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Design and control of energy integrated SOFC systems for in situ hydrogen production and power generation
Computers and Chemical Engineering 35 (2011) 1691–1704
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Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng
Design and control of energy integrated SOFC systems for in situ hydrogen production and power generation Dimitrios Georgis a , Sujit S. Jogwar a , Ali S. Almansoori b , Prodromos Daoutidis a,∗ a b
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates
a r t i c l e
i n f o
Article history: Received 22 October 2010 Received in revised form 7 February 2011 Accepted 8 February 2011 Available online 15 February 2011 Keywords: SOFC Methane reforming Energy integration Process control
a b s t r a c t This paper studies the design and operation of energy integrated solid oxide fuel cell (SOFC) systems for in situ hydrogen production and power generation. Two configurations are considered: one where the hot effluent stream from the fuel cell is used directly to provide heat to the endothermic reforming reaction, and another where the hot effluent streams are mixed and combusted in a catalytic burner before the energy integration. A comparative evaluation of the two configurations is presented in terms of their design, open-loop dynamics and their operation under linear multi-loop controllers. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Fuel cells provide the most efficient path for the conversion of chemical energy into electrical energy (Varigonda & Kamat, 2006). Recognizing the need for efficient energy production systems and the fact that fuel cells are not limited by Carnot efficiencies, there has been an increasing interest in developing fuel cell systems for stationary and transportation applications (see e.g. Bavarian, Soroush, Kevrekidis, & Benziger, 2010; Bhattacharyya & Rengaswamy, 2009; Chaisantikulwat, Diaz-Goano, & Meadows, 2008; Cresswell & Metcalfe, 2006; Kee, Zhu, Sukeshini, & Jackson, 2008; Pukrushpan, Stefanopoulou, & Peng, 2004; Varigonda & Kamat, 2006, for excellent overviews on recent developments and opportunities in modeling and control of fuel cell systems). Hydrogen is the most preferred fuel for a fuel cell. Given the safety issues associated with the storage and transportation of hydrogen, in situ production of hydrogen from a hydrocarbon fuel, coupled with a H2 -fed SOFC, presents a promising approach for power production, especially for stationary fuel cell applications. Two approaches have been proposed to this end. One of the approaches uses an external reformer (e.g. Adams, Thomas, & Barton, 2010; Braun, Klein, & Reindl, 2006; Mueller, Jabbari, Gaynor, & Brouwer, 2007; Murshed, Huang, & Nandakumar, 2007) to generate a hydrogen-rich stream which is then fed to the fuel cell. The other approach uses the principle of internal reforming (e.g.
∗ Corresponding author. Tel.: +1 612 625 8818; fax: +1 612 626 7246. E-mail address: [email protected] (P. Daoutidis). 0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2011.02.006
Al-Qattan & Chmielewski, 2004; Braun et al., 2006), wherein both the reforming and the electrochemical reactions take place in a single unit. The internal reforming approach offers benefits in terms of energy consumption, however at the cost of operating challenges (carbon deposition on electrodes, fewer inputs available for control, etc.). One variant of this approach uses indirect internal reforming, wherein the reforming and the electrochemical compartments are only in thermal contact, thereby avoiding the direct physical contact (Aguiar, Chadwick, & Kershenbaum, 2002). In this paper, we focus on the approach based on external reforming as it offers more opportunities for integration and control design. A power system consisting of an external reformer and a fuel cell shows a lower overall efficiency, since additional energy is required to drive the endothermic reforming reactions. SOFCs are high temperature fuel cells with an operating temperature range between 800 ◦ C and 1000 ◦ C. The hot stream leaving the SOFC shows potential for energy integration by supplying energy to the endothermic reformer, and thereby improving the overall efficiency. Different integration strategies for SOFC energy systems have been proposed (see e.g. Zhang et al., 2010 which reviews most of these strategies). These include hybrid integration strategies with direct thermal coupling (Chan, Ho, & Tian, 2002; Zhang, Li, Li, & Feng, ˙ Santarelli, & Leone, 2006) 2006), indirect thermal coupling (Cale, as well as fuel coupling (Yi, Rao, Brouwer, & Samuelsen, 2005), and advanced integration strategies using gas/humid air/steam turbines (Kandepu et al., 2007; Mueller et al., 2008; Oh & Sun, 2010; Varbanov & Klemes, 2008). Some of these strategies directly (without mixing the anodic and cathodic streams) use the hot SOFC effluent for energy recovery (e.g. Bents, 1987; Sadhukhan,
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Nomenclature Capital letters Universal gas constant R T Temperature F Faraday constant VFC Voltage of single cell Exchange apparent current Io I Current Ri Resistance of each compartment Limiting current IL N Number of cells in the SOFC stack V Output voltage P Output power Cpi Heat capacity of component Volume of each compartment Vi Pi Operating pressure of each process Hirxn Heat of reaction Enthalpy flow Q˙ i U A TLM UF L W
Overall heat transfer coefficient Area Logarithmic mean temperature difference Fuel utilization Length Width
Small letters n Number of transferred electrons pi Partial pressure of each species n˙ i Molar flow rate Mass m ri Reaction rate Thickness Greek letters Number of transferred electrons Charge transfer coefficient ˛ Density ε Void fraction Subscripts FC Fuel cell Open-circuit voltage OCV act Activation ohm Ohmic Concentration conc an Anode el Electrolyte ca Cathode Interconnect int fuel Fuel stream air Air stream SR Steam reformer Catalyst cat
Zhao, Leach, Brandon, & Shah, 2010), while others use a catalytic burner to further recover energy from the unreacted fuel and use this stream for energy integration (e.g. Chan et al., 2002; Mueller et al., 2007). While each of these approaches has obvious advantages/disadvantages in terms of capital and operating costs, compatibility with downstream processes, and environmental impact, they also offer different opportunities and challenges in terms of overall integrated system design, dynamics and control. This is a rather untouched subject in the literature. Motivated by
Fig. 1. Generic design structure of the SOFC energy system.
this, in this paper we compare (and contrast) these two approaches at the design and operational stages. The results of this study can guide the selection of a particular approach. To this end, we consider a generic SOFC energy system with an external methane steam reformer. Energy recovery is achieved by designing a network of heat exchangers (HE). Through open-loop simulations under imposed step changes in the current, the dynamic behavior of each of the configurations is analyzed. Linear multi-loop control strategies are proposed for each case and their operational characteristics are compared through closed-loop simulations. The rest of the paper is organized as follows. The modeling details for the fuel cell and the reformer are presented in Section 2. The selection of operating points for each of these units based on steady state analysis is presented in Section 3. The design, dynamics and control aspects of the energy integrated configurations are analyzed in Sections 4, 5 and 6, respectively. Lastly, Section 7 includes a detailed discussion comparing the two configurations. 2. SOFC energy system with external reformer A generic SOFC energy system with an external methane steam reformer is shown in Fig. 1. As the reformer and the fuel cell operate at a high temperature, three heat transfer units are required to heat the methane steam mixture, fuel cell anode and cathode inlet streams. Furthermore, energy is required for sustained hydrogen production in the endothermic steam reformer. In the following subsections, we present the modeling details for the fuel cell and the reformer which are the main units of the system. 2.1. Solid oxide fuel cell The SOFC stack consists of individual cells connected in series. This is a common approach to scale-up the output voltage, thereby resulting in an increased supply of power (NETL, 2004). A hydrogenrich stream is fed to the anodic compartment of the fuel cell, while air is supplied to the cathodic compartment. The following exothermic redox reactions take place in the fuel cell, thereby generating an electrochemical potential: H2 + O2− → H2 O + 2e− 1 O2 + 2e− → O2− , Cathode: 2 Anode:
◦
H298 = −241.83 kJ/mol
The open-circuit voltage that can be generated by the fuel cell is given by the Nernst equation:
EOCV
RTFC = Eo (TFC ) + ln 2F
pFC,H2 · p0.5 FC,O
2
pFC,H2 O
(1)
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704 20
a
1
a
V P
1693
:S/C=2 :S/C=3 :S/C=4 :S/C=5
0.95
400
0.9 15
CH4
0.8 x
10
P (kW)
N VFC (V)
0.85 300
0.75
200
0.7 0.65
5 100
0.6 0.55
0
b
0
10
20
30
40 I (A)
50
60
70
0 80
0.5 800
850
900
950
1000 T (K)
1050
1100
1150
1200
SR
1450
b
1400
0.5
1350 1300
0.4
:CH
1200
4
0.3
:H O
yi
TFC (K)
1250
1150
2
:CO
2
1100
:CO :H
0.2
2
1050 1000 950
0.1 0
10
20
30
40
50
60
70
80
I (A)
0 800
850
900
Fig. 2. SOFC steady states of the voltage, power and temperature as a function of the current.
where Eo (TFC ) is the temperature dependent standard potential (Li, 2006), pi denotes the partial pressure of species i at the anode, TFC is the temperature of the fuel cell and F is the Faraday constant. However, when connected in a circuit, the output voltage of the fuel cell decreases due to the existence of irreversible losses (called polarizations). The output voltage of the fuel cell delivered to the load is given by the following equation: VFC = EOCV − act − ohm − conc
(2)
where act , ohm , and conc represent the activation, ohmic and concentration polarizations respectively. Activation polarization is described as the energy barrier that should be overcome by the reacting species. It is calculated using the Bulter–Volmer equation (Hamann, Hamnett, & Vielstich, 2007): I = Io ·
exp
˛nF
act
RTFC
− exp −(1 − ˛)
nFact RTFC
(3)
where Io is the apparent exchange current (calculated following Wang & Nehrir, 2007) and ˛ the transfer coefficient. The voltage drop due to the resistance in the flow of electrons and ions can be described by the ohmic polarization which is determined by Ohm’s law as shown below: ohm = I · (Ran + Rel + Rca + Rint )
(4)
where Ri is the resistance of each compartment (calculated from Ferguson, Fiard, & Herbin, 1996) and the subscripts (an, el, ca, int) refer to the anode, the electrolyte, the cathode and the interconnector. Moreover, concentration polarization represents the voltage
950
1000 T (K)
1050
1100
1150
1200
SR
Fig. 3. Steam reformer methane conversion at different S/C ratios and mole fraction steady states as a function of the reformer temperature. Table 1 General parameters. Parameter N V (V) I (A) P (kW) S/C UF
Value 384 272 60.3 16.4 4 0.8
Configuration 1 ˇ1 b2 b3
Parameter
Value
PFC (kPa) PSR (kPa) QF (kW) xCH4 n˙ SR,in (mol/s) n˙ air (mol/s)
101.3 150.0 4.347 0.926 0.225 2.111
Configuration 2 0.09 0.10 0.10
b1 b2 b3
0.10 0.10 0.10
drop due to the concentration gradients between the bulk gases and the triple phase boundary point, the interface between the electrolyte and the electrode where the electrochemical reactions occur. It is calculated from the following equation: conc =
RTFC ln 2F
I L IL − I
(5)
where IL is the limiting current in the fuel cell. The output voltage and the power for the entire SOFC stack are given below: V = N · VFC
(6)
P =I·V
(7)
where N is the number of individual cells in the stack.
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Fig. 4. Energy integrated SOFC system – Configuration 1.
Fig. 5. Energy integrated SOFC system – Configuration 2.
We now move to the material and energy balance equations for the fuel cell. The objective of this study is to analyze the systemwide characteristics of energy integrated SOFC systems. Recent studies have shown, through experimental validation, that lumped parameter models are sufficiently accurate for such systems-level analysis and control (Xi, Varigonda, & Jing, 2010). Numerous other papers also employ lumped parameter models for analysis and control of SOFC systems (see e.g. Mueller et al., 2008; Murshed et al., 2007; Sorrentino, Pianese, & Guezennec, 2008). Therefore, we have used such a lumped parameter model to describe the dynamics of the fuel cell. It is assumed that there is no interaction
between each individual cell. Therefore, the inlet anode and cathode flows are split into N streams. The model assumes constant pressure and physical properties, ideal gas behavior and adiabatic operation. The species and energy balances then take the following form: dnFC,H2 dt
= n˙ FC,H2 ,in − n˙ FC,H2 −
dnFC,H2 O dt
I 2F
= n˙ FC,H2 O,in − n˙ FC,H2 O +
(8) I 2F
(9)
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704 Table 2 Stream composition at the outlet of each major process.
yCH4 yH2 O yCO yCO2 yH2 yO2 yN2 n˙ total (mol/s) n˙ an,total (mol/s) n˙ ca,total (mol/s)
1695
Table 4 UA values for heat exchangers and steam reformer.
SR
SOFC
CB
UAi (W/K)
Configuration 1
Configuration 2
0.011 0.368 0.054 0.081 0.486 – – 0.308 – –
0.011 0.757 0.054 0.081 0.097 0.184 0.816 – 0.308 1.840
0 0.116 0 0.019 0 0.151 0.714 2.336 – –
SR HE1 HE2 HE3 HE4 HE5 HE6 HE7
51.42 24.45 49.05 15.36 2.31 4.63 2.31 1170
67.10 8.09 104.80 11.62 108.10 3.23 58.37 3.91
Table 5 MCp values used in the case study. Table 3 Physical properties of each component. Component
i (kg/m3 )
Cpi (J/mol/K)
CH4 H2 O (g) H2 O (l) CO CO2 H2 O2 N2
0.717 0.804 1000 1.250 1.977 0.089 1.429 1.251
58.381 38.459 75.327 31.374 49.561 30.236 32.582 31.394
dnFC,O2 dt
= n˙ FC,O2 ,in − n˙ FC,O2 −
I 4F
(10)
1 dTFC = · (Q˙ fuel,in − Q˙ fuel,out + Q˙ air,in SOFC CpSOFC VSOFC dt rxn − Q˙ air,out − n˙ reacted · HFC − I · VFC ) H
(11)
2
n˙ reacted = H 2
Q˙ i =
I 2F
(12)
n˙ j Cpj (Ti − Tref )
(13)
j
where the subscripts (i) and (j) refer to the corresponding streams and components while (FC) denotes the fuel cell and Q˙ i represents the enthalpy flow. Eq. (12) represents Faraday’s law.
MCpi (J/K)
Configuration 1
Configuration 2
SRH F CB HE1,HOT HE2,HOT HE3,HOT HE4,HOT HE5,HOT HE6,HOT HE7,HOT HE1,COLD HE2,COLD HE3,COLD HE4,COLD HE5,COLD HE6,COLD HE7,COLD
26.45 35.31 – 2.61 0.19 2.61 2.61 5.84 5.84 26.46 857.89 3.52 3.52 1.30 4.74 5.36 35.31
36.54 – 36.54 36.54 36.54 36.54 36.54 36.54 36.54 36.54 857.89 3.52 4.74 26.48 5.36 26.48 0.86
Table 6 Detailed parameters used in the case study. Parameter
Value
Parameter
Value
L (m) W (m) A (cm2 ) SOFC (kg/m3 ) CpSOFC (J/(kg K)) an (mm) el (m) ca (m)
0.1 0.1 100 4200 640 1 8 50
VSR (L) cat (kg/m3 ) ε Cpcat (J/(kg K)) rxn HFC (kJ/mol) H1rxn (kJ/mol) H2rxn (kJ/mol) int (mm)
3.3 2335 0.4 444 −241.83 206.10 −41.15 1
two catalytic reactions: Reforming reaction:
CH4 + H2 O CO + 3H2 ,
◦
2.2. Methane steam reformer
H298 = +206.10 kJ/mol
A methane steam reformer is used to convert methane into a hydrogen-rich stream. This is accomplished through the following
Shift reaction:
CO + H2 O CO2 + H2 ,
◦
H298 = −41.15 kJ/mol
Table 7 Stream temperatures for each configuration. Configuration 1
Configuration 2
Temperature
(K)
Temperature
(K)
Temperature
(K)
Temperature
(K)
TCH4 ,in TH2 O,in Tair,in THE1C THE1H THE2C THE2H THE3C THE3H THE4C THE5C,in THE4H
298.0 298.0 298.0 373.0 308.2 373.4 383.0 669.3 481.7 669.3 669.3 831.2
THE5H THE5C TSR TSRH TSRH,out TFC THE6H THE6C THE7H THE7C TF TSRH,in
1001.4 822.9 932.3 981.5 997.6 1162.6 1125.3 973.0 306.8 907.9 973.1 1143.1
TCH4 ,in TH2 O,in Tair,in THE1C THE1H THE2C THE2H THE3C THE3H THE4C THE4H THE5H
298.0 298.0 298.0 373.1 457.3 515.7 470.6 823.0 925.6 729.0 586.8 1087.1
THE5C TSR TSRH TSRH,out TFC THE6H THE6C THE7H THE7C TCB,in THE3C,in TCA,in TCB
973.0 932.3 950.1 963.8 1162.6 1092.9 1048.0 579.2 520.0 1143.1 516.9 973.0 1343.7
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Table 8 Controller parameters for both configurations (K: controller gain, I : integral time constant). −1
−3
4 × 10 5 × 10−2 1 × 10−2 5 × 10−4 20
KFC (K ) KSR (K−1 ) KUF (mol/s) KCa (K−1 ) KF (W/K)
I,FC (s) I,SR (s) I,UF (s) I,Ca (s) I,F (s)
and ideal gas behavior, the species mass balances take the form: dnSR,CH4 dt
200 100 10 80 80
dnSR,H2 O dt dnSR,CO2 dt
Note that even though the first reaction is endothermic and the second is exothermic, the net system of reactions is endothermic, requiring external energy input for sustained hydrogen production. Here, we model the reformer as a well-mixed reactor with a heating jacket. Assuming constant pressure, constant physical properties
a
955
= n˙ SR,CH4 ,in − n˙ SR,CH4 − mcat · r1
(14)
= n˙ SR,H2 O,in − n˙ SR,H2 O − mcat · (r1 + r2 )
(15)
= n˙ SR,CO2 ,in − n˙ SR,CO2 + mcat · r2
(16)
dnSR,CO = n˙ SR,CO,in − n˙ SR,CO + mcat · (r1 − r2 ) dt dnSR,H2 dt
(17)
= n˙ SR,H2 ,in − n˙ SR,H2 + mcat · (3r1 + r2 )
(18)
b 1195 1190
950
1185
TFC (K)
TSR (K)
945
940
1180
1175
935 1170 930
1165 Configuration 1 Configuration 2
925
0
20
40
60
80
Configuration 1 Configuration 2 1160
100
0
20
40
1000
d
80
100
0.835
0.83
990
0.825
985
0.82
UF
995
980
0.815
975
0.81
970
0.805 Configuration 1 Configuration 2
965
0
20
40
60
80
Configuration 1 Configuration 2
100
0.8
0
20
40
time (min)
e
60
time (min)
1344
1342
1340
TCB (K)
TCA,in (K)
c
60
time (min)
time (min)
1338
1336
1334
1332
0
20
40
60
80
100
time (min) Fig. 6. Open-loop simulation under a small step in the current from 60.3 A to 62 A.
80
100
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
a
1150
b
1697
1450
1400
1100
1350
TFC (K)
TSR (K)
1050
1000
1300
1250 950 1200 Configuration 1 Configuration 2 900
0
20
40
60
80
Configuration 1 Configuration 2
100
0
20
40
60
time (min) 1400
d
0.98
1300
0.96
1250
0.94
1200
0.92
1150
0.9
1100
0.88
1050
0.86
1000
0.84
950 900
0.82
Configuration 1 Configuration 2 0
20
40
60
80
100
0.8
Configuration 1 Configuration 2 0
20
40
time (min)
e
100
1
1350
UF
TCA,in (K)
c
80
time (min)
60
80
100
time (min)
1400
TCB (K)
1350
1300
1250
0
20
40
60
80
100
time (min) Fig. 7. Open-loop simulation under a large step in the current from 60.3 A to 70 A.
where mcat is the mass of the catalyst and ri is the rate of each reaction. The reaction rate expressions are obtained based on a Langmuir–Hinshelwood reaction mechanism as proposed in Xu and Froment (1989). The energy balances for the reactor and the jacket have the following form: (Q˙ fuel,in − Q˙ fuel,out − mcat (r1 H1rxn + r2 H2rxn ) + UASR TLM ) dTSR = (εg Cpg + (1 − ε)cat Cpcat )VSR dt (19) (Q˙ SR,HOT,in − Q˙ SR,HOT,out − UASR TLM ) dTSR,HOT = MCpSR,HOT dt
(20)
where the subscripts (g) and (cat) refer to the gas and catalyst properties, VSR is the volume of the steam reformer, ε is the void fraction,
UASR is the product of the overall heat transfer coefficient and the heat exchange area and TLM is the mean logarithmic temperature difference. 3. Steady state analysis In what follows, a steady state analysis is performed for the SOFC and the reformer in order to select the operating points for these units. This will provide a starting point for the design of the integrated SOFC energy system. 3.1. Solid oxide fuel cell The steady state values of the output voltage, output power and the cell temperature as a function of the current are shown in Fig.
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a
1168 Configuration 1 Configuration 2 set point
1167
b
936 Configuration 1 Configuration 2 set point
935
c
0.825 Configuration 1 Configuration 2 set point
1165
933
1164
0.815
UF
934
TSR (K)
TFC (K)
0.82 1166
932
1163
931
1162
930
0.81
0.805
1161 0
20
40
60
80
929
100
0
20
time (min)
60
80
0.8
100
0.11 Configuration 1 Configuration 2
e
Configuration 1 Configuration 2
f
0.14
b3
b2
0.12
0.07 0.1 0.06
0.06
0.04
0.04
60
80
100
80
100
0.233 Configuration 1 Configuration 2
0.23 0.229 0.228 0.227
0.08
0.05
60
0.231
0.08
40
40
0.232
0.16
0.09
20
20
time (min)
0.2 0.18
0.1
0
0
time (min)
n fuel (mol/s)
d
40
0.226 0.225 0
20
time (min)
40
60
80
100
0.224 0
20
40
time (min)
60
80
100
time (hr)
Fig. 8. Closed-loop responses for both configurations under a current step increase from 60.3 A to 62 A.
2. It is desirable to operate the SOFC close to the highest power production point with high fuel utilization (UF ). The fuel utilization represents the fraction of the incoming hydrogen that is electrochemically converted in the fuel cell. We selected the operating point corresponding to a current of 60.3 A. At this point, the power delivered by the fuel cell is 16.4 kW (99% of the maximum power), the output voltage is 272 V and the fuel cell temperature is 1162.6 K.
3.2. Methane steam reformer It is desired to operate the steam reformer at a temperature where a stream rich in hydrogen is produced with a high methane conversion (Mueller et al., 2008). We first explored the effect of the steam-to-carbon (S/C) ratio on methane conversion. Fig. 3(a) shows the variation of methane conversion with respect to reformer temperature for various values of S/C ratios. High S/C values show enhanced methane conversion, however, at the cost of additional heating load. We selected S/C = 4 for this study. Fig. 3(b) shows the steady state profiles for various species at the outlet of reformer as a function of operating temperature. Note that the hydrogen mole fraction shows a maximum for a reformer temperature close to 980 K. We selected the operating point to be 932.3 K. For this state, the methane conversion is 92.6% and the reformate gas contains approximately 49% hydrogen.
4. Energy integration The system in Fig. 1 requires four external energy inputs. On the other hand, the SOFC exit streams leave at a high temperature thus, showing a potential for energy integration. Motivated by the previously proposed integration strategies (e.g. Bents, 1987; Chan et al., 2002; Mueller et al., 2007; Sadhukhan et al., 2010), two integration alternatives were considered: in the first, the hot anodic and cathodic exit streams from the fuel cell are used directly as two hot streams, while in the other, the anodic and cathodic streams are mixed together and are combusted in a catalytic burner to generate a single hot stream.
As the first step in the design of the energy integrated systems, we used pinch analysis (Linnhoff & Hindmarsh, 1983). Pinch analysis indicated that external hot utility is required for the first system while the second system is self sustaining. Pinch analysis also indicated the absence of a pinch point for both the cases, thus allowing for a variety of possible design alternatives (Kemp, 2007). • Design of integrated configuration based on alternative 1: Most of the existing configurations (e.g. Bents, 1987; Sadhukhan et al., 2010) following this alternative focus only on the fuel cell and do not incorporate any fuel processing unit. In this study we incorporated such a fuel processing unit and we designed the heat exchanger network with the objective of achieving the minimum external utility predicted by the pinch analysis. The resulting integrated configuration is depicted in Fig. 4. The cathode outlet stream provides energy to the steam reformer (SR) and then it is split into two streams. One preheats the air in HE7 , while the other supplies energy for preheating methane in HE4 , water in HE1 and steam in HE3 . The anode outlet stream covers the heating requirement of the anode inlet in HE6 . Then, it preheats the fuel mixture to the required reformer inlet temperature in HE5 and then supplies the required energy for steam generation in HE2 . An external hot utility is supplied to the furnace in order to heat the air to the required temperature. The resulting energy requirement (see Table 1) in this configuration is exactly the one predicted by the pinch analysis. • Design of integrated configuration based on alternative 2: In this case, we used the integrated configuration proposed in Mueller et al. (2007) as a basis and achieved further recovery and recycle of energy, specifically through the addition of heat exchangers (1–3), (5) and (7) as shown in Fig. 5. The anodic and cathodic outlet streams are fed to a catalytic burner, where the complete combustion of methane, carbon monoxide and unreacted hydrogen takes place. The required air is supplied by the SOFC cathodic stream. The high temperature stream leaving the burner heats the air in HE6 and provides energy to the anode inlet stream in HE5 . Then, it passes through the steam reformer (SR) in order to cover its endothermic demand. Leaving the reformer, the hot
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
a
982 Configuration 1 Configuration 2 set point
980
Tca,in (K)
978
976
1699
first configuration, while bypasses b1 –b3 are placed in the second configuration for the same reason. Tables 1 and 3–6 present the parameters that have been used for both configurations. Note that the same operating points (as selected in the previous section) are used for the fuel cell and the reformer. The composition and the total molar flow rate at the outlet of each major process are tabulated in Table 2. The temperatures at each stream arising from the energy integration are tabulated in Table 7. 5. Open-loop analysis
974
We next studied the dynamic response of each of these configurations. We considered a scenario where current changes are imposed which may be caused by power changes.
972
970
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Fig. 6 shows the response of key variables for a step in the current from 60.3 A to 62 A. The increase in current causes an instantaneous increase in the amount of hydrogen reacted in the fuel cell (Eq. (12)). This is reflected in the corresponding increase in the fuel utilization and the decrease in the burner temperature (less fuel for combustion) for the second configuration. The increased hydrogen consumption also results in increased fuel cell temperature, however over a longer horizon. Yet, the impact of the disturbance is different for the two configurations. The rise in the reformer temperature is much larger for configuration 1 than configuration 2. This is due to the fact that the inlet temperature for configuration 1 is higher than the nominal value, while for the second configuration, it is lower than the nominal value. The responses of the reformer temperature and the cathode inlet temperature show striking differences between the two configurations. In configuration 1, the increase in the fuel cell temperature increases the reformer temperature and the cathode inlet temperature in the same fashion. In the case of configuration 2, the increased current triggers opposing forces in the burner (increase the inlet temperature and decrease the temperature rise) resulting in an inverse response. For the magnitude of current change considered here, the net effect is the reduction in burner temperature below the nominal value. This drives similar responses in the reformer temperature and cathode inlet temperature. Thus configuration 2 is less sensitive to the current disturbance than configuration 1.
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stream heats the fuel mixture to the temperature required by the reformer in HE3 and then preheats the air stream in HE4 . Afterwards, it provides energy for both the preheating of the methane in HE7 and the steam generation in HE2 and HE1 . Both configurations use seven process-to-process heat exchangers. While the first configuration uses a furnace (external energy source), the other uses a combustion unit (internal energy source). Bypasses b2 and b3 are placed to improve the controllability of the
We now subject the system to a large disturbance in current. Fig. 7 shows the open-loop response of key variables for a step in the current from 60.3 A to 70 A. The responses for the first configuration indicate an open-loop instability triggered by the change in the operating region of the steam reformer. More precisely, the increase in the current causes an increase in the reformer temperature. This increases the hydrogen production rate supplying more fuel to the fuel cell. However, when the reformer temperature reaches to a point beyond the maximum hydrogen production (see Fig. 3(b)), any further increase in reformer temperature decreases hydrogen production and hence, reduces the fuel supply to the cell. This drives the cell towards fuel starvation conditions, resulting in higher temperatures. In the case of the second configuration, the system reaches a new steady state with responses similar to the case of a small current step. However, in this case, the catalytic burner temperature is higher than the nominal value, resulting in similar higher value in the reformer temperature. Note that the temperature increase in the steam reformer is quite small to trigger any instability. This again shows the ability of this configuration to maintain open-loop stability.
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Remark 5.1. Both open-loop simulation scenarios discussed above were performed for an increase in the current drawn from the SOFC. In the case of a decrease in the applied current, both configurations give stable open-loop responses even for large steps in the current (plots not included in the paper). 6. Control design 6.1. Closed-loop analysis In this paper we focus on the control problem only on the chemical side of the SOFC energy system. As chemical side of a SOFC system we refer to the part of the SOFC system which includes only the electrochemical phenomena taking place inside the SOFC, without including any power conditioning unit after the SOFC. The corresponding control objectives considered involve: 1. SOFC temperature: The SOFC is an exothermic system. An increase in the SOFC temperature shows potential for material damages while a decrease drops the ionic conductivity of the electrolyte. Thus, there is a need to regulate the SOFC temperature. In this case, the SOFC temperature is controlled by manipulating the air inlet flow rate via the bypass b2 . 2. Reformer temperature: The reformer temperature affects the hydrogen production and hence, the stability, the performance, and the power production level of the entire energy system. We therefore control the reformer temperature through the jacket stream flow rate via the bypass b3 .
3. Fuel utilization: High fuel utilization values (>0.95) lead to fuel starvation which can damage the anode (Mueller et al., 2007). Also, low fuel utilization values reflect inefficient operation. Motivated by this, fuel utilization is controlled in the system by manipulating the fuel inlet flow rate (n˙ fuel ). 4. Cathode inlet temperature: In order to maintain a desired operating point of the SOFC (especially the SOFC temperature), the cathode inlet temperature is also controlled. In the first configuration, it is controlled by manipulating the furnace heat duty while in the other configuration, it is controlled via the bypass (b1 ). Proportional integral (PI) controllers were implemented to realize the above control strategy. Initially, the Ziegler–Nicholds tuning technique was followed with the ultimate gain (Ku ) and the ultimate period (Pu ) obtained through the autotuning (ATV) method (Luyben, 1990). The controller parameters calculated from the above procedure resulted in aggressive control action leading to unstable closed-loop behavior (plots not included in the paper). Therefore, we detuned the controllers to get a smoother and stable closed-loop response as well as similar settling times. The parameters obtained are presented in Table 8. The same controller parameters were used in both the configurations, except for the cathode inlet temperature control loop. In this loop, the same time constant but a different controller gain has been used since the manipulated variable is different in the two configurations.
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6.2. Closed-loop simulations We compared the closed-loop performance of both configurations under a small and a large current step increase (similar to the steps applied in Sections 5.1 and 5.2). We also identified the operating ranges for each of the configurations. Note that the operating range here is defined as the range of achievable current for which no bypasses are saturated. 6.2.1. Small step increase in current A step change from 60.3 A to 62 A in the current is applied and the evolution of the controlled variables along with their manipulated variables is presented in Figs. 8 and 9. As the step in the current is applied, hydrogen consumption in the fuel cell increases, thereby causing an increase in the fuel utilization. The fuel utilization controller increases the fuel flow into the system, in order to increase the hydrogen production and hence, to decrease and bring the fuel utilization back to the set point. The increasing current also causes the SOFC temperature to rise, therefore the SOFC temperature controller reduces the bypass ratio to reduce the SOFC temperature. The increase in the fuel inlet flow leads to higher energy demand required by the reformer. According to this, we expect the controller to decrease the bypass on the reformer hot stream in order to provide more energy to the reformer. This is the case for the first configuration. However, the controller corresponding to the second configuration increases the bypass ratio. This action reveals a surplus of energy in the reformer jacket-side inlet stream compared to its nominal value. This contrasting behavior comes from the dif-
ferent types of heating streams used in the reformer jacket. In the first configuration, the cathode exit stream (consisting of oxygen and nitrogen) supplies the energy to the reformer. The flow rate of this stream remains almost constant (slight decrease in oxygen flow occurs due to electrochemical reactions) during the operation. Thus the increased heating demand of the reformer causes a decrease in the bypass ratio b3 . On the other hand, the other configuration uses a mixture of anodic and cathodic streams in the reformer jacket. The flow rate of this stream changes almost in accordance with the change in the reformer inlet flow. The surplus of energy comes from the increased burner temperature. The second configuration exhibits higher overshoots compared to the first configuration. This difference again comes from the different nature of the heating streams used in the reformer jacket. The cathode exit stream (with controlled temperature) introduces a negligible disturbance into the reformer in the first configuration, as compared to the burner temperature (with uncontrolled temperature) in the second configuration.
6.2.2. Large step increase in current In Section 5.2 we showed that the open-loop response of the first configuration is driven to instability while the second configuration remains stable under a large step increase in the current. In this section, we perform a closed-loop simulation of the above configurations under the same large disturbance (60.3–70 A) and we show the capability of the proposed control scheme to stabilize the open-loop unstable system.
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Table 9 Comparison of the two configurations. Characteristic
Configuration 1
Configuration 2
Design of integrated system Open-loop dynamics
No pinch – extra energy is required Stable (small disturbance) Unstable (large disturbance) Smaller overshoots Broader (bypass saturated for current increase) No combustion No mixing of SOFC outlet streams (promising for further integration with a CO2 capture unit)
No pinch – surplus of energy Stable (small disturbance) Stable (large disturbance) Larger overshoots Narrower (bypass saturated for current increase and decrease) Combustion unit (potential for NOx) Mixing of SOFC outlet streams
Closed-loop dynamics Operational Range Environmental Impact
According to the closed-loop responses (Figs. 10 and 11), the first configuration remains stable under the imposed large disturbance. Stability is achieved since the reformer temperature controller keeps the operating temperature away from the maximum hydrogen production point (see Fig. 3(b)). Note that both the SOFC and reformer bypasses are saturated resulting in small offsets in the SOFC and reformer temperatures. The second configuration remains stable even if the temperature bypass is saturated causing an offset in the SOFC temperature. 6.2.3. Operating range investigation In this section, we impose positive and negative changes in current (Fig. 12(g)) in order to identify the operating range for both the configurations. The controlled and corresponding manipulated variables are presented in Figs. 12 and 13. The first configuration shows a broader operating range (I ≤ 66.5 A) compared to the second configuration (58 A ≤ I < 66.5 A). During the first step increase in the current, the first configuration is very close to saturation while the second configuration shows a bypass (b2 ) saturation (Fig. 12(d)) resulting in an offset in the SOFC temperature. As the current decreases there is no operational and controllability limitation for the first configuration since less energy is required, and hence the controllers increase the bypasses. However, in the second configuration there is a decrease in the reformer bypass (b3 ), leading to saturation (Fig. 12(e)). Note that under saturation conditions the systems remain operable (but not controllable) showing offsets from the set point. 7. Discussion Let us now compile the various similarities and contrasting features exhibited by these two configurations. Table 9 summarizes and compares the major characteristics of these configurations. • Design of integrated system: Both configurations do not show a pinch point. Additional energy is required (and supplied via a furnace) in the first configuration while energy is available for further integration in the second configuration. Both configurations use seven process-to-process heat exchangers. • Open-loop dynamics: Both configurations are stable for small disturbances in current. However, the first configuration is driven to instability for a large disturbance in current, whereas the second configuration remains stable. • Closed-loop dynamics: The proposed control scheme is capable of stabilizing the open-loop unstable configuration. Additionally, the first configuration shows smaller overshoots compared to the second configuration (for the same controller parameters). • Operational range: The first configuration has a broader operational range compared to the second configuration. More precisely, the first configuration shows a limitation (due to bypass saturation) at higher current, while the second configuration shows limitations for both the increase and the decrease in the current.
• Environmental impact: The first configuration is less amenable to NOx production (due to the absence of a combustion unit). Moreover, this configuration looks promising for further integration with a carbon dioxide capture unit as the anodic (CH4 , H2 O, CO2 , CO and H2 ) stream is not mixed with the cathodic (O2 and N2 ) stream (Adams et al., 2010). 8. Conclusions In this paper we studied two energy integrated configurations comprising a SOFC, a methane steam reformer and energy transfer units. In the first configuration, the SOFC outlet streams were used directly for energy integration, while in the second, these streams were fed to a catalytic burner for more energy recovery and recycle. The first configuration was shown to become unstable for large changes in current. This is the result of a positive energy feedback loop which results in high temperatures and fuel starvation. A linear multi-loop control strategy was developed for the entire integrated system. It was shown to be successful in suppressing the instability in the first configuration and to provide satisfactory closed-loop responses for a broad range of positive and negative changes in the current. Acknowledgements Partial financial support for this work from the Abu DhabiMinnesota Institute for Research Excellence, National Science Foundation Grant CBET-0756363 and the ACS-PRF is gratefully acknowledged. References Adams, I., Thomas, A., & Barton, P. (2010). High-efficiency power production from natural gas with carbon capture. Journal of Power Sources, 195, 1971–1983. Aguiar, P., Chadwick, D., & Kershenbaum, L. (2002). Modelling of an indirect internal reforming solid oxide fuel cell. Chemical Engineering Science, 57, 1665–1677. Al-Qattan, A., & Chmielewski, D. (2004). Distributed feed design for SOFCs with internal reforming. Journal of the Electrochemical Society, 151, A1891. Bavarian, M., Soroush, M., Kevrekidis, I., & Benziger, J. (2010). Mathematical modeling, steady-state and dynamic behavior, and control of fuel cells: A review. Industrial & Engineering Chemistry Research, 49, 7922–7950. Bents, D. (1987). High temperature solid oxide regenerative fuel cell for solar photovoltaic energy storage. In Proceedings of the 22nd intersociety energy conversion engineering conference AIAA, (pp. 808–817). Bhattacharyya, D., & Rengaswamy, R. (2009). A review of solid oxide fuel cell (SOFC) dynamic models. Industrial & Engineering Chemistry Research, 48, 6068–6086. Braun, R., Klein, S., & Reindl, D. (2006). Evaluation of system configurations for solid oxide fuel cell-based micro-combined heat and power generators in residential applications. Journal of Power Sources, 158, 1290–1305. ˙ M., Santarelli, M., & Leone, P. (2006). Computer experimental analysis of the Cale, CHP performance of a 100 kWe SOFC field unit by a factorial design. Journal of Power Sources, 156, 400–413. Chaisantikulwat, A., Diaz-Goano, C., & Meadows, E. (2008). Dynamic modelling and control of planar anode-supported solid oxide fuel cell. Computers & Chemical Engineering, 32, 2365–2381. Chan, S., Ho, H., & Tian, Y. (2002). Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant. Journal of Power Sources, 109, 111–120. Cresswell, D., & Metcalfe, I. (2006). Energy integration strategies for solid oxide fuel cell systems. Solid State Ionics, 177, 1905–1910. Ferguson, J., Fiard, J., & Herbin, R. (1996). Three-dimensional numerical simulation for various geometries of solid oxide fuel cells. Journal of Power Sources, 58, 109–122.
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Sadhukhan, J., Zhao, Y., Leach, M., Brandon, N., & Shah, N. (2010). Energy integration and analysis of solid oxide fuel cell based microcombined heat and power systems and other renewable systems using biomass waste derived syngas. Industrial & Engineering Chemistry Research, 49, 11506–11516. Sorrentino, M., Pianese, C., & Guezennec, Y. (2008). A hierarchical modeling approach to the simulation and control of planar solid oxide fuel cells. Journal of Power Sources, 180, 380–392. Varbanov, P., & Klemes, J. (2008). Analysis and integration of fuel cell combined cycles for development of low-carbon energy technologies. Energy, 33, 1508–1517. Varigonda, S., & Kamat, M. (2006). Control of stationary and transportation fuel cell systems: Progress and opportunities. Computers & Chemical Engineering, 30, 1735–1748. Wang, C., & Nehrir, M. (2007). A physically based dynamic model for solid oxide fuel cells. IEEE Transactions on Energy Conversion, 22, 887–897. Xi, H., Varigonda, S., & Jing, B. (2010). Dynamic modeling of a solid oxide fuel cell system for control design. In American Control Conference (ACC) (pp. 423–428). IEEE. Xu, J., & Froment, G. (1989). Methane steam reforming, methanation and water-gas shift: I. Intrinsic kinetics. AIChE Journal, 35, 88–96. Yi, Y., Rao, A., Brouwer, J., & Samuelsen, G. (2005). Fuel flexibility study of an integrated 25 kW SOFC reformer system. Journal of Power Sources, 144, 67–76. Zhang, X., Chan, S., Li, G., Ho, H., Li, J., & Feng, Z. (2010). A review of integration strategies for solid oxide fuel cells. Journal of Power Sources, 195, 685–702. Zhang, X., Li, J., Li, G., & Feng, Z. (2006). Dynamic modeling of a hybrid system of the solid oxide fuel cell and recuperative gas turbine. Journal of Power Sources, 163, 523–531.
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Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng
Design and control of energy integrated SOFC systems for in situ hydrogen production and power generation Dimitrios Georgis a , Sujit S. Jogwar a , Ali S. Almansoori b , Prodromos Daoutidis a,∗ a b
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates
a r t i c l e
i n f o
Article history: Received 22 October 2010 Received in revised form 7 February 2011 Accepted 8 February 2011 Available online 15 February 2011 Keywords: SOFC Methane reforming Energy integration Process control
a b s t r a c t This paper studies the design and operation of energy integrated solid oxide fuel cell (SOFC) systems for in situ hydrogen production and power generation. Two configurations are considered: one where the hot effluent stream from the fuel cell is used directly to provide heat to the endothermic reforming reaction, and another where the hot effluent streams are mixed and combusted in a catalytic burner before the energy integration. A comparative evaluation of the two configurations is presented in terms of their design, open-loop dynamics and their operation under linear multi-loop controllers. © 2011 Elsevier Ltd. All rights reserved.
1. Introduction Fuel cells provide the most efficient path for the conversion of chemical energy into electrical energy (Varigonda & Kamat, 2006). Recognizing the need for efficient energy production systems and the fact that fuel cells are not limited by Carnot efficiencies, there has been an increasing interest in developing fuel cell systems for stationary and transportation applications (see e.g. Bavarian, Soroush, Kevrekidis, & Benziger, 2010; Bhattacharyya & Rengaswamy, 2009; Chaisantikulwat, Diaz-Goano, & Meadows, 2008; Cresswell & Metcalfe, 2006; Kee, Zhu, Sukeshini, & Jackson, 2008; Pukrushpan, Stefanopoulou, & Peng, 2004; Varigonda & Kamat, 2006, for excellent overviews on recent developments and opportunities in modeling and control of fuel cell systems). Hydrogen is the most preferred fuel for a fuel cell. Given the safety issues associated with the storage and transportation of hydrogen, in situ production of hydrogen from a hydrocarbon fuel, coupled with a H2 -fed SOFC, presents a promising approach for power production, especially for stationary fuel cell applications. Two approaches have been proposed to this end. One of the approaches uses an external reformer (e.g. Adams, Thomas, & Barton, 2010; Braun, Klein, & Reindl, 2006; Mueller, Jabbari, Gaynor, & Brouwer, 2007; Murshed, Huang, & Nandakumar, 2007) to generate a hydrogen-rich stream which is then fed to the fuel cell. The other approach uses the principle of internal reforming (e.g.
∗ Corresponding author. Tel.: +1 612 625 8818; fax: +1 612 626 7246. E-mail address: [email protected] (P. Daoutidis). 0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2011.02.006
Al-Qattan & Chmielewski, 2004; Braun et al., 2006), wherein both the reforming and the electrochemical reactions take place in a single unit. The internal reforming approach offers benefits in terms of energy consumption, however at the cost of operating challenges (carbon deposition on electrodes, fewer inputs available for control, etc.). One variant of this approach uses indirect internal reforming, wherein the reforming and the electrochemical compartments are only in thermal contact, thereby avoiding the direct physical contact (Aguiar, Chadwick, & Kershenbaum, 2002). In this paper, we focus on the approach based on external reforming as it offers more opportunities for integration and control design. A power system consisting of an external reformer and a fuel cell shows a lower overall efficiency, since additional energy is required to drive the endothermic reforming reactions. SOFCs are high temperature fuel cells with an operating temperature range between 800 ◦ C and 1000 ◦ C. The hot stream leaving the SOFC shows potential for energy integration by supplying energy to the endothermic reformer, and thereby improving the overall efficiency. Different integration strategies for SOFC energy systems have been proposed (see e.g. Zhang et al., 2010 which reviews most of these strategies). These include hybrid integration strategies with direct thermal coupling (Chan, Ho, & Tian, 2002; Zhang, Li, Li, & Feng, ˙ Santarelli, & Leone, 2006) 2006), indirect thermal coupling (Cale, as well as fuel coupling (Yi, Rao, Brouwer, & Samuelsen, 2005), and advanced integration strategies using gas/humid air/steam turbines (Kandepu et al., 2007; Mueller et al., 2008; Oh & Sun, 2010; Varbanov & Klemes, 2008). Some of these strategies directly (without mixing the anodic and cathodic streams) use the hot SOFC effluent for energy recovery (e.g. Bents, 1987; Sadhukhan,
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Nomenclature Capital letters Universal gas constant R T Temperature F Faraday constant VFC Voltage of single cell Exchange apparent current Io I Current Ri Resistance of each compartment Limiting current IL N Number of cells in the SOFC stack V Output voltage P Output power Cpi Heat capacity of component Volume of each compartment Vi Pi Operating pressure of each process Hirxn Heat of reaction Enthalpy flow Q˙ i U A TLM UF L W
Overall heat transfer coefficient Area Logarithmic mean temperature difference Fuel utilization Length Width
Small letters n Number of transferred electrons pi Partial pressure of each species n˙ i Molar flow rate Mass m ri Reaction rate Thickness Greek letters Number of transferred electrons Charge transfer coefficient ˛ Density ε Void fraction Subscripts FC Fuel cell Open-circuit voltage OCV act Activation ohm Ohmic Concentration conc an Anode el Electrolyte ca Cathode Interconnect int fuel Fuel stream air Air stream SR Steam reformer Catalyst cat
Zhao, Leach, Brandon, & Shah, 2010), while others use a catalytic burner to further recover energy from the unreacted fuel and use this stream for energy integration (e.g. Chan et al., 2002; Mueller et al., 2007). While each of these approaches has obvious advantages/disadvantages in terms of capital and operating costs, compatibility with downstream processes, and environmental impact, they also offer different opportunities and challenges in terms of overall integrated system design, dynamics and control. This is a rather untouched subject in the literature. Motivated by
Fig. 1. Generic design structure of the SOFC energy system.
this, in this paper we compare (and contrast) these two approaches at the design and operational stages. The results of this study can guide the selection of a particular approach. To this end, we consider a generic SOFC energy system with an external methane steam reformer. Energy recovery is achieved by designing a network of heat exchangers (HE). Through open-loop simulations under imposed step changes in the current, the dynamic behavior of each of the configurations is analyzed. Linear multi-loop control strategies are proposed for each case and their operational characteristics are compared through closed-loop simulations. The rest of the paper is organized as follows. The modeling details for the fuel cell and the reformer are presented in Section 2. The selection of operating points for each of these units based on steady state analysis is presented in Section 3. The design, dynamics and control aspects of the energy integrated configurations are analyzed in Sections 4, 5 and 6, respectively. Lastly, Section 7 includes a detailed discussion comparing the two configurations. 2. SOFC energy system with external reformer A generic SOFC energy system with an external methane steam reformer is shown in Fig. 1. As the reformer and the fuel cell operate at a high temperature, three heat transfer units are required to heat the methane steam mixture, fuel cell anode and cathode inlet streams. Furthermore, energy is required for sustained hydrogen production in the endothermic steam reformer. In the following subsections, we present the modeling details for the fuel cell and the reformer which are the main units of the system. 2.1. Solid oxide fuel cell The SOFC stack consists of individual cells connected in series. This is a common approach to scale-up the output voltage, thereby resulting in an increased supply of power (NETL, 2004). A hydrogenrich stream is fed to the anodic compartment of the fuel cell, while air is supplied to the cathodic compartment. The following exothermic redox reactions take place in the fuel cell, thereby generating an electrochemical potential: H2 + O2− → H2 O + 2e− 1 O2 + 2e− → O2− , Cathode: 2 Anode:
◦
H298 = −241.83 kJ/mol
The open-circuit voltage that can be generated by the fuel cell is given by the Nernst equation:
EOCV
RTFC = Eo (TFC ) + ln 2F
pFC,H2 · p0.5 FC,O
2
pFC,H2 O
(1)
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704 20
a
1
a
V P
1693
:S/C=2 :S/C=3 :S/C=4 :S/C=5
0.95
400
0.9 15
CH4
0.8 x
10
P (kW)
N VFC (V)
0.85 300
0.75
200
0.7 0.65
5 100
0.6 0.55
0
b
0
10
20
30
40 I (A)
50
60
70
0 80
0.5 800
850
900
950
1000 T (K)
1050
1100
1150
1200
SR
1450
b
1400
0.5
1350 1300
0.4
:CH
1200
4
0.3
:H O
yi
TFC (K)
1250
1150
2
:CO
2
1100
:CO :H
0.2
2
1050 1000 950
0.1 0
10
20
30
40
50
60
70
80
I (A)
0 800
850
900
Fig. 2. SOFC steady states of the voltage, power and temperature as a function of the current.
where Eo (TFC ) is the temperature dependent standard potential (Li, 2006), pi denotes the partial pressure of species i at the anode, TFC is the temperature of the fuel cell and F is the Faraday constant. However, when connected in a circuit, the output voltage of the fuel cell decreases due to the existence of irreversible losses (called polarizations). The output voltage of the fuel cell delivered to the load is given by the following equation: VFC = EOCV − act − ohm − conc
(2)
where act , ohm , and conc represent the activation, ohmic and concentration polarizations respectively. Activation polarization is described as the energy barrier that should be overcome by the reacting species. It is calculated using the Bulter–Volmer equation (Hamann, Hamnett, & Vielstich, 2007): I = Io ·
exp
˛nF
act
RTFC
− exp −(1 − ˛)
nFact RTFC
(3)
where Io is the apparent exchange current (calculated following Wang & Nehrir, 2007) and ˛ the transfer coefficient. The voltage drop due to the resistance in the flow of electrons and ions can be described by the ohmic polarization which is determined by Ohm’s law as shown below: ohm = I · (Ran + Rel + Rca + Rint )
(4)
where Ri is the resistance of each compartment (calculated from Ferguson, Fiard, & Herbin, 1996) and the subscripts (an, el, ca, int) refer to the anode, the electrolyte, the cathode and the interconnector. Moreover, concentration polarization represents the voltage
950
1000 T (K)
1050
1100
1150
1200
SR
Fig. 3. Steam reformer methane conversion at different S/C ratios and mole fraction steady states as a function of the reformer temperature. Table 1 General parameters. Parameter N V (V) I (A) P (kW) S/C UF
Value 384 272 60.3 16.4 4 0.8
Configuration 1 ˇ1 b2 b3
Parameter
Value
PFC (kPa) PSR (kPa) QF (kW) xCH4 n˙ SR,in (mol/s) n˙ air (mol/s)
101.3 150.0 4.347 0.926 0.225 2.111
Configuration 2 0.09 0.10 0.10
b1 b2 b3
0.10 0.10 0.10
drop due to the concentration gradients between the bulk gases and the triple phase boundary point, the interface between the electrolyte and the electrode where the electrochemical reactions occur. It is calculated from the following equation: conc =
RTFC ln 2F
I L IL − I
(5)
where IL is the limiting current in the fuel cell. The output voltage and the power for the entire SOFC stack are given below: V = N · VFC
(6)
P =I·V
(7)
where N is the number of individual cells in the stack.
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D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
Fig. 4. Energy integrated SOFC system – Configuration 1.
Fig. 5. Energy integrated SOFC system – Configuration 2.
We now move to the material and energy balance equations for the fuel cell. The objective of this study is to analyze the systemwide characteristics of energy integrated SOFC systems. Recent studies have shown, through experimental validation, that lumped parameter models are sufficiently accurate for such systems-level analysis and control (Xi, Varigonda, & Jing, 2010). Numerous other papers also employ lumped parameter models for analysis and control of SOFC systems (see e.g. Mueller et al., 2008; Murshed et al., 2007; Sorrentino, Pianese, & Guezennec, 2008). Therefore, we have used such a lumped parameter model to describe the dynamics of the fuel cell. It is assumed that there is no interaction
between each individual cell. Therefore, the inlet anode and cathode flows are split into N streams. The model assumes constant pressure and physical properties, ideal gas behavior and adiabatic operation. The species and energy balances then take the following form: dnFC,H2 dt
= n˙ FC,H2 ,in − n˙ FC,H2 −
dnFC,H2 O dt
I 2F
= n˙ FC,H2 O,in − n˙ FC,H2 O +
(8) I 2F
(9)
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704 Table 2 Stream composition at the outlet of each major process.
yCH4 yH2 O yCO yCO2 yH2 yO2 yN2 n˙ total (mol/s) n˙ an,total (mol/s) n˙ ca,total (mol/s)
1695
Table 4 UA values for heat exchangers and steam reformer.
SR
SOFC
CB
UAi (W/K)
Configuration 1
Configuration 2
0.011 0.368 0.054 0.081 0.486 – – 0.308 – –
0.011 0.757 0.054 0.081 0.097 0.184 0.816 – 0.308 1.840
0 0.116 0 0.019 0 0.151 0.714 2.336 – –
SR HE1 HE2 HE3 HE4 HE5 HE6 HE7
51.42 24.45 49.05 15.36 2.31 4.63 2.31 1170
67.10 8.09 104.80 11.62 108.10 3.23 58.37 3.91
Table 5 MCp values used in the case study. Table 3 Physical properties of each component. Component
i (kg/m3 )
Cpi (J/mol/K)
CH4 H2 O (g) H2 O (l) CO CO2 H2 O2 N2
0.717 0.804 1000 1.250 1.977 0.089 1.429 1.251
58.381 38.459 75.327 31.374 49.561 30.236 32.582 31.394
dnFC,O2 dt
= n˙ FC,O2 ,in − n˙ FC,O2 −
I 4F
(10)
1 dTFC = · (Q˙ fuel,in − Q˙ fuel,out + Q˙ air,in SOFC CpSOFC VSOFC dt rxn − Q˙ air,out − n˙ reacted · HFC − I · VFC ) H
(11)
2
n˙ reacted = H 2
Q˙ i =
I 2F
(12)
n˙ j Cpj (Ti − Tref )
(13)
j
where the subscripts (i) and (j) refer to the corresponding streams and components while (FC) denotes the fuel cell and Q˙ i represents the enthalpy flow. Eq. (12) represents Faraday’s law.
MCpi (J/K)
Configuration 1
Configuration 2
SRH F CB HE1,HOT HE2,HOT HE3,HOT HE4,HOT HE5,HOT HE6,HOT HE7,HOT HE1,COLD HE2,COLD HE3,COLD HE4,COLD HE5,COLD HE6,COLD HE7,COLD
26.45 35.31 – 2.61 0.19 2.61 2.61 5.84 5.84 26.46 857.89 3.52 3.52 1.30 4.74 5.36 35.31
36.54 – 36.54 36.54 36.54 36.54 36.54 36.54 36.54 36.54 857.89 3.52 4.74 26.48 5.36 26.48 0.86
Table 6 Detailed parameters used in the case study. Parameter
Value
Parameter
Value
L (m) W (m) A (cm2 ) SOFC (kg/m3 ) CpSOFC (J/(kg K)) an (mm) el (m) ca (m)
0.1 0.1 100 4200 640 1 8 50
VSR (L) cat (kg/m3 ) ε Cpcat (J/(kg K)) rxn HFC (kJ/mol) H1rxn (kJ/mol) H2rxn (kJ/mol) int (mm)
3.3 2335 0.4 444 −241.83 206.10 −41.15 1
two catalytic reactions: Reforming reaction:
CH4 + H2 O CO + 3H2 ,
◦
2.2. Methane steam reformer
H298 = +206.10 kJ/mol
A methane steam reformer is used to convert methane into a hydrogen-rich stream. This is accomplished through the following
Shift reaction:
CO + H2 O CO2 + H2 ,
◦
H298 = −41.15 kJ/mol
Table 7 Stream temperatures for each configuration. Configuration 1
Configuration 2
Temperature
(K)
Temperature
(K)
Temperature
(K)
Temperature
(K)
TCH4 ,in TH2 O,in Tair,in THE1C THE1H THE2C THE2H THE3C THE3H THE4C THE5C,in THE4H
298.0 298.0 298.0 373.0 308.2 373.4 383.0 669.3 481.7 669.3 669.3 831.2
THE5H THE5C TSR TSRH TSRH,out TFC THE6H THE6C THE7H THE7C TF TSRH,in
1001.4 822.9 932.3 981.5 997.6 1162.6 1125.3 973.0 306.8 907.9 973.1 1143.1
TCH4 ,in TH2 O,in Tair,in THE1C THE1H THE2C THE2H THE3C THE3H THE4C THE4H THE5H
298.0 298.0 298.0 373.1 457.3 515.7 470.6 823.0 925.6 729.0 586.8 1087.1
THE5C TSR TSRH TSRH,out TFC THE6H THE6C THE7H THE7C TCB,in THE3C,in TCA,in TCB
973.0 932.3 950.1 963.8 1162.6 1092.9 1048.0 579.2 520.0 1143.1 516.9 973.0 1343.7
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D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
Table 8 Controller parameters for both configurations (K: controller gain, I : integral time constant). −1
−3
4 × 10 5 × 10−2 1 × 10−2 5 × 10−4 20
KFC (K ) KSR (K−1 ) KUF (mol/s) KCa (K−1 ) KF (W/K)
I,FC (s) I,SR (s) I,UF (s) I,Ca (s) I,F (s)
and ideal gas behavior, the species mass balances take the form: dnSR,CH4 dt
200 100 10 80 80
dnSR,H2 O dt dnSR,CO2 dt
Note that even though the first reaction is endothermic and the second is exothermic, the net system of reactions is endothermic, requiring external energy input for sustained hydrogen production. Here, we model the reformer as a well-mixed reactor with a heating jacket. Assuming constant pressure, constant physical properties
a
955
= n˙ SR,CH4 ,in − n˙ SR,CH4 − mcat · r1
(14)
= n˙ SR,H2 O,in − n˙ SR,H2 O − mcat · (r1 + r2 )
(15)
= n˙ SR,CO2 ,in − n˙ SR,CO2 + mcat · r2
(16)
dnSR,CO = n˙ SR,CO,in − n˙ SR,CO + mcat · (r1 − r2 ) dt dnSR,H2 dt
(17)
= n˙ SR,H2 ,in − n˙ SR,H2 + mcat · (3r1 + r2 )
(18)
b 1195 1190
950
1185
TFC (K)
TSR (K)
945
940
1180
1175
935 1170 930
1165 Configuration 1 Configuration 2
925
0
20
40
60
80
Configuration 1 Configuration 2 1160
100
0
20
40
1000
d
80
100
0.835
0.83
990
0.825
985
0.82
UF
995
980
0.815
975
0.81
970
0.805 Configuration 1 Configuration 2
965
0
20
40
60
80
Configuration 1 Configuration 2
100
0.8
0
20
40
time (min)
e
60
time (min)
1344
1342
1340
TCB (K)
TCA,in (K)
c
60
time (min)
time (min)
1338
1336
1334
1332
0
20
40
60
80
100
time (min) Fig. 6. Open-loop simulation under a small step in the current from 60.3 A to 62 A.
80
100
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
a
1150
b
1697
1450
1400
1100
1350
TFC (K)
TSR (K)
1050
1000
1300
1250 950 1200 Configuration 1 Configuration 2 900
0
20
40
60
80
Configuration 1 Configuration 2
100
0
20
40
60
time (min) 1400
d
0.98
1300
0.96
1250
0.94
1200
0.92
1150
0.9
1100
0.88
1050
0.86
1000
0.84
950 900
0.82
Configuration 1 Configuration 2 0
20
40
60
80
100
0.8
Configuration 1 Configuration 2 0
20
40
time (min)
e
100
1
1350
UF
TCA,in (K)
c
80
time (min)
60
80
100
time (min)
1400
TCB (K)
1350
1300
1250
0
20
40
60
80
100
time (min) Fig. 7. Open-loop simulation under a large step in the current from 60.3 A to 70 A.
where mcat is the mass of the catalyst and ri is the rate of each reaction. The reaction rate expressions are obtained based on a Langmuir–Hinshelwood reaction mechanism as proposed in Xu and Froment (1989). The energy balances for the reactor and the jacket have the following form: (Q˙ fuel,in − Q˙ fuel,out − mcat (r1 H1rxn + r2 H2rxn ) + UASR TLM ) dTSR = (εg Cpg + (1 − ε)cat Cpcat )VSR dt (19) (Q˙ SR,HOT,in − Q˙ SR,HOT,out − UASR TLM ) dTSR,HOT = MCpSR,HOT dt
(20)
where the subscripts (g) and (cat) refer to the gas and catalyst properties, VSR is the volume of the steam reformer, ε is the void fraction,
UASR is the product of the overall heat transfer coefficient and the heat exchange area and TLM is the mean logarithmic temperature difference. 3. Steady state analysis In what follows, a steady state analysis is performed for the SOFC and the reformer in order to select the operating points for these units. This will provide a starting point for the design of the integrated SOFC energy system. 3.1. Solid oxide fuel cell The steady state values of the output voltage, output power and the cell temperature as a function of the current are shown in Fig.
1698
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
a
1168 Configuration 1 Configuration 2 set point
1167
b
936 Configuration 1 Configuration 2 set point
935
c
0.825 Configuration 1 Configuration 2 set point
1165
933
1164
0.815
UF
934
TSR (K)
TFC (K)
0.82 1166
932
1163
931
1162
930
0.81
0.805
1161 0
20
40
60
80
929
100
0
20
time (min)
60
80
0.8
100
0.11 Configuration 1 Configuration 2
e
Configuration 1 Configuration 2
f
0.14
b3
b2
0.12
0.07 0.1 0.06
0.06
0.04
0.04
60
80
100
80
100
0.233 Configuration 1 Configuration 2
0.23 0.229 0.228 0.227
0.08
0.05
60
0.231
0.08
40
40
0.232
0.16
0.09
20
20
time (min)
0.2 0.18
0.1
0
0
time (min)
n fuel (mol/s)
d
40
0.226 0.225 0
20
time (min)
40
60
80
100
0.224 0
20
40
time (min)
60
80
100
time (hr)
Fig. 8. Closed-loop responses for both configurations under a current step increase from 60.3 A to 62 A.
2. It is desirable to operate the SOFC close to the highest power production point with high fuel utilization (UF ). The fuel utilization represents the fraction of the incoming hydrogen that is electrochemically converted in the fuel cell. We selected the operating point corresponding to a current of 60.3 A. At this point, the power delivered by the fuel cell is 16.4 kW (99% of the maximum power), the output voltage is 272 V and the fuel cell temperature is 1162.6 K.
3.2. Methane steam reformer It is desired to operate the steam reformer at a temperature where a stream rich in hydrogen is produced with a high methane conversion (Mueller et al., 2008). We first explored the effect of the steam-to-carbon (S/C) ratio on methane conversion. Fig. 3(a) shows the variation of methane conversion with respect to reformer temperature for various values of S/C ratios. High S/C values show enhanced methane conversion, however, at the cost of additional heating load. We selected S/C = 4 for this study. Fig. 3(b) shows the steady state profiles for various species at the outlet of reformer as a function of operating temperature. Note that the hydrogen mole fraction shows a maximum for a reformer temperature close to 980 K. We selected the operating point to be 932.3 K. For this state, the methane conversion is 92.6% and the reformate gas contains approximately 49% hydrogen.
4. Energy integration The system in Fig. 1 requires four external energy inputs. On the other hand, the SOFC exit streams leave at a high temperature thus, showing a potential for energy integration. Motivated by the previously proposed integration strategies (e.g. Bents, 1987; Chan et al., 2002; Mueller et al., 2007; Sadhukhan et al., 2010), two integration alternatives were considered: in the first, the hot anodic and cathodic exit streams from the fuel cell are used directly as two hot streams, while in the other, the anodic and cathodic streams are mixed together and are combusted in a catalytic burner to generate a single hot stream.
As the first step in the design of the energy integrated systems, we used pinch analysis (Linnhoff & Hindmarsh, 1983). Pinch analysis indicated that external hot utility is required for the first system while the second system is self sustaining. Pinch analysis also indicated the absence of a pinch point for both the cases, thus allowing for a variety of possible design alternatives (Kemp, 2007). • Design of integrated configuration based on alternative 1: Most of the existing configurations (e.g. Bents, 1987; Sadhukhan et al., 2010) following this alternative focus only on the fuel cell and do not incorporate any fuel processing unit. In this study we incorporated such a fuel processing unit and we designed the heat exchanger network with the objective of achieving the minimum external utility predicted by the pinch analysis. The resulting integrated configuration is depicted in Fig. 4. The cathode outlet stream provides energy to the steam reformer (SR) and then it is split into two streams. One preheats the air in HE7 , while the other supplies energy for preheating methane in HE4 , water in HE1 and steam in HE3 . The anode outlet stream covers the heating requirement of the anode inlet in HE6 . Then, it preheats the fuel mixture to the required reformer inlet temperature in HE5 and then supplies the required energy for steam generation in HE2 . An external hot utility is supplied to the furnace in order to heat the air to the required temperature. The resulting energy requirement (see Table 1) in this configuration is exactly the one predicted by the pinch analysis. • Design of integrated configuration based on alternative 2: In this case, we used the integrated configuration proposed in Mueller et al. (2007) as a basis and achieved further recovery and recycle of energy, specifically through the addition of heat exchangers (1–3), (5) and (7) as shown in Fig. 5. The anodic and cathodic outlet streams are fed to a catalytic burner, where the complete combustion of methane, carbon monoxide and unreacted hydrogen takes place. The required air is supplied by the SOFC cathodic stream. The high temperature stream leaving the burner heats the air in HE6 and provides energy to the anode inlet stream in HE5 . Then, it passes through the steam reformer (SR) in order to cover its endothermic demand. Leaving the reformer, the hot
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
a
982 Configuration 1 Configuration 2 set point
980
Tca,in (K)
978
976
1699
first configuration, while bypasses b1 –b3 are placed in the second configuration for the same reason. Tables 1 and 3–6 present the parameters that have been used for both configurations. Note that the same operating points (as selected in the previous section) are used for the fuel cell and the reformer. The composition and the total molar flow rate at the outlet of each major process are tabulated in Table 2. The temperatures at each stream arising from the energy integration are tabulated in Table 7. 5. Open-loop analysis
974
We next studied the dynamic response of each of these configurations. We considered a scenario where current changes are imposed which may be caused by power changes.
972
970
5.1. Small step increase in the current 968
0
20
40
60
80
100
time (min)
b
4360 4350 4340
QEH (W)
4330 4320 4310 4300 4290 4280 4270
0
20
40
60
80
100
time (min)
c
0.125
0.12
b1
0.115
5.2. Large step increase in the current
0.11
0.105
0.1
0.095
Fig. 6 shows the response of key variables for a step in the current from 60.3 A to 62 A. The increase in current causes an instantaneous increase in the amount of hydrogen reacted in the fuel cell (Eq. (12)). This is reflected in the corresponding increase in the fuel utilization and the decrease in the burner temperature (less fuel for combustion) for the second configuration. The increased hydrogen consumption also results in increased fuel cell temperature, however over a longer horizon. Yet, the impact of the disturbance is different for the two configurations. The rise in the reformer temperature is much larger for configuration 1 than configuration 2. This is due to the fact that the inlet temperature for configuration 1 is higher than the nominal value, while for the second configuration, it is lower than the nominal value. The responses of the reformer temperature and the cathode inlet temperature show striking differences between the two configurations. In configuration 1, the increase in the fuel cell temperature increases the reformer temperature and the cathode inlet temperature in the same fashion. In the case of configuration 2, the increased current triggers opposing forces in the burner (increase the inlet temperature and decrease the temperature rise) resulting in an inverse response. For the magnitude of current change considered here, the net effect is the reduction in burner temperature below the nominal value. This drives similar responses in the reformer temperature and cathode inlet temperature. Thus configuration 2 is less sensitive to the current disturbance than configuration 1.
0
20
40
60
80
100
time (min) Fig. 9. Closed-loop responses for both configurations under a current step increase from 60.3 A to 62 A.
stream heats the fuel mixture to the temperature required by the reformer in HE3 and then preheats the air stream in HE4 . Afterwards, it provides energy for both the preheating of the methane in HE7 and the steam generation in HE2 and HE1 . Both configurations use seven process-to-process heat exchangers. While the first configuration uses a furnace (external energy source), the other uses a combustion unit (internal energy source). Bypasses b2 and b3 are placed to improve the controllability of the
We now subject the system to a large disturbance in current. Fig. 7 shows the open-loop response of key variables for a step in the current from 60.3 A to 70 A. The responses for the first configuration indicate an open-loop instability triggered by the change in the operating region of the steam reformer. More precisely, the increase in the current causes an increase in the reformer temperature. This increases the hydrogen production rate supplying more fuel to the fuel cell. However, when the reformer temperature reaches to a point beyond the maximum hydrogen production (see Fig. 3(b)), any further increase in reformer temperature decreases hydrogen production and hence, reduces the fuel supply to the cell. This drives the cell towards fuel starvation conditions, resulting in higher temperatures. In the case of the second configuration, the system reaches a new steady state with responses similar to the case of a small current step. However, in this case, the catalytic burner temperature is higher than the nominal value, resulting in similar higher value in the reformer temperature. Note that the temperature increase in the steam reformer is quite small to trigger any instability. This again shows the ability of this configuration to maintain open-loop stability.
1700
D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
a
1200
938
b
Configuration 1 Configuration 2 set point
1195
Configuration 1 Configuration 2 set point
936
1190
c
934 0.88 932
UF
TSR (K)
TFC (K)
1180
0.86
930
1175
0.84 928
1170
0.82
926
1165
0
20
40
60 time (min)
80
924
100
e
0.12
d
Configuration 1 Configuration 2 set point
0.9
1185
1160
0.92
Configuration 1 Configuration 2
0
20
40
60 time (min)
80
0.4 Configuration 1 Configuration 2
0.35
0.1
0.8
100
f
nfuel (mol/s)
b2
b3
0.15 0.1
20
40
60 time (min)
80
100
80
100
0.27 Configuration 1 Configuration 2
0.25 0.245 0.24 0.235
0.02
−0.02 0
60 time (min)
0.255
0.2
0
40
0.26
0.3 0.25
0.04
20
0.265
0.08 0.06
0
0.05
0.23
0
0.225
−0.05 0
20
40
60 time (min)
80
100
0.22 0
20
40
60 time (hr)
80
100
Fig. 10. Closed-loop responses for both configurations under a current step increase from 60.3 A to 70 A.
a
1010 Configuration 1 Configuration 2 set point
1000
b
4450 4400 4350 4300
QEH (W)
980
4250 4200 4150
970
4100 4050
960
4000
950
0
20
40
60
80
100
3950
0
20
40
time (min)
c
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time (min) Fig. 11. Closed-loop responses for both configurations under a current step increase from 60.3 A to 70 A.
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D. Georgis et al. / Computers and Chemical Engineering 35 (2011) 1691–1704
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Fig. 12. Closed-loop responses under two current changes.
Remark 5.1. Both open-loop simulation scenarios discussed above were performed for an increase in the current drawn from the SOFC. In the case of a decrease in the applied current, both configurations give stable open-loop responses even for large steps in the current (plots not included in the paper). 6. Control design 6.1. Closed-loop analysis In this paper we focus on the control problem only on the chemical side of the SOFC energy system. As chemical side of a SOFC system we refer to the part of the SOFC system which includes only the electrochemical phenomena taking place inside the SOFC, without including any power conditioning unit after the SOFC. The corresponding control objectives considered involve: 1. SOFC temperature: The SOFC is an exothermic system. An increase in the SOFC temperature shows potential for material damages while a decrease drops the ionic conductivity of the electrolyte. Thus, there is a need to regulate the SOFC temperature. In this case, the SOFC temperature is controlled by manipulating the air inlet flow rate via the bypass b2 . 2. Reformer temperature: The reformer temperature affects the hydrogen production and hence, the stability, the performance, and the power production level of the entire energy system. We therefore control the reformer temperature through the jacket stream flow rate via the bypass b3 .
3. Fuel utilization: High fuel utilization values (>0.95) lead to fuel starvation which can damage the anode (Mueller et al., 2007). Also, low fuel utilization values reflect inefficient operation. Motivated by this, fuel utilization is controlled in the system by manipulating the fuel inlet flow rate (n˙ fuel ). 4. Cathode inlet temperature: In order to maintain a desired operating point of the SOFC (especially the SOFC temperature), the cathode inlet temperature is also controlled. In the first configuration, it is controlled by manipulating the furnace heat duty while in the other configuration, it is controlled via the bypass (b1 ). Proportional integral (PI) controllers were implemented to realize the above control strategy. Initially, the Ziegler–Nicholds tuning technique was followed with the ultimate gain (Ku ) and the ultimate period (Pu ) obtained through the autotuning (ATV) method (Luyben, 1990). The controller parameters calculated from the above procedure resulted in aggressive control action leading to unstable closed-loop behavior (plots not included in the paper). Therefore, we detuned the controllers to get a smoother and stable closed-loop response as well as similar settling times. The parameters obtained are presented in Table 8. The same controller parameters were used in both the configurations, except for the cathode inlet temperature control loop. In this loop, the same time constant but a different controller gain has been used since the manipulated variable is different in the two configurations.
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time (min) Fig. 13. Closed-loop responses under two current changes.
6.2. Closed-loop simulations We compared the closed-loop performance of both configurations under a small and a large current step increase (similar to the steps applied in Sections 5.1 and 5.2). We also identified the operating ranges for each of the configurations. Note that the operating range here is defined as the range of achievable current for which no bypasses are saturated. 6.2.1. Small step increase in current A step change from 60.3 A to 62 A in the current is applied and the evolution of the controlled variables along with their manipulated variables is presented in Figs. 8 and 9. As the step in the current is applied, hydrogen consumption in the fuel cell increases, thereby causing an increase in the fuel utilization. The fuel utilization controller increases the fuel flow into the system, in order to increase the hydrogen production and hence, to decrease and bring the fuel utilization back to the set point. The increasing current also causes the SOFC temperature to rise, therefore the SOFC temperature controller reduces the bypass ratio to reduce the SOFC temperature. The increase in the fuel inlet flow leads to higher energy demand required by the reformer. According to this, we expect the controller to decrease the bypass on the reformer hot stream in order to provide more energy to the reformer. This is the case for the first configuration. However, the controller corresponding to the second configuration increases the bypass ratio. This action reveals a surplus of energy in the reformer jacket-side inlet stream compared to its nominal value. This contrasting behavior comes from the dif-
ferent types of heating streams used in the reformer jacket. In the first configuration, the cathode exit stream (consisting of oxygen and nitrogen) supplies the energy to the reformer. The flow rate of this stream remains almost constant (slight decrease in oxygen flow occurs due to electrochemical reactions) during the operation. Thus the increased heating demand of the reformer causes a decrease in the bypass ratio b3 . On the other hand, the other configuration uses a mixture of anodic and cathodic streams in the reformer jacket. The flow rate of this stream changes almost in accordance with the change in the reformer inlet flow. The surplus of energy comes from the increased burner temperature. The second configuration exhibits higher overshoots compared to the first configuration. This difference again comes from the different nature of the heating streams used in the reformer jacket. The cathode exit stream (with controlled temperature) introduces a negligible disturbance into the reformer in the first configuration, as compared to the burner temperature (with uncontrolled temperature) in the second configuration.
6.2.2. Large step increase in current In Section 5.2 we showed that the open-loop response of the first configuration is driven to instability while the second configuration remains stable under a large step increase in the current. In this section, we perform a closed-loop simulation of the above configurations under the same large disturbance (60.3–70 A) and we show the capability of the proposed control scheme to stabilize the open-loop unstable system.
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Table 9 Comparison of the two configurations. Characteristic
Configuration 1
Configuration 2
Design of integrated system Open-loop dynamics
No pinch – extra energy is required Stable (small disturbance) Unstable (large disturbance) Smaller overshoots Broader (bypass saturated for current increase) No combustion No mixing of SOFC outlet streams (promising for further integration with a CO2 capture unit)
No pinch – surplus of energy Stable (small disturbance) Stable (large disturbance) Larger overshoots Narrower (bypass saturated for current increase and decrease) Combustion unit (potential for NOx) Mixing of SOFC outlet streams
Closed-loop dynamics Operational Range Environmental Impact
According to the closed-loop responses (Figs. 10 and 11), the first configuration remains stable under the imposed large disturbance. Stability is achieved since the reformer temperature controller keeps the operating temperature away from the maximum hydrogen production point (see Fig. 3(b)). Note that both the SOFC and reformer bypasses are saturated resulting in small offsets in the SOFC and reformer temperatures. The second configuration remains stable even if the temperature bypass is saturated causing an offset in the SOFC temperature. 6.2.3. Operating range investigation In this section, we impose positive and negative changes in current (Fig. 12(g)) in order to identify the operating range for both the configurations. The controlled and corresponding manipulated variables are presented in Figs. 12 and 13. The first configuration shows a broader operating range (I ≤ 66.5 A) compared to the second configuration (58 A ≤ I < 66.5 A). During the first step increase in the current, the first configuration is very close to saturation while the second configuration shows a bypass (b2 ) saturation (Fig. 12(d)) resulting in an offset in the SOFC temperature. As the current decreases there is no operational and controllability limitation for the first configuration since less energy is required, and hence the controllers increase the bypasses. However, in the second configuration there is a decrease in the reformer bypass (b3 ), leading to saturation (Fig. 12(e)). Note that under saturation conditions the systems remain operable (but not controllable) showing offsets from the set point. 7. Discussion Let us now compile the various similarities and contrasting features exhibited by these two configurations. Table 9 summarizes and compares the major characteristics of these configurations. • Design of integrated system: Both configurations do not show a pinch point. Additional energy is required (and supplied via a furnace) in the first configuration while energy is available for further integration in the second configuration. Both configurations use seven process-to-process heat exchangers. • Open-loop dynamics: Both configurations are stable for small disturbances in current. However, the first configuration is driven to instability for a large disturbance in current, whereas the second configuration remains stable. • Closed-loop dynamics: The proposed control scheme is capable of stabilizing the open-loop unstable configuration. Additionally, the first configuration shows smaller overshoots compared to the second configuration (for the same controller parameters). • Operational range: The first configuration has a broader operational range compared to the second configuration. More precisely, the first configuration shows a limitation (due to bypass saturation) at higher current, while the second configuration shows limitations for both the increase and the decrease in the current.
• Environmental impact: The first configuration is less amenable to NOx production (due to the absence of a combustion unit). Moreover, this configuration looks promising for further integration with a carbon dioxide capture unit as the anodic (CH4 , H2 O, CO2 , CO and H2 ) stream is not mixed with the cathodic (O2 and N2 ) stream (Adams et al., 2010). 8. Conclusions In this paper we studied two energy integrated configurations comprising a SOFC, a methane steam reformer and energy transfer units. In the first configuration, the SOFC outlet streams were used directly for energy integration, while in the second, these streams were fed to a catalytic burner for more energy recovery and recycle. The first configuration was shown to become unstable for large changes in current. This is the result of a positive energy feedback loop which results in high temperatures and fuel starvation. A linear multi-loop control strategy was developed for the entire integrated system. It was shown to be successful in suppressing the instability in the first configuration and to provide satisfactory closed-loop responses for a broad range of positive and negative changes in the current. Acknowledgements Partial financial support for this work from the Abu DhabiMinnesota Institute for Research Excellence, National Science Foundation Grant CBET-0756363 and the ACS-PRF is gratefully acknowledged. References Adams, I., Thomas, A., & Barton, P. (2010). High-efficiency power production from natural gas with carbon capture. Journal of Power Sources, 195, 1971–1983. Aguiar, P., Chadwick, D., & Kershenbaum, L. (2002). Modelling of an indirect internal reforming solid oxide fuel cell. Chemical Engineering Science, 57, 1665–1677. Al-Qattan, A., & Chmielewski, D. (2004). Distributed feed design for SOFCs with internal reforming. Journal of the Electrochemical Society, 151, A1891. Bavarian, M., Soroush, M., Kevrekidis, I., & Benziger, J. (2010). Mathematical modeling, steady-state and dynamic behavior, and control of fuel cells: A review. Industrial & Engineering Chemistry Research, 49, 7922–7950. Bents, D. (1987). High temperature solid oxide regenerative fuel cell for solar photovoltaic energy storage. In Proceedings of the 22nd intersociety energy conversion engineering conference AIAA, (pp. 808–817). Bhattacharyya, D., & Rengaswamy, R. (2009). A review of solid oxide fuel cell (SOFC) dynamic models. Industrial & Engineering Chemistry Research, 48, 6068–6086. Braun, R., Klein, S., & Reindl, D. (2006). Evaluation of system configurations for solid oxide fuel cell-based micro-combined heat and power generators in residential applications. Journal of Power Sources, 158, 1290–1305. ˙ M., Santarelli, M., & Leone, P. (2006). Computer experimental analysis of the Cale, CHP performance of a 100 kWe SOFC field unit by a factorial design. Journal of Power Sources, 156, 400–413. Chaisantikulwat, A., Diaz-Goano, C., & Meadows, E. (2008). Dynamic modelling and control of planar anode-supported solid oxide fuel cell. Computers & Chemical Engineering, 32, 2365–2381. Chan, S., Ho, H., & Tian, Y. (2002). Modelling of simple hybrid solid oxide fuel cell and gas turbine power plant. Journal of Power Sources, 109, 111–120. Cresswell, D., & Metcalfe, I. (2006). Energy integration strategies for solid oxide fuel cell systems. Solid State Ionics, 177, 1905–1910. Ferguson, J., Fiard, J., & Herbin, R. (1996). Three-dimensional numerical simulation for various geometries of solid oxide fuel cells. Journal of Power Sources, 58, 109–122.
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