GT Hybrid Power Generation System

Article pubs.acs.org/IECR

Design and Control of an SOFC/GT Hybrid Power Generation System with Low Carbon Emissions Wei Wu,* Shin-An Chen, and Ying-Chuan Chiu Department of Chemical Engineering, National Cheng Kung University, Tainan 70101, Taiwan ABSTRACT: The process design, simulation, and control of a solid oxide fuel cell (SOFC)/gas turbine (GT) hybrid power generation system combined with a compressed-fuel processing unit (CFPU) are presented. Given that CO2 is the input of the CFPU, the net CO2 emissions of this hybrid power system are suppressed under 324.2 g of CO2/kWh. Using the combined heat and power (CHP) approach, the hybrid power efficiency increases from 33% to 50%. Based on a single-input−single-output (SISO) control configuration, an inferential power control strategy using a static inferential model is implemented to improve the accuracy of the power estimation and effectively regulates the SOFC power output.

1. INTRODUCTION The control of greenhouse gas emissions is probably the most challenging environmental policy issue today. Although carbon capture and storage (CCS) technologies are integrated into energy systems to reduce CO2 emissions, they require additional energy from external sources. To reduce the resulting energy penalty, process design, simulation, and optimization become more important such as for a natural-gas-based hydrogen plant that uses gas-separation membranes for CO2 capture,1 a naturalgas combined-cycle power plant that includes a precombustion cycle to separate out CO2 from flue gases,2 and a stand-alone energy system that uses the precombustion design to replace the external energy demand and reduce CO2 production in a reforming process.3 The solid oxide fuel cell (SOFC) is considered to be the most efficient device for producing electricity directly from the oxidation of a fuel. Advantages of this class of fuel cells include high efficiency, long-term stability, low emissions, and relatively low costs.4 In addition, the fuel flexibility of SOFCs is usually higher than those of other types of fuel cells, such as protonexchange-membrane fuel cells (PEMFCs), but carbon emissions are inevitable. Because the operating temperature of the SOFC is very high, a combined heat and power (CHP) system is connected to it to recover waste heat and develop secondary power generation. It has been verified that hydrogen-based SOFC systems do not provide efficiency performance advantages over methane-fueled SOFC systems,5 and the technoeconomic performance of a methane-fueled SOFC combined with a CHP system was successfully achieved.6 Recently, a hybrid power plant consisting of an SOFC system coupled with a gas turbine (GT) has been considered a promising technology to improve overall efficiency and effectively reduce pollutants.7,8 The modeling and operation of SOFC/GT hybrid power plants with regard to power efficiency were developed in the Aspen Plus environment,9,10 and the results indicated that the efficiency of the integrated system can be significantly improved if the fuel cell is operated under pressurized conditions and the heat integration method is taken into consideration. Moreover, SOFC/GT hybrid dynamic models and their control implementation were developed in a Matlab/Simulink environment.11 Buonomano et al.12 provided a comprehensive review of the possible layout © XXXX American Chemical Society

configurations of SOFC/GT hybrid power plants using different approaches, such as numerical simulations, experimental analyses, and thermoeconomic optimizations. The dry reforming of methane (DRM) is a potential process for producing syngas with low CO2 emissions because CO2 is treated as one of the reactants. In the past few years, the integrated processes of steam methane reforming (SMR) with DRM have been systematically evaluated.13−15 The results showed that the combined process generates much less CO2 than the conventional SMR process. Recently, a nonlinear feedback control was implemented to control a combined SMR and DRM process in which almost net-zero CO2 emissions were guaranteed.16 Because the CO present in syngas is not harmful to SOFCs and CO is an effective fuel, Suwanwarangkul et al.17 showed that a syngas-fueled SOFC can improve the carbon formation compared to a methanol-fueled SOFC. For an SOFC using external reforming, a combined DRM with SOFC (DRM-SOFC) process not only exhibits a higher efficiency performance than an SMR-SOFC process, but also generates lower CO2 emissions than the SMR-SOFC process.18 However, the DRM process should be operated at temperatures greater than 800 °C, so the external energy consumption from sources or products of the processes is quite large. In this article, an SOFC/GT hybrid power system combined with a compressed-fuel processing unit (CFPU) is designed using Aspen Plus simulator. The CFPU not only consumes CO2 from exhaust gas but also produces pressurized syngas as the fuel of the SOFC system. To meet the external energy demand of the CFPU and carry out cogeneration, a new CHP design is used that combines a post-SOFC burner, a waste-heat recovery scheme, and a series of GTs to improve the total electrical efficiency. The hybrid power generation performance is sensitive to the pressurized and high-temperature flue gas, so the traditional control method is employed to regulate the SOFC power output in the presence of unknown perturbations. Received: May 27, 2015 Revised: December 28, 2015 Accepted: January 15, 2016

A

DOI: 10.1021/acs.iecr.5b01961 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Appendix section A. According to recent studies,3,20 a simplified reaction network of DRM is given by

2. PROCESS DESIGN For a class of SOFC/GT hybrid power generation systems, the combined heat and power (CHP) process in Figure 1 plays a role

CO2 + CH4 ↔ 2CO + 2H 2 (rCO2R ), 0 ΔH298 = 247.2 kJ·mol−1

(4)

. CH4 + H 2O ↔ CO + 3H 2 ,

0 ΔH298 = 206.2 kJ·mol−1

(5)

. CO2 + H 2 ↔ CO + H 2O,

0 ΔH298 = 41.2 kJ·mol−1

(6)

. Figure 1. Schematic of an SOFC/GT hybrid power generation system.

2CO ↔ CO2 + C, CH4 → C + 2H 2 ,

(8)

Notably, eq 4 is the main reaction of the DRM, and eqs 5−8 are the accompanying reactions. The DRM is a useful approach for suppressing net CO2 emissions if the operating temperature is higher than 900 °C. Similarly, the Aspen module RPLUG is used to model the DRM reactor where the corresponding rate equation is simplified as shown in Appendix section A. In Figure 2, a combination of SMR and DRM is developed as a compressed-fuel processing unit (CFPU). Three feed flows (CH4,in, H2Oin, CO2,in) are mixed in a mixer. The first heater (HU1) with heating rate Q1 is used to adjust the inlet temperature of the SMR reactor, TSMR. A condenser described by a cooler (CU) with cooling rate QC is added to adjust the outlet temperature of the SMR reactor from 700 to 25 °C, which causes the high-temperature steam to condense into liquid water. A separator is connected to remove the water in the outlet stream of the SMR reactor, and then the dry stream is compressed from 1 to 10 atm by the fuel compressor (Compr1) with an energy penalty of Q2. The compressed stream is heated by the second heater (HU2) with heating rate Q3 to meet the inlet temperature requirements of the DRM, TDRM. Finally, heating rate Q4 is added to maintain a constant temperature in the DRM reactor. Notably, the thermodynamic properties of some species are specified according to the Peng−Robinson equation of state, and the specifications of major process units are listed in Table 1. Assuming that perfect heat recovery can be achieved by a heatexchanger network, the net energy demand Qnet is given by ∑4i=1Qi − QC. Moreover, Figure 3 shows that the ratio of H2 to CO in the product of the CFPU is affected by adjusting the feed flow rate of CH4 or CO2 if the feed flow rate of H2O is fixed at 10 kmol/h. In Figure 3a, the syngas yield increases with

(1)

. CO + H 2O ↔ CO2 + H 2 (rSMR,2), (2)

. CH4 + 2H 2O ↔ CO2 + 4H 2 (rSMR,3), 0 ΔH298 = 165.0 kJ·mol−1

0 ΔH298 = 75.6 kJ·mol−1

.

CH4 + H 2O ↔ CO + 3H 2 (rSMR,1),

0 ΔH298 = −41.2 kJ·mol−1

(7)

.

in supplying the heat for fuel processing and simultaneously generating electricity. In our approach, the compressed-fuel processing unit (CFPU), by consuming greenhouse gases (CH4 and CO2), is intended to produce pressurized syngas that is fed into the anode side of the SOFC. On the other side, air is preheated and compressed as the feed of the cathode site of the SOFC. Moreover, the process modeling, design, and analysis are addressed as follows. 2.1. Compressed-Fuel Processing Unit. A fuel processing unit is implemented to produce syngas from natural gas; the fuel is considered to be pure methane in this study. Both reforming processes, SMR and DRM, are integrated to produce syngas, where the SMR reactor is considered to be a plug-flow reactor in which three exothermic/endothermic reactions occur

0 ΔH298 = 206.2 kJ·mol−1

0 ΔH298 = − 171 kJ ·mol−1

(3)

. Notably, the kinetics are formulated by a Langmuir− Hinshelwood−Hougen−Watson- (LHHW-) type kinetic rate expressions. The Aspen module RPLUG is used to model the SMR reactor with the kinetic model for the main reactions in eqs 1−3. The corresponding rate equations are listed in

Figure 2. Schematic of a compressed-fuel processing unit. B


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Industrial & Engineering Chemistry Research Table 1. Specifications for the CFPU Aspen model

equipment/configuration SMR design III: adiabatic reactor

RPLUG

DMR; nonisothermal unit and heating jacket required separator compressor (Compr1, Compr2); isentropic unit heat exchanger (EX1, EX2, EX3, EX4)

RPLUG Sep Compr

burner gas turbine (GT1, GT2); isentropic unit

RGibbs Compr

HeatX

specifications length = 5 m, diameter = 1.5 m, pressure drop = 0.01 atm, amount of catalyst (Ni/MgAl2O4) = 0.1 kg, TSMR = 1100 K length = 5 m, diameter = 1.5 m, pressure drop = 0.01 atm, amount of catalyst (Ni/La2O3) = 0.1 kg, TDRM = 900 K, UA = 58875.00 W/K water split fraction = 1 for stream H2Oout discharge pressure = 10 atm, ηcomp = 0.95 shell-and-tube exchanger; countercurrent EX1UA1 = 632.39 W/K, EX2UA2 = 794.71 W/K, EX3UA3 = 163.99 W/K, EX4UA4 = 2122.07 W/K pressure = 10 atm, heat duty = 200 kW GT1 discharge pressure = 5 atm, GT2 discharge pressure = 1 atm, ηcomp = 0.99

Figure 3. Sensitivity analysis of the CFPU with regard to (a) CH4,in/ H2Oin and (b) CO2,in/H2Oin. Figure 4. Profiles of SOFC power at different (a) cell temperatures and (b) operating pressures.

increasing CH4,in, but H2-rich syngas (i.e., syngas with H2/CO > 1) is achieved for CH4,in > 6 kmol/h. The increase in net energy duty becomes slower for CH4,in ≥ 10 kmol/h. This means that the SMR unit dominates the fuel processing. In Figure 3b, the syngas yield cannot be improved by increasing CO2,in, but the total energy duty obviously increases for CO2,in ≥ 8 kmol/h. This shows that the DRM unit dominates the fuel processing. Although the CFPU consumes CO2 and produces syngas, the extra energy demand is large. To evaluate the performance of the CFPU, the thermal efficiency ηt,CFPU is expressed as ηt,CFPU =

.where yCFPU,i represents the mole fraction of each component i at the outlet of the CFPU. The lower heating value of each component (LHVi) can be obtained from Aspen Plus. Equation 9 can also be modified to evaluate the thermal efficiency of the SMR unit ηt,SMR =

2

2

4

CH4,inLHVCH4 + Q 1

(10)

.where ySMR,i represents the mole fraction of each component i at the outlet of the SMR reactor. When the desired inlet conditions are given by CH4,in = H2O = 10 kmol/h and CO2,in = 8 kmol/h, the thermal efficiencies of the CFPU and SMR reactor are ηt,CFPU = 0.86 and ηt,SMR = 0.94, respectively. Although the CFPU consumes CO2 to suppress net CO2 emissions, the

FCFPU,out ∑i ∈ [H ,CO,CH ] yCFPU, i LHVi 4

CH4,inLHVCH4 + Q net

FSMR,out ∑i ∈ [H ,CO,CH ] ySMR, i LHVi

(9) C


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2.2. Solid Oxide Fuel Cell. Referring to the model for an SOFC given by eqs B1−B16 in Appendix section B, a nonlinear state-space model for a 1-MW SOFC stack system is given by

large Qnet value due to the strongly endothermic DRM reaction degrades its thermal efficiency.

ξ ̇ = f (ξ , u) y = h(ξ)

(11)

where ξ = [pH2, pO2, pH2O, pCO, pCO2, Tfc]T are the state variables. The cell voltage VN in eq B1 is set as the output variable y. The inlet molar flow rate of the SOFC, FSOFC,in, is denoted as the input variable u, in which the corresponding mole fractions are analyzed from the product of the CFPU with prescribed operating conditions. For the sake of simplicity, it is assumed that CO consumption occurs only due to the water−gas-shift (WGS) reaction at the anode. Notably, the kinetics of the WGS reaction are described by eqs B12 and B13. The dynamic simulation of the SOFC is carried out in the Matlab/Simulink environment. The characteristics of the SOFC with regard to temperature and pressure are shown in panels a and b, respectively, of Figure 4. It can be seen that the SOFC power increases with increasing operating temperature or pressure. Notably, the maximum power outputs appear at higher current densities. The open-loop tests of the SOFC with regard to an changes in the inlet composition (such as xan H2 and xCO) and the air flow rate (Fair) are depicted in panels a and b, respectively, of Figure 5. Figure 5a shows that stable output responses of the SOFC are achieved when changes in the inlet compositions of ±10% H2 or ∓10% CO occur. It is noted that an increase in the CO concentration in the syngas can increase the SOFC electrical power because the WGS reaction at the anode of the SOFC produces hydrogen. 2.3. Combined Heat and Power. In general, the SOFC system produces electrical power and simultaneously releases high-grade waste heat. A new CHP design uses a combination of a post-SOFC burner, a waste-heat recovery scheme, and a series of GTs to improve the hybrid power efficiency. In Figure 6, pressurized flue gas from the post-SOFC burner is arranged to meet the energy demand of the CFPU and preheat the compressed air, and the series of gas turbines GT1 and GT2 produce the secondary electrical power and provide different powers to compress fuel and air in the fuel compressor (Compr1) and air

Figure 5. SOFC power reponses in the case of syngas feed with (a) ±10% H2 and (b) ±10% Fair.

Figure 6. Design and simulation of an SOFC/GT hybrid power generation system combined with CFPU. D


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Figure 7. Sensitivity analysis of the hybrid power system at different Fair and QH values: (a) PSOFC, (b) PGT, (c) Tflue, and (d) CO2,out.

QH but it decreases with increasing Fair. Figure 7d shows that CO2 emissions decrease with decreasing Fair or increasing QH. An insufficient amount of O2 causes incomplete combustion reactions when Fair is low. The complete combustion reaction is reduced when QH is large. Notably, GT power is workable for QH ≥ 200 kW, and CO2 reduction becomes obvious for Fair = 100 kmol/h and QH > 300 kW. 2.4. Power Efficiency versus CO2 Emissions. The performance of the SOFC/GT hybrid power system combined with a CPFU can be evaluated by the following factors: (i) Hybrid power efficiency ηe,HPG

compressor (Compr2), respectively. Notably, the compressed air is split into two streams with a fixed split ratio (α); one is fed into the cathode of the SOFC, and the other is fed to the burner for complete combustion. Compared to the total energy demand of the CFPU in Figure 2, the post-SOFC burner and four heat exchangers (EX1, ..., EX4) contribute to replace external energy supplies. Furthermore, the specifications of Aspen modes for the burner, gas turbine, and compressor are summarized in Table 1. The calculations of the GT power are described in Appendix section C. The combustion reactions in the burner, assumed to be at chemical equilibrium and driven to completion, are CH4 + 2O2 → CO2 + 2H 2O

(12)

H 2 + 0.5O2 → H 2O

(13)

CO + 0.5O2 → CO2

(14)

ηe,HPG =

.

PSOFC + PGT − Wc CH4,inLHVCH4 + Q H

(15)

.where Wc represents the total duty of the fuel compressor (Compr1) and air compressor (Compr2). Specific CO2 emission SCO2 (g of CO2/kWh)

.

SCO2 =

The RGibbs mode with specifications in Table 1 is selected to describe the combustion process, which can predict the outlet temperature of the flue gas and its compositions. Because the external heating duty (QH) and air flow rate (Fair) could affect the flue gas temperature (Tflue), the flue gas flow rate (Ṅ flue), and the amount of CO2 emitted (CO2,out), both power outputs, PSOFC = iVN according to eq B1 and PGT according to eq C1, are varied in the Brayton cycle. Based on prescribed feed conditions, CH4,in = H2Oin = 10 kmol/h, CO2,in = 8 kmol/h, and α = 0.75, Figure 7a,b shows that both power outputs increase with increasing QH and Fair. Figure 7c shows that Tflue increases with increasing

CO2,out − CO2,in PSOFC + PGT − Wc

(16)

. Referring to the data from the steady-state simulations shown in Figure 6, the hybrid power efficiency according to eq 15 is ηe,HPG = 0.5, and the corresponding specific CO2 emission by eq 16 is SCO2 = 324.18 g of CO2/kWh. If a series of GTs is not taken into account, ηe,HPG = 0.33 and SCO2 = 487.26 g of CO2/kWh. Notably, the CHP design using a series of GTs can improve the power efficiency by over 35% and simultaneously reduce CO2 emissions by over 33%. E


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Figure 8. Open-loop tests of the SOFC/GT hybrid power system in the case of ±10% Fair: (a) PSOFC, (b) PGT, (c) Tflue, and (d) CO2,out.

according to the Ziegler−Nichols rule,25 and a reverse-acting controller is selected. Panels a and c of Figure 12 show that ±10% changes in Fair and CH4,in, respectively, are gradually attenuated. The corresponding control actions are depicted in panels b and d, respectively, of Figure 12. Notably, no-offset tracking performance is achieved, and closed-loop stability is guaranteed as well. By observing Figures 6 and 10, the flue gas temperature directly affects the syngas production rate, i.e. FSOFC,in, and it also affects the SOFC power (PSOFC). To address the fuel cell power control, an inferential control algorithm is aided to indirectly control the power output of the SOFC when the flue gas temperature is measurable. If the estimation of PSOFC by measuring Tflue is feasible, the implicit function for the prediction of the steady state SOFC power using the steady state value of Tflue is described as

3. PROCESS CONTROL Because the integration of the SOFC/GT hybrid power system is quite complex, an analysis of the system dynamic behavior is essential. From the process control viewpoint, the control implementation is an effective approach to address the stable operation of this hybrid power system when unknown perturbations appear. Because both Fair and QH strongly affect the flue gas temperature and CO2 emissions, the corresponding open-loop tests with respect to different inlet perturbations of Fair and QH are depicted in Figures 8 and 9, respectively. These dynamic responses in Aspen Plus dynamics show that this hybrid power system is locally openloop-stable when bounded inlet perturbations by ±10% Fair or ±10% QH appear. The open-loop responses of the SOFC power in Figure 8a are asymmetric under ±10% Fair, but they become nearsymmetric in Figure 9a under ±10% QH. The open-loop response of the flue gas temperature in Figure 8c under ±10% Fair is slower than that in Figure 9c under ±10% QH. Moreover, Figures 8d and 9d show that the manipulation of QH directly affects the amount of CO2 emitted from the burner as compared to the manipulation of Fair. In a single-input−single-output (SISO) control configuration, QH is selected as the control variable, whereas flue gas temperature is denoted as the controlled variable. In Figure 10, the temperature control loop, which consists of a temperature transmitter (TT), a temperature controller (TC), and a heater, is added to control the flue gas temperature by manipulating the control variable QH. Based on an autotune-variation(ATV-) based proportional−integral (PI) control method, the closed-loop ATV tests shown in Figure 11a is used to estimate ultimate gain and period. Figure 11b shows that the tuning parameters of PI control, namely, KC = 5.02 and τ1 = 2, are obtained

̂ PSOFC,ss = φ(Tflue,ss)

(17)

.

Inspired by the steady-state approach,26 Figure 13 shows that curve fitting uses a polynomial and steady-state data of Tflue,ss versus P̂ SOFC,ss to find an approximation of eq 14 as ̂ PSOFC,ss = −3.49 × 10−4Tflue,ss 2 + 1.47Tflue,ss − 225.91 (18)

. If the inversion of eq 18 exists, it is given by SP SP SP Tflue = 0.146(PSOFC )2 − 375.94PSOFC + 243123.31

(19)

.It is assumed that P̂ SOFC,ss and Tflue,ss are specified as the set SP points, PSP SOFC and Tflue, respectively. Based on the same control F


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Figure 9. Open-loop tests of the SOFC/GT hybrid power system in the case of ±10%QH: (a) PSOFC, (b) PGT, (c) Tflue, and (d) CO2,out.

Figure 10. Flue gas temperature control loop in the SOFC/GT hybrid power generation system.

method as used for controlling Tflue, the set-point tracking control performance is shown in Figure 14. Figure 14a shows that no-offset power output tracking is almost achieved when TSP flue shown in Figure 14b is specified. The corresponding manipulated input, QH, is depicted in Figure 14c. An inferential model is treated to predict the set point of the SOFC power, but it might fail because of modeling errors and disturbances. Referring the concept of the use of past measurements to improve the accuracy of the estimation,27 an inferential model is extended by measuring more steady-state points ̂ PSOFC,ss = Φ(Tflue , Tfc , Vcell , ...)|ss

Figure 11. ATV control algorithm: (a) closed-loop ATV tests, (b) PI controller.

(20) G


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Figure 12. ATV-based PI control for disturbance rejection: (a) output responses in the case of ±10% Fair and (b) the corresponding control action of QH; (c) output responses in the case of ±10% CH4,in and (d) the corresponding control action of QH.

4. CONCLUSIONS In this article, the new design of an SOFC/GT hybrid power generation system is verified to reduce carbon emissions and provide clean power. The fuel processing unit consists of two reforming processes (SMR plus DRM) to produce the fuel source of an SOFC. Based on a thermodynamic cycle, a combined heat and power process is utilized to reduce the external energy supply and improve the hybrid power efficiency. In a SISO control framework, the dynamic manipulation of the pressurized and high-temperature flue gas temperature is investigated in Aspen Plus Dynamics environment. An ATV-based PI control settings is based on an inferential power control strategy using the static inferential model which is successfully demonstrated by the integration of Aspen and Matlab. Although the static inferential model is not robust against unknown perturbations, the accuracy of the power estimation could be improved by increasing the number of measurements.

Figure 13. Static inferential model using data on Tflue,ss vs PSOFC,ss.

■

. If the function Φ can be obtained by nonlinear regression, then the set point of Tflue can be specified by an inversion of eq 20 to give SP Tflue

−1

=Φ

SP (PSOFC ,

Tfc , Vcell , ...)|ss

APPENDIX

A. Kinetics in SMR and DRM

The kinetics of the SMR on a Ni/MgAl2O4 catalyst are given by19

(21)

. According to the above assumptions, the steady-state errors between the true and predictive values of PSOFC could be reduced by increasing measurements.

rSMR,1 =

PH2 0.5PCO ⎞ ⎛ 240.1 ⎞⎛ PCH4PH2O 4.225 × 1015 ⎟ ⎜ ⎟⎜ − exp ⎝ RT ⎠⎜⎝ PH 2.5 K1 ⎟⎠ (Den)2 2 (A1)

H


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where K1 = exp(−26830/T + 30.114), K2 = exp(4400/ T − 4.036), and ⎛ −70.65 ⎞ ⎟P Den = 1 + 8.23 × 10−5 exp⎜ ⎝ RT ⎠ CO ⎛ −82.90 ⎞ ⎟P + 6.12 × 10−9 exp⎜ ⎝ RT ⎠ H2 ⎛ −38.28 ⎞ ⎟P + 6.65 × 10−4 exp⎜ ⎝ RT ⎠ CH4 ⎛ 88.68 ⎞⎛ PH2O ⎞ ⎟⎜ ⎟ + 1.77 × 105 exp⎜ ⎝ RT ⎠⎜⎝ PH ⎟⎠ 2

(A4)

The kinetics for DMR on a highly active Ni/La2O3 catalyst are assumed as follows:21 ⎡ ⎛ 529.2 ⎞ ⎟P P rDRM = ⎢1.35 × 10−7 exp⎜ ⎝ RT ⎠ CH4 CO2 ⎣ ⎛ −517.2 ⎞ ⎟P + 2.61 × 10−3 exp⎜ ⎝ RT ⎠ CH4 ⎤−1 ⎛ 144.3 ⎞ ⎟P + 2.77 × 10−5 exp⎜ ⎝ RT ⎠ CO2 ⎥⎦ ⎛ −372.9 ⎞ ⎟P P × 7.22 × 10−8 exp⎜ ⎝ RT ⎠ CH4 CO2

(A5)

B. Dynamic Model of SOFC

Based on the specifications for the SOFC stack system under assumptions, the cell voltage Vcell is calculated as22−24 Vcell = VN − Vact − Vohm − Vconc

(B1)

where the reversible Nernst voltage VN is given by 0.5 ⎞ ⎛ RTfc ⎜ pH2 pO2 ⎟ VN = 1.2723 − 2.7645 × 10 Tfc + ln 2F ⎜⎝ pH O ⎟⎠ 2 −4

(B2)

If the SOFC is operating in low-activation polarization conditions, the activation overvoltage Vact is given by Vact =

RTfci ⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ + 2F ⎝ i0,an 2i0,ca ⎠

(B3)

where ⎛ pH ⎞⎛ pH O ⎞ ⎛ −110 ⎞ i0,an = 7 × 109⎜⎜ 2 ⎟⎟⎜⎜ 2 ⎟⎟ exp⎜ ⎟ ⎝ RTfc ⎠ ⎝ pref ⎠⎝ pref ⎠

(B4)

and

Figure 14. Inferential control for set-point tracking: (a) power SP , (b) flue temperature responses at TSP responses at PSOFC flue, (c) corresponding control action of QH.

i0,ca

PCO2 ⎞ ⎛ 67.13 ⎞⎛ PCOPH2O 1.955 × 10 ⎟⎜ ⎟ exp⎜ = − ⎜ 2 ⎝ RT ⎠⎝ PH K 2 ⎟⎠ (Den) 2

⎛ p ⎞0.25 ⎛ −120 ⎞ = 7 × 10 ⎜ ⎟ exp⎜ ⎟ ⎝ RTfc ⎠ ⎝ pref ⎠ 9⎜ O2 ⎟

(B5)

6

rSMR,2

Because the cell equivalent ohmic resistance depends on the anode, cathode, and electrolyte resistances, the ohmic overvoltage Vohm according to the second Ohm’s law is written as

(A2)

Vohm = i(Ωan + Ωca + Ωel)

2 PH2 0.5PCO2 ⎞ ⎛ 243.9 ⎞⎛⎜ PCH4PH2O 1.02 × 1015 ⎟ ⎜ ⎟ rSMR,3 = exp − ⎝ RT ⎠⎜⎝ PH 3.5 K1K 2 ⎟⎠ (Den)2 2

(B6)

where Ωan = 2.98 × 10−9 exp( − 1392/Tfc)

(A3) I

(B7)


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Industrial & Engineering Chemistry Research Ωca = 1.78 × 10−7 exp(600/Tfc)

(B8)

Ωel = 1.18 × 10−9 exp(10350/Tfc)

(B9)

⎧ ⎫ ⎛ T + Tref ⎞ Cj 0 ⎜ ⎟ + hj = H298, [(T + Tref )2 − (TTref )]⎬ j + R ⎨A j + Bj ⎝ ⎠ 2 3 ⎩ ⎭ × (T − Tref )

If the heat convection is neglected and only the diffusion phenomenon is taken into account, the concentration overvoltage is simplified as Vconc =

where Aj, Bj, and Cj are coefficients for species at the anode and cathode that can be found in Table 2. Table 2. Heat Capacities of SOFC Components

RTfc ⎛ i⎞ ln⎜1 − ⎟ 2F ⎝ iL ⎠

heat capacity (J/mol·K)

(B10) component

Aj

Bj × 103

Cj × 106

H0298,j(J/mol)

H2(g) CH4(g) CO(g) CO2(g) H2O(l) H2O(g) O2(g) N2(g)

3.249 1.702 3.376 5.457 8.712 3.470 3.639 8.712

0.422 9.081 0.557 1.045 1.25 1.45 0.506 0.593

− −2.167 − − −0.18 − − −

0 −74520 −110525 −393509 −285830 −241818 0 0

where iL is the limiting current density and is estimated to be 1.6 A·cm−2 at 800 °C.22 We assume that the water−gas shift reaction is taken into consideration in the anode channel rWGS

CO + H 2O ⎯⎯⎯→ CO2 + H 2 ,

ΔHWGS = − 41.1 kJ·mol−1 (B11)

where the reaction rate is given by ⎛ −103.191 ⎞⎛ PCO2PH2 /PCOPH2O ⎞ ⎟⎟ rWGS = 0.0171 exp⎜ ⎟⎜⎜1 − Keq ⎝ RTfc ⎠⎝ ⎠

C. Gas Turbine and Compressor

Because the gas turbine is used to drive the compressor as well as to produce electricity, the net power of the gas turbine, PGT, is given by

(B12)

and

PGT = Pturb − Pcomp

⎡ ⎛ 1000 ⎞3 ⎛ 1000 ⎞2 ⎢ − 1⎟ + 0.6351⎜ − 1⎟ K ps = exp −0.2935⎜ ⎢⎣ ⎝ Tfc ⎠ ⎝ Tfc ⎠ ⎤ ⎛ 1000 ⎞ + 4.1788⎜ − 1⎟ + 0.3169⎥ ⎥⎦ ⎝ Tfc ⎠

Pturb = ηturbFflueΔhturb(T , P) (B13)

Pcomp =

■

dTfc = dt

Fair Δhcomp(T , P) ηcomp

(C3)

AUTHOR INFORMATION

Corresponding Author

*Tel.:+886 6 2757575. Fax: +886 6 2344496. E-mail: weiwu@ mail.ncku.edu.tw. Notes

The authors declare no competing financial interest.

■

(B14)

ACKNOWLEDGMENTS The authors thank the Ministry of Science and Technology of Taiwan for its partial financial support of this research under Grant MOST 103-2221-E-006-251.

Notably, the electrochemical conversion rate of CO is negligible compared to that of H2, and the partial pressures are assumed to be related by the ideal gas equation, that is, pj = NjRTfc/V, j ∈ S = {H2, CO, CO2, H2O, O2}. Based on the adiabatic conditions, the energy balance accounting for the SOFC volume, including the anode and cathode volumes, is given by Cps

(C2)

Notably, the efficiencies of both devices, ηcomp and ηturb, are taken into consideration. The changes in isentropic enthalpy of the two devices, Δhcomp and Δhturb, are evaluated by Aspen Plus at the prescribed temperature and pressure. The flow rates of both devices, Fflue and Fair, directly affect the magnitude of power.

I = x Han2FCFPU,out − ṄH 2,out + rWGS − 2F

dt dNCO an ̇ FCFPU,out − NCO,out = xCO − rWGS dt dNCO2 an ̇ ,out + rWGS F = xCO − NCO 2 CFPU,out 2 dt dNH2O = x Han2OFCFPU,out − ṄH2O,out − rWGS dt dNO2 I = xOca2αFair − NO2,out − dt 4F

(C1)

where Pturb and Pcomp are the power of the gas turbine and compressor, respectively. The formulations of both devises are given by

The mass balances for the anode and cathode volumes are given by dNH2

(B16)

■

∑ Nj̇ (hj̅ ,in − hj̅ ,out) − ΔHWGSrWGS − VcellI j∈S

(B15)

and J

NOMENCLATURE Csp = specific heat capacity, J/K CHP = combined heat and power DRM = dry reforming of methane F = Faraday constant, C mol−1 Fair = air flow rate, kmol/h FSOFC,in = inlet molar flow rate of the SOFC, kmol/h i = current density, A/cm2 I = current load, A DOI: 10.1021/acs.iecr.5b01961 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article


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LHV = lower heating value, kJ/mol Nj = amount of component j, mol P = cell power, W pj = partial pressure of component j, atm QH = external energy duty, W R = universal gas constant, J/mol·K SMR = steam methane reforming SOFC = solid oxide fuel cell T = temperature of each unit, K Tflue = flue gas temperature, K V = volume, m3 Vact = activation overvoltage, V Vcell = terminal voltage of SOFC cell, V Vconc = concentration overvoltage, V VN = Nernst voltage, V Vohm = ohmic overvoltage, V Wc = total duty of fuel and air compressors, kW Subscripts

an = anode ca = cathode comp = compressor fc = SOFC in = at unit inlet out = at unit outlet ss = steady state turb = turbine Greek Symbols

α = flow split factor ΔH = heat of reaction, kJ/mol η = efficiency

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GT Hybrid Power Generation System

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