Dynamic modeling of solid oxide fuel cell and engine hybrid system for distributed power generation

Dynamic modeling of solid oxide fuel cell and engine hybrid system for distributed power generation

Applied Energy xxx (2017) xxx–xxx Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Dynam...

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Applied Energy xxx (2017) xxx–xxx

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Dynamic modeling of solid oxide fuel cell and engine hybrid system for distributed power generation Sanggyu Kang ⇑, Kook-Young Ahn Korea Institute of Machinery and Materials, Daejeon 34103, Republic of Korea

h i g h l i g h t s  Development of a SOFC-Engine hybrid system dynamic model.  Integrating the component models of SOFC, reformer, heat exchanger, engine, blower.  Investigating the dynamic behavior of the hybrid system during transients.

a r t i c l e

i n f o

Article history: Received 11 June 2016 Received in revised form 14 March 2017 Accepted 15 March 2017 Available online xxxx Keywords: Hybrid system Solid oxide fuel cell Dynamic modeling Engine Optimal control strategy

a b s t r a c t Novel hybrid system composed of solid oxide fuel cell (SOFC) and engine has been presented by our previous study. The fuel contents remained in the anode tail gas from the SOFC is reutilized in the engine to improve the system electrical efficiency. Our previous research has confirmed the electrical efficiency of the SOFC-engine hybrid system can be enhanced by about 7.8% compared to the SOFC stand-alone system. Although the hybrid system has higher electrical efficiency than the stand-alone system, higher elaboration for the system operation should be necessary due to higher degree of system complication. The objective of the present study is to develop the dynamic modeling of the SOFC-engine hybrid system. The component dynamic modeling of SOFC, engine, external reformer, air blower, and heat exchanger are developed and integrated into a system using Matlab-SimulinkÒ. Component models of SOFC, external reformer, and engine have been verified by comparison with the experimental data. The dynamic behavior of the hybrid system during transients is investigated. Since the time scale for the engine operation is much shorter than that of the SOFC stack, the power generated by the engine is mainly dependent on the characteristics variation of the anode tail gas. Consequently, the overshoot behavior is appeared in the engine power generation during increase of the demand SOFC power. This model is useful to develop the optimal control strategy for the SOFC-engine hybrid system. Ó 2017 Published by Elsevier Ltd.

1. Introduction High temperature fuel cell system has been regarded as a promising power source for the stationary application due to high fuel flexibility, high efficiency, low emission, and high capability for combined heat and power (CHP) [1,2]. Our previous researches have presented the solid oxide fuel cell (SOFC)-homogeneous charge compression ignition (HCCI) engine hybrid system [3]. While SOFC stand-alone system uses the anode tail gas as a fuel for the catalytic combustor to supply the heat for the external reforming reaction, presented hybrid system uses that as a fuel for the engine to generate the additional electrical power. The SOFC-engine hybrid system has the 7.8% and 0.9% enhancement ⇑ Corresponding author. E-mail address: [email protected] (S. Kang).

of the system electrical efficiency compared to the SOFC standalone system and SOFC-micro gas turbine (MGT) system, respectively. And the SOFC-engine hybrid system achieved respective 12.9% and 7.6% LCOE reduction by comparing the SOFC standalone system and SOFC-MGT hybrid system. Many researchers have been trying to develop the SOFC hybrid system to increase the overall system electrical efficiency. The most common SOFC hybrid system is the SOFC-GT hybrid system [4–7]. The SOFC-GT hybrid system could be designed as several configurations by varying the design parameters of temperature, pressure, fuel type, reforming type, and steam supply [8]. The pressurized SOFC-GT hybrid system is the most common SOFC-GT hybrid system [4,6,9,10]. The conventional pressurized Brayton cycle can be employed for the SOFC-GT hybrid system by replacing the combustor with a SOFC stack [4–6,11]. The air entering the SOFC is heated by system exhaust gas by flowing through the

http://dx.doi.org/10.1016/j.apenergy.2017.03.077 0306-2619/Ó 2017 Published by Elsevier Ltd.

Please cite this article in press as: Kang S, Ahn K-Y. Dynamic modeling of solid oxide fuel cell and engine hybrid system for distributed power generation. Appl Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.03.077

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Nomenclature A * B C CP C *V C D *H D DE F f DG h

DH io i iL kb Ke K k M N *

N N_ n P Q_ R

r_ rp * _ R Re Sh T t V — V _ W * X

active area [m2] mass transport coefficient [m s1] specific heat capacity of solid [kJ kg1 K1] constant pressure gas specific heat capacity [kJ kg1 K1] constant volume gas specific heat capacity [kJ kg1 K1] molar concentration [kmol m3] hydraulic diameter [m] diffusion coefficient [m2 s1] activation energy [kJ kmol1] Faraday’s constant [96,485 Cmol1] friction factor [–] Gibbs energy [kJ kmol1] enthalpy [kJ kmol1], or heat transfer coefficient [kW m1 K1] formation enthalpy [kJ kmol1] exchange current density [A m2] current [A] limiting current density [A m2] Boltzmann’s constant equilibrium constant of reaction [bar2] adsorption constant kinetic rate constant [kmol kg1 h1] molecular Weight [kg kmol1] molar capacity, or total number of moles [kmol], or number of fuel cells [–] species molar capacity [kmol] molar flow rate [kmol s1] electron number [–] pressure [kPa] heat transfer rate [kW] external load resistance [ohm], or Universal gas constant [8.3145 kJ kmol1 K1] reaction rates [kmol s1] pore radius [m] reaction rate [kmol s1] Reynolds number [–] Sherwood number [–] temperature [K] time [s], or thickness [m] voltage [V], or velocity [m s1] volume [m3] generated Work species mole fraction [–]

recuperator [5]. Ambient air is compressed up to the SOFC operating pressure. McLarty et al. investigated the steady-state and dynamic performance of the pressurized SOFC and GT hybrid system [12,13]. In the steady-state and dynamic study, they compared the system efficiency among various fuel cell hybrid system and investigated the dynamic performance with proposed system control logic, respectively. Ferrari presented the novel advanced control strategy consists of the feed-forward and proportional integral techniques for the SOFC hybrid system [14]. Since the SOFC-GT hybrid system used the natural gas as a fuel, the hydrocarbon fuel should be reformed to be used for electrochemical reaction. The hybrid systems with the internal reforming configuration can decrease the system cost and complexity because no external fuel processor is necessary [4–6,15–19]. In case of the direct internal reforming (DIR), the natural gas is reformed in the anode electrode of the SOFC. DIR has a system simplicity and low capital cost. However, the carbon deposition and the temperature gradient through the cell could be increased [4–6,20]. Indirect internal reforming [IIR] separated the reforming channel and the

Greek letters tuning coefficient of activation overpotential [–] electrode mean porosity [–] U diffusion flux through electrode [kmol s1] Wref refoming reaction rates [kmol s1] s tortuosity [–], or timing, or torque [Nm] r mean characteristic length [XX] X dimensionless diffusion collision [–] q density [kg m3] g efficiency [–] k air stoichiometric ratio [–] x rotational speed [rad s1]

a e

Subscripts A anode act activation b burned C cathode c cylinder, or isentropic CO carbon monoxide carbon monoxide CO2 cell fuel cell con concentration eff effective elec anode anode electrode elec cathode cathode electrode f fuel hr heat release rate H2 hydrogen ign ignition in in to control volume L limiting LHV low heating value local local section Nernst Nernst 0 standard condition O2 oxygen ohm ohmic out out of control volume p pore ref reference condition, or reforming reaction s solid phase tr transfer

anode electrode to mitigate the issues of the DIR configuration. However, IIR configuration has a higher system complexity and capital costs [21,22]. In order to attain the internal reforming reaction, adequate amount of steam should be supplied [21–23]. The steam could be generated by the heat recovery steam generator (HRSG) driven by system exhaust gas [11,24,25]. The steam could also be supplied by recirculating the anode tail gas from the SOFC stack [23]. Even though the advantage of the internal reforming, certain systems equipped the external reformer for converting more complex types of fuels (biogas, syngas, and liquids) [4,6,26,27]. Yang et al. compared the internally and externally SOFC-GT hybrid system [28]. They concluded that the external reforming configuration has a penalty such as a more complex thermal management, which may require fuel addition to achieve the desire SOFC and turbine inlet temperatures. Other researchers studied on the integration of the SOFC, GT, and Steam Turbine (ST) in single combined cycle [29]. Arsalis presented a numerical study on the SOFC-GT-steam turbine (ST) hybrid system ranging from 1.5 to 10 MWe [29]. They concluded that the hybrid SOFC-GT-ST con-

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figuration could have the ultra high efficiency. While common Rankine cycles are based on water as working fluids, when the operating temperature of the system is low, organic fluid could be utilized for the working fluids [30]. Ebrahimi presented the SOFC hybrid system combined with the GT and organic Rankine cycle (ORC) and performed the numerical study by varying the operating parameters [31]. Even though the pressurized SOFC-GT cycle has higher efficiency, some researchers studied on the ambient pressure SOFC-GT hybrid system. In the atmospheric SOFC-GT hybrid system, the SOFC system is indirectly coupled with the Brayton cycles, which results in more simplicity compared to the pressurized SOFC-GT cycle. Park and Kim compared the pressurized and atmospheric SOFC-GT cycles [32]. The ambient SOFC-GT system has 5–10% lower efficiency than that of the pressurized SOFC-GT system. As listed above, most previous researches on the SOFC hybrid system are based on the SOFC-GT hybrid system. However, our group has been interested on the combination of SOFC system with other power application instead of GT. There is few researcher who have studied on the SOFC-engine hybrid system for distributed power application. Our group has previously published the papers on the SOFC-engine hybrid system and MCFC-engine hybrid system [5,33,34]. The system electrical efficiency and levelized cost of electricity (LCOE) of the SOFC-engine hybrid system has been compared with those of the SOFC standalone system and SOFC-GT hybrid system [3]. However, our previous researches are only focused on the steady-state performance and system optimization of the SOFC-engine hybrid system. In order to use the system as a distributed power application, the system dynamic analysis should be conducted. The objective of the work is to develop the dynamic modeling of the SOFC-engine hybrid system. To investigate the dynamic behavior of the hybrid system, which was developed by incorporating the quasi three-dimensional dynamic model of the SOFC, twodimensional dynamic model of the external reformer and heat exchanger, lumped dynamic model of engine and air blower using Ò Matlab-Simulink . The SOFC is discretized into seven and five control volumes along the cross-sectional direction to resolve the energy and mass conservation, respectively. The SOFC is also discretized into nine control volumes along the anode channel to investigate the SOFC characteristics distribution. The external reformer is two-dimensionally discretized into axial and radial direction to capture the reformer characteristics distribution and to resolve the heat transfer and the reforming reaction, respectively. The heat exchager is two-dimensionally discretized into stream-wise and cross-sectional direction to capture the distribution of heat exchanger characteristics and to calculate the heat transfer between hot fluid and cold fluid, respectively. Lumped dynamic engine model is developed using the Arrhenius knock integral approach to predict the auto-ignition timing [35]. Lumped dynamic air blower model is developed considering the inertia of the motor and blower to predict the dynamic behavior of air blower. Each component models of SOFC, engine, and external reformer have been verified by comparison with the experimental data. The dynamic behaviors and correlations of each component in the SOFC-engine hybrid system were investigated during increase of the demand SOFC power. The present model can be utilized to develop the optimal control strategy of the SOFC-engine hybrid system during various transients.

2. Modeling description 2.1. SOFC-engine hybrid system In order to capture the dynamic behavior among the components in the SOFC-engine hybrid system, the hybrid system model

3

composed of the SOFC stack, engine, external reformer, heat exchanger, and air blower has been developed using MatlabSimulinkÒ. Fig. 1 shows the schematic diagram of the proposed SOFC-engine hybrid system. The natural gas (NG) mainly composed of methane is partially reformed by flowing through the external reformer. The partial reformed gas enters the SOFC stack to generate the electrical power. Since the anode tail gas includes the high amount of steam, which flows into the condenser to remove the water contents to increase the fuel concentration. Then, the dehydrated anode tail gas enters the engine to generate additional electrical power. Engine exhaust gas provides the heat for the methane steam reforming (MSR) reaction in the external reformer. Then, the reformer exhaust gas flows into the heat exchanger to supply the heat for the generation of the steam required for the MSR reaction. On the cathode side, ambient air enters the heat exchanger to be heated by the cathode exhaust air of the SOFC stack. Fig. 2 presents the simulation flow diagram for the SOFC-engine hybrid system model. The heat exchanger is not described in the simulation chart. When the demand power for the SOFC system is determined, the initial current of the SOFC stack is determined. The adequate fuel and air flow rate are proportional to the SOFC stack current. The system model doesn’t consider the fuel supply system. Thus, the target value of the fuel is assumed to be supplied to the system. When the target value of the air flow rate is calculated, the air blower manipulate the blower rpm to blow the target value of the air flow rate. After the characteristics of the fuel and air inlet such as flow rate, species mole fraction, and temperature are determined, the SOFC stack model determines the internal reforming reaction rate, heat generation rate, net voltage, work generation, and the anode and cathode exhaust characteristics including the flow rate, species mole fraction, and temperature. The PI controller implemented in the SOFC system model manipulates the input current to generate the power to meet the demand SOFC power. When the anode tail gas characteristics of flow rate, species mole fraction, and temperature are determined, the amount of air supplying to the engine is calculated. The combustion timing, work generation, maximum temperature and pressure, and the characteristics of the exhaust gas such as flow rate, species mole fraction, and temperature are determined in the engine model. Then, the characteristics of the fuel at the reformer exhaust are determined by the sensible enthalpy of the engine exhaust gas. 2.1.1. Assumptions The followings are the major assumptions made for the SOFCengine hybrid system: 1. All electrodes are good conductors for which an equipotential electrode surface is assumed [36]. 2. The power generation by the SOFC stack is determined by multiplying the cell number with the unit cell power. The error could be introduced by ignoring the interconnection voltage loss among each cells. 3. Each control volume has the single value of the temperature, species mole fraction, and pressure. 4. All gases are assumed to be ideal gases [37]. 5. The gas flow in channels is assumed to be a fully developed laminar flow [37]. 6. In the SOFC model, the parallel diffusion flux in the electrode and electrolyte are ignored [37]. 7. In the SOFC model, the electrochemical reaction is quasisteady due to rapid electrochemistry (occurring at time scales on the order of 103 s) [38]. Since the electrochemical reaction may not be fast in certain section of the cell, the model could introduce the error into SOFC performance during transients.

Please cite this article in press as: Kang S, Ahn K-Y. Dynamic modeling of solid oxide fuel cell and engine hybrid system for distributed power generation. Appl Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.03.077

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Fig. 1. Schematic diagram of the SOFC-engine hybrid system model.

Fig. 2. Simulation flowchart of the SOFC-engine hybrid system model.

8. The adequate fuel and air flow rate are proportional to the stack current [39]. The target value of the fuel flow rate is assumed to be supplied to the system. By ignoring the dynamics of the fuel supply, the model could introduce the error into system dynamic behavior during transients. 9. In the MSR model, the gas is uniformly distributed along the radial direction. 10. The steam to carbon ratio is assumed to be kept to 3.0. By ignoring the dynamics of the steam generation and supply, the error in the external reforming reaction could be introduced. 11. In the MSR and engine model, heat losses to the surroundings is neglected due to perfect insulation. The model could cause the error in resolving the energy balance in the MSR by ignoring the heat losses.

12. In the HCCI engine model, throttle valve is adequately controlled to meet the demand air feeding rate to the engine [33,34]. The model could introduce the error into engine dynamic behavior during transients. 13. In the HCCI engine model, the intake temperature is assumed to be maintained a constant by adequately controlling the air inlet temperature [33,34]. The model could introduce the error into engine dynamic behavior during transients. 14. In the HCCI engine model, the intake pressure is assumed to be adequately controlled to feed the anode tail gas by manipulating the fuel valve [33,34]. The model could introduce the error into engine dynamic behavior during transients.

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2.2. SOFC stack A quasi three-dimensional dynamic model of SOFC stack has been developed and integrated into a system model to capture the SOFC performance. Table 1 presents the specifications for the SOFC stack. The SOFC is discretized into five control volumes such as anode channel, anode electrode, electrolyte, cathode electrode, and cathode channel along the cross-sectional direction to resolve the mass conservation, which is shown in Fig. 3(a). To resolve the energy conservation, the SOFC is discretized into seven control volumes of interconnector, anode channel, anode electrode, electrolyte, cathode electrode, cathode channel, and interconnector along the cross-sectional direction as shown in Fig. 3(b). As the partial reformed gas from the anode channel diffuses through the anode electrode, which is reformed, then oxidized at the TPB (triple phase boundary). The internal reforming reaction rates are determined at the local temperature of the anode electrode. When the temperature is increased higher than 700 °C, most of the methane could be reformed in the anode electrode [23]. Diffusion fluxes of the oxygen ion to the anode electrode control volume is determined for the boundary between the electrolyte and the electrode control volume. The heat generated at TPB is transferred to the electrode, the gas channel, and the solid plate by conduction or convection. Some portion of the heat is used for the internal reforming reaction through the anode electrode. The SOFC model is discretized into nine control volumes in the stream-wise direction to resolve the heat transfer between each local section, shown in Fig. 4. The natural convection at the outside of solid plate and the conduction between each local solid plate and are considered. The radiative heat transfer has been neglected in this simulation. The model could overestimate the temperature gradient through the stack [40]. 2.2.1. Energy conservation The solid plate temperature is determined by the dynamic energy conservation equation: —

qV C

dT X _ Q in ¼ dt

ð1Þ

where Q_ in is heat transfer to the control volume. The temperature out of the gas channel is determined:

NC v

X X dT X _ N_ out hout þ Q_ in Nin hin  ¼ dt

ð2Þ

where N_ in hin and N_ out hout represent the enthalpy flux into or out of the control volume, respectively. Temperature of electrolyte and electrode is determined by combined dynamic energy conservation of the solid plate and gas. Heat generation is calculated by the irreversibility in the electrochemical reactions:

X



ðq V CÞs

X dT X _ ¼ Q in þ Q_ ref þ N_ in hin  N_ out hout dt i V i  þ DH  nF 1000

ð3Þ

where Q_ ref , DH, i, and V are the internal reforming reaction energy, water formation enthalpy, current, and voltage, respectively. Amount of heat produced in the fuel cell is determined by subtracting the formation enthalpy of H2O and CO2 with the generated electric work:

DH 

i V i  nF 1000

ð4Þ

2.2.2. Species conservation The species mole flow rate out of the channel is calculated by the dynamic species conservation equation: *

X * * dðNX Þ ¼ N_ in X in  N_ out X out þ U dt

ð5Þ

*

where U is the diffusion flux from the electrode. The species concentration at the electrode is determined: *

X* X * _ dN Uþ Wref þ RH2 O or CO2 ¼ dt

ð6Þ

* _ where Wref and ðR Þ are the local rates of the internal reforming reaction and electrochemical reactions, respectively.

2.2.3. Species diffusion and reactions The electrochemical reaction rates of H2 and CO oxidation occurred in the SOFC is proportional to the current by Faraday’s law:

R_ H2 or CO ¼ 2R_ O2 ¼ R_ H2 O or CO2 ¼

i nF

ð7Þ *

The species transport coefficient (B ) in the channel is determined: Table 1 The SOFC specifications.

*

Sh  Deff B¼ DH

*

Parameter

Unit

Value

Cell number Cell active area Anode electrode depth (z) Electrolyte thickness (z) Cathode electrode depth (z) Conductivity of anode plate Conductivity of cathode plate Conductivity of anode electrode Conductivity of cathode electrode Conductivity of electrolyte Density of anode plate Density of cathode plate Density of anode electrode Density of cathode plate Density of electrolyte Specific heat capacity of anode plate Specific heat capacity of cathode plate Specific heat capacity of anode electrode Specific heat capacity of cathode electrode Specific heat capacity of electrolyte

– cm2 lm lm lm kW/m K kW/m K kW/m K kW/m K kW/m K kg/m3 kg/m3 kg/m3 kg/m3 kg/m3 kJ/kg K kJ/kg K kJ/kg K kJ/kg K kJ/kg K

160 144 600 10 40 0.02 0.02 0.011 0.006 0.0027 3030 3030 3310 3030 5160 0.55 0.55 0.45 0.43 0.47

ð8Þ

*

where Sh, Deff , and DH are the Sherwood number, effective diffusivity, and the hydraulic diameter, respectively. The effective diffusivity in gas mixture is determined [41]:

0P

1 *

eff

Di;m

Xj

rffiffiffiffiffiffiffiffiffi

1

s B j–i *Dij 3 pMi C ¼ @ þ A e 1  X i 2rp 8RT

* 0:0026T 1:5 Dij ¼ qffiffiffiffiffiffiffiffiffiffiffi  2Mi Mj ri þrj 2 p Mi þM XD 2 j

ð9Þ

ð10Þ

where s, e, and r p is the tortuosity, porosity, and the pore radius of the electrode, respectively. r, kb , and XD is the mean value of species characteristic length, Boltzmann’s constant, and dimensionless diffusion collision, respectively.

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Fig. 3. Control volumes for (a) Species and (b) Energy conservation of SOFC into flow perpendicular direction (not drawn to scale).

r3 ¼

k3

  P 4H P CO P CH4 P2H2 O  2K e3 2

P3:5 H2

DEN2

DEN ¼

Fig. 4. Schematic diagram of the SOFC discretization (not drawn to scale).

2.2.4. Pressure loss The friction factor and head loss were calculated [42]:

Re 6 2100 f ¼

64 Re

ð11Þ 2

3000 6 Re 6 5  106

f ¼ ð0:79 ln Re  1:64Þ

ð12Þ

2.2.5. Internal reforming reaction The SOFC model resolves the direct internal reforming reaction. Main reaction for the internal reforming reaction considered in the model is MSR reaction, WGS reaction, and DSR reaction as follows.

DH298 ¼ þ2:06e5 kJ=kmol

CH4 þ H2 O ! CO þ 3H2 CO þ H2 O ! CO2 þ H2

DH298 ¼ 4:1e4 kJ=kmol

CH4 þ 2H2 O ! CO2 þ 4H2

DH298 ¼ 1:65e5 kJ=kmol

ð13Þ

r1 ¼

k1 P2:5 H2

DEN 2 

r2 ¼

k2 P H2

PCO PH2 O 

PH P CO

DEN 2

2

K e2

1 þ K CO PCO þ K H2 PH2 þ K CH4 PCH4 þ K H2 O PH2 O P H2

ð15Þ

ð16Þ

2.2.6. Electrochemical model Each net local voltage is determined by subtracting the local value of activation, ohmic, and concentration overvoltage from the local Nernst voltage:

V local ¼ V Nernst; H2

or CO

 V act; H2

or CO

 V ohm  V con

 ð17Þ

ð20Þ

Local Nernst voltage is determined based on the species mole fractions at the electrode and the temperature of electrolyte. Since the SOFC is using the partial reformed gas mainly composed of H2 and CO, the SOFC model should resolve each electrochemical reaction to predict the performance accurately, as follows:

0

V Nernst;H2

or CO

2 31 1 aH2 or CO  a2O2 DGðTÞH2 or CO R  T 5A ln 4 ¼ @ þ nF nF aH2 O or CO2

elec

ð21Þ The rate of CO oxidation is 2–3 times less than that of H2 oxidation by Matsuzaki and Yasuda [45]. The activation overpotentials for H2 and CO oxidation are determined by the Butler-Volmer equation based on the anode electrolyte temperature [39]:

V act ¼

RT elec

anode

aA F

þ

2

ð19Þ

where ki , K ei , and K i is the kinetic rate constant and equilibrium constant of reaction i, and adsorption constant of species i, respectively [44]. The same values for the equilibrium constant, kinetic constant, and adsorption constant have been used with those of Lee et al. [44].

ð14Þ

Corresponding rates for reactions (13)–(15) are determined by the Xu and Froment as follows [43]:

  P 3H PCO PCH4 PH2 O  K2e1

ð18Þ

RT elec

cathode

aC F

1



sinh

i0;H2 

1

sinh



i or CO ðTÞ

i



2i0;O2 ðTÞ

ð22Þ

where a and io are the charge transfer coefficient and exchange current density, respectively. The ohmic overvoltage is determined

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based on the electrolyte temperature and membrane thickness [39]:

V ohm ¼ i

t MEA   ASOFC  exp DRTGact

ð23Þ

The model is operated at relative low operating current density in the system simulation. This means that the concentration overvoltage affected by the limiting current density is not a dominant factor to determine the SOFC performance. Thus, we set the limiting current density as a constant in this study. The concentration overvoltage is calculated [39]:

V con ¼

    RT 1 iL ln 1þ nF ac iL  i

X

ilocal  R

2.3.1. Cylinder dynamics The species concentration in the cylinder is determined by the dynamic species conservation: *

ð24Þ

Since the unit cell has same potential over the whole cell area, according to assumption 1, the variation of the internal resistance in each local section affects the local current density variation. That is, the local current density is strongly dependent on the local value of species mole fraction, temperature, and pressure. When certain value of current is demanded to the fuel cell as an input load, the external resistance is manipulated by the feedback loop to make the total current generated from the fuel cell to be the same value with the input current. When the iteration is completed, the internal resistance and current density of each local section is defined. Finally, the cell voltage is calculated by multiplying the total current of the cell and the external resistance:

V local ¼ V cell ¼

characteristics of pressure and temperature should be calculated 75 times in 1 s, because the one cycle of engine is including the intake, compression, combustion, expansion, and exhaust process. The engine characteristics of temperature, pressure, and species mole fraction are obtained by the lumped engine dynamic model at various operating conditions, which is utilized for the mapbased engine model.

ð25Þ

2.3. HCCI engine Since the anode tail gas of the SOFC is fuel lean condition, HCCI engine is selected for the combustion of the anode tail gas instead of the conventional engine of spark ignition and compression ignition [3,33,34]. The lumped dynamic model of HCCI engine is developed in this study. In this study, the engine model doesn’t consider the dynamics for the intake and exhaust of the gas. And the dynamics for the throttle valve should be further considered to predict the engine dynamics accurately. Theoretically, the intake temperature and intake pressure affect the auto ignition timing for the HCCI engine [33,34,46]. As the intake temperature increased, the auto ignition is occurred earlier in the HCCI engine because the gas temperature reaches the auto ignition temperature earlier. When the intake pressure is increased, the auto ignition temperature is decreased. In this model, in order to keep the ignition timing constant, the intake temperature is assumed to be maintained a constant. And the throttle valve is assumed to be controlled to maintain the target value of the equivalence ratio. In this simulation, the engine operating rpm is 1800. This means that the time scale for the engine reaction is much shorter than 1/1800 s. However, the temperature and pressure variation of the anode tail gas in this simulation is much slower compared to the engine operation. Thus, the engine could be reached steady state at every cycle during the load change used in this simulation. Theoretically, the feeding rate of the gas to the engine is proportional to the intake pressure [33,34,46]. In this simulation, the molar flow rate of the anode tail gas is increased up to twice during transients. This means that the intake pressure should be increased up to twice. Since there is no booster between SOFC stack and engine, the intake pressure of the anode tail gas could be controlled in fuel valve. In this study, the map-based engine model has been used to the hybrid system model to predict the work generation and the characteristics of the engine exhaust gas such as flow rate, species mole fraction, and temperature for the computational time. That is, when the engine is operated at 1800 rpm, the engine

* * dðN X Þ ¼ N_ in X in  N_ out X out þ R_ dt

ð26Þ

The temperature in the cylinder is calculated by the dynamic energy conservation:

X dðmc uc Þ _ cþ _ j hj ¼ Q_ c þ Q_ tr  W m dt

ð27Þ

where mc , uc , and Q_ c are the species molar concentration, the internal energy, and the heat generation rate in the cylinder, respec_ c are the rate for the heat transfer and the work tively. Q_ tr and W generation, respectively. 2.3.2. Combustion model 2.3.2.1. Ignition model for syngas. Modified Knock-integralapproach was used to predict the auto-ignition timing of a HCCI engine [35]. When the integral of the reciprocal of the ignition delay time reaches 1 ms, auto-ignition occurs:

Z

SOC

TDC

1

sign

¼ 0:001

ð28Þ

where TDC and sign is the top dead center and ignition delay time (IDT), respectively. The ignition delay time for the syngas composed of H2 and CO is determined by Walton et al. [47]:

sign ¼ 3:7e  6P0:5 /0:4 X O5:4 exp 2

  52083 RT

ð29Þ

where /, P, T, and X O2 are the equivalence ratio, cylinder pressure, cylinder temperature, and oxygen mole fraction, respectively. 2.3.2.2. Combustion heat release. The heat release during the combustion process is determined by a single zone combustion model:

Q_ hr ¼ Q LHV mf x_ b

ð30Þ

xb is the burned mass fraction determined by an exponential Wiebe function [46]:

"

xb ¼ 1  exp aw

x_ b ¼

 n þ1 # t  tsoc w Dt

"  n  n þ1 # @xb aw ðnw þ 1Þ t  tsoc w t  t soc w exp aw ¼ @t Dt Dt Dt

ð31Þ

ð32Þ

where Dt is combustion duration [48]. aw and nw are empirical parameters [46]. 2.3.3. Heat transfer The heat transfer coefficient is determined by Woschni’s correlation [46]:

hc ¼ CBg1 ðP c Þg wg ðT c Þ0:751:62g

ð33Þ

where B and w are cylinder bore length and gas velocity, respectively. C and g are empirical parameters [46].

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2.4. External reformer

2.6. Air blower

The external reformer used in this study is shell-and-tube type. Engine exhaust gas flows through the bundle of tubes and transfers heat to the natural gas flowing through the shell. The specifications of the reformer used in this study are presented in Table 2. The reformer model is two-dimensionally discretized in the axial and radial directions to solve the reformer characteristics. The reformer is discretized into three control volumes in the radial direction: (1) shell, (2) tube wall, and (3) tube, which are shown in Fig. 5(a). When the hot engine exhaust gas flows through the inside of the tube control volumes, the heat is first transferred to the tube wall, which is then transferred to the shell control volumes by convection, which is finally utilized for the MSR reaction. In this fashion, the MSR reached the equilibrium, and temperature and species concentration of the reforming gas is determined. The reformer is also discretized into five control volumes in the flow parallel direction to capture the distributions of the dynamic characteristics, which is shown in Fig. 5(b). Dominant reactions occurred in the external reformer are same with those of the internal reforming reaction in the SOFC, Eqs. (13)–(19).

The air flow rate to be used for electrochemical reaction in the SOFC is proportional to the input load current [39]:

2.4.1. Species conservation The species mole flow rate out of the reforming channel is determined: *

X * * dðNX Þ Wref ¼ N_ in X in  N_ out X out þ dt

ð34Þ

_ air ¼ m

smotor ¼ gmotor

NC V

dT ¼ dt

N_ in hin 

X

N_ out hout þ

X

Q_ tr

ð35Þ

jt Rmotor

ðV motor  jv xblower Þ

ð37Þ

where gblower and xblower is the motor mechanical efficiency and blower speed, respectively. jt , Rmotor , and jv are empirical parameters. The torque required to drive the blower is calculated:

sblower ¼

_ air DT Cpm

xblower

ð38Þ

The blower dynamics is determined by considering the inertia of the motor and blower:

J blower

dxblower ¼ ðsmotor  sblower Þ dt

ð39Þ

where Jblower is the blower inertia. The temperature at the out-of-air blower is determined:

T out

X

ð36Þ

After the target value of the air flow rate and pressure ratio are calculated, the air blower rotational speed has been determined based on the map of rpm vs. performance. Then, the input voltage was fed into the air blower to drive the blower motor. The blower motor torque is calculated:

where Wref is the methane steam reforming reaction rate. 2.4.2. Energy conservation The temperature out of the reforming channel is determined:

icell  Ncell  kair 4  F  X O2

" # c1 Pout c ¼ T in þ 1 gc Pout T in

ð40Þ

where gc and c are the isentropic efficiency and the specific heat ratio, respectively. 3. Simulation results and discussion

where Q_ tr is the heat transfer rate to the control volume.

3.1. Model verification 2.5. Heat exchanger The heat exchangers used in the study is planar type. The heat exchangers specifications are presented in Table 3. The heat exchanger is two-dimensionally discretized in the parallel and perpendicular direction of the gas flow to solve for the local characteristics of the heat exchanger. The heat exchanger control volumes along the flow perpendicular direction are the (1) hot channel, (2) wall, and (3) cold channel, shown in Fig. 6(a). In order to investigate the distribution of the dynamic characteristics of the heat exchanger, the heat exchanger is also discretized into five control volumes along the gas flow direction, presented in Fig. 6(b). To determine the temperature through the heat exchanger, dynamic energy conservation Eqs. (1) and (2) are used. The pressure drop along the gas flow direction in the gas channel is determined by Eqs. (11) and (12).

Table 2 The specifications of the external reformer. Parameter

Unit

Value

Tube number Tube diameter Tube thickness Tube volume Reformer inner diameter Reformer wall thickness Reformer volume Reformer length

– mm mm L mm mm L mm

21 25.4 2 0.47 129 5.5 3.91 377

Since no experimental research on the SOFC-engine hybrid system has been performed previously, the proposed system model cannot be validated at the system level. Thus, each component models of SOFC stack, external reformer, and HCCI engine have been verified by comparison with the experimental data. The experiments for the SOFC stack, HCCI engine, and external reformer are performed by the MICO, Seoul National University, and our institute, respectively, involved in the project associated with this study. Tables 1–3 shows the respective specifications of the SOFC, external reformer, and HCCI engine, which are the references of each component model. In order to verify the component model of SOFC, external reformer, and engine, parameters in Eqs. (22), (23), and (31) have been selected and tuned, presented in Table 4. The current-voltage polarization curve of SOFC stack was compared between the experiment and the simulation, shown in Fig. 7(a). The hydrogen and air flow rates are 3.4 and 14 standard liters per minute (SLPM), respectively. Both the inlet temperature of the anode and cathode is approximately 750 °C. The simulation data are in good agreement with the experiments, within an error of ±0.6 V. Fig. 7(b) and (c) present an external reformer comparison of the temperature out and species mole fraction out from both the experiments and simulations, respectively. The inlet temperature of hot gas and cold gas are 680 °C and 307 °C, respectively. The cold gas is composed of methane and steam. The S/C ratio is 3.0. Air is used as a hot gas. The simulation data are in good agreement with the experiments, within an error of 10 °C and 2%, respectively. Fig. 7-(d) presents an engine comparison of the temperature and

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Fig. 5. Schematic diagram of the external reformer discretization.

Table 3 The HCCI engine specifications.

Table 4 The tuning parameters for the model validation.

Parameter

Unit

Value

Model

Parameter

Value

Bore Stroke Connecting rod length Compression ratio Displacement

mm mm mm – cc

88 64 112 8.2 389

SOFC SOFC SOFC SOFC Engine Engine Engine Engine

aA aB ac

0.45 0.45 0.5 6.908 1.575 0.0016 3.26 0.8

pressure variation in the cylinder from both the experiments and the simulations. The inlet temperature of the fuel and air mixture is 675 K. The equivalence ratio is 0.7, 0.8, and 0.9. The simulation results of peak pressure are in good agreement with the experimental data, with an error of ± 0.2 bar.

3.2. Simulation results To investigate the dynamic behavior of the SOFC-engine hybrid system, the system model is simulated at the ramp increase of demand SOFC power. Table 5 shows the operating conditions. The inlet temperature of both of the fuel and air into the system is 25 °C. The target value of the air utilization for the SOFC stack is 25%. During transients, the air blower is controlled to meet the target value of the air utilization. The dynamic mode of the air blower in this system model can capture the dynamic behavior

aw nw Dt C

g

of the air supply during transients. Even though, the fuel valve has the dynamics during transients, the model doesn’t consider the fuel valve dynamics because the fuel flow rate is than air flow rate. The fuel utilization is assumed to be maintained as 70% during transients, in this simulation. The target value of the external reforming ratio is 50%. The S/C ratio for the MSR reaction is 3.0. Equivalence ratio for the engine operation is 1.0. Fig. 8(a) shows the variation of the demand SOFC power, which is increased from 2.40 kW to 4.80 kW at from 50,000 s until 50,240 s. As the demand power is increased, the power generated by the SOFC stack is gradually increased to 4.82 kW from 2.40 kW until 51,496 s and then decreased slightly and reached another state of 4.80 kW at 66,635 s. Aforementioned, since the time scale for the engine operation is much shorter than that of the SOFC stack, the power

Fig. 6. Schematic diagram of the heat exchanger discretization.

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Fig. 7. Comparison of (a) current-voltage polarization curve of SOFC, (b) Temperature out of external reformer, (c) Species mole fraction out of external reformer, and (d) Cylinder pressure and temperature variation in HCCI engine during one cycle between experiment and simulation.

generated by the engine is mainly dependent on the characteristics of the anode tail gas. During increase of the demand input power of SOFC, power generated by the engine is increased from 0.418 kW to 0.912 kW until 51,069 s and then decreased and reached 0.8724 kW at 66,635 s. Fig. 8(b) presents the variation of the input current and output voltage of the SOFC stack. The input current is instantly increased to 39.398 A from 18.048 A until 51,094 s and then decreased and reached 37.683 A at 68,635 s. On the other hand, the output voltage is instantly decreased to 120.63 V from 132.98 V until 50,640 s and then increased and reached to 127.381 V at 72,635 s. Since the SOFC power is calculated by multiplying the current and voltage, the SOFC input current is determined by SOFC output voltage. That is, the overshoot behavior appeared in the current is resulted from the undershoot behavior of the voltage variation. Aforementioned, this model considers both of the H2 and CO oxidation reaction. The respective current from the H2 and CO oxidation reaction were captured, which is shown in Fig. 8(c). Even though the exchange current density of the CO is 3.5 times lower than that of H2, the current from the CO oxidation reaction is much lower than than that from the H2 oxidation reaction. This is because the reaction rates of the WGS reaction is much higher than that of the electrochemical reaction of the H2 and CO. Most of the CO is converted into the CO2 by the WGS reaction. The net voltage of SOFC stack is obtained by subtracting the overpotentials of activation, Ohmic, and concentration from the Nernst voltage. The undershoot behavior of the SOFC output voltage in Fig. 7(b) is caused by the overshoot behavior of the overpotentials of activation and Ohmic, which is shown in Fig. 9(a). Because the input current density for the simulation is relatively low value from 0.123 A/cm2 to 0.262 A/cm2, the concentration overpotential is negligible during whole simulation. The concentration overvoltage is gradually increased from 0.0011 V to 0.0024 V during transients. The magnitude of the activation overpotential is the highest among three overpotentials. The activation overvoltage is instantly increased up to 0.102 V at 50,613 s from 0.057 V then gradually decreased and reached 0.065 V at 68,635 s. Activation overvoltage is highly dependent on the current density and temperature. The temperature increase results in Table 5 The operating parameters for the SOFC-engine hybrid system simulation. Parameter

Unit

Value

Fuel inlet temperature Air inlet temperature Fuel utilization Air utilization External reforming ratio S/C ratio Engine equivalence ratio

°C °C % % % – –

25 25 70 25 50 3.0 1.0

increase of the exchange current density, which could decrease the activation overvoltage. However, the overshoot behavior of the current density made a higher effect than temperature variation on the overshoot behavior of the activation overvoltage during transients. At the same manner, the Ohmic overvoltage is suddenly increased up to 0.059 V at 50,559 s from 0.031 V, then gradually decreased and reached 0.032 V at 64,635 s. Even though the overshoot behavior is appeared in the Ohmic overpotential during transients, the steady-state value after the transients is almost same with that before the transients due to temperature increase. The overshoot behavior of the Ohmic overvoltage is caused by the current density transient behavior. That indicates that the activation overpotential dominantly affects the steady-state value of the SOFC output voltage after the transients. Fig. 9(b) shows the variations of the formation enthalpy, work generation, and heat generation during transients, respectively. The overshoot behavior exists only in the variation of the work generated by the CO oxidation reaction. This means that the overshoot behavior of the SOFC output voltage is mainly caused by the undershoot behavior of the activation overvoltage of the CO oxidation reaction due to its lower value of exchange current density compared to that of H2 oxidation reaction. The internal reforming ratio of the presented hybrid system is 50%. Fig. 10(a) shows the reaction rates variation of the H2 and CO oxidation reaction and the internal reforming reaction of the MSR, WGS, and DSR. Due to the operating temperature of the SOFC is around 700 °C, the MSR reaction rates is the highest among three internal reforming reactions. Because the MSR reaction is strong endothermic reaction, SOFC should supply the thermal energy for the MSR reaction. The amount of heat generated by the oxidation reaction of H2 and CO is high enough to provide the heat required for the internal MSR reaction during whole simulation, which is shown in Fig. 10(b). The heat generation rate after the transient is higher than two times of that value before the transient due to increased amount of overvoltages at high operating current density. Fig. 11 shows the variation of the current density distribution at the steady-state before the transient, at the moment of the highest current, and at the steady-state after the transient. In both steady-states, the current density distribution is similar. That is, highest current density is appeared at the anode inlet section due to high fuel contents, and which is decreased along the anode channel. At the moment of the highest current, the current density distribution became more uniform than other cases. This is because of the increasing rate difference between the fuel flow rate and the electrolyte temperature. At the moment of the highest current, the fuel concentration is the highest due to the highest fuel flow rate. On the other hand, the temperature is lower than that at the steady-state after the transients. Thus, at this moment, the temperature is more significant factor to determine the stack performance. Fig. 12(a) presents the distribution of the reforming

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Fig. 8. Variation of (a) The demand SOFC power and respective power generated by SOFC and HCCI engine, (b) Current and voltage of SOFC, and (c) Respective current from H2 and CO oxidation reaction during increase of the demand SOFC power.

Fig. 9. Variation of (a) Activation, Ohmic, and concentration overpotentials and (b) Formation enthalpy, work, and heat during increase of the demand SOFC power.

Fig. 10. Variation of (a) Internal reforming reaction rates and (b) Heat absorption rate for the internal reforming reactions and heat generation rate during increase of the demand SOFC power.

reaction rate of MSR, WGS, and DSR in the external reformer along the fuel flow direction. In order to attain the stability of the system operation during transient, maintaining the external reforming ratio is crucial. During the current increase, all of the reforming reaction is increased. The DSR reaction rate is negligible compared

to other reforming reaction of MSR and WGS. As expected, the MSR reaction rate is the highest among other reactions. Since the operating temperature of the external reformer is around 550 °C, the WGS reaction rates of the external reformer is higher than that of the internal reforming reaction occurred in the SOFC stack.

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Fig. 11. Variation of current density distribution (a) At the steady-state before the transients, (b) At the moment of maximum current, and (c) At the steady-state after the transients.

Fig. 12. Variation of (a) Reforming reaction rates distribution, (b) Temperature distribution, and (c) Species mole fraction out in the external reformer during increase of the demand SOFC power.

Fig. 13. Variation of temperature distribution in (a) Heat exchanger 1 and (b) Heat exchanger 2 during increase of the demand SOFC power.

Fig. 12(b) shows the temperature distribution of the reformer, wall, and tube in the external reformer along the fuel flow direction. As the fuel flows through the reformer, the fuel absorbs the heat from the engine exhaust gas by convection and the heat is utilized for the reforming reaction. Since the reforming reaction rate is highly dependent upon the temperature, reforming reaction is instantly increased from the fractional distance of 0.6. When the SOFC power is increased, the flow rate of the anode tail gas is increased, and in order to increase the feeding rate of the fuel to the engine, the engine intake pressure should be increased. The increase of

the engine intake pressure increases the cylinder peak pressure and maintains the engine peak temperature. Thus, increase of the anode tail gas flow rate has a negligible effect on the temperature of the engine exhaust gas. Due to small increase of the reformer temperature, the species mole fraction at the reformer out is slightly changed during transients, shown in Fig. 12(c). Fig. 13 shows the variation of temperature distribution in HEX1 and HEX 2, respectively. Aforementioned, in the presented hybrid system model, the air flow rate is determined proportional to the SOFC input current. And air is utilized as a coolant, thus air flow

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rate is dominant factor to determine the SOFC operating temperature. In HEX1, as the demand SOFC power is increased, the temperature of anode tail gas is gradually increased, and the temperature of the partial reformed gas entering the SOFC is gradually increased. At the same manner, the temperature of fresh air is gradually increased by the temperature increase of the cathode exhaust air. The temperature difference of anode and cathode between inlet and outlet is almost maintained about approximately 37 °C and 170 °C, respectively. 4. Conclusions The dynamic model of the SOFC-engine hybrid system has been developed by Matlab-SimulinkÒ. The summary of the work and findings are as follows: 1. The system model consists of a quasi three-dimensional SOFC dynamic model, two-dimensional dynamic model of external reformer and heat exchanger, and lumped dynamic model of air blower and engine. 2. The SOFC is discretized into five and seven control volumes in the through-plane direction to resolve the mass and energy balance, respectively. The SOFC is also discretized into flow parallel direction to capture the SOFC characteristics distribution. In order to predict the combustion timing of the HCCI engine, modified Knock-integral-approach is adopted. After conversion of the engine dynamic model into the map-based model, which is incorporated to the system model for computational time. External reformer and heat exchanger model are twodimensionally discretized into flow perpendicular direction and flow parallel direction to resolve the energy balance and to capture the characteristics distribution, respectively. 3. The SOFC-engine hybrid system model has been simulated to capture the system dynamic behavior during increase of the demand SOFC power. Due to high thermal mass of the SOFC, it took more than one hour for the SOFC temperature to reach another steady-state value. The overshoot behavior of the current density has higher effect than temperature variation on the overshoot behavior of the activation and Ohmic overvoltages during transients. This finally influence on the overshoot behavior of the SOFC power generation. Since the time scale for the engine operation is much shorter than that of the SOFC stack, the engine could be reached steady state at every cycle during the load change used in this simulation. This means that the power generated by the engine is mainly dependent on the characteristics of the anode tail gas. The small overshoot behavior of the engine power generation is caused by the anode tail gas variation during the transients. 4. The present model can provide the basic insight to establish the optimal control strategy of the SOFC-engine hybrid system during various transients.

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