PROCESS DESIGN AND OPTIMIZATION OF SOLID OXIDE FUEL CELLS AND PRE- REFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS

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1 PROCESS DESIGN AND OPTIMIZATION OF SOLID OXIDE FUEL CELLS AND PRE- REFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS By TAE SEOK LEE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA

2 2008 Tae Seok Lee 2

3 To my beloved wife and son 3

4 ACKNOWLEDGMENTS This research project would not have been possible without the support of many people. I wish to express my gratitude to my supervisor, Dr. Chung, who was abundantly helpful and offered invaluable assistance, support and guidance. Deepest gratitude also goes to the members of the supervisory committee, Dr. Sherif and Dr. Ingley. Without their knowledge and assistance this study would not have been successful. Special thanks also go to all my colleagues and graduate friends, especially group member, Yun Whan Na for invaluable advice and my contemporaries; Minki Hwang, Jung Hwan Kim, Sung Jin Lee, and Gun Lee. Not forgetting to my bestfriends as well as UFMAEKR members who always been there. Finally but not least, I would like to express my love and gratitude to my beloved families; for their understanding and endless love, through the duration of my studies. 4

5 TABLE OF CONTENTS ACKNOWLEDGMENTS...4 LIST OF TABLES...7 LIST OF FIGURES...8 ABSTRACT...9 CHAPTER 1 INTRODUCTION AND BACKGROUND...11 page Steam Reforming Reaction...11 Solid-Oxide Fuel Cells...11 Chemical Reaction Equilibrium...12 Stoichiometry and Extent of Reaction...12 Chemical Reaction Equilibrium and Equilibrium Constant THERMODYNAMIC MODEL...16 Introduction...16 Assumption...17 Thermodynamic Properties of Chemical Species...17 Justification for Ideal Gas Assumption...17 Heat Capacity...18 Heat Capacity for Fuel (n-dodecane)...18 Molar Balance...19 Chemical Equilibrium at the Pre-Reformer...19 SOFC Model...20 Recycle Ratio...22 Energy Balance RESULTS AND OPTIMIZATION...31 Results...31 Chemical Equilibrium at Pre-Reformer and Optimum Pre-Reformer Temperature...31 Fuel and Oxygen Consumption Results without Recirculation and CO 2 Capture...31 Recycle Ratio and Water Management...32 Energy Balance and Efficiency Results without Recirculation and CO 2 Capture...32 Carbon Dioxide Capture Effects...34 Recirculation Effects...35 Optimization SUMMARY AND CONCLUSION

6 LIST OF REFERENCES...62 BIOGRAPHICAL SKETCH

7 LIST OF TABLES Table page 1-1 Types of fuel cells, their characteristics Critical and reduced temperature and pressure Heat capacities of gases in the ideal-gas state Coefficients for dodecane heat capacity in the ideal-gas state Overall molar balance results Dependency on CO 2 adsorption percentage and recirculation ratio Maximum overall efficiencies for given SC and T SOFC with corresponding recirculation ratio and CO 2 capture percent

8 LIST OF FIGURES Figure page 2-1 Process flow diagram Effect of number of transfer units, NTU, on the effectiveness, ε, with several heat capacity ratios, C r, for crossflow and both fluids mixed heat exchanger Reaction equilibrium results for steam reforming and water-gas shift reaction for several steam to carbon ratios Produced hydrogen per consumed energy Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio, where no CO 2 capture and no recirculation Effect of SOFC temperature on oxygen consumption rate with different steam to carbon ratio, where no CO 2 capture and no recirculation AOG recycle percent versus SOFC temperature with different steam to carbon ratio, where no CO 2 capture and no recirculation Effect of SOFC temperature on additional heat transferred rate for pre-reformer unit with different steam to carbon ratio, where no CO 2 capture and no recirculation Effect of SOFC temperature on detailed additional heat transferred rate for prereformer unit with S/C =4, where no CO 2 capture and no recirculation Effect of SOFC temperature on efficiency based on LHV with different steam to carbon ratio, where no CO 2 capture and no recirculation Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratios and several CO 2 adsorption percents, where no recirculation Carbon dioxide capture effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no recirculation Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio and several recirculation ratio, where no CO 2 adsorption Recirculation effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no CO 2 adsorption Efficiency based on LHV of fuel Effects of SOFC temperature and SC on maximum system efficiency

9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science PROCESS DESIGN AND OPTIMIZATION OF SOLID OXIDE FUEL CELLS AND PRE- REFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS Chair: Jacob N. Chung Major: Mechanical Engineering By Tae Seok Lee December 2008 We conducted optimization for a flow process consisting of a typical direct internal reforming Solid Oxide Fuel Cell (SOFC) utilizing synthesis gas (syngas) produced through steam reforming of the liquid hydrocarbon inside the external reforming unit. The anode off gas recycling system and after-burner unit are introduced to maximize its efficiency. The mass and energy balance analysis for the whole system has been carried out. Mass balance (or molar balance) analysis includes optimization for minimum fuel and oxygen consumption rates corresponding to the temperatures of pre-reformer and SOFC, the steam to carbon ratio inside the pre-reformer, recirculation ratio, and rate of CO 2 capture. Studies on the reforming chemical reactions and chemical equilibria are presented. The results include CO 2 adsorption in the adsorbent bed as well as recirculation. For the molar balance study, we provided dodecane consumption rate and overall molar balance results. With the energy balance analysis, the temperature distributions in the system are calculated by means of solving energy balance for each device. However, energy is not perfectly balanced. So, another heat effect is introduced on the pre-reformer unit. This could be either heat surplus or insufficient heat depending on SOFC temperature. The temperature, which makes heat balanced without newly introduced heat effect 9

10 on pre-reformer, is named as self-energy balanced operating temperature. It have been investigated the total system efficiency based on the first law of thermodynamics. The overall efficiency is defined as the total net power output divided by the lower heating value rate of fuel input. Considering net power output, produced electrical work should reimburse insufficient heat on the pre-reformer. It is also provided optimal case operating parameters. Thermodynamic efficiency is mainly affected by CO 2 adsorption percentage under low steam to carbon ratio region, while efficiency is mainly affected by the recirculation rate under high temperature operation. In accordance with simulation, recommend operating conditions are SC =2, 800 o C SOFC temperature, 550 o C Pre-Reformer temperature, 0.35 recirculation ratio and 25% carbon dioxide adsorption yielding the highest efficiency as 74.79%. 10

11 CHAPTER 1 INTRODUCTION AND BACKGROUND Steam Reforming Reaction The catalytic conversion of hydrocarbons with water steam is one of the most widely used industrial methods for production of hydrogen-containing gases. The first industrial steam reformer was installed at Baton Rouge by Standard Oil of New Jersey and commissioned in Steam reforming is an essential process in the manufacture of synthesis gas (syngas) and hydrogen from hydrocarbons [1, 2]. Solid-Oxide Fuel Cells A fuel cell is an electrochemical energy conversion device that converts chemical energy of fuel directly into electricity, promising power generation with high efficiency and low environmental impact. Because the intermediate steps of producing heat and mechanical work are avoided, fuel cells are not limited by thermodynamic limitations of heat engines such as the Carnot efficiency. A fuel cell is similar to a battery in aspects that both have an electrolyte, and negative and positive electrodes, and generate DC electricity through electrochemical reactions. However, fuel cells continuously consume reactant, which must be replenished, whereas batteries generate electricity by depleting materials in electrodes inside the batteries. Because of this, batteries may be discharged, whereas fuel cells cannot be discharged as long as the reactants are supplied [3, 4]. Fuel cells can be categorized by the type of electrolyte used in the cells: Polymer Electrolyte Fuel Cell (PEFC) Alkaline Fuel Cell (AFC) Phosphoric Acid Fuel Cell (PAFC) Molten Carbonate Fuel Cell (MCFC) Solid Oxide Fuel Cell (SOFC) Table 1-1 provides an overview of the key characteristics of the main fuel cell types. Solid oxide fuel cells (SOFCs) have an electrolyte that is a solid, non-porous metal oxide. The cell is constructed with two porous electrodes that sandwich an electrolyte. Air (or oxygen) 11

12 flows along the cathode. When an oxygen molecule contacts the cathode/electrolyte interface, it acquires electrons from the cathode. The oxygen ions diffuse into the electrolyte material and migrate to the other side of the cell where they contact the anode. The oxygen ions encounter the fuel at the anode/electrolyte interface and react catalytically, giving off water, carbon dioxide, heat, and electrons. The electrons transport through the external circuit, providing electrical energy [4]. Chemical Reaction Equilibrium Stoichiometry and Extent of Reaction The general chemical reaction may be written ν M + ν M + ν M + ν M + (1-1) where ν i is a stoichiometric coefficient, positive sign for a product and negative sign for a reactant, and M i stands for a chemical species i. As the reaction represented by Eq. (1-1) progresses, the changes in the numbers of moles of species M i, dn i, are in direct proportion to the stoichiometric numbers. Introducing variable ε, called the extent of reaction or progress variable, it is possible to represent an amount of reaction. The general relation connecting the differential change dn i with dε is therefore: dni dni = νidε or dε = (1-2) ν Integration of Eq. (1-2) from an initial un-reacted state to a state reached after an arbitrary amount of reaction gives: The molar fractions of the species i, y i, are as follows: n i i dni = ν i dε or ni = nio + νiε (1-3) n io ε o 12

13 y i ni nio + ν iε = = n n + ε ν i io i i i i (1-4) Equation (1-4) represents molar fraction of the i-th species for an arbitrary amount of reaction. However, in general, two or more independent chemical reactions occur simultaneously. So, subscript j serves as the reaction index. The general equation analogous to Eq. (1-3) is as follow: dn = ν dε (1-5) i i, j j j where ν i,j denotes the stoichiometric number of species i in reaction j. The number of moles of i- th species may change because of several reactions, identified by subscript j. This is why Eq. (1-5) contains summation for j. Integration of Eq. (1-5) from an initial un-reacted state to a state reached after an arbitrary amount of reaction gives: n = n + ν ε (1-6) i io i, j j j Therefore, molar fraction of the i-th species in progress of multireaction can be expressed as follow y i n + ν ε io i, j j ni j = = (1-7) ni i nio + ν i, j ε j i j i Chemical Reaction Equilibrium and Equilibrium Constant Consider a closed system containing an arbitrary number of species and comprised of an arbitrary number of phases in which the temperature and pressure are uniform. Combining the first law with the second law of the thermodynamics yields ( ), t t t 0 or t du + PdV TdS dg 0 (1-8) TP 13

14 where superscript t denotes total properties of the system. This equation (1-8) represents that all irreversible processes occurring at constant temperature and pressure proceed in such a direction as to cause a decrease in the Gibbs energy of the system. For the single-phase, open system, mixture, the total Gibbs energy (ng or G t ) of the system becomes a function is the numbers of moles of the chemical species as well as pressure and temperature. And its total differential is as follow ( ) ( ) ( ) µ i i d ng = nv dp ns dt + dn (1-9) where µ i is the chemical potential of species i in the mixture defined by i ( ng) µ i = ni P, Tn, j (1-10) Substituting Eq. (1-2) into Eq. (1-9) gives ( ) ( ) ( ) i i i d ng = nv dp ns dt + ν µ dε (1-11) The right hand side of Eq.(1-11), is an exact differential expression; whence, t ( ng) ( G ) νµ i i = = i ε ε (1-12) TP, TP, Considering Eq. (1-8), a criterion of chemical reaction equilibrium is therefore: νµ i i = 0 (1-13) By assuming the equilibrium mixture behaves as an ideal gas, Eq. (1-13) becomes i νi i i i ( yi ) = exp = K o o (1-14) i o i igi P ν ν P P RT P This expression is also the definition of the equilibrium constant, K [5, 6]. ν i 14

15 Table 1-1. Types of fuel cells, their characteristics Electrolyte Electrodes PEFC AFC PAFC MCFC SOFC Hydrated Polymeric Ion Exchange Membranes Carbon Mobilized or Immobilized Potassium Hydroxide in asbestos matrix Transition metals Immobilized Liquid Phosphoric Acid in SiC Carbon Catalyst Platinum Platinum Platinum Interconnect Operating Temperature Carbon or metal Metal Graphite Immobilized Liquid Molten Carbonate in LiAlO 2 Nickel and Nickel Oxide Electrode material Stainless steel or Nickel Porovskites (Ceramics) Perovskite and perovskite / metal cermet Electrode material Nickel, ceramic, or steel C C 205 C 650 C C Charge Carrier External Reformer HC External shift conversion of CO to H 2 Prime Cell Components Product Water Management Product Heat Management H + OH H + CO 3 2 Yes Yes Yes Yes, plus purification to remove trace CO Carbon-based Yes, plus purification to remove CO and CO 2 Carbon-based No, for some fuels O 2 No, for some fuels and cell designs Yes No No Evaporative Evaporative Evaporative Process Gas + Liquid Cooling Medium Process Gas + Electrolyte Circulation Process Gas + Liquid cooling medium or steam generation Graphitebased Stainlessbased Gaseous Product Internal Reforming + Process Gas Ceramic Gaseous Product Internal Reforming + Process Gas 15

16 CHAPTER 2 THERMODYNAMIC MODEL Introduction The molar balance including chemical equilibrium is considered. After evaluating molar composition of each steam, energy balance is solved for each device. Figure 2-1 shows the process flow diagram which consists of recirculated direct internal reforming SOFC, prereforming unit, recuperator, carbon dioxide adsorbent, pre-heater, flue gases condenser and Anode off gas (AOG) recycling system. The AOG has, generally, high water content due to the fact that water is only product of the electrochemical reaction which produces electrical power in a SOFC. With appropriate AOG recycle, it is possible to maintain steam to carbon ratio (SC) as preset value. If AOG does not contain enough water, water should be added with fuel to keep the desired steam to carbon ratio. It is obvious that AOG compressor is required for this AOG circulation system. From thermodynamics point of view, high temperature compressing process requires more work than low temperature compression. Therefore, AOG should be cooled down before the compressing process. After compressed, temperature of AOG is recuperated passing through a heat exchanger. Un-recycled AOG is burned at the after-burner, instead of venting, on purpose to not only provide heat to the reformer but also prevent wasting useful gases such as hydrogen. Flue gases from after-burner could be used to heat up mixture of fuel and recycled AOG or oxygen flows by passing through fuel pre-heater and/or condenser. As shown in Figure 2-1, each stream is labeled in two letters with combination of letter and number corresponding to its molar composition and temperature. The first letter denotes molar composition or concentration, while the second letter denotes temperature. Therefore, streams 1a and 1b are the same molar composition but in different temperature. 16

17 Assumption The following assumptions are made in the analysis: Steady state operation All gaseous phases are ideal gas. Gas mixture at the exit is at chemical and thermal equilibrium. All devices are assumed perfect insulation. Fuel or hydrocarbon is reacted with water vapor and produces only carbon monoxide and hydrogen. Only hydrogen is electrochemically reacted inside SOFC. Pressure drop is ignored on calculation of molar balance or chemical equilibrium. This means pressure effect is ignored on equilibrium constant. Complete combustion occurs at the after-burner. So, it is assumed that flue gases consist of carbon dioxide, water vapor and excess oxygen. Temperature increase in compression process is neglected. 85% fuel utilization at the SOFC 85% of enthalpy change for electrochemical reaction is converted into electrical work instead of taking into account voltage losses consisting of activation, ohmic (or resistive), and concentration polarization. Justification for Ideal Gas Assumption Thermodynamic Properties of Chemical Species As mentioned in assumption section, all gases are assumed as the ideal gases. This condition should be justified before evaluating thermodynamic properties of chemical species. It is well-known that all gases and vapors approach ideal-gas behavior under the low density condition. At higher densities the behavior may deviate substantially from the ideal-gas equation of state. By introducing compressibility factor, Z, this ambiguousness, low density, condition could be cleared. Compressibility factors Z for different chemical species exhibit similar behavior when correlated as a function of reduced temperature, T r, and reduced pressure, P r. 17

18 Critical temperature and pressure as well as reduced temperature and pressure data are provided in Table 2-1. Reduced temperatures in the Table 2-1 are evaluated at the lowest temperature, T 2b, in the process flow diagram. If the pressure is very low (that is, P r << 1), the ideal-gas model can be assumed with good accuracy, regardless of the temperature. Furthermore, at high temperatures (that is, T r > 2), the ideal-gas model can be assumed with good accuracy to reduced pressures as high as four or five [5, 6]. As shown in Table 2-1, reduced pressures are significantly small, P r ~ 10 2, so ideal gas assumption is reliable. Heat Capacity In this work, the empirical equation for heat capacity as a function of the temperature is used. This relationship is as follow, C P R 2 2 = A+ BT + CT + DT (2-1) where either C or D is zero, depending on the substance considered and T is in Kelvin. Equation (2-1) is applied for Hydrogen, Water vapor, Methane, Carbon Monoxide and Carbon Dioxide. The coefficients are presented in the Table 2-2 [5]. This empirical relationship is valid from room temperature ( K) to Tmax presented in Table 2-2. Heat Capacity for Fuel (n-dodecane) The specific heat of dodecane is interpolated into 3 rd order polynomial, Eq. (2-2), using data achieved by Lemmon and Huber [7] and Span and Wagner [8]. Interpolation result is presented in Table 2-3. C P 2 3 A BT CT DT R = (2-2) 18

19 Molar Balance Chemical Equilibrium at the Pre-Reformer As shown in Fig. 2-1, pre-reformer unit consists of external reformer and after-burner. Preheated mixture of fuel and recycled AOG is passing through reforming channel of the external reformer. In the presence of catalysis, steam reforming reactions and water-gas shift (WGS) reaction, which are shown in Eqs. (2-3)-(2-5), occur and find chemical equilibrium under the given temperature and pressure [9]. CH + H O CO + 3H (2-3) CO + H2O H 2 + CO2 (2-4) CH + 2H O CO + 4H (2-5) Reforming reactions (2-3) and (2-5) are strongly endothermic, so the forward reaction is favored by high temperature, while the water-gas shift reaction (2-4) is exothermic and is favored by low temperature. The overall reaction is endothermic, so heat should be supplied into reforming channel in two ways; the sensible heat of AOG from SOFC and combustion heat from the after-burner. Let the extents of reaction, which are defined as Eq. (1-5), be ε R1, ε R2, and ε R3 for chemical equilibrium reactions (2-3), (2-4), and (2-5), respectively. Then equilibrium molar fractions are expressed as follows; y HO 2 = F oho, R1 R2 R3 2 ε ε 2ε F + 2ε + 2ε o R1 R3 (2-6) y CH 4 = F och, R1 R3 4 ε ε F + 2ε + 2ε o R1 R3 (2-7) y H 2 = F oh, R1 R2 R ε + ε + 4ε F + 2ε + 2ε o R1 R3 (2-8) 19

20 y CO = F + ε ε oco, R1 R2 F + 2ε + 2ε o R1 R3 (2-9) y CO2 = F + ε + ε oco, 2 R2 R3 F + 2ε + 2ε o R1 R3 (2-10) where, F o and F o,i denote inlet total molar flow rate, label 3b, and inlet molar flow rate of i component, respectively. Once extents of reaction are obtained, evaluation of the equilibrium molar fraction is straightforward. Therefore, one needs three equations to be solved simultaneously to find ε R1, ε R2 and ε R3 under equilibrium condition. These are the chemical equilibrium equations corresponding to the steam reforming and water-gas shift reaction, as following; 2 3 yh yco GR 1 p 2 KR 1 ( T) = exp o = p y y RT 0 CH4 H2O p yh y 2 CO2 GR2 KR2 ( T) = exp o = p y yco RT HO yh yco GR3 p 2 2 KR3 ( T) = exp o = 2 p y y RT HO 2 CH4 (2-11) (2-12) (2-13) The temperature dependent equilibrium constant is solved by the classical method in which the change in Gibbs free energy of the reactions is used. After Gibbs energy difference obtained, equilibrium molar fractions, Eqs. (2-6)-(2-10), are substituted into Eqs. (2-11)-(2-13) and then the system of equations is solved by Newton-Rahpson method with 10 7 tolerance [10]. SOFC Model In this work, direct internal reforming SOFC model is based on achievement done by Colpan et al. [11]. The steam reforming reaction for methane, Eq. (2-3), water-gas shift reaction, 20

21 Eq.(2-4), and electrochemical reaction, Eq.(2-14), occur simultaneously at the direct internal reforming SOFC. 1 H2 + O2 H2O (2-14) 2 The extent of reaction for electrochemical reaction, ε S3, can be expressed using molar balance, definition of molar fraction, and recirculation ratio [11]. ε S 3 U F = ( oh, + 3ε S1+ ε S2) 2 1 r+ ru (2-15) Here, r is the recirculation ratio, U is fuel utilization, ε Si is reaction coordinates for i-th reaction at the SOFC, respectively. Also, F o denotes inlet of SOFC anode, label 5. With the above assumptions and Eq. (2-15), molar fractions for all the species at the exit of the anode of fuel cell are given as below : y CH 4 = F och, S1 o 4 ε F + 2ε S1 (2-16) y HO 2 = F oho, S1 S2 2 F + ε ε + F + 2ε o oh, S1 S2 S ε + ε 1 r+ ru U (2-17) y H2 ( )( ) FoH, + 3ε 2 S1+ εs2 1 r 1 U = Fo + 2ε S1 1 r+ ru (2-18) y CO = F + ε ε oco, S1 S2 F + 2ε o S1 (2-19) y CO2 = F oco, 2 S2 F + 2ε o + ε S1 (2-20) 21

22 Here, ε S1 and ε S2 are only unknowns. Likewise chemical equilibrium at the external reformer, molar fractions at the exit of SOFC anode, Eqs. (2-16)-(2-20), are evaluated using equilibrium constants, Eqs. (2-11) and (2-12). Recycle Ratio In the molar balance aspect, the last step for AOG recycle system is determination of the recycle ratio. The amount of recycled AOG is manipulated to maintain the desired SC value. The AOG recycle ratio is defined as recycled AOG to pre-recycled AOG, Rc = F 2 /F 1. The steam to carbon ratio is defined as; F 2, HO SC 2 = F 2, CH + F NC 4 f (2-21) where, F f and NC denote molar flow rate of fuel and the number of carbon in the fuel e.g., for methane NC = 1, for dodecane NC = 12. Substituting definition of recycle ratio into Eq. (2-21) yields 0 < SCFf NC Rc = 1 F SCF 1, HO 1, CH 2 4 (2-22) The numerator of Eq. (2-22) denotes required amount of steam due to newly added fuel for the given conditions and the denominator means amount of excess steam available before recycling. The range of recycle AOG is between 0 and 1. It is obvious that recycle ratio is always greater than zero because operator manipulates recycle ratio to regulate SC and SC is greater than zero. Mathematically it, however, could be greater than 1. This means shortage of the water content in AOG. In this case, recycle ratio should be set as unity, i.e. total recycle, and water deficiency should be added with fuel at the injector. Un-recycled AOG comprises mostly water vapor but also contains small fraction of un-reacted hydrogen as well as carbon monoxide which can be utilized through the after-burner. 22

23 Energy Balance With the energy balance analysis, the temperature of the each stream and capacity of the cooler can be calculated. Basically, it is assumed that all devices are adiabatic open systems except SOFC, external reformer, and afterburner. As mentioned in the previous molar balance section, temperature of flow leaving SOFC and pre-reformer unit is assumed thermal equilibrium with these devices. Therefore, those temperatures are assumed equal to their operating temperature. This means T SOFC = T 1a = T o3 and T PRE = T 1b = T 4 = T a1. Concerning AOG compressor work, low temperature is favored. In this work, temperature of the AOG compressor is fixed (T 2b = T comp =150 o C). The temperature of the feedstock, fuel and oxygen, is assumed room temperature, T f = T o1 = T 0 (= K). The molar composition and temperature are unchanged at the splitter where recycle ratio is determined, T 1c = T 2a = T v. Now, temperature of 10 streams out of 18 streams is preset so unknown stream temperatures, T 1c, T 2c, T 3a, T 3b, T 5, T o2, T a2, and T a3, should be evaluated with applying appropriate energy balance equations. However, 6 devices are available for applying first law of thermodynamics (adsorbent, condenser, cooler, injector, pre-heater, and recuperator). Unknown temperature and cooler duty cannot be solved only applying first law of thermodynamics because number of unknowns are larger than number of equations. This lack of equations could be overcome by applying ε-ntu method to the heat exchanger, i.e. pre-heater and recuperator [12] because both outlet temperature of each stream could be evaluated by means of this method. So, it is possible to evaluate the temperature of T 1c and T 2c applying ε-ntu method to recuperator. Once the temperature of injector outlet obtained, it is straightforward to compute both outlet temperature of the pre-heater, T 3b and T a2, by applying ε-ntu method. Temperature of stream leaving adsorbent, T 5, and injector, T 3a, and cooler duty could be computed by applying the first law of thermodynamics to adsorbent, injector, and cooler, respectively. Now, temperatures of departing 23

24 from the pre-heater for oxygen, or condenser, are undetermined and these temperatures could be obtained by the same method used for recuperator. However, it is assumed that oxygen stream is heated up to SOFC operating temperature because there is no necessity to overheat for oxygen flow. If flue gases leaving fuel pre-heater have not enough sensible heat to heat up oxygen flow, pre-heater should be replaced with condenser. For recuperator and fuel pre-heater, applied ε-ntu method is as follow (crossflow, both fluids mixed); NTU ε = NTU CNTU r exp 1 exp ( NTU ) ( C NTU ) r (2-23) where, ε=q/q max =q/c min (T h,i -T c,i ), C r =C min /C max, and NTU=AU o /C min. It is assumed NTU as 4 despite of small overall heat transfer coefficient, U o, for gases. This may be possible by means of increasing total surface area, A, replenishing high conductivity porous material into the flow channels. The effect of number of transfer units, NTU, on the effectiveness, ε, with several heat capacity ratios, Cr, is shown in figure 2-2. The classical expression of the first law of thermodynamics is applied into other devices, evidently, kinetic and potential energy terms are neglected in this work. For calculation of the enthalpy difference, specific heats for ideal gas mixture are integrated with respect to temperature. Regarding the reaction, heat of reaction for occurring reactions for SOFC, external reformer, CO 2 adsorbent, and after-burner is taking into account as well as sensible heat. In this work, the value of heat of adsorption is used literature value, J/mol [13]. It is assumed that heat of combustion from the after-burner is completely transferred into external reformer to provide heat of reforming reaction which is strongly endothermic. AOG recycle ratio, however, is controlled to maintain desired SC ratio not to supply enough heat into the external reformer. This may cause energy imbalance on the 24

25 external reformer. To make energy balanced, additional heat transfer term is taking into account on external reformer which could be surplus or insufficient. Once energy balance set, evaluation of temperature carried out by Newton-Rahpson method with 10 7 tolerance. 25

26 Figure 2-1. Process flow diagram 26

27 Cr = 0 Cr = 0.2 Cr = 0.4 Cr = 0.6 Effectiveness, ε Cr = 0.8 Cr = No. of transfer Units, NTU Figure 2-2. Effect of number of transfer units, NTU, on the effectiveness, ε, with several heat capacity ratios, C r, for crossflow and both fluids mixed heat exchanger 27

28 Table 2-1. Critical and reduced temperature and pressure Substance Formula Critical Temperature (K) Critical Pressure (MPa) Reduced Temperature Reduced Pressure Hydrogen H Methane CH Water H 2 O Carbon monoxide CO Carbon Dioxide CO Dodecane a) C 12 H From Ref. [5] a) Critical temperature and pressure data are from NIST chemistry webbook. 28

29 Table 2-2. Heat capacities of gases in the ideal-gas state Substance Formula Tmax (K) A 10 3 B 10 6 C 10 5 D Hydrogen H Methane CH Water H 2 O Carbon monoxide CO Carbon Dioxide CO

30 Table 2-3. Coefficients for dodecane heat capacity in the ideal-gas state Substance Formula A B C D Dodecane C 12 H

31 CHAPTER 3 RESULTS AND OPTIMIZATION Results Chemical Equilibrium at Pre-Reformer and Optimum Pre-Reformer Temperature Figure 3-1 shows reaction equilibrium results for steam reforming and water-gas shift reaction. Steam to carbon ratio was adjusted by methane and water vapor. The dry molar fraction is plotted versus reaction temperature with several SC ratios. Total fuel conversion and saturation of hydrogen molar fraction can be achieved low temperature with increasing SC ratio. The dry molar fractions of carbon monoxide and carbon dioxide appear in opposite manner with increasing SC ratio. With regard to determination of the operating temperature of pre-reformer, it should be considered energy requirement as well as produced amount of the hydrogen due to endothermic reaction. The amount of created hydrogen per consumed energy is plotted in Figure 3-2 for two different input temperatures, 25 and 100 C. In the energy efficiency aspect, it is considered that operation of pre-reformer in temperature range from 500 C to 600 C is the optimum case regardless of SC ratio. In this work, temperature of the pre-reformer unit is fixed as 550 C. Fuel and Oxygen Consumption Results without Recirculation and CO 2 Capture A parametric study is performed to find the optimal operating condition such as temperature of SOFC, SC ratio, recirculation ratio, and CO 2 adsorption. Illustrative computations are performed considering fixed electrical work output, 1 kw, from SOFC. It is assumed 25% excess oxygen is supplied into the afterburner for complete combustion of un-recycled AOG. Figures 3-3 and 3-4 demonstrate how fuel and oxygen consumption rates depend on variations of the SOFC temperature as well as SC ratio without recirculation and CO 2 capture. Regardless of SC ratio, required fuel and oxygen rates increase with increasing SOFC operating temperature. 31

32 On the other hand, fuel and oxygen consumption rates always decreases with increasing SC ratio in any temperature. Also, shape of the two graphs is quite similar to each other. This is evident taking whole system as control volume. Apparent reaction is as follow taking into account adsorbed carbon dioxide; ( ) C H x O 13H O+ 12CO + xo (3-1) Several overall molar balance results are provided in Table 3-1. Recycle Ratio and Water Management Figure 3-5 shows AOG recycle percentage, i.e. F 2a /F 1c 100. As mentioned in molar balance section, AOG recycle percentage is determined to adjust SC ratio. AOG recycle percent increases with increasing SC ratio. With fixed fuel input, AOG recycle percentage should be doubled when SC ratio becomes doubled. As shown in Fig. 3-3, fuel consumption rate decreases with SC ratio so AOG recycle percent does not increase by double with doubled SC ratio. AOG recycle percent is independent with SOFC temperature despite of the fact that fuel requirement increases with SOFC temperature. This means AOG water content increases with SOFC temperature so it is possible to maintain SC ratio though fuel flow rate is increased with SOFC temperature. Also, Fig 3-5 shows that AOG has enough water content to adjust SC ratio up to 5 by recycling. Therefore, water is self sufficient, in other words there is no necessity to add water with fuel. Energy Balance and Efficiency Results without Recirculation and CO 2 Capture As mentioned in energy balance section, un-recycled AOG acts an important role in energy balance for external reformer, since un-recycled AOG is burned at the after-burner and provides heat into external reformer for steam reforming reaction. Heat, however, is imbalanced on prereformer unit. To make energy balanced, another heat effect, Q PRE, is introduced on pre-reformer 32

33 unit. The amount of this newly introduced heat effect is dependent upon SOFC temperature. This could be either heat surplus or insufficient heat depending on SOFC temperature. Figure 3-6 shows energy balance results for the external reformer. The negative Q PRE means heat is rejected from the external reformer, heat surplus, while the positive Q PRE means heat from AOG and after-burner is insufficient for heat of reforming reaction. From the energy and molar balance results, high SC ratio case requires more heat of reforming reaction. Both excess heat and insufficient heat cases are not favored in efficiency point of view. In Figure 3-7, detailed heat analysis is presented for SC = 4. Shaded region named H AOG represents heat transferred from sensible heat of AOG stream and under the shaded region denotes heat transferred from the afterburner, Q AB. The magnitude of heat requirement for reforming reactions, H PRE, is decreased slightly with SOFC temperature. The magnitude of transferred heat from the after-burner increases with SOFC temperature due to increasing of carbon monoxide content into the afterburner. The major reason of changing from insufficient heat region to excess heat region is sensible heat of AOG. Two different efficiencies, η LHV and η Th, are evaluated. The first efficiency, η LHV, is based on lower heating value of fuel, while the second efficiency, η Th, is based on total enthalpy change of Eq. (3-1). Seemingly, apparent chemical reaction, Eq. (3-1), is similar to combustion process. In this work, efficiency based on lower heating value is used despite of water condensing. Definition of efficiency considering heat imbalance for Prereformer unit is as follows; η LHV Welect FLHV f = W Q ( Q < 0) PRE ( Q 0) elect PRE PRE > FLHV f (3-2) 33

34 In insufficient heat case, heat deficiency at the pre-reformer unit is subtracted from SOFC electrical work. Figure 3-8 demonstrates how the efficiency changes with variations of SOFC temperature as well as SC ratio. Dotted lines in Fig. 3-8 represent efficiency under no consideration of heat imbalance at pre-reformer unit and correspond with fuel consumption rate. Figure 3-8 allows us to understand the significance of heat imbalance adjudging operation conditions. System efficiency has the maximum value for given SC ratio. Considering energy imbalance on pre-reformer, the temperature, which makes heat balanced without Q PRE, is named as self-energy balanced operating temperature. It is possible to obtain the maximum efficiency operating SOFC with this self-energy balanced operating temperature. The higher temperature operation yields the more fuel consumption. Lower temperature operation gives heat insufficiency on the pre-reformer unit. Therefore, produced electrical work should reimburse this insufficient heat on the pre-reformer. Carbon Dioxide Capture Effects In this work, it is assumed only hydrogen is electrochemically reacted and carbon monoxide is converted to hydrogen and carbon dioxide by WGS reaction, Eq. (2-4), inside the SOFC. Figure 3-1 is obtained assuming initially methane and water vapor corresponding to given SC ratio. With recycling AOG, reforming channel inlet gases consist of all 5 chemical components. After the equilibrium achieved inside the external reformer, outlet of reforming channel contains unreacted methane. This unreacted methane is undergone reforming reaction, Eq. (2-3), in SOFC. Both internal reforming and WGS reactions are limited by equilibrium. If it is possible to manipulate both forward reactions getting over the equilibrium, fuel consumption rate will decrease. With regard to concentration under constant temperature and pressure condition, there are two ways getting over the equilibrium; to remove product of forward reaction, and to add more reactant of forward reaction. The first concept is ineffective to steam 34

35 reforming reaction, Eq. (2-3), because products, CO and H 2, are already consuming by WGS and electrochemical reactions. For WGS reaction, CO 2 capture corresponds to the first concept. Concerning the second concept, it is effective for both WGS and steam reforming reactions to put in more water vapor into the anode which can be achieved by recirculation of AOG back into anode inlet due to high water content of AOG. Carbon dioxide capture effects on fuel consumption rate are illustrated in Fig. 3-9 for several SC ratios. For the comparison, decreased fuel consumption rate due to CO 2 capture is expressed in a fraction to the fuel consumption rate for the same condition, expect CO 2 capture. These reduced fractions are depicted in Fig Fuel consumption rate is definitely decreased with CO 2 capture but decreased amount is not directly proportional to CO 2 capture. From the Fig. 3-10, it is found that CO 2 capture effects are conspicuous in high temperature region and low SC ratio rather than low temperature and high SC ratio. Recirculation Effects In Figure 3-11, fuel consumption rate is calculated with variations of the recirculation ratio as well as SOFC temperature and SC ratio. And reduced fractions compared with no recirculation case are illustrated in Fig Fuel consumption rate decreases with increasing recirculation ratio. In this simulation, recirculation ratio is limited up to 0.5 because current density is affected by recirculation ratio. It can be verified that recirculation effects are conspicuous in high temperature region and low SC ratio rather than low temperature and high SC ratio. Optimization Concerning efficiency, heat imbalance on the pre-reformer should be considered with CO 2 capture rate and recirculation ratio. Total 4620 cases of parametric studies had been conducted 35

36 concerning efficiency with variations of SC, T SOFC, CO 2 capture and recirculation ratio. Parameters for optimization are as follows; SC: 2, 3, 4, and 5 T SOFC : 600, 700, 800, 900 and 1000 C CO2 capture: 21 cases (0 ~ 100 %) Recirculation ratio: 11 cases (0 ~ 0.5) Concerning maximum efficiency, these parametric studies could be classified 6 unique types according to dependency on CO 2 adsorption and recirculation; a) high CO 2 adsorption and low recirculation b) moderate CO 2 adsorption and low recirculation c) low CO 2 adsorption and low recirculation d) low CO 2 adsorption and high recirculation e) moderate CO 2 adsorption and high recirculation f) high CO 2 adsorption and high recirculation Distribution map for those 6 categories is provided in the Table 3-2. Representative overall efficiencies of the each category, depending on CO 2 capture and recirculation ratio at given SC and T SOFC, are illustrated in Figure Among all 4620 cases, 20 maximum efficiencies for given SC and T SOFC are presented in the Table 3-3 and Figure Data in the Table 3-3 and Figure 3-14 is representation of the highest efficiency with given SC and T SOFC. In the Table 3-3, carbon dioxide capture and recirculation effects appear in opposite manner although they have a common tendency for dependency on SC and temperature. Low temperature cases prefer maximum CO 2 capture and no recirculation, while maximum recirculation and low CO 2 capture are preferred in high temperature. 36

37 0.9 (a) S/C = 2 (b) S/C = molar fraction, y i,dry [-] H 2 CH 4 CO CO molar fraction, y i,dry [-] (c) S/C = 4 (d) S/C = molar fraction, y i,dry [-] molar fraction, y i,dry [-] Temperature [ o C] Figure 3-1. Reaction equilibrium results for steam reforming and water-gas shift reaction for several steam to carbon ratios 37

38 12 Hydrogen output / required heat [mmol/kj] T R = 25 o C S/C = 2 S/C = 3 S/C = 4 S/C = Pre-Reformer Temperature, [ o C] Figure 3-2. Produced hydrogen per consumed energy A) T R = 25 C, B) T R = 100 C A 38

39 12 Hydrogen output / required heat [mmol/kj] T R = 100 o C S/C = 2 S/C = 3 S/C = 4 S/C = Pre-Reformer Temperature, [ o C] Figure 3-2. Continued B 39

40 Dodecane consumption rate for 1 kw operation [g/min] T PR = 550 o C U = 0.85 η FC = 0.85 no CO 2 capture r = 0 S/C = 2 S/C = 3 S/C = 4 S/C = SOFC Temperature, T S [ o C] Figure 3-3. Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio, where no CO 2 capture and no recirculation 40

41 Oxygen consumption rate for 1 kw operation [g/min] 7.4 T PR = 550 o C U = η FC = 0.85 no CO 2 capture r = S/C = 5 S/C = 4 S/C = 2 S/C = SOFC Temperature, T S [ o C] Figure 3-4. Effect of SOFC temperature on oxygen consumption rate with different steam to carbon ratio, where no CO 2 capture and no recirculation 41

42 AOG Recycle percent [%] T PR = 550 o C U = 0.85 η FC = 0.85 no CO 2 capture r = 0 S/C = 5 S/C = 4 S/C = 3 68 S/C = SOFC Temperature, T S [ o C] Figure 3-5. AOG recycle percent versus SOFC temperature with different steam to carbon ratio, where no CO 2 capture and no recirculation 42

43 S/C = 5 S/C = 4 S/C = 3 S/C = 2 T PR = 550 o C U = 0.85 η FC = 0.85 no CO 2 capture r = 0 Q PRE [Watt] insufficient Heat region surplus Heat region SOFC Temperature, T S [ o C] Figure 3-6. Effect of SOFC temperature on additional heat transferred rate for pre-reformer unit with different steam to carbon ratio, where no CO 2 capture and no recirculation 43

44 Rate of required and transferred heat [Watt] T PR = 550 o C U = 0.85 η FC = 0.85 S/C = 4 no CO 2 capture r = 0 Insufficient Heat H AOG + Q AB H PRE H AOG Excess Heat Q AB SOFC temperature, T S [ o C] Figure 3-7. Effect of SOFC temperature on detailed additional heat transferred rate for prereformer unit with S/C =4, where no CO 2 capture and no recirculation 44

45 η LHV [%] S/C = 2 S/C = 3 S/C = 4 S/C = 5 T PR = 550 o C U = 0.85 η FC = 0.85 no CO 2 capture r = SOFC Temperature, T S [ o C] Figure 3-8. Effect of SOFC temperature on efficiency based on LHV with different steam to carbon ratio, where no CO 2 capture and no recirculation 45

46 Dodecane consumption rate [g/min] T PR = 550 o C U = 0.85 η FC = 0.85 r = 0 CO 2 capture 0 % 50 % 100 % Line color S/C = 2 S/C = 3.5 S/C = SOFC Temperature, T S [ o C] Figure 3-9. Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratios and several CO 2 adsorption percents, where no recirculation 46

47 Dodecane consumption rate ratio to no CO 2 capture T PR = 550 o C U = 0.85 η FC = 0.85 r = 0 CO 2 capture 50 % 100 % Line color S/C = 2 S/C = 3.5 S/C = SOFC Temperature, T S [ o C] Figure Carbon dioxide capture effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no recirculation 47

48 2.10 Dodecane consumption rate [g/min] T PR = 550 o C U = 0.85 η FC = 0.85 no CO 2 capture Line color S/C = 2 S/C = 3.5 S/C = 5 recirculation, r r = 0 r = 0.25 r = 0.5 S/C = 5, r = 0 S/C = 3.5, r = 0.25 S/C = 2, r = SOFC Temperature, T S [ o C] Figure Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio and several recirculation ratio, where no CO 2 adsorption 48

49 Dodecane consumption rate ratio to no recirculation Line color S/C = 2 S/C = 3.5 S/C = 5 T PR = 550 o C U = 0.85 recirculation ratio, r η FC = no CO 2 capture SOFC Temperature, T S [ o C] Figure Recirculation effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no CO 2 adsorption 49

50 CO 2 Adsorption percent [%] Recirculation ratio, r [-] Figure Efficiency based on LHV of fuel; A) S/C = 2, T SOFC =600 o C (example (a), low temperature region), B) S/C = 3, T SOFC =700 o C (example (b), low or moderate temperature region), C) S/C = 4, T SOFC =800 C (example (c), moderate temperature and medium to high S/C region), D) S/C = 5, T SOFC =900 o C (example (d), moderate or high temperature and high S/C region), E) S/C = 5, T SOFC =1000 o C (example (e), high temperature and high S/C region), and F) S/C = 2, T SOFC =900 o C (example (f), high temperature and low S/C region) 50

51 CO 2 Adsorption percent [%] Recirculation ratio, r [-] Figure Continued B 51

52 CO 2 Adsorption percent [%] Recirculation ratio, r [-] C Figure Continued 52

53 CO 2 Adsorption percent [%] Recirculation ratio, r [-] D Figure Continued 53

54 100 CO 2 Adsorption percent [%] Recirculation ratio, r [-] Figure Continued E 54

55 CO 2 Adsorption percent [%] Recirculation ratio, r [-] Figure Continued F 55

56 Steam to carbon ratio, S/C SOFC temperature, T S [ o C] Figure Effects of SOFC temperature and SC on maximum system efficiency 56

57 Table 3-1. Overall molar balance results S/C T SOFC [ o C] C 12 H 26 Input [mmol/sec] O 2 /C 12 H 26 H 2 O/C 12 H 26 O 2 /C 12 H 26 Output CO 2 /C 12 H 26 total adsorbed output

58 Table 3-2. Dependency on CO 2 adsorption percentage and recirculation ratio S/C T SOFC 600 o C 700 o C 800 o C 900 o C 1000 o C 2 (a) (b) (a) or (d) (f) (f) 3 (a) (b) (c) (d) (f) 4 (a) (b) (c) (d) (e) 5 (a) (b) (c) (d) (e) 58