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Effects of gas recycle on performance of solid oxide fuel cell power systems
Energy 36 (2011) 1068e1075
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Energy journal homepage: www.elsevier.com/locate/energy
Effects of gas recycle on performance of solid oxide fuel cell power systems Junxi Jia a, *, Qiang Li a, Ming Luo a, Liming Wei b, Abuliti Abudula c a
College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China School of Electric and Electronic Information Engineering, Jilin Architectural and Civil Engineering Institute, Changchun 130021, China c North Japan New Energy Research Center, Hirosaki University, Aomori 030-0813, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 April 2010 Received in revised form 9 August 2010 Accepted 2 December 2010 Available online 6 January 2011
An energy analysis of solid oxide fuel cell (SOFC) power systems with gas recycles fed by natural gas is carried out. Simple SOFC system, SOFC power systems with anode and cathode gas recycle respectively and SOFC power system with both anode and cathode gas recycle are compared. Influences of reforming rate, air ratio and recycle ratio of electrode exhaust gas on performance of SOFC power systems are investigated. Net system electric efficiency and cogeneration efficiency of these power systems are given by a calculation model. Results show that internal reforming SOFC power system can achieve an electrical efficiency of more than 44% and a system cogeneration efficiency including waste heat recovery of 68%. For SOFC power system with anode gas recycle, an electrical efficiency is above 46% and a cogeneration efficiency of 88% is obtained. In the case of cathode gas recycle, an electrical efficiency and a cogeneration efficiency is more than 51% and 78% respectively. Although SOFC system with both anode and cathode gas is more complicated, the electrical efficiency of it is close to 52%. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Solid oxide fuel cell Power system Gas recycle Electric efficiency
1. Introduction Solid oxide fuel cell (SOFC) converts the chemical energy of fuel directly to electrical energy. It can achieve high electrical efficiency and is a highly environmentally benign method of electric power production. The operating temperature of SOFC is sufficiently high to provide necessary heat to support endothermic reforming of methane. SOFC is therefore more tolerant of fuel impurities and can operate using hydrogen and carbon monoxide fuels directly at the anode. It does not require costly external reformers or catalysts to produce hydrogen, and the use of internal reforming actually increases overall system efficiency. Previous work by Jia et al. [1,2] investigated the effects of two structural parameters such as thickness of electrolyte and pore size of electrolyte on performance of SOFC. Jia et al. [3] have compared the steady and transient characteristics of a tubular SOFC when operation parameters such as inlet fuel temperature, inlet oxidant temperature, and inlet oxidant flow rate are changed, respectively. The position of hot spot and the temperature gradients are calculated when the different operation parameters are changed. When SOFC works in a cell stack, the combustion zone should be considered. The work of Jia et al. [4] has examined the operation of a tubular
* Corresponding author. Tel./fax.: þ86 0451 82519305. E-mail address: [email protected] (J. Jia). 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.12.001
SOFC with combustion zone at the steady and transient operation states. These models mentioned above includes all the three polarizations: ohmic, activation and concentration polarization. The high operating temperature of SOFC gives good possibilities for cogeneration applications. There have been numerous models are developed to simulate performance of SOFC power systems [5e19], the features of these models are different. A simple solid oxide fuel cell system can be used for residential scales power applications. Bedringas et al. [5] have reported that a system electrical efficiency near 60% could be achieved for a SOFC system with external reforming. Chan et al. [6] present a discussion of simple SOFC system without gas turbine fed by hydrogen and methane, respectively and results shows both a H2-fed system and a CH4-fed system can achieve an electrical efficiency of more than 50%. Other models available in the literatures [7e18] focus on complicated hybrid SOFC and gas turbine power system. The works of literatures [7,8] examined effects of operating pressure, steam-to-carbon ration, and fuel flow rate on performance of SOFC-GT power systems. Refs [9e16] address a full and partial load analysis of hybrid SOFC-GT power plant. Electric efficiencies of these hybrid systems are high than 60% at design point and also very high at part load condition. Yi et al. [17] introduced a SOFC and intercooled gas turebine (SOFC-ICGT) hybrid cycle, and system electrical efficiency is even high than 75% when operating pressure is 50 bara and an excess air in the SOFC is low.
J. Jia et al. / Energy 36 (2011) 1068e1075
Fig. 1. SOFC power system with pre-reforming and internal reforming.
Prediction of transient performance of SOFC power systems is important for control purposes. Lin et al. [18] have developed a dynamic model of the hybrid SOFC-GT system to investigate the transient behavior during cold start. Murshed et al. [19] provides a dynamic model of planer solid oxide fuel cell system which include heat exchanger, reformer and after-burner. Many cogeneration system concepts[5e19] are conceivable with SOFC as mentioned above, however, anode gas recycling concept were found only in Refs[5,9,10,12],not discussed in detail and none of them are involved with cathode gas recycling concept. As few of the papers mentioned above compared and analyzed all three gas recycling types together, this work focuses on simple SOFC power system with anode or cathode gas recycle. An integration of both anode and cathode gas recycle is also discussed. A mathematical model of internal-reforming SOFC(IR-SOFC),which is heart of the system, has been developed that taking into account influences of cell operative temperature, air ratio, etc. An external or internal reforming SOFC power system with gas recycle under different recycle ratios is compared by an energy analysis. 2. System configurations and description Fig. 1 shows a natural gas fed simple SOFC system with heat recovery. Methane fuel enters the plant and is compressed to a system pressure requirement. Before entering a prereformer, it is mixed with steam produced in a heat integrated boiler. The prereformer is heated by hot gas leaving a combustor. Nature gas is externally reformed in the prereformer and hydrogen-rich gas is produced. Air is pressurized and preheated to a temperature approximately blow the cell stack temperature before admittance into the SOFC stack. Reforming gas and oxygen are channeled through anode and cathode compartments, respectively. Reforming gas is internally reformed further in the anode compartment. Oxygen in the air fed to the cathode accepts electrons from external circuit to form oxygen ions. The ions are conducted through solid electrolyte to the anode. At the fuel electrode, the ions combine with hydrogen in the fuel to form water. Electrons flow from the anode through the external circuit back to the cathode. Since the
Fig. 2. Equilibrium composition vs. reactor temperature.
electrochemical is exothermic, the cell produces heat as well as electricity. After exiting the cell, the residual fuel and excess air mix and react in the combustor. The combusted exhaust gases then flow through the prereformer and heat exchangers to preheat the fuel and air. The exhaust gases then go into a boiler to produce superheated steam. The heat recovery is used to collect useful heat, which similar to that in a cogeneration plant. The system exhaust gases exit the system near 120 C. 3. System modeling 3.1. Reformer model For a natural gas fed SOFC system, either external or internal reforming is needed. Nature gas mixed with superheated steam is delivered to a prereformer where an endothermic reaction is driven by the SOFC stack exhaust gas to produce a hydrogen-rich fuel mixture for fuel cell anode. Nature gas is a fuel mixture which is typically methane rich, methane is reformed to produce hydrogen according to the high endothermic reforming reaction and the mildly exothermic shifting reaction.
CH4 þ H2 O/CO þ 3H2 ðreformingÞ
(1)
CO þ H2 O/CO2 þ H2 ðshiftingÞ
(2)
The overall reaction is
CH4 þ 2H2 O/CO2 þ 4H2
Table 1 Values of equilibrium constants of reforming and shifting reactions.
A B C D E
Reforming
Shifting
2.63121 1011 1.24065 107 2.25232 107 1.95028 101 66.1395
5.47301 1011 2.57479 107 4.63742 107 3.91500 101 13.2097
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Fig. 3. Effect of steam-to-carbon ratio on equilibrium composition.
(3)
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J. Jia et al. / Energy 36 (2011) 1068e1075
Table 2 Properties of SOFC components.
Cathode Electrolyte Anode Interconnection
ri (Ucm)
di (cm)
0.008114exp(600/T) 0.00294exp(10350/T) 0.00298exp(-1392/T) e
0.200 0.004 0.015 0.01
Assuming the reforming and shifting reactions at chemical equilibrium, equilibrium constants can be calculated from the partial pressures of reactants and products.
KPR ¼
KPS ¼
3 P PH 2 CO
PCH4 PH2 O
ðreformingÞ
(4)
PH2 PCO2 ðshiftingÞ PCO PH2 O
(5)
where the equilibrium constants KPR and KPS have been correlated to the temperature.
logKp ¼ AT 4 þ BT 3 þ CT 2 þ DT þ E
(6)
where the constant values are listed in Table 1[7]. Assuming that x, y are the molar flow rates of CH4 and CO respectively, participating in the reactions, then
KPR ¼
H2in þ 3x þ y 3 COin þ x y nin nin tot þ 2x tot þ 2x in CH4 x H2 Oin x y nin tot þ 2x
P2 (7)
nin tot þ 2x
ratio(S/C) of inlet gas. The effect of S/C on the equilibrium composition is shown in Fig. 3. However, increasing S/C negatively affects the overall performance of the system. As S/C increasing, hydrogen yield decreases. At the same time, increasing of the S/C results in an increasing of heat available for generating vapor in a boiler, then vapor mole fraction of water increase in exhaust gas, the sensible heat available in exhaust gas for recovery is reduced. In the fuel cell, the heat required for reforming increases with increasing the S/C, and more chemical energy has to be translated into heat energy rather than electric energy. In this paper, S/C is selected as 2.2. 3.2. SOFC model
KPS
Fig. 4. Prediction and experiment results of cell voltage vs. current density.
in þ 3x þ y COin þ yÞðH 2 2 ¼ H2 Oin x y COin þ x y
(8)
In general, the ideal reversible potential of H2eO2 SOFC can be calculated by Nernst equation:
E0 ¼
where superscript in is inlet. The term nin tot
is total mole flow rates of the inlet gas mixture include the methane and the steam vapor. When temperature is known, the equilibrium constants can be calculated from Eq. (6) and unknowns x and y are given by solving Eqs. (7) and (8) using a numerical calculated method at given inlet conditions of the flow. The equilibrium composition at different operating temperature is shown in Fig. 2. As temperature is increased, H2 is produced and the hydrogen output increases in a nearly linear way. At 850 C, almost all the methane is converted into hydrogen, and H2 yield reaches a maximum value. From Eqs. (1)e(3), it is clear that these processes require steam. This can be produced externally by a boiler or by a heat recovery steam generator supplied by the exhaust gases from a combustor. Carbon deposition should be avoided by increasing steam to carbon Table 3 Setting values of parameters. Parameter
Setting Value
Compressor adiabatic efficiency Inverter efficiency Fuel cell press drop Preheater press drop Combustor press drop Fuel temperature at system inlet Air inlet temperature
70% 98% 3% 3% 3% 298K 298K
1=2 pH , pO2 DG0 RT þ ln 2 2F pH2 O 2F
(9)
The reversible potential is reduced to terminal voltage by the sum of local voltage polarizations. Three polarizations are ohmic, activation and concentration polarization. Therefore the cell terminal voltage is given:
V ¼ E0 hact;a hact;c hohm hcon
(10)
where V is the cell potential.
Table 4 State-points main properties for simple SOFC power system.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
T(K)
H2(%)
H2O(%)
O2(%)
N2(%)
CH4(%)
CO2(%)
CO(%)
298 321 1023 1167 298 327 371 1023 1167 1205 1127 546 502 393 393 298
0 0 0 0 0 0 0 44.55 41.80 0 0 0 0 0 0 0
0 0 0 0 0 0 68.75 31.68 38.97 5.47 5.47 5.47 5.47 5.47 100 100
21.00 21.00 21.00 19.13 0 0 0 0 0 17.51 17.51 17.51 17.51 17.51 0 0
79.00 79.00 79.00 80.87 0 0 0 0 0 75.76 75.76 75.76 75.76 75.76 0 0
0 0 0 0 100 100 31.25 11.79 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 8.62 16.66 1.26 1.26 1.26 1.26 1.26 0 0
0 0 0 0 0 0 0 3.36 2.57 0 0 0 0 0 0 0
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Table 5 Main results of the simulation for the external prereforming SOFC power systems. Parameter
Value
Compressor work(air side) Compressor work(fuel side) SOFC Stack power Net power output Waste heat recovery Electrical efficiency Total efficiency
42.73 kW 0.9 kW 322.38 kW 278.75 kW 216.13 kW 39% 65%
3.3. Activation polarization The development of electrochemical reaction requires overcoming an activation energy barrier. The electrode potential to overcome this activation energy is called the activation polarization. This phenomenon can be described by the Bulter-volmer equation
aZF hact ð1 aÞZF hact i ¼ i0 exp exp RT RT
(11)
where a is the transfer coefficient, Z is the number of electrons participating in the electrode reaction, F is the Faraday constant, and i0 is the exchange current density that can be calculated as:
i0;a ¼ ga
pH2 p0;a
i0;c ¼ gc
pO2 p0;c
! pH2 O Eact;a exp p RT
!0:25
Eact;c exp RT
(12)
(13)
Values for ga ,gc ,Eact;a ,Eact;c could be found in literature[20].
Fig. 6. Effect of internal reforming rate on air ratio.
where Ri ¼ ri di is the ohmic resistance of anode, cathode, and electrolyte, di is the corresponding thickness of them and ri is the material resistivity, which is the strong function of temperature. Bothri anddi are given in Table 2[9,21]. 3.5. Concentration polarization The electrode concentration polarization considers the difference in gas concentrations between the electrodeeelectrolyte interface and the bulk. In this paper, the overall concentration polarization calculation is simplified assuming a constant value for the limiting current density.
h¼
RT i ln 1 2F iL
(15)
3.4. Ohmic polarization Ohmic losses occur because of resistance resulting from the flow of ions in the electrolyte and the flow of electrons through the electrode. Ohmic polarization is expressed by Ohm’s law:
hohm ¼ i
X
Ri
(14)
3.6. Electrochemical reaction In SOFC, the overall electrochemical is as follows, which is significantly exothermic.
1 H2 þ O2 /H2 O 2
(16)
The reforming and shifting reactions take place in the SOFC at the same time, the equilibrium constants of the reactions can be derived by
Fig. 5. Effect of internal reforming rate on efficiency.
Fig. 7. SOFC power system with anode gas recycle..
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J. Jia et al. / Energy 36 (2011) 1068e1075 Table 6 Main results of the simulation for the internal reforming SOFC power systems with anode gas recycle (Recycle ratio ¼ 0.5). Parameter
Value
Compressor work(air side) Compressor work(fuel side) SOFC Stack power Net power output Waste heat recovery Electrical efficiency Total efficiency
21.94 kW 1.05 kW 389.84 kW 366.85 kW 343.67 kW 46% 88%
H2in þ 3x þ y z 3 COin þ x y nin nin tot þ 2x tot þ 2x in in CH4 x H2 O x y þ z
KPR ¼
P2
nin nin tot þ 2x tot þ 2x in þ 3x þ y z COin þ y H 2 2 ¼ H2 Oin x y þ z COin þ x y
(17) Fig. 9. Effect of recycle ratio of anode gas on total efficiency.
4. Results and discussion
In this study, it is assumed that all system components are working at their respective designed conditions under steady-state operation. A set of operating parameters and the assumed efficiencies of these system components are given in Table 3[8,9].
The key parameter in SOFC computation is the operating temperature which is dependent on various operating and design data. The electrochemical model is solved with a tentative temperature. The electrochemical model determines terminal voltage and electric power. The energy balance (Eq. (21)) accepts these results from electrochemical model and calculates the temperature of SOFC.The temperature is applied to the electrochemical model for the next calculation of cell terminal voltage and power. As the simulation progressed the model steps back and forth between electrochemical and thermal calculations until the convergence is obtained. The details of SOFC simulation can be obtained from our previous studies [1e4]. For the whole system model, since recuperators need the heating fluid parameters(such as the exit gas temperature of the combustor),which are not known at the beginning of the simulation, a set of initial parameters has to be assumed in order to run the system model until convergence is met eventually. The simulations were done using Matlab 7.0. In order to investigate the accuracy of the model, the calculate V-i curve is compared with the experimental data in reference [22] in Fig. 4 The relative deviation between the calculated voltage and experimental voltage in reference [22] is no larger than 5%. Such a good agreement for the terminal voltages between the model prediction and the experiment shows that the present model is reliable.
Fig. 8. Effect of recycle rate on electric efficiency and air ratio.
Fig. 10. SOFC power system with cathode gas recycle..
KPS
(18)
The reaction rate z is determined by the Faraday’s Law.
z ¼ I=ð2FÞ
(19)
The electric power produced is given by
We ¼ IV
(20)
The equation for the energy balance of SOFC is
X i
Hiin þ
X
Rk ðDHk Þ ¼ We þ
k
X
Hiout
(21)
i
The energy balance includes the electrical power We and the enthalpy changes of the chemical and electrochemical reactions, and gives the evaluation of the outlet temperature of the gases, which is equal to the average temperature of the stack.
3.7. Parameter settings
J. Jia et al. / Energy 36 (2011) 1068e1075
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Table 7 Main results of the simulation for the internal reforming SOFC power systems with cathode gas recycle(Recycle ratio ¼ 0.5). Parameter
Value
Compressor work(air side) Compressor work(fuel side) SOFC Stack power Net power output Waste heat recovery Electrical efficiency Total efficiency
6.79 kW 0.65 kW 256.49 kW 249.05 kW 137.13 kW 51% 78%
4.1. The simple SOFC power system The temperature and molar composition at each state-point of the system shown in Fig.1 are listed in Table 4. Some results relating to system performance are listed in Table 5. The heat recovery is referred to the amount of energy that is obtainable from the exhaust leaving from the boiler which can be used to produce steam or hot water for industrial and commercial applications. The results of the simulation show that the waste heat recovered is 216.13 kW. The net electrical power output of the plant is 278.75 kW. The thermal-to-electric ratio is 0.77.The electrical is 39% and total efficiencies of the plant is 65%. The electrical efficiency is defined as the ratio of electrical power output to LHV of the fuel. The total efficiency is defined as the ratio of the sum of net electrical power and the heat recovery to LHV of the fuel. The most irreversibility process occurs in air preheater because air flow rate and temperature differences are large. Here, a large amount of heat equal to about 4.27 times the power output of SOFC is transferred to the entering air. However, excess air is needed to provide air-cooling in SOFC and excess air reduces the temperature gradient and make cell temperature more uniform [3]. The influence of the internal reforming rate on air ratio and efficiency are shown in Figs. 5 and 6, respectively. When the internal reforming rate increased, that is the external prereforming rate decreased, the flow rate of air decreased, which leads to the heat requirement reduced. Therefore, the irreversibility is reduced, too. When internal reforming rate reaches 100%, the prereformer becomes a preheater completely and the capital cost of the equipment is reduced. When the internal reforming rate increases from 30% to 100%, the electrical efficiency increases from 39% to 44%.
Fig. 11. Effect of recycle ratio of cathode gas on air ratio.
Fig. 12. Effect of recycle ratio of cathode gas on efficiency.
4.2. The SOFC power system with anode gas recycle The SOFC power systems with anode gas recycle is shown in Fig. 7.Instead of generating steam for the reforming reaction externally in the boiler as in the Fig. 1, H2O produced in the electrochemical reactions at the anode can be used by recycle a portion of the deleted anode exhaust back to the inlet of the preheater. When the recyle ratio is 0.5, main simulation results for the power system are listed in Table 6. The recycle ratio of anode gas is defined as the fraction of the anode outlet molar flow that is recirculated back to the preheater inlet, that is always be less than or equal to one. The influence of the recycle ratio on air ratio and efficiency are shown in Figs. 8 and 9, respectively. When the recycle ratio of anode gas increases, the air ratio is reduced, irreversibility is reduced and electric efficiency increases. Compared with external steam generation, anode gas recycling provides an internal steam circuit which elimination of the waste heat recovery steam generator such as the boiler, and the capital cost of system is reduced. At the same time, the steam content of the exhaust gas is reduced, which elevates the total system efficiency by increase the sensible thermal energy of exhaust gas. The total efficiency is 88%, which is 20% larger than that of the external steam generation system shown in Fig. 1. However, the total efficiency decreases slightly as the recycle ratio increasing,that is because more chemical energy in the fuel are translated into electric instead of heat energy to heat the cooling air and the sensible enthalpy of fuel is much less than that of air.
Fig. 13. Anode gas recycle and cathode gas recycle.
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J. Jia et al. / Energy 36 (2011) 1068e1075
a SOFC power system with anode gas recycle to achieve an electrical efficiency greater than 45%, and a total efficiency near 88%. Increasing in recycle ratio improves electrical efficiency. However, the total efficiency increases slightly as recycle ratio of anode gas increasing. When it comes to the cathode gas recycle, electric efficiency of this power system is close to 51% by reducing the fresh air flow rate. The application of gas recycle reduces the exchanger size and eliminates the steam generator such as vaporizer or boiler and leads to falling of investment cost of the whole power system. References
Fig. 14. Electric efficiency and total efficiency for the five discussed cases.
4.3. The SOFC power system with cathode gas recycle The power system with cathode gas recycle has been described in Fig. 10. The purpose of cathode gas recycle is to preheat the inlet air by recirculating cathode outlet gases to a location upstream of the cell stack. Main results of the simulation for internal reforming SOFC power systems with cathode gas recycle are listed in Table 7. The influence of recycle ratio of cathode gas on air ratio and efficiency are shown in Figs. 11 and 12, respectively. When recycle ratio of cathode gas increases, the fresh air required is reduced which makes the irreversibility decreased and the electric efficiency increases evidently. When the recycle ratio of cathode gas increases from 0.4 to 0.55, the net electric efficiency is improved from 45% to 51%.As mentioned above, because the sensible enthalpy of fuel is much less than that of the air, the recycle ration of the cathode gas has a more obvious effect on the efficiency of power system than that of the anode gas. The adoption of the cathode gas recycle offer the advantage of reduction in fresh air feed and reduced air preheater size, which lowering the investment cost. 4.4. The SOFC power system with anode gas recycle and cathode gas recycle The SOFC power system with anode gas recycle and cathode gas recycle is shown in Fig. 13. Integration the advantage of the lower air ratio with the reduced air preheater size and the elimination of the boiler for generating steam, high electrical efficiency of 52% and total efficiency of 93% are obtained and the investment is reduced. Performance comparisons of five SOFC system designs are shown in Fig. 14. Case(1): Prereforming, internal reforming rate ¼ 50% Case(2): Internal reforming, internal reforming rate ¼ 100% Case(3): Anode gas recycle, recycle rate ¼ 0.5 Case(4): Cathode gas recycle, recycle ratio ¼ 0.5 Case(5): Both anode gas and cathode gas recycle, recycle ratio ¼ 0.5
[1] Jia J, Shen S, Riffat SB, Gillott M. Structural parameters study of a tubular solid oxide fuel cell. Journal of the Energy Institute 2005;78(2):76e80. [2] Jia JX, Abudula A. Performance comparison of solid oxide fuel cell with different structural parameters of electrode. Journal of the Energy Institute 2009;82(2):64e8. [3] Jia Junxi, Jiang Renqiu, Shen Shengqiang, Abudula Abuliti. Effect of operation parameters on performance of tubular solid oxide fuel cell. AIChE Journal 2008;54(2):554e64. [4] Jia Junxi, Abudula Abuliti, Wei Liming, Jiang Renqiu, Shen Shengqiang. A mathematical model of a tubular solid oxide fuel cell with specified combustion zone. Journal of Power Sources 2007;171(2):696e705. [5] Kai Bedringas W, Ivan Ertesvag S. Exergy analysis of solid oxide fuel cell (SOFC) systems. Energy 1997;22(4):403e12. [6] Chan SH, Low CF, Ding OL. Energy and exergy analysis of simple solid oxide fuel cell power systems. Journal of Power Sources 2002;103:188e200. [7] Massardo AF, Lubelli F. Internal reforming solid oxide fuel cell-gas turbine combined cycles. Journal of Engineering for Gas Turbines and Power 2000;122:27e35. [8] Chan SH, Ho HK, Tian Y. Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant. Journal of Power Sources 2002;109:111e20. [9] Campanari. S. Full load and part-load performance prediction for integrated SOFC and microturbine systems. Journal of Engineering for Gas Turbine and Power 2000;122:239e46. [10] Costanmagna P, magistri L, Massardo AF. Design and part-load performance of a hybrid system based on a solid oxide fuel reactor and a micro gas turbin. Journal of Power Sources 2001;96:352e68. [11] Chan SH, .Ho HK, Tian Y. Modelling for part-load operation of solid oxide fuel cellgas turbine hybrid power plant. Journal of Power Sources 2003;144:213e27. [12] Calise F, Palombo A, Vanoli L. Design and partial load exergy analysis of hybrid SOFC-GT power plant. Journal of Power Sources 2006;158:225e44. [13] Calise F, Dentice d’Accadia M, Palombo A, Vanoli L. Simulation and exergy analysis of a hybrid solid oxide fuel cell(SOFC)-gas turbine system. Energy 2006;31:3278e99. [14] Cocco D, Tola V. Externally reformed solid oxide fuel cell-micro-gas turbine (SOFC-MIT) hybrid systems fueled by methanol and di-methyl-ether (DME). Energy 2009;34:2124e30. [15] Traverso A, Magistri L, Massardo AF. Turbomachinery for the air management and energy recovery in fuel cell gas turbine hybrid systems. Energy 2010;35:764e77. [16] Komatsu Y, Kimijima S, Szmyd JS. Performance analysis for the part-load operation of a solid oxide fuel cell-micro gas turbine hybrid system. Energy 2010;35:982e8. [17] Yi Yaofan, .Rao AD, Brouwer Jacob, Samuelsen GS. Analysis and optimization of a solid oxide fuel cell and intercooled gas turebine(SOFC-ICGT) hybrid cycle. Journal of Power Sources 2004;132:77e85. [18] Lin Po-Hsu, Hong Che-Wun. On the start-up transient simulation of a turbo fuel cell system. Journal of Power Sources 2006;160(2):1230e41. [19] Murshed AKMM, Huang Biao, Nandakmar K. Control relevant modeling of planer solid oxide fuel cell system. Journal of Power Sources 2007;163: 830e45. [20] Costamagna P, Honegger K. Modeling of solid oxide heat exchanger integrated stacks and simulation at high fuel utilization. Journal of the Electrochemical Society 1998;145(11):3995e4007. [21] Bessette II NF, Wepter WJ, Winnick J. A mathematical model of a solid oxide fuel cell. Journal of the Electrochemical Society 1995;42(11):3792e800. [22] Singhal SC. Advances in solid oxide fuel cell technology. Solid State Ionics 2000;135:305e13.
5. Conclusions
Glossary
In this paper, SOFC power systems fed by nature gas are compared by energetic analysis. Simulations reveal that efficiencies of 44% electric, 68% cogenerative are feasible for internal reforming SOFC system. Decreasing excess air in the SOFC has a positive effect on electric and total efficiency. It is possible for
Eact: activation energy, J/mol E0: reversible cell potential, V F: Faraday Constant, 96485C/mol DG: change in Gibbs Free Energy, J/mol H: enthalpy, J/mol DH: enthalpy change of reaction, J/mol i: current density, A/m2
J. Jia et al. / Energy 36 (2011) 1068e1075 i0: exchange current density, A/m2 iL: limiting current density, A/m2 I: current, A K: equilibrium constant LHV: lower heating value, J/mol P: pressure, bar R: universal gas constant, 8.314 J/(mol K) Ri: ohmic resistant Ucm2 Rk: reaction rate mol s1 T: temperature, K V: terminal voltage, V Uf: fuel utilization Uo: oxidant utilization W: electrical power, W z: H2 reacted moles, mol s1 Z: electrons transferred per reaction
Greek Letters a: transfer coefficient r: specific resistivity, Ucm d: thickness, cm h: polarization, V h: efficiency Subscripts a: anode act: activation polarization c: cathode con: concentration polarization ohm: ohm polarization r: reforming reaction s: shifting reaction
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Effects of gas recycle on performance of solid oxide fuel cell power systems Junxi Jia a, *, Qiang Li a, Ming Luo a, Liming Wei b, Abuliti Abudula c a
College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China School of Electric and Electronic Information Engineering, Jilin Architectural and Civil Engineering Institute, Changchun 130021, China c North Japan New Energy Research Center, Hirosaki University, Aomori 030-0813, Japan b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 April 2010 Received in revised form 9 August 2010 Accepted 2 December 2010 Available online 6 January 2011
An energy analysis of solid oxide fuel cell (SOFC) power systems with gas recycles fed by natural gas is carried out. Simple SOFC system, SOFC power systems with anode and cathode gas recycle respectively and SOFC power system with both anode and cathode gas recycle are compared. Influences of reforming rate, air ratio and recycle ratio of electrode exhaust gas on performance of SOFC power systems are investigated. Net system electric efficiency and cogeneration efficiency of these power systems are given by a calculation model. Results show that internal reforming SOFC power system can achieve an electrical efficiency of more than 44% and a system cogeneration efficiency including waste heat recovery of 68%. For SOFC power system with anode gas recycle, an electrical efficiency is above 46% and a cogeneration efficiency of 88% is obtained. In the case of cathode gas recycle, an electrical efficiency and a cogeneration efficiency is more than 51% and 78% respectively. Although SOFC system with both anode and cathode gas is more complicated, the electrical efficiency of it is close to 52%. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Solid oxide fuel cell Power system Gas recycle Electric efficiency
1. Introduction Solid oxide fuel cell (SOFC) converts the chemical energy of fuel directly to electrical energy. It can achieve high electrical efficiency and is a highly environmentally benign method of electric power production. The operating temperature of SOFC is sufficiently high to provide necessary heat to support endothermic reforming of methane. SOFC is therefore more tolerant of fuel impurities and can operate using hydrogen and carbon monoxide fuels directly at the anode. It does not require costly external reformers or catalysts to produce hydrogen, and the use of internal reforming actually increases overall system efficiency. Previous work by Jia et al. [1,2] investigated the effects of two structural parameters such as thickness of electrolyte and pore size of electrolyte on performance of SOFC. Jia et al. [3] have compared the steady and transient characteristics of a tubular SOFC when operation parameters such as inlet fuel temperature, inlet oxidant temperature, and inlet oxidant flow rate are changed, respectively. The position of hot spot and the temperature gradients are calculated when the different operation parameters are changed. When SOFC works in a cell stack, the combustion zone should be considered. The work of Jia et al. [4] has examined the operation of a tubular
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SOFC with combustion zone at the steady and transient operation states. These models mentioned above includes all the three polarizations: ohmic, activation and concentration polarization. The high operating temperature of SOFC gives good possibilities for cogeneration applications. There have been numerous models are developed to simulate performance of SOFC power systems [5e19], the features of these models are different. A simple solid oxide fuel cell system can be used for residential scales power applications. Bedringas et al. [5] have reported that a system electrical efficiency near 60% could be achieved for a SOFC system with external reforming. Chan et al. [6] present a discussion of simple SOFC system without gas turbine fed by hydrogen and methane, respectively and results shows both a H2-fed system and a CH4-fed system can achieve an electrical efficiency of more than 50%. Other models available in the literatures [7e18] focus on complicated hybrid SOFC and gas turbine power system. The works of literatures [7,8] examined effects of operating pressure, steam-to-carbon ration, and fuel flow rate on performance of SOFC-GT power systems. Refs [9e16] address a full and partial load analysis of hybrid SOFC-GT power plant. Electric efficiencies of these hybrid systems are high than 60% at design point and also very high at part load condition. Yi et al. [17] introduced a SOFC and intercooled gas turebine (SOFC-ICGT) hybrid cycle, and system electrical efficiency is even high than 75% when operating pressure is 50 bara and an excess air in the SOFC is low.
J. Jia et al. / Energy 36 (2011) 1068e1075
Fig. 1. SOFC power system with pre-reforming and internal reforming.
Prediction of transient performance of SOFC power systems is important for control purposes. Lin et al. [18] have developed a dynamic model of the hybrid SOFC-GT system to investigate the transient behavior during cold start. Murshed et al. [19] provides a dynamic model of planer solid oxide fuel cell system which include heat exchanger, reformer and after-burner. Many cogeneration system concepts[5e19] are conceivable with SOFC as mentioned above, however, anode gas recycling concept were found only in Refs[5,9,10,12],not discussed in detail and none of them are involved with cathode gas recycling concept. As few of the papers mentioned above compared and analyzed all three gas recycling types together, this work focuses on simple SOFC power system with anode or cathode gas recycle. An integration of both anode and cathode gas recycle is also discussed. A mathematical model of internal-reforming SOFC(IR-SOFC),which is heart of the system, has been developed that taking into account influences of cell operative temperature, air ratio, etc. An external or internal reforming SOFC power system with gas recycle under different recycle ratios is compared by an energy analysis. 2. System configurations and description Fig. 1 shows a natural gas fed simple SOFC system with heat recovery. Methane fuel enters the plant and is compressed to a system pressure requirement. Before entering a prereformer, it is mixed with steam produced in a heat integrated boiler. The prereformer is heated by hot gas leaving a combustor. Nature gas is externally reformed in the prereformer and hydrogen-rich gas is produced. Air is pressurized and preheated to a temperature approximately blow the cell stack temperature before admittance into the SOFC stack. Reforming gas and oxygen are channeled through anode and cathode compartments, respectively. Reforming gas is internally reformed further in the anode compartment. Oxygen in the air fed to the cathode accepts electrons from external circuit to form oxygen ions. The ions are conducted through solid electrolyte to the anode. At the fuel electrode, the ions combine with hydrogen in the fuel to form water. Electrons flow from the anode through the external circuit back to the cathode. Since the
Fig. 2. Equilibrium composition vs. reactor temperature.
electrochemical is exothermic, the cell produces heat as well as electricity. After exiting the cell, the residual fuel and excess air mix and react in the combustor. The combusted exhaust gases then flow through the prereformer and heat exchangers to preheat the fuel and air. The exhaust gases then go into a boiler to produce superheated steam. The heat recovery is used to collect useful heat, which similar to that in a cogeneration plant. The system exhaust gases exit the system near 120 C. 3. System modeling 3.1. Reformer model For a natural gas fed SOFC system, either external or internal reforming is needed. Nature gas mixed with superheated steam is delivered to a prereformer where an endothermic reaction is driven by the SOFC stack exhaust gas to produce a hydrogen-rich fuel mixture for fuel cell anode. Nature gas is a fuel mixture which is typically methane rich, methane is reformed to produce hydrogen according to the high endothermic reforming reaction and the mildly exothermic shifting reaction.
CH4 þ H2 O/CO þ 3H2 ðreformingÞ
(1)
CO þ H2 O/CO2 þ H2 ðshiftingÞ
(2)
The overall reaction is
CH4 þ 2H2 O/CO2 þ 4H2
Table 1 Values of equilibrium constants of reforming and shifting reactions.
A B C D E
Reforming
Shifting
2.63121 1011 1.24065 107 2.25232 107 1.95028 101 66.1395
5.47301 1011 2.57479 107 4.63742 107 3.91500 101 13.2097
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Fig. 3. Effect of steam-to-carbon ratio on equilibrium composition.
(3)
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Table 2 Properties of SOFC components.
Cathode Electrolyte Anode Interconnection
ri (Ucm)
di (cm)
0.008114exp(600/T) 0.00294exp(10350/T) 0.00298exp(-1392/T) e
0.200 0.004 0.015 0.01
Assuming the reforming and shifting reactions at chemical equilibrium, equilibrium constants can be calculated from the partial pressures of reactants and products.
KPR ¼
KPS ¼
3 P PH 2 CO
PCH4 PH2 O
ðreformingÞ
(4)
PH2 PCO2 ðshiftingÞ PCO PH2 O
(5)
where the equilibrium constants KPR and KPS have been correlated to the temperature.
logKp ¼ AT 4 þ BT 3 þ CT 2 þ DT þ E
(6)
where the constant values are listed in Table 1[7]. Assuming that x, y are the molar flow rates of CH4 and CO respectively, participating in the reactions, then
KPR ¼
H2in þ 3x þ y 3 COin þ x y nin nin tot þ 2x tot þ 2x in CH4 x H2 Oin x y nin tot þ 2x
P2 (7)
nin tot þ 2x
ratio(S/C) of inlet gas. The effect of S/C on the equilibrium composition is shown in Fig. 3. However, increasing S/C negatively affects the overall performance of the system. As S/C increasing, hydrogen yield decreases. At the same time, increasing of the S/C results in an increasing of heat available for generating vapor in a boiler, then vapor mole fraction of water increase in exhaust gas, the sensible heat available in exhaust gas for recovery is reduced. In the fuel cell, the heat required for reforming increases with increasing the S/C, and more chemical energy has to be translated into heat energy rather than electric energy. In this paper, S/C is selected as 2.2. 3.2. SOFC model
KPS
Fig. 4. Prediction and experiment results of cell voltage vs. current density.
in þ 3x þ y COin þ yÞðH 2 2 ¼ H2 Oin x y COin þ x y
(8)
In general, the ideal reversible potential of H2eO2 SOFC can be calculated by Nernst equation:
E0 ¼
where superscript in is inlet. The term nin tot
is total mole flow rates of the inlet gas mixture include the methane and the steam vapor. When temperature is known, the equilibrium constants can be calculated from Eq. (6) and unknowns x and y are given by solving Eqs. (7) and (8) using a numerical calculated method at given inlet conditions of the flow. The equilibrium composition at different operating temperature is shown in Fig. 2. As temperature is increased, H2 is produced and the hydrogen output increases in a nearly linear way. At 850 C, almost all the methane is converted into hydrogen, and H2 yield reaches a maximum value. From Eqs. (1)e(3), it is clear that these processes require steam. This can be produced externally by a boiler or by a heat recovery steam generator supplied by the exhaust gases from a combustor. Carbon deposition should be avoided by increasing steam to carbon Table 3 Setting values of parameters. Parameter
Setting Value
Compressor adiabatic efficiency Inverter efficiency Fuel cell press drop Preheater press drop Combustor press drop Fuel temperature at system inlet Air inlet temperature
70% 98% 3% 3% 3% 298K 298K
1=2 pH , pO2 DG0 RT þ ln 2 2F pH2 O 2F
(9)
The reversible potential is reduced to terminal voltage by the sum of local voltage polarizations. Three polarizations are ohmic, activation and concentration polarization. Therefore the cell terminal voltage is given:
V ¼ E0 hact;a hact;c hohm hcon
(10)
where V is the cell potential.
Table 4 State-points main properties for simple SOFC power system.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
T(K)
H2(%)
H2O(%)
O2(%)
N2(%)
CH4(%)
CO2(%)
CO(%)
298 321 1023 1167 298 327 371 1023 1167 1205 1127 546 502 393 393 298
0 0 0 0 0 0 0 44.55 41.80 0 0 0 0 0 0 0
0 0 0 0 0 0 68.75 31.68 38.97 5.47 5.47 5.47 5.47 5.47 100 100
21.00 21.00 21.00 19.13 0 0 0 0 0 17.51 17.51 17.51 17.51 17.51 0 0
79.00 79.00 79.00 80.87 0 0 0 0 0 75.76 75.76 75.76 75.76 75.76 0 0
0 0 0 0 100 100 31.25 11.79 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 8.62 16.66 1.26 1.26 1.26 1.26 1.26 0 0
0 0 0 0 0 0 0 3.36 2.57 0 0 0 0 0 0 0
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Table 5 Main results of the simulation for the external prereforming SOFC power systems. Parameter
Value
Compressor work(air side) Compressor work(fuel side) SOFC Stack power Net power output Waste heat recovery Electrical efficiency Total efficiency
42.73 kW 0.9 kW 322.38 kW 278.75 kW 216.13 kW 39% 65%
3.3. Activation polarization The development of electrochemical reaction requires overcoming an activation energy barrier. The electrode potential to overcome this activation energy is called the activation polarization. This phenomenon can be described by the Bulter-volmer equation
aZF hact ð1 aÞZF hact i ¼ i0 exp exp RT RT
(11)
where a is the transfer coefficient, Z is the number of electrons participating in the electrode reaction, F is the Faraday constant, and i0 is the exchange current density that can be calculated as:
i0;a ¼ ga
pH2 p0;a
i0;c ¼ gc
pO2 p0;c
! pH2 O Eact;a exp p RT
!0:25
Eact;c exp RT
(12)
(13)
Values for ga ,gc ,Eact;a ,Eact;c could be found in literature[20].
Fig. 6. Effect of internal reforming rate on air ratio.
where Ri ¼ ri di is the ohmic resistance of anode, cathode, and electrolyte, di is the corresponding thickness of them and ri is the material resistivity, which is the strong function of temperature. Bothri anddi are given in Table 2[9,21]. 3.5. Concentration polarization The electrode concentration polarization considers the difference in gas concentrations between the electrodeeelectrolyte interface and the bulk. In this paper, the overall concentration polarization calculation is simplified assuming a constant value for the limiting current density.
h¼
RT i ln 1 2F iL
(15)
3.4. Ohmic polarization Ohmic losses occur because of resistance resulting from the flow of ions in the electrolyte and the flow of electrons through the electrode. Ohmic polarization is expressed by Ohm’s law:
hohm ¼ i
X
Ri
(14)
3.6. Electrochemical reaction In SOFC, the overall electrochemical is as follows, which is significantly exothermic.
1 H2 þ O2 /H2 O 2
(16)
The reforming and shifting reactions take place in the SOFC at the same time, the equilibrium constants of the reactions can be derived by
Fig. 5. Effect of internal reforming rate on efficiency.
Fig. 7. SOFC power system with anode gas recycle..
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J. Jia et al. / Energy 36 (2011) 1068e1075 Table 6 Main results of the simulation for the internal reforming SOFC power systems with anode gas recycle (Recycle ratio ¼ 0.5). Parameter
Value
Compressor work(air side) Compressor work(fuel side) SOFC Stack power Net power output Waste heat recovery Electrical efficiency Total efficiency
21.94 kW 1.05 kW 389.84 kW 366.85 kW 343.67 kW 46% 88%
H2in þ 3x þ y z 3 COin þ x y nin nin tot þ 2x tot þ 2x in in CH4 x H2 O x y þ z
KPR ¼
P2
nin nin tot þ 2x tot þ 2x in þ 3x þ y z COin þ y H 2 2 ¼ H2 Oin x y þ z COin þ x y
(17) Fig. 9. Effect of recycle ratio of anode gas on total efficiency.
4. Results and discussion
In this study, it is assumed that all system components are working at their respective designed conditions under steady-state operation. A set of operating parameters and the assumed efficiencies of these system components are given in Table 3[8,9].
The key parameter in SOFC computation is the operating temperature which is dependent on various operating and design data. The electrochemical model is solved with a tentative temperature. The electrochemical model determines terminal voltage and electric power. The energy balance (Eq. (21)) accepts these results from electrochemical model and calculates the temperature of SOFC.The temperature is applied to the electrochemical model for the next calculation of cell terminal voltage and power. As the simulation progressed the model steps back and forth between electrochemical and thermal calculations until the convergence is obtained. The details of SOFC simulation can be obtained from our previous studies [1e4]. For the whole system model, since recuperators need the heating fluid parameters(such as the exit gas temperature of the combustor),which are not known at the beginning of the simulation, a set of initial parameters has to be assumed in order to run the system model until convergence is met eventually. The simulations were done using Matlab 7.0. In order to investigate the accuracy of the model, the calculate V-i curve is compared with the experimental data in reference [22] in Fig. 4 The relative deviation between the calculated voltage and experimental voltage in reference [22] is no larger than 5%. Such a good agreement for the terminal voltages between the model prediction and the experiment shows that the present model is reliable.
Fig. 8. Effect of recycle rate on electric efficiency and air ratio.
Fig. 10. SOFC power system with cathode gas recycle..
KPS
(18)
The reaction rate z is determined by the Faraday’s Law.
z ¼ I=ð2FÞ
(19)
The electric power produced is given by
We ¼ IV
(20)
The equation for the energy balance of SOFC is
X i
Hiin þ
X
Rk ðDHk Þ ¼ We þ
k
X
Hiout
(21)
i
The energy balance includes the electrical power We and the enthalpy changes of the chemical and electrochemical reactions, and gives the evaluation of the outlet temperature of the gases, which is equal to the average temperature of the stack.
3.7. Parameter settings
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Table 7 Main results of the simulation for the internal reforming SOFC power systems with cathode gas recycle(Recycle ratio ¼ 0.5). Parameter
Value
Compressor work(air side) Compressor work(fuel side) SOFC Stack power Net power output Waste heat recovery Electrical efficiency Total efficiency
6.79 kW 0.65 kW 256.49 kW 249.05 kW 137.13 kW 51% 78%
4.1. The simple SOFC power system The temperature and molar composition at each state-point of the system shown in Fig.1 are listed in Table 4. Some results relating to system performance are listed in Table 5. The heat recovery is referred to the amount of energy that is obtainable from the exhaust leaving from the boiler which can be used to produce steam or hot water for industrial and commercial applications. The results of the simulation show that the waste heat recovered is 216.13 kW. The net electrical power output of the plant is 278.75 kW. The thermal-to-electric ratio is 0.77.The electrical is 39% and total efficiencies of the plant is 65%. The electrical efficiency is defined as the ratio of electrical power output to LHV of the fuel. The total efficiency is defined as the ratio of the sum of net electrical power and the heat recovery to LHV of the fuel. The most irreversibility process occurs in air preheater because air flow rate and temperature differences are large. Here, a large amount of heat equal to about 4.27 times the power output of SOFC is transferred to the entering air. However, excess air is needed to provide air-cooling in SOFC and excess air reduces the temperature gradient and make cell temperature more uniform [3]. The influence of the internal reforming rate on air ratio and efficiency are shown in Figs. 5 and 6, respectively. When the internal reforming rate increased, that is the external prereforming rate decreased, the flow rate of air decreased, which leads to the heat requirement reduced. Therefore, the irreversibility is reduced, too. When internal reforming rate reaches 100%, the prereformer becomes a preheater completely and the capital cost of the equipment is reduced. When the internal reforming rate increases from 30% to 100%, the electrical efficiency increases from 39% to 44%.
Fig. 11. Effect of recycle ratio of cathode gas on air ratio.
Fig. 12. Effect of recycle ratio of cathode gas on efficiency.
4.2. The SOFC power system with anode gas recycle The SOFC power systems with anode gas recycle is shown in Fig. 7.Instead of generating steam for the reforming reaction externally in the boiler as in the Fig. 1, H2O produced in the electrochemical reactions at the anode can be used by recycle a portion of the deleted anode exhaust back to the inlet of the preheater. When the recyle ratio is 0.5, main simulation results for the power system are listed in Table 6. The recycle ratio of anode gas is defined as the fraction of the anode outlet molar flow that is recirculated back to the preheater inlet, that is always be less than or equal to one. The influence of the recycle ratio on air ratio and efficiency are shown in Figs. 8 and 9, respectively. When the recycle ratio of anode gas increases, the air ratio is reduced, irreversibility is reduced and electric efficiency increases. Compared with external steam generation, anode gas recycling provides an internal steam circuit which elimination of the waste heat recovery steam generator such as the boiler, and the capital cost of system is reduced. At the same time, the steam content of the exhaust gas is reduced, which elevates the total system efficiency by increase the sensible thermal energy of exhaust gas. The total efficiency is 88%, which is 20% larger than that of the external steam generation system shown in Fig. 1. However, the total efficiency decreases slightly as the recycle ratio increasing,that is because more chemical energy in the fuel are translated into electric instead of heat energy to heat the cooling air and the sensible enthalpy of fuel is much less than that of air.
Fig. 13. Anode gas recycle and cathode gas recycle.
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a SOFC power system with anode gas recycle to achieve an electrical efficiency greater than 45%, and a total efficiency near 88%. Increasing in recycle ratio improves electrical efficiency. However, the total efficiency increases slightly as recycle ratio of anode gas increasing. When it comes to the cathode gas recycle, electric efficiency of this power system is close to 51% by reducing the fresh air flow rate. The application of gas recycle reduces the exchanger size and eliminates the steam generator such as vaporizer or boiler and leads to falling of investment cost of the whole power system. References
Fig. 14. Electric efficiency and total efficiency for the five discussed cases.
4.3. The SOFC power system with cathode gas recycle The power system with cathode gas recycle has been described in Fig. 10. The purpose of cathode gas recycle is to preheat the inlet air by recirculating cathode outlet gases to a location upstream of the cell stack. Main results of the simulation for internal reforming SOFC power systems with cathode gas recycle are listed in Table 7. The influence of recycle ratio of cathode gas on air ratio and efficiency are shown in Figs. 11 and 12, respectively. When recycle ratio of cathode gas increases, the fresh air required is reduced which makes the irreversibility decreased and the electric efficiency increases evidently. When the recycle ratio of cathode gas increases from 0.4 to 0.55, the net electric efficiency is improved from 45% to 51%.As mentioned above, because the sensible enthalpy of fuel is much less than that of the air, the recycle ration of the cathode gas has a more obvious effect on the efficiency of power system than that of the anode gas. The adoption of the cathode gas recycle offer the advantage of reduction in fresh air feed and reduced air preheater size, which lowering the investment cost. 4.4. The SOFC power system with anode gas recycle and cathode gas recycle The SOFC power system with anode gas recycle and cathode gas recycle is shown in Fig. 13. Integration the advantage of the lower air ratio with the reduced air preheater size and the elimination of the boiler for generating steam, high electrical efficiency of 52% and total efficiency of 93% are obtained and the investment is reduced. Performance comparisons of five SOFC system designs are shown in Fig. 14. Case(1): Prereforming, internal reforming rate ¼ 50% Case(2): Internal reforming, internal reforming rate ¼ 100% Case(3): Anode gas recycle, recycle rate ¼ 0.5 Case(4): Cathode gas recycle, recycle ratio ¼ 0.5 Case(5): Both anode gas and cathode gas recycle, recycle ratio ¼ 0.5
[1] Jia J, Shen S, Riffat SB, Gillott M. Structural parameters study of a tubular solid oxide fuel cell. Journal of the Energy Institute 2005;78(2):76e80. [2] Jia JX, Abudula A. Performance comparison of solid oxide fuel cell with different structural parameters of electrode. Journal of the Energy Institute 2009;82(2):64e8. [3] Jia Junxi, Jiang Renqiu, Shen Shengqiang, Abudula Abuliti. Effect of operation parameters on performance of tubular solid oxide fuel cell. AIChE Journal 2008;54(2):554e64. [4] Jia Junxi, Abudula Abuliti, Wei Liming, Jiang Renqiu, Shen Shengqiang. A mathematical model of a tubular solid oxide fuel cell with specified combustion zone. Journal of Power Sources 2007;171(2):696e705. [5] Kai Bedringas W, Ivan Ertesvag S. Exergy analysis of solid oxide fuel cell (SOFC) systems. Energy 1997;22(4):403e12. [6] Chan SH, Low CF, Ding OL. Energy and exergy analysis of simple solid oxide fuel cell power systems. Journal of Power Sources 2002;103:188e200. [7] Massardo AF, Lubelli F. Internal reforming solid oxide fuel cell-gas turbine combined cycles. Journal of Engineering for Gas Turbines and Power 2000;122:27e35. [8] Chan SH, Ho HK, Tian Y. Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant. Journal of Power Sources 2002;109:111e20. [9] Campanari. S. Full load and part-load performance prediction for integrated SOFC and microturbine systems. Journal of Engineering for Gas Turbine and Power 2000;122:239e46. [10] Costanmagna P, magistri L, Massardo AF. Design and part-load performance of a hybrid system based on a solid oxide fuel reactor and a micro gas turbin. Journal of Power Sources 2001;96:352e68. [11] Chan SH, .Ho HK, Tian Y. Modelling for part-load operation of solid oxide fuel cellgas turbine hybrid power plant. Journal of Power Sources 2003;144:213e27. [12] Calise F, Palombo A, Vanoli L. Design and partial load exergy analysis of hybrid SOFC-GT power plant. Journal of Power Sources 2006;158:225e44. [13] Calise F, Dentice d’Accadia M, Palombo A, Vanoli L. Simulation and exergy analysis of a hybrid solid oxide fuel cell(SOFC)-gas turbine system. Energy 2006;31:3278e99. [14] Cocco D, Tola V. Externally reformed solid oxide fuel cell-micro-gas turbine (SOFC-MIT) hybrid systems fueled by methanol and di-methyl-ether (DME). Energy 2009;34:2124e30. [15] Traverso A, Magistri L, Massardo AF. Turbomachinery for the air management and energy recovery in fuel cell gas turbine hybrid systems. Energy 2010;35:764e77. [16] Komatsu Y, Kimijima S, Szmyd JS. Performance analysis for the part-load operation of a solid oxide fuel cell-micro gas turbine hybrid system. Energy 2010;35:982e8. [17] Yi Yaofan, .Rao AD, Brouwer Jacob, Samuelsen GS. Analysis and optimization of a solid oxide fuel cell and intercooled gas turebine(SOFC-ICGT) hybrid cycle. Journal of Power Sources 2004;132:77e85. [18] Lin Po-Hsu, Hong Che-Wun. On the start-up transient simulation of a turbo fuel cell system. Journal of Power Sources 2006;160(2):1230e41. [19] Murshed AKMM, Huang Biao, Nandakmar K. Control relevant modeling of planer solid oxide fuel cell system. Journal of Power Sources 2007;163: 830e45. [20] Costamagna P, Honegger K. Modeling of solid oxide heat exchanger integrated stacks and simulation at high fuel utilization. Journal of the Electrochemical Society 1998;145(11):3995e4007. [21] Bessette II NF, Wepter WJ, Winnick J. A mathematical model of a solid oxide fuel cell. Journal of the Electrochemical Society 1995;42(11):3792e800. [22] Singhal SC. Advances in solid oxide fuel cell technology. Solid State Ionics 2000;135:305e13.
5. Conclusions
Glossary
In this paper, SOFC power systems fed by nature gas are compared by energetic analysis. Simulations reveal that efficiencies of 44% electric, 68% cogenerative are feasible for internal reforming SOFC system. Decreasing excess air in the SOFC has a positive effect on electric and total efficiency. It is possible for
Eact: activation energy, J/mol E0: reversible cell potential, V F: Faraday Constant, 96485C/mol DG: change in Gibbs Free Energy, J/mol H: enthalpy, J/mol DH: enthalpy change of reaction, J/mol i: current density, A/m2
J. Jia et al. / Energy 36 (2011) 1068e1075 i0: exchange current density, A/m2 iL: limiting current density, A/m2 I: current, A K: equilibrium constant LHV: lower heating value, J/mol P: pressure, bar R: universal gas constant, 8.314 J/(mol K) Ri: ohmic resistant Ucm2 Rk: reaction rate mol s1 T: temperature, K V: terminal voltage, V Uf: fuel utilization Uo: oxidant utilization W: electrical power, W z: H2 reacted moles, mol s1 Z: electrons transferred per reaction
Greek Letters a: transfer coefficient r: specific resistivity, Ucm d: thickness, cm h: polarization, V h: efficiency Subscripts a: anode act: activation polarization c: cathode con: concentration polarization ohm: ohm polarization r: reforming reaction s: shifting reaction
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