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Thermodynamic analysis of an integrated solid oxide fuel cell cycle with a rankine cycle
Energy Conversion and Management 51 (2010) 2724–2732
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Thermodynamic analysis of an integrated solid oxide fuel cell cycle with a rankine cycle Masoud Rokni Technical University of Denmark, Dept. Mechanical Engineering, Thermal Energy System, Building 402, 2800 Kgs, Lyngby, Denmark
a r t i c l e
i n f o
Article history: Received 23 September 2009 Accepted 1 June 2010
Keywords: SOFC Rankine Steam plant Hybrid plant CPO ASR
a b s t r a c t Hybrid systems consisting of solid oxide fuel cells (SOFC) on the top of a steam turbine (ST) are investigated. The plants are fired by natural gas (NG). A desulfurization reactor removes the sulfur content in the fuel while a pre-reformer breaks down the heavier hydro-carbons. The pre-treated fuel enters then into the anode side of the SOFC. The remaining fuels after the SOFC stacks enter a burner for further burning. The off-gases are then used to produce steam for a Rankine cycle in a heat recovery steam generator (HRSG). Different system setups are suggested. Cyclic efficiencies up to 67% are achieved which is considerably higher than the conventional combined cycles (CC). Both adiabatic steam reformer (ASR) and catalytic partial oxidation (CPO) fuel pre-reformer reactors are considered in this investigation. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The solid oxide fuel cell (SOFC) is an electrochemical reactor currently under development by some companies for power and heat generation application. Depending on the type of the electrolyte they are operating at temperature levels of more than about 750–1000 °C. The lower temperature alternative is now being developed for market entry during the next decade. Due to material complication on the balance of plant (BoP) components many companies are trying to find new materials for the SOFC cells to decrease the operating temperature of the SOFC stacks. Temperatures of about 650 °C are also mentioned. The biggest advantage of the SOFC in comparison with other types of fuel cells may be in its flexibility in using different types of fuel. However, in planar SOFCs one needs to pre-process most kind of fuels in order to break down the heavier hydro-carbons which may otherwise damage the fuel cells. The sulphur content in the fuels must firstly be removed and then pre-reformed before entering the anode side of the SOFC. Such fuel pre-processing can be done in two different catalytic reactors operating at different temperature levels indicated by reactor manufacturers. SOFC-based power plants have been studied for a while and some companies, such as Wärtsilä, are trying to realize such a system for combined heat and power (CHP) applications; see e.g. Fontell et al. [1]. The SOFC is also combined with combined cycles (CC) in the literature to achieve ultra high electrical efficiencies, see e.g.
E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.06.008
Rokni [2] and Riensche et al. [3]. Due to the current operating temperature of the SOFC stacks (more than about 750 °C), hybrid SOFC and GT (gas turbine) systems have also been studied extensively in the literature, e.g. in Pålson et al. [4] for CHP and in Proell et al. [5] with internal biomass gasification. Characterization, quantification and optimization of hybrid SOFC–GT systems have been studied by e.g. Subramanyan et al. [6] and Calise et al. [7]. The dynamics and control concept of a pressurized SOFC–GT hybrid system has also been studied, such as in Wächter et al. [8]. In Roberts and Brouwer [9] modeling results are compared with measured data for a 220 kW hybrid SOFC–GT power plant. Details on design, dynamics, control and startup of such hybrid power plants are studied in Rokni et al. [10]. Part–load characteristics of a SOFC–micro GT were also studied in Costamagna et al. [11]. While hybrid SOFC–GT plants have been extensively studied by many researchers, the investigations on combined SOFC and steam turbine (ST) are very limited see Dunbar et al. [12]. In addition the SOFC manufacturers are trying to decrease the operating temperature of the SOFC stacks, and then the combination of SOFC–ST hybrid system would be more attractive than the SOFC–GT systems. By decreasing the operating temperature, the material cost for the SOFC stacks will be decreased as well as many problems associated with the BoP components will be diminished. In hybrid SOFC–GT plants the SOFC stacks must be pressurized in an extremely large vessel (depending on the size of the plant which is usually in mega Watt classes). Such a practical problem will be diminished in hybrid SOFC–ST systems, because the stacks will work under atmospheric pressure. Another disadvantage of a SOFC–GT system is that the startup simplicity of the GT is
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
diminished since the startup time of a SOFC plant is much longer than that of a GT plant. Fuel pre-reforming can be done in different reactors such as adiabatic steam reformer (ASR) and catalytic partial oxidation (CPO). The disadvantage of an ASR reactor is that it needs superheated steam during startup (depending on the operating temperature of the reactor, i.e. 400 °C) which is an extremely power consuming process. During normal operation steam is available after the anode side of the SOFC stacks, which can be recycled into the system. However, in a CPO reactor additional air is needed for the fuel prereforming process, which in turn increases the plant power consumption (compressor work) and thereby the plant efficiency will be decreased. In this study, ASR reforming process versus CPO reforming process is studied in terms of plant design, plant efficiency and plant output power. In the Rankine cycle a single pressure level is proposed to study plant design, plant efficiency and plant output power. Further, plants characteristics of such system configurations are also studied. In addition, the off-gases from the heat recovery steam generator (HRSG) are used to preheat the incoming air into the SOFC stacks. The effect of such suggested air pre-heating on plant efficiency and output power is thus studied. All the configurations studied here are novel in terms of designing new plants with very high efficiencies. It should be noted that the systems presented here are studied thermodynamically and the objective of this study is not to present or discuss associated costs.
thermodynamic properties of the fluids involved. In addition, the components include a number of constitutive equations representing their physical properties, e.g. heat transfer coefficients for heat exchangers and isentropic efficiencies for compressors and turbines. During the development of DNA the four key terms, portability, robustness, efficiency, and flexibility have been kept in mind as the important features for making a generally applicable tool for energy system studies. In recent years DNA has been introduced into the education at the Department and has been applied to numerous different types of systems. The program is written in FORTRAN. 2.1. Modelling of SOFC The SOFC model used in this investigation is based on the planar type developed by DTU-Risø and TOPSØE Fuel Cell. The model is calibrated against experimental data in the range of 650–800 °C (SOFC operational temperature) as described in Petersen et al. [15]. The operational voltage (EFC) is found to be
EFC ¼ ENernst DEact DEohm DEconc DEoffset
where ENernst , Eact , Eohm , Econc , Eoffset are the Nernst ideal reversible voltage, activation polarization, ohmic polarization, concentration polarization and the offset polarization respectively. The activation polarization can be evaluated from Butler–Volmer equation (see Keegan et al. [16]). The activation polarization is isolated from other polarization to determine the charge transfer coefficients as well as exchange current density from the experiment by curve fitting technique. It follows,
2. Methodology
DEact ¼ The results of this paper are obtained using the simulation tool dynamic network analysis (DNA), see Elmegaard and Houbak [13], which is a simulation tool for energy system analysis. It is the present result of an ongoing development at the Department of Mechanical Engineering, Technical University of Denmark, which began with a Master’s Thesis work in Perstrup [14]. Since then the program has been developed to be generally applicable covering unique features, and hence supplementing other simulation programs. Some of the important features are:
RT ð0:001698T 1:254ÞF " sin h
The component library includes models of, heat exchangers, burners, Gasifiers, turbo machinery, dryers and decanters, energy storages, engines, valves, controllers as well as more specialized components and utility components. The user may also implement additional components. In DNA the physical model is formulated by connecting the relevant component models through nodes and by including operating conditions for the complete system. The physical model is converted into a set of mathematical equations to be solved numerically. The mathematical equations include mass and energy conservation for all components and nodes, as well as relations for
1
id
#
2ð13:087T 1:096 104 Þ
ð2Þ
where R, T, F and id are the universal gas constant, operating temperature, Faradays constant and current density respectively. Ohmic polarization depends on the electrical conductivity of the electrodes as well as the ionic conductivity of the electrolyte and can be described as
DEohm ¼ Simulation of both steady state (algebraic equations) and dynamic models (differential equations). Handling of discontinuities in dynamic equations. Use of a sparse-matrix-based simultaneous solver for algebraic equations. No causality implied on the model input, i.e. no restriction of the choice of inputs and outputs. Medium compositions can be variables. Models of thermodynamic states, transport variables and radiative properties for relevant fluids, e.g. steam, ideal gases and refrigerants. Features for modeling solid fuels of arbitrary components.
ð1Þ
t an
ran
þ
t el
rel
þ
tca
rca
id
ð3Þ
where tan = 600 lm, tel = 50 lm and tca = 10 lm are the anode thickness, electrolyte thickness and cathode thickness respectively. ran, rel and rca are the conductivity of anode, electrolyte and cathode respectively.
ran ¼ 105 ; rca ¼
5:760 107 0:117 exp 5 T 8:617 10 T
rel ¼ 8:588 108 T 3 1:101 104 T 2 þ 0:04679T 6:54
ð4Þ ð5Þ
Concentration polarization is dominant at high current densities for anode-supported SOFC, wherein insufficient amounts of reactants will be transported to the electrodes and the voltage will then reduce significantly. Neglecting the cathode contribution (see e.g. Kim and Virkar) [17], it can be modeled as
DEconc ¼ B ln 1 þ
pH2 id pH2 O; ias
!
! id ln 1 ias
ð6Þ
where B is the diffusion coefficient and is calibrated against experimental data which found to be,
B ¼ ð0:008039X 1 H2 0:007272Þ
T T ref
ð7Þ
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
In the above equations pH2 and pH2 O are the partial pressures for the H2 and H2O respectively, while Tref is the reference temperature (1023 K). The anode limiting current is defined as
ias ¼
2FpH2 Dbin V an RTt an san
ð8Þ
where Van and san are the porosity and tortuosity of the anode and are the physical characteristics as 30% and 2.5 lm in the experimental setup. The binary diffusion coefficient is given by
T 1:75 P ref ¼ 4:107 105 X H2 þ 8:704 105 T ref P
Dbin
n_ H2 2F A
ð9Þ
ð10Þ
where n_ H2 is molar reaction rate of H2. The area A is the physical property of the cell and is 144 cm2. The fuel composition leaving the anode is calculated by the Gibbs minimization method as described in Smith et al. [18]. Equilibrium at the anode outlet temperature and pressure is assumed for the following species: H2, CO, CO2, H2O, CH4 and N2. The equilibrium assumption is fair since the methane content in this study is low enough. The power production from the SOFC (PSOFC) depends on the amount of chemical energy fed to the anode, the reversible efficiency (grev), the voltage efficiency (gv) and the fuel utilization factor (UF). It is defined in mathematical form as
PSOFC ¼ ðLHVH2 n_ H2 ;in þ LHVCO n_ CO;in þ LHVCH4 n_ CH4 ;in Þgrev gv U F
ð11Þ
where both gv and UF are the set values while the reversible efficiency is the maximum possible efficiency defined as the relationship between the maximum electrical energy available (change in Gibbs free energy) and the fuels LHV (Lower Heating Value) as follows
grev ¼
ðDgf Þfuel LHVfuel
ð12Þ
1 ðDgf Þfuel ¼ ðgf ÞH2 O ðgf ÞH2 ðgf ÞO2 yH2 ;in 2 1 þ ðgf ÞCO2 ðgf ÞCO ðgf ÞO2 yCO;in 2 þ ðgf ÞCO2 þ 2ðgf ÞH2 O ðgf ÞCH4 2ðgf ÞO2 yCH4 ;in
ð13Þ
2.2. Modelling of fuel pre–reforming The reforming process is assumed to be equilibrium by minimizing the Gibbs free energy. The Gibbs free energy of a gas (assumed to be a mixture of k perfect gases) is given by
G_ ¼
k X n_ i g 0i þ RT lnðni pÞ
ð14Þ
i¼1
where g0, R and T are the specific Gibbs free energy, universal gas constant and gas temperature respectively. Each atomic element in the inlet gas is in balance with the outlet gas composition, which yields the flow of each atom has to be conserved. For N elements this is expressed as (see, e.g. Elmegaard and Houbak) [19] k X i¼1
n_ i;in Aij ¼
k X i¼1
n_ i;out Aij
for j ¼ 1; N
/ ¼ G_ out þ
N X j¼1
which is also calibrated against the experimental data. Pref is the reference pressure as 1.013 bar and X H2 is the mass reaction rate of H2. Finally the current density id is directly proportional to the amount of reacting hydrogen according to the Faraday’s law:
id ¼
The N elements corresponds to H2, CO2 , H2O and CH4 in such pre – reforming process. Ai,j is a matrix with information of the mole j in each mole of i (H2, CO2 , H2O and CH4). The minimization of Gibbs free energy can be formulated by introducing a Lagrange multiplier, l, for each of the N constraints obtained in Eq. (15). After adding the constraints, the expression to be minimized is then
ð15Þ
"
lj
k X ðn_ i;out n_ i;out ÞAij
!# ð16Þ
i¼1
The partial derivation of this equation with respect to n_ i;out can be writes as k X g 0i;out @/ ¼ lj Aij þ lnðni;out pout Þ þ _ @ ni;out RT j¼1
for i ¼ 1; k
ð17Þ
At the minimum each of these is then zero. The additional equation to make the system consistent is the summation of molar fractions of the outlet gas to be k X
ni;out ¼ 1
ð18Þ
i¼1
3. Plant configurations The first configuration studied is shown in Fig. 1a. The fuel (NG) is preheated in a heat exchanger before it is sent to a desulphurization unit to remove the sulphur content in the NG. This unit is assumed to be using a catalyst, operating at temperature of 200 °C. Thereafter the heavier carbon contents in the NG are cracked down in a CPO type pre-reformer catalyst. Before that the fuel must be preheated again to reach to the operational temperature of the CPO catalyst. The CPO catalyst needs additional air which is supplied by a small pump as shown in the figure. It is assumed that the supplied NG is pressurized and therefore no pump is needed for the fuel. The pre-reformed fuel is now sent to the anode side of the SOFC stacks. Due to the exothermic nature of the CPO catalyst, no pre-heating of the fuel is required. The fuel has a temperature of about 650 °C before entering the stacks. The operating temperature of the SOFC stacks as well as outlet temperatures is assumed to be 780 °C. Therefore, the burned fuel after the stacks has a temperature of about 780 °C which is used to preheat the fuel in the heat exchangers mentioned above. On the other side, air is compressed in a compressor and then preheated in a recuperator to about 600 °C before entering the cathode side of the SOFC stacks. It should be mentioned that these entering temperatures are essential requirements for proper functioning of SOFC stacks. Otherwise, the stacks will shut down automatically. Since the fuel in the SOFC stacks will not burn completely the rest of the fuel together with the air coming out of the cathode side of the stacks are sent to a burner (catalytic burner) for further burning. The off-gases from the burner have a high heat quality which can be used to generate steam in a heat recovery steam generator (HRSG). In the Rankine cycle, the pressurized water after the feed pump is heated up to steam in the economizer (ECO), evaporator (EVA) and super-heater (SUP). The generated steam is then expanded in a steam turbine to generate electricity. Part of the expanded steam is then extracted for the deaerator. The expanded steam after the ST is then cooled down in a condenser (including a sub-cooler part) before pumping to the deaerator. The water is preheated in the deaerator before being recycled. As mentioned earlier the ASR reformer needs super heated steam for operation. Such steam must be supplied to the reformer externally during startup. However, during normal operation steam is available after SOFC stacks due to reactions of hydrogen
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
(a) SOFC
Prereformer
Fuel
Desuplhurizer
HEX
HEX HEX
Burner Air Air ECO
EVA
SUP
ST
Condenser Deaerator
(b) Recycle Fuel SOFC HEX
HEX
HEX
HEX
Prereformer
Desuplhurizer
Burner
Air ECO
EVA
SUP
ST
Condenser Deaerator Fig. 1. Combined SOFC–ST cycle plants, (a) with CPO reformer and (b) with ASR reformer. Rankine cycle with a single pressure level.
and oxygen. Therefore, the stream after the anode side of SOFC is recycled as shown in Fig. 1b. There are three alternatives for such a recirculation unit, a pump, a turbocharger and an ejector. In a real plant, due to high temperature of this stream (more than 700 °C) the cost of a pump will be rather expensive. This is also true for a turbocharger working at such mass flows and pressures. Moreover, using an ejector brings up problems associated with the size and dimensioning of the ejector (due to combination of pressure drop and mass flows), which is out of the scope of this investigation. In fact, the author is studying the possibilities of including an ejector into the DNA program which takes into account the size
of ejectors and nuzzle area. Based on these facts and for the sake of simplicity a pump is used in this investigation. Besides the recycle part, the plant configuration is the same as in the CPO reformer case, see Fig. 1b. The main parameters for the plant are given in Table 1. Number of SOFC stacks is assumed to be 10,000 and number of cells per stacks is assumed to be 74. The pressure drops in the cathode and anode sides of the fuel cell are assumed to be 0.05 respective 0.01 bars. These values are the setting values for the program, however, pressure drops are a function of channel sizes and mass flows and the channel geometry is not kwon. Therefore, these
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
Table 1 Main parameters for design point calculations of Fig. 1.
Table 2 Main calculated parameters for design point calculations of Fig. 1.
Parameter
CPO
ASR
Parameter
CPO
ASR
Compressor intake temperature Compressor isentropic efficiency Compressor mechanical efficiency SOFC cathode inlet temperature SOFC cathode outlet temperature SOFC utilization factor SOFC number of cells SOFC number of stacks SOFC cathode side pressure drop ratio SOFC anode side pressure drop ratio Heat exchangers pressure drops Fuel inlet temperature Desulphurizer operation temperature SOFC anode inlet temperature SOFC anode outlet temperature Burner efficiency ST isentropic efficiency Feed water pump pressure Extraction pressure Extraction steam temperature Generators efficiency
25 °C 0.85 0.95 600 °C 780 °C 0.80 74 10,000 0.05 bar 0.01 bar 0.01 bar 25 °C 200 °C 650 °C 780 °C 0.97 0.9 70 bar 2 bar 120.2 °C 0.97
25 °C 0.85 0.95 600 °C 780 °C 0.80 74 10,000 0.05 bar 0.01 bar 0.01 bar 25 °C 200 °C 650 °C 780 °C 0.97 0.9 60 bar 2 bar 120.2 °C 0.97
Compressor mass flow Fuel mass flow SOFC anode mass flow Burner inlet fuel mass flow Burner inlet air mass flow HRSG gas side inlet temperature HRSG gas side outlet temperature HRSG water side inlet temperature ST inlet steam temperature ST pressure ST inlet mass flow Extraction mass flow
51.4 kg/s 1.32 kg/s 1.45 kg/s 5.17 kg/s 47.7 kg/s 526.3 °C 218.2 °C 121.1 °C 496.3 °C 69.97 bar 6.33 kg/s 5.40 kg/s
59.0 kg/s 1.30 kg/s 1.72 kg/s 5.13 kg/s 55.11 kg/s 455.6 °C 232.0 °C 121.0 °C 425.6 °C 59.97 bar 5.47 kg/s 4.64 kg/s
values are calculated based on the available data for each channel mass flow and dimensions. In addition, the calculations show that the final values in terms of plant power and efficacy do not change significantly if these values are changed slightly. The pressure drops for all heat exchangers are assumed to 0.01 bars. Again these values depend on the heat exchanger types and channel geometries, but they are reasonable for plate heat exchanger types. The minimum temperature differences at pinch (Tmin) are assumed to be 30 °C, 15 °C and 17 °C for superheat, evaporator and economizer respectively. The compressor isentropic efficiency and mechanical efficiency are assumed to be 0.85 respective 0.97, while the generator efficiency is assumed to be 0.97. The SOFC plant provides direct current and must be converted to AC through a converter. Further, the efficiency of the DC/AC converter is assumed to be 100%, due to lack of such component in the DNA program. In reality there would be some losses trough the converter and efficiencies of 97% could be assumed for plants of such sizes studied in this investigation. The output power would therefore be somewhat lower while the plant efficiency would not change significantly. Furthermore, the utilization factor for the SOFC cells is assumed to be 0.8. Several calculations have been carried out to find the optimal extraction pressure as well as the optimum live steam pressure which are not included here. The main calculated parameters are provided in Table 2. The main difference in the Rankine cycle from CPO and ASR are the off-gases temperatures entering the HRSG. The CPO pre-reforming plant provides much higher temperature for the off-gases, which is due to the fact that the air mass flow to its burner is lower than the corresponding one for the ASR pre-reforming plant. Consequently, the feeding temperature for the Rankine cycle will be higher in the CPO type, which will results in higher net power from the steam cycle, see Table 3. The plants net powers and thermal efficiencies (based on LHV, lower heating value) are shown in Table 3. The net power output of the hybrid plant with CPO pre-reforming is calculated to be about 1 MW higher than the corresponding plant with the ARS pre-reforming. The main reason is that the steam cycle in the CPO type plant produces somewhat higher power than the corresponding ASR type plant (higher off-gases temperature for the CPO pre-reforming). As a result the thermal efficiency of the plant with CPO pre-reforming will be higher than the corresponding plant with ASR pre-reforming. However, the thermal efficiency of the SOFC plant (not the hybrid one) with ASR pre-reforming is cal-
Table 3 Net powers and efficiencies of the plants for Fig. 1. Parameter
CPO
ASR
Net power output Output power from SOFC cycle Output power from ST cycle Thermal efficiency of steam cycle (LHV) Thermal efficiency of SOFC cycle (LHV) Thermal efficiency (LHV)
38.03 MW 31.04 MW 6.99 MW 0.382 0.514 0.630
36.72 MW 31.23 MW 5.49 MW 0.368 0.524 0.617
culated to be about 1% point higher than the SOFC plant with CPO pre-reforming. This is due to the fact that CPO pre-reforming needs additional air mass flow which must be provided by additional compressor flow (or additional compressor) which in turn needs additional electrical power. The cycle efficiencies are defined as
gSOFC;a ¼ Net power form SOFC cycle=fuel consumption gST ¼ Net power form steam cycle=heat into steam gHybrid
cycle through HRSG ¼ Net power form hybrid plant=fuel consumption
ð19Þ
Some of the compressor effect is used to provide the pressure drops in the heat exchangers of the HRSG. Therefore the compressor effect has been divided into two part; one part which is intent for the ST cycle only and the rest which applied to the SOFC cycle only. It can be shown that the thermal efficiency of the integrated systems can be calculated by
gth ¼ gSOFC þ gST ð1 gSOFC ÞeHRSG
ð20Þ
T HRSG;in T HRSG;out T HRSG;in T air
ð21Þ
eHRSG ¼
where gSOFC and gST are the SOFC cycle efficiency and steam cycle efficiency respectively. HRSG is the effectiveness of the heat recovery steam generator, which describes the amount of heat that has been transferred from the SOFC cycle to the steam cycle. These equations provide HRSG efficiencies 0.615 and 0.519 for CPO respective ARS. Thermal efficiencies can then be calculated as 0.628 and 0.615 for CPO respective ASR. These values are in agreement with the numerical results given in Table 3. In order to optimize the systems presented above, the plants efficiencies versus live steam pressures and moisture contents are presented in Fig. 2. The results indicate that for the CPO case the maximum efficiency appears to be at about 45 bar while for the ASR case this maxima is around 22 bar. At optimal live steam pressure the efficiency of the CPO pre-reformer case is higher than the corresponding optimal live steam pressure for the ASR pre-reformer case. The moisture content after the steam turbine is an
2729
64
20
63.2
16
63.2
16
62.4
12
62.4
12
61.6
8
61.6
8
60.8
4
moisture
moisture
60.8
60 10
20
30
40
50
60
4
ηth
ηth
0
Moisture content [%]
20
Thermal Efficiency [%]
64
Moisture content [%}]
Thermal Efficiency [%]
M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
70
0 80
60
0
10
Live Steam Pressure [bar]
20
30
40
50
60
70
0 80
Live Steam Pressure [bar]
(a)
(b)
Fig. 2. Thermal efficiency and moisture content of the combined SOFC–ST plants as function of live steam pressure: (a) with CPO reformer and (b) with ASR reformer. Rankine cycle with single pressure level.
important issue to be considered. Too high level of moisture (more than about 16%) may cause blades corrosion located at the last stage, see e.g. Kehlhofer et al. [20]. Further, the results indicate that for the CPO pre-reforming plant the moisture content more than 16% may occur for pressures above 75 bar, while for the ASR prereforming plant this is true for pressures above 48 bar. Although, both are much higher than the optimized pressures mentioned above. 3.1. Effects of cathode air pre-heating (hybrid recuperating) The energy left after the HRSG in the previous designs are rather high; see the outlet temperatures of HRSG in both cases. The reason is that decreasing the live steam pressure decreases the depleted gas temperature form the HRSG, but also the steam cycle thermal efficiency and thereby the combined plant efficiency. However, at the given pressures above the combined plants efficiencies are close to their respective optimum and the depleted gas temperatures are high as well. Therefore, this energy can be used to preheat the cathode air flow and thereby decrease the energy from the SOFC cycle which is used for pre-heating. This will in turn increase the energy of the off-gases through the HRSG and thereby increase the efficiency of the steam cycle. Fig. 3 shows the suggested plants. The SOFC cycle efficiency will not decrease significantly by such pre-heating. It may be mentioned that such a pre-heating cannot be done in a combined cycle (gas turbine on the top of a steam turbine cycle) since the temperature after the compressor is too high because of compressor pressure ratio, usually much higher than the HRSG outlet gas temperature (gas side). Several calculations for each pre-reformer case are carried out to find the optimal thermal efficiency of the systems. The optimal pressure for the steam turbine is calculated as 70 bar and 60 bar for respective CPO and ASR pre-reforming cases. The most calculated important results are shown in Table 4. It is assumed that the HRSG outlet gas-side temperature is 90 °C. This is due to the fact that the off-gases are pure enough to allow to recover the energy to such temperature. However, in order to see how the thermal efficiencies of the proposed systems will change if the outlet gas temperatures from the HRSG is increased, Fig. 4 is presented. As the results show the efficiencies decreases by increasing the HRSG outlet temperature. At 120 °C the thermal efficiency of the CPO case drops to 0.668 from 0.680, while
for the ARS case the thermal efficiency is decreased to 0.664 from 0.677. However, these efficiencies are still much higher compared to the traditional plants for such sizes. Further, the drop in efficiency for the ASR pre-reforming case is more sensible than the CPO case, the lines are getting wider. It can be shown by a simple mathematic that the efficiency of any hybrid plants with hybrid recuperating concept (using dissipated heat from the bottoming cycle to the topping cycle) can be calculated from
gth ¼ 1 þ
Q recuperated ðgSOFC þ gST ð1 gSOFC ÞeHRSG Þ Q in
ð22Þ
where Qrecuperated is the heat recuperated to the SOFC cycle and Qin is the heat supplied to the plant through fuel. Note that the ratio Qrecuperated/Qin in this equation is very small and therefore it is simplified. For the CPO pre-reforming case Qrecuperated/Qin and HRSG are calculated as 0.096 and 0.731 respectively. Inserting these values into the Eq. (22) together with cycle efficiencies provides plant thermal efficiency as 0.680 which is in agreement with the corresponding calculated value shown in Table 4. For the ASR pre-reforming case Qrecuperated/Qin and HRSG are calculated as 0.122 and 0.680 respectively. Inserting these values into Eq. (22) gives plant thermal efficiency as 0.677 which is again in agreement with the corresponding calculated value shown in Table 4. 3.2. Effects of SOFC fuel utilization factor The SOFC fuel utilization factor in the previous calculations was set to 0.8. However, the computed results changes if the fuel utilization factor varies. Fig. 5a shows the SOFC cycle efficiency as function of fuel utilization factor for the four cases considered. In this figure and from now on the SOFC cycle efficiency is defined as (due to recuperation),
gSOFC;b ¼ Net power form SOFC cycle=ðfuel consumption þ recuperated heatÞ
ð23Þ
Without recuperating the SOFC cycle efficiency will be increased by increasing cell utilization factor. However, at some point the demanding cooling effect will be very significant and the SOFC cycle efficiency starts to decrease. Therefore, the SOFC cycle efficiency has maxima at 0.78 and 0.76 with CPO respective ASR pre-reforming, if no recuperating is used. At utilization factor of
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
(a) SOFC
Prereformer
HEX
HEX HEX
Fuel
Desuplhurizer
HEX
Burner Air Air ECO
EVA
SUP
ST
Condenser Deaerator
(b) Recycle Fuel SOFC HEX HEX
HEX
HEX
HEX
Prereformer
Desuplhurizer
Burner
Air ECO
EVA
SUP
ST
Condenser Deaerator Fig. 3. Combined SOFC–ST cycle plants, (a) with CPO reformer and (b) with ASR reformer. Rankine cycle with a single pressure level and cathode pre-heating in the SOFC cy.
about 0.81 the SOFC cycle efficiency decreases sharply, which is more significant in the ASR pre-reforming than the CPO prereforming type. Further, the SOFC cycle efficiency with ASR prereforming is higher than CPO pre-reforming without recuperating. With hybrid recuperating, SOFC cycle efficiency increases with decreasing fuel utilization factor. This can mainly be explained by Eq. (23) in which the recuperated heat to the SOFC cycle increases mach faster than the changes on SOFC power output. (Fuel consumption remains constant.) To give an example, if utilization factor is increased from 0.72 to 0.82 then the recuperated heat will
be about four times larger. The SOFC cycle efficiency is lower with recuperating than without recuperating which is mainly due to definition used in Eq. (23). The steam cycle efficiency decreases with increasing fuel utilization as shown in Fig. 5b. This is because less fuel will be burned in the burner and consequently HRSG inlet temperature decreases. The steam plant efficiency for CPO case is higher than the corresponding one with ASR case, if no recuperating is used. This is because the SOFC cycle efficiency with ASR pre-reforming is higher than the corresponding one with CPO pre-reforming. If
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732 Table 4 Net powers and efficiencies of the plants for Fig. 3.
0.685
Parameter
CPO
ASR
Net power output Output power from SOFC cycle Output power from ST cycle Depleted gas temperature Steam Pressure/temperature Thermal efficiency of steam cycle (LHV) Moisture content after ST Thermal efficiency of SOFC cycle (LHV) Thermal efficiency (LHV)
41.06 MW 30.92 MW 10.14 MW 90 °C 70 bar/569.9 °C 0.395 11.5% 0.512 0.680
40.34 MW 31.13 MW 9.21 MW 90 °C 60 bar/532.2 °C 0.381 12.9% 0.523 0.677
recuperating is used then the steam plant efficiency is similar with both pre-reforming types. The hybrid plant efficiency as function of SOFC fuel utilization factor is shown in Fig. 6a. Decreasing the fuel utilization factor would result in increasing hybrid plant efficiency, for all cases considered. This is a consequent of what has been explained earlier. Decreasing fuel cell utilization factor increases ST inlet temperature significantly. Such an increase is more sever for the CPO
Efficiency
0.68
0.675
0.67 ASR CPO
0.665
0.66 90
95
100
105
110
115
120
HRSG outlet T [C] Fig. 4. Thermal efficiencies as function of HRSG outlet gas temperature.
pre-reformer without recuperating than the other three configurations. Further, if the temperature limit for ST is set to 600 °C then the fuel cell utilization factor cannot be below about 0.74, 0.77,
0.6
0.5
0.5
Steam cycle efficiency
SOFC cycle efficiency
0.45
0.4 CPO - no recuperating ASR - no recuperating CPO - with recuperating
0.3
ASR - with recuperating
0.4 0.35 0.3 0.25 CPO- no recuperating ASR - no recuperating
0.2
CPO - with recuperating 0.15
0.2 0.72
0.74
0.76
0.78
0.8
0.1 0.72
0.82
ASR - with recuperating
0.74
0.76
0.78
0.8
SOFC fuel utilization factor
SOFC fuel utilization factor
(a)
(b)
0.82
Fig. 5. Cycle efficiencies as function of SOFC utilization factors for four cases considered: (a) SOFC cycle efficiency, (b) steam cycle efficiency.
0.8 1000
CPO without recuperating ASR without recuperating CPO with recuperating ASR with recuperating
0.7
0.6
800 700
0.5
T[C]
Hybrid plant efficiency
900
CPO - no recuperating
0.4
ASR - no recuperating
500
CPO - with recuperating
0.3
400
ASR - with recuperating 0.2 0.72
600
0.74
0.76
0.78
0.8
0.82
300 0.72
0.75
0.78
0.81
SOFC fuel utilization factor
SOFC fuel utilization factor
(a)
(b)
Fig. 6. (a) Hybrid plant efficiency as function of fuel cell utilization factors and (b) inlet temperature of the high pressure steam turbine as function of fuel cell utilization factor.
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
0.77 and 0.8 for ARS without recuperating, ASR with recuperating, CPO without recuperating and CPO with recuperating respectively. 4. Conclusions Hybrid combined SOFC–ST plants are presented and analyzed. The plants are fired by natural gas and therefore the fuel is desuphurized and then pre-reformed before sending to the anode side of the SOFC. Both CPO and ARS pre-reforming processes are used. The results indicate that for simple combinations the thermal efficiencies of the system can reach to about 62–63% depending on the choice of pre-reforming type. The SOFC cycle efficiency in the ASR performing type is higher than the corresponding SOFC cycle with CPO pre-reforming type. However, the efficiency of the hybrid plants with CPO case is larger than the corresponding hybrid plants with ARS case. This is due to the fact that in the CPO case the temperature of the off-gases entering the HRSG is larger than the corresponding temperature in the ARS case. This results in higher efficiency in the bottoming cycle (steam cycle) and thereby better efficiency for the hybrid plants. In another suggested system configurations the off-gases from the HRSG is recuperated to the SOFC cycle by pre-heating incoming air flow after the compressor and before entering the cathode side of the SOFC. In this way the energy of off-gases in the HRSG can be further used and thereby the electrical efficiencies of the systems are increased to about 68% for both CPO and ASR pre-reforming types. Such cathode air pre-heating does not change the SOFC plant efficiency but increases the steam cycle efficiency significantly due to better use of the off-gases energy and lowering the stack temperature. Decreasing the SOFC fuel utilization factor increases plant electrical efficiency significantly. However, this parameter cannot be less than a certain value (due to configuration) since the inlet temperature of the steam turbine would be too large. References [1] Fontell E, Kivisaari T, Christiansen N, Hansen J, Pålsson J-B. Conceptional study of a 250 kW planar SOFC system for CHP application. J Power Sources 2004;131:49–56. [2] Rokni M. Introduction of a fuel cell into combined cycle: a competitive choice for future cogeneration. ASME Cogen – Turbo IGTI 2003;8:255–61.
[3] Riensche E, Achenbach E, Froning D, Haines MR, Heidug WK, Lokurlu A, et al. Clean combined-cycle SOFC power plant–cell modeling and process analysis. J Power Sources 2000;86:404–10. [4] Pålsson J, Selimovic A, Sjunnesson L. Combined solid oxide fuel cell and gas turbine system for efficient power and heat generation. J Power Sources 2000;86:442–8. [5] Proell T, Rauch R, Aichering C, Hofbauer H. Coupling of biomass steam gasification and an SOFC–GT hybrid system for highly efficient electricity generation. In: ASME Turbo Expo Proceeding, GT2004-53900; 2004. p. 103–9. [6] Subramanyan K, Diwekar UM. Characterization and quantification of uncertainty in solid oxide fuel cell hybrid power plants. J Power Sources 2005;142:103–16. [7] Calise F, Dentice d’ Accadia M, Vanoli L, von Spakovsky MR. Single-level optimization of hybrid SOFC–GT power plant. J Power Sources 2006;159:1169–85. [8] Wächter C, Lunderstädt R, Joos F. Dynamic model of a pressurized SOFC–GT hybrid power plant for the development of control concept. J Fuel Cell Sci Technol 2006;3(3):271–9. [9] Roberts RA, Brouwer J. Dynamic simulation of a pressurized 220 kW solid oxide fuel-cell–gas-turbine hybrid system: modeled performance compared to measured Results. J Fuel Cell Sci Technol 2006;3(1):18–25. [10] Rokni M, Fontell E, Ylijoki Y, Tiihonen O, Hänninen M. Dynamic modeling of wärtsilä 5kW SOFC system. In: Singhal SC, Mizusaki J, editors. Ninth International symposium on solid oxide fuel cell (SOFC IX), Quebec; 2005. p. 865–75. [11] Costamagna P, Magistri L, Massardo AF. Design and part-load performance of a hybrid system based on a solid oxide fuel cell reactor and a micro gas turbine. J Power Sources 2001;96:352–68. [12] Dunbar WR, Lior N, Gaggioli RA. Combining fuel cells with fuel-fired power plants for improved exergy efficiency. J Energy 1991;16(10):1259–74. [13] Elmegaard B, Houbak N. DNA – a general energy system simulation tool, Proceeding of SIMS, Trondheim, Norway; 2005. [14] Perstrup C. Analysis of power plant installation based on network theory (in Danish). M.Sc. thesis, Technical University of Denmark, Laboratory of Energetics, Denmark; 1989. [15] Petersen TF, Houbak N, Elmegaard B. A zero-dimensional model of a 2nd generation planar SOFC with calibrated parameters. Int J Thermodyn 2006;9(4):161–8. [16] Keegan KM, Khaleel M, Chick LA, Recknagle K, Simner SP. Diebler J. Analysis of a planar solid oxide fuel cell based automotive auxiliary power unit. SAE technical paper series No. 2002-01-0413; 2002. [17] Kim JW, Virkar AV. The effect of anode thickness on the performance of anodesupported solid oxide fuel cell. In: Proceedings of the sixth international symposium on SOFCs, (SOFC-VI), PV99-19. The Electrochemical Society; 1999. p. 830–9. [18] Smith JM, Van Ness HC, Abbott MM. Introduction to chemical engineering thermodynamics. 7th ed. Boston: McGraw-Hill; 2005. [19] Elmegaard B. Houbak N. On the implementation of energy simulators with emphasis on chemical equilibrium gasifier models. In: Proceedings of ECOS’99. Tokyo; 1999. p. 258–63. ISBN: 4-9980762-0-5 [20] Kehlhofer RH, Warner J, Nielsen H, Bachmann R. Combined–cycle gas steam turbine power plants. PennWell; 1999. ISBN: 0-87814-736-5.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Thermodynamic analysis of an integrated solid oxide fuel cell cycle with a rankine cycle Masoud Rokni Technical University of Denmark, Dept. Mechanical Engineering, Thermal Energy System, Building 402, 2800 Kgs, Lyngby, Denmark
a r t i c l e
i n f o
Article history: Received 23 September 2009 Accepted 1 June 2010
Keywords: SOFC Rankine Steam plant Hybrid plant CPO ASR
a b s t r a c t Hybrid systems consisting of solid oxide fuel cells (SOFC) on the top of a steam turbine (ST) are investigated. The plants are fired by natural gas (NG). A desulfurization reactor removes the sulfur content in the fuel while a pre-reformer breaks down the heavier hydro-carbons. The pre-treated fuel enters then into the anode side of the SOFC. The remaining fuels after the SOFC stacks enter a burner for further burning. The off-gases are then used to produce steam for a Rankine cycle in a heat recovery steam generator (HRSG). Different system setups are suggested. Cyclic efficiencies up to 67% are achieved which is considerably higher than the conventional combined cycles (CC). Both adiabatic steam reformer (ASR) and catalytic partial oxidation (CPO) fuel pre-reformer reactors are considered in this investigation. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The solid oxide fuel cell (SOFC) is an electrochemical reactor currently under development by some companies for power and heat generation application. Depending on the type of the electrolyte they are operating at temperature levels of more than about 750–1000 °C. The lower temperature alternative is now being developed for market entry during the next decade. Due to material complication on the balance of plant (BoP) components many companies are trying to find new materials for the SOFC cells to decrease the operating temperature of the SOFC stacks. Temperatures of about 650 °C are also mentioned. The biggest advantage of the SOFC in comparison with other types of fuel cells may be in its flexibility in using different types of fuel. However, in planar SOFCs one needs to pre-process most kind of fuels in order to break down the heavier hydro-carbons which may otherwise damage the fuel cells. The sulphur content in the fuels must firstly be removed and then pre-reformed before entering the anode side of the SOFC. Such fuel pre-processing can be done in two different catalytic reactors operating at different temperature levels indicated by reactor manufacturers. SOFC-based power plants have been studied for a while and some companies, such as Wärtsilä, are trying to realize such a system for combined heat and power (CHP) applications; see e.g. Fontell et al. [1]. The SOFC is also combined with combined cycles (CC) in the literature to achieve ultra high electrical efficiencies, see e.g.
E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.06.008
Rokni [2] and Riensche et al. [3]. Due to the current operating temperature of the SOFC stacks (more than about 750 °C), hybrid SOFC and GT (gas turbine) systems have also been studied extensively in the literature, e.g. in Pålson et al. [4] for CHP and in Proell et al. [5] with internal biomass gasification. Characterization, quantification and optimization of hybrid SOFC–GT systems have been studied by e.g. Subramanyan et al. [6] and Calise et al. [7]. The dynamics and control concept of a pressurized SOFC–GT hybrid system has also been studied, such as in Wächter et al. [8]. In Roberts and Brouwer [9] modeling results are compared with measured data for a 220 kW hybrid SOFC–GT power plant. Details on design, dynamics, control and startup of such hybrid power plants are studied in Rokni et al. [10]. Part–load characteristics of a SOFC–micro GT were also studied in Costamagna et al. [11]. While hybrid SOFC–GT plants have been extensively studied by many researchers, the investigations on combined SOFC and steam turbine (ST) are very limited see Dunbar et al. [12]. In addition the SOFC manufacturers are trying to decrease the operating temperature of the SOFC stacks, and then the combination of SOFC–ST hybrid system would be more attractive than the SOFC–GT systems. By decreasing the operating temperature, the material cost for the SOFC stacks will be decreased as well as many problems associated with the BoP components will be diminished. In hybrid SOFC–GT plants the SOFC stacks must be pressurized in an extremely large vessel (depending on the size of the plant which is usually in mega Watt classes). Such a practical problem will be diminished in hybrid SOFC–ST systems, because the stacks will work under atmospheric pressure. Another disadvantage of a SOFC–GT system is that the startup simplicity of the GT is
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
diminished since the startup time of a SOFC plant is much longer than that of a GT plant. Fuel pre-reforming can be done in different reactors such as adiabatic steam reformer (ASR) and catalytic partial oxidation (CPO). The disadvantage of an ASR reactor is that it needs superheated steam during startup (depending on the operating temperature of the reactor, i.e. 400 °C) which is an extremely power consuming process. During normal operation steam is available after the anode side of the SOFC stacks, which can be recycled into the system. However, in a CPO reactor additional air is needed for the fuel prereforming process, which in turn increases the plant power consumption (compressor work) and thereby the plant efficiency will be decreased. In this study, ASR reforming process versus CPO reforming process is studied in terms of plant design, plant efficiency and plant output power. In the Rankine cycle a single pressure level is proposed to study plant design, plant efficiency and plant output power. Further, plants characteristics of such system configurations are also studied. In addition, the off-gases from the heat recovery steam generator (HRSG) are used to preheat the incoming air into the SOFC stacks. The effect of such suggested air pre-heating on plant efficiency and output power is thus studied. All the configurations studied here are novel in terms of designing new plants with very high efficiencies. It should be noted that the systems presented here are studied thermodynamically and the objective of this study is not to present or discuss associated costs.
thermodynamic properties of the fluids involved. In addition, the components include a number of constitutive equations representing their physical properties, e.g. heat transfer coefficients for heat exchangers and isentropic efficiencies for compressors and turbines. During the development of DNA the four key terms, portability, robustness, efficiency, and flexibility have been kept in mind as the important features for making a generally applicable tool for energy system studies. In recent years DNA has been introduced into the education at the Department and has been applied to numerous different types of systems. The program is written in FORTRAN. 2.1. Modelling of SOFC The SOFC model used in this investigation is based on the planar type developed by DTU-Risø and TOPSØE Fuel Cell. The model is calibrated against experimental data in the range of 650–800 °C (SOFC operational temperature) as described in Petersen et al. [15]. The operational voltage (EFC) is found to be
EFC ¼ ENernst DEact DEohm DEconc DEoffset
where ENernst , Eact , Eohm , Econc , Eoffset are the Nernst ideal reversible voltage, activation polarization, ohmic polarization, concentration polarization and the offset polarization respectively. The activation polarization can be evaluated from Butler–Volmer equation (see Keegan et al. [16]). The activation polarization is isolated from other polarization to determine the charge transfer coefficients as well as exchange current density from the experiment by curve fitting technique. It follows,
2. Methodology
DEact ¼ The results of this paper are obtained using the simulation tool dynamic network analysis (DNA), see Elmegaard and Houbak [13], which is a simulation tool for energy system analysis. It is the present result of an ongoing development at the Department of Mechanical Engineering, Technical University of Denmark, which began with a Master’s Thesis work in Perstrup [14]. Since then the program has been developed to be generally applicable covering unique features, and hence supplementing other simulation programs. Some of the important features are:
RT ð0:001698T 1:254ÞF " sin h
The component library includes models of, heat exchangers, burners, Gasifiers, turbo machinery, dryers and decanters, energy storages, engines, valves, controllers as well as more specialized components and utility components. The user may also implement additional components. In DNA the physical model is formulated by connecting the relevant component models through nodes and by including operating conditions for the complete system. The physical model is converted into a set of mathematical equations to be solved numerically. The mathematical equations include mass and energy conservation for all components and nodes, as well as relations for
1
id
#
2ð13:087T 1:096 104 Þ
ð2Þ
where R, T, F and id are the universal gas constant, operating temperature, Faradays constant and current density respectively. Ohmic polarization depends on the electrical conductivity of the electrodes as well as the ionic conductivity of the electrolyte and can be described as
DEohm ¼ Simulation of both steady state (algebraic equations) and dynamic models (differential equations). Handling of discontinuities in dynamic equations. Use of a sparse-matrix-based simultaneous solver for algebraic equations. No causality implied on the model input, i.e. no restriction of the choice of inputs and outputs. Medium compositions can be variables. Models of thermodynamic states, transport variables and radiative properties for relevant fluids, e.g. steam, ideal gases and refrigerants. Features for modeling solid fuels of arbitrary components.
ð1Þ
t an
ran
þ
t el
rel
þ
tca
rca
id
ð3Þ
where tan = 600 lm, tel = 50 lm and tca = 10 lm are the anode thickness, electrolyte thickness and cathode thickness respectively. ran, rel and rca are the conductivity of anode, electrolyte and cathode respectively.
ran ¼ 105 ; rca ¼
5:760 107 0:117 exp 5 T 8:617 10 T
rel ¼ 8:588 108 T 3 1:101 104 T 2 þ 0:04679T 6:54
ð4Þ ð5Þ
Concentration polarization is dominant at high current densities for anode-supported SOFC, wherein insufficient amounts of reactants will be transported to the electrodes and the voltage will then reduce significantly. Neglecting the cathode contribution (see e.g. Kim and Virkar) [17], it can be modeled as
DEconc ¼ B ln 1 þ
pH2 id pH2 O; ias
!
! id ln 1 ias
ð6Þ
where B is the diffusion coefficient and is calibrated against experimental data which found to be,
B ¼ ð0:008039X 1 H2 0:007272Þ
T T ref
ð7Þ
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
In the above equations pH2 and pH2 O are the partial pressures for the H2 and H2O respectively, while Tref is the reference temperature (1023 K). The anode limiting current is defined as
ias ¼
2FpH2 Dbin V an RTt an san
ð8Þ
where Van and san are the porosity and tortuosity of the anode and are the physical characteristics as 30% and 2.5 lm in the experimental setup. The binary diffusion coefficient is given by
T 1:75 P ref ¼ 4:107 105 X H2 þ 8:704 105 T ref P
Dbin
n_ H2 2F A
ð9Þ
ð10Þ
where n_ H2 is molar reaction rate of H2. The area A is the physical property of the cell and is 144 cm2. The fuel composition leaving the anode is calculated by the Gibbs minimization method as described in Smith et al. [18]. Equilibrium at the anode outlet temperature and pressure is assumed for the following species: H2, CO, CO2, H2O, CH4 and N2. The equilibrium assumption is fair since the methane content in this study is low enough. The power production from the SOFC (PSOFC) depends on the amount of chemical energy fed to the anode, the reversible efficiency (grev), the voltage efficiency (gv) and the fuel utilization factor (UF). It is defined in mathematical form as
PSOFC ¼ ðLHVH2 n_ H2 ;in þ LHVCO n_ CO;in þ LHVCH4 n_ CH4 ;in Þgrev gv U F
ð11Þ
where both gv and UF are the set values while the reversible efficiency is the maximum possible efficiency defined as the relationship between the maximum electrical energy available (change in Gibbs free energy) and the fuels LHV (Lower Heating Value) as follows
grev ¼
ðDgf Þfuel LHVfuel
ð12Þ
1 ðDgf Þfuel ¼ ðgf ÞH2 O ðgf ÞH2 ðgf ÞO2 yH2 ;in 2 1 þ ðgf ÞCO2 ðgf ÞCO ðgf ÞO2 yCO;in 2 þ ðgf ÞCO2 þ 2ðgf ÞH2 O ðgf ÞCH4 2ðgf ÞO2 yCH4 ;in
ð13Þ
2.2. Modelling of fuel pre–reforming The reforming process is assumed to be equilibrium by minimizing the Gibbs free energy. The Gibbs free energy of a gas (assumed to be a mixture of k perfect gases) is given by
G_ ¼
k X n_ i g 0i þ RT lnðni pÞ
ð14Þ
i¼1
where g0, R and T are the specific Gibbs free energy, universal gas constant and gas temperature respectively. Each atomic element in the inlet gas is in balance with the outlet gas composition, which yields the flow of each atom has to be conserved. For N elements this is expressed as (see, e.g. Elmegaard and Houbak) [19] k X i¼1
n_ i;in Aij ¼
k X i¼1
n_ i;out Aij
for j ¼ 1; N
/ ¼ G_ out þ
N X j¼1
which is also calibrated against the experimental data. Pref is the reference pressure as 1.013 bar and X H2 is the mass reaction rate of H2. Finally the current density id is directly proportional to the amount of reacting hydrogen according to the Faraday’s law:
id ¼
The N elements corresponds to H2, CO2 , H2O and CH4 in such pre – reforming process. Ai,j is a matrix with information of the mole j in each mole of i (H2, CO2 , H2O and CH4). The minimization of Gibbs free energy can be formulated by introducing a Lagrange multiplier, l, for each of the N constraints obtained in Eq. (15). After adding the constraints, the expression to be minimized is then
ð15Þ
"
lj
k X ðn_ i;out n_ i;out ÞAij
!# ð16Þ
i¼1
The partial derivation of this equation with respect to n_ i;out can be writes as k X g 0i;out @/ ¼ lj Aij þ lnðni;out pout Þ þ _ @ ni;out RT j¼1
for i ¼ 1; k
ð17Þ
At the minimum each of these is then zero. The additional equation to make the system consistent is the summation of molar fractions of the outlet gas to be k X
ni;out ¼ 1
ð18Þ
i¼1
3. Plant configurations The first configuration studied is shown in Fig. 1a. The fuel (NG) is preheated in a heat exchanger before it is sent to a desulphurization unit to remove the sulphur content in the NG. This unit is assumed to be using a catalyst, operating at temperature of 200 °C. Thereafter the heavier carbon contents in the NG are cracked down in a CPO type pre-reformer catalyst. Before that the fuel must be preheated again to reach to the operational temperature of the CPO catalyst. The CPO catalyst needs additional air which is supplied by a small pump as shown in the figure. It is assumed that the supplied NG is pressurized and therefore no pump is needed for the fuel. The pre-reformed fuel is now sent to the anode side of the SOFC stacks. Due to the exothermic nature of the CPO catalyst, no pre-heating of the fuel is required. The fuel has a temperature of about 650 °C before entering the stacks. The operating temperature of the SOFC stacks as well as outlet temperatures is assumed to be 780 °C. Therefore, the burned fuel after the stacks has a temperature of about 780 °C which is used to preheat the fuel in the heat exchangers mentioned above. On the other side, air is compressed in a compressor and then preheated in a recuperator to about 600 °C before entering the cathode side of the SOFC stacks. It should be mentioned that these entering temperatures are essential requirements for proper functioning of SOFC stacks. Otherwise, the stacks will shut down automatically. Since the fuel in the SOFC stacks will not burn completely the rest of the fuel together with the air coming out of the cathode side of the stacks are sent to a burner (catalytic burner) for further burning. The off-gases from the burner have a high heat quality which can be used to generate steam in a heat recovery steam generator (HRSG). In the Rankine cycle, the pressurized water after the feed pump is heated up to steam in the economizer (ECO), evaporator (EVA) and super-heater (SUP). The generated steam is then expanded in a steam turbine to generate electricity. Part of the expanded steam is then extracted for the deaerator. The expanded steam after the ST is then cooled down in a condenser (including a sub-cooler part) before pumping to the deaerator. The water is preheated in the deaerator before being recycled. As mentioned earlier the ASR reformer needs super heated steam for operation. Such steam must be supplied to the reformer externally during startup. However, during normal operation steam is available after SOFC stacks due to reactions of hydrogen
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
(a) SOFC
Prereformer
Fuel
Desuplhurizer
HEX
HEX HEX
Burner Air Air ECO
EVA
SUP
ST
Condenser Deaerator
(b) Recycle Fuel SOFC HEX
HEX
HEX
HEX
Prereformer
Desuplhurizer
Burner
Air ECO
EVA
SUP
ST
Condenser Deaerator Fig. 1. Combined SOFC–ST cycle plants, (a) with CPO reformer and (b) with ASR reformer. Rankine cycle with a single pressure level.
and oxygen. Therefore, the stream after the anode side of SOFC is recycled as shown in Fig. 1b. There are three alternatives for such a recirculation unit, a pump, a turbocharger and an ejector. In a real plant, due to high temperature of this stream (more than 700 °C) the cost of a pump will be rather expensive. This is also true for a turbocharger working at such mass flows and pressures. Moreover, using an ejector brings up problems associated with the size and dimensioning of the ejector (due to combination of pressure drop and mass flows), which is out of the scope of this investigation. In fact, the author is studying the possibilities of including an ejector into the DNA program which takes into account the size
of ejectors and nuzzle area. Based on these facts and for the sake of simplicity a pump is used in this investigation. Besides the recycle part, the plant configuration is the same as in the CPO reformer case, see Fig. 1b. The main parameters for the plant are given in Table 1. Number of SOFC stacks is assumed to be 10,000 and number of cells per stacks is assumed to be 74. The pressure drops in the cathode and anode sides of the fuel cell are assumed to be 0.05 respective 0.01 bars. These values are the setting values for the program, however, pressure drops are a function of channel sizes and mass flows and the channel geometry is not kwon. Therefore, these
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
Table 1 Main parameters for design point calculations of Fig. 1.
Table 2 Main calculated parameters for design point calculations of Fig. 1.
Parameter
CPO
ASR
Parameter
CPO
ASR
Compressor intake temperature Compressor isentropic efficiency Compressor mechanical efficiency SOFC cathode inlet temperature SOFC cathode outlet temperature SOFC utilization factor SOFC number of cells SOFC number of stacks SOFC cathode side pressure drop ratio SOFC anode side pressure drop ratio Heat exchangers pressure drops Fuel inlet temperature Desulphurizer operation temperature SOFC anode inlet temperature SOFC anode outlet temperature Burner efficiency ST isentropic efficiency Feed water pump pressure Extraction pressure Extraction steam temperature Generators efficiency
25 °C 0.85 0.95 600 °C 780 °C 0.80 74 10,000 0.05 bar 0.01 bar 0.01 bar 25 °C 200 °C 650 °C 780 °C 0.97 0.9 70 bar 2 bar 120.2 °C 0.97
25 °C 0.85 0.95 600 °C 780 °C 0.80 74 10,000 0.05 bar 0.01 bar 0.01 bar 25 °C 200 °C 650 °C 780 °C 0.97 0.9 60 bar 2 bar 120.2 °C 0.97
Compressor mass flow Fuel mass flow SOFC anode mass flow Burner inlet fuel mass flow Burner inlet air mass flow HRSG gas side inlet temperature HRSG gas side outlet temperature HRSG water side inlet temperature ST inlet steam temperature ST pressure ST inlet mass flow Extraction mass flow
51.4 kg/s 1.32 kg/s 1.45 kg/s 5.17 kg/s 47.7 kg/s 526.3 °C 218.2 °C 121.1 °C 496.3 °C 69.97 bar 6.33 kg/s 5.40 kg/s
59.0 kg/s 1.30 kg/s 1.72 kg/s 5.13 kg/s 55.11 kg/s 455.6 °C 232.0 °C 121.0 °C 425.6 °C 59.97 bar 5.47 kg/s 4.64 kg/s
values are calculated based on the available data for each channel mass flow and dimensions. In addition, the calculations show that the final values in terms of plant power and efficacy do not change significantly if these values are changed slightly. The pressure drops for all heat exchangers are assumed to 0.01 bars. Again these values depend on the heat exchanger types and channel geometries, but they are reasonable for plate heat exchanger types. The minimum temperature differences at pinch (Tmin) are assumed to be 30 °C, 15 °C and 17 °C for superheat, evaporator and economizer respectively. The compressor isentropic efficiency and mechanical efficiency are assumed to be 0.85 respective 0.97, while the generator efficiency is assumed to be 0.97. The SOFC plant provides direct current and must be converted to AC through a converter. Further, the efficiency of the DC/AC converter is assumed to be 100%, due to lack of such component in the DNA program. In reality there would be some losses trough the converter and efficiencies of 97% could be assumed for plants of such sizes studied in this investigation. The output power would therefore be somewhat lower while the plant efficiency would not change significantly. Furthermore, the utilization factor for the SOFC cells is assumed to be 0.8. Several calculations have been carried out to find the optimal extraction pressure as well as the optimum live steam pressure which are not included here. The main calculated parameters are provided in Table 2. The main difference in the Rankine cycle from CPO and ASR are the off-gases temperatures entering the HRSG. The CPO pre-reforming plant provides much higher temperature for the off-gases, which is due to the fact that the air mass flow to its burner is lower than the corresponding one for the ASR pre-reforming plant. Consequently, the feeding temperature for the Rankine cycle will be higher in the CPO type, which will results in higher net power from the steam cycle, see Table 3. The plants net powers and thermal efficiencies (based on LHV, lower heating value) are shown in Table 3. The net power output of the hybrid plant with CPO pre-reforming is calculated to be about 1 MW higher than the corresponding plant with the ARS pre-reforming. The main reason is that the steam cycle in the CPO type plant produces somewhat higher power than the corresponding ASR type plant (higher off-gases temperature for the CPO pre-reforming). As a result the thermal efficiency of the plant with CPO pre-reforming will be higher than the corresponding plant with ASR pre-reforming. However, the thermal efficiency of the SOFC plant (not the hybrid one) with ASR pre-reforming is cal-
Table 3 Net powers and efficiencies of the plants for Fig. 1. Parameter
CPO
ASR
Net power output Output power from SOFC cycle Output power from ST cycle Thermal efficiency of steam cycle (LHV) Thermal efficiency of SOFC cycle (LHV) Thermal efficiency (LHV)
38.03 MW 31.04 MW 6.99 MW 0.382 0.514 0.630
36.72 MW 31.23 MW 5.49 MW 0.368 0.524 0.617
culated to be about 1% point higher than the SOFC plant with CPO pre-reforming. This is due to the fact that CPO pre-reforming needs additional air mass flow which must be provided by additional compressor flow (or additional compressor) which in turn needs additional electrical power. The cycle efficiencies are defined as
gSOFC;a ¼ Net power form SOFC cycle=fuel consumption gST ¼ Net power form steam cycle=heat into steam gHybrid
cycle through HRSG ¼ Net power form hybrid plant=fuel consumption
ð19Þ
Some of the compressor effect is used to provide the pressure drops in the heat exchangers of the HRSG. Therefore the compressor effect has been divided into two part; one part which is intent for the ST cycle only and the rest which applied to the SOFC cycle only. It can be shown that the thermal efficiency of the integrated systems can be calculated by
gth ¼ gSOFC þ gST ð1 gSOFC ÞeHRSG
ð20Þ
T HRSG;in T HRSG;out T HRSG;in T air
ð21Þ
eHRSG ¼
where gSOFC and gST are the SOFC cycle efficiency and steam cycle efficiency respectively. HRSG is the effectiveness of the heat recovery steam generator, which describes the amount of heat that has been transferred from the SOFC cycle to the steam cycle. These equations provide HRSG efficiencies 0.615 and 0.519 for CPO respective ARS. Thermal efficiencies can then be calculated as 0.628 and 0.615 for CPO respective ASR. These values are in agreement with the numerical results given in Table 3. In order to optimize the systems presented above, the plants efficiencies versus live steam pressures and moisture contents are presented in Fig. 2. The results indicate that for the CPO case the maximum efficiency appears to be at about 45 bar while for the ASR case this maxima is around 22 bar. At optimal live steam pressure the efficiency of the CPO pre-reformer case is higher than the corresponding optimal live steam pressure for the ASR pre-reformer case. The moisture content after the steam turbine is an
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64
20
63.2
16
63.2
16
62.4
12
62.4
12
61.6
8
61.6
8
60.8
4
moisture
moisture
60.8
60 10
20
30
40
50
60
4
ηth
ηth
0
Moisture content [%]
20
Thermal Efficiency [%]
64
Moisture content [%}]
Thermal Efficiency [%]
M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
70
0 80
60
0
10
Live Steam Pressure [bar]
20
30
40
50
60
70
0 80
Live Steam Pressure [bar]
(a)
(b)
Fig. 2. Thermal efficiency and moisture content of the combined SOFC–ST plants as function of live steam pressure: (a) with CPO reformer and (b) with ASR reformer. Rankine cycle with single pressure level.
important issue to be considered. Too high level of moisture (more than about 16%) may cause blades corrosion located at the last stage, see e.g. Kehlhofer et al. [20]. Further, the results indicate that for the CPO pre-reforming plant the moisture content more than 16% may occur for pressures above 75 bar, while for the ASR prereforming plant this is true for pressures above 48 bar. Although, both are much higher than the optimized pressures mentioned above. 3.1. Effects of cathode air pre-heating (hybrid recuperating) The energy left after the HRSG in the previous designs are rather high; see the outlet temperatures of HRSG in both cases. The reason is that decreasing the live steam pressure decreases the depleted gas temperature form the HRSG, but also the steam cycle thermal efficiency and thereby the combined plant efficiency. However, at the given pressures above the combined plants efficiencies are close to their respective optimum and the depleted gas temperatures are high as well. Therefore, this energy can be used to preheat the cathode air flow and thereby decrease the energy from the SOFC cycle which is used for pre-heating. This will in turn increase the energy of the off-gases through the HRSG and thereby increase the efficiency of the steam cycle. Fig. 3 shows the suggested plants. The SOFC cycle efficiency will not decrease significantly by such pre-heating. It may be mentioned that such a pre-heating cannot be done in a combined cycle (gas turbine on the top of a steam turbine cycle) since the temperature after the compressor is too high because of compressor pressure ratio, usually much higher than the HRSG outlet gas temperature (gas side). Several calculations for each pre-reformer case are carried out to find the optimal thermal efficiency of the systems. The optimal pressure for the steam turbine is calculated as 70 bar and 60 bar for respective CPO and ASR pre-reforming cases. The most calculated important results are shown in Table 4. It is assumed that the HRSG outlet gas-side temperature is 90 °C. This is due to the fact that the off-gases are pure enough to allow to recover the energy to such temperature. However, in order to see how the thermal efficiencies of the proposed systems will change if the outlet gas temperatures from the HRSG is increased, Fig. 4 is presented. As the results show the efficiencies decreases by increasing the HRSG outlet temperature. At 120 °C the thermal efficiency of the CPO case drops to 0.668 from 0.680, while
for the ARS case the thermal efficiency is decreased to 0.664 from 0.677. However, these efficiencies are still much higher compared to the traditional plants for such sizes. Further, the drop in efficiency for the ASR pre-reforming case is more sensible than the CPO case, the lines are getting wider. It can be shown by a simple mathematic that the efficiency of any hybrid plants with hybrid recuperating concept (using dissipated heat from the bottoming cycle to the topping cycle) can be calculated from
gth ¼ 1 þ
Q recuperated ðgSOFC þ gST ð1 gSOFC ÞeHRSG Þ Q in
ð22Þ
where Qrecuperated is the heat recuperated to the SOFC cycle and Qin is the heat supplied to the plant through fuel. Note that the ratio Qrecuperated/Qin in this equation is very small and therefore it is simplified. For the CPO pre-reforming case Qrecuperated/Qin and HRSG are calculated as 0.096 and 0.731 respectively. Inserting these values into the Eq. (22) together with cycle efficiencies provides plant thermal efficiency as 0.680 which is in agreement with the corresponding calculated value shown in Table 4. For the ASR pre-reforming case Qrecuperated/Qin and HRSG are calculated as 0.122 and 0.680 respectively. Inserting these values into Eq. (22) gives plant thermal efficiency as 0.677 which is again in agreement with the corresponding calculated value shown in Table 4. 3.2. Effects of SOFC fuel utilization factor The SOFC fuel utilization factor in the previous calculations was set to 0.8. However, the computed results changes if the fuel utilization factor varies. Fig. 5a shows the SOFC cycle efficiency as function of fuel utilization factor for the four cases considered. In this figure and from now on the SOFC cycle efficiency is defined as (due to recuperation),
gSOFC;b ¼ Net power form SOFC cycle=ðfuel consumption þ recuperated heatÞ
ð23Þ
Without recuperating the SOFC cycle efficiency will be increased by increasing cell utilization factor. However, at some point the demanding cooling effect will be very significant and the SOFC cycle efficiency starts to decrease. Therefore, the SOFC cycle efficiency has maxima at 0.78 and 0.76 with CPO respective ASR pre-reforming, if no recuperating is used. At utilization factor of
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
(a) SOFC
Prereformer
HEX
HEX HEX
Fuel
Desuplhurizer
HEX
Burner Air Air ECO
EVA
SUP
ST
Condenser Deaerator
(b) Recycle Fuel SOFC HEX HEX
HEX
HEX
HEX
Prereformer
Desuplhurizer
Burner
Air ECO
EVA
SUP
ST
Condenser Deaerator Fig. 3. Combined SOFC–ST cycle plants, (a) with CPO reformer and (b) with ASR reformer. Rankine cycle with a single pressure level and cathode pre-heating in the SOFC cy.
about 0.81 the SOFC cycle efficiency decreases sharply, which is more significant in the ASR pre-reforming than the CPO prereforming type. Further, the SOFC cycle efficiency with ASR prereforming is higher than CPO pre-reforming without recuperating. With hybrid recuperating, SOFC cycle efficiency increases with decreasing fuel utilization factor. This can mainly be explained by Eq. (23) in which the recuperated heat to the SOFC cycle increases mach faster than the changes on SOFC power output. (Fuel consumption remains constant.) To give an example, if utilization factor is increased from 0.72 to 0.82 then the recuperated heat will
be about four times larger. The SOFC cycle efficiency is lower with recuperating than without recuperating which is mainly due to definition used in Eq. (23). The steam cycle efficiency decreases with increasing fuel utilization as shown in Fig. 5b. This is because less fuel will be burned in the burner and consequently HRSG inlet temperature decreases. The steam plant efficiency for CPO case is higher than the corresponding one with ASR case, if no recuperating is used. This is because the SOFC cycle efficiency with ASR pre-reforming is higher than the corresponding one with CPO pre-reforming. If
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732 Table 4 Net powers and efficiencies of the plants for Fig. 3.
0.685
Parameter
CPO
ASR
Net power output Output power from SOFC cycle Output power from ST cycle Depleted gas temperature Steam Pressure/temperature Thermal efficiency of steam cycle (LHV) Moisture content after ST Thermal efficiency of SOFC cycle (LHV) Thermal efficiency (LHV)
41.06 MW 30.92 MW 10.14 MW 90 °C 70 bar/569.9 °C 0.395 11.5% 0.512 0.680
40.34 MW 31.13 MW 9.21 MW 90 °C 60 bar/532.2 °C 0.381 12.9% 0.523 0.677
recuperating is used then the steam plant efficiency is similar with both pre-reforming types. The hybrid plant efficiency as function of SOFC fuel utilization factor is shown in Fig. 6a. Decreasing the fuel utilization factor would result in increasing hybrid plant efficiency, for all cases considered. This is a consequent of what has been explained earlier. Decreasing fuel cell utilization factor increases ST inlet temperature significantly. Such an increase is more sever for the CPO
Efficiency
0.68
0.675
0.67 ASR CPO
0.665
0.66 90
95
100
105
110
115
120
HRSG outlet T [C] Fig. 4. Thermal efficiencies as function of HRSG outlet gas temperature.
pre-reformer without recuperating than the other three configurations. Further, if the temperature limit for ST is set to 600 °C then the fuel cell utilization factor cannot be below about 0.74, 0.77,
0.6
0.5
0.5
Steam cycle efficiency
SOFC cycle efficiency
0.45
0.4 CPO - no recuperating ASR - no recuperating CPO - with recuperating
0.3
ASR - with recuperating
0.4 0.35 0.3 0.25 CPO- no recuperating ASR - no recuperating
0.2
CPO - with recuperating 0.15
0.2 0.72
0.74
0.76
0.78
0.8
0.1 0.72
0.82
ASR - with recuperating
0.74
0.76
0.78
0.8
SOFC fuel utilization factor
SOFC fuel utilization factor
(a)
(b)
0.82
Fig. 5. Cycle efficiencies as function of SOFC utilization factors for four cases considered: (a) SOFC cycle efficiency, (b) steam cycle efficiency.
0.8 1000
CPO without recuperating ASR without recuperating CPO with recuperating ASR with recuperating
0.7
0.6
800 700
0.5
T[C]
Hybrid plant efficiency
900
CPO - no recuperating
0.4
ASR - no recuperating
500
CPO - with recuperating
0.3
400
ASR - with recuperating 0.2 0.72
600
0.74
0.76
0.78
0.8
0.82
300 0.72
0.75
0.78
0.81
SOFC fuel utilization factor
SOFC fuel utilization factor
(a)
(b)
Fig. 6. (a) Hybrid plant efficiency as function of fuel cell utilization factors and (b) inlet temperature of the high pressure steam turbine as function of fuel cell utilization factor.
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M. Rokni / Energy Conversion and Management 51 (2010) 2724–2732
0.77 and 0.8 for ARS without recuperating, ASR with recuperating, CPO without recuperating and CPO with recuperating respectively. 4. Conclusions Hybrid combined SOFC–ST plants are presented and analyzed. The plants are fired by natural gas and therefore the fuel is desuphurized and then pre-reformed before sending to the anode side of the SOFC. Both CPO and ARS pre-reforming processes are used. The results indicate that for simple combinations the thermal efficiencies of the system can reach to about 62–63% depending on the choice of pre-reforming type. The SOFC cycle efficiency in the ASR performing type is higher than the corresponding SOFC cycle with CPO pre-reforming type. However, the efficiency of the hybrid plants with CPO case is larger than the corresponding hybrid plants with ARS case. This is due to the fact that in the CPO case the temperature of the off-gases entering the HRSG is larger than the corresponding temperature in the ARS case. This results in higher efficiency in the bottoming cycle (steam cycle) and thereby better efficiency for the hybrid plants. In another suggested system configurations the off-gases from the HRSG is recuperated to the SOFC cycle by pre-heating incoming air flow after the compressor and before entering the cathode side of the SOFC. In this way the energy of off-gases in the HRSG can be further used and thereby the electrical efficiencies of the systems are increased to about 68% for both CPO and ASR pre-reforming types. Such cathode air pre-heating does not change the SOFC plant efficiency but increases the steam cycle efficiency significantly due to better use of the off-gases energy and lowering the stack temperature. Decreasing the SOFC fuel utilization factor increases plant electrical efficiency significantly. However, this parameter cannot be less than a certain value (due to configuration) since the inlet temperature of the steam turbine would be too large. References [1] Fontell E, Kivisaari T, Christiansen N, Hansen J, Pålsson J-B. Conceptional study of a 250 kW planar SOFC system for CHP application. J Power Sources 2004;131:49–56. [2] Rokni M. Introduction of a fuel cell into combined cycle: a competitive choice for future cogeneration. ASME Cogen – Turbo IGTI 2003;8:255–61.
[3] Riensche E, Achenbach E, Froning D, Haines MR, Heidug WK, Lokurlu A, et al. Clean combined-cycle SOFC power plant–cell modeling and process analysis. J Power Sources 2000;86:404–10. [4] Pålsson J, Selimovic A, Sjunnesson L. Combined solid oxide fuel cell and gas turbine system for efficient power and heat generation. J Power Sources 2000;86:442–8. [5] Proell T, Rauch R, Aichering C, Hofbauer H. Coupling of biomass steam gasification and an SOFC–GT hybrid system for highly efficient electricity generation. In: ASME Turbo Expo Proceeding, GT2004-53900; 2004. p. 103–9. [6] Subramanyan K, Diwekar UM. Characterization and quantification of uncertainty in solid oxide fuel cell hybrid power plants. J Power Sources 2005;142:103–16. [7] Calise F, Dentice d’ Accadia M, Vanoli L, von Spakovsky MR. Single-level optimization of hybrid SOFC–GT power plant. J Power Sources 2006;159:1169–85. [8] Wächter C, Lunderstädt R, Joos F. Dynamic model of a pressurized SOFC–GT hybrid power plant for the development of control concept. J Fuel Cell Sci Technol 2006;3(3):271–9. [9] Roberts RA, Brouwer J. Dynamic simulation of a pressurized 220 kW solid oxide fuel-cell–gas-turbine hybrid system: modeled performance compared to measured Results. J Fuel Cell Sci Technol 2006;3(1):18–25. [10] Rokni M, Fontell E, Ylijoki Y, Tiihonen O, Hänninen M. Dynamic modeling of wärtsilä 5kW SOFC system. In: Singhal SC, Mizusaki J, editors. Ninth International symposium on solid oxide fuel cell (SOFC IX), Quebec; 2005. p. 865–75. [11] Costamagna P, Magistri L, Massardo AF. Design and part-load performance of a hybrid system based on a solid oxide fuel cell reactor and a micro gas turbine. J Power Sources 2001;96:352–68. [12] Dunbar WR, Lior N, Gaggioli RA. Combining fuel cells with fuel-fired power plants for improved exergy efficiency. J Energy 1991;16(10):1259–74. [13] Elmegaard B, Houbak N. DNA – a general energy system simulation tool, Proceeding of SIMS, Trondheim, Norway; 2005. [14] Perstrup C. Analysis of power plant installation based on network theory (in Danish). M.Sc. thesis, Technical University of Denmark, Laboratory of Energetics, Denmark; 1989. [15] Petersen TF, Houbak N, Elmegaard B. A zero-dimensional model of a 2nd generation planar SOFC with calibrated parameters. Int J Thermodyn 2006;9(4):161–8. [16] Keegan KM, Khaleel M, Chick LA, Recknagle K, Simner SP. Diebler J. Analysis of a planar solid oxide fuel cell based automotive auxiliary power unit. SAE technical paper series No. 2002-01-0413; 2002. [17] Kim JW, Virkar AV. The effect of anode thickness on the performance of anodesupported solid oxide fuel cell. In: Proceedings of the sixth international symposium on SOFCs, (SOFC-VI), PV99-19. The Electrochemical Society; 1999. p. 830–9. [18] Smith JM, Van Ness HC, Abbott MM. Introduction to chemical engineering thermodynamics. 7th ed. Boston: McGraw-Hill; 2005. [19] Elmegaard B. Houbak N. On the implementation of energy simulators with emphasis on chemical equilibrium gasifier models. In: Proceedings of ECOS’99. Tokyo; 1999. p. 258–63. ISBN: 4-9980762-0-5 [20] Kehlhofer RH, Warner J, Nielsen H, Bachmann R. Combined–cycle gas steam turbine power plants. PennWell; 1999. ISBN: 0-87814-736-5.