m7, Norag

Thermoeconomics

reasduco prcosto.is n

improved denition of waste cost distribution ratios, based on the premise that waste must be allocated

d ower streis catemportaironmewaste

economy, becoming a long lasting irreversibility with serious futureimplications. This is the case of CO2 emissions.

The existence of waste creates the need to determine their cost,which is necessary for decision making in the industry sector on

[6]. There are several thermoeconomic approaches to the problemof waste allocation. The rst method used was applied in closedcycles, such as Rankine cycles, in which the cost of the waste (heat)from the dissipative unit (condenser) is allocated to the othercomponents of the cycle using the negentropy concept (see forinstance references [4,7,8]). Negentropy was dened in reference[7] as the negative of entropy multiplied by the temperature of theenvironment. Other researchers have dened the negentropy ofa stream as the product of the temperature of the environment and

* Corresponding author.E-mail addresses: afagudelo@udea.edu.co (A. Agudelo), valero@unizar.es

Contents lists available at

Ener

els

Energy 45 (2012) 634e643(A. Valero), cesar.torres@endesa.es (C. Torres).in industrial ecology, where a closed-loop of production is pursuedthrough recycling [1,2].

Most industrial systems are based on a linear productionstructure consisting in the use of a given energy resource to obtaina nal product, with associated irreversibilities and often gener-ating several waste. As stated in the laws of energy efciency [3],every waste is a failure: the more waste generated the worst theperformance of production processes. Waste from industrialsystems may affect the natural environment, society and the

the allocation of waste cost affects the calculation of the cost ofsystem products. In order to assign the cost of waste it is necessaryto identify their formation process and the responsibility of eachproductive unit on it [4], which makes the allocation of wastesa complex problem because there is no a general methodology: itdepends on where and how wastes are formed [5].

The problem of waste in thermoeconomics has gained impor-tance in recent years, because it allows to use this discipline asa tool for helping to assess and attain sustainable energy systems1. Introduction

In any system there are undesireobtain the products. Ashes, hot watparticular CO2 emissions are in thknown as waste and are gaining ienergy systems because of envsustainability assessment. The cost of0360-5442/$ e see front matter 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2012.07.034process of waste is identied, allowing to perform an improved thermoeconomic analysis. 2012 Elsevier Ltd. All rights reserved.

s that are necessary toams, ue gases, and ingory. These ows arence in the analysis ofntal regulations andis of capital importance

one side, and for the imposition of restrictions by the society, on theother. The cost of waste requires disaggregation of the system inorder to be determined.

The components that eliminate waste ows from the systemare called dissipative units, and the remainder components arecalled productive. The exergy cost of residual ows and the cost ofthe resources used to abate themmust be charged to the productiveunits of the system that generated thesewaste [4,5]. For this reason,Formation process of the cost of wasteSymbolic exergoeconomicsdemonstrate the methodology. It was found that the allocation of waste is signicantly improved withthe new methodology. Quantitative and qualitative results are satisfactory, since the cost formationAllocation of waste to the productive units that generated their cost. Two energy systems are used as case studies toAllocation of waste cost in thermoecono

Andrs Agudelo a,*, Antonio Valero b, Csar Torres b

aGroup of Efcient Management of Energy e GIMEL, Universidad de Antioquia, Calle 6bCentre of Research for Energy Resources and Consumption e CIRCE, Universidad de Za

a r t i c l e i n f o

Article history:Received 7 February 2012Received in revised form15 June 2012Accepted 14 July 2012Available online 14 August 2012

Keywords:

a b s t r a c t

In any energy system theproducts. These are knowncharged to the useful proon the allocation of these tformation process of theira waste cost it contributedratios. Nevertheless, there

journal homepage: www.All rights reserved.ic analysis

. 53 e 108, Medelln, Colombiaoza, Mariano Esquillor, 15, 50018 Zaragoza, Spain

are unwanted residual output ows that are necessary to obtain nalwaste, and represent an exergy loss that has an inherent cost that must bets of the system. Calculation of production costs including waste dependsoductive components. The right way to allocate waste is by identifying thet, since every productive component must be charged only by the part ofWaste cost allocation is done by means of so called waste cost distributiono a denitive way to determine these ratios. In this work we propose an

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ergythe difference of the entropy of the stream and that of the envi-ronment [9,10]. In this approach, it is considered that the purpose ofa dissipative component (condenser or chimney) is to producenegentropy, in order to balance the entropy increases in the othercomponents of the system [4]. This allows to allocate the heat lossof the condenser to productive components, as a function of theentropy increase in each of them [11]. This means that thecomponents which increase the entropy of ue gases are charged,and those that reduce it receive a credit [12,4]. This method haslimitations when applied to open systems, such as Brayton cycles[13].

A drawback of the negentropy approach is that waste are in

Nomenclature

_C Vector of cost rates V=h or [kW]_E Exergy ow [kW]f FractionF Fuel rate [kW]FP Table FP (n n)FPhHi Table FP on energy basis (n n)FPhSi Table FP on entropy basis (n n)hFPi Matrix of exergy distribution ratios (n n)_H Enthalpy ow [kW]I Irreversibility rate [kW]m Number of streams of the system_m Mass ow rate [kg/s]n Number of components of the systemp Pressure [bar]P Product rate [kW]hP* Cost matrix operator (n n)hRPi Matrix for the allocation of waste cost (n n)T Temperature [K]Un Identity matrix (n n)y Distribution ratios: elements of matrix hFPi

A. Agudelo et al. / Enmost of cases not related to their entropy content (nor to theirexergy content) but to the damage they cause or to our inability toconvert them into something useful. No matter what we produce,we generate wastes. And we always need to spend some additionalamount of exergy to get rid of them. So we are interested inassessing what this additional amount of exergy is, i.e. the exergycost of wastes. On the other side, it is more practical to use exergy toaccount for wastes, because it is the basis for calculation in ther-moeconomics and it can be considered ameasure of environmentaldisturbance caused by human activities [14].

It is important to distinguish between where the waste andwhere its cost are formed within the system. The description of theprocess of waste cost formation is a key tool for systems efciencyimprovement and for a rational allocation of the outputs of thesystem. If a process generates or contributes to generate a waste,that process must share the responsibility for eliminating it. Thedetailed exergy accounting procedure is what we name theprocess of waste cost formation.

It has been common in the literature (see for instance reference[15]) to allocate the cost of waste to dissipative components or todirectly allocate them to the nal products of the system. It hasalso been common to use entropy, negentropy or mixedproperty changes in Rankine cycles. In any of these cases there aresubjective, incomplete, inconsistent or particular criteria behindallocation, which prevents the process of waste cost formation to bereected. For instance, when negentropy is considered as a cti-tious ow, used only to allocatewaste, theremay be inconsistencieswhen calculating unit exergy costs, since the product of dissipativeunits might be higher than its resource, yielding unit costs lesserthan one for some ows [10]. This happens because exergy loss isconsidered as fuel and negentropy as product. To overcome thisproblem, Santos [5] developed what he called the H&S model toallocate waste in the thermoeconomic analysis of energy systems.The basis of this method is the breakup of exergy into enthalpy andnegentropy, except for mechanical or electrical power, and for inputows and nal products of the system. Enthalpy ows replaceexergy ows, and negentropy ows are used as a component ofexergy. Therefore, the productive structure is dened usingenthalpy and negentropy ows. For open systems, such as gas

_Z Vector of non-thermodynamic cost rate of thecomponents V=hn 1

Greek lettersj Waste cost distribution ratiosp* Element of matrix hP*y Set of system components

Subscripts0 Environmente External resourcesD Dissipative componentsj General indexP Productr WasteR Waste

Superscriptse Processing of external resourcesn Componentsr Wastez Non-thermodynamic costs

45 (2012) 634e643 635turbine cycles, the environment is included as an imaginarycomponent that produces the negentropy needed by the systemand consumes the chemical exergy of ue gases (which is allocatedto the combustion chamber). Therefore, the fuel of the environmentis made up of residual enthalpy and chemical exergy, while itsproduct is negentropy [9,10,13,16].

The H&S model simplies to some extent the productivestructure, because it allocates waste based explicitly on entropychanges. The relationships among components can be morecomplex than this, affecting the formation of the cost of waste ina way that can be more representative of the true process of wastecost formation. The allocation of the chemical part of wastes only tothe combustion process is an unnecessary simplication, given thatthe interaction of other components with the combustion chambermay alter fuel consumption, generating indirect responsibilities forthe generation of ue gases. The breakup of exergy owsmay causethat the parts of an exergy ow (enthalpy, negentropy, and chem-ical exergy) have different unit exergy costs, which has no sensebecause all these parts belong to the same physical stream andwere generated simultaneously in the same physical process. Alimitation of this approach is revealed when it is applied toa combined cycle [9]. In this case, waste heat from the condenser isallocated to the bottoming cycle components only. Nevertheless,some components of the top cycle may also contribute to theformation of waste, and therefore to its cost.

Regarding the allocation of condenser waste heat, Mendes et al.[17] propose to do such allocation considering that the product of

ergycondenser is the electric power generated by the steam turbinefrom environmental pressure down to condensing pressure. Theargument of the authors is that without the condenser, steam couldonly be expanded down to atmospheric pressure. Using thisapproach yields the same results that allocating the waste of thecondenser only to the product of the steam turbine. This methodleaves free of charge other components that might also beresponsible for that waste.

Borelli and de Oliveira [18] consider that ue gases at the stackof a combined cyclemust have nomonetary value, so they force thissituation by allocating the cost of gases exiting the gas turbine tothe components of the heat recovery steam generator (HRSG). Theauthors use a linear rule that allocates a cost to each component ofthe HRSG according to the exergy decrease of ue gases when theygo through it. It is clear that there are components involved in theformation of ue gases that are not included.

Gonlez et al. [19] present a methodology for allocation of theenvironmental cost of ue gases consisting in charging part of thiscost to the components which have external input resources. Thefraction of the environmental cost of ue gases charged to everycomponent is calculated as the ratio of the exergy entering thecomponent as an external resource and the total exergy of externalresources. This allocation method has the advantage of allocatingthe cost of waste and not their exergy, but the criterion employedmay leave other responsible components uncharged if they are notdirectly associated with external resources.

Regardless of their drawbacks, all these methods have the meritof trying to distribute waste costs along the systems structure,looking for a more rational and comprehensive way to allocate thewaste cost.

There are several recent published works that study varioussystems using the conventional thermoeconomic approach. Amongtheseworks there are some that perform thermoeconomic analysis,such as reference [20], which studies a steam electrolysis systemassisted by geothermal energy. Reference [21] presents the ther-moeconomic analysis of a refrigeration plant. Reference [22]analyzes a district heating system enhanced with absorption heatexchange. Hydrogen production from biomass gasication isstudied in reference [23]. Reference [24] presents the analysis ofseveral small-scale power generation systems based on energyfrom biomass. In reference [25], a gas turbine cogeneration systemfrom an iron and steel factory is analyzed. Also, a diesel engine-based cogeneration system is analyzed in reference [26]. Finally,reference [27] presents the analysis of a micro-cogeneration systemfor the tertiary sector.

Other works perform thermoeconomic and/or exergoeconomicoptimization of energy systems, such as reference [28], whichpresents the thermoeconomic optimization of an ice storagesystem for gas turbine inlet air cooling. Conventional cost balancesare applied, but the total cost of exergy destruction is included inthe objective function at the plant-level. Although this approachdoes not perform waste cost allocation, it takes into account theeffect of exergy loss due to irreversibilities and waste on the wholeplant. The same treatment is used by Hosseini et al. [29] in theanalysis of a combined power and water desalination plant. Thiskind of system is also optimized in reference [30]. Sayyaadi et al.[31] revisit the CGAM problem [32], making a parallel thermody-namic, exergoeconomic and environmental optimization. Wastecosts are not considered explicitly in this analysis. Reference [33]presents a similar analysis of a hydrogen production system frombiomass. Finally, Xiong et al. [34] present the optimization of a coal-red power plant.

All of these works on thermoeconomic analysis or optimizationdo not account explicitly for the cost of waste, which demonstrates

A. Agudelo et al. / En636the need to work in this subject.Ahmadi et al. [35] perform the exergoenvironmental optimiza-tion of a combined heat and power (CHP) system at a paper mill.The CHP analyzed has the same physical structure of the CGAMproblem [32]. The exergoeconomic model used by the authors doesnot include waste in the cost balance, which using the words of theauthors, makes it a hidden cost. A similar approach is applied toa regenerative gas turbine system in references [36] and [37],lacking an explicit treatment of the cost of waste. The same opti-mization approach is used reference [38] for simple combined cyclepower plants. Although in these references the environmental costof pollutants (part of a waste ow) is included at the plant-level todene the objective function, the cost of waste is not considered atcomponent-level balances, which prevents its detailed treatment.

In a recent study [39], the cost of exergy destruction is includedat the component-level in the analysis of a geothermal power plant.Exergy destruction of a component encompasses waste exergy andirreversibility, which may have different costs. Its inclusion in thecost balance of the components is an indirect way of consideringthe cost of waste, but only takes into account the cost of wastegenerated directly in each component.

An alternative allocation criteria for the cost of waste has beenused in a recent work [40]. These authors analyze a refrigerationsystem, where the waste is heat loss from the condenser. Theyallocate the cost of waste among productive components in directproportion to their exergy destruction. This approach solves theproblem of waste cost allocation, but its suitability is to be ques-tioned, given that the contribution of a productive component tothe cost of waste is not necessarily directly proportional to itsirreversibility. This argument gains strength as the number of wastein a system rises.

In a recent publication, Li et al. [41] present the thermoeconomicoptimization of the condenser in an organic Rankine cycle. Theseauthors consider the cost of waste in an explicit fashion in the costbalance of the dissipative component, but this cost is allocated onlyto the condenser.

A relevant work recently published [42] highlights the lack ofdetail regarding waste treatment in conventional thermoeconomicanalysis, and proposes a methodology to assess their cost indecentralized energy systems in the case that some of the wastecan be sold and thus generate a revenue. The authors combinethermoeconomics with cost to benet analysis to develop amethodto internalize the revenue that might be generated by a waste ow,using the allocation method proposed in reference [43]. Themethodology proposed is useful for the internalization of externalcosts into the internal cost structure of the system, but it does notcontribute to the problem of waste cost allocation.

The calculation of the cost of waste was developed by Torreset al. [43]. These authors present the mathematical structurenecessary to calculate the cost of waste and to reect its effect onproduction costs. The allocation problem is addressed by means ofwaste cost distribution ratios among the productive components ofthe system. They present a preliminary method to calculate distri-bution ratios, but state that this is not necessarily the best optionand that the eld is open to research on this direction. Following theprevious development, Seyyedi et al. [44] propose an alternativecalculation method for waste cost distribution ratios based on theentropy distribution ratios in the system. Thismethod is close to theoriginal one discussed above and gives similar results. The previoustwo approaches have the advantage that they are based on theproductive structure of the system, which reduces signicantly thesubjectivity involved in the allocation of waste cost.

This work presents a newmethodology to allocate waste cost inthermoeconomic analysis, based on the mathematical structure ofreference [43]. Themethodology is based on the premise that waste

45 (2012) 634e643must be allocated to the productive units that generated their cost.

non-thermodynamic costs, and waste:

follows:

jj;r _Ej;rFr

(11)

where _Ej;r is the exergy ow from productive unit j to dissipativeunit r, and Fr is the fuel of dissipative unit r. This method facilitatesthe calculation since the required information is extracted from theFP table dened in reference [46]. Nevertheless, it is not clear if thisis the best way to allocate waste [43].

Seyyedi et al. [44] propose another criterion to calculate the costdistribution ratios for waste, which is similar to that proposed inreference [43]. These authors propose to calculate waste costdistribution ratios as a function of the entropy distribution amongthe components of the system:

jj;r FPhSij;rPFPhSi

(12)

ergyAn improved denition ofwaste cost distribution ratios is proposed,which has an objective character because it is based onphysical lawsand on the productive structure of the system. Using symbolicexergoeconomics, the processes that generate the cost of waste areidentied and allocation of waste cost is performed according to thetrue responsibility of every productive component. This representsa contribution relative to previous developments,most ofwhich usesubjective or inconsistent criteria for waste cost allocation.

A combined cycle plant and a cogeneration system are used ascase studies to illustrate the application of the proposed method-ology. Results show an improvement in the allocation of waste cost,which allows an improved thermoeconomic analysis.

2. The cost of waste in thermoeconomic analysis

Torres et al. [43] present the mathematical structure to calculateproduction costs taking into account the effect of waste. Exer-goeconomic costs of production, _Cp, can be found by solving thefollowing system of linear equations:

UnehFPiehRPi _CP _Cne _Z (1)

Matrix Un is the identity matrix of size n, where n is the numberof components in the system. Matrix operator hFPin n isa matrix that contains the distribution coefcients of the system,and depends only on the productive structure and on the exergyows of the streams [45], andmatrix hRPin n contains thewastecost distribution ratios. Vector _C

ne n 1contains the exer-

goeconomic cost rates of input resources to the components, and_Zn 1 contains the non-thermodynamic cost rates associatedwith the components: capital, operation, and maintenance costs.

It was established in reference [43] that the cost rate of a givenwaste _Cr;0 can be distributed among productive components ofthe system according to the following expression:

_Cr;0 XjyP

_Cr;j for ryD (2)

where yP is the set of productive components of the system and yD isthe set of dissipative components. The term _Cr;j is the cost rate ofthe waste dissipated by component r that was generated inproductive component j. Therefore, the total waste cost ratecharged to a given productive unit can be calculated as follows:

_CR;j XryD

_Cr;j for jyP (3)

Cost rates _Cr;j are determined by means of waste cost distribu-tion ratios dened as [43]:

_Cr;j jj;r _Cr;0 for jyP and ryD (4)

whereP

jyPjj;r 1 for ryDCost distribution ratio jj,r represents the fraction of the waste

cost rate generated in dissipative component r that is charged toproductive unit j (see Fig. 1).

The product of dissipative units is their own outlet stream, i.e.,thewaste itself. Therefore, using Equations (3) and (4), the total costrate of waste charged to a productive unit can be expressed as:

_CR;j XryD

jj;r_CP;r (5)

where _C is the cost rate of product of dissipative unit r. Equation

A. Agudelo et al. / EnP;r(5) can be written in matrix notation as:_CP _CeP _C

zP _C

rP (7)

where:

_CeP

DP* _Cne (8)

_CzP

DP* _Z (9)

_CrP

DP* _CR (10)

The matrix operator in these equations is dened ashP* UnehFPie1 [45].

3. Allocation of waste cost

According to the previous structure for cost calculation, wasteare allocated by means of the waste cost distribution ratios denedin Equation (4). Torres et al. [43] propose to calculate these ratios as_CR hRPi _CP (6)

where hRPii;j jj;i.As stated in reference [43], production costs can be broken

down into three contributions: processing of external resources,

Fig. 1. Allocation of the cost of waste.

45 (2012) 634e643 637jyPj;r

ergyTable FPhSi is calculated as:

FPhSi FPhHieFP (13)

where table FPhHi is equivalent to table FP, only that energy owsare used instead of exergy ows. This way of allocating waste yieldsslightly different values than the proposal of reference [43].

4. Proposal of a method to determine waste cost distributionratios

A given waste in a system exists because some productiveprocess has to generate it in order to fulll its purpose, which maybe to provide the resources for other processes and/or to contributeto the net product of thewhole plant. If a component that generatesa waste provides the resources for other components, then theresponsibility for that waste relies also on those components fueledby it, given that they indirectly determine the amount of wastegenerated, by demanding resources for their operation. As anexample, think of a boiler generating steam in a Rankine cycle. Ata given efciency of the boiler, ashes and ue gases (waste)generated in it are determined by the steam demand, which is xedby the external power demand and by the efciency of the othercomponents of the system.

The amount to which a component is responsible for a givenwaste depends on its relationshipwith the other components of thesystem, i.e. it depends on the productive structure of the system.Therefore, it is necessary to identify the processes that contribute tothe formation of a waste and the magnitude of this contribution, inorder to perform a suitable allocation of its cost, which will allowa more signicant thermoeconomic evaluation.

Aiming at this goal, the search for an improved allocation of thecost of waste must unveil the true responsibility of each productivecomponent for every waste of the system. First, it is necessary toanswer the question: Which components must be charged bya given waste? This is the qualitative character of allocation. Then,the quantitative character must be determined by answering thefollowing question: To which extent must the responsible compo-nents be charged? The answers to these questions are obtained bymeans of a series of premises stated as follows:

1. The costs of waste must be charged to the productive units thathave generated them [4].

Here it is important to establish a conceptual differencebetween waste and their cost. The former are identied by theirexergy, but their cost also encompasses exergy consumptionsinvolved in the elimination of waste from the system. Therefore,it is the cost of waste what is of real interest. This raises a need thatis expressed in the next premise.

2. It is necessary to identify the process of formation of the cost ofwaste.

The starting point is the concept of cost (exergy or monetary) inthermoeconomics, which is dened as the amount of resourcesspent to obtain a given product. Therefore, the concept of cost givesinformation about the product itself, as well as about the particularprocess in which it was obtained. As the efciency of processesdecrease, the cost of products rises because more resources have tobe used to obtain the same effect. This fact reveals the inverserelation between cost and efciency.

In an energy system external resources (with a given cost) are

A. Agudelo et al. / En638processed to obtain energy products. The original costs of theseresources turn into the costs of nal products trough the produc-tive processes that take place inside the system. This trans-formation of input costs into nal product costs depends on theefciency of every component of the system and on the way theyare interrelated. It is known as the process of cost formation(of products) [47], and can be determined by means of thermoe-conomic analysis.

If we recall that waste are the product of dissipative units, then itis clear that the process of waste cost formation is parallel to theprocess of product cost formation. As a consequence, the exergycost of waste can be written as [45]:

_CeP;r Pr

Xn

j1p*r;jIj Fr

XjyP

p*r;jIj (14)

The term Pr is the product rate of dissipative component r, and Ijis the irreversibility rate of productive component j. Coefcients p*r;jare the elements of matrix hP* corresponding to dissipativecomponents. Equation (14) presents the part of the cost associatedwith the processing of external resources, which is the only partknown at this phase of the process, when waste cost distributionratios are unknown. The previous equation reveals that the cost ofwaste is made up by the exergy resources of the dissipativecomponents, Fr, and by the irreversibility of productive componentsthat is associated with the generation of waste.

Using the results of references [45] and [48], the fuel of dissi-pative components can be expressed as:

Fr Fe;r XjyP

yr;jPjePe;j

(15)

where yr,j are the distribution coefcients given by matrix operatorhFPi. The term Pe,j is the part of the product of component j that isformed by an input stream from the environment.

Combining Equations (14) and (15), the exergy cost of waste canbe expressed as:

_Cr;0 _CeP;r Fe;r

XjyP

hyr;jPjePe;j

p*r;jIji

(16)

The term Fe,r will have a value of zero in most of the situations,the exception being the case in which external resources enterdirectly to a dissipative component.

The previous expression is of capital importance, since it allowsto identify the contribution of productive components to the cost ofwaste as the argument of the summation. It is worth to mentionthat this result takes into account the fact that the cost of a wasteconsists of the direct cost of eliminating it from the system and of anindirect cost generated along its formation process.

Equation (16) is a mathematical representation of the process offormation of the cost of waste. The contribution of each productivecomponent to the cost of waste is then:

_Cj;r yr;jPj Pe;j

p*r;jIj (17)Therefore, Equation (16) can be rewritten as:

_Cr;0 Fe;r XjyP

_Cj;r (18)

This equation allows to depict a graphical representation of theformation process of waste cost, as shown in Fig. 2, where np is the

45 (2012) 634e643number of productive components of the system.

5.1. Combined cycle power plant

The combined cycle used in reference [43] is shown inFig. 3.

Fig. 2. Formation process of the cost of waste.

Table 1Waste cost distribution ratios for the combined cycle.

Component _CeP kW _Cj;10kW jj,10 _Cj;11 kW jj,11

C. Chamber 219,880.32 3058.01 0.381480 15,956.56 0.724598Compressor 176,459.94 262.86 0.032791 5616.44 0.255046Gas turbine 289,755.91 163.66 0.020416 448.27 0.020356Steam turbine 76,894.51 0.55 0.000069 0 0Superheater 14,743.22 787.10 0.098189 0 0Evaporator 48,651.10 2597.37 0.324020 0 0Economizer 21,181.89 1131.14 0.141110 0 0Pump 334.42 14.97 0.001867 0 0Generator 190,190.48 0.46 0.000058 0 0Condenser 8016.12 0 0 0 0Stack 22,021.27 0 0 0 0Total 8016.12 1 22,021.27 1

A. Agudelo et al. / Energy 45 (2012) 634e643 639jj;r _Cj;rP

jyP

_Cj;r(19)

Waste cost distribution ratios of Equation (19) reect the totalcontribution of productive components to the cost of waste. In thisway the qualitative and quantitative characters of waste allocationare met, because these are allocated to the productive componentsthat generated them, in proportion to their respective responsi-bility. Summarizing, by using Equation (19) the allocation of wasteis done according to the formation process of their cost.

5. Case studies

The allocation method developed in the previous section isapplied to a combined cycle power plant used in previous investi-gations on the cost of waste, and to a cogeneration plant.3. The responsibility of a productive component for a waste lies inits contribution to the formation of the cost of that waste.

Therefore, to express the responsibility of productive compo-nents for the cost of waste, the proposed denition of waste costdistribution ratios is as follows:Fig. 3. Combined cycThe system is fueled by natural gas (stream 7). Hot gases exitingthe gas turbine (stream 4) enter the HRSG, after which they enterthe stack (stream 10) before leaving the system to enter the envi-ronment (stream 21). Waste heat (stream 20) leaves the systemthrough the condenser. The nal product of the system is electricpower (90 MW), represented by stream 19.

Thermodynamic properties of the ows and the productivestructure of this system are presented in references [43] and [44].Condenser and stack are the dissipative units.

Cost distribution ratios are calculated from Equation (11) for themethod of Torres et al. [43], from Equation (12) for the method ofSeyyedi et al. [44], and from Equation (19) for the method proposedhere.

The contribution of productive components to the cost of wasteis shown in Table 1, as well as the resulting waste cost distributionratios.

The results of this table show that for the combined cycle plantthe cost of waste is made up completely by the contributions ofproductive components. It can be observed that the combustionchamber has the greatest responsibility for both waste. Thecompressor has a signicant responsibility for ue gases, anda small one for condenser waste heat. The responsibility of the gasturbine for both waste is rather small. The components of thebottoming cycle are responsible only for the formation of wastele power plant.

heat in the condenser. In the Rankine cycle, the components withgreater responsibility are the evaporator and economizer, followedby the superheater. This hierarchy is proportional to the exergyaddition to the working uid in each component, and it coincideswith the result of the other allocation methods. The pump hasa small responsibility, as in the other methodologies. The generator

Another rational way to dene the fuel and product of thecombustion chamber is: F1 _E7 _E2 and P1 _E3. When thisproductive structure is used, the methods of the other authorsassign the ue gases only to the combustion chamber: j1;11 1,while by using Equation (19) they are still allocated to the threecomponents of the Brayton cycle, although in this case the

Table 2Contributions to the cost of production for the combined cycle.

Component _CeP [V/h] _C

zP V=h This work Reference [43] Reference [44]

_CrP V=h fr,n[%] _C

rP V=h fr,n[%] _C

rP V=h fr,n[%]

C. Chamber 3466.00 0.98 402.06 10.39 270.15 7.23 318.70 8.42Compressor 2781.40 960.74 557.06 12.96 532.15 12.45 483.60 11.44Gas turbine 4567.10 992.70 714.32 11.39 586.52 9.54 586.52 9.54Steam turbine 1212.00 415.20 284.49 14.88 334.47 17.05 334.47 17.05Superheater 232.38 49.38 54.52 16.21 66.01 18.98 58.22 17.13Evaporator 766.84 187.28 179.92 15.87 216.92 18.52 206.83 17.82Economizer 333.87 86.84 78.34 15.70 84.76 16.77 102.99 19.67Pump 5.27 1.56 1.35 16.50 1.65 19.42 1.30 15.97Generator 2997.80 813.23 563.80 12.89 563.80 12.89 563.80 12.89Condenser 126.35 35.93 29.66 15.45 34.87 17.69 34.87 17.69Stack 347.10 53.43 53.29 11.74 44.58 10.02 44.58 10.02

A. Agudelo et al. / Energy 45 (2012) 634e643640and steam turbine have very small responsibilities, but are stillresponsible, because the power that moves the pump comes fromthe generator, which input is mechanical power from the turbines.

With the cost distribution ratios of other authors for this system[43,44], residual heat from the Rankine cycle is allocated amongsuperheater, evaporator, economizer, and pump. Steam turbine andgenerator are not charged. The twomethods give similar qualitativeresults, as they have the same responsibility hierarchy amongcomponents. In a combined cycle like the one studied here, the heatsource is the combustion of natural gas. Therefore, it would beexpected that some components of the Brayton cycle would becharged by the residual heat of the bottoming cycle, as is reectedby the results of Table 1. It is worth to mention that the methods ofreferences [43] and [44] allocate residual gases to compressor andcombustion chamber only, without charging the gas turbine. Thisresult does not meet the essential condition of waste allocation,because the gas turbine shares the responsibility for the generationof the cost of gases due to its thermodynamic coupling with thecombustion chamber and compressor.Fig. 4. COGEN cogenerresponsibility of the combustion chamber is about 95%.Waste cost distribution ratios for this system were also deter-

mined in references [43] and [44] using the classical criterion ofentropy generation. In the case of ue gases, all the components ofthe Brayton cycle are charged, but there are values greater than one(for the combustion chamber) and lesser than zero (for HRSGcomponents). Here, it is important to recall that the value of wastecost distribution ratios must be between 0 and 1 0 jj;r 1,because they represent the fraction of the total cost of a waste thatis allocated to a given productive component. This condition is metin the allocation of the waste heat of the condenser.

Exergoeconomic analysis is performed using unit cost of fueland non-thermoeconomic costs given in reference [43]. The threecontributions to the cost of product are shown in Table 2.

The previous table also presents the proportional contributionof waste to the cost of product of the components, fr,n.

The contributions of external resources and non-thermodynamic costs are the same for all the cases. As expected,the contribution of waste to production cost of the generator is theation power plant.

productive components to the cost of this waste is shown in Table 5.It is observed that those components directly responsible for thewaste, namely the combustion chamber, burner, and ICE, have the

Table 3Properties of ows for the COGEN system.

Stream _mkg=s T [C] p [bar] _HkW _EkW1 93.97 25.00 1.013 0 02 93.97 321.10 9.117 27,939.00 26,204.003 93.97 607.30 8.661 54,935.00 41,732.004 1.58 25.00 10.000 75,837.00 78,643.005 95.55 1218.00 8.401 128,157.00 94,210.006 95.55 678.80 1.096 70,218.00 33,696.007 e e e 27,939.00 27,939.008 e e e 30,000.00 30,000.00

A. Agudelo et al. / Energysame for the three allocation methods used. This is so because theproduct of the generator is the only product of the system. It isobserved that, in general, the method proposed here yields highercontribution by the components of the Brayton cycle and lower bythe components of the Rankine cycle, when compared to the othertwo approaches. The reason is that the former has a greatercontribution to the formation of the cost of waste.

5.2. Cogeneration system

The methodology developed is also applied to a cogenerationpower plant (COGEN) composed by a gas turbine cycle withregeneration and a cogeneration Diesel engine with a postcombustion system. A sketch of the COGEN system is shown in

9 95.55 427.40 1.064 43,221.00 16,271.0010 18.70 25.00 1.013 0 011 0.3146 25.00 1.013 13,529.00 14,456.0012 0.3313 25.00 1.013 12,203.00 13,112.0013 19.35 483.20 1.096 10,000.00 3949.0014 e e e 10,000.00 10,000.0015 119.10 90.00 3.000 44,905.00 3116.0016 119.10 81.00 3.000 40,405.00 2357.0017 0.218 25.00 5.000 10,106.00 10,717.0018 19.57 875.40 1.064 19,101.00 10,073.0019 26.92 25.00 12.360 2851.00 30.6320 26.92 65.00 12.000 7351.00 307.0021 15.43 25.00 21.000 1647.00 30.9222 15.43 212.40 20.000 43,191.00 14,091.0023 115.10 185.00 1.013 20,778.00 4129.0024 115.10 185.00 1.013 20,778.00 4129.00Fig. 4. There are 9 components (n 9) and 24 streams (m 24).The Brayton cycle is fueled by natural gas (stream 4), and

the internal combustion engine (ICE) is fueled by a 50% blend(in volume basis) of mineral diesel (stream 11) and palm oil bio-diesel fuel (stream 12). The ICE produces 10 MW (stream 14),operating with an excess air (stream 10) of 220%. The energy fromthe cooling system of the engine (streams 15 and 16) is used to heata stream of water (streams 19 and 20). Exhaust gases from theengine (stream 13) are fed to the burner, which is fueled by propane(stream 17). The resulting hot gases (stream 18) are taken to theHRSG, which produces saturated steam at 20 bar (stream 22). Netpower from the gas turbine is 30 MW (stream 8).

Air and combustion gases are treated as mixtures of ideal gases,and combustion processes are assumed to be complete. Natural gas

Table 4Productive structure of the COGEN system.

Component Fuel Product

1 Compressor _E7 _E2e _E12 Regenerator _E6e _E9 _E3e _E23 Combustion chamber _E4 _E3 _E54 Turbine _E5e _E6 _E7 _E85 ICE _E10 _E11 _E12 _E14 _E13 _E15e _E166 Water heater _E15e _E16 _E20e _E197 Burner _E13 _E17 _E188 HRSG _E9 _E18e _E23 _E22e _E219 Stack _E23 _E24is assumed to be CH4. Properties of diesel and biodiesel fuels aretaken from reference [49]. Chemical exergy of natural gas is takenfrom reference [32], that of propane is taken from [50], and thatof diesel and biodiesel fuels is calculated from their compositionand lower heating values [50]. The state of the system used isshown in Table 3, and the productive structure is that shown inTable 4.

This system has only one waste: ue gases. The contribution of

Table 6Contributions to the cost of production for the COGEN system.

Component _CeP [kW] This work Reference [43] Reference [44]

_CrP kW fr,n[%] _C

rP kW fr,n[%] _C

rP kW fr,n[%]

Compressor 48,207.00 2939.30 5.75 2944.10 5.76 3359.20 6.51Regenerator 28,786.00 1784.70 5.84 1758.00 5.76 2005.90 6.51C. Chamber 155,640.00 9048.00 5.49 9504.90 5.76 10,845.00 6.51Turbine 99,970.00 5884.60 5.56 6105.30 5.76 6966.30 6.51ICE 27,568.00 592.13 2.10 0 0 0 0Water heater 1422.60 30.56 2.10 0 0 0 0Burner 18,119.00 2674.10 12.86 2973.30 14.10 2213.10 10.88HRSG 37,946.00 3572.70 8.61 3891.60 9.30 3445.80 8.32Stack 7052.80 664.04 8.61 723.31 9.30 640.45 8.32

Table 5Cost distribution ratios for ue gases in the COGEN system.

Component _CeP kW _Cj;9kW jj,9

Compressor 48,207.00 92.95 0.01318Regenerator 28,786.00 101.62 0.01441C. Chamber 155,640.00 3951.85 0.56033Turbine 99,970.00 66.52 0.00943ICE 27,568.00 541.16 0.07673Water heater 1422.60 0 0Burner 18,119.00 2298.70 0.32592HRSG 37,946.00 0 0Stack 7052.80 0 0Total 7052.80 1

45 (2012) 634e643 641highest responsibility for the formation of its cost, and this isreected in the values of cost distribution ratios. The water heaterand HRSG do not participate in the formation process of the cost ofwaste ue gases. The remaining components of the Brayton cycleare also charged, but in a lesser extent, because they indirectlyaffect the formation process of the cost of waste by means of theirthermodynamic coupling with the combustion chamber.

When the allocation methods of other authors are applied to theCOGEN system, they assign the residual gases only to the burnerand combustion chamber. The remaining components of theBrayton cycle are not charged by waste, although they are alsoresponsible for the generation of ue gases. Evenmore important isthe fact that the ICE is not charged by residual ue gases, although itis clear that a part of these is formed in this component.

Table 6 shows the contribution of waste to production costs forthe COGEN system on an exergy basis.

The results are similar for all the allocation methods, with theexception that for the proposed method the product of the ICE isalso affected by waste, modifying the cost of product in the waterheater as a consequence.

6. Conclusions

This work presents a methodology for allocation of waste costin thermoeconomic analysis. Allocation is done by means of costdistribution ratios, as part of the mathematical structure proposed

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[8] Frangopoulos CA. Thermoeconomic functional analysis. In: Frangopoulos CA,editor. Exergy, energy system analysis and optimization. Encyclopedia of lifeby Torres et al. [43]. Allocation of waste begins by identifying thecost formation process of waste. Using results from symbolicexergoeconomics, it is found the extent to which every productivecomponent of the system contributes to the cost of every wastestream. This contribution is used to dene waste cost distributionratios, which determine the responsibility of productive compo-nents for waste.

The proposed allocation method meets the essential conditionfor allocation of waste, i.e. that only those components contributingto the cost of a waste are charged. In addition, the respective chargereects directly that contribution.

The allocation scheme proposed was applied to a combinedcycle plant and to a cogeneration system, showing outstandingresults regarding the allocation of waste. The methodologyproposed can be used to perform improved thermoeconomicanalysis and to contribute to rational internalization of the cost ofwaste, while keeping subjectivity on a minimum.

Acknowledgments

One of the authors (Andrs Agudelo) acknowledges the supportof the Programme Alban, the European Union Programme of HighLevel Scholarships for Latin America, under scholarship No.E07D403613CO. This author also acknowledges the supportprovided by the 2011e2012 Sustainability Program of the Uni-versidad de Antioquia.

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A. Agudelo et al. / Energy 45 (2012) 634e643 643

Allocation of waste cost in thermoeconomic analysis1. Introduction2. The cost of waste in thermoeconomic analysis3. Allocation of waste cost4. Proposal of a method to determine waste cost distribution ratios5. Case studies5.1. Combined cycle power plant5.2. Cogeneration system

6. ConclusionsAcknowledgmentsReferences