tsatsaronis1993

G. Tsatsaronis

L. Lin

J. Pisa

Center for Electric Power, Tennessee Technological University,

Cookeville, TN 38505

Exergy Costing in Exergoeconomics Existing methods of exergoeconomic analysis and optimization of energy systems operate with single average or marginal cost values per exergy unit for each material stream in the system being considered. These costs do not contain detailed information on (a) how much exergy, and (b) at what cost each exergy unit was supplied to the stream in the upstream processes. The cost of supplying exergy, however, might vary significantly from one process step to the other. Knowledge of the exergy addition and the corresponding cost at each previous step can be used to improve the costing process. This paper presents a new approach to exergy costing in exergoeconomics. The monetary flow rate associated with the thermal, mechanical and chemical exergy of a material stream at a given state is calculated by considering the complete previous history of supplying and removing units of the corresponding exergy form to and from the stream being considered. When exergy is supplied to a stream, the cost of adding each exergy unit to the stream is calculated using the cost of product exergy unit for the process or device in which the exergy addition occurs. When the stream being considered supplies exergy to another exergy carrier, the last-in-first-out (LIFO) principle of accounting is used for the spent exergy units to calculate the cost of exergy supply to the carrier. The new approach eliminates the need for auxiliary assumptions in the exergoeconomic analysis of energy systems and improves the fairness of the costing process by taking a closer look at both the cost-formation and the monetary-value-use processes. This closer look mainly includes the simultaneous consideration of the exergy and the corresponding monetary values added to or removed from a material stream in each process step. In general, the analysis becomes more complex when the new approach is used instead of the previous exergoeconomic methods. The benefits of using the new approach, however, significantly outweigh the increased efforts. The new approach, combined with some other recent developments, makes exergoeconomics an objective methodology for analyzing and optimizing energy systems.

Introduction Exergoeconomics (thermoeconomics), a relatively new field

of thermal sciences, combines a detailed exergy (second-law) analysis with appropriate cost balances to study and optimize the performance of energy systems from the cost viewpoint. The analyses and balances are usually formulated for single components of an energy system. Exergy costing, one of the basic principles of exergoeconomics, means that exergy, rather than energy or mass, should serve as a basis for costing energy carriers. This paper presents a contribution to exergy costing.

Until now, all theoretical approaches and applications of exergoeconomics have assigned a single cost value to the unit of total, physical, chemical, thermal, or mechanical exergy of a material stream at a given state. This value represents either an average cost in the methods of exergoeconomic accounting (Obert, Gaggioli, Reistad and Wepfer, 1963, 1970, 1977, 1980, 1983; Tsatsaronis et al., 1984, 1985, 1986, 1990; Valero et al.,

Contributed by the Advanced Energy Systems Division and presented at WAM, Dallas, Texas, November 25-30, 1990, of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript received by the AES Division, December 20, 1990; revised manuscript received June 22, 1992. Technical Editor: A. 6 . Arnas.

1986) or a marginal cost in the exergoeconomic optimization techniques developed by Tribus, Evans, El-Sayed and followers (1962, 1966, 1970, 1980, 1983). This single cost value assigned to the unit of an exergy form of a stream actually depends not only on the cost formation process, but also on additional explicit or implicit assumptions (auxiliary equations) necessary for calculating the stream costs. This value has no memory of the history of the cost formation process. As discussed later, detailed knowledge of this history eliminates the need for additional assumptions and facilitates exergy costing.

The assignment of cost values to the exergy unit of material streams (c,-) has been criticized in the past as arbitrary because of the use of auxiliary assumptions that are arbitrary to some extent even when they are meaningful from the exergoeconomic viewpoint. Tsatsaronis et al. (1984, 1985, 1986, 1990) have used the stream costs (c,) only as auxiliary variables to calculate the average unit costs of fuel exergy (cF) and product exergy (cP) for the system components. They have shown that the latter costs (cF and cP) have a much smaller dependence than the stream costs (c,) on the auxiliary assumptions.

One of the most important aspects of exergy costing is cal-

Journal of Energy Resources Technology MARCH 1993, Vol. 115/9

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REGENERATOR

BM™M Ai r s t r eam = P l an t Fue l D P o w e r

W N f f r = 1.052 MW

Table 1 Total exergy flow rale (£), flow rates of thermal (E7) and mechanical {£**) exergy and cost flow rates (D) associated with the material streams and the mechanical power and heat transfer of the system shown in Fig. 1

Fig. 1 A simplified gas turbine system with regenerator

Stream

1

2

3

4

5

6

wT

wc

Q

E [MW]

0.000

0.946

1.693

3.452

1.239

0.428

2.132

1.080

2.500

E T

[MW]

0.000

0.276

1.023

2.782

1.239

0.428

E M

[MW]

0.000

0.670

0.670

0.670

0.000

0.000

A

0.00

18.93

35.97

62.97

25.62

8.57

37.35

18.93

[27.00

D

B

0.0

19.91

34.32

61.32

22.02

7.61

39.30

19.91

27.00

[$/hr]

C

0.0

18.72

34.92

61.92

24.98

8.77

36.95

18.72

27.00

D

0.00

20.38

33.93

60.93

20.72

7.16

40.22

20.38

27.00

culating the cost of exergy destruction in each component of the energy system being considered. This cost could be used in optimizing single components or a complex plant. The value of this cost depends on the exergy-costing method and the auxiliary assumptions used in the exergoeconomic analysis. It is apparent that using an objective costing method that eliminates the need for auxiliary assumptions is of great importance in calculating the "correct" cost of exergy destruction in each component.

In the new approach discussed in the following, single stream costs are used only for transports of heat and power and for the resources supplied externally to the energy system. All calculations are conducted in terms of monetary (cost) flow rates (Dj) associated with each exergy stream. The single cost values (Cj) associated with the exergy unit of material streams are no longer used. The average cost (cP) of product-exergy unit of a component (Tsatsaronis and Winhold, 1984, 1985) plays a central role in computing the cost flow rates Z),. In a detailed and systematic accounting process, we register every exergy addition—together with the corresponding cost—and every exergy removal from a stream in each process step. This information, continuously updated, moves along with the stream from state to state. With this approach we conduct a continuous cost accounting for each exergy unit from the moment it is supplied to the stream unit until either it is removed from the stream, or the stream leaves the total system.

The New Approach to Exergy Costing

To illustrate the new concept, a simplified gas turbine system is used, Fig. 1. The combustion chamber has been replaced by a heat exchanger in which EQ = 2.5 MW of exergy are externally supplied at a cost of cQ = S3.0/GJ exergy. This results

in a cost flow rate of DQ = $27/hr (or Z>G = 0.75<t/s) associated with the external energy source. The turbine generates a total of WT = 2.132 MW. The new power generated by the system is WNET = 1.052 MW and the compressor consumes Wc = 1.080 MW. Pressure drops in the regenerator and the heat exchanger are neglected. Table 1 shows the exergy flow rates of air at the six states shown in Fig. 1.

In the following we formulate for each component (a) the cost balances, neglecting the contributions of plant investment costs and operating (other than fuel) and maintenance expenses', and (b) the relationships for calculating the cost of the product-exergy unit (cP). These equations are written for an analysis based on physical exergy values. The variable D™ denotes the cost flow rate associated with the physical exergy of the rth stream. The corresponding equations when the physical exergy is split into thermal and mechanical exergy are presented later in this section.

(1)

Compressor (I)

Cost balance: E%H - D^H = c„ Wc

Cost of product-exergy unit:

<#?= {i%H-DpxH)/{$»-$») (2)

Regenerator (II)

Cost balance: £>f-E% H = DfH-ifbH (3)


cff, = (#"-#") /<#"-#") (4)

If these costs are considered in the analysis, they should be added to the right-hand side of the cost-balance equations.

c COND

CP DEA FW« HPP HPT IPP IPT

LPP LPT

d D e

= cost per exergy unit ($/GJ) = condenser = coal preparation = deaerator = nth feedwater heater = high-pressure pump = high-pressure turbine = intermediate-pressure pump = intermediate-pressure tur

bine = low-pressure pump = low-pressure turbine = cost per mass unit ($/kg) = cost flow rate ($/hr) = specific exergy (kJ/kg)

E = m = W =

Subscripts

C = D = F = i =

in =

J = NET =

out = Q = p =

exergy flow rate (MW) mass flow rate (kg/s) mechanical power (MW)

compressor exergy destruction fuel exergy fth stream inlet y'th system component net power outlet heat transfer rate product exergy

T = turbine W = mechanical power I = compressor

II = regenerator III = heat exchanger IV = turbine

Superscripts M = mechanical exergy

PH = physical exergy T = thermal exergy

= real cost of net power (including cost of exergy losses)

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[cPH $/GJ ;

4

PH C P , I

5 '

3 • •!;!

cp 3^! = $ 6.33/GJ

$ 5 .56/GJ

^ f 100 PH „PH 1 e 6

.PH - PH . d 4 = D

4 / m

.PH - PH , -d 5 = D 5 / m

, .PH - PH , . d , = D _ / m ' 6 6

tfH = iXH+cPPd%H-tfH)+c%dEgH-%H)

CPHIII = $ 4 . 2 6 / G J

PH PH 2 e 5

^ 300 e P H e 3

400 500 4. ,PH -4

[ e P H , kJ/kg] -

Fig. 2 Cost at which physical exergy is supplied to the air stream as a function of the specific physical exergy for the gas turbine system shown in Fig. 1

Heat Exchanger (III)

Cost balance: DPH-DPH=DQ = cQEP}H=0J50<t/s (5)


cpP%=(DPH-DPH)/(EPH-EPH) (6)

Turbine (IV) Cost balance: DPH-DPH=cw( Wc+ WNEr) (7)

Cost of product-exergy unit: cPtW = cw (8)

According to existing methods of exergoeconomic accounting, in addition to Eqs. (1), (3), (5), and (7), two auxiliary equations are required to calculate the six unknowns 1%H, Dpn, DPH, if5

H, If^ and cw(since DfH = 0 when EPH = 0). The auxiliary equations used in the past include

or

for the turbine, and

rPH_

rPH_

rPH_

rPH

rPH

C4

-Cw

rPH

= 0

(9b)

(10fl)

(106)

for the regenerator. In the new approach, however, we systematically follow the

cost formation process as the air moves from state 1 to state 6. In the compressor (I), the air physical exergy increases from zero to EPH. The average cost per unit of physical exergy at which this exergy supply occurs in the compressor is given by Cpf, Eq. (2). In the regenerator (II), the air physical exergy increases from EPH to EPH. The exergy rate difference (EPH -EPH) is added at an average cost per exergy unit equal to c™, Eq. (4). In the same way, the addition of the exergy rate (EpH-EPH) in the heat exchanger (III) occurs at an average cost per unit of physical exergy of cPI{n, Eq. (6). It is apparent that, in general, the values of Cfff, cp\w and cp% differ. Figure 2 shows the cost per unit of physical exergy as a function of the specific physical exergy for the air.

The physical exergy of the air increases from state 1 through states 2 and 3 to state 4. At any of these points the corresponding cost flow rate is computed by taking into account the complete previous history of the same stream. Thus, the cost flow rate at state 4, for example, is given by (Fig. 2)

±rPH <WPH + Cp,in(fi4 - EPH)- •dPHm4 (11)

where dPH represents the physical-exergy cost per unit of mass ($/kg) for stream 4. The value of dPH is graphically presented in Fig. 2. The area below the solid line in Fig. 2 corresponds to the mass-specific cost d (cost flow rate divided by the mass flow rate). The foregoing general procedure is used at any step at which exergy .is supplied to the stream being considered.

One of the major differences between the new approach and the existing methods of exergoeconomic accounting is in the costing procedure when exergy is removed from a stream. The new method assumes that the units of exergy that were supplied last to the stream are removed first. This corresponds to the last-in-first-out (LIFO) principle of accounting. Thus, an exergy unit is removed from a stream at the same cost at which it was previously supplied to the same stream. By keeping track of the cost of supplying exergy at any process step and by knowing the amount of exergy removed from the stream, the cost flow rates after the removal can be calculated. Thus, the cost flows at states 5 and 6, when physical exergy is considered, are calculated directly from the following equations, as shown in Fig. 2:

DPH=lf4H- rPH ,pPH EPH)- PH , pPH EPH) (12)

or, since m\ = m2 = m3 = w4 = m5 = m6, dPH=dP«- cPHm^H_f^H) _ cPpHl{ePH_ ePH) ( 1 2 f l )

and

DPH^H-c^l(MH-^H)-c^(EPH-^H) (13)

or

dPH = dPH-c%dePH-egH)-c%H<£H-e$H) (13a)

Using Fig. 2 (or by substituting Eq. (11) into (12) and Eq. (14) into (13) it can be easily verified that Eqs. (12) and (13) are equivalent to Eqs. (14) and (15), respectively.

$H = tf»+c%!(Ep«-EPH)+c%l(EPH-EZ«) (14)

or

(9«) and

1PH=dPH + cp%tfH-ePH)+c%1(e?f-ePH) (14a)

DPI, = EPH+c%(ESH-EFt)

dPH=dPH+cPH(ePH_ePH)

(15)

(15a)

In the new approach, Eqs. (12) and (13) (or 14 and 15) are used together with Eqs. (1) through (8) to calculate the unknowns cw, c™, CpJ, cp%, Cp,ivi a n d DjH, J = 2, . . . , 6. The auxiliary Eqs. (9) and (10) are no longer needed to compute these unknowns because they have been replaced by Eqs. (12) and (13) (or (14) and (15)). Equations (14) and (15) demonstrate that after the cost at the state of maximum specific exergy (e4

in the system shown in Fig. 1) has been established for a stream, all other costs downstream of this state can be easily computed. The results obtained in the new approach from the simultaneous solution of Eqs. (1) through (8), (12) and (13) are different than the results calculated from the previous approaches using Eqs. (1), (3), (5), (7), (9) and (10).

Application of the New Approach When Physical Exergy is Split Into Thermal and Mechanical Exergy. The analysis of the gas turbine system when the exergy-costing method is based on the thermal and mechanical exergy values requires the following equations:

Compressor I (supply of mechanical and thermal exergy)

Dl+Dy-D{-D?=c„Wc (16)

CTP,I= (Dl-Dj)/(El-E\) = (dl-d\)/(el-e[) (17)

Journal of Energy Resources Technology MARCH 1993, Vol. 115 /11


[(?", $/GJ] 4 . T = $ 5.50/GJ

T T | : : : ; : ; : |d 4 = D 4 / m

|::::*::'::::| d 5 - D 1 m

T - T -K i l l d , = D* / m 1 ' o 6

[<?", kJ/kg]

[<** $/GJ]

4

^ . 1

tnn * -

M d 2 =

#

M d 3 =

-?

M d 4

= 0

$ 5.SO/GJ

„M M M e2 = e 3 = e4

= 134 kJ/kg

0

( a )

100 eM_ eM_ e 5 " e 6 -

[e f kJ/kg] *-

(b)

Fig. 3 Cost at which thermal (a) and mechanical (b) exergy is supplied to the air streams as a function of the corresponding specific exergy for the gas turbine system shown in Fig. 1

c%l=(D?-DY)/(E?-E?)=(d¥-d?)/(e?-e?) (18) CP, i-°p,i

Regenerator II (supply of thermal exergy) D^+D^-D;

(19)

(20)

<£...= (D\-Dl)/{El-El) = (dj - dl)/(ej - e$) (21)

Heat Exchanger III (supply of thermal exergy) Dj+DF-Dj-D?=DQ = cQEQ = 0.150 C/s

T Cp.III : (Dj-Dl)/(El- Ej) (dj-dj)/(ej-eh

(22)

(23).

Turbine IV (removal of thermal and mechanical exergy)

Dl+D%-DTs-D%=cw(Wc+WIKd (24)

The system, of equations used to calculate the fifteen unknowns Df, Df (i = 2, . . . , 6), c„, cpj, cî, cp,n, and cj>ra (since Dj = Df = Owhen^f = £ f = 0) includes the following six equations in addition to Eqs. (16) through (24):

ds= cpêi- ef) + c£„ (ef- el) + c£,m {el- el) dl=cT

Pil(el-e[)+cTPv( el - el)

<# = &(#-#) df=cfl(ef-tf)

df-

(25) (26) (27) (28) (29)

--cfêf-tf) (30) Equations (25) and (26) are graphically represented by the

corresponding dotted areas in Fig. 3 (a). Equations (27) through (30) are graphically represented in Fig. 3(b). Since in this example a zero pressure drop was assumed in the regenerator and the heat exchanger, the mechanical exergy values in states 2, 3 and 4 are equal, and the same values in states 1, 5 and 6 are zero. More details about the application of the new approach are given by Tsatsaronis and Pisa (1993).

Now the question arises why is LIFO a more appropriate principle to be used in exergy costing than any other accounting principle, e.g., FIFO (first-in-first-out). To answer this question, we must take a closer look at the process of supplying exergy to a material stream. Each physical exergy unit supplied to a stream is associated with a small temperature and/or pressure interval in which this unit was added to the stream. From the thermodynamic viewpoint, all exergy units of a stream at a given state are equivalent; we do not distinguish between

exergy units supplied at a low temperature and/or pressure and exergy units supplied at higher values of these variables. From the practical and economic viewpoints, however, all exergy units are not equivalent. Each exergy unit has been provided in general, at a different cost than the other units. This cost is, therefore, indirectly connected with the corresponding temperature and pressure at which the exergy unit being considered was supplied to a stream.

When physical exergy is removed from a material stream, the temperature and/or pressure are reduced. Since we have already established the correspondence of exergy units and their costs with temperature and pressure intervals, it is apparent that when any of these variables are reduced we must assume that the exergy units associated with the same temperature and/or pressure interval are used. Thus, the exergy units that were supplied last to the material stream are used first. This observation allows us to directly calculate the cost associated with the exergy units removed from a material stream in a process step provided that we computed this cost in the previous steps during which the exergy units now removed from the stream were then supplied to it.

In the previous discussion of the new method applied to the gas turbine system (Fig. 1), mean cost values were used for the exergy addition to the air stream in the compressor, Eqs. (2), (17) and (18), regenerator, Eqs. (4) and (21), and heat exchanger, Eqs. (6) and (23). These costs do not have to remain constant for a given component, as it was done here. Theoretically, any appropriate function

i<e<emi,j (31) cpj=f(e), einJ out ,y

could be used as long as the following equation is fulfilled

iout

Cpjde (32) tn

A outj

• Here, the subscripts (in, j) and (out, j) refer to the values of the stream being considered at the inlet and outlet of the yth system component. With the aid of Eqs. (31) and (32), marginal costs could be calculated and used in exergoeconomic optimization procedures. For practical applications, however, the use of incremental costs is more realistic. These incremental costs could be calculated in the following manner. We start with the smallest feasible size of the component (compressor, heat exchanger, etc.) being considered and calculate the average cost of the product for this size. Then we consider incremental

12/Vol. 115, MARCH 1993 Transactions of the ASME


Table 2 Cost of a unit of product exergy, cft (in $/GJ) for each system component (Fig. 1) in cases A through D

Component

I. Compressor

II. Regenerator

III. Heat Exclianger

IV. Turbine

A

5.56

6.33

4.26

4.86

B

5.86

5.35

4.26'

5.12

C

5.50

6.02

4.26

4.81

D

5.98

5.03

4.26

5.24

Table 3 Cost rate of exergy destruction, (DD), (in $/hr) for each system component (Fig. 1) in cases A through D. The values in parentheses represent the cost per unit exergy destruction (in S/GJ).

Component

I. Compressor

II. Regenerator

III. Heat Exchanger

IV. Turbine

A

2.36 (4.87)

1.33 (5.84)

8.00 (3.00)

1.35 (4.69)

B

2.48 (5.12)

1.13 (4.93)

8.00 (3.00)

1.42 (4.93)

C

2.33 (4.81)

1.27 (5.55)

8.00 (3.00)

1.34 (4.64)

D

2.54 (5.24)

1.06 (4.63)

8.00 (3.00)

1.45 (5.03)

increases in the component size, which simultaneously represent incremental increases in the exergy supplied to the stream being considered, and calculate the incremental investment and fuel costs. This continues until the largest feasible size of the component has been reached. The incremental costs obtained in this way may be used to compute the function in Eq. (31), and the marginal costs required for plant optimization.

In a mixing process, according to the new procedure, we first calculate the history (i.e., the cost per exergy unit as a function of the specific exergy, Fig. 2) of each one of the streams that are mixed. Subsequently, the lines representing the individual histories of each stream are combined into one line which now represents the history of the mixture. This combination is done using the mass rates as relative weights. In all calculations downstream of the mixing process, only the mixture history is used; the individual histories of the streams that were mixed are not further needed. More details of the calculations in mixing processes are given in a forthcoming review article (Tsatsaronis, 1993).

Results and Discussion

Tables 1, 2 and 3 summarize the results obtained from the analysis of the system shown in Fig. 1 in the following four cases. Case A uses the new exergy-costing approach (Eqs. (1) through (8), (12) and (13)) applied to the physical exergy of each stream, Fig. 2. In case B the "old" approach (Eqs. (1), (3), (5), (7), (9) and (11)) based on average costs per exergy unit of each stream (c,) was applied to the physical exergy of each stream. In cases C and D, separate equations were formulated for the mechanical and thermal exergy values of material streams. These exergy forms are calculated as discussed by Tsatsaronis, et al. (1990). In case C, the new exergy costing method was applied to the mechanical and thermal exergy separately (Fig. 3), whereas case D uses the same approach as case B (average cost, per stream exergy unit) for the mechanical and thermal exergy of each stream. In the simplified system of Fig. 1, mechanical exergy is supplied only through the compressor (Fig. 3(b)), whereas the thermal exergy of stream 4 entering the turbine is supplied by the compressor, regenerator and heat exchanger at a different cost in each component (Fig. 3(a)).

Among the four cases, case A shows the highest monetary flow rates at states 3, 4 and 5 and the highest cost of exergy destruction in the regenerator. Case C leads to the lowest cost of (a) mechanical power and (b) exergy destruction in the compressor and the turbine, and to the highest cost flow rate at state 6. Case D has the largest number of extreme values

among the four cases; it has the lowest values for (a) the cost flows at states 3, 4, 5 and 6, and (b) the cost of exergy destruction in the regenerator whereas it leads to the highest cost for (a) mechanical power, (b) cost flow at state 2 and exergy destruction in the compressor and turbine. The cost values vary by more than 20 percent in the regenerator and the states 5 and 6.

Generally, the cost deviations between cases A and C or between B and D are considerably smaller than the same cost deviations between cases A and B, or C and D. This means that in this system the selection of the exergy-costing method has a stronger effect on the results than the decision to distinguish between mechanical and thermal exergy.

Table 2 clearly indicates that regardless of the case being considered, the cost of supplying exergy from state 1 to state 4 in components I, II and III is different. This cost varies in all four cases by more than 30 percent. In cases B and D, the cost of supplying exergy in the compressor is higher than the cost of supplying exergy in the regenerator, whereas in cases A and C the opposite is true.

Among the cases discussed, case C is preferred. It is based on the new approach, and it simultaneously takes a more detailed look at the cost-formation and the cost-usage by considering the process and cost of supplying and using mechanical and thermal exergy separately.

Compared with previous methods, the new approach increases the size of the linear system of equations to be solved simultaneously for calculating the monetary flow rates because new unknowns (such as cPii, cP^ and cP<m) are introduced. Thus, both the complexity of the exergoeconomic analysis and the cost of computations increase considerably, particularly when mechanical and thermal exergy are considered separately. This fact, however, should not inhibit use of a fair exergy costing method that is based on sound cost accounting principles.

In previous exergoeconomic analyses conducted by the authors and other investigators, a zero cost was usually assigned to streams rejected to the environment (e.g., to stream No. 6 in Fig. 1, Eq. (10b)). This resulted in a zero cost for the exergy losses (exergy of the streams rejected to the environment) and unfairly raised the costs of exergy destruction in some system components. Using the new approach for exergy costing, a nonzero monetary flow rate is automatically calculated for the exergy losses. A comparison of the values of D6 in Table 1 with the costs of exergy destruction presented in Table 3 shows that the cost of the exergy loss (D6) is comparable with the cost of exergy destruction in the heat exchanger (III). Although there is no reason for not assigning a zero cost, or a negative monetary flow rate (e.g., to consider the cost of stream disposal), to at least some exergy losses when the new approach is used, it seems more appropriate to charge the total cost of exergy losses in a system directly to the main product when (a) the objective of the analysis is to calculate the cost of exergy destruction, and (b) the specific exergy of the rejected stream is significant. In this case for the system shown in Fig. 1, the real cost of net power unit C^NET (neglecting the contributions of investment costs and O&M expenses other than fuel) is

c ; ^ = ^ r ^ + A = g N s r ± A = A . = a 7 1 3 < / M J WT-WC WNET WNET

It is apparent that this cost is independent of the costing method used in cases A through D. On the contrary, the cost CW,NKT calculated for cases A through D and given on the last line of Table 2 (ciyiNET = cw = cP l v) depends on the case being considered. The two variables cWt^Er and c ^ E T have the following meaning: If we would be able to further use the exergy of stream 6, then the net power produced by the gas turbine system would be CjyNET and, from the use of the stream



Table 4 Cost at which each unit of physical (a), thermal (b), and mechanical (c) exergy is supplied to the water/steam in each component of the steam plant shown in Fig. 4. Part (a) of the table corresponds to case A, whereas parts (b) and (c) refer to case C.

Stream cp" [kJ/kg]

Component c,™ [S/GJ]

29 0.69

34 0.88

MIX 138.88 '

35 1.31

LPP 211.30

38 7.55

FWI 75.34

41 22.32

42 45.82

FW2 FW3 44.72 1 37.44

44 79.95

45 83.35

DEA IPP 34.41 1 91.66

48 126.47

FW5 32.67

51 183.59

FW6 32.03

52 204.61

HPP 52.11

53 267.67

FW7 30.53

1 1492.43

BOILER 25.88

(a)

Stream eT(U/kg] '

Component cP

T [S/GJ]

29 0.79

34 0.97

MIX 153.90

38 7.24

FWI 93.33

41 22.01

FW2 44.45

42 45.54

FW3 36.83

44 79.70

DEA 32.82

48 122.90

FW5 32.61

51 180.23

FW6 31.55

52 185.87

HPP 40.79

53 250.03

FW7 30.64

I 909.50

BOILER 25.71

(b)

Stream eM [Id/kg]

Component cP

M f$/GJ]

28 -342.96

34 -0.09

COND 7.38

44 0.25

LPP 205.60

51 3.35

IPP 85.93

53 17.64

HPP 40.79

1 582.93

BOILER 25.71

(0

Table 5 Cost of a unit product exergy, cP, (in S/GJ) for each component of the steam plant (Fig. 4) in cases A through D

COMPONENT

BOILER

HPT

IPT

LPT

LPP

FWI

FW2

FW3

DEA

IPP

FW5

FW6

HPP

FW7

A

25.88

30.59

30.63

34.89

211.30

75.34

44.72

37.44

41.31

91.66

32.67

32.03

52.11

30.53

B

25.83

32.30

32.02

34.61

212.91

55.10

38.27

34.51

33.25

93.28

31.58

31.38

52.52

31.82

C

25.71

30.40

30.44

25.07

205.60

93.3

44.45

36.83

73.26

85.93

32.61

31.55

40.79

30.64

D

25.82

32.60

31.86

34.32

212.80

55.45

38.42

34.48

30.82

93.17

31.47

31.18

52.65

31.57

Table 6 Cost rate of exergy destruction, DD, (in S/hr) for each component of the steam plant (Fig. 4) in cases A through D

COMPONENT

BOILER

HPT

IPT

LPT

LPP

FWI

FW2

FW3

DEA

IPP

FW5

FW6

HPP

FW7

A

29,198

1,412

1,714

3,833

13

275

215

217

230

131

304

382

256

285

B

29,125

1,497

1,797

3,800

13 •

197

183

199

185

134

294

374

259

298

C

28,973

1,403

1,702

2,669

12

346

214

213

410

119

304

377

196

287

D

29,118

1,512

1,788

3,767

13

199

183

199

171

134

293

372

259

296

6, we should expect to receive D6 (Table 1) dollars per hour to cover our costs. If, however, we cannot use the exergy of stream 6, cWjNEr gives the real cost of a net-power unit. By charging the cost flow rate D6 to the net power after the exergy

Fig. 4 Flow diagram of a steam power plant (Tsatsaronis and Winhold, 1984)

costing process has been completed we (a) avoid an artificial inflation of the cost of exergy destruction in the compressor, regenerator and turbine, and (b) can more easily compare technically alternative solutions for the gas turbine system with different specific exergies at state 6. By doing so, we also indicate that every exergy loss is associated with ' 'money loss,'' i.e., a cost flow that leaves the system in connection with an exergy loss. Ultimately, all these cost flows in a system must be charged to the final product.

For systems producing more than one product, the engineer conducting the exergoeconomic analysis should decide which cost flows (or parts of them) associated with exergy losses must

• be charged to each product; here, the criterion of causality must be considered: which product is responsible for what exergy loss and to what extent. In some cases, it might seem expedient to apportion the total cost of exergy losses among the main products according to their exergy content. This, however, is an arbitrary solution and every effort should be made to avoid it.

Tables 4, 5 and 6 show a comparison of the results obtained after applying the new approach to a more complex plant (steam power plant, Fig. 4) with results obtained for the same

14/Vo l . 115, MARCH 1993 Transactions of the ASME


plant using previous approaches. In these calculations we used the same four study cases applied to the gas turbine system: new and old approach combined with either physical, or thermal and mechanical exergy values. The plant investment costs and the operating and maintenance expenses (Tsatsaronis and Winhold, 1984) were included in the cost balances for the power-plant components.

When conducting an exergoeconomic analysis of this steam cycle according to the new approach, it becomes apparent that by far the largest part of physical, thermal and mechanical exergy is supplied to the water in the boiler at the same cost for both the new and old approaches. This effect can be measured by calculating the ratio (efH - es")/e^H that is equal to 82.1 percent according to Table 4(a).

Tables 4(a) and (b) and (c) represent the exergoeconomic results in a form similar to Figs. 2 and 3. The following examples demonstrate how the values in this table should be read. Table 4(a) shows that the specific physical exergy of streams 38 and 41 is 7.55 and 22.32 kJ/kg, respectively. This exergy increase occurs in feedwater 2 at an average cost per physical-exergy unit of 44.72 $/GJ. Similarly, Table 4(b) indicates that in the boiler the specific thermal exergy of water/ steam increases from 250.03 kJ/kg (stream 53) to 909.5 kJ / kg (stream 1) at an average cost of 25.71 $/GJ. The very small differences in specific exergy during the feedwater preheating processes makes the graphic representation less clear than in the gas turbine system. The cP and e values in Table 4 allow the calculation of d values for process streams.

Table 5 shows that the LIFO concept (cases A and C) used in the new approach leads, in general, to a lower cost of the exergy used in the HPT, IPT, and LPT; consequently, the cost of power produced in the three turbine stages is significantly lower in cases A and C than in the old approach (cases B and D). When thermal and mechanical exergy values are considered and the new approach is used (case C), the cost of the power produced by the LPT is the lowest because of the low cost associated with steam below atmospheric pressure where the mechanical exergy values are negative.

It must be noted that in this system the real cost of the net power unit, tv i N E T , is calculated as the sum of the cost of the power produced in the generator plus the cost flow rate of the stream leaving the LPT. The values in Tables 4(b) and (c) make it apparent that the condenser is used not only to reject heat to the environment but also to supply mechanical exergy to the stream existing the LPT before any water preheating takes place.

The lower cost of the power produced when the new approach is applied results in a lower cost of product-exergy unit in the pumps. Compared with the old approach, the cost of exergy destruction (Table 6) calculated with the new method is lower in the HPT and IPT when the analysis is based on the physical exergy and in all three turbines when based on the thermal and mechanical exergy, with the exception of pre-heater 7; the cost of exergy destruction is lower in all feedwater preheaters, due to the decreasing cost of fuel (and product) with decreasing extraction pressure.

Conclusions Working exclusively with single average cost variables as

signed to material streams is convenient from the mathematical viewpoint and helps introduce the concept of exergoeconomics to persons not familiar with it. This procedure, however, requires auxiliary assumptions and could sometimes lead to misleading conclusions. For instance, a small pressure drop in a stream operating at ambient temperature and at a pressure slightly higher than the ambient pressure might reduce the physical exergy of the stream by 50 percent. This would double the cost per unit of physical exergy and, if no other exergoeconomic variables are consulted, it would make the small pres

sure drop appear to be a significant cost contributor. However, considering the cost flow D, or the cost per unit mass avoids misleading conclusions.

It is suggested that an exergoeconomic analysis be conducted in terms of df', dj, c^j and cpj. The first two terms represent the mass specific cost of mechanical and thermal exergy, respectively, associated with the rth stream, whereas the last two terms refer to the cost of supplying mechanical and thermal exergy to the product of they'th component. Very similar considerations can also be applied to the chemical exergy of a material stream.

The average costs per exergy unit (c,) of a material stream, on which most previous exergoeconomic methods were based, should be used only as a convenient way of communicating the analysis results, but not for drawing conclusions. A more appropriate method for presenting the analysis results for material streams, however, might be in specific costs (dh dollars per kilogram), or in terms of cost flow rates (Dj, dollars per hour). It is apparent that for energy streams (work and heat transfer), for fuel and product exergy, and for exergy destruction, the specific values should be presented in terms of cost per exergy unit.

The new concept for exergy costing presented here is based on a simple idea. For each material stream in a system, we follow successively and systematically all additions and removals of exergy to and from the stream. Every time exergy is added in a process step, we store the average cost at which that happens. When exergy is removed, the monetary flow rate removed from the stream is calculated by going backwards and considering the cost at which those exergy units were previously supplied, as shown in Figs. 2 and 3 and in Eqs. (12), (13), and (25) through (30). This approach is objective, general, systematic and it eliminates the need for auxiliary assumptions.

Tsatsaronis et al. (1989) introduced the reaction exergy as the economically relevant part of chemical exergy. The remaining part (environmental exergy), which depends on the reference state, has no economic value. The concept of reaction exergy leads to costs which are independent of the arbitrary reference state used to calculate the chemical exergy values. (The absolute total exergy values still depend on the reference state.) In the new approach presented here, no arbitrary auxiliary equations are used. The exergetic efficiency of a plant component defined according to the component purpose (Tsatsaronis et al., 1984, 1985, 1986, 1990) should no longer be considered as arbitrary. Thus, exergoeconomics has reached a state of development, at which it is practically free of any arbitrariness. This is important not only for the confidence to be associated with the analysis results, but also for the general acceptance of exergoeconomics as an objective methodology for analyzing and optimizing energy systems.

References El-Sayed, Y. M., and Evans, R. B., 1970, "Thermoeconomics and the Design

of Heat Systems," ASME Journal of Engineering for Power, Vol. 92, pp. 27-34.

El-Sayed, Y. M., and Tribus, M., 1983, "Strategic Use of Thermoeconomics for System Improvement," Efficiency and Costing—Second Law Analysis of Processes, ed., R. A. Gaggioli, American Chemical Society Symposium Series 235, Washington, D.C., pp. 215-238.

Evans, R. B., and Tribus, M., 1962, "A Contribution to the Theory of Thermoeconomics," UCLA Department of Engineering, Report No. 62-63, Los Angeles, Calif.

Evans, R. B., Greilin, G. L., and Tribus, M., 1966, "Thermoeconomic Considerations of Sea Water Demineralization," Principles of Desalination, ed., K. S. Spiegler, Academic Press, pp. 21-7)5.

Gaggioli, R. A., 1977, "Proper Evaluation and Pricing of Energy," Proceedings of the International Conference on Energy Use Management, Tucson, Ariz., October 24-28, Pergamon Press, Vol. II, pp. 41-43.

Gaggioli, R. A., and Wepfer, W. J., 1980, "Exergy Economics," Energy, Vol. 5, pp. 823-838.

Gaggioli, R. A., 1983, "Second Law Analysis for Process and Energy En-



gineering," Efficiency and Costing—Second Law Analysis of Processes, ed., R. A. Gaggioli, American Chemical Society Symposium Series 235, Washington, D.C., pp. 3-50.

Obert, E. F., and Gaggioli, R. A., 1963, Thermodynamics, McGraw-Hill, New York.

Reistad, G. M., 1970, "Availability: Concepts and Applications," Ph.D. thesis, University of Wisconsin.

Reistad, G. M., and Gaggioli, R. A., 1980, "Available—Energy Costing," Thermodynamics: Second Law Analysis, ed., R. A. Gaggioli, American Chemical Society Symposium Series 122, Washington, D.C., pp. 143-159.

Tribus, M., and El-Sayed, Y. M., 1980, "Thermoeconomic Analysis of an Industrial Process," Center for Advanced Engineering Study, M.I.T., Cambridge, Mass.

Tsatsaronis, G., 1993, "Thermoeconomic Analysis and Optimization of Energy Systems," Progress in Energy and Combustion Science, to be published.

Tsatsaronis, G,, and Winhold, M., 1984, "Thermoeconomic Analysis of Power Plants," EPRI AP-3651, RP 2029-8, Final Report, Electric Power Research Institute, Palo Alto, Calif., Aug. 1984.

Tsatsaronis, G., and Winhold, M., 1985, "Exergoeconomic Analysis and Evaluation of Energy-Conversion Plants," Energy, Vol. 10, Part I: "A New General Methodology," pp. 69-80; Part II: "Analysis of a Coal-Fired Steam Power Plant," pp. 81-94.

Tsatsaronis, G., Winhold, M., and Stojanoff, C. G., 1986, "Thermoeconomic Analysis of a Gasification-Combined-Cycle Power Plant," EPRI Final Report, AP-4734, Electric Power Research Institute, Palo Alto, Calif.

Tsatsaronis, G., Pisa, J. J., and Gallego, L. M., 1989, "Chemical Exergy in Exergoeconomics," Thermodynamic Analysis and Improvement of Energy Systems, Proceedings of the International Symposium, Beijing, China, June 5-8, Pergamon Press, pp. 195-200.

Tsatsaronis, G., Pisa, J. J., and Lin, L., 1990, "The Effect of Assumptions on the Detailed Exergoeconomic Analysis of a Steam Power Plant Design Configuration," A Future for Energy, Proceedings of the Florence World Energy Research Symposium, Florence, Italy, May 28-June 1, pp. 771-792.

Tsatsaronis, G., and Pisa, J., 1993, "Exergoeconomic Evaluation of Energy Systems — The CGAM Problem," Thermoeconomic Analysis of Energy Systems, eds., A. Valero, G. Tsatsaronis, and M. A. Lozano, ASME, New York.

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Wepfer, W. J., 1980, "Applications of Available-Energy Accounting" Thermodynamics: Second Law Analysis, ed., R. A. Gaggioli, American Chemical Society Symposium Series 122, Washington, D.C., pp. 161-186.

Announcement FLOWERS '94

Energy for the 21st Century: Conversion, Utilization and Environmental Quality

Site: July 6-8, 1994 Date: Florence, Italy

The third Florence World Energy Research Symposium will be held at Palazzo degli Affari in Florence, Italy.

As in the past, the official language of FLOWERS will be English. The papers will be peer-reviewed according to ASME format and the Proceedings will be published by NOVA SCIENCE, New York, NY.

The following deadlines have been set:

September 15, 1993 November 1, 1993 January 15, 1994 February 1, 1994 March 15, 1994 April 2, 1994

Abstracts are due Draft of the paper due Review of papers Notification of acceptance Camera-ready manuscripts due NOVA SCIENCE starts printing of Proceedings

Further information may be obtained from:

Prof. Giampaolo Manfrida General Secretariat FLOWERS '94 DEF—Department of Energy Engineering University of Florence Via S. Marta, 3 1-50139 Firenze Italy TEL: 39-55-479 6235 FAX: 39-55-479 6342

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