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Dynamic performance of a reformer for molten carbonate fuel cell power-generation systems
FUEL PROCESSING TECHNOLOGY ELSEVIER
Fuel Processing Technology 53 (1997) 99%113
Dynamic performance of a reformer for molten carbonate fuel cell power-generation systems W. He * Department
of’Mechanica1
Engineering
und Marine Del&
Technology,
De@ Unirwsity
of Technology,
2628 CD
Netherlands
Received 14 March 1997; accepted 4 July 1997
Abstract The dynamic performance of a reformer has a major impact on the safe and efficient operation of an overall molten carbonate fuel cell power-generation system. Hence, an investigation on the dynamic characteristics of a reformer with regard to its operation in the fuel cell systems is carried out. A numerical model is developed and it is capable of calculating the dynamic responses with regard to load-following modes and disturbances. In particular, the model can consider simultaneously the dominant processes of a reformer, such as chemical reactions and heat transfer as well as mass-transport. In this paper, the dynamic responses of the processed gas from the reformer corresponding to the step changes are performed, and these responses have provided valuable insight into the characteristics of the reformer operating in fuel cell systems. 0 1997 Elsevier Science B.V. Keywurdst
Fuel cell system; Dynamic;
Modelling;
Reformer;
Step change
1. Pntroduction Electrochemical fuel cells convert chemical energy derived from a fuel directly into electrical energy by oxidizing the fuel in the cell. Power systems that generate electrical energy from electrochemical fuel cells are of particular interest to utilities because they can provide incremental and dispersed electric power. In addition, the fuel cell powergeneration systems are capable of operating at higher electrical efficiency than conventional systems, and substantially reducing the so-called ‘green house’ effect.
* Corresponding
author. Tel.: + 31-152786978;
fax: + 31-152782460;
0378-3820/97/$17.00 0 1997 El sevier Science B.V. All rights reserved. PII SO378-3820(97)00039-S
e-mail: [email protected]
100
W. He/Fuel
Processing Technology 53 (I 997) 99- 113
fluegas andair
anode offgas
cathode off-gas
Fig. 1. A MCFC system schematic
The molten carbonate fuel cell (MCFC) system using natural gas is generally considered a ‘second-generation’ fuel cell system, whose entry into the power generation market will follow that of the phosphoric acid fuel cell (PAFC) system [ 11. As shown in Fig. 1, a MCFC system often comprises the following major subsystems: (1) a fuel processing subsystem, (2) a MCFC power generation subsystem, (3) a power conversion subsystem and (4) a co-generation subsystem for utilization of the excess heat. Natural gas, steam and air are the raw sources introduced into the fuel processing subsystem. Then, the processed gas, rich in hydrogen, is provided to the subsequent MCFC power generation subsystem. A reformer, which converts the hydrocarbons in the natural gas into hydrogen-rich gas, has been used in the fuel processing subsystem. Generally, a reformer is a well established equipment for the manufacture of hydrogen in a process plant. However, the operation requirements of the reformer in a MCFC system differ essentially from those encountered in process plant, where continuous full load operation is the rule. A reformer for the MCFC system is required to operate in such a manner that the production of hydrogen-rich gas to the fuel cell power subsystem always follows the changes in the demand of power, and it is therefore required that the reformer should display rapid responsiveness to load changes and flexible controllability. There are still few investigations on the dynamic performance of fuel processing in MCFC system. In the parallel field of fuel cell systems for transportation applications, a recent study by Oh1 [2] has indicated that the operation of reformer is the limiting factor for a fuel cell system’s ability to achieve fast dynamic response. Hence, the studying of the dynamic performance of the fuel processing with regard to its operating in MCFC system is motivated. In addition, the MCK system refers to external reforming throughout this paper.
2. Description of a reformer There are at least two main types of reformers for MCFC systems, that have been or will be used in the recent MCFC demonstration projects. These are the heat exchange
W.
He/Fuel Processing
Technology 53 ( 19Y71 YY-I13
REFORMED OUTLET PROCESS INLET
I0 I
GAS
GAS
FLUE GAS OUTLET
-2.
1.
CATALYST
BED
CATALYST
BED
BURNER
FUEL INLET
AIR
INLET
Fig. 2. A heat exchanger
reformer (HER).
reformer (HER) from Haldor Topsoe and the plate reformer from Ishikawajima-harim Heavy Industries [3]. The HER has been used in the Unocal 250 kW MCFC demonstration project, USA and has also been chosen in Dutch 50 kW MCFC system. Thus the investigation of HER is carried out and the modelling approach is described in this paper. The principles of a HER is shown in Fig. 2 ([4]). The HER consists of: (1) a pressure shell, (2) a catalyst basket, and (3) a combustion chamber with a burner. The pressure shell is equipped with a flanged cover to facilitate the installation of the catalyst basket. The catalyst consists of two catalyst beds in series and a number of annuli for the process mixture flow. The catalyst beds normally contain dispersed nickel on an alumina or magnesium spine1 carrier in the shape of cylinders. Combustion takes place outside of the reformer tubes from a burner located at the bottom of the HER. The HER uses a patented principle with a combination of counter- and co-current heat exchange between the process gas and the flue gas, in order to maximize thermal efficiency and to optimize usage of construction materials. Consequently, the idea of HER is to combine the two heat transfer principles in a two-bed catalyst system. That is, the heat exchange of counter-current flow is used at the low temperature side and co-current flow is used at the high temperature side.
W. He/Fuel
102 Table 1 Composition
Processing Technology 53 (I 997) 99-113
of a typical natural gas
Component % (mol/mol)
CH, 81.29
C,H, 2.87
C,H, 0.38
C,H,, 0.15
C,H,, 0.04
C,H,, 0.05
N, 14.32
02 0.01
CO, 0.89
The main processes which determine the HER dynamic performances corresponding to its operating in MCFC systems, are identified as chemical reactions in the process and flue gas, the heat transfer from the flue gas to the process gas, and mass-transport of flue and process gases. These processes and the modelling approach are described in the subsequent sections.
3. Main processes 3. I. Chemical
reactions
3.1.1. Reactions modelled in the process The major constituent of natural gas here is referred to the Dutch natural gas Table 1 ([5]). The following reactions are generally [6,7].(i) Methane-steam reaction: CH,+H,O+3H,+CO (ii) Water-shift
gas is methane. (Groningen
The composition of the natural gas gas) and its composition is listed in
chosen to describe steam reforming
(AH&=206kJ/mol)
of methane
(1)
reaction:
CO+H,O+CO,+H,
(AGss=
-4lkJ/mol)
(2)
The methane-steam reforming reaction (1) and the water-shift reaction (2) are reversible at reforming temperatures. It is evident that at the higher temperatures less methane and more carbon monoxide are present in the equilibrium gas, and that the methane content increases with pressure and decreases with increasing ratio of steam to carbon&ii) Hydrocracking reaction: C!ZH*!f+ 2 + (k - l)H,
+ KH,
(3)
Hydrocarbons higher than CH, may exist in the natural gas feedstock. It is assumed that the higher hydrocarbons instantaneously hydrocrack to CH, at the HER inlet. This CH,, plus the CH, originally in the feedstock, is frequently termed the ‘methane equivalent’ of the fuel. 3.1.2. Reactions modelled in the flue gas The fresh natural gas (or anode off-gas) and air are fed to the burner of the reformer, where the following combustion reactions take place to provide heat for the reactions in
W. He /Furl
Processing Technology 53 C1997) 9% II3
Fig. 3. Cross-section
of a HER in a schematic
IO3
representation.
the process gas. It is assumed that the methane, hydrogen and carbon monoxide in the flue gas completely reacts to the excess air. The air excess coefficient is assumed to be 1.2. CH, + 20, = 2H,O + CO, Hz + 0.50,
+ ~~0
CO + 0.502 + CO2
3.2. Processes
(AH;,,
(A Hi,, = - 802.3 kJ/mol) = -241.8
(4)
kJ/mol)
(A HE,, = - 283.0 kJ/mol)
(6)
of heat trunsji?r und mass-transport
Heat transfer and mass-transport strongly affect reformer performance. As shown in the Fig. 3, the process feed is passed downwards through the first catalyst bed receiving heat from the partly cooled combustion gas and the product gas, both in counter-current flow with the process feed. The process gas from the first catalyst bed is then transferred to the top of the second catalyst through a number of tubes or a channel, whereafter it flows downs through the second catalyst bed receiving heat from the hot combustion gas in co-current flow with the process gas. The product gas from the second catalyst is finally passed through an annular space supplying part of its heat back to the process gas flowing in the first catalyst bed in counter-current flow. There are both convective and radiative heat-transfer phenomena between the flue gas and the shell wall, and between process gas and the shell wall. The heat transfer within the shell wall is considered by conduction.
104
W. He/Fuel
Processing
Technology 53 (I 997) 99- I13
4. Modelling approach 4.1. Objective The primary objective of this reformer model is to develop a simple but sufficiently accurate description to demonstrate its dynamic responses operating in MCFC systems with regard to load-following. 4.2. Mass and heat interconnections The mass flow on the boundary of HER is illustrated in the Fig. 4. On the flue gas side, the preheated fuel gas and air go into the burner of HER. On the process gas side, the preheated natural gas and steam input go to the reformer. There are two outputs: the flue and the process gasses. Furthermore, the principal chemical reactions for the process gas are implemented consecutively in the first catalyst bed and the second catalyst bed, which is presented by two series connected modules (BED1 and BED2). The heat transfer processes between process gas and the catalyst beds are presented by module RHXl and RHX2. The combustion process is presented by module BURNER, and the heat transfer process between flue gas and the catalyst bed is presented by module BHX2 and BHXl. 4.3. General assumptions A number of simplifying assumptions are introduced here to facilitate the complete HER description. (a) The composition of process and flue gasses consists of seven gases (Hz, CH,, N,, CO, CO,, 0, and H,O). (b) The function of the burner in HER is considered to provide high temperature flue gas. No heat transfers between burner chamber and shell are calculated. (c) The reformer is perfectly isolated from the environment. (d) The gas flow-pattern through the channels in HER is assumed to be plugflow based on the length of a bed exceeding the breadth many times. Furthermore, the modules in Fig. 4 are approximated by a sequence of well-mixed sub-modules. (e> _ / /
r-j
I I / I I I
, t
1 I / I I
BED2 A
mass flow
-
I -,
preheated
air
fuel cell anode RHXl
II
I
I
I
I_.-._
heat flow
-._
_ _ _ -._
_._._._._._.___._._.-.-.-.-._._._._.-.-.-.-.-.-.-.-.-.-._~
Fig. 4. Mass and heat flow diagram in HER.
W. He / Fuel Processing
Technology
105
53 (1997) YY- I 13
fuel cell anode
Natural gas Steam
Preheated
fuel cell cathode
Preheated
Fig. 5. Causality
diagram of HER modules.
The following equations facilitate the description for the sub-modules. Thus, the partial differential equations for the whole distributed modules can be approximately approached by a sequence of ordinary equations for the lumped sub-modules. 4.4. Input and output variables for the modules One set of meaningful input and output variables for the reformer between the modules is illustrated in the causality diagram of Fig. 5.
boundaries
and
4.5. Dynamic equations The load following rate for the whole integrated fuel cell system is at the time scale of lo2 to 10” second, thus the dynamic behavior of HER is also considered at the time scale of 10’ to 10”. With this simplification, the only dynamic phenomena described are the storage of mass and heat in the burner, catalyst beds and heat exchangers. The main dynamic equations are described as follows. 4.5. I. Mass balance The composition balance respectively derived as:
for the process
gas in the first or the second
V d( PY) - ___ = m - mout + stoich,,u,,,rate,,,,,,, Wdt ‘” The composition
beds is
+ stoich\hil,rate~hlrt
(7)
balance for the flue gas in the burner is readily derived as:
V d( PY) - ___ = rn. - mout + stoich,, Wdt In
.lrate,, 4 + stoich,_rate,,
+ stoichcorate,, (8)
106
4.5.2.
W. He / Fuel Processing
Energy
balance
Within the burner, combustion reactions.
/4___ Ph) dt
Technology 53 (I 997) 99-113
the temperature
of the flue gas output
= m( hi - h) - A Hcu,ratecu,
- AH,>rate,,
is determined
by the
- AHcorateco
(9)
Within the HER, the energy balance consists of heat sources from the reforming reactions and the heat transfers (which are presented by one counter-flow and three co-flow heat exchangers). The process gas with solid objects (e.g., metal walls and catalyst bed), is assumed to have the same temperature. Hence, the energy balance for BED1 or BED2 sub-module can be written as:
“4~
Ph) dt
= m( hi - h) + C,M,( - A H,hiftrate,;hift+
q - T) -
A H,ef,,,mrate,,fO,m
(10)
EQ
The energy balance for the gas in the heat exchanger BHX2) can be written as:
(RHXl,
RHX2,
BHXl
“d( Ph) --=m(hi-h)-Q
(11)
dt
4.6. Principles,for
derivation
or
of the algebraic
equations
The algebraic equations are required to calculate the reaction rates, heat-transfer coefficient, pressure drop and the mixture gas physical properties. The principles for the derivation of the algebraic equations are provided as follows. For the related equations, see Ref. [Sl. 4.6.1. Reaction rates The reaction rates in the flue gas are based on the methane, hydrogen and carbon monoxide in the flue gas completely reacts to the excess air. The reaction rates in the process gas can be calculated by assuming reactions reaching equilibrium or by using known kinetic equations. 4.6.2. Heat-transfer coeficient The convective and radiant heat transfers are considered from the hot gas to the solid objects. Thus, the heat-transfer coefficient calculation can refer to standard equations [9]. 4.6.3. Pressure drop The pressure drop is approached by a simple empirical equation, which considers main factors, such as gas flow rate, gas temperature, pressure and geometry.
the
4.64. Physical properties of mixture gas In view of the gases within the range of high temperature (400- 1400°C) and relative low pressure (4-10 bar) in HER, the physical properties of both the flue gas and the process gas are considered as ideal gas. All the thermodynamic equations about the ideal gas are applicable. 4.65. Spec$cution of the initiul conditions The specification of the initial conditions should obey illustrated in Fig. S to guarantee the set of differential-algebraic one. 4.7. Program
the causality principles equations having index
implementation
The present reformer model has been implemented in the SpeedUp code [lo], which has the following three significant features: (a)SpeedUp is a flowsheeting system, which is designed to model processes as they occur in chemical or process engineering environments as a series of unit operations interconnected by process streams; (b) SpeedUp simulator allows to carry out state and dynamic runs using the same software tool and the same program input, this also means that the results of stationary simulation can be used to initialize the dynamic simulation; (c) SpeedUp simultaneously solves the explicit or implicit differential and algebraic equations. According to the implementation practice [8], divergency is the usual cause of the failure during steady-state simulation. An accurate estimation of the major variables’ limits and the proper default values may effectively help steady-state simulation convergence. On the other hand, matrix singularity is the usual cause of the failure during dynamic simulation. Reformulating some equations by consideration the causeeffect among the major variables may reduce the possibility of the matrix singularity. The dynamic simulation of the fuel cell model has been performed on a Sun IPX computer and leads to the following results.
5. Dynamic
performance
5.1. Setting-up
cases
The process gas from HER goes to the fuel cell component, thus the variation of the stream under any operations or disturbances should be always within the tolerable degree. To evaluate the usefulness of the present HER model, the following three step testing cases are carried out to investigate the dynamic behavior: * flow rate of process gas + 10% * temperature of flue gas at inlet f 10% * pressure of process gas at outlet - 10%.
108
W. He / Fuel Processing Technology 53 (19971 99- I13
5.2. Step change offlow-rate
of process gas
In order to get a different process gas output, manipulating the flow-rate at process gas inlet is one of the frequent occurrences in HER operations. Thus, in this section, the dynamic behavior of the HER with regard to the flow-rate of process gas k 10% step change is examined. Fig. 6 shows the responses of flow-rate, hydrogen concentration and temperature at
NaIunl gas 10%
at outlet
Process gas
T
I=7
z
*,a
$
..__..,..........................................
2
L,)
ii
stepchange
__
.___._.,.,_.
.
. . .
.
.
. .
. . .
.
. .
..__.
2.w
0
!ow
xa .oca Tms (L)
ma0
Process gas
5ca
8cw
at outlet
. __ .._....... .... .... . ....... .... ...... .......
;” \ .._.__.._. (1,
. .
. . . .. . .
p. i c
),)
“,,,* w,
,I,
.____,.._.
$
..__
;/
. . .
. . . . .
. .
.
____..,.______....._...................................
.,_....__...._.__...._.................................,...
I __._. _._ ,__
1 i
-;:-----tmo
0
moo
xa .ow l-m* (5)
Process gas
rwo
nca
at outlet
~~~~ i q
&3** : I
0
tom
Fig. 6. Responses
looD
cc”l Tl~~W
to flow-rate
HMO
A wca
+ 10% step change.
W. He / Fuel Processing
Technology
109
53 ( 19971 9% I13
the processed gas outlet. The quantitative responses to the - 10% step change is described as follows. The flow-rate decreases from 3 to 2.75 mol/s, the net gain is - 0.25 mol/s ( - 8.3%). The molar concentration of Hz increases from 47.3 to 48.8%. the net gain is 1.65%. The temperature increases from 607 to 628”C, the net gain is 2 1“C (3.4%). It is noticed that the response consists of the fast beginning and then a slow following. Consequently, a fast response results from the mass transport phenomenon and the slow response results from the heat transfer phenomenon. This case also confirms that the manipulation of the flow-rate of natural gas for reforming is an effective strategy for changing the output flow-rate of process gas (&- 8.1%, within a few 10 s). One side effect, the H, concentration 1.65% change, is not serious. But the other side effect, the temperature of the process gas, will influence the fuel-cell power generation subsystem performance. 5.3. Step chunge
of temperature
of,fuel gas
The temperature disturbance of the fuel gas going to the burner may exists during the operation of HER (specially the fuel gas using off-gas). Hence, in this section, the dynamic behavior of the HER with regard to the temperature disturbance of fuel gas going to the burner + 10% step change is examined. Fig. 7 shows the responses of flow-rate, hydrogen concentration and temperature at the outlet of the process gas. The quantitative responses to the -10% step change is described as follows. Both the flow-rate and the molar concentration of H, has no significant influence. The temperature decreases from 607 to 603”C, the net is -4°C ( - 0.6%). The results are in good agreement with the HER claimed characteristic, which has low sensitivity to flue gas inlet temperature variations [ 111. This has provided good chance for the reformer using the off-gas from the fuel-cell power generation subsystem. 5.4. Pressure
change of process gas
The pressure disturbance is considered to be one of the most significant factors which influence the safe operation of HER [12]. Thus, the dynamic behavior of the HER with regard to the pressure disturbance - 10% step change from the process gas is examined. Fig. 8 shows the responses of flow-rate, hydrogen concentration and temperature at the outlet of the process gas. The flow-rate at the outlet of the process gas immediately
Table 2
Process ES at outlet responses to the three - IO’% step changes - IO% step change flow-rate of natural gas for reforming temperature of gases to burner pressure at oullet of process gas
Change of flowrate (mol/s) -0.25 (-8.3%). with very small overshoot 0
Change of Hz molar concentration I .65%, with small overshoot 0
Change of temperature (“C) 21 (3.4%)
0.02 (1.770)~ with a large overshoot
0.5%. with overshoot
-h(-
-4
(-0.6%) I’%)
110
W. He/Fuel
Processing
Technology 53 (1997) 99-113
jumps to a maximum value, drops and then goes back to almost original flow-rate. The molar concentration of H, increases rapidly from 47.3% to a maximum value and then goes to a stable value of 47.8%, the net gain is 0.5%. The temperature decreases from 607 to 601°C tbe net is -6°C (- 1%). It is noticed that the response consists of a fast beginning and then a slow following. This case has indicated that the pressure disturbance from the process gas causes the disturbance of flow-rate of the process gas. Here, the large part of flow-rate disturbance of the process gas is within a few seconds. If the flow-rate disturbances last longer time, it may be harmful for the MCFC operation [81. Purl gas 10% *,.p chang* ¶aa.a +,O%
p’
III lzzl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. .. . . .
~ r-
....
~44.,r
4
O,.”
400.”
.. . . .. .
. . . . . . . . . . . .._...............................................
.
,....................
*ma
0
_)W
zoo0
. . . . . . . . . . . .
Proc*ss
,..I
1..
1
1.”
..“.
.“.
0
ID%
laD
?? m
WJO
lims
ga, aI
. . . . . . . . . . .
(ooo
. . .
(ooo
(I,
ou,,.,
.._..._. _.“,.._,,.........._..,. “.._
,m
am
Moo
mo
Tima ,S)
Process gas A oullal
Fig. 7. Responses
to temperature
k 10% step change.
W. He/ Fuel Processing Technology 53 (1997) 99-113
III
6. Discussions A comparison of the process gas responses to the aforementioned three cases with different step changes may be carried out in various way. Here, one example is given to illustrate the influences (Table 2). Comments on the above three cases: (a> The largest flow-rate response and the overshoot respectively result from the step change of the flow-rate case and pressure case; (b) The largest H2 molar concentration response results from the flow-rate case;
Fig. 8. Responses
to pressure
- 10% step change
112
W. He/Fuel
Processing Technology 53 (1997) 99-113
cc> The largest temperature response results from the flow-rate case; (d) Figs. 7 and 8 show that the responses of the process gas to the three different step changes are all stable, and the temperature following will be in the range of lo3 s and with no significant overshoot.
7. Conclusions The techniques for numerically investigating the dynamic performance of a HER reformer are presented. A conceptual HER is described for the modelling and the dynamic equations are derived. Furthermore, the numerical HER reformer model has been constructed using the SpeedUp code. The three dynamical cases have been demonstrated. The simulation results indicate that the responses of the process gas are all stable, and the temperature responses are in the range of IO3 s. Furthermore, the step change of the flow-rate has the most significant response, and the step change of the pressure has the largest overshoot. Therefore, the present HER model is effective in predicting the responses of the process gas and indicate the ‘bottlenecks’ of HER operating in fuel cell systems.
Acknowledgements The author thanks the guidance of Prof.ir. R.W.J. Kouffeld and Prof.ir. O.H. Bosgra throughout this study. The substantial help from ir. A. Korving and Dr.ir. J.G.M. Becht, as well as the contributions from the graduate students 0. Cobben and A.V. Tilburg are gratefully acknowledged.
Appendix A List of symbols Abbreviations MCFC Molten carbonate fuel cell HER Heat exchange reformer Roman letters C Heat capacity, kJ/kg K Gas flow rate, kmol/s m,F h Enthalpy, kJ/kg K Standard reaction heat, kJ/mol A%!% M Weight of mass, kg Total pressure, bar Heat transfer, kJ/s ; rate Reaction rate, kmol/s stoech Stoichiometric coefficient of reaction
W. He/Fuel
T V W Y? y
Processing Technology 53 (1997) 99-113
113
Temperature, “C Volume, m3 Gas molar weight, kg/kmol Gas molar fraction
Greek letters Density, P
kg/m
Subscripts Hz CH, co in out reform S shift
H, burning reaction CH, burning reaction CO burning reaction Parameters at inlet Parameters at outlet Methane-steam reaction Solid objects Water-shift reaction
References [l] J.R. Selman, Research, development, and demonstration of molten carbonate fuel cell systems, in: J.M.J. Blomen, N.N. Mugerwa (Eds.), Fuel Cell Systems, Plenum, New York, 1993, 578 pp. [2] G.L. Ohl, G.E. Simth, J.L. Stein, Dynamic models of a methanol to hydrogen steam reformer for transportation applications, presented at Fuel Cell Seminar, November 28-December I, San Diego, CA. USA, 1994. 491-494. [3] T. Watanabe, M. Koga, S. Morishim, Experimental results of plate type reformer for fuel cell systems, Ishikawajima-harima Heavy Industries, presented at 1989 International Gas Research Conference, Tokyo, Japan, 6-9 November, 1989. [4] L.J. Christiansen, C.L. Laursen, Fuel cell activities at Haldor Topsoc A/S, Fuel cell workshop, Center for Nordic Gas Technique, Horsholm, Denmark, April 10-l 1, 1991. [5] N.V. Nederlandse Gasunie, Physical properties of natuml gases, Groningen, Netherlands, 1989. [6] E.S. Wagner, Steam reforming analyzed, KTI, San Dimas, CA, 1992 171 G.F. Froment, Steam reforming analyzed, Ghent University, Belgium, Hydrocarbon processing, July. 1992. 181 W. He, Dynamic modelling and control of integrated fuel cell power-generation systems, Ph.D thesis, Delft University of Technology (in preparation), 1995. [9] A.J. Chapman, Heat Transfer, Macmillan, New York, USA, 1974. [lo] Aspen Technology, SpeedUp User Manual, Version 5.4, Cambridge, MA, USA, 1993. [l I] H. Stahl, C. Laursen, New concept heat exchange reformer for fuel cell applications, presented at Fuel Cell Seminar, November 29-December 2, 1992, Tucson, AZ, USA, 465-468. [I21 M. Yamaguch, Analysis of control characteristics using fuel cell plant simulator, IEEE Trans. Ind. Electron. 37 (5) (1990) 378-386.
Fuel Processing Technology 53 (1997) 99%113
Dynamic performance of a reformer for molten carbonate fuel cell power-generation systems W. He * Department
of’Mechanica1
Engineering
und Marine Del&
Technology,
De@ Unirwsity
of Technology,
2628 CD
Netherlands
Received 14 March 1997; accepted 4 July 1997
Abstract The dynamic performance of a reformer has a major impact on the safe and efficient operation of an overall molten carbonate fuel cell power-generation system. Hence, an investigation on the dynamic characteristics of a reformer with regard to its operation in the fuel cell systems is carried out. A numerical model is developed and it is capable of calculating the dynamic responses with regard to load-following modes and disturbances. In particular, the model can consider simultaneously the dominant processes of a reformer, such as chemical reactions and heat transfer as well as mass-transport. In this paper, the dynamic responses of the processed gas from the reformer corresponding to the step changes are performed, and these responses have provided valuable insight into the characteristics of the reformer operating in fuel cell systems. 0 1997 Elsevier Science B.V. Keywurdst
Fuel cell system; Dynamic;
Modelling;
Reformer;
Step change
1. Pntroduction Electrochemical fuel cells convert chemical energy derived from a fuel directly into electrical energy by oxidizing the fuel in the cell. Power systems that generate electrical energy from electrochemical fuel cells are of particular interest to utilities because they can provide incremental and dispersed electric power. In addition, the fuel cell powergeneration systems are capable of operating at higher electrical efficiency than conventional systems, and substantially reducing the so-called ‘green house’ effect.
* Corresponding
author. Tel.: + 31-152786978;
fax: + 31-152782460;
0378-3820/97/$17.00 0 1997 El sevier Science B.V. All rights reserved. PII SO378-3820(97)00039-S
e-mail: [email protected]
100
W. He/Fuel
Processing Technology 53 (I 997) 99- 113
fluegas andair
anode offgas
cathode off-gas
Fig. 1. A MCFC system schematic
The molten carbonate fuel cell (MCFC) system using natural gas is generally considered a ‘second-generation’ fuel cell system, whose entry into the power generation market will follow that of the phosphoric acid fuel cell (PAFC) system [ 11. As shown in Fig. 1, a MCFC system often comprises the following major subsystems: (1) a fuel processing subsystem, (2) a MCFC power generation subsystem, (3) a power conversion subsystem and (4) a co-generation subsystem for utilization of the excess heat. Natural gas, steam and air are the raw sources introduced into the fuel processing subsystem. Then, the processed gas, rich in hydrogen, is provided to the subsequent MCFC power generation subsystem. A reformer, which converts the hydrocarbons in the natural gas into hydrogen-rich gas, has been used in the fuel processing subsystem. Generally, a reformer is a well established equipment for the manufacture of hydrogen in a process plant. However, the operation requirements of the reformer in a MCFC system differ essentially from those encountered in process plant, where continuous full load operation is the rule. A reformer for the MCFC system is required to operate in such a manner that the production of hydrogen-rich gas to the fuel cell power subsystem always follows the changes in the demand of power, and it is therefore required that the reformer should display rapid responsiveness to load changes and flexible controllability. There are still few investigations on the dynamic performance of fuel processing in MCFC system. In the parallel field of fuel cell systems for transportation applications, a recent study by Oh1 [2] has indicated that the operation of reformer is the limiting factor for a fuel cell system’s ability to achieve fast dynamic response. Hence, the studying of the dynamic performance of the fuel processing with regard to its operating in MCFC system is motivated. In addition, the MCK system refers to external reforming throughout this paper.
2. Description of a reformer There are at least two main types of reformers for MCFC systems, that have been or will be used in the recent MCFC demonstration projects. These are the heat exchange
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REFORMED OUTLET PROCESS INLET
I0 I
GAS
GAS
FLUE GAS OUTLET
-2.
1.
CATALYST
BED
CATALYST
BED
BURNER
FUEL INLET
AIR
INLET
Fig. 2. A heat exchanger
reformer (HER).
reformer (HER) from Haldor Topsoe and the plate reformer from Ishikawajima-harim Heavy Industries [3]. The HER has been used in the Unocal 250 kW MCFC demonstration project, USA and has also been chosen in Dutch 50 kW MCFC system. Thus the investigation of HER is carried out and the modelling approach is described in this paper. The principles of a HER is shown in Fig. 2 ([4]). The HER consists of: (1) a pressure shell, (2) a catalyst basket, and (3) a combustion chamber with a burner. The pressure shell is equipped with a flanged cover to facilitate the installation of the catalyst basket. The catalyst consists of two catalyst beds in series and a number of annuli for the process mixture flow. The catalyst beds normally contain dispersed nickel on an alumina or magnesium spine1 carrier in the shape of cylinders. Combustion takes place outside of the reformer tubes from a burner located at the bottom of the HER. The HER uses a patented principle with a combination of counter- and co-current heat exchange between the process gas and the flue gas, in order to maximize thermal efficiency and to optimize usage of construction materials. Consequently, the idea of HER is to combine the two heat transfer principles in a two-bed catalyst system. That is, the heat exchange of counter-current flow is used at the low temperature side and co-current flow is used at the high temperature side.
W. He/Fuel
102 Table 1 Composition
Processing Technology 53 (I 997) 99-113
of a typical natural gas
Component % (mol/mol)
CH, 81.29
C,H, 2.87
C,H, 0.38
C,H,, 0.15
C,H,, 0.04
C,H,, 0.05
N, 14.32
02 0.01
CO, 0.89
The main processes which determine the HER dynamic performances corresponding to its operating in MCFC systems, are identified as chemical reactions in the process and flue gas, the heat transfer from the flue gas to the process gas, and mass-transport of flue and process gases. These processes and the modelling approach are described in the subsequent sections.
3. Main processes 3. I. Chemical
reactions
3.1.1. Reactions modelled in the process The major constituent of natural gas here is referred to the Dutch natural gas Table 1 ([5]). The following reactions are generally [6,7].(i) Methane-steam reaction: CH,+H,O+3H,+CO (ii) Water-shift
gas is methane. (Groningen
The composition of the natural gas gas) and its composition is listed in
chosen to describe steam reforming
(AH&=206kJ/mol)
of methane
(1)
reaction:
CO+H,O+CO,+H,
(AGss=
-4lkJ/mol)
(2)
The methane-steam reforming reaction (1) and the water-shift reaction (2) are reversible at reforming temperatures. It is evident that at the higher temperatures less methane and more carbon monoxide are present in the equilibrium gas, and that the methane content increases with pressure and decreases with increasing ratio of steam to carbon&ii) Hydrocracking reaction: C!ZH*!f+ 2 + (k - l)H,
+ KH,
(3)
Hydrocarbons higher than CH, may exist in the natural gas feedstock. It is assumed that the higher hydrocarbons instantaneously hydrocrack to CH, at the HER inlet. This CH,, plus the CH, originally in the feedstock, is frequently termed the ‘methane equivalent’ of the fuel. 3.1.2. Reactions modelled in the flue gas The fresh natural gas (or anode off-gas) and air are fed to the burner of the reformer, where the following combustion reactions take place to provide heat for the reactions in
W. He /Furl
Processing Technology 53 C1997) 9% II3
Fig. 3. Cross-section
of a HER in a schematic
IO3
representation.
the process gas. It is assumed that the methane, hydrogen and carbon monoxide in the flue gas completely reacts to the excess air. The air excess coefficient is assumed to be 1.2. CH, + 20, = 2H,O + CO, Hz + 0.50,
+ ~~0
CO + 0.502 + CO2
3.2. Processes
(AH;,,
(A Hi,, = - 802.3 kJ/mol) = -241.8
(4)
kJ/mol)
(A HE,, = - 283.0 kJ/mol)
(6)
of heat trunsji?r und mass-transport
Heat transfer and mass-transport strongly affect reformer performance. As shown in the Fig. 3, the process feed is passed downwards through the first catalyst bed receiving heat from the partly cooled combustion gas and the product gas, both in counter-current flow with the process feed. The process gas from the first catalyst bed is then transferred to the top of the second catalyst through a number of tubes or a channel, whereafter it flows downs through the second catalyst bed receiving heat from the hot combustion gas in co-current flow with the process gas. The product gas from the second catalyst is finally passed through an annular space supplying part of its heat back to the process gas flowing in the first catalyst bed in counter-current flow. There are both convective and radiative heat-transfer phenomena between the flue gas and the shell wall, and between process gas and the shell wall. The heat transfer within the shell wall is considered by conduction.
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4. Modelling approach 4.1. Objective The primary objective of this reformer model is to develop a simple but sufficiently accurate description to demonstrate its dynamic responses operating in MCFC systems with regard to load-following. 4.2. Mass and heat interconnections The mass flow on the boundary of HER is illustrated in the Fig. 4. On the flue gas side, the preheated fuel gas and air go into the burner of HER. On the process gas side, the preheated natural gas and steam input go to the reformer. There are two outputs: the flue and the process gasses. Furthermore, the principal chemical reactions for the process gas are implemented consecutively in the first catalyst bed and the second catalyst bed, which is presented by two series connected modules (BED1 and BED2). The heat transfer processes between process gas and the catalyst beds are presented by module RHXl and RHX2. The combustion process is presented by module BURNER, and the heat transfer process between flue gas and the catalyst bed is presented by module BHX2 and BHXl. 4.3. General assumptions A number of simplifying assumptions are introduced here to facilitate the complete HER description. (a) The composition of process and flue gasses consists of seven gases (Hz, CH,, N,, CO, CO,, 0, and H,O). (b) The function of the burner in HER is considered to provide high temperature flue gas. No heat transfers between burner chamber and shell are calculated. (c) The reformer is perfectly isolated from the environment. (d) The gas flow-pattern through the channels in HER is assumed to be plugflow based on the length of a bed exceeding the breadth many times. Furthermore, the modules in Fig. 4 are approximated by a sequence of well-mixed sub-modules. (e> _ / /
r-j
I I / I I I
, t
1 I / I I
BED2 A
mass flow
-
I -,
preheated
air
fuel cell anode RHXl
II
I
I
I
I_.-._
heat flow
-._
_ _ _ -._
_._._._._._.___._._.-.-.-.-._._._._.-.-.-.-.-.-.-.-.-.-._~
Fig. 4. Mass and heat flow diagram in HER.
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105
53 (1997) YY- I 13
fuel cell anode
Natural gas Steam
Preheated
fuel cell cathode
Preheated
Fig. 5. Causality
diagram of HER modules.
The following equations facilitate the description for the sub-modules. Thus, the partial differential equations for the whole distributed modules can be approximately approached by a sequence of ordinary equations for the lumped sub-modules. 4.4. Input and output variables for the modules One set of meaningful input and output variables for the reformer between the modules is illustrated in the causality diagram of Fig. 5.
boundaries
and
4.5. Dynamic equations The load following rate for the whole integrated fuel cell system is at the time scale of lo2 to 10” second, thus the dynamic behavior of HER is also considered at the time scale of 10’ to 10”. With this simplification, the only dynamic phenomena described are the storage of mass and heat in the burner, catalyst beds and heat exchangers. The main dynamic equations are described as follows. 4.5. I. Mass balance The composition balance respectively derived as:
for the process
gas in the first or the second
V d( PY) - ___ = m - mout + stoich,,u,,,rate,,,,,,, Wdt ‘” The composition
beds is
+ stoich\hil,rate~hlrt
(7)
balance for the flue gas in the burner is readily derived as:
V d( PY) - ___ = rn. - mout + stoich,, Wdt In
.lrate,, 4 + stoich,_rate,,
+ stoichcorate,, (8)
106
4.5.2.
W. He / Fuel Processing
Energy
balance
Within the burner, combustion reactions.
/4___ Ph) dt
Technology 53 (I 997) 99-113
the temperature
of the flue gas output
= m( hi - h) - A Hcu,ratecu,
- AH,>rate,,
is determined
by the
- AHcorateco
(9)
Within the HER, the energy balance consists of heat sources from the reforming reactions and the heat transfers (which are presented by one counter-flow and three co-flow heat exchangers). The process gas with solid objects (e.g., metal walls and catalyst bed), is assumed to have the same temperature. Hence, the energy balance for BED1 or BED2 sub-module can be written as:
“4~
Ph) dt
= m( hi - h) + C,M,( - A H,hiftrate,;hift+
q - T) -
A H,ef,,,mrate,,fO,m
(10)
EQ
The energy balance for the gas in the heat exchanger BHX2) can be written as:
(RHXl,
RHX2,
BHXl
“d( Ph) --=m(hi-h)-Q
(11)
dt
4.6. Principles,for
derivation
or
of the algebraic
equations
The algebraic equations are required to calculate the reaction rates, heat-transfer coefficient, pressure drop and the mixture gas physical properties. The principles for the derivation of the algebraic equations are provided as follows. For the related equations, see Ref. [Sl. 4.6.1. Reaction rates The reaction rates in the flue gas are based on the methane, hydrogen and carbon monoxide in the flue gas completely reacts to the excess air. The reaction rates in the process gas can be calculated by assuming reactions reaching equilibrium or by using known kinetic equations. 4.6.2. Heat-transfer coeficient The convective and radiant heat transfers are considered from the hot gas to the solid objects. Thus, the heat-transfer coefficient calculation can refer to standard equations [9]. 4.6.3. Pressure drop The pressure drop is approached by a simple empirical equation, which considers main factors, such as gas flow rate, gas temperature, pressure and geometry.
the
4.64. Physical properties of mixture gas In view of the gases within the range of high temperature (400- 1400°C) and relative low pressure (4-10 bar) in HER, the physical properties of both the flue gas and the process gas are considered as ideal gas. All the thermodynamic equations about the ideal gas are applicable. 4.65. Spec$cution of the initiul conditions The specification of the initial conditions should obey illustrated in Fig. S to guarantee the set of differential-algebraic one. 4.7. Program
the causality principles equations having index
implementation
The present reformer model has been implemented in the SpeedUp code [lo], which has the following three significant features: (a)SpeedUp is a flowsheeting system, which is designed to model processes as they occur in chemical or process engineering environments as a series of unit operations interconnected by process streams; (b) SpeedUp simulator allows to carry out state and dynamic runs using the same software tool and the same program input, this also means that the results of stationary simulation can be used to initialize the dynamic simulation; (c) SpeedUp simultaneously solves the explicit or implicit differential and algebraic equations. According to the implementation practice [8], divergency is the usual cause of the failure during steady-state simulation. An accurate estimation of the major variables’ limits and the proper default values may effectively help steady-state simulation convergence. On the other hand, matrix singularity is the usual cause of the failure during dynamic simulation. Reformulating some equations by consideration the causeeffect among the major variables may reduce the possibility of the matrix singularity. The dynamic simulation of the fuel cell model has been performed on a Sun IPX computer and leads to the following results.
5. Dynamic
performance
5.1. Setting-up
cases
The process gas from HER goes to the fuel cell component, thus the variation of the stream under any operations or disturbances should be always within the tolerable degree. To evaluate the usefulness of the present HER model, the following three step testing cases are carried out to investigate the dynamic behavior: * flow rate of process gas + 10% * temperature of flue gas at inlet f 10% * pressure of process gas at outlet - 10%.
108
W. He / Fuel Processing Technology 53 (19971 99- I13
5.2. Step change offlow-rate
of process gas
In order to get a different process gas output, manipulating the flow-rate at process gas inlet is one of the frequent occurrences in HER operations. Thus, in this section, the dynamic behavior of the HER with regard to the flow-rate of process gas k 10% step change is examined. Fig. 6 shows the responses of flow-rate, hydrogen concentration and temperature at
NaIunl gas 10%
at outlet
Process gas
T
I=7
z
*,a
$
..__..,..........................................
2
L,)
ii
stepchange
__
.___._.,.,_.
.
. . .
.
.
. .
. . .
.
. .
..__.
2.w
0
!ow
xa .oca Tms (L)
ma0
Process gas
5ca
8cw
at outlet
. __ .._....... .... .... . ....... .... ...... .......
;” \ .._.__.._. (1,
. .
. . . .. . .
p. i c
),)
“,,,* w,
,I,
.____,.._.
$
..__
;/
. . .
. . . . .
. .
.
____..,.______....._...................................
.,_....__...._.__...._.................................,...
I __._. _._ ,__
1 i
-;:-----tmo
0
moo
xa .ow l-m* (5)
Process gas
rwo
nca
at outlet
~~~~ i q
&3** : I
0
tom
Fig. 6. Responses
looD
cc”l Tl~~W
to flow-rate
HMO
A wca
+ 10% step change.
W. He / Fuel Processing
Technology
109
53 ( 19971 9% I13
the processed gas outlet. The quantitative responses to the - 10% step change is described as follows. The flow-rate decreases from 3 to 2.75 mol/s, the net gain is - 0.25 mol/s ( - 8.3%). The molar concentration of Hz increases from 47.3 to 48.8%. the net gain is 1.65%. The temperature increases from 607 to 628”C, the net gain is 2 1“C (3.4%). It is noticed that the response consists of the fast beginning and then a slow following. Consequently, a fast response results from the mass transport phenomenon and the slow response results from the heat transfer phenomenon. This case also confirms that the manipulation of the flow-rate of natural gas for reforming is an effective strategy for changing the output flow-rate of process gas (&- 8.1%, within a few 10 s). One side effect, the H, concentration 1.65% change, is not serious. But the other side effect, the temperature of the process gas, will influence the fuel-cell power generation subsystem performance. 5.3. Step chunge
of temperature
of,fuel gas
The temperature disturbance of the fuel gas going to the burner may exists during the operation of HER (specially the fuel gas using off-gas). Hence, in this section, the dynamic behavior of the HER with regard to the temperature disturbance of fuel gas going to the burner + 10% step change is examined. Fig. 7 shows the responses of flow-rate, hydrogen concentration and temperature at the outlet of the process gas. The quantitative responses to the -10% step change is described as follows. Both the flow-rate and the molar concentration of H, has no significant influence. The temperature decreases from 607 to 603”C, the net is -4°C ( - 0.6%). The results are in good agreement with the HER claimed characteristic, which has low sensitivity to flue gas inlet temperature variations [ 111. This has provided good chance for the reformer using the off-gas from the fuel-cell power generation subsystem. 5.4. Pressure
change of process gas
The pressure disturbance is considered to be one of the most significant factors which influence the safe operation of HER [12]. Thus, the dynamic behavior of the HER with regard to the pressure disturbance - 10% step change from the process gas is examined. Fig. 8 shows the responses of flow-rate, hydrogen concentration and temperature at the outlet of the process gas. The flow-rate at the outlet of the process gas immediately
Table 2
Process ES at outlet responses to the three - IO’% step changes - IO% step change flow-rate of natural gas for reforming temperature of gases to burner pressure at oullet of process gas
Change of flowrate (mol/s) -0.25 (-8.3%). with very small overshoot 0
Change of Hz molar concentration I .65%, with small overshoot 0
Change of temperature (“C) 21 (3.4%)
0.02 (1.770)~ with a large overshoot
0.5%. with overshoot
-h(-
-4
(-0.6%) I’%)
110
W. He/Fuel
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Technology 53 (1997) 99-113
jumps to a maximum value, drops and then goes back to almost original flow-rate. The molar concentration of H, increases rapidly from 47.3% to a maximum value and then goes to a stable value of 47.8%, the net gain is 0.5%. The temperature decreases from 607 to 601°C tbe net is -6°C (- 1%). It is noticed that the response consists of a fast beginning and then a slow following. This case has indicated that the pressure disturbance from the process gas causes the disturbance of flow-rate of the process gas. Here, the large part of flow-rate disturbance of the process gas is within a few seconds. If the flow-rate disturbances last longer time, it may be harmful for the MCFC operation [81. Purl gas 10% *,.p chang* ¶aa.a +,O%
p’
III lzzl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. .. . . .
~ r-
....
~44.,r
4
O,.”
400.”
.. . . .. .
. . . . . . . . . . . .._...............................................
.
,....................
*ma
0
_)W
zoo0
. . . . . . . . . . . .
Proc*ss
,..I
1..
1
1.”
..“.
.“.
0
ID%
laD
?? m
WJO
lims
ga, aI
. . . . . . . . . . .
(ooo
. . .
(ooo
(I,
ou,,.,
.._..._. _.“,.._,,.........._..,. “.._
,m
am
Moo
mo
Tima ,S)
Process gas A oullal
Fig. 7. Responses
to temperature
k 10% step change.
W. He/ Fuel Processing Technology 53 (1997) 99-113
III
6. Discussions A comparison of the process gas responses to the aforementioned three cases with different step changes may be carried out in various way. Here, one example is given to illustrate the influences (Table 2). Comments on the above three cases: (a> The largest flow-rate response and the overshoot respectively result from the step change of the flow-rate case and pressure case; (b) The largest H2 molar concentration response results from the flow-rate case;
Fig. 8. Responses
to pressure
- 10% step change
112
W. He/Fuel
Processing Technology 53 (1997) 99-113
cc> The largest temperature response results from the flow-rate case; (d) Figs. 7 and 8 show that the responses of the process gas to the three different step changes are all stable, and the temperature following will be in the range of lo3 s and with no significant overshoot.
7. Conclusions The techniques for numerically investigating the dynamic performance of a HER reformer are presented. A conceptual HER is described for the modelling and the dynamic equations are derived. Furthermore, the numerical HER reformer model has been constructed using the SpeedUp code. The three dynamical cases have been demonstrated. The simulation results indicate that the responses of the process gas are all stable, and the temperature responses are in the range of IO3 s. Furthermore, the step change of the flow-rate has the most significant response, and the step change of the pressure has the largest overshoot. Therefore, the present HER model is effective in predicting the responses of the process gas and indicate the ‘bottlenecks’ of HER operating in fuel cell systems.
Acknowledgements The author thanks the guidance of Prof.ir. R.W.J. Kouffeld and Prof.ir. O.H. Bosgra throughout this study. The substantial help from ir. A. Korving and Dr.ir. J.G.M. Becht, as well as the contributions from the graduate students 0. Cobben and A.V. Tilburg are gratefully acknowledged.
Appendix A List of symbols Abbreviations MCFC Molten carbonate fuel cell HER Heat exchange reformer Roman letters C Heat capacity, kJ/kg K Gas flow rate, kmol/s m,F h Enthalpy, kJ/kg K Standard reaction heat, kJ/mol A%!% M Weight of mass, kg Total pressure, bar Heat transfer, kJ/s ; rate Reaction rate, kmol/s stoech Stoichiometric coefficient of reaction
W. He/Fuel
T V W Y? y
Processing Technology 53 (1997) 99-113
113
Temperature, “C Volume, m3 Gas molar weight, kg/kmol Gas molar fraction
Greek letters Density, P
kg/m
Subscripts Hz CH, co in out reform S shift
H, burning reaction CH, burning reaction CO burning reaction Parameters at inlet Parameters at outlet Methane-steam reaction Solid objects Water-shift reaction
References [l] J.R. Selman, Research, development, and demonstration of molten carbonate fuel cell systems, in: J.M.J. Blomen, N.N. Mugerwa (Eds.), Fuel Cell Systems, Plenum, New York, 1993, 578 pp. [2] G.L. Ohl, G.E. Simth, J.L. Stein, Dynamic models of a methanol to hydrogen steam reformer for transportation applications, presented at Fuel Cell Seminar, November 28-December I, San Diego, CA. USA, 1994. 491-494. [3] T. Watanabe, M. Koga, S. Morishim, Experimental results of plate type reformer for fuel cell systems, Ishikawajima-harima Heavy Industries, presented at 1989 International Gas Research Conference, Tokyo, Japan, 6-9 November, 1989. [4] L.J. Christiansen, C.L. Laursen, Fuel cell activities at Haldor Topsoc A/S, Fuel cell workshop, Center for Nordic Gas Technique, Horsholm, Denmark, April 10-l 1, 1991. [5] N.V. Nederlandse Gasunie, Physical properties of natuml gases, Groningen, Netherlands, 1989. [6] E.S. Wagner, Steam reforming analyzed, KTI, San Dimas, CA, 1992 171 G.F. Froment, Steam reforming analyzed, Ghent University, Belgium, Hydrocarbon processing, July. 1992. 181 W. He, Dynamic modelling and control of integrated fuel cell power-generation systems, Ph.D thesis, Delft University of Technology (in preparation), 1995. [9] A.J. Chapman, Heat Transfer, Macmillan, New York, USA, 1974. [lo] Aspen Technology, SpeedUp User Manual, Version 5.4, Cambridge, MA, USA, 1993. [l I] H. Stahl, C. Laursen, New concept heat exchange reformer for fuel cell applications, presented at Fuel Cell Seminar, November 29-December 2, 1992, Tucson, AZ, USA, 465-468. [I21 M. Yamaguch, Analysis of control characteristics using fuel cell plant simulator, IEEE Trans. Ind. Electron. 37 (5) (1990) 378-386.