform treatment for all non-externalities. 2003 Elsevier Science Ltd. All rights reserved.

∗ Tel.: +39 064 4458 5244.E-mail address: enrico.sciubba@uniroma1.it (E. Sciubba).

0360-5442/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved.doi:10.1016/S0360-5442(02)00096-8

458 E. Sciubba / Energy 28 (2003) 457–477

1. Introduction

For all practical and theoretical modelling and simulation purposes, it is convenient to considerproduction processes (and even more so, energy conversion processes) not as independent func-tional units, but rather as “objects” connected to each other and constituting a very large complexsystem (VLCS). Not only does this allow a correct treatment of the VLCS, but it also yieldssurprisingly practical results from the application point of view. Depending on the level at whichthe available data can be collected, one can disaggregate the VLCS and independently analyseits smaller sub-units, sub-sub-units and so on, down to the single component. The same processis possible in reverse: given a simple system, we can join (aggregate) it with other systems it isdirectly or indirectly connected to by extending the control volume to encompass a certain numberof mass- and energy exchanging systems. Both of these procedures are facilitated if we considereach component as an “object” endowed with its own physical, material and economic character-istics: aggregation requires a proper “assembly” of the single objects into a superstructure that

Nomenclature

cex: specific exergetic cost, J/Jcw: monetary cost of work, $/Je: specific exergy of stream, J/kgE: total exergy flow, Wee: specific extended exergy, J/kgh: specific total enthalpy, J/kgI: exergy input flow, WKCap: monetary equivalent of exergy, $/MJKLab: exergetic equivalent of Labour, MJ/(work hour)m: mass flow rate, kg/sn: number of individualsO: exergy flow output, WPF: plant factor [(equivalent operating hours per year)/8760]R: Capital Recovery Factor (Sect. 7)R: Gas constant, kJ/(kg K)s: specific entropy, J/(kg °K)T: Temperature, °Kw: specific work, Jβ: compression ratio�: exergetic conversion efficiencyη: energetic conversion efficiencyµ: chemical potential, J/kgζ: environmental penalty factor (Sect. 7.2)

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reproduces the real complex System, while disaggregation conversely requires a “disassembly”of the superstructure into single objects each one of which reproduces a real component.

The importance of such a structured representation of a VLCS can be fully appreciated if weconsider the effects of an industrial structure on the environment. In this respect, as correctly notedin [1], it is not convenient to compare different production lines that adopt the same technology: itis more meaningful to raise the level of aggregation and compare the resource efficiency of differ-ent technological lines that can substitute for each other. This implies the study of energy andmaterial flow over the entire “cradle-to-grave” path of each product, starting from the extractionsites of the respective resources and ending at the site (and time) of the final discharge of theby-products into the environment.

As it shall become apparent in the subsequent Sections, our objects-components actually interactwith the environment in more than one way. First, of course, they may directly exchange matter-and energy fluxes with their immediate surroundings: such fluxes are accounted for in the mass-and energy balances, and included explicitly in the environmental analysis relative to each compo-nent. But, there is a more fundamental interaction that goes unaccounted for in all current analysismethods: each object-component embodies, in a very real sense, all the material and energy fluxesthat went into its production. In fact, it is possible to define a “ resource embodiment indicator”that provides a quantitative measure of this Cumulative Exergy Content [2] of each device. Sucha cradle-to-grave approach is not new: Embodied Energy Analysis [3,4], Life-Cycle Analysis,Emergy Analysis [5,6], Exergy Life-Cycle Analysis [7] have already adopted time-weighted ortime-integrated indicators. The novelty in EEA resides in the definition of the indicator.

The Second Law of Thermodynamics shows that the degree of irreversibility of any processdepends on its own intrinsic “energy degradation rate” and not only on the ratio between theenergetic intensities of the output and input flows [8]. Today, there is universal agreement on thefact that a “conversion efficiency” based solely on First Law considerations is misleading, becausethe scale of energy quality can be quantified only by an entropy analysis “Exergy Analysis”[9,8,10], a 1980 revival of a classical method (“Availability Analysis” ) proposed by Gibbs andapplied by Keenan, has been accepted by the Energy Conversion System community and allcurrent design standards make direct or indirect use of exergetic concepts in the search for an“optimal” configuration. The same method has been successfully applied to “Complex Systems” ,like industrial settlements [10,9,2], complete industrial sectors [11,12,13,2], and even entireNations [11,14,13,15]: results invariably show that introducing “Second Law” considerations inthe analysis generates more precise and useful information for the Design Engineer and for theEnergy Planner. When, most recently, resource scarcity and environmental issues have madeapparent that some “ limits to growth” indeed exist, Exergy Analysis has also been proposed[16,17,7,10,18,19] as an auxiliary tool for Energy Managers and Policymakers. When associatedwith monetary cost-analysis, Exergy Analysis becomes “Thermoeconomics” [8,20,21,10,22,23],where efficiencies are calculated via an exergy analysis and “non-energetic expenditures”(financial, labour and environmental remediation costs) are expressed as functions of the technical-and thermodynamic parameters of the process under consideration: the optimisation consists ofdetermining the design point and the operative schedule [24] that minimise the overall (monetary)cost, under a proper set of financial, normative, environmental and technical constraints. Thoughnot new (the first publication explicitly referring to it, [25], appeared more than 40 years ago),Thermoeconomics was recently “ rediscovered” , thanks to the formal and substantial systematis-

460 E. Sciubba / Energy 28 (2003) 457–477

ation operated on it first by Gaggioli [10] and then by Valero [22,23] and Tsatsaronis [8]. Therm-oeconomics is much more than just an “Engineering Optimisation Method” : as clearly explainedin some of the works of Valero [15,22], it may be thought of a general well-structured frameworkin which all balances (mass, energy, exergy, capital, etc.) can be unified by a single formalism.

If one examines anthropic activities from a broader point of view, it appears that everythingwe produce (even crops) “consumes” exergy, so that exergy destruction, as correctly remarkedby Naredo and Valero [15] represents the driving force for all life forms: in fact, Extended ExergyAccounting (“EEA” ) was designed to exploit this intrinsic and direct correlation between exergyand economic values. This new method aims to the development of a formally complete theoryof “value” based on an exergetic- metric that can complement and integrate our present monetaryvalue-based estimates, so that, for example, a general costing procedure in which kJ/kg or kJ/kWare consistently equivalent to /kg and /kW respectively becomes viable. As clearly implied bythe context, the “value” we discuss here is not to be intended in the current economic sense(“consumer preference scale” ), but in its actual physical meaning of “amount of resources thatwere used in the commodity formation process” . It is worth mentioning here that, in a strikingsimilarity to biology, where different ecological niches have different exergy cascades, this corre-spondence between “exergetic value” and “monetary cost” is not valid in an absolute sense, butdepends on the boundary conditions imposed by the specific Societal niche we are considering(our “System” ).

EEA may be considered as a synthesis of some of the pre-existing theories and procedures of“Engineering Cost Analysis” , because its main features combine indeed those of some of theprevious methods:

� The time span of an EEA assessment covers the entire life of the plant, exactly like in Life-Cycle Analysis;

� In EEA, all of the inputs that contribute to the formation of a product are accounted for on anexergetic basis. The “zero-level” input is a flux of raw materials, like in Cumulative ExergyAnalysis [2];

� EEA assigns labour an intrinsic value depending on the local exergy resource flow, with amethod in principle very similar to that proposed by Emergy Analysis [5,6];

� EEA, like Thermoeconomics [8,23], uses “exergy cost balances” to quantify the “ resource-based value” of every flow of matter and energy that interacts with the System under consider-ation.

The attribute “Extended” signifies the additional and explicit inclusion in the exergetic flow-sheets of the terms corresponding to non-energetic costs, including labour and environmentalremediation expenditures. The word “Accounting” is a reminder that exergy does not satisfy abalance proper: indeed, it clearly relates the idea that to produce any output, some resources haveto be irrevocably consumed [15].

A point where EEA can make an impact is the definition of the criterion under which an optimalsolution (a process structure, or a set of operational parameters) is to be searched for. In thissense, the extended exergy content of a commodity is a synthetic and very powerful indicatorthat undoubtedly provides Designers and Planners with more insight than previous methods,because its objective function is expressed homogeneously in terms of prime resources.

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2. Methodology

Consider the production of a commodity (good or service) by means of a Complex Systemoperating over a considerable time span. For simplicity, we can adopt a continuous approach, andconsider a generic interval of time (year, second, etc.) as the unit period to which our analysisapplies.

EEA is based on two fundamental assumptions:

1. All activities (including non-anthropic ones) are aggregated production processes that transformflows of a certain number of “ inputs” with respect to space, time and properties by means ofadditional “ inputs” consisting of other materials, energy, labour and capital.

2. Each activity can be represented by its transfer function, i.e., a relation between output andinput flows. This transfer function, denoted � in the following, depends on the physical stateof the Production System.

3. The cumulative exergy content of any product (a physical commodity or a non-material service)is equal to the sum of the raw exergy of the original constituents plus a properly weightedsum of all the additional exergetic inputs into the process.

4. Non-energetic externalities also admit of an exergetic formulation, in the sense that they havean exergetic equivalent that can be computed from proper (System + Environment) balances.

Point 3 is just a rephrasing of Szargut’s “Cumulative Exergy Content” [2]. Point 4 is the originalcontribution of EEA.

2.1. Calculation of the extended exergy content

Given a certain production System P (Fig. 1), and assuming for the moment that it generatesone single commodity, we define the Extended Exergy Content of this product as the sum of:

Fig. 1. The representation of production factors as a process flow diagram.

462 E. Sciubba / Energy 28 (2003) 457–477

1. The exergy EMat( = m∗emat) of material inputs, i.e., the raw material exergy influx;The exergiesEQ and EW of heat and work input flows, i.e., the non-material exergy influx;

2. The equivalent exergy ECap of the monetary flows contributing to product formation;3. The equivalent exergy ELab of the labour input that constitutes the (human) work flow contribu-

ting to product formation;4. The equivalent exergy EEnv of the environmental remediation expenses (material, exergy, labour

and capital) required for a zero environmental impact.

These flow quantities, all expressed in kW, are defined on the basis of their specific equivalentsas follows:

1. The exergy of a stream of matter at a certain thermodynamic state “1” is

e1 � h1�h0�T0(s1�s0) � �i(mici�m0c0) [kJ /kg] (1)

This is a state property once the reference state “0” has been selected, and as such its valueis uniquely determined by the state parameters. Notice that the quantity defined by Eq. (1)represents only the mechanical, thermal and chemical exergy components of a system, becausethese are the only ones considered in this paper, and neglects other contributions (molecular,nuclear, magnetic, etc.) that may become important in specific cases.

2. Physical exergy is additive, and its content in a stream can be augmented or decreased by anycombination of work-, heat- and chemical interactions of that stream with other systems. Thus,in complete analogy with Szargut’s “Cumulative Exergetic Content” , for a certain commodityEEA calculates the sum of all the contributions to the different streams that were used in theproduction (conversion) process, starting with the original exergetic values of the mineral oresthat constitute the initial inputs.

3. The chemical portion of the “ raw” exergy EMat of a mineral ore is either equal to zero (if theore is at the average composition of the Earth’s crust) or attains a value exactly computableon the basis of the ore’s chemical composition, its physical state and the Gibbs energy offormation of its constituents. This requires by necessity the definition of a “universally validreference state” for the Earth’s crust. There is no final agreement on this issue, but the methodrecently proposed by Valero et al. [25] is likely to provide a solution to this problem.

4. The sum of the fluxes of “non-energetic externalities” (Labour and Capital) used in the con-struction and operation of the plant in which the product is generated may be considered as aflow of invested exergy, ELab + ECap, that generates an added value when it “fl ows” into theproduced commodity. The expression “ invested exergy” was coined by E. Yantowsky [26].Provided the production chain is structurally and quantitatively known, the invested exergydepends on the characteristics of both the Process under consideration and the Society in whichit is immersed.

5. If an effluent stream of a generic process is required to have a zero impact on the environment,the stream must be brought to a state of thermodynamic equilibrium with the reference statebefore being discharged into the environment. The minimum amount of exergy that must beused to perform this task by means of ideal transformations is a function of the exergy of thestream measured by Eq. (1) [27]. That is, the potential environmental impact of an effluent ismeasured by EEnv, which represents the cumulative amount of exergetic resources that must

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be consumed to attain an ideal, zero-impact disposal of both the effluent itself and the equip-ment that handles it. If the analysis is to be conducted on the basis of the allowable emissionlimits, then, as discussed in [27], the numerical value of EEnv will be different, reflecting boththe lower resource consumption in the effluent treatment operations and the higher load imposedon the environment to nullify the exergy of effluent.

2.2. Exergy algebra for efficiency and cost calculations

Let us disaggregate (Fig. 2) the inputs and outputs of the process P: the inputs consist in generalof a stream of raw materials (I1), exergy supply (I2), human labour (I3) and capital (I4), while theoutputs are the desired product (O1), some low-quality energy rejection to the environment (O2),a by-product (O3), and some waste (O4). The formalism adopted here can easily accommodateseveral types of raw materials and several types of different energy inputs or outputs. Assume itis indeed possible to attribute an exergetic value to each one of the input- and output fluxesaccording to the procedures discussed in Section 3 and 5 here below. The internal structure ofthe process can be used by the designer to compute the transfer function of P, i.e., the (matricial)expression � that links the outputs with the inputs [2], and that in the representation of Fig.1 becomes:

EO � �EI⇒

EO1

EO2

EO3

EO4

� �|EI1

EI2

EI3| (2)

Due to the unavoidable presence of the physical exergy destruction Eλ, the algebraic sum ofthe inputs and the outputs (EO–EI) may assume only negative values. The conversion efficiencyof P is defined as the ratio of the useful output to the sum of the inputs that concurred to produce it:

Fig. 2. A detailed Extended Exergy process flow diagram.

464 E. Sciubba / Energy 28 (2003) 457–477

eP �EO1

�Ein

(3)

The exergetic cost of the output is defined as the amount of input required (“used” ) to generatethe output, and is the reciprocal of the conversion efficiency:

cP ��Ein

EO1

(4)

If a portion of the exergy discarded in the form of low-quality energy, say αO2, and of wastematerials, say βO4, are recycled as inputs of some other process belonging to the productivestructure of which P is part, the value of the overall process efficiency must reflect this increased“usefulness” of the waste streams:

e �EO1 � EαO2 � EβO4

�Ein

(5)

And the exergetic cost of the output can now be correspondingly computed1

c(O1+αO2+βO3) ��Ein

EO1 � EαO2 � EβO3

(6)

Consider now a chain of technological processes that represents all of the individual productionsteps in the fabrication of some generic product O6 (Fig. 4): the inputs can be classified asMaterials and Feedstocks (I1, I4), Labour (I3, I7, I10), Energy in various forms (I2, I5 I9), and inputsfrom previous fabrication steps (I5, I8). The corresponding outputs are Waste Materials (O2, O5),Waste Energy in various forms (O9), and Recyclable By-products (O3). The primary conversionefficiencies of the single processes are:

eP1�

eO1� eO2

�3

j � 1

eIj

(7)

1 If, as it is sometimes the case in complex production cycles, a portion O5 = wO3 is recycled internally to P (feedback, Fig. 3),then the overall efficiency of the combined process (P + Pr) is given by:

e(P � Pr) � eP

1 �1 � ePePrw

1 � ePr

w

1 � ePePrw(5a)

and the corresponding cost for the entire process (P + Pr) is:

c(P � Pr) �1 � ePrew

eP�1 �1 � ePePrw

1 � ePr� (5b)

where w = O5 /O3 is the energetic recycle ratio and ePr is the exergetic efficiency of the recycling process Pr.

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Fig. 3. A process with feedback.

Fig. 4. Extended exergy diagram of a production chain.

eP2�

eO3� eO4

eO1� eI4 � eI7

(8)

eP3�

eO5� eO6

� eO9

eO4� eI6 � eI10

(9)

and the overall efficiency of the conversion from the resource base to the final product is:

e(P1+P2+P3) �eO6

�10

j � 1

eIj

(j � 5,8) (10)

The above equations express the exergetic conversion efficiency and the corresponding exerg-etic costs of a given technological chain, once its structure and the transfer function � of eachfabrication step are known. Notice that these expressions imply that the extended exergetic

466 E. Sciubba / Energy 28 (2003) 457–477

efficiency is not associative and that the extended exergetic cost is not additive: in other words,ηP1 + P2 + P3 is different from ηP1∗ηP2∗ηP3 and cP1 + P2 + P3 is not given by cP1∗cP2∗cP3. Thisis an important preliminary result [28], and leads to the consequence (also derived from Thermoe-conomics, but on a different basis, [2,22]) that the most energy-intensive steps in a technologicalchain should be given priority in the optimisation procedure.

An EEA procedure can be easily nested, i.e., applied at different levels of aggregation in aproductive structure [11,29], because the results, being all expressed in homogeneous units, canbe transferred from one aggregation level to another without adjustment or re-normalisation.

3. Choice of the control volume and of the relevant time window

In EEA, the choice of CV is dictated by two orders of considerations (see also [28]):

1. The CV must include a portion of the environment large enough to allow for the treated efflu-ents to exit the CV boundary in a state of zero physical exergy. This portion has been called“ immediate surroundings” [30];

2. If the inputs include unrefined fossil fuels or minerals at mouth-of-mine conditions, the CVmust include the portion of the environment whence the original materials were extracted, sothat their raw exergy may be computed. As a more practical alternative, one can directly assignthe extended exergetic value for every input, estimating this “ initial guess” on the basis ofan approximate knowledge of the relevant extraction, pre-treatment and transportation process(Fig. 5).

As in LCA, the time window over which the calculation of the exergy flow diagrams is perfor-

Fig. 5. The properly expanded control volume for EEA analysis.

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med affects the outcome of an EEA analysis (Fig. 6). There are different time scales that mustbe considered when assessing this relevant time interval, and care should be exercised in alwayschoosing the longest meaningful timescale involved. In most problems, the “biodegradability”timescale is the longest relevant one: current environmental regulations conservatively prescribea certain time interval within which the effects of the effluents must be completely buffered bythe immediate surroundings. Extending this time interval decreases the clean-up costs, but leadsto a substantial departure from the “zero-impact” assumption; on the other hand, shortening itexcessively imposes a useless penalty on the exergetic balance of the process, because it fails toexploit the buffering capacity of the biosphere. No general rule is apparent for a deterministiccompromise, and decisions have to be made on a case-specific basis (see also [28]).

Any variation of the invested exergetic “content” of mineral ores or fossil fuels can beaccounted for by standard accounting methods: for instance, possible changes in the mining con-ditions due to an increased local relative scarcity of the material may be easily included in anEEA analysis.

4. The exergetic content of a stream

In this Section, a detailed account is given of the calculation of the exergetic content of individ-ual streams according to the EEA paradigm.

4.1. Material and energy flows

A material stream is assigned a total (or cumulative) exergetic content defined as the sum ofits “ raw state exergy” and of all the net exergetic inputs received, directly or indirectly, in theextraction, preparation, transportation, pre-treatment and manufacturing processes. The first contri-bution, the raw state exergy, is easily computed (as specified in Section 3.1, point 3) in the case

Fig. 6. The time span of an EEA analysis.

468 E. Sciubba / Energy 28 (2003) 457–477

of mineral ores or fossil fuels. In the case of crops, and in general of land products, the rawexergy is the sum of the incident solar exergy augmented of all the contributions due to fertilisers,artificial irrigation, etc.: usually, the solar contribution by far exceeds the remaining inputs thatmay thus be often neglected. The second part of the exergetic content may assume differentnumerical values for different production chains: for instance, the cumulative exergetic value ofback-pressure steam is different from that of the same steam, co-generated in a gas turbine plant.

An energy flux (mechanical power, electrical energy, heat transferred under whatever mode,chemical or nuclear energy, etc.), is directly assigned its corresponding exergy value. For consist-ency, all exergies must be calculated with respect to the same set of reference conditions.

4.2. Labour and human services

The capability of attaching a properly computed exergetic value to a labour input (taken hereto include all service-related, blue- and white collar human activities) is perhaps the most relevantnovelty of EEA. Currently, all practical applications of engineering cost accounting, includingThermoeconomics, account for labour on a purely monetary basis: but very reasonable alternativeapproaches have been formulated. We consider particularly important Odum’s “emergeticapproach” [5], in which a “solar equivalent” value for labour is computed on the basis of thetotal time-averaged embodied energy content of the “human life” in the particular area where aworker happens to live and work. A fundamental reason for including the purely exergetic contentof labour even in energy-intensive industrial processes, where the exergetic bodily output rate(what we call “physical work” in layman terms) is, per se, numerically negligible with respectto the much higher power of the machines and processes that this work commands, is that labourconstitutes a substantial controlling factor on the overall productive process: it is, so to say, asmall but irreplaceable production factor. When labour is properly accounted for in the exergeticanalysis its contribution may so distort the objective function that new solutions emerge.

In EEA, labour -and in general human services- in each portion of a Society is assigned anexergetic value computed as the total (yearly averaged) exergetic resource input into that portiondivided by the number of working hours “generated” therein2:

eeL,Sector �Ein,Sector

nworkhours,Sector

[J / (work � hours∗year)] (11)

4.3. Environmental impact

Let us consider now how EEA addresses the issue of environmental impact. Refer to Fig. 7ashowing a process P, and assume that its only effluent is a stream which contains hot chemicals,some of which not at their standard environmental concentration. To achieve a zero environmentalimpact, these chemicals must be brought to both thermal and chemical equilibrium with the sur-

2 Notice that this definition of equivalent Labour exergy can be directly recast in terms of the postulated equivalence betweenmonetary circulation and input exergy flow described in Section 5.4. Therefore, only one of the two assumptions is logically necessary,while the second follows from it. We prefer to consider the monetary circulation/exergy input as the fundamental assumption, so theEq. (11) follows from Eq. 12

469E. Sciubba / Energy 28 (2003) 457–477

Fig. 7a O2 not at reference conditions. Fig. 7b Treatment of O2: O2,1, O2,2 and O2,3 are at their respective referenceconditions. Fig. 7c Only a portion of the clean-up is performed by man-made treatment: the remaining takes placespontaneously by bio-degradation in the immediate surroundings.

470 E. Sciubba / Energy 28 (2003) 457–477

roundings: thus, the real (exergetic) cost of the zero-impact would exactly correspond to theextended exergy ideally required to cool the effluent to T0 and break it up into its constituentssuch that each one of them is in equilibrium conditions with the surroundings. A possible represen-tation of such an effluent treating process is shown in Fig. 7b: the additional process Pt requiresa work or/and heat input, possibly some auxiliary materials, labour and invested exergy, so thatits output will have a zero physical exergy. These additional exergetic expenditures required byPt must be charged to the effluent O2, whose extended exergy will now be higher than its originalone. Therefore, the overall conversion efficiency of the joint process (P + Pt) is decreased. Theremay be effluents for which some of the chemical decomposition reactions take place “spon-taneously” , in a short time and in the immediate surroundings of the emitting source: in suchcases (Fig. 7c) the reactions must draw on some exergy source within the environment (a certainparticular chemical catalyst, oxygen, water, solar radiation, or even a biological system), and thisexergy flow must be accounted for as well [31,27].

EEA thus allows for a consistent incorporation of the effects of effluent treatment in theextended exergetic balance of a process, and provides an estimate of the minimum exergeticresource consumption necessary to achieve zero-impact. Notice that, if an acceptable level ofpollutant is specified, then the minimum exergetic expenditure will be proportional to the differ-ence between the values of the physical exergy of the effluent stream between the point of itsrelease and the “ regulated” state point. Thus, we recover one of the desirable features of presentenvironmental cost estimates and at the same time effectively avoid the considerable effortrequired to determine what the “ tolerable environmental impact limit” for a certain pollutantwould be.

4.4. Capital

When it comes to including capital and in general financial costs into the balance sheet of anEnergy Conversion System, we employ money and its time-value as the sole quantifier for goods,services, resources, etc. This paradigm of money as a basic metric for energy-related activities isso deeply rooted in our culture that all industrial accounting statements are expressed in monetaryprice per unit of product rather than per energetic (not to mention exergetic) content. The verystructure in which we live and function today requires the use of the “price-tag” concept in everyday’s economic activities and on a world-wide scale. What EEA advocates is that this tag be alsocalculated on the basis of the extended exergetic content, EEC, of a good or service. It is intuitivethat there ought to be a numerical relation between the EEC and the price of a product: EEApostulates that the conversion factor KCap is the ratio of a proper measure of the monetary circu-lation to the global exergetic input, because just like the monetary flux is the “driving agent” ofsocietal development in current economic theory, so the exergy flow is its physical “driving force” .The choice of the indicator for the “monetary flux” is of course somewhat arbitrary: we havechosen the absolute measure of the global monetary circulation (“M2” ), which for each countryis computed and published by the Central Bank.

KCap �monetary circulationtotal exergetic input

�M2

Ein

(12)

Notice that a more rational (albeit more complex) procedure has been proposed for the calcu-

471E. Sciubba / Energy 28 (2003) 457–477

lation of the capital-equivalent exergy [32]: that of defining a sort of a “basket” of commodities(similarly to what is done to determine the inflation rate), and to assume for KCap the weighted

average of the individual conversion factors: KCap = Σi�ai

pi

eei�, where pi are the prices of the single

commodities and ai is the “weight” of the i-th commodity in that basket. For simplicity, we willkeep referring to Eq. (12) in the following.

When processes are analysed, it is the exergetic equivalent of the financial expenditures thatmust be inserted in the balance as an input, and the same applies to the revenues. It is noteworthythat for most state-of-the-art processes the substitution of the equivalent exergetic value for themonetary price causes a significant discrepancy in the exergy balance: the reason is clearly thecurrent over- or underestimating of the real extended exergetic content of materials, feed stocks,labour and energy flows. For the correct estimate of resource consumption, it is necessary thatthe economic and the exergetic value become locally consistent in the long run, allowing the twovalue scales to reach a sort of local fixed parity. The very same definition of the exergy-equivalentimplies though that different countries may have different KCap, due to their different productiveand economic structures and lifestyles, and that for a country KCap may vary over time, due toits evolving social structure. Notice that EEA does not imply the re-definition of what is presentlycalled the “economic theory of value” : while it is true that the extended exergy content of acommodity constitutes a powerful indicator that ought to be included in any decision-support tool,there are many consumer-choice factors it cannot capture. In general, these include all consumerpreference indexes based on aesthetic, artistic, etc. reasons.

5. Two practical applications of the EEA method

5.1. Extended exergy accounting of a process compressor

Consider the process air compressor shown in Fig. 8 for which all relevant design and operationdata are given in Table 1. According to Thermoeconomics, the exergetic cost of the compressedair is:

Fig. 8. The flow diagrams for a process compressor according to thermoeconomics and EEA.

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Table 1Process parameters (with reference to Fig. 7)

Air inlet temperature, T1 300°K Capital recovery factor, R5%,20 0.08Air inlet pressure, p1 1 bar Equipment cost, installed [5], c11 5.15 106 $Air outlet pressure, p2 12 bar Cost of electrical energy, cw 19.84 10�6 $/kJMass flow rate, m 340 kg/s Plant book life 20 yearsCompressor polytropic efficiency ηpc 0.86 Fuel price 0.2 $/kgInlet air exergy, e1 0 kJ/kg Labour costs (ee equivalent), KLab 235.5 MJ/(man∗h)Outlet air exergy, e2 155 kJ/kg Capital costs (ee equivalent), KCap 0.055 $/MJ

c2 �cww � CFinancial � CLab

e2

� 30.95∗10�6 /kJ (about 0.11 /kWh) (13)

While an EEA provides:

ee2 �ee1m1 � EEw � EELab � EECap��Eirr

m2

� 1132 kJ /kg (14)

The comparison must be made on a life-cycle basis, but if we assume a constant Capital Exerg-etic Factor KCap and equally constant interest rate, tax levels etc., a “steady-state” comparison isindicative as well. Converting the Extended Exergy given by Eq. (14) back into its “equivalent”monetary value, we obtain:

c2,EEA,tot,$ � ee2KCap � 0.0656/kg (about 0.223 /kWh) (15)

Thus, in the first approximation employed here, the ratio of the resource-equivalent monetaryvalue to the thermoeconomic monetary cost is about 2: this suggests that the resource consumptionis strongly underestimated (“underpriced” ) by current analysis methods. This example leads to aninteresting consideration: since the equipment cost parameters used in Eq. (13) are taken fromgeneral (international) published data, while the KLab in the same equation and the KCap used inEqs. (14) and (15) are computed for Italy in 1998, the comparison drawn here is of limited valuebecause it has no general validity. But this is exactly one of the main points of the EEA analysis:(extended) exergetic costs represent “equivalent amounts of resource” used in the productionprocess, and are therefore intrinsically local in space and time. This constitutes a merit, and nota limit, of the present theory, because in fact the indications provided by an EEA analysis aremore detailed than those drawn with monetary methods, and can be easily generalised by a properextension of the control volume (Figs. 5 and 7c).

5.2. EEA analysis of a gas-turbine based cogeneration process

For the gas turbine-based cogeneration system shown in Fig. 9, the turbine inlet temperature(T4, “TIT” in the following) and the compressor delivery pressure (p2) were varied stepwise, andfor each (TIT,p2) pair the extended exergetic cost of the process was calculated. Design and costdata are reported in Table 2, and the calculation proceeds long the following steps:

1. Exergetic costs of all equipment are computed by first calculating their monetary cost by proper

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Fig. 9. Simplified process scheme of a GT-based cogeneration plant.

Table 2Process Parameters (with reference to Fig. 8)

Air inlet temperature, T1 300°K Boiler water inlet temperature, T11 350°KAir inlet pressure, p1 1 bar Boiler efficiency, ηb 95%Compressor polytropic efficiency, ηpc 0.85 Gas temperature at DeSox inlet, T12 450°KFuel lower heating value, LHV 41000kJ/kg Min. allowable stack gas temp., T13 400°KPressure loss in the combustor, �pcc 2%p2 Plant book life 20 yearsTurbine polytropic efficiency, ηpt 0.87 Fuel price 0.2 $/kgTurbine discharge pressure, p5 1.1 bar Labour costs (ee equivalent), KLab 235.5 MJ/(man∗h)Steam temperature, T10 420°K Capital costs (ee equivalent), KCap 0.055 $/ MJNet electrical power output P 110 MW

costing tables [8], and then by converting the capital- into exergetic cost via the exergetic costfactor KCap = 0.058 /MJ. Operating costs were also adapted from [8]. A fixed-load operationthroughout the year was assumed, with a Plant Factor PF = 0.6 (corresponding to 5250hours/year).

2. Labour costs are computed by converting industrial work-hours estimates into equivalent exerg-etic values via the exergetic cost factor KLab [235.5 MJ/(work hour) for Italy in 1998].

3. Environmental costs are computed on the basis of an Extended Exergy Accounting of the stackgas treatment plant (in this case, only the Desulphuration and Denitrification unit wasconsidered). EEEnv has then expressed as ζEgas, where Egas is the stack gas physical exergy(including its chemical portion) and ζ is a “penalty factor” computed by the same methodemployed for calculating the other “costs” : the monetary installation and operation costs of theDesulphurisation unit have been calculated, and the result has then been expressed in terms ofthe exergy of the gas to maintain congruency with the EEA theory. It turns out that the additionof the gas treatment corresponds to a monetary cost ranging from 0.0013 to 0.0016 /kWh, inline with current industrial estimates: this correspondence is important, because it has not been“ forced” in any way (the monetary cost figure is converted into the factor ζ by use of theKCap), and represents a direct confirmation of the reliability of EEA calculations.

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4. The “objective function” is the extended exergetic cost of the “global” product, i.e., steam pluselectrical energy, normalised over the generated electrical energy. No attempt has been madeto separately compute the cost of the steam.

Results are displayed in Figs. 10 and 11 for three values of the TIT. The following remarksapply:

1. The real, resource-based efficiency of the process, equal to the inverse of the Extended Exerg-etic cost, takes substantially lower values than the ones we are accustomed to: its range is0.24–0.32 instead of the 0.4–0.5 of the Second Law efficiency (Fig. 10b);

2. The minimum Extended Exergetic cost (Fig. 11) is seen to correspond to different “optimal”

Fig. 10.a Thermoeconomic cumulative cost of the products as a function of pressure ratio (β) and turbine inlet tempera-ture (TIT).Fig. 10b Extended exergetic efficiency as a function of β and TIT.Fig. 10c Extended exergetic cost as afunction of β and TIT.

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Fig. 11. “Optimal” turbogas pressure ratio for the cogeneration plant of Fig. 9, as predicted by First Law (η1), SecondLaw (η2) and EEA analysis.

pressure ratios than the ones suggested by a First Law, or a Second Law, or even a thermoecon-omic analysis. This indicates that the externalities introduced into the efficiency calculation bythe EEA technique are relevant to the overall exergetic budget;

3. Under the assumptions adopted here, labour’s direct exergetic equivalent amounts to about 2–3% of the overall exergetic expenditure. Considering the “hidden” contribution of labour, i.e.,the labour equivalent contained in the Extended Exergetic cost of each piece of equipment, itcan be estimated (from an analysis of disaggregated industrial cost data for Italy in the period1996–2000 [11,13]) that about 15% of the exergetic content of each component of the classconsidered here consists of Labour exergy: the contribution is therefore not negligible in theoverall budget.

6. Conclusions

A new exergy-based quantifier, recently proposed [28] on the ground of theoretical and thermo-dynamic considerations as a general paradigm for the assessment of energy conversion systems,is presented and discussed. It constitutes a substantial extension of the cumulative exergetic indexproposed two decades ago by Szargut, in that it includes the so-called non-energetic externalities(capital, labour and environmental costs) in the exergy budget. The new quantifier, calledExtended Exergy, can treat especially well environmental externalities that are difficult to allocateproperly in Thermoeconomics. Two examples of application of the resulting method of analysis,named Extended Exergy Accounting, are given in this paper.

In spite of the limitations posed by the many necessary assumptions required to close the model,results are very encouraging: EEA indeed offers more insight than “simple” exergy analysis andeven Thermoeconomics. To this regard, it must be stressed that EEA ought not to be regardedjust as an “adjustment” of previous Second Law-based methods: while it is true that extendedexergy could be used as a quantifier in the Structured Thermo-Economics of Valero [23] andTsatsaronis [8], and that it could be introduced with some modification even in earlier formulations[13,15], it is also true that none of these previous methods included capabilities to take intoaccount, in a rational and homogeneous form, capital, labour and environmental externalities. Asa matter of fact, EEA reduces to Thermoeconomics in the special (but unrealistic) case in which

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both capital and labour cost factors are equal to 1. The two applications discussed herein providean idea of the capabilities of the method and demonstrate that EEA provides a new and differentinsight in both component and system analysis.

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