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Analysis of a SOFC energy generation system fuelled with biomass reformate
Applied Thermal Engineering 27 (2007) 738–747 www.elsevier.com/locate/apthermeng
Analysis of a SOFC energy generation system fuelled with biomass reformate Stefano Cordiner, Massimo Feola, Vincenzo Mulone *, Fabio Romanelli Dipartimento di Ingegneria Meccanica, Universita` di Roma ‘‘Tor Vergata’’, via del Politecnico 1, 00133, Roma, Italy
Abstract Biomass reformation is an interesting path for hydrogen production and its use for efficient energy generation. The main target is the fully exploitation of the potential of renewable fuels. To this aim, the coupling a biomass reformer together with a high temperature solid oxide fuel cell (SOFC) stack shows some advantages for the similar operating temperature of the two processes and the internal reforming capability of the SOFC. The latter further allows less stringent composition requirements of the feed gas from a gasifier and internal cooling of the SOFC. In this work, a complete model of a SOFC coupled with a biomass gasifier is used to identify the main effects of the operating conditions on the fuel cell performance. The gasification process has been simulated by an equilibrium model able to compute the reformate composition under different operating conditions, whereas a 3D fluid dynamics simulation (FLUENT) coupled with an external model for the electrochemical reactions has been used to predict the fuel cell performance in terms of electrical response and mass-energy fluxes. A 14 kW integrated SOFC-gasifier system has been analysed with this model to address the response of a planar SOFC as a function of the gasifier operating conditions. 2006 Elsevier Ltd. All rights reserved. Keywords: Solid oxide fuel cells; Fuel cell modelling; Biomass gasification; Thermal integration
1. Introduction The increase of atmospheric greenhouse gas concentration requires that the use of renewable fuels for energy production becomes more and more diffused. Biomass is already widely used to this aim representing some 35– 38% of the energetic resource on a worldwide scale, reaching 80% in some countries such as India or Sub-tropical Africa. As far as Europe is concerned, the resources in lignocellulosic biomass are assuming an increasing importance in the energy mix having the potential to substitute several Mtoe per year of fossil fuels also avoiding significant CO2 emissions. The thermochemical transformation is certainly the most diffused method of heat production from biomass *
Corresponding author. Tel.: +39 06 72597170; fax: +39 06 2021351. E-mail address: [email protected] (V. Mulone).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.10.015
so far with combustion representing the leading technology. Heat produced by combustion may be used as energy input in a steam cycle. However, other thermochemical methods such as gasification and pyrolysis also have a great potential producing a syngas mainly composed of H2 and CO with traces of different gases such as CH4 in different proportions, together with variable quantities of tars. If carefully cleaned, synthetic gas could be directly used as a fuel for gas turbines in different configurations and, potentially, with high efficiency. In the search for higher efficiency converters, fuel cell energy generation systems are assuming a role of increasing importance. Being the most suitable systems for hydrogen utilization, fuel cells represent the basis for the development of an energy economy based on this energy carrier but they may also be efficiently fed with different fuels. In particular, high temperature fuel cells, such as SOFC and molten carbonate fuel cells (MCFC), are especially
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Nomenclature D dHint E E0 F G h i0 J K Ki le M MC m_ p P R Re S T u w
diffusion coefficient integration heat flux cell voltage Nernst voltage Faraday constant Gibbs energy enthalpy exchange current density current density permeability tensor equilibrium constant electrolyte thickness molecular weight moisture content mass flow rate pressure power gas constant electrolyte ionic resistance source term temperature velocity vector amount of water per mol of wood
attractive since they can be efficiently used both for combined heat and power (CHP) generation applications and integrated within high efficiency hybrid cycles. It is also largely believed that combining traditional cycles with fuel cells (e.g. Auxiliary Power Units) could accelerate the market introduction of the latter. Fuel flexibility constitutes a typical attractive characteristic of high temperature fuel cells [1]: these devices are in fact capable of operating with traditional light hydrocarbon fuels (e.g., methane) for their tolerance to carbon monoxide. They have also internal reforming potential and allow the design of highly integrated systems with a limited or even without the external fuel processor. Rather tight limits on fuel sulphur contents are nevertheless still required. In particular, SOFC are in principle characterized by rather high efficiency in converting chemical fuels directly into electrical power (more than 40% [2]) and by high temperature exhaust gases which could be used in combined cycles. According to the previous considerations, the use of biomass to fuel SOFC represents an interesting opportunity for an efficient deployment of biomass potential. The integration of a downdraft gasifier with a SOFC stack has been recently proposed in [3,4] the hot reformate gas stream is directly fed into the SOFC where the reforming and electrochemical reactions simultaneously occur. The SOFC off-gas, still rich in hydrogen and carbon monoxide, is used in an integrated combustor providing heat for the gasifica-
x Y
mol fraction mass fraction
Greek symbols bi ionic conductibility parameter e porosity k thermal conductivity g efficiency gact activation loss gohm ohmic loss l viscosity lf fuel utilization q density re electrolyte ionic conductibility Subscripts A anode C cathode e electrolyte el electric g global i species s solid
tion process. A simplified scheme for such a system is provided in Fig. 1. To avoid carbon deposition problems in the gasification process, high operating temperature and water content are required which can be efficiently get only with an integration of the gasifier with the downstream component [5]. Biomass sulfur levels must anyway be carefully controlled since the occurrence of even several ppm could cause the cell poisoning [6]. SOFC have been tested since 1930 under several configurations among which the most widespread and tested are the planar and tubular arrangements [2]. However, a number of technological problems still need to be solved, basically related to the high operating temperature and then to thermal cycling issue. Both material and design issues rise for the cell configuration, as thermal stress resistance must be guaranteed together with a good deployment of the
Fig. 1. Simplified scheme of an integrated gasifier-SOFC system.
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reactant-fluid potential. Research and development are therefore still proceeding both to test new materials and to optimize the design of single cells and complete stack as well. The role of numerical simulation in supporting this development effort is clearly important as it constitutes an effective way to speed-up the design phase both for component development and system integration. Different approaches have been developed in the literature using different levels of approximation for the description of the involved phenomena [7–12]. In this paper, a simulation tool is proposed to predict the performance and the main electro-thermal-fluid dynamic characteristics of an integrated biomass fuelled gasifierSOFC system. In the proposed approach, the SOFC behaviour is predicted by means of a 3D fluid dynamic simulation of the cell, while the gasifier is modelled by a lumped approach, able to evaluate the reformate characteristics starting from the biomass composition and its moisture content. With the previous characteristics, the model is able to address both component level (in particular how the SOFC design is affected by the reformate gas composition and characteristics) and system level issues (e.g., the influence of rejected heat and exhaust gas temperature on the overall system efficiency). The main objective of this work is, therefore, to analyze the performance of this integrated energy production system operating with biomass characterized by high water content.
where: • CH1.44O0.66 is the composition of woody material per unit carbon atom; • w is the amount of water per mol wood related to the biomass moisture content ðMCÞ by w ¼
24MC ; 18ð1 MCÞ
• m is the amount of oxygen per mol wood; • xi are the gas products molar fractions. The input and output parameters of the module, sketched in Fig. 2, are the following: • Input parameters: – biomass composition and water content (MC); – operating temperature; – integration heat (dHint); • Output parameters (problem unknowns): – required amount of air (m, i.e., molar oxygen/carbon ratio); – composition (xi). Given the elemental and energy balances 1 ¼ x2 þ x3 þ x5 2w þ 1:44 ¼ 2x1 þ 2x4 þ 4x5 w þ 0:66 þ 2m ¼ x2 þ 2x3 þ x4
The overall numerical model is constituted by two modules which allow to represent, respectively, a biomass gasifier and a SOFC behaviour. The gasifier module has been modelled by a 0D chemical equilibrium approach, assuming the reactor residence time high enough to let the pyrolisis products entirely convert into gas products. The SOFC module is conversely based on 3D computational fluid dynamics (CFD) analysis to model the gas evolution into the gas channels and porous electrodes, and the electrochemical cell response. The modules are separately illustrated below; details of the interconnection strategy to realize the integrated biomass gasifier-SOFC model are also provided in the final section.
¼ x1 dHH2 þ x2 dHCO þ x3 dHCO2 þ x4 dHH2 OðvapÞ ð6Þ
additional relations must be introduced to close the problem and finally find xi and m. Methane formation and water shift reactions are then supposed to be at equilibrium: • C + 2H2 = CH4 • CO + H2O = CO2 + H2 The corresponding equilibrium constants (K1 and K2, respectively), whose values can be evaluated by a minimization of Gibbs free energy, provide two further equations: K1 ¼
x5 x21
ð7Þ
K2 ¼
x1 x3 x2 x4
ð8Þ
2.1. Gasifier module The 0D biomass gasifier module is based on a global gasification reaction [13], which may be written for woody material as: CH1:44 O0:66 þ wH2 O þ mO2 þ 3:76mN2 ! x1 H2 þ x2 CO þ x3 CO2 þ x4 H2 O þ x5 CH4 þ 3:76mN2 ð1Þ
ð3Þ ð4Þ ð5Þ
dHfwood þ wdHH2 OðlÞ þ dHint þ x5 dHCH4 þ 3:76mdHN2
2. Numerical model
ð2Þ
Fig. 2. Gasifier module black-box layout.
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Fig. 3. MC effect on outlet gasifier composition at 800 C.
The six Eqs. (3)–(8), after some algebraic passages here omitted (details are available in [13]), can be reduced to a three non-linear equation set and solved by means of a Newton–Raphson method. The module has been validated against experimental data [14] in the case of an adiabatic gasifier (dHint = 0). The effect of input water content (MC) on the reformate composition in terms of dry basis volume fractions at 800 C is reported in Fig. 3. It is worth noting that:
It can be observed that the equilibrium hypothesis may represent rather well the reformate calorific value for higher temperature conditions where reaction kinetic effects assume less importance. On the basis of the previous results, the 0D gasifier module has been evaluated accurate enough in the range of high temperatures (more than 800 C) operating conditions where the SOFC is expected to be operated. 2.2. SOFC module
• CH4 fraction is negligible; • H2 and CO2 fractions increase with increasing MC, as expected; • CO diminishes with increasing MC, as expected. • A high N2 fraction may be observed throughout the MC range: this is due to a certain amount of required air to allow the gasifier to run autothermal (dHint = 0): it exploits therefore biomass oxidation to sustain chemical reactions. Less air, and therefore N2, may be conversely required depending on the amount of integration heat: high amounts could even lead to the obtainment of steam reforming operating conditions; gasification in those cases is performed without air. The validation with respect to experimental data have been performed in terms of reformate calorific value for different operating temperatures and MC equal to 0.2. The results of this comparison are summarized in Table 1.
Table 1 Experimental-numerical comparison: MC = 0.2
750 C 800 C 900 C
Calorific value (MJ/m3) present work
Calorific value (MJ/m3) experimental [14]
Error (%)
5.5 5.3 4.9
4.9 4.8 4.6
10.7 8.7 6.1
The SOFC module is based on a 3D computational fluid dynamic (CFD) approach, and it has been used to predict the behaviour of the smallest repeated geometrical element (unit cell), so realizing the so-called unit cell approach. Results can then be extended to the entire stack having assumed all the cells behaving in the same way. This assumption may be reasonable for stationary conditions but it is not limitative of the model potential as it may be easily substituted by a more detailed description of the complete FC geometry. The module is based on the following main hypothesis: • • • • • • •
planar co-flow configuration laminar flow steady state isotropic porous media infinite electrodes conductivity adiabatic channel no radiative heat transfer
3D mass, momentum and energy equations allow to represent the evolution of a gas-mixture of Ng = 7 chemical species (H2, O2, H2O, CH4, CO, CO2, N2) in the fuel and oxidant channels and porous electrodes. An electrochemical submodel has been implemented to locally represent the electrolyte behaviour in terms of mass/energy/charge fluxes based on rather standard 1D assumptions [2,9,15–20].
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The equation set assumes the following form: • Mass: r qu ¼ 0
ð9Þ
• ith species (i = 1, Ng): r qY i u r ðqDi rY i Þ ¼ S i
ð10Þ
where Yi represents the examined species mass fraction, Di its diffusion coefficient and Si its source term, which depends on the occurring chemical mechanism and local current in the electrolyte region. The internal reforming chemical process has been modelled by the introduction of homogeneous phase methane reforming reactions and water–gas-shift (WGS) reaction [21]: • CH4 + H2O ! 3H2 + CO • CO + H2O M H2 + CO2 The first reaction has been modelled by a kinetic approach following the hypothesis reported in [22], while the second one has been considered to be always at equilibrium [17]. • Momentum:
2 l r ðquu lruÞ ¼ r p þ lr u ðeuÞ 3 K
ð11Þ
K being an equivalent permeability tensor, which allows to take into account the flow in the porous electrodes. • Enthalpy: r ðquh krT Þ ¼ S h
ð12Þ
where k represents the local thermal conductivity: it generally depends on composition and gas pure species thermal conductivities, which are defined by means of the ideal gas kinetic theory. In the electrodes, k expression takes into proper account the solid thermal conductivity (ks = 2.25 W/mK [12]) using an average gas–solid value mass-weighted by the electrodes porosity e. Sh represents the energy source PN term which is related to the species change by S h ¼ i g hi S i .
" 1# ðpH2 =p0 Þ ðpO2 =p0 Þ2 DGðT Þ R T þ ln E0 ¼ 2F 2F ðpH2 O =p0 Þ 2RT j sinh1 gact;A ¼ F 2i0A 2RT j sinh1 gact;C ¼ F 2i0C p p H2 O 100 103 H2 i0;A ¼ 5:5 104 exp p0 p0 RT 0:25 3 p 120 10 O2 exp i0;C ¼ 7:0 104 p0 RT
ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ
Ohmic losses are computed as: gohm ¼ Re j le Re ¼ ; ½X cm2 re
ð19Þ ð20Þ
j being local current, le and re the electrolyte thickness and conductivity; the latter can be expressed as: b2 1 re ¼ b1 exp ð21Þ ; X cm T The electrochemical model has been set-up, in terms of b1 and b2 (Table 1) parameters, on the basis of similar models available in the literature [2,9,15,16,19,20]. The reference SOFC polarization curve has been calculated by imposing uniform temperature, O2 mass fraction equal to 0.23 and pure H2. Results are plotted in Fig. 4 with respect to typical operating temperatures. The model does not require any evaluation of concentration losses, which are directly taken into account via the 3D species fields. The electrochemical model is called by the 3D main solver, and provides the local current on the basis of local reactant distributions and temperature. Species and energy source terms Si and Sh, representing the link between the electrochemical model and the 3D solver, are then provided by the following relations as functions of the local current j: • Electrolyte on the cathode side: j M O2 4F S h ¼ ð1:25 EÞj S O2 ¼
ð22Þ ð23Þ
• Electrochemical submodel: The electrochemical submodel solves the mass/current/ energy problem across the electrolyte. It is mainly based on the electrochemical reaction: H2 þ 12O2 ! H2 O Cell voltage E is imposed on the electrolyte: E ¼ E0 gact gohm
ð13Þ
where E0, gact = gact,A + gact,C and gohm represent ideal voltage, activation and ohmic losses defined as it follows [17]:
Fig. 4. 0D SOFC polarization curve with fixed temperatures and gas fractions.
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• The 0D gasifier module has been implemented into a FORTRAN subroutine; • The 3D SOFC module has been implemented into the FLUENT 6.2 CFD package [23] where the electrochemical phenomena have been taken into account developing specific ANSI-C User Defined Functions (UDF). 0D gasifier module and 3D SOFC modules are managed by a main program whose flow diagram refers to Fig. 7. 3. Analysis of results Fig. 5. Electrochemical model and 3D solver coupling schematic.
• Electrolyte on the anode side: j M H2 2F j M H2 O ¼ 2F
S H2 ¼
ð24Þ
S H2 O
ð25Þ
The coupling strategy between electrochemical model and CFD solver is illustrated in Fig. 5. The 3D module input and output parameters, summarized in Fig. 6, are the following: • Input parameters: – material/electrochemical parameters; – geometry; – boundary conditions (cathode and anode inlet parameters: mass flow rate, composition and temperature); – cell voltage. • Output parameters: – current field on the electrolyte; – cathode and anode outlet parameters: composition, temperature, residual calorific value. 2.3. Whole numerical model implementation details and management strategy From a computational point of view the modules have been implemented into different computational environments. More specifically:
The numerical model has been applied to the analysis of a 14 kW SOFC-gasifier integrated system whose layout is reported in Fig. 1. The system is fed by woody material biomass CH1.44O0.66, and a co-flow planar anode supported configuration has been chosen for the SOFC (see Table 2). Integration heat flux dHint, defined as the heat provided by the SOFC anode off-gas combustion, is used to reduce the amount of external heat required. In these conditions, the gasifier can exploit the integration heat flux as a substitute of heat otherwise provided by biomass combustion, and can operate with high MC and without air so realizing a biomass steam reforming process. High water and temperature SOFC operating conditions are in fact favourable to avoid carbon formation and deposition problems [5]. Starting from the above considerations, operating conditions have been chosen as it is displayed in Table 3, where 0.65 V cell voltage has been selected as a representative average load condition. The gasifier output gas composition (Table 4), which is actually the result of the iterative loop procedure described in Fig. 7, represents also the SOFC anode inlet gas composition. The SOFC main geometrical characteristics are reported in Table 5 and sketched in Fig. 8, where the computational domain layout is also presented: it is composed by about 100,000 cells. The model has been used to compute the SOFC and entire system performance (fuel utilization lf, cell efficiency gSOFC, entire system efficiency gg whose definitions are reported below), as well as specific power. P lf ¼
_ in i i ðm
gSOFC ¼ P gg ¼
Fig. 6. SOFC module black-box layout.
m_ out i Þ in _ m i i
ð26Þ
P el in _ m i i LHVi
ð27Þ
P
P el LHV m_ in biomass biomass
ð28Þ
In the previous equations m_ i terms represent the ith fuel component (CO or H2) mass flow rates, LHVi the ith fuel component low heating value (Table 6) and Pel, the output electric power.
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Fig. 7. Whole numerical model flow diagram.
Table 2 SOFC module electrochemical parameters
b1 b2
Table 5 SOFC geometrical characteristics
Value
Units
334 10,300
(1/X cm) (K)
Table 3 Gasifier-SOFC operating conditions
Gasifier moisture content Gasifier operating temperature Anode and cathode inlet pressure Cell voltage Cathode/anode mass flow ratio
Value
Units
0.4 1173 1 0.65 15
K atm V –
Cell length Gas channel height Gas channel width Rib Anode electrode thickness Cathode electrode thickness Electrode porosity Stack total active area
Value
Units
71 0.8 0.8 0.4 1 0.2 0.4 76,860
mm mm mm mm mm mm cm2
Table 4 Gasifier output composition Dry basis mole fractions H2 CO CO2 CH4 N2 O2
0.56 0.39 0.06 0 0 0
The analysis of the model results for the examined configuration shows that global efficiency gg gets a rather high
Fig. 8. SOFC transversal section dimensions (left) and 3D layout (right).
value. This is due to the integrated design which minimize the requirement of external heat by the exploitation of the integration heat. This choice is nevertheless very much dependant on the system application and requires a case by case analysis.
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Table 6 Fuels low heating values
CO H2 CH4 Biomass (wood) CH1.44O0.66
Value
Units
10,106 120,910 50,144 15,940
kJ/kg kJ/kg kJ/kg kJ/kg
The average current of 0.28 A/cm2 obtained from the SOFC module corresponds to a specific power of 0.182 W/cm2. On the basis of the previous specific values and using the unit cell hypothesis, results may be scaled-up to propose a layout of the complete 14 kW system, reported in the flow diagram of Fig. 9. The model is here used to give a first idea on this systemPcharacteristic mass and energy fluxes; LHV is defined as i m_ i LHVi summed over CO and H2 everywhere except in the gasifier inlet section where LHV must be defined as a function of biomass characteristics as m_ biomass LHVbiomass . It is worth noting that the presence of residual LHV at the SOFC outlet (21% with respect to the SOFC inlet one), is needed to integrate the gasifier. This is then responsible for the obtainment of a 34.3% SOFC efficiency due to a corresponding 57% fuel utilisation. The 3D SOFC module characteristics also allow the analysis of phenomena occurring in the gas channels, electrodes and electrolyte. This approach is of particular interest in system design as it is capable of giving accurate information which may not be easily accessed via experimental techniques. As an example, current distribution on the electrolyte is reported in Fig. 10 in a top view, showing a characteristic decreasing pattern in the stream-wise direction. Current intensity, in fact, depends both on H2 availability (in terms of local mass fraction) and temperature local value. H2 and temperature distributions are further provided in Figs. 11 and 12. An H2 deployment (due to H2 consumption) and
Fig. 10. Current (A/cm2) distribution on the electrolyte and detail.
Fig. 11. H2 distribution and detail on a transversal section.
an increase of temperature (due to electrochemical and WGS reactions heat release and to the imposition of adiabatic heat flux on the boundaries [24]) may be observed in
Fig. 9. Mass-energy fluxes of the 14 kW integrated generation system.
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S. Cordiner et al. / Applied Thermal Engineering 27 (2007) 738–747 Table 7 System performance indicators Value lf (%) gSOFC (%) gg (%) Average current Specific electric power
Fig. 12. Temperature distribution on an axial section (inlet on the right).
the stream-wise direction. It can be finally concluded that H2 influence on current distribution is everywhere heavier than the temperature one for the examined case. The detail of Fig. 10 puts also into evidence the uneven distribution of current in the rib-region: this behaviour is the result of the variable H2 fluxes along the electrolyte (Fig. 11, detail). In fact, under the rib, mass diffusion towards the electrolyte surface is less efficient. WGS equilibrium moves towards the H2 side, as it appears by the analysis of CO and CO2 distributions for the electrochemical H2O flux (Fig. 13). This circumstance allows to exploit CO to produce current via H2 internal production. As a final remark, it can be observed how the model has then proved to be capable of predicting both the integrated system main performance parameters and the main fluid dynamic and electrochemical SOFC 3D fields (species, temperature, current). This circumstance suggests the use of the proposed approach as a basic support for design since
57 34.3 45.8 0.28 A/cm2 0.182 W/cm2
it gives the possibility of evaluating the SOFC response by varying geometrical and material parameters without any modifications of the described model structure. 4. Conclusions A 14 kW energy generation system has been where a SOFC is supplied by a biomass gasifier. In the proposed layout, the gasifier is integrated by heat recovered by SOFC off-gas combustion, to realize a high efficiency concept and a high water content SOFC input gas to avoid carbon deposition. The system performance has been analyzed using a specifically developed numerical model, mainly constituted by two modules which, respectively, allow to represent a gasifier and SOFC behaviour. The gasifier has been modelled by a 0D equilibrium approach, since the related performance in terms of maximum error (6%) have been retained acceptable for the present application typical operating conditions. The SOFC has been modelled by a 3D CFD based approach, which allows to directly represent the coupling among the different phenomena occurring, namely diffusion, convection and electrochemistry (see Table 7).
Fig. 13. CO (top-left), CO2 (top-right) and H2O (bottom) distributions on an axial section (inlet on the right).
S. Cordiner et al. / Applied Thermal Engineering 27 (2007) 738–747
Results mainly indicate that: • the numerical model represents a point of departure both to evaluate the system performance and to give a quantitative idea about the distribution of current on the electrolyte and the main species into the gas channels and electrodes taking into account also the fluiddynamic rib effect • the needed integration heat flux requires a 21% fraction of the SOFC inlet LHV which corresponds to a 57% fuel utilization and therefore to a 34.3% SOFC efficiency • from a global point of view the system presents good performance in terms of efficiency (45.8%) The model could possibly be extended, without any major modifications, to study more complicated fluid dynamic configurations and their impact on the system performance, and/or the behaviour of entire SOFC assemblies once evaluated the increase of required computational resources. References [1] S.L. Douvartzides, F.A. Coutelieris, A.K. Demin, P.E. Tsiakaras, Fuel options for solid oxide fuel cells: a thermodynamic analysis, AIChE J. 49 (2003) 248–257. [2] S.C. Singhal, K. Kendall, High Temperature Solid Oxide Fuel Cells, Elsevier, New York, 2003. [3] P.N. Hutton, M.A. Musich, N. Patel, D.D. Schmidt, R.C. Timpe, feasibility study of a thermally integrated SOFC-gasification system for biomass power generation. US Department of Energy, National Energy Technology Laboratory Cooperative Agreement. Phase 1. Interim report, No. DE-FC26-98FT40321, Energy and Environmental Research Center, University of North Dakota, 2003. [4] A.O. Omosun, A. Bauen, N.P. Brandon, C.S. Adjiman, D. Hart, Modelling system efficiencies and costs of two biomass-fuelled SOFC systems, J. Pow. Sources 131 (2004) 96–106. [5] D. Singh, E. Hernandez Pacheco, P.N. Hutton, N. Patel, M.D. Mann, Carbon deposition in a SOFC fuelled by tar-laden biomass gas: a thermodynamic analysis, J. Pow. Sources 142 (2005) 194–199. [6] Y. Matsuzaki, I. Yasuda, The poisoning effect of sulfur-containing impurity gas on a SOFC anode: Part I. Dependence on temperature, time and impurity concentration, Solid State Ion. 132 (2000) 261–269.
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[7] N. Autissier, D. Larrain, J. Van herle, D. Favrat, CFD simulation tool for solid oxide fuel cells, J. Pow. Sources 131 (2004) 313–319. [8] S. Campanari, P. Iora, Definition and sensitivity analysis of a finite volume SOFC Model for a tubular cell geometry, J. Pow. Sources 132 (2004) 113–128. [9] J.R. Ferguson, J.M. Fiard, R. Herbin, Three-dimensional numerical simulation for various geometries of solid oxide fuel cells, J. Pow. Sources 58 (1996) 109–122. [10] U. Pasaogullari, C.Y. Wang, Electrochem. Soc. Proc., (2003–07), 1403. [11] K.P. Recknagle, R.E. Williford, L.A. Chick, D.R. Rector, M.A. Khaleel, Three-dimensional thermo-fluid electrochemical modeling of planar SOFC stacks, J. Pow. Sources 113 (2003) 109–114. [12] H. Yakabe, T. Ogiwara, M. Hishimuma, I. Yasuda, 3D model calculation for planar SOFC, J. Pow. Sources 102 (2001) 144–154. [13] Z.A. Zainal, R. Ali, C.H. Lean, K.N. Seetharamu, Prediction of performance of a downdraft gasifier using equilibrium modeling for different biomass materials, Energ. Convers. Manag. 42 (2001) 1499– 1515. [14] Z.A. Alauddin, Performance and Characteristics of a Biomass Gasifier System, PhD Thesis, University of Wales, College of Cardiff, UK, 1996. [15] E. Achenbach, SOFC Stack Modelling. Final Report on Activity A2, annex II. Modelling and Evaluation of Advanced Solid Oxide Fuel Cells, March 1996. [16] S.H. Chan, K.A. Khor, Z.T. Xia, A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness, J. Pow. Sources 93 (2001) 130–140. [17] E. Hernandez-Pacheco, M.D. Mann, P.N. Hutton, D. Singh, K.E. Martin, A cell-level model for a solid oxide fuel cell operated with syngas from a gasification process, Int. J. Hyd. Energ. 30 (2005) 1221– 1233. [18] J. Larminie, A. Dicks, Fuel Cell Systems Explained, Wiley & Sons Ltd., New York, 2000. [19] C.G. Motloch, Thermochemical Modeling and Performance of a Methane Reforming Solid Oxide Fuel Cell, PhD Thesis, Idaho State University, 1998. [20] C.Y. Wang, Fundamental models for fuel cell engineering, Chem. Rev. 104 (2004) 4727–4766. [21] Li. Pei-Wen, M.K. Chyu, Simulation of the chemical/electrochemical reactions and heat/mass transfer for a tubular SOFC in a stack, J. Pow. Sources 124 (2003) 487–498. [22] E. Achenbach, E. Riensche, Methane/steam reforming kinetics for solide oxide fuel cells, J. Pow. Sources 52 (1994) 283–288. [23] FLUENT 6.2, User Guide, Fluent Inc., Lebanon, NH, 2004. [24] M. Iwata, T. Hikosaka, M. Morita, T. Iwanari, K. Ito, K. Onda, et al., Performance analysis of planar-type unit SOFC considering current and temperature distributions, Solid State Ion 132 (2000) 297– 308.
Analysis of a SOFC energy generation system fuelled with biomass reformate Stefano Cordiner, Massimo Feola, Vincenzo Mulone *, Fabio Romanelli Dipartimento di Ingegneria Meccanica, Universita` di Roma ‘‘Tor Vergata’’, via del Politecnico 1, 00133, Roma, Italy
Abstract Biomass reformation is an interesting path for hydrogen production and its use for efficient energy generation. The main target is the fully exploitation of the potential of renewable fuels. To this aim, the coupling a biomass reformer together with a high temperature solid oxide fuel cell (SOFC) stack shows some advantages for the similar operating temperature of the two processes and the internal reforming capability of the SOFC. The latter further allows less stringent composition requirements of the feed gas from a gasifier and internal cooling of the SOFC. In this work, a complete model of a SOFC coupled with a biomass gasifier is used to identify the main effects of the operating conditions on the fuel cell performance. The gasification process has been simulated by an equilibrium model able to compute the reformate composition under different operating conditions, whereas a 3D fluid dynamics simulation (FLUENT) coupled with an external model for the electrochemical reactions has been used to predict the fuel cell performance in terms of electrical response and mass-energy fluxes. A 14 kW integrated SOFC-gasifier system has been analysed with this model to address the response of a planar SOFC as a function of the gasifier operating conditions. 2006 Elsevier Ltd. All rights reserved. Keywords: Solid oxide fuel cells; Fuel cell modelling; Biomass gasification; Thermal integration
1. Introduction The increase of atmospheric greenhouse gas concentration requires that the use of renewable fuels for energy production becomes more and more diffused. Biomass is already widely used to this aim representing some 35– 38% of the energetic resource on a worldwide scale, reaching 80% in some countries such as India or Sub-tropical Africa. As far as Europe is concerned, the resources in lignocellulosic biomass are assuming an increasing importance in the energy mix having the potential to substitute several Mtoe per year of fossil fuels also avoiding significant CO2 emissions. The thermochemical transformation is certainly the most diffused method of heat production from biomass *
Corresponding author. Tel.: +39 06 72597170; fax: +39 06 2021351. E-mail address: [email protected] (V. Mulone).
1359-4311/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2006.10.015
so far with combustion representing the leading technology. Heat produced by combustion may be used as energy input in a steam cycle. However, other thermochemical methods such as gasification and pyrolysis also have a great potential producing a syngas mainly composed of H2 and CO with traces of different gases such as CH4 in different proportions, together with variable quantities of tars. If carefully cleaned, synthetic gas could be directly used as a fuel for gas turbines in different configurations and, potentially, with high efficiency. In the search for higher efficiency converters, fuel cell energy generation systems are assuming a role of increasing importance. Being the most suitable systems for hydrogen utilization, fuel cells represent the basis for the development of an energy economy based on this energy carrier but they may also be efficiently fed with different fuels. In particular, high temperature fuel cells, such as SOFC and molten carbonate fuel cells (MCFC), are especially
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Nomenclature D dHint E E0 F G h i0 J K Ki le M MC m_ p P R Re S T u w
diffusion coefficient integration heat flux cell voltage Nernst voltage Faraday constant Gibbs energy enthalpy exchange current density current density permeability tensor equilibrium constant electrolyte thickness molecular weight moisture content mass flow rate pressure power gas constant electrolyte ionic resistance source term temperature velocity vector amount of water per mol of wood
attractive since they can be efficiently used both for combined heat and power (CHP) generation applications and integrated within high efficiency hybrid cycles. It is also largely believed that combining traditional cycles with fuel cells (e.g. Auxiliary Power Units) could accelerate the market introduction of the latter. Fuel flexibility constitutes a typical attractive characteristic of high temperature fuel cells [1]: these devices are in fact capable of operating with traditional light hydrocarbon fuels (e.g., methane) for their tolerance to carbon monoxide. They have also internal reforming potential and allow the design of highly integrated systems with a limited or even without the external fuel processor. Rather tight limits on fuel sulphur contents are nevertheless still required. In particular, SOFC are in principle characterized by rather high efficiency in converting chemical fuels directly into electrical power (more than 40% [2]) and by high temperature exhaust gases which could be used in combined cycles. According to the previous considerations, the use of biomass to fuel SOFC represents an interesting opportunity for an efficient deployment of biomass potential. The integration of a downdraft gasifier with a SOFC stack has been recently proposed in [3,4] the hot reformate gas stream is directly fed into the SOFC where the reforming and electrochemical reactions simultaneously occur. The SOFC off-gas, still rich in hydrogen and carbon monoxide, is used in an integrated combustor providing heat for the gasifica-
x Y
mol fraction mass fraction
Greek symbols bi ionic conductibility parameter e porosity k thermal conductivity g efficiency gact activation loss gohm ohmic loss l viscosity lf fuel utilization q density re electrolyte ionic conductibility Subscripts A anode C cathode e electrolyte el electric g global i species s solid
tion process. A simplified scheme for such a system is provided in Fig. 1. To avoid carbon deposition problems in the gasification process, high operating temperature and water content are required which can be efficiently get only with an integration of the gasifier with the downstream component [5]. Biomass sulfur levels must anyway be carefully controlled since the occurrence of even several ppm could cause the cell poisoning [6]. SOFC have been tested since 1930 under several configurations among which the most widespread and tested are the planar and tubular arrangements [2]. However, a number of technological problems still need to be solved, basically related to the high operating temperature and then to thermal cycling issue. Both material and design issues rise for the cell configuration, as thermal stress resistance must be guaranteed together with a good deployment of the
Fig. 1. Simplified scheme of an integrated gasifier-SOFC system.
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reactant-fluid potential. Research and development are therefore still proceeding both to test new materials and to optimize the design of single cells and complete stack as well. The role of numerical simulation in supporting this development effort is clearly important as it constitutes an effective way to speed-up the design phase both for component development and system integration. Different approaches have been developed in the literature using different levels of approximation for the description of the involved phenomena [7–12]. In this paper, a simulation tool is proposed to predict the performance and the main electro-thermal-fluid dynamic characteristics of an integrated biomass fuelled gasifierSOFC system. In the proposed approach, the SOFC behaviour is predicted by means of a 3D fluid dynamic simulation of the cell, while the gasifier is modelled by a lumped approach, able to evaluate the reformate characteristics starting from the biomass composition and its moisture content. With the previous characteristics, the model is able to address both component level (in particular how the SOFC design is affected by the reformate gas composition and characteristics) and system level issues (e.g., the influence of rejected heat and exhaust gas temperature on the overall system efficiency). The main objective of this work is, therefore, to analyze the performance of this integrated energy production system operating with biomass characterized by high water content.
where: • CH1.44O0.66 is the composition of woody material per unit carbon atom; • w is the amount of water per mol wood related to the biomass moisture content ðMCÞ by w ¼
24MC ; 18ð1 MCÞ
• m is the amount of oxygen per mol wood; • xi are the gas products molar fractions. The input and output parameters of the module, sketched in Fig. 2, are the following: • Input parameters: – biomass composition and water content (MC); – operating temperature; – integration heat (dHint); • Output parameters (problem unknowns): – required amount of air (m, i.e., molar oxygen/carbon ratio); – composition (xi). Given the elemental and energy balances 1 ¼ x2 þ x3 þ x5 2w þ 1:44 ¼ 2x1 þ 2x4 þ 4x5 w þ 0:66 þ 2m ¼ x2 þ 2x3 þ x4
The overall numerical model is constituted by two modules which allow to represent, respectively, a biomass gasifier and a SOFC behaviour. The gasifier module has been modelled by a 0D chemical equilibrium approach, assuming the reactor residence time high enough to let the pyrolisis products entirely convert into gas products. The SOFC module is conversely based on 3D computational fluid dynamics (CFD) analysis to model the gas evolution into the gas channels and porous electrodes, and the electrochemical cell response. The modules are separately illustrated below; details of the interconnection strategy to realize the integrated biomass gasifier-SOFC model are also provided in the final section.
¼ x1 dHH2 þ x2 dHCO þ x3 dHCO2 þ x4 dHH2 OðvapÞ ð6Þ
additional relations must be introduced to close the problem and finally find xi and m. Methane formation and water shift reactions are then supposed to be at equilibrium: • C + 2H2 = CH4 • CO + H2O = CO2 + H2 The corresponding equilibrium constants (K1 and K2, respectively), whose values can be evaluated by a minimization of Gibbs free energy, provide two further equations: K1 ¼
x5 x21
ð7Þ
K2 ¼
x1 x3 x2 x4
ð8Þ
2.1. Gasifier module The 0D biomass gasifier module is based on a global gasification reaction [13], which may be written for woody material as: CH1:44 O0:66 þ wH2 O þ mO2 þ 3:76mN2 ! x1 H2 þ x2 CO þ x3 CO2 þ x4 H2 O þ x5 CH4 þ 3:76mN2 ð1Þ
ð3Þ ð4Þ ð5Þ
dHfwood þ wdHH2 OðlÞ þ dHint þ x5 dHCH4 þ 3:76mdHN2
2. Numerical model
ð2Þ
Fig. 2. Gasifier module black-box layout.
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Fig. 3. MC effect on outlet gasifier composition at 800 C.
The six Eqs. (3)–(8), after some algebraic passages here omitted (details are available in [13]), can be reduced to a three non-linear equation set and solved by means of a Newton–Raphson method. The module has been validated against experimental data [14] in the case of an adiabatic gasifier (dHint = 0). The effect of input water content (MC) on the reformate composition in terms of dry basis volume fractions at 800 C is reported in Fig. 3. It is worth noting that:
It can be observed that the equilibrium hypothesis may represent rather well the reformate calorific value for higher temperature conditions where reaction kinetic effects assume less importance. On the basis of the previous results, the 0D gasifier module has been evaluated accurate enough in the range of high temperatures (more than 800 C) operating conditions where the SOFC is expected to be operated. 2.2. SOFC module
• CH4 fraction is negligible; • H2 and CO2 fractions increase with increasing MC, as expected; • CO diminishes with increasing MC, as expected. • A high N2 fraction may be observed throughout the MC range: this is due to a certain amount of required air to allow the gasifier to run autothermal (dHint = 0): it exploits therefore biomass oxidation to sustain chemical reactions. Less air, and therefore N2, may be conversely required depending on the amount of integration heat: high amounts could even lead to the obtainment of steam reforming operating conditions; gasification in those cases is performed without air. The validation with respect to experimental data have been performed in terms of reformate calorific value for different operating temperatures and MC equal to 0.2. The results of this comparison are summarized in Table 1.
Table 1 Experimental-numerical comparison: MC = 0.2
750 C 800 C 900 C
Calorific value (MJ/m3) present work
Calorific value (MJ/m3) experimental [14]
Error (%)
5.5 5.3 4.9
4.9 4.8 4.6
10.7 8.7 6.1
The SOFC module is based on a 3D computational fluid dynamic (CFD) approach, and it has been used to predict the behaviour of the smallest repeated geometrical element (unit cell), so realizing the so-called unit cell approach. Results can then be extended to the entire stack having assumed all the cells behaving in the same way. This assumption may be reasonable for stationary conditions but it is not limitative of the model potential as it may be easily substituted by a more detailed description of the complete FC geometry. The module is based on the following main hypothesis: • • • • • • •
planar co-flow configuration laminar flow steady state isotropic porous media infinite electrodes conductivity adiabatic channel no radiative heat transfer
3D mass, momentum and energy equations allow to represent the evolution of a gas-mixture of Ng = 7 chemical species (H2, O2, H2O, CH4, CO, CO2, N2) in the fuel and oxidant channels and porous electrodes. An electrochemical submodel has been implemented to locally represent the electrolyte behaviour in terms of mass/energy/charge fluxes based on rather standard 1D assumptions [2,9,15–20].
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The equation set assumes the following form: • Mass: r qu ¼ 0
ð9Þ
• ith species (i = 1, Ng): r qY i u r ðqDi rY i Þ ¼ S i
ð10Þ
where Yi represents the examined species mass fraction, Di its diffusion coefficient and Si its source term, which depends on the occurring chemical mechanism and local current in the electrolyte region. The internal reforming chemical process has been modelled by the introduction of homogeneous phase methane reforming reactions and water–gas-shift (WGS) reaction [21]: • CH4 + H2O ! 3H2 + CO • CO + H2O M H2 + CO2 The first reaction has been modelled by a kinetic approach following the hypothesis reported in [22], while the second one has been considered to be always at equilibrium [17]. • Momentum:
2 l r ðquu lruÞ ¼ r p þ lr u ðeuÞ 3 K
ð11Þ
K being an equivalent permeability tensor, which allows to take into account the flow in the porous electrodes. • Enthalpy: r ðquh krT Þ ¼ S h
ð12Þ
where k represents the local thermal conductivity: it generally depends on composition and gas pure species thermal conductivities, which are defined by means of the ideal gas kinetic theory. In the electrodes, k expression takes into proper account the solid thermal conductivity (ks = 2.25 W/mK [12]) using an average gas–solid value mass-weighted by the electrodes porosity e. Sh represents the energy source PN term which is related to the species change by S h ¼ i g hi S i .
" 1# ðpH2 =p0 Þ ðpO2 =p0 Þ2 DGðT Þ R T þ ln E0 ¼ 2F 2F ðpH2 O =p0 Þ 2RT j sinh1 gact;A ¼ F 2i0A 2RT j sinh1 gact;C ¼ F 2i0C p p H2 O 100 103 H2 i0;A ¼ 5:5 104 exp p0 p0 RT 0:25 3 p 120 10 O2 exp i0;C ¼ 7:0 104 p0 RT
ð14Þ ð15Þ ð16Þ ð17Þ ð18Þ
Ohmic losses are computed as: gohm ¼ Re j le Re ¼ ; ½X cm2 re
ð19Þ ð20Þ
j being local current, le and re the electrolyte thickness and conductivity; the latter can be expressed as: b2 1 re ¼ b1 exp ð21Þ ; X cm T The electrochemical model has been set-up, in terms of b1 and b2 (Table 1) parameters, on the basis of similar models available in the literature [2,9,15,16,19,20]. The reference SOFC polarization curve has been calculated by imposing uniform temperature, O2 mass fraction equal to 0.23 and pure H2. Results are plotted in Fig. 4 with respect to typical operating temperatures. The model does not require any evaluation of concentration losses, which are directly taken into account via the 3D species fields. The electrochemical model is called by the 3D main solver, and provides the local current on the basis of local reactant distributions and temperature. Species and energy source terms Si and Sh, representing the link between the electrochemical model and the 3D solver, are then provided by the following relations as functions of the local current j: • Electrolyte on the cathode side: j M O2 4F S h ¼ ð1:25 EÞj S O2 ¼
ð22Þ ð23Þ
• Electrochemical submodel: The electrochemical submodel solves the mass/current/ energy problem across the electrolyte. It is mainly based on the electrochemical reaction: H2 þ 12O2 ! H2 O Cell voltage E is imposed on the electrolyte: E ¼ E0 gact gohm
ð13Þ
where E0, gact = gact,A + gact,C and gohm represent ideal voltage, activation and ohmic losses defined as it follows [17]:
Fig. 4. 0D SOFC polarization curve with fixed temperatures and gas fractions.
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• The 0D gasifier module has been implemented into a FORTRAN subroutine; • The 3D SOFC module has been implemented into the FLUENT 6.2 CFD package [23] where the electrochemical phenomena have been taken into account developing specific ANSI-C User Defined Functions (UDF). 0D gasifier module and 3D SOFC modules are managed by a main program whose flow diagram refers to Fig. 7. 3. Analysis of results Fig. 5. Electrochemical model and 3D solver coupling schematic.
• Electrolyte on the anode side: j M H2 2F j M H2 O ¼ 2F
S H2 ¼
ð24Þ
S H2 O
ð25Þ
The coupling strategy between electrochemical model and CFD solver is illustrated in Fig. 5. The 3D module input and output parameters, summarized in Fig. 6, are the following: • Input parameters: – material/electrochemical parameters; – geometry; – boundary conditions (cathode and anode inlet parameters: mass flow rate, composition and temperature); – cell voltage. • Output parameters: – current field on the electrolyte; – cathode and anode outlet parameters: composition, temperature, residual calorific value. 2.3. Whole numerical model implementation details and management strategy From a computational point of view the modules have been implemented into different computational environments. More specifically:
The numerical model has been applied to the analysis of a 14 kW SOFC-gasifier integrated system whose layout is reported in Fig. 1. The system is fed by woody material biomass CH1.44O0.66, and a co-flow planar anode supported configuration has been chosen for the SOFC (see Table 2). Integration heat flux dHint, defined as the heat provided by the SOFC anode off-gas combustion, is used to reduce the amount of external heat required. In these conditions, the gasifier can exploit the integration heat flux as a substitute of heat otherwise provided by biomass combustion, and can operate with high MC and without air so realizing a biomass steam reforming process. High water and temperature SOFC operating conditions are in fact favourable to avoid carbon formation and deposition problems [5]. Starting from the above considerations, operating conditions have been chosen as it is displayed in Table 3, where 0.65 V cell voltage has been selected as a representative average load condition. The gasifier output gas composition (Table 4), which is actually the result of the iterative loop procedure described in Fig. 7, represents also the SOFC anode inlet gas composition. The SOFC main geometrical characteristics are reported in Table 5 and sketched in Fig. 8, where the computational domain layout is also presented: it is composed by about 100,000 cells. The model has been used to compute the SOFC and entire system performance (fuel utilization lf, cell efficiency gSOFC, entire system efficiency gg whose definitions are reported below), as well as specific power. P lf ¼
_ in i i ðm
gSOFC ¼ P gg ¼
Fig. 6. SOFC module black-box layout.
m_ out i Þ in _ m i i
ð26Þ
P el in _ m i i LHVi
ð27Þ
P
P el LHV m_ in biomass biomass
ð28Þ
In the previous equations m_ i terms represent the ith fuel component (CO or H2) mass flow rates, LHVi the ith fuel component low heating value (Table 6) and Pel, the output electric power.
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Fig. 7. Whole numerical model flow diagram.
Table 2 SOFC module electrochemical parameters
b1 b2
Table 5 SOFC geometrical characteristics
Value
Units
334 10,300
(1/X cm) (K)
Table 3 Gasifier-SOFC operating conditions
Gasifier moisture content Gasifier operating temperature Anode and cathode inlet pressure Cell voltage Cathode/anode mass flow ratio
Value
Units
0.4 1173 1 0.65 15
K atm V –
Cell length Gas channel height Gas channel width Rib Anode electrode thickness Cathode electrode thickness Electrode porosity Stack total active area
Value
Units
71 0.8 0.8 0.4 1 0.2 0.4 76,860
mm mm mm mm mm mm cm2
Table 4 Gasifier output composition Dry basis mole fractions H2 CO CO2 CH4 N2 O2
0.56 0.39 0.06 0 0 0
The analysis of the model results for the examined configuration shows that global efficiency gg gets a rather high
Fig. 8. SOFC transversal section dimensions (left) and 3D layout (right).
value. This is due to the integrated design which minimize the requirement of external heat by the exploitation of the integration heat. This choice is nevertheless very much dependant on the system application and requires a case by case analysis.
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Table 6 Fuels low heating values
CO H2 CH4 Biomass (wood) CH1.44O0.66
Value
Units
10,106 120,910 50,144 15,940
kJ/kg kJ/kg kJ/kg kJ/kg
The average current of 0.28 A/cm2 obtained from the SOFC module corresponds to a specific power of 0.182 W/cm2. On the basis of the previous specific values and using the unit cell hypothesis, results may be scaled-up to propose a layout of the complete 14 kW system, reported in the flow diagram of Fig. 9. The model is here used to give a first idea on this systemPcharacteristic mass and energy fluxes; LHV is defined as i m_ i LHVi summed over CO and H2 everywhere except in the gasifier inlet section where LHV must be defined as a function of biomass characteristics as m_ biomass LHVbiomass . It is worth noting that the presence of residual LHV at the SOFC outlet (21% with respect to the SOFC inlet one), is needed to integrate the gasifier. This is then responsible for the obtainment of a 34.3% SOFC efficiency due to a corresponding 57% fuel utilisation. The 3D SOFC module characteristics also allow the analysis of phenomena occurring in the gas channels, electrodes and electrolyte. This approach is of particular interest in system design as it is capable of giving accurate information which may not be easily accessed via experimental techniques. As an example, current distribution on the electrolyte is reported in Fig. 10 in a top view, showing a characteristic decreasing pattern in the stream-wise direction. Current intensity, in fact, depends both on H2 availability (in terms of local mass fraction) and temperature local value. H2 and temperature distributions are further provided in Figs. 11 and 12. An H2 deployment (due to H2 consumption) and
Fig. 10. Current (A/cm2) distribution on the electrolyte and detail.
Fig. 11. H2 distribution and detail on a transversal section.
an increase of temperature (due to electrochemical and WGS reactions heat release and to the imposition of adiabatic heat flux on the boundaries [24]) may be observed in
Fig. 9. Mass-energy fluxes of the 14 kW integrated generation system.
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S. Cordiner et al. / Applied Thermal Engineering 27 (2007) 738–747 Table 7 System performance indicators Value lf (%) gSOFC (%) gg (%) Average current Specific electric power
Fig. 12. Temperature distribution on an axial section (inlet on the right).
the stream-wise direction. It can be finally concluded that H2 influence on current distribution is everywhere heavier than the temperature one for the examined case. The detail of Fig. 10 puts also into evidence the uneven distribution of current in the rib-region: this behaviour is the result of the variable H2 fluxes along the electrolyte (Fig. 11, detail). In fact, under the rib, mass diffusion towards the electrolyte surface is less efficient. WGS equilibrium moves towards the H2 side, as it appears by the analysis of CO and CO2 distributions for the electrochemical H2O flux (Fig. 13). This circumstance allows to exploit CO to produce current via H2 internal production. As a final remark, it can be observed how the model has then proved to be capable of predicting both the integrated system main performance parameters and the main fluid dynamic and electrochemical SOFC 3D fields (species, temperature, current). This circumstance suggests the use of the proposed approach as a basic support for design since
57 34.3 45.8 0.28 A/cm2 0.182 W/cm2
it gives the possibility of evaluating the SOFC response by varying geometrical and material parameters without any modifications of the described model structure. 4. Conclusions A 14 kW energy generation system has been where a SOFC is supplied by a biomass gasifier. In the proposed layout, the gasifier is integrated by heat recovered by SOFC off-gas combustion, to realize a high efficiency concept and a high water content SOFC input gas to avoid carbon deposition. The system performance has been analyzed using a specifically developed numerical model, mainly constituted by two modules which, respectively, allow to represent a gasifier and SOFC behaviour. The gasifier has been modelled by a 0D equilibrium approach, since the related performance in terms of maximum error (6%) have been retained acceptable for the present application typical operating conditions. The SOFC has been modelled by a 3D CFD based approach, which allows to directly represent the coupling among the different phenomena occurring, namely diffusion, convection and electrochemistry (see Table 7).
Fig. 13. CO (top-left), CO2 (top-right) and H2O (bottom) distributions on an axial section (inlet on the right).
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Results mainly indicate that: • the numerical model represents a point of departure both to evaluate the system performance and to give a quantitative idea about the distribution of current on the electrolyte and the main species into the gas channels and electrodes taking into account also the fluiddynamic rib effect • the needed integration heat flux requires a 21% fraction of the SOFC inlet LHV which corresponds to a 57% fuel utilization and therefore to a 34.3% SOFC efficiency • from a global point of view the system presents good performance in terms of efficiency (45.8%) The model could possibly be extended, without any major modifications, to study more complicated fluid dynamic configurations and their impact on the system performance, and/or the behaviour of entire SOFC assemblies once evaluated the increase of required computational resources. References [1] S.L. Douvartzides, F.A. Coutelieris, A.K. Demin, P.E. Tsiakaras, Fuel options for solid oxide fuel cells: a thermodynamic analysis, AIChE J. 49 (2003) 248–257. [2] S.C. Singhal, K. Kendall, High Temperature Solid Oxide Fuel Cells, Elsevier, New York, 2003. [3] P.N. Hutton, M.A. Musich, N. Patel, D.D. Schmidt, R.C. Timpe, feasibility study of a thermally integrated SOFC-gasification system for biomass power generation. US Department of Energy, National Energy Technology Laboratory Cooperative Agreement. Phase 1. Interim report, No. DE-FC26-98FT40321, Energy and Environmental Research Center, University of North Dakota, 2003. [4] A.O. Omosun, A. Bauen, N.P. Brandon, C.S. Adjiman, D. Hart, Modelling system efficiencies and costs of two biomass-fuelled SOFC systems, J. Pow. Sources 131 (2004) 96–106. [5] D. Singh, E. Hernandez Pacheco, P.N. Hutton, N. Patel, M.D. Mann, Carbon deposition in a SOFC fuelled by tar-laden biomass gas: a thermodynamic analysis, J. Pow. Sources 142 (2005) 194–199. [6] Y. Matsuzaki, I. Yasuda, The poisoning effect of sulfur-containing impurity gas on a SOFC anode: Part I. Dependence on temperature, time and impurity concentration, Solid State Ion. 132 (2000) 261–269.
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