Nowadays, the increment of the petrol price has been a major problem for the consumers and it will increase more than 4 cent per litter in period of 6 to 12 month. Thus, there are many new energy developments that friendly

to the environment have been commercialized to overcome this phenomenon such as solar energy and fuel cells technology. Among these, fuel cell power systems for transportation applications have received increased attention in recent years because of the potential for high fuel efficiency and lower emissions. A fuel cell

converts hydrogen and oxygen into water, directly generating electrical energy from chemical energy without being restricted by efficiency limits of the Carnot thermal cycle (Larminie et al., 2000)

Ahmad, Arshad

Ibrahim, Norazana

Lee, Hock Weng

Ramli, Ahmad Raoof

Repository@USM

[AMN04] Dynamic modelling of fuel cell system for mobile application using Simulink environment  Ahmad Raoof Ramli , Arshad Ahmad , Norazana Ibrahim , Lee Hock Weng  Laboratory of Process Control, Department of Chemical Engineering, Faculty of Chemical and Natural Resources Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia.  Introduction Material and Methods    Nowadays, the increment of the petrol price has been a major problem for the consumers and it will increase more than 4 cent per litter in period of 6 to 12 month. Thus, there are many new energy developments that friendly to the environment have been commercialized to overcome this phenomenon such as solar energy and fuel cells technology. Among these, fuel cell power systems for transportation applications have received increased attention in recent years because of the potential for high fuel efficiency and lower emissions. A fuel cell converts hydrogen and oxygen into water, directly generating electrical energy from chemical energy without being restricted by efficiency limits of the Carnot thermal cycle (Larminie et al., 2000).    Proton exchange membrane (PEM) fuel cells are preferred for mobile application, because their low operating temperatures (around 80OC) and have provided more work from a given quantity of fuel and less polluting  than internal combustion and gas turbine engines. Although, the limitation of hydrogen produce may become a minor problem, a fuel processor may be required to generate a hydrogen-rich stream using natural gas such as methane and methanol. So, the complete fuel cell system consists of a fuel processor unit and a PEM fuel cell stack unit as shown in Figure 1 and the aim of this study was to develop the plant simulation as a read for plantwide control configuration.  FIGURE 1   Flow diagram of PEM fuel cell plant   The model development is divided into two main categories which are the development of the fuel processor and PEM fuel cell stack. The system generated a power of 5 kW and has been developed using Simulink environment (Matlab 6.5.1).   Fuel processor unit development    A fuel processor unit consists of an autothermal reactor (ATR), a water gas shift reactor (WGSR), a preferential oxidation reactor and two units of heat exchanger. The combinations of all these units produce a rich hydrogen stream and below 10 ppm CO concentration feed to PEM fuel cell stack.  Autothermal reactor mathematical model    A one-dimensional heterogeneous model is chosen in this work to simulate a tubular fixed-bed reactor. The mass and energy equations for the bulk and gas phase as well as the corresponding initial and boundary conditions are described below (De Smet et al., 2001):  Gas phase    ( ) 0, =−+⎟⎟⎠⎞⎜⎜⎝⎛ ssiiVRsim CCakCdzdρϕ          (1) ( ) 0=−+ sgVfgpm TTahdzdTcϕ           (2)  Solid phase 01 ,,22,2 =+⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛siwfsiiepf RCddddDrρρεεεερ     (3) ( ) ( ) ( ) 01 , =∆−Σ−+− iwsifBsgVf RHTTah ρε  (4)   Gas-phase boundary conditions oggoii TTCCz ===0              (5)  Solid-phase boundary conditions 00 , =⎟⎟⎠⎞⎜⎜⎝⎛=fsiCddρεε            (6) 01 ,, =⎟⎟⎠⎞⎜⎜⎝⎛=fsipiefCddrDρερε                      (7)   The 4th Annual Seminar of National Science Fellowship 2004315The simulation of the autothermal reaction is based on the following set of differential equations (Ann De Groote et al., 1996).  Continuity Equations ( 33221144 rrrFdzdxoCHbCH ηηηρ −−Ω= )              (8) ( )11222 rFdzdxoObO ηρ Ω=          (9) ( )224rFdzdxoCHbCO ηρ Ω=        (10) ( )331142 rrFdzdxoCHbCO ηηρ +Ω=       (11)  Energy equation ( )iiipgsb HrCudzdT ∆−Σ= ηρρ       (12)  The effectiveness factors, η are taken from an average value based upon a number of off-line pellet simulations for the various effectiveness factors (Ann De Groote et al., 1996).    In the modelling of autothermal reforming of methane, it is necessary to combine all the rate equations for the total combustion, steam reforming for CO production and CO2 production in the calculations. In this paper, the intrinsic reforming models (Xu et al., 1989) are adopted as presented below. These authors derived the intrinsic rate equations for the steam reforming of methane on Ni/MgAl2O3 catalyst. Total oxidation OHCOOCH 2224 22 +⇒+                        (13) ( ) ( )2244 241222442411 11 OoxOCHoxCHOCHbooxOCHoxCHOCHapKpKppkpKpKppkr +++++=  (14)  Steam reforming (CO production)                (15)    224 3 HCOOHCH +⇔+( )222244223,32245.2222 /1)/(/HOHOHCHCHHHCOCOeqCOHOHCHHxuppKpKpKpKKpppppkr ++++−=   (16)  Steam reforming (CO2 production) 2224 42 HCOOHCH +⇔+                   (17) ( )222244224,2422245.3233/1)/(/HOHOHCHCHHHCOCOeqCOHOHCHHxuppKpKpKpKKpppppkr ++++−=   (18)  Water gas shift reactor mathematical model    The water gas shift reactor (WGSR) provides primary CO cleanup, as well a secondary H2 production. In most hydrocarbon processor, the water gas shift reactor is the biggest and heaviest component because the reaction is relatively slow compared to the other reactions and is inhibited at higher temperatures by thermodynamic (Tongtaek et al., 2003). Therefore, the simulation of the WGSR reaction is based on the following set of differential equations.  Mass balance equations rCVFCVFdtdCoutcooutincoinCO −⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛= ,,       (19) rCVFCVFdtdCoutHoutinHinH +⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛= ,, 222     (20) rCVFCVFdtdCoutcooutincoinCO +⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛= ,, 222   (21) rCVFCVFdtdCoutOHoutinOHinOH −⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛= ,, 222   (22)  Energy equation ( )iiipgsbw HrCudzdT ∆−Σ= ηρρ           (23)  The kinetic for WGSR is known critical when designing an efficient fuel reformer and optimizing its operating conditions. So, in this paper, the reaction kinetic proposed by Yongtaek and Stenger (2003) is used as presented below. The authors derived the reaction kinetic on Cu/ZnO/Al2O3 catalyst under operating temperature between 200oC to 250oC. 222 HCOOHCO +⇔+                                   (24) )1(exp β−⎟⎠⎞⎜⎝⎛ −= n OHmCOo wppRTEkr                  (25) where eqOHCOHCOKpppp222=β   Preferential oxidation reactor    The preferential oxidation reactor (PROX) is used to eliminate the CO that has not been converted in the WGSR. This reactor required to reach very low level of CO content in the fuel stream at the fuel cell inlet in order to avoid poisoning of the membrane (Zalc et al., 2002). It is assumed that the PROX is operating under an isothermal condition at a temperature of 250oC. The representative model can be described in the differential equations of mass and energy balance. Mass balance equations rCVFCVFdtdCoutcoPROXoutincoPROXinCO −⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛= ,,       (26) The 4th Annual Seminar of National Science Fellowship 2004316rCVFCVFdtdCoutCOPROXoutinCOPROXinCO +⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛= ,2,22     (27) rCVFCVFdtdCoutOPROXoutinOPROXinO 5.0,2,22 −⎟⎠⎞⎜⎝⎛−⎟⎠⎞⎜⎝⎛=   (28)  Energy balance equation ( ) PROXoutrxninPROX ChQEQdtdT/−+=         (29)  In this paper the kinetic of selective CO oxidation over the Cu0.1Ce0.9O2-y nanostructured catalyst can be well by employing the Liu and Flytzani-Stephanopoulus model equations (Sedmark et al., 2003). 2221 COOCO ⇔+         (30) COLmOCOLLpKppKkr += 12                                        (31) where ⎟⎠⎞⎜⎝⎛ −= RTEAk LaLL ,exp ⎟⎠⎞⎜⎝⎛= RTQBK LL exp   Cooler Units    Two cooler units are needed in order to reduce the temperatures of the outlet gas streams from the ATR and the PROX respectively. In these equipments, the cooling water charged into the shell is from the PEM fuel cell water produce and the products of the ATR and PROX enter at the tube side. Each cooler unit have different configurations and specifications. It is assumed that the cooler unit is perfectly insulated, so that no energy lose to surrounding. Furthermore, no reaction occurs during the cooling. The models were represented by the energy balances of gases and cooling water.  First cooler unit energy balance equations Gases ( ) CLTCLoutoinoinWGSR ChQQQdtdT/1,,, −−=         (32)  Cooling water ( ) WCLTCLoutWCinWCWCL ChQQQdtdT /1,, +−=       (33)  Second cooler unit energy balance equations Gases ( ) 12,,, / CLTCLoutoinoinPEMFC ChQQQdtdT −−=           (34)  Cooling water ( ) WCLTCLoutWCinWCWCL ChQQQdtdT /1,, +−=         (35)  PEM fuel cell stack unit development   The dynamic model developed is based on appropriated energy, mass and electrochemical equations as applied to PEM fuel cell (Yerramalla et al., 2003). The whole modelling process can be divided into two parts.  Individual cell modelling    The chemical reactions occurring at the oxidation and reduction electrode of a PEM fuel cell are as follows: −+ +⎯⎯ →⎯ eHH oxidation 442 2                   (36) OHeHO reduction 22 244 ⎯⎯⎯ →⎯++ −+                      (37) Total cell reaction:        (38) OHO 22H 22 →+2The various equations necessary for the modelling of an individual cell are presented below.  Butler-Volmer equation    The equation shows the net current density for one-step electrochemical reaction flowing through a metallic electrode is expressed using the following equation: ⎥⎦⎤⎢⎣⎡ −=−−TRFnTRFno eeii ...).1(.... ηαηα          (39) Normally the variables associated with this equation (the exchange current density io and the charge transfer coefficient α) are obtained from empirical procedures.  The anode overvoltage    The anode overvoltage can be represent by (Mann et al., 1996): ( ) iFRTcFAkFRTFGHoaecaact ln24ln22 2,−+−=η         (40)  Equation (36) after the insertion of the known parameter values and rearrangement, gives: ( ) ( )⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛+××+∆×−= −−ikAcTGoaHecaact256,ln863.1210309.41018.5η        (41)  The cathode overvoltage    Again, as previously proposed ((Mann et al., 1996), the cathode overvoltage can be given by The 4th Annual Seminar of National Science Fellowship 2004317] icccRTGnFAkFnRTcOHcHcOeoCCcactlnexpln2)1(2)1(2,−×⎜⎜⎝⎛⎢⎣⎡⎜⎜⎝⎛ ⎟⎠⎞∆−=−− ααααη      (42) As previously, after the insertation of the known parameter values and rearrangement, equation (38) becomes: ( ) (()lnln)1('ln863.121062.81036.101256,ickATGOcceccact−−+++××+∆×−= −−ααη )   (43)  The ohmic overvoltage    The resistance to electron transfer in the graphite collector plates and graphite electrodes plus resistance to proton transfer in the solid polymer membrane produce ohmic polarization. This could be expressed using ohm’s law equations such as: ernalohmic iRint−=η        (44) The Rinternal can be obtained from experimental results (Xue et al., 2003)  Fuel cell stack modelling    In this section, the various equations necessary for the modelling of the overall fuel cell system are presented. For ‘N’ single cells connected in a fuel cell stack system, the total stack voltage (∆VT) is calculated by: NVcellVT =∆        (45) Thus, for the current of a fuel cell stack is calculated by: cellstack NII =         (46) Finally the total power produced by the entire stack is calculated by multiply the total stack voltage and the current of the stack. stackTstack IVP ∆=        (47)  Results and Discussion  Fuel cell system dynamic model simulation   In this section, a detailed parametric analysis to study the dynamic effects within the system was carried out. The parameters and variables used in this part of study are listed in Table 1. The model was developed under Simulink environment (Matlab 6.5.1) and as some parameters are small such as a cell volume, stiff differential equation solver ODE23S is employed in the simulation. The time length for the simulation is 3500 s.  TABLE 1  Parameters and variables used in system simulation Parameter Value Dr Diameter of ATR, m 0.4 Lr Length of ATR, m 0.5 T Temperature of ATR, K,) 800 pr ATR operating pressure, atm 1 ρs Catalyst density, kg/m3 1870  CH4/O2 ratio 2  H2O/CH4 ratio 2 xi Species mole fraction  Ci Species concentration, mole/m3  pi Species partial pressure  Keq Equilibrium Constant  Dw Diameter of WGSR, m 0.2 Lw Length of WGSR, m 0.5 Tw Initial WGSR temperature, K 523.15Pw WGSR operating pressure, atm 1 Dp Diameter of PROX, m 0.1 Lp Length of PROX, m 0.5 Tp Initial PROX temperature, K 523.15Pp PROX operating pressure, atm 1 LWCL First cooler unit length, m 0.56 n Number of tube 25 To Initial cooler temperature 302.1 LWCL1 Second cooler unit length, m 0.12 n Number of tube 25 α Transfer coefficient, anode  0.5 α Transfer coefficient, cathode 1 F Faraday costant, C/mole 96485 R Universal constant of gases, J/mole.K 8.314 pc Air side pressure, atm 5 pa Fuel side pressure, atm 1 Tcell Initial cell temperature, K 353.15N Number of cell 39  MEA active area, cm2 360  The parametric sensitivity of fuel cell system behaviour and its performance have been investigated for several parameters including operating temperatures and kinetic parameter. The influence of these operational parameters on the product composition depends strongly on the thermodynamics of the reactions. For this purpose, analysis has been studied over the ATR temperature of 800-1015 K and total feed flowrate from 2.0-3.0 m3/s to see the effect on other units compositions and power production.  The results are as follow: 1. Effect of step change in temperature The 4th Annual Seminar of National Science Fellowship 2004318 FIGURE 2   Results of step change in temperature  Figure 2 shows the CH4 and H2 concentrations of ATR, the ATR CH4 and WGSR CO conversions, the power production, the temperature of WGSR and PROX units and the gas stream temperatures of first cooler and second cooler units. While the results of step change in temperature are shown in Table 2.  TABLE 2  The Effect of step change in temperature  Parameter 800K 1015KATR H2 concentration, mol/m3ATR CH4 concentration, mol/m3ATR CH4 conversion, % WGSR CO conversion, % WGSR temperature, K PROX temperature, K Gas stream temperature of first cooler, K Gas stream temperature of second cooler, K Power production, kW 0.2469  0.2428  48.86 4.242 514.3 509.7  515.9  350.4 4.661 0.7725  0.0563  88.15 42.81 523.7 519.1  526  352 5.126  From the simulation results, temperature has a significant effect on kinetic productions of hydrogen and carbon monoxide due to the increment of methane converted toward high temperature. Furthermore, the temperature of other units increase since more heat energy is supplied.  2. Effect of step change in  steam feed flowrate Figure 3 shows the ATR products concentration, the WGSR products concentration, the PROX products concentration, the conversion of CH4 for ATR and CO for WGSR and PROX. While Figure 4 indicates the power production towards step change in steam feed flowrate. The results of step change 0.5 m3/s to 1 m3/s in steam feed flowrate are shown in table 3.  FIGURE 3   Results of step change in steam feed flowrate  FIGURE 4   Power production of step change in steam feed flowrate  TABLE 3   The Effect of step change in steam feed flowrate  Parameter 0.5 1.0 ATR concentration, mol/m3H2H2O CO CO2O2CH4WGSR concentration, mol/m3H2H2O CO CO2PROX concentration, mol/m3CO CO2O2ATR CH4 conversion, % WGSR CO conversion, % PROX CO conversion, % Power production, kW  0.7725 0.4272 0.4112 0.2675 0.0307 0.0563  1.207 0.2979 0.2352 0.2234  0.0314 0.2744 0.0315 88.15 42.81 87 5.126  0.5788 0.4594 0.2897 0.1748 0.0148 0.0058  0.9657 0.2383 0.1881 0.1787  0.0269 0.2352 0.0230 98.47 35.07 85.71 3.877 The 4th Annual Seminar of National Science Fellowship 2004319Base on the results, the increment of steam flowrate has a significant effect on methane consumption in ATR. Since, more steam feed to the ATR, more CH4 is reacted. But the production of CO, CO2 and H2 become lower   since the steam to methane ratio is constant. It is also resulted in other units’ productions.   3. Effect of step change in methane feed flowrate  FIGURE 5 Results of step change in CH4 feed flowrate  FIGURE 6 Power production of step change in CH4 feed flowrate  Figure 5 and figure 6 show the same parameters as figure 3 and figure 4. The results of step change 1.0 m3/s to 2 m3/s in methane feed flowrate are shown in Table 4.  TABLE 4 The Effect of step change in methane feed flowrate Parameter 1.0 2.0 ATR concentration, mol/m3H2H2O CO CO2O2CH4WGSR concentration, mol/m3H2H2O CO  0.7725 0.4272 0.4112 0.2675 0.0307 0.0563  1.207 0.2979 0.2352  0.5695 0.2304 0.3285 0.2328 0.0069 0.0919  0.8048 0.1986 0.1568 CO2PROX concentration, mol/m3CO CO2O2ATR CH4 conversion, % WGSR CO conversion, % PROX CO conversion, % Power production, kW 0.2234  0.0314 0.2744 0.0315 88.15 42.81 87 5.126 0.1489  0.0235 0.2058 0.0176 70.95 52.28 85 3.307  In this study, the increment of methane flowrate has a significant effect on methane and oxygen consumption in ATR. Since, more methane feed to the ATR, less methane and oxygen are reacted. So, the production of CO, CO2 and H2 become lower   since the methane to oxygen ratio is constant. It is also effected other units’ productions.    From the thermodynamic analyses and kinetic simulation performed, the optimal operating conditions of the temperature is 1015 K, H2O/CH4 and CH4/O2 ratios of 2-3, feed flowrate of 2.0 m3/s (1 m3/s for CH4, 0.5 m3/s for H2O and O2) for ATR and fuel processor pressure at 1 atm is favourable for PEM fuel cell stack.   Acknowledgements    The authors would to praise a gratitude to Ministry of Science, Technology and Innovation (MOSTI), Malaysia for the National Science Fellowship awarded to Ahmad Raoof Ramli and IRPA research grant. Our heartiest appreciations are for everybody who has directly or in directly contribute to the success of this project.  References Ann De Groote, M. and Gilbert Froment, F. (1996). Simulation of the catalytic partial oxidation of methane to synthesis gas. Applied Catalyst 138: 245-264.  De Smet, C.R.H., De Croon, M.H.J.M., Berger, R.J., Marin, G.B. and Schouten, J.C. (2001). Design of adiabatic fixed bed reactors for the partial oxidation of methane to synthesis gas. Application to Production of Methanol and Hydrogen-for-Fuel-Cells Science 56:4849-4861.  Larminie, J. and Dick, A.(2000). Fuel Cell Systems, New York. Wiley.  Mann, R.F., Amphlett, J.C., Hooper, M.A.I., Jensen, H.M., Peppley, B.A. and Roberge, P.R.(2000). Development and application of a generalised steady-state electrochemical model The 4th Annual Seminar of National Science Fellowship 2004320for a PEM fuel cell. Journal of Power Sources 86: 173-180.  Sedmak, G., Hocevar, S. and Levec, J. (2003). Kinetics of selective CO oxidation in excess of H2 over the nanostructured Cu0.1Ce0.9O2-y catalyst. Journal of Catalysis 213: 135-150.  Xu, J. and Froment, G.F. (1989). Methane Steam Reforming, Methanation and Water-gas shift: I. Intrinsic Kinitecs. A.I.Ch.E. Journal 35: 88-96.  Xue, X., Tang, J., Smirnova, A., England, R. and Sammes, N. (2004). System level lumped-parameter dynamic modelling of PEM fuel cell. Journal of Power Sources 133: 188-204.  Yerramala, S., Davari, A., Feliachi, A. and Biswas, T. (2003). Modelling and simulation of the dynamic behaviour of a polymer electrolyte membrane fuel cell. Journal of Power Sources 124: 104-113.  Yongtaek, C. and Stenger, H.G. (2003). Water gas shift reaction kinetics and reactor modelling for fuel cell grade hydrogen. Journal of power Sources 124: 432-439.  Zalc, J.M. and Loffler, D.G. (2002). Fuel processing for PEM fuel cells: transport and kinetic issues of system design. Journal of Power Sources 111: 58-64. The 4th Annual Seminar of National Science Fellowship 2004321

Dynamic modelling of fuel cell system for mobile application using Simulink environment

Abstract

Similar works

Full text

Available Versions

Repository@USM