Open access peer-reviewed chapter

# Exergetic Costs for Thermal Systems

By Ho-Young Kwak and Cuneyt Uysal

Submitted: September 14th 2017Reviewed: December 13th 2017Published: June 6th 2018

DOI: 10.5772/intechopen.73089

## Abstract

Exergy costing to estimate the unit cost of products from various power plants and refrigeration system is discussed based on modified-productive structure analysis (MOPSA) method. MOPSA method provides explicit equations from which quick estimation of the unit cost of products produced in various power plants is possible. The unit cost of electricity generated by the gas-turbine power plant is proportional to the fuel cost and inversely proportional to the exergetic efficiency of the plant and is affected by the ratio of the monetary flow rate of non-fuel items to the monetary flow rate of fuel. On the other hand, the unit cost of electricity from the organic Rankine cycle power plant with heat source as fuel is proportional to the unit cost of heat and the ratio of the monetary flow rate of non-fuel items to the generated electric power, independently. For refrigeration system, the unit cost of heat is proportional to the consumed electricity and inversely proportional to the coefficient of performance of the system, and is affected by the ratio of the monetary flow rate of non-fuel items to the monetary flow rate of consumed electricity.

### Keywords

• exergy
• thermoeconomics
• unit exergy cost
• power plant
• refrigeration system

## 1. Introduction

Exergy analysis is an effective tool to accurately predict the thermodynamic performance of any energy system and the efficiency of the system components and to quantify the entropy generation of the components [1, 2, 3]. By this way, the location of irreversibilities in the system is determined. Furthermore, thermoeconomic analysis provides an opportunity to estimate the unit cost of products such as electricity and/or steam from thermal systems [4, 5] and quantifies monetary loss due to irreversibility for the components in the system [6]. Also, thermoeconomic analysis provides a tool for optimum design and operation of complex thermal systems such as cogeneration power plant [7] and efficient integration of new and renewable energy systems [8]. Recently, performance evaluation of various plants such as sugar plant [9], drying plant [10], and geothermal plant [11] has been done using exergy and thermoeconomic analyses. In this chapter, a procedure to obtain the unit cost of products from the power plants and refrigeration system is presented by using modified-productive structure analysis (MOPSA) method. The power plants considered in this chapter are gas-turbine power plant and organic Rankine cycle power plant. These systems generate electricity as a product by consuming the heat resultant from combustion of fuel and by obtaining heat from any hot stream as fuel, respectively. In addition, MOPSA method is applied to an air-cooled air conditioning system, which removes heat like a product while the consumed electricity is considered as fuel. Explicit equations to estimate the unit cost of electricity generated by the gas-turbine power plant and organic Rankine cycle plant, and the unit cost of heat for the refrigeration system are obtained and the results are presented.

## 2. A thermoeconomic method: modified productive structure analysis (MOPSA)

### 2.1. Exergy-balance and cost balance equations

A general exergy-balance equation that can be applied to any component of thermal systems may be formulated by utilizing the first and second law of thermodynamics [12]. Including the exergy losses due to heat transfer through the non-adiabatic components, and with decomposing the material stream into thermal and mechanical exergy streams, the general exergy-balance equation may be written as [6]

ĖxCHE+inletĖxToutletĖxT+inletĖxPoutletĖxP+ToinletṠioutletṠi+Q̇cv/To=ĖxWE1

The fourth term in Eq. (1) is called the neg-entropy which represents the negative value of the rate of lost work due to entropy generation, which can be obtained from the second law of thermodynamics. The term ĖxCHEin Eq. (1) denotes the rate of exergy flow of fuel, and Q̇cvin the fourth term denotes heat transfer interaction between a component and the environment, which can be obtained from the first law of thermodynamics.

Q̇cv+inḢi=outḢi+ẆcvE2

However, the quantity Q̇cvfor each component, which is usually not measured, may be obtained from the corresponding exergy-balance equation with the known values of the entropy flow rate at inlet and outlet.

Exergy, which is the ability to produce work, can be defined as the differences between the states of a stream or matter at any given particular temperature and pressure and the state of the same stream at a reference state. The exergy stream per unit mass is calculated by the following equation:

ex=hTPhrefTrefPrefTosTPsref(TrefPref)E3

where T is temperature, P is pressure, and the subscript ref denotes reference values. The exergy stream per unit mass can be divided into its thermal (T) and mechanical (P) components as follows [3]:

ex=exT+exPE4

and

exT=hTPh(TrefP)TosTPs(TrefP)E5
exP=hTrefPhref(TrefPref)TosTrefPsref(TrefPref)E6

Assigning a unit exergy cost to every exergy stream, the cost-balance equation corresponding to the exergy-balance equation for any component in a thermal system [13] may be written as

ĖxCHEC0+inletĖx,iToutletĖx,iTCT+inletĖx,iPoutletĖx,iPCP+T0inletṠioutletṠj+Q̇cv/ToCS+Żk=ĖxWCW,E7

The term Żkincludes all financial charges associated with owning and operating the kth component in the thermal system. We call the thermoeconomic analysis based on Eqs. (1) and (7) as modified-productive structure analysis (MOPSA) method because the cost-balance equation in Eq. (7) yields the productive structure of the thermal systems, as suggested and developed by Lozano and Valero [5] and Torres et al. [14]. MOPSA has been proved as very useful and powerful method in the exergy and thermoeconomic analysis of large and complex thermal systems such as a geothermal district heating system for buildings [15] and a high-temperature gas-cooled reactor coupled to a steam methane reforming plant [16]. Furthermore, the MOPSA can provide the interaction between the components in the power plant through the entropy flows [17] and a reliable diagnosis tool to find faulty components in power plants [18].

### 2.2. Levelized cost of system components

All costs due to owning and operating a plant depend on the type of financing, the required capital, the expected life of components, and the operating hours of the system. The annualized (levelized) cost method of Moran [1] was used to estimate the capital cost of components in this study. The amortization cost for a particular plant component is given by

PW=CiSnPWFinE8

The present worth of the component is converted to annualized cost by using the capital recovery factor CRF(i, n):

Ċ$/year=PWCRFinE9 The capital cost rate of the kth component of the thermal system can be obtained by dividing the levelized cost by annual operating hours δ. Żk=ϕkĊk/3600δE10 The maintenance cost is taken into consideration through the factor ϕk. It is noted that the operating hours of thermal systems is largely dependent on the energy demand patterns of end users [19]. ## 3. Gas-turbine power plant A schematic of a 300 MW gas-turbine power plant considered in this chapter is shown in Figure 1. The system includes five components: air compressor (1), combustor (2), gas turbines (3), fuel preheater (5), and fuel injector (6). A typical mass flow rate of fuel to the combustor at full load condition is 8.75 kg/s and the air–fuel mass ratio is about 50.0. Thermal and mechanical exergy flow rates and entropy flow rate at various state points shown in Figure 1 are presented in Table 1. These flow rates were calculated based on the values of measured properties such as pressure, temperature, and mass flow rate at various state points. ### 3.1. Exergy-balance equation for gas-turbine power plant The following exergy-balance equations can be obtained by applying the general exergy-balance equation given in Eq. (1) to each component in the gas-turbine power plant. Air compressor Ėx,1TĖx,2T+Ėx,1PĖx,2P+ToṠ1Ṡ2+Q̇1/To=Ėx,1WE11 Combustor ĖxCHE+Ėx,23T+Ėx,55T+Ėx,65TĖx,24T+Ėx,23P+Ėx,55P+Ėx,65PĖx,24P+ToṠ23+Ṡ55+Ṡ65Ṡ24+Q̇2/To=0E12 Turbine Ėx,25TĖx,26T+Ėx,25PĖ26P+ToṠ25Ṡ26+Q̇3/To=Ėx,3WE13 Fuel preheater Ėx,51TĖx,52T+Ėx,51PĖx,52P+Ėx,221TĖx,222T+Ėx,221PĖx,222P+ToṠ51Ṡ52+Ṡ221Ṡ222+Q̇5/To=0E14 Steam injector Ėx,53TĖx,54T+Ėx,63TĖx,64T+Ėx,53PĖx,54P+Ėx,63PĖx,64P+ToṠ53Ṡ54+Ṡ63Ṡ64+Q̇6/To=Ėx,6WE15 Boundary Ėx,1T+Ėx,51T+Ėx,63TĖx,26T+Ėx,1P+Ėx,51P+Ėx,63PĖx,26P+Ėx,221TĖx,222T+Ėx,221PĖx,222P+ToṠ1+Ṡ51+Ṡ63Ṡ26+Ṡ221Ṡ222+Q̇boun/To=0E16 The net flow rates of the various exergies crossing the boundary of each component in the gas-turbine power plant at 100% load condition are shown in Table 2. Positives values of exergies indicate the exergy flow rate of “products,” while negative values represent the exergy flow rate of “resources” or “fuel.” The irreversibility rate due to entropy production in each component acts as a product in the exergy-balance equation. The sum of exergy flow rates of products and resources equals to zero for each component and the overall system; this zero sum indicates that perfect exergy balances are satisfied. Statesṁ(kg / s)P(MPa)TC)ĖxT(MW)ĖxP(MW)Ṡ(MW/ K) 1862.7220.10315.0000.000−0.5580.121 2862.7221.025323.58988.176164.5720.193 23862.7221.025323.58988.176164.5720.193 24891.0561.0251130.775702.452173.5501.201 25891.0561.0251130.775702.452173.5501.201 26891.0560.107592.700261.9962.6611.262 5117.5000.10315.0000.0000.0180.001 5217.5000.103185.0001.5630.0180.018 5317.5000.103185.0001.5630.0180.018 5417.5001.025415.3147.7355.3370.021 5517.5001.025415.3147.7355.3370.021 6310.8330.103(1.000)6.0640.0000.004 6410.8331.025418.17612.3380.0100.006 6510.8831.025418.17612.3380.0100.006 22111.1113.540220.1002.4170.0380.028 22211.1113.54072.9410.2390.0380.011 ### Table 1. Property values and thermal, and mechanical exergy flows and entropy production rates at various state points in the gas-turbine power plant at 100% load condition. ComponentNet exergy flow rates (MW)Irreversibility rate (MW) Ė(k)WĖxCHEĖxTĖxP Compressor−274.040.0088.18165.1320.73 Combustor0.00−881.22594.203.63283.39 Gas turbine593.740.00−440.46−170.8917.61 Fuel preheater0.000.00−0.610.000.61 Steam injector−18.680.0011.915.331.44 Boundary0.000.00−253.22−3.20 Total301.02−881.22253.223.20323.78 ### Table 2. Exergy balances of each component in the gas-turbine power plant at 100% load condition. ### 3.2. Cost-balance equation for gas-turbine power system When the cost-balance equation is applied to a component, a new unit cost must be assigned to the component’s principle product, whose unit cost is expressed as Gothic letter. After a unit cost is assigned to the principal product of each component, the cost-balance equations corresponding to the exergy-balance equations are as follows: Air compressor Ėx,1TĖx,2TCT+Ėx,1PĖx,2PC1P+ToṠ1Ṡ2+Q̇1/ToCS+Ż1=Ė1WCWE17 Combustor ĖxCHECo+Ėx,23T+Ėx,55T+Ėx,65TĖx,24TC2T+Ėx,23P+Ėx,55P+Ėx,65PĖx,24PCP+ToṠ23+Ṡ55+Ṡ65Ṡ24+Q̇2/ToCS+Ż2=0E18 Turbine Ėx,25TĖx,26TCT+Ėx,25PĖ26PCP+ToṠ25Ṡ26+Q̇3/ToCS+Ż3=Ė3WCWE19 Fuel preheater Ėx,51TĖx,52T+Ėx,221TĖx,222TC5T+Ėx,51PĖx,52P+Ėx,221PĖx,222PCP+ToṠ51Ṡ52+Ṡ221Ṡ222+Q̇5/ToCP+Ż5=0E20 Steam injector Ėx,53TĖx,54T+Ėx,63TĖx,64TCT+Ėx,53PĖx,54P+Ėx,63PĖx,64PC6P+ToṠ53Ṡ54+Ṡ63Ṡ64+Q̇6/ToCS+Ż6=Ėx,6WCWE21 Applying the general cost-balance equation to the system components, five cost-balance equations are derived. However, these equations present eight unknown unit exergy costs, which are CT, CS, CW, C1P, C2T, CP, C5T, and C6P. To calculate the value of these unknown unit exergy costs, three more cost-balance equations are required. These additional equations can be obtained from the thermal and mechanical junctions and boundary of the plant. Thermal exergy junction Ėx,23T+Ėx,55T+Ėx,65TĖx,24T+Ėx,51TĖx,52T+Ėx,221TĖx,222TCT=Ėx,23T+Ėx,55T+Ėx,65TĖx,24TC2T+Ėx,51TĖx,52T+Ėx,221TĖx,222TC5TE22 Mechanical exergy junction Ėx,1PĖx,2P+Ėx,53PĖx,54P+Ėx,63PĖx,64PCP=Ėx,1PĖx,2PC1P+Ėx,53PĖx,54P+Ėx,63PĖx,64PC6PE23 Boundary Ėx,1T+Ėx,51T+Ėx,63TĖx,26T+Ėx,221TĖx,222TCT+Ėx,1P+Ėx,51P+Ėx,63PĖx,26P+Ėx,221PĖx,222PCP+ToṠ1+Ṡ51+Ṡ63Ṡ26+Ṡ221Ṡ222+Q̇boun/ToCS+Żboun=0E24 In Table 3, initial investments, the annuities including the maintenance cost, and the corresponding monetary flow rates for each component are given. The cost flow rates corresponding to a component’s exergy flow rates at 100% load condition are given in Table 4. The same sign convention for the cost flow rates related to products and resources was used as the case of exergy balances shown in Table 2. The lost cost due to the entropy production in a component is consumed cost. The fact that the sum of the cost flow rates of each component in the plant becomes zero, as verified in Table 4, shows that all the cost balances for the components are satisfied. ComponentInitial investment cost (US$106)
Annualized cost
(×US$103/year) Monetary flow rate (US$/h)
Compressor36.9764744.997628.712
Combustor2.169278.34036.880
Gas turbine29.2133748.799496.716
Fuel preheater7.487960.780127.303
Steam injector14.7871897.562251.427
Total90.54211,630.4781531.038

### Table 3.

Initial investments, annualized costs, and corresponding monetary flow rates of each component in the gas-turbine power plant.

ComponentĊW(US$/h)Ċo(US$/h)ĊT(US$/h)ĊP(US$/h)ĊS(US$/h)Ż(US$/h)
Compressor−17732.470.004217.9115,071.00−927.63−628.71
Combustor0.00−15861.9628238.85341.28−12681.19−36.88
Gas turbine38419.490.00−21068.79−16066.19−787.79−496.72
Fuel preheater0.000.00154.920.00−27.52−127.30
Steam injector−1208.410.00569.65954.76−64.44−251.43
Boundary0.000.00−12112.54−300.8514488.57−2075.18
Total19478.61−15861.960.000.000.00−3616.22

### Table 4.

Cost flow rates of various exergies and neg-entropy of each component in the gas-turbine power plant at 100% load condition.

The overall cost-balance equation for the power system is simply obtained by summing Eqs. (17)(24).

ĖxCHECo+i=1nŻi=Ėx,1W+Ėx,3W+Ėx,6WCWE25

From the above equation, the unit cost of electricity for the gas-turbine power system is given as [1]

CW=Coηe1+ZiCoĖxCHEE26

The production cost depends on fuel cost and the exergetic efficiency of the system, and is affected by the ratio of the monetary flow rate of non-fuel items to the monetary flow rate of fuel. With the unit cost of fuel, Co = 5.0 $/GJ, an exergetic efficiency of the gas-turbine power plant, 0.341, and a value of the ratio of the monetary flow rate of non-fuel items to the monetary flow rate of fuel, 0.22, the unit cost of electricity estimated from Eq. (26) is approximately 17.97$/GJ. However, one should solve Eqs. (17)(24) simultaneously to obtain the unit cost of electricity and the lost cost flow rate occurred in each component.

## 4. Organic Rankine cycle power plant using heat as fuel

A schematic of the 20-kW ocean thermal energy conversion (OTEC) plant [20] operated by organic Rankine cycle, which is considered to apply MOPSA method, is illustrated in Figure 2. Five main components exist in the system: the evaporator (1), turbine (2), condenser (3), receiver tank (4) and pump (5). The refrigerant stream is heated by a heat source in the evaporator, and then the refrigerant stream is divided into two streams. A portion of this stream is passed through the throttling valve and reaches the receiver tank, while the remaining part of the refrigerant stream leaving from evaporator is sent to turbine. A portion of the stream flowing to turbine is throttled and bypassed to turbine outlet. The “pipes” are introduced into the analysis as a component to consider the heat and pressure losses in the pipes and the exergy removal during the throttling processes. Refrigerant of R32 is used as a working fluid in the organic Rankine cycle. At the full load condition, the mass flow rate of the refrigerant is 3.62 kg/s. The warm sea water having mass flow rate of 86.99 kg/s is used as a heat source for the plant, while the cold sea water having mass flow rate of 44.85 kg/s is used as a heat sink for the plant. The reference temperature and pressure for the refrigerant R32 are −40°C and 177.60 kPa, respectively. For water, the reference point was taken as 0.01°C, the triple point of water.

### 4.1. Exergy-balance equations for the organic Rankine cycle power plant

The exergy-balance equations obtained using Eq. (1) for each component in the organic Rankine cycle plant shown in Figure 2 are as follows.

Evaporator

Ėx,102TĖx,103T+Ėx,102PĖx,103P+Ėx,201Ėx,202+ToṠ102Ṡ103+Ṡ201Ṡ202+Q̇1/To=0E27

Turbine

Ėx,104TĖx,105T+Ėx,104PĖx,105P+ToṠ104Ṡ105+Q̇2/To=Ėx,2WE28

Condenser

Ėx,106TĖx,107T+Ėx,106PĖx,107P+Ėx,301Ėx,302+ToṠ106Ṡ107+Ṡ301Ṡ302+Q̇3/To=0E29

Ėx,107T+Ėx,108TĖx,109T+Ėx,107P+Ėx,108TĖx,109P+ToṠ107+Ṡ108Ṡ109+Q̇4/To=0E30

Pump

Ėx,109TĖx,102T+Ėx,109PĖx,102P+ToṠ109Ṡ102+Q̇5/To=Ėx,5WE31

Pipes

αĖx,103TĖx,104T+Ėx,105TĖx,106T+1αĖx,103TĖx,108T+αĖx,103PĖx,104P+Ėx,105PĖx,106P+1αĖx,103PĖx,108P+ToṠ103+Ṡ105Ṡ104Ṡ106Ṡ108+Q̇pipes/To=0E32

Boundary

Ėx,201Ėx,202Ėx,301Ėx,302ToṠ201Ṡ202+Ṡ301Ṡ302+Q̇boun/To=0E33

The α term given in Eq. (32) is the ratio of the bypass streams from state 103 to 108. The value of the α term can be calculated by applying the mass and energy conservation equations to the receiver tank. The stream bypassed from state 103 to 105 may be neglected. An example of exergy calculation for the organic Rankine cycle plant using a stream of warm water at 28°C as a heat source to the evaporator [20] is shown in Table 5. As mentioned in the previous section, a positive value of exergy flow rate represents “product,” while a negative value of exergy flow rate indicates “fuel.” The last two columns clearly indicate that the electricity comes from expenditure of heat input.

ComponentRefrigerantWater streamIrreversibility rateHeat transfer rateWork input/output rate
Evaporator224.59−233.2117.52−8.90
Turbine−24.243.310.8320.10
Condenser−178.00171.265.221.51
Pump1.501.69−0.15−3.04
Pipes−21.3320.311.02
Boundary61.95−36.36−25.58
Total0.000.000.00−17.0617.06

### Table 5.

Exergy balances for each component in the organic Rankine cycle plant (Unit: kW) [20].

### 4.2. Cost-balance equations for the organic Rankine cycle power plant

By assigning a unit cost to every thermal exergy of the refrigerant stream (C1T, C2T, C3T, and CT), mechanical exergy for the refrigerant stream (CP), cold water (C3), neg-entropy (Cs), and electricity (CW), the cost-balance equations corresponding to the exergy-balance equations which are Eqs. (27)(33) are given as follows. When the cost-balance equation is applied to a specific component, one may assign a unit cost to its main product, which is represented by a Gothic letter.

Evaporator

Ėx,102TĖx,103TC1T+Ėx,102PĖx,103PCP+Ėx,201Ėx,202C2+ToṠ102Ṡ103+Ṡ201Ṡ202+Q̇1/ToCS+Ż1=0E34

Turbine

Ėx,104TĖx,105TCT+Ėx,104PĖx,105PCP+ToṠ104Ṡ105+Q̇2/ToCS+Ż2=Ėx,2WCWE35

Condenser

Ėx,106TĖx,107TCT+Ėx,106PĖx,107PCP+Ėx,301Ėx,302C3+ToṠ106Ṡ107+Ṡ301Ṡ302+Q̇3/ToCS+Ż3=0E36

Ėx,107T+Ėx,108TĖx,109TC2T+Ėx,107P+Ėx,108PĖx,109PCP+ToṠ107+Ṡ108Ṡ109+Q̇4/ToCS+Ż4=0E37

Pump

Ėx,109TĖx,102TCT+Ėx,109PĖx,102PCP+ToṠ109Ṡ102+Q̇5/ToCS+Ż5=Ėx,5WCWE38

Pipes

αĖx,103TĖx,104T+Ėx,105TĖx,106T+1αĖx,103TĖx,108TC3T+αĖx,103PĖx,104P+Ėx,105PĖx,106P+1αĖx,103PĖx,108PCP+ToṠ103+Ṡ105Ṡ104Ṡ106Ṡ108+Q̇pipes/ToCs+Żpipes=0E39

Boundary

Ėx,201Ėx,202C2Ėx,301Ėx,302C3ToṠ201Ṡ202+Ṡ301Ṡ302+Q̇boun/ToCS+Żboun=0E40

Seven cost-balance equations for the five components of the plant, pipes, and the boundary were derived with eight unknown unit exergy costs of C1T, C2T, C3T, CT, CP, C3, CS, and CW. We can obtain an additional cost-balance equation for the junction of thermal exergy of the refrigerant stream.

Thermal junction

Ėx,102TĖx,103TC1T+Ėx,107T+Ėx,108TĖx,109TC2T+Ėx,103T+Ėx,105TĖx,104TĖx,106TĖx,108TC3T=Ėx,102T+Ėx,105T+Ėx,107TĖx,104TĖx,106TĖx,109TCTE41

With Eq. (41), we have all the necessary cost-balance equations to calculate the unit cost of all exergies (C1T, C2T, C3T, CT, and C3, neg-entropy (Cs) and a product (electricity, CW) by input (given) of thermal energy (C2) to the evaporator. The overall cost-balance equation for the Rankine power plant can be obtained by summing Eqs. (34)(41), which is given by

absĊH+Żk+Żboun=ĖxWCWE42

where ĊH=Q̇kCSis the net cost flow rate due to the heat transfer to/from the organic Rankine cycle plant. The term Żbounin Eq. (42) may represent the cost flow rate related to the construction of the plant [6]. Rewriting Eq. (42), we have the unit cost of electricity from the Rankine cycle power plant.

CW=absĊH+Żk+Żboun/ĖxWE43

where ĖxWis the net electricity obtained from the organic Rankine cycle plant and abs denotes the absolute value of the quantity in parentheses.

Figure 3 shows that the unit cost of electricity from the organic Rankine cycle plant and the net cost flow rate due to the heat transfer rate to the plant vary depending on the unit cost of warm water in the evaporator, C2, appeared in Eq. (34). As the unit cost of warm water increases, the net cost flow rate due to heat transfer to the plant decreases while the unit cost of electricity increases. The cross point between the line for the unit cost of electricity and the line for the total cost flow rate due to heat transfer determines unit cost of electricity. The unit cost of electricity and the net cost flow rate due to heat transfer for a case whose detailed calculation results shown in Table 6 are $0.205 and −$0.941/kWh, respectively. The value of the unit cost C2 appeared in the cost balance equation, Eq. (34), is approximately $0.117/kWh for this particular case, which may be considered as a fictional one. ComponentĊTĊPĊSĊHĊWĊwswĊdswŻk Evaporator27.502−0.0260.967−0.491−27.285−0.666 Turbine−3.101−0.6130.1830.0464.126−0.640 Condenser−23.569−0.0040.2880.08423.867−0.666 Receiver tank0.0210.012−0.6450.784−0.172 Pump0.0790.6780.093−0.008−0.624−0.218 Pipes−0.932−0.0481.1210.056−0.198 Boundary−2.006−1.41227.285−23.867 Total−0.0000.000−0.000−0.9413.502−2.561 ### Table 6. Cost flow rates of various exergies, lost work rate due to heat transfer, heat transfer rate, and work input/out rate of each component in the organic Rankine cycle plant (Unit:$/h).

Using hot water from an incinerator plant as the heat source, C2=$0.117/kWh, C2=$0.055/kWh [20].

ComponentInitial investment ($)Annualized cost ($/year)Monetary flow rate ($/h) Compressor5000393.40.0918 Condenser4000314.80.0735 TXV2000157.40.0367 Evaporator + Suction line6000472.10.1102 Total17,0001337.70.3122 ### Table 8. Initial investments, annualized costs, and corresponding monetary flow rates of each component in air conditioning system with a 120-kW capacity. The cost flow rates of various exergies and irreversibility rate at each component in the air conditioning system at the normal operation are shown in Table 9. The sign convention for the cost flow rates is that minus and plus signs indicate the resource and product cost flow rates, respectively. Erroneously, reverse sign convention was used in their study on the thermoeconomic analysis of ground-source heat pump systems [25]. The lost cost flow rate due to the entropy generation appears as consumed cost in the evaporator; on the other hand, it appears as production cost in other components. The unit cost of heat delivered to the room or the unit cost of the cooling capacity is estimated to be 0.0344$/kWh by solving the four cost-balance equations given from Eqs. (53) to (59) with unit cost of electricity of 0.120 $/kWh. The unit cost of thermal and mechanical exergies and the irreversibility are CT = 0.1948, CP = 0.1636, and CS = 0.0187$/kWh at the normal operation. It is noted that the unit cost of heat CH can be obtained from Eq. (60) directly with known values of CW, COP (β) and the ratio of the monetary flow rate of non-fuel items to the monetary flow rate of input (electricity). Table 9 confirms that cost-balance balance is satisfied for all components and the overall system.

ComponentĊTĊPĊHĊWĊSŻ
Compressor0.035063.73914−3.85200.16960−0.09180
Condenser−1.74352−0.014731.83175−0.07350
TXV3.56302−3.595130.06881−0.03670
Evaporator+ Suction line−1.85456−0.129284.16420−2.07016−0.11020
Total0.00.04.16420−3.85200.0−0.3122

Cost flow rates of various exergies and irreversibility of each component in the air conditioning unit at normal operation (Unit: $/h). The unit cost of irreversibility, CS is 0.00187$/kWh and the unit cost of cooling capacity, CH is 0.0344$/kWh Rewriting Eq. (59), we have [25] CH=CWβ1+ŻkCWĖx,compWE60 where β is the COP of the air conditioning units. Equation (60) provides the unit cost of cooling capacity as 0.0344$/kWh with a unit cost of electricity of 0.120 $/kWh, β of 3.77, and a value of 0.081 for the ratio of the monetary flow rate of non-fuel items to the monetary flow rate of consumed electricity. Advertisement ## 6. Conclusions Explicit equations to obtain the unit cost of products from gas-turbine power plant and organic Rankin cycle plant operating by heat source as fuel and the unit cost heat for refrigeration system using the modified-productive structure analysis (MOPSA) method were obtained. MOPSA method provides two basic equations for exergy-costing method: one is a general exergy-balance equation and the other is cost-balance equation, which can be applicable to any components in power plant or refrigeration system. Exergy-balance equations can be obtained for each component and junction. The cost-balance equation corresponding to the exergy-balance equation can be obtained by assigning a unit cost to the principal product of each component. The overall exergy-costing equation to estimate the unit cost of product from the power plant and refrigeration system is obtained by summing up all the cost-balance equations for each component, junctions, and boundary of the system. However, one should solve the cost-balance equations for the components, junctions, and system boundary simultaneously to obtain the lost cost flow rate due to the entropy generation in each component. It should be noted that the lost work rate due to the entropy generation plays as “product” in the exergy-balance of the component, while the lost cost flow rate plays as “consumed resources” in the cost-balance equation. This concept is very important in the research area of thermoeconomic diagnosis [18, 26, 27, 28]. ## Nomenclature  C unit cost of exergy ($/kJ) Ci initial investment cost ($) CH unit cost of heat ($/kWh) Co unit cost of fuel ($/kWh) CS unit cost of lost work due to the entropy generation ($/kWh) CW unit cost of electricity ($/kWh) C ̇ monetary flow rate ($/h) COP coefficient of performance CRF capital recovery factor ex exergy per mass E ̇ x exergy flow rate (kW) h enthalpy per mass H ̇ enthalpy flow rate (kW) i interest rate I ̇ irreversibility rate (kW) m ̇ mass flow rate PW amortization cost PWF(i,n) present worth factor Q ̇ cv heat transfer rate (kW) S ̇ entropy flow rate (kW/K) Sn salvage value (KRW) To ambient temperature (°C) W ̇ cv work production rate (kW) Z ̇ k capital cost flow rate of unit k (\$/h) β coefficient of performance δ operating hours ηe exergy efficiency ϕ k maintenance factor of unit k a air stream comp compressor con condenser env environment evap evaporator H heat k kth component r refrigerant stream ref. reference condition room room s entropy sl suction line W work or electricity a air stream CHE chemical exergy H heat P mechanical exergy r refrigerant stream T thermal exergy W work or electricity

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Ho-Young Kwak and Cuneyt Uysal (June 6th 2018). Exergetic Costs for Thermal Systems, Application of Exergy, Tolga Taner, IntechOpen, DOI: 10.5772/intechopen.73089. Available from:

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