Thermoeconomic Analysis of 200kw Phosphoric Acid Fule Cell Plant

7/27/2019 Thermoeconomic Analysis of 200kw Phosphoric Acid Fule Cell Plant

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Exergetic and thermoeconomic analysis of a 200-kW phosphoric acidfuel cell plant

Ho-Young Kwaka,*, Hyun-Soo Leea, Jung-Yeul Junga, Jin-Seok Jeonb, Dal-Ryung Parkb

aMechanical Engineering Department, Chung-Ang University, 221, Huksuk-Dong, Dongjak-Ku, Seoul 156-756, South KoreabR&D Center, Korea Gas Corporation, A nsan 425-790, South Korea

Received 9 February 2002; revised 9 February 2002; accepted 7 April 2004; available online 4 May 2004

Abstract

Exergetic and thermoeconomic analysis were performed for a 200-kW phosphoric acid fuel cell plant which offers many advantages for

co-generation in the aspect of high electrical efficiency and low emission. This analytical study was based on the data obtained by in-field

measurement of PC25C fuel cell plant to find whether this system is viable economically. For 100% load condition, the electrical efficiency

obtained, 43.7% turned out to be much better than that for the 1000-kW gas turbine co-generation plant. However, the calculated unit cost of

electricity with the initial investment cost per power of fuel cell plant of 3000 $/kW, 0.068 $/kWh turned out to be 125% higher than the cost

obtained for the 1000-kW gas turbine co-generation plant. This fuel cell system may be viable economically when the initial investment cost

per power is reduced to the level of the gas turbine co-generation plant of 1500 $/kW.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Exergy analysis; Fuel cell plant; Modified Productive structure; Phosphoric acid fuel cell; Thermoeconomic analysis

1. Introduction

Exergetic analysis permits to predict the performance of

energy systems as well as the efficiency of each component

of the systems. On the other hand, thermoeconomic analysis

provides a tool to estimate the unit cost of products properly

and the monetary loss associated with the entropy

generation in the components of the system. One of the

merits of the fuel cell system is that considerable entropy

generation occurred during combustion process inevitablyat gas burner can be saved by reformer where endothermic

reaction takes place, even though only 40% of the chemical

exergy of natural gas is utilized to produce electricity at fuel

cell stack and the life time of the system is shorter [1].

In this study, exergetic and thermoeconomic analysis

were performed for a 200-kW phosphoric acid fuel cell

(PAFC) plants which offers many advantages for co-gen-

eration in the aspect of high electrical efficiency and low

emissions [2] to find whether the system is

viable economically. This system analysis based on the

detailed conservation laws employed the data obtained by

the in-field measurement of PC25C fuel cell power plant

(ONSI corporation), installed and operated at Korea Gas

Corporation.

The exergy-balance equation developed by Oh et al. [3]

and the corresponding cost-balance equation by Kim et al.

[4] were utilized in this analysis. Detail computational

works on the estimation of property values were done by

using the polynomial for gases [5] and the equations

suggested by International Formulation Committee for

water and steam [6]. For hydrocarbon fuels, BenedictWebb Rubin equation of state [7] was utilized. Rearrange-

ment of the components depending on their function of the

PAFC system was done to apply the developed cost-balance

equation with integrated exergy stream [8] to the system

concerned. The performance and the unit cost of products of

the system were evaluated at various loads.

For 100% load condition, the electrical efficiency of the

PAFC system was about 43.7%, which turned out to be

much better than that for the 1000-kW gas turbine co-

generation plant [4]. However, the calculated unit cost of

electricity with the initial investment cost of fuel cell

plant of 3000 $/kW, 0.068 $/kWh turned out to be 125%

higher than the cost obtained for the gas turbine co-genera-tion plant.

0016-2361/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2004.04.002

Fuel 83 (2004) 20872094www.fuelfirst.com

* Corresponding author. Tel.: 82-28205278; fax: 82-28267464.

E-mail address: [email protected] (H.-Y. Kwak).
http://www.fuelfirst.com/http://www.fuelfirst.com/


2/8

2. Cost-balance equation based on modified productive

structure analysis

A general exergy-balance equation that is applicable to

any component of thermal system may be formulated by

utilizing the first and second law of thermodynamics [3].

With some modification on the exergy-balance equation for

the non-adiabatic components to account the exergy losses

due to heat transfer, the general exergy-balance equation

may be written as with integrated exergy stream

_ECHEx

Xinput

_EBQx;i 2

Xoutput

_EBQx;j

0@

1A X

inlet

_Ex;i 2X

outlet

_Ex;j

!

To Xinlet

_Si 2 Xoutlet

_Sj _QCV=T ! _EW 1

where _E and _S denote the flow rate of exergy and entropy,

respectively, and _QCV in the fifth term denotes the heat

transfer interaction between a component and environment.

The superscripts CHE, BQ and W denote chemical exergy,

steam and work (or electricity), respectively.

Assigning a unit exergy cost to each decomposed exergy

system, the cost-balance equation corresponding to the

exergy-balance equation given in Eq. (1) may be written as

_ECHEx Co

Xinput

_EBQx;i 2

Xoutput

_EBQx;j

0

@

1

ACBQ

Xinlet

_Ex;i2X

outlet

_Ex;j

!CE

ToXinlet

_Si2X

outlet

_Sj2 _QCV=To

!CS _Zk _E

WCW 2

where Co;CBQ;CE;CS and CW are the unit cost of fuel,

steam, gas exergy and negentropy, and electricity, respect-

ively. The term _Zk includes all financial charges associated

with owning and operating the kth plant component. Eqs. (1)

and (2) are two basic equations used in this analysis. We call

the exergy-costing method based on these equations as

modified productive structure analysis (MOPSA) one in the

sense that the cost-balance equation given in Eq. (2) yields

the productive structure of thermal system at hand [4],

which has been suggested and developed by Lozano and

Valero [9] and Torres et al. [10].

3. Cost equation for plant component

All costs due to owing and operating a plant depend on

the type of financing, required capital, expected life of a

component, etc. The annualized (levelized) cost method of

Moran [11] was employed in this study.

The amortization cost for a particular plant component

may be written as present worth (PW)

PW Ci 2 SnPWFi; n 3

where Ci is initial investment cost and PWFi; n is the PWfactor. The PW of the component may be converted to

the annualized cost by using the capital recovery factor

CRFi; n; i.e.

_C$=year PW CRFi; n 4

Dividing the levelized cost by 8000 annual operating hours,

we obtain the following capital cost for the kth component

of the plant.

_Zk fk _Ck=3600 8000 5

The maintenance cost is taken into consideration through

the factor of fk 1:06 for each plant component whose

expected life is assumed to be 15 years.

4. System descrition for 200-kW phosphoric acid

fuel cell plant

A schematic of a 200-kW phosphoric acid fuel cell

(PAFC) is given in Fig. 1, and shows every state point

which we accounted for in this analysis. Every state in the

plant is described by three digits. The first digit indicates

a specific fluid stream (0 for natural gas, 1 for air, 2 for

hydrogen-rich gas, 3 for steam, 4 for water and 5 for flue

gas), and the second digit indicates each component in the

plant (1 for the first heat exchanger [HTX1], 2 for CO

shift converter [COSC], 3 for reformer [RFM], 4 for gasburner [GASB], 5 for the air preheater [HTX2], 6 for fuel

cell stack [FCS], 7 for the third heat exchanger [HTX3], 8

for steam/water separator [SWS] and 9 for the fourth heat

exchanger [HTX4]). The final digit indicates the inlet (1)

and outlet (2) stream of working fluids at each component.

The fuel cell plant consists of fuel process system

([HTX1], [COSC], [RFM], and [GASB]) which convertsnatural gas into hydrogen-rich gas, power system ([FCS])

which converts chemical exergy of gas into electricity by

electrochemical process and thermal management system

([SWS], [HTX4], and water treatment system [WTS]). At

full load condition, the air to [GASB] and the fuel flow

rate to the system are approximately 248 and 35 kg/h,respectively. The air flow rate to the cathode in [FCS] at

the full load is about 678 kg/h. Part load condition canbe achieved by controlling the air flow rate to [GASC]

and to the cathode in [FCS] and the fuel flow rate to

[RFM]. More detailed description including the first law

of thermodynamics for the major components is as

follows.

4.1. Fuel process system

Hydrogen-rich gas needed for the electrochemical

reaction in [FCS] can be produced from the natural gas

(primary CH4) via the reforming process of steam from[HTX1]. The possible reactions in the reforming process

H.-Y. Kwak et al. / Fuel 83 (2004) 208720942088


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[12] are given as

CnHm 2nH2O! nCO2 2n 1

2m

H2 6

CnHm nH2O! nCO n 1

2m

H2 7

The chemical reaction in [RFM] including these endother-

mic reactions may be written as

aCajHbj bCakHbk cCalHbl dCamHbm yH2O

!fnatCO2 12fnatCO 1 fnat 1

2nbt H2

y2 1 fnat

H2O 8

where aaj bak cal dam nat;

abj bbk cbl dbm nbt;

and f is the ratio of the reaction given in Eq. (6) to the

reaction given in Eq. (7), which may be determined from the

heat balance for [RFM] and [GASB]. The value of f which

affects the outlet temperature of the hydrogen-rich gas

stream in [HTX1] is about 0.7950.80. Applying the first

law to [RFM], we obtain

QRFM QEXRFM hRP;RFM 9

where hRP;RFM is the enthalpy of combustion for the reaction

given in Eq. (8), which is given byhRP;RFM

Xproduct

neh0f Dhe2

Xreactant

nih0f Dhi

fnath0f CO2 12fnat

h0f CO21fnath

0f H2O

2ah0f Caj Hbj2bh0f CakHbk

2ch0f Cal Hbl

2dh0f Cam Hbm fnatDhCO2 12fnatD

hCO

n1fnat

1

2nbtDhH2 y21fnat

DhH2O

oTe;RFM

2 aDhCaj HbjbDhCakHbk

ncDhCa

l

Hbl

dDhCam

Hbm

yDhH2OoTi;RFM

10

where h0f is the enthalpy of formation and Dh is the sensible

enthalpy. The heat transfer rates, QRFM and QEXRFM are heat

exchange with environment and gas burner, respectively.

The reformed hydrogen-rich gas is cooled by the natural

gas and steam in [HTX1], and the remaining CO gas from

[RFM] is converted to CO2 in [COSC] through the following

reaction. These gases are fed into the anode in [FCS].

fnatCO2 12fnatCO 1 fnat 1

2nbt

H2

y2 1 fnatH2O!pCO nat2pCO2

2nat2p 12

nbt

H2 y2 2nat pH2O 11

Fig. 1. Schematic of 200-kW phosphoric acid fuel cells (PAFC) system (modified from Ref. [12]).

H.-Y. Kwak et al. / Fuel 83 (2004) 20872094 2089


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The concentration of CO gas leaving [COSC] may be

estimated by the following equation

CO CO2H2H2O

KPT 12

where [ ] in Eq. (12) denotes gas concentration and KPT is

the equilibrium constant for the reaction, CO H2O!

CO2 H2 [13].The first law in [COSC] is given by

aDhCaj HbjbDhCakHbk

cDhCal HbldDhCam Hbm Ti;COSC

QCOSC hRP;COSC aDhCaj HbjbDhCakHbk

cDhCal HbldDhCam Hbm Te;COSC 13

where QCOSC is the heat exchange with environment and thehRP;COSC is the enthalpy of combustion for the reaction given

in Eq. (11). That is

hRP;COSC p212fnath0f CO2h

0f CO2

h0f H2O

pDhCO nat2pDhCO2

n 2nat

1

2nbt2p

DhH2 y22natp

DhH2O

oTe;COSC

2 fnatDhCO2

n

12fnatDhCO 1fnat1

2nbt

DhH2

y21fDhH2O

oTi;COSC

14

The heat required for the endothermic reactions in [RFM] issupplied from the combustion process in [GASB]. The

unconsumed hydrogen-rich gas after the anodic reaction in

[FCS] with additional natural gas from line are burned with

heated airfrom [HTX2]. This combustion process in [GASB]

may be described as

a0Caj Hbj b

0CakHbk c0Cal Hbl d

0Cam Hbm ntoO2

3:728ntoN2 0:044ntoArnwv y22natpH2O

eH2 nat2pCO2 pCO!natn0atCO2

12 nbtn0btnwv y

22g

H2O

nto g2natn0at2

1

4nbtn

0bt

O2

3:728ntoN2 0:044ntoAr 15

where

n0at a

0aj b0akc

0al d0am

n0bt a

0bj b0bkc

0bl d0bm

e 2nat1

2

nbt2p22g

nto ntoH ntoG

nwv nwvH nwvG

The first law in [GASB] may be written as

QGASB2QEXRFM hRP;GASB 16

where QGASB is the heat exchanger with environment andhRP;GASB is the enthalpy of combustion for the reaction given

in Eq. (15). This is given by

hRP;GASB n0atph

0f CO2

1

2nbtn

0bt2nat22g2p

h0f H2O2a0h0f Caj Hbj

2b0h0f CakHbk

2c0h0f Cal Hbl

2d0h0f Cam Hbm natn

0atDhCO2

n

1

2

nbtn0btnwv y22g DhH2O

nto g2natn0at2

1

4nbtn

0bt

DhO2

3:728ntoDhN2 0:044ntoDhArgTe;GASB

2 ntoDhO2 3:728ntoDhN2 0:044ntoD

hAr

nnwv y22natpDhH2O eD

hH2

nat2pDhCO2 pDhCOa

0DhCaj Hbj

2b0h0f CakHbk

2c0h0f Cal Hbl

2d0h0f Cam Hbm

oTi;GASB

17

4.2. Power system

The PAFC stack, which has been used in co-generationsystem produces electricity and heat from the reaction of

hydrogen and oxygen. The primary reaction in [FCS] are

given as

Anode : 2H2 ! 4H 4e2 18

Cathode : O2 4H 4e2! 2H2O 19

So that the overall reaction is as

2H2 O2 ! 2H2O HEAT 20

Assuming that only 2 g kmol among the hydrogen gas from

[COSC] participates in the above anodic reaction, all the

gases such as N2 and O2 escaped through cathode and anode

in [FCS] may be written as

pCO nat2pCO2 2nat 1

2nbt2p2 2g

H2

y2 2nat pH2O anode ntoH3 2 gO2

3:728ntoH3N2 0:044ntoH3Ar nwvH3H2O 2g

H2O cathode 21

The value ofg is to be determined by the input flow rate offuel and air to the system.

H.-Y. Kwak et al. / Fuel 83 (2004) 208720942090


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The electricity produced from the above reaction is given

as

WT 131:74ghFCS kJ=kmol 22

where hFCS is the efficiency of the FCS.

The heat release inside components due to condensation

or any other chemical reaction described in Eq. (20) wastreated as a kind of water (or steam) exergy in this analysis

because the heat released contributes increases the water

(or steam) exergy.

5. Cost-balance equations

In the fuel cell plant, the species of the fluid streams

change after reforming or any other chemical processes. So,it is convenient to divide all the working fluids as gas and

water (or steam) stream simply. Also it is better to use

integrated exergy without decomposing the exergy stream

into thermal and mechanical exergy. In this case, the concept

of junction and branch related to thermal and mechanical

exergy is no longer needed so that the number of unknowns

for the unit exergy costs are considerably reduced. Therefore,

the cost-balance equation given in Eq. (2) should be applied

to an appropriate component or a group of component

depending on the function of its principal product in the

energy system. For example, all the components in the fuelcell plant may be rearranged into four groups of components

anda systemboundaryto provide sufficientbut notredundant

cost-balance equations. Thegroups of components are(1) the

first heat exchanger, and CO shift converter, reformer, gas

burner and air preheater for the fuel process system (2) fuel

cell stack and the third heat exchanger for power system (3)

steam/water separator, the fourth heat exchanger and system

boundary for the water treatment system. The cost-balance

equations for those groups of components yield the unit cost

of each exergy. These are unit costs of gas stream, CE;

electricity, CW; and steam exergy, CBQ: All the cost-balance

equations formulated for fuel cell plant are as follows.

(1) Fuel process system ([HTX1], [COSC], [GASB],

[RFM], and [HTX2])

_ELHV;2 _ELHV;3 _ELHV;4Co _Ex;011 _Ex;041 _Ex;141

_Ex;151 _Ex;2412 _Ex;5522 _Ex;222CE _Ex;311CBQ

_ZHTX1 _ZCOSC _ZGASB _ZRFM _ZHTX2 0 23

(2) Power system ([FCS] and [HTX3])

_ELHV;6Co _Ex;171 _Ex;2612 _Ex;5722 _Ex;262CE

_

Ex;4612

_

Ex;462CBQ_

ZFCS_

ZHTX3_

EWCW

24

(3) Water treatment system ([SWS], [HTX4], [WTS], and

system boundary)

_Ex;5912 _Ex;592CE _Ex;481 _Ex;485 _Ex;4912 _Ex;382

2_Ex;3842 _Ex;4612 _Ex;492CBQ _ZSWS _ZHTX4

_ZWTS 0 25

The cost structure of the thermal system turned out to be

dependent on the chosen level of aggregation that specifies

the subsystems [10,14]. In this study, the cost-balance

equations for the PAFC system were formulated based on

the lowest level of aggregation, which are represented by

Eqs. (23)(25) because the unit cost of products does not

Table 1

Property values and enthalpy, entropy and exergy at various state points in

the PAFC system for the case of 100% load condition

State _m (kg/h) T (K) P (kPa) H (kJ/h) S (kJ/h) Ex (kJ/h)

011 34.24 288.15 1 01.30 2697.29 22.38 0.00012 34.24 723.15 101.30 39,785.03 79.76 16,814.16021 34.24 5 73.15 101.30 23,338.37 54.35 7690.43022 34.24 723.15 101.30 39,785.03 79.76 16,814.16041 0.64 288.15 101.30 212.97 2 .04 0.00141 13.04 298.15 101.30 0.00 2.13 2.24143 234.92 703.15 101.30 99,146.45 274.32 38,957.52151 234.92 298.15 101.30 0.00 38.30 40.37152 234.92 703.15 101.30 99,146.45 247.32 38,957.52

161 677.63 423.15 101.30 86,268.37 352.06 16,780.22171 677.63 298.15 101.30 0.00 110.36 116.31172 677.63 424.96 101.30 87,413.64 354.57 17,160.93211 135.35 823.15 101.30 117,816.25 348.71 44,321.56212 135.35 343.08 101.30 15,296.24 141.25 1581.95221 135.35 343.08 101.30 15,296.24 141.25 1581.95222 135.35 463.15 101.30 60,934.39 242.92 14,184.01231 34.24 723.15 101.30 41,435.27 90.38 17,524.06232 135.35 823.15 101.30 120,344.03 352.37 45,701.97241 122.85 453.15 101.30 29,441.23 130.68 6607.83261 135.35 463.15 101.30 61,150.20 242.85 14,241.29262 122.85 453.15 101.30 29,441.23 130.68 6607.83311 101.10 443.15 790.20 279,916.86 673.96 85,858.42312 101.10 723.15 101.30 341,954.76 878.30 89,430.72331 101.10 723.15 101.30 341,954.76 878.30 89,430.73382 101.10 443.15 790.20 279,916.86 673.96 85,858.42384 216.18 443.15 792.00 598,540.33 1441.12 183,589.26

4101 101.10 353.15 792.00 33,771.20 107.75 3278.124102 100.63 323.15 792.00 21,131.57 70.82 1280.31461 387.32 443.15 790.20 278,565.29 790.86 51,333.92462 387.32 443.15 800.00 1,072,551.88 2580.65 329,592.61481 387.32 443.58 800.00 1,072,551.88 2580.65 329,592.61482 387.32 443.15 790.20 278,565.29 790.86 51,333.92483 101.00 323.15 792.00 21,141.31 71.08 831.41485 216.00 363.15 792.00 81,412.49 257.57 7558.24491 1212.00 316.15 101.30 218,258.32 742.05 6481.92492 1212.00 338.15 101.30 329,709.21 1082.79 19,749.98494 101.10 353.15 792.00 33,699.01 108.19 2693.08542 371.44 820.00 101.30 236,336.77 581.03 106,119.16551 371.44 820.00 101.30 236,336.77 581.03 106,119.16552 371.44 611.10 101.30 137,194.62 441.69 47,128.84562 689.39 463.15 101.30 134,195.42 542.05 31,186.85571 689.39 463.15 101.30 129,538.15 519.84 30,102.33572 689.39 352.15 101.30 42,125.09 304.14 4841.61

591 1060.83 442.82 101.30 175,184.06 804.79 37,481.20592 959.73 323.20 101.30 30,021.87 422.89 2365.09

H.-Y. Kwak et al. / F uel 83 (2004) 20872094 2091


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depend on the level of aggregation crucially. The overall

cost-balance equation for the PAFC system, which may be

obtained from the first principle in the thermoeconomics

[11], is given by

_ECHE

xC

oX _Z

ic _EW

xC

W _EBQ

xC

BQ26

The calculated unit cost of products should satisfy the above

equation.

6. Computer program

A computer program for the exergetic and thermoeco-

nomic analyses of a 200-kW PAFC plant has been

developed. The program was designed to use the following

input data.

(a) Standard pressure P0 and temperature T0;

(b) Fuel compositions and its mass flow rate to the plant,

(c) Air composition, relative humidity and its mass flow

rate,

(d) Pressure (kPa) and temperature (K) for every fluid

streams at the inlet and outlet of each component

(e) Fuel exergy cost and initial investment for each

component.

Using these input data, one can calculate the number of

moles produced and the corresponding enthalpy of combus-

tion in the various chemical reactions, enthalpy and entropy

for fluid streams at various state points. The temperature ofone of the outlet streams in heat exchangers was calculated

by the heat balance equation. Also the outlet temperature ofthe hydrogen-rich gas in the [COSC] was calculated by

the first law. For the case of mixing of gas streams, the final

gas temperature was also estimated by the energy

conservation.

The net flow rate of various exergy and entropy, the

exergy efficiency of the components and the lost exergy

occurred in each component were then calculated by using

these property values obtained. Once exergy-balances for

the components were established, the unit cost of various

exergies and products were calculated by solving the cost-

balance equations for the group of componentssimultaneously.

7. Results and discussions

Table 1 gives details of thermal, mechanical exergy flow

rates and entropy flow rates at various state points shown in

Fig. 1. These flow rate values were calculated based on the

measured property values such as pressures and tempera-

tures and mass flow rates at the points. The enthalpy and

entropy of each non-interacting gas species were calculated

by using appropriate polynomials [5] fitted into the

thermophysical data in the JANAF Tables [15]. Also

the values of the physical properties such as enthalpy and

entropy for water and steam were evaluated by using the

equations suggested by the IFC (International Formulation

Committee) [6].

The net flow rates for the various exergies crossing the

boundaries of each physical component in the PAFC plant

for the case of 100% load condition are shown in Table 2.

The positive value of exergies indicate the exergy flow

rate of products while the negative values represent the

exergy flow rate of resource or fuel in the sense thatthe product of a component corresponds to the added

exergy while the resource to the consumed one [16] so

that the Table itself represents the productive structure

of the system. The entropy productions in each component

play as products in the exergy-balance equations.

Considerable entropy generation due to combustion

process in the [GASB] can be reduced by the heat transfer

to the [RFM] where an endothermic process takes

place for the reforming process of steam. In fact, the heat

transfer from the [GASB] to the [RFM] at full load

condition is about 490,000 kJ/h, which is about 87% of

LHV of the fuel consumed in the [GASB]. This is

remarkable exergy saving which can be possible in thePAFC plant in the sense that almost 50% chemical exergy

is destroyed during combustion process. The productive

structure for the PAFC, shown in Table 2 states

that electricity is produced by consuming fuel exergy.

Table 2

Exergy-balances at each group of components in the PAFC system for the case of 100% load condition

Component_

ELHV (kJ/h)_

Ex (kJ/h)_

EBQ

x (kJ/h)_

Elost

x (kJ/h)_

EW

x (kJ/h)

Fuel processing system 2266,544.4 54,335.4 285,858.4 298,067.4 0.0

Power system 2749,719.5 21434.9 2531,967.5 547,906.1 735,220.8

Water treatment system 0.0 232,740.1 530,795.6 2498,055.5 0.0

Table 3

Cost flow rate for each group of components in the PAFC system for the

case of 100% load condition

Group of components Co($/h)

CE($/h)

CBQ($/h)

CW($/h)

_ZK($/h)

Fuel processing system 22.186 6.519 20.670 0.0 23.659

Power system2

6.1482

0.1722

4.152 13.8042

3.336Water treatment system 0.0 23.928 4.143 0.0 20.215

H.-Y. Kwak et al. / Fuel 83 (2004) 208720942092


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On the other hand, the gas exergy for the reforming

process turns out to be produced by consuming steam

exergy from the [SWS]. It is inevitable, of course, that

some exergy is destructed during this process.The cost flow rates corresponding to the various exergy

flow rates at each group of components aggregated in the

plant in the case of 100% load condition are given in

Table 3. The unit cost value of primary fuel, 5 1023 $/

MJ ( 0.018 $/kWh) was used in this calculation.

However, only 60% of the chemical exergy of the

primary fuel is utilized in the fuel cell system so that

the unit cost of fuel increases to 8.2 1023 $/MJ in the

estimation of the unit cost of products. Same sign

convention for the cost flow rates related to the products

and resources was used as the case of the exergy-balances

shown in Table 2. The overall cost-balance for the system

indicates that the cost flow rates of products such aselectricity and steam are determined primary from the

input cost flow rates of fuel and initial investment. Note

that the steam plays a role as fuel rather than product

because the heat release in FCS is regarded as steam

exergy flow.

The unit cost of electricity and hot water (or steam) at

various loads estimated by the thermoeconomic analysis

of MOPSA are shown in Table 4. Calculation results

show that the unit costs of electricity increases

significantly at lower loads. However, the overall

exergetic efficiency rather increases at lower loads. The

reason is that almost same amount of heat with less fuelis recovered by water at part loads. The unit cost of

electricity at full load, 0.068 $/kWh ( 18.78 $/GJ) is

higher than that obtained from the 1000 kW gas turbine

co-generation plant, 0.054 $/kWh ( 15.06 $/GJ) [4].

Such higher unit cost of electricity reduces to 0.0526 $/

kWh ( 14.6 $/GJ), which is comparable to the unit cost

of electricity for the 1000-kW gas turbine co-generation

plant if the initial investment per power for the PAFC

system reduces to 1500 $/kW. The input cost flow rate

for the PAFC system, which is represented by the LHS

of Eq. (26) is about 15.62 $/h for 100% load, 14.02 $/h

for the 75% load and 11.86 $/h for 50% load condition.

On the other hand, the values of the RHS of Eq. (26)with the calculated unit cost of products at each load

condition are 15.29, 14.10 and 12.82 $/h, respectively, so

that our calculation results have maximum error of 8%.

Also the electrical and the overall exergetic efficiency

based on the LHV of the primary fuel fed into the system,which are about 43.7 and 55.0%, respectively, at the full

load are better than those from any other co-generation

plants so that the PAFC plant may be an excellent candidate

for a co-generation system if one overcomes long term

reliability of the system and the investment cost per power

becomes cheaper.

8. Conclusion

Thermoeconomic analysis with integrated exergy

stream of working fluids has been done to a 200-kW

PAFC plant. The calculated cost of electricity, based onthe primary fuel cost of 0.018 $/kWh, which is about

0.068 $/kWh is 125% higher than that obtained from the

1000-kW gas turbine co-generation plant. However, this

fuel cell system can be viable economically when the

initial investment cost per power is reduced to

1500 $/kW.

References

[1] Betts DA, Roan VP. Discussion and analysis of fuel gas utilization in a

phosphoric acid fuel cell engine during idle operation. In: AESVol.

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recovery enhancement and operational issues of a 200-kW fuel cell

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Table 4

Calculated production rate and the corresponding unit cost of electricity and water for the PAFC system at various load conditions with 15 years service of the

system

Load (%) _mfuel (kg/h) _ELHV;p=_ELHV;f (kJ/h) _EWx (kJ/h) Electrical

efficiency

Overall exergetic

efficiency

CW ($/GJ) CBQ ($/GJ)

50 18.96 576,681.2/930,911.8 367,610.4 39.5 59.5 30.38 8.82

75 27.72 836,131.5/1,361,165.1 551,415.6 40.5 54.3 22.80 8.30

100 34.88 1,016,263.9/1,681,899.4 735,220.8 55.0 55.0 18.78 7.80

_ELHV;p and _ELHV;f are the utilized chemical exergy flow of fuel and the lower heating value of the primary fuel flow. The unit cost of fuel Co employed in the

calculation is 8.2 $/GJ.

H.-Y. Kwak et al. / F uel 83 (2004) 20872094 2093


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H.-Y. Kwak et al. / Fuel 83 (2004) 208720942094

Documents

Thermoeconomic Analysis of 200kw Phosphoric Acid Fule Cell Plant