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Process Design and Optimization of Solid Oxide Fuel Cells and Pre-Reformer System Utilizing Liquid Hydrocarbons

Permanent Link: http://ufdc.ufl.edu/UFE0022733/00001

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Title: Process Design and Optimization of Solid Oxide Fuel Cells and Pre-Reformer System Utilizing Liquid Hydrocarbons
Physical Description: 1 online resource (63 p.)
Language: english
Creator: Lee, Tae-Seok
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: 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 CO2 capture. Studies on the reforming chemical reactions and chemical equilibria are presented. The results include CO2 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 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 CO2 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 oC SOFC temperature, 550 oC Pre-Reformer temperature, 0.35 recirculation ratio and 25% carbon dioxide adsorption yielding the highest efficiency as 74.79%.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Tae-Seok Lee.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Chung, Jacob N.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022733:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022733/00001

Material Information

Title: Process Design and Optimization of Solid Oxide Fuel Cells and Pre-Reformer System Utilizing Liquid Hydrocarbons
Physical Description: 1 online resource (63 p.)
Language: english
Creator: Lee, Tae-Seok
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: 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 CO2 capture. Studies on the reforming chemical reactions and chemical equilibria are presented. The results include CO2 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 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 CO2 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 oC SOFC temperature, 550 oC Pre-Reformer temperature, 0.35 recirculation ratio and 25% carbon dioxide adsorption yielding the highest efficiency as 74.79%.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Tae-Seok Lee.
Thesis: Thesis (M.S.)--University of Florida, 2008.
Local: Adviser: Chung, Jacob N.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022733:00001


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1 PROCESS DESIGN AND OPTI MIZATION OF SOLID OXIDE FUEL CELLS AND PREREFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS By TAE SEOK LEE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2008

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2 2008 Tae Seok Lee

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3 To my beloved wife and son

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4 ACKNOWLEDGMENTS This research project would not have been possible without the s upport of many people. I wish to express my gratitude to my supervisor, Dr. Chung, who was abundantly helpful and offered invaluable assistance, support and guidan ce. 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 w ould like to express my l ove and gratitude to my beloved families; for their unders tanding and endless love, thr ough the duration of my studies.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES................................................................................................................ .........8 ABSTRACT....................................................................................................................... ..............9 CHAPTER 1 INTRODUCTION AND BACKGROUND...........................................................................11 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............................................13 2 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....................................................................................................................2 0 Recycle Ratio.................................................................................................................. .22 Energy Balance................................................................................................................. ......23 3 RESULTS AND OPTIMIZATION........................................................................................31 Results........................................................................................................................ .............31 Chemical Equilibrium at Pre-Reformer and Optimum Pre-Reformer Temperature.......31 Fuel and Oxygen Consumption Resu lts without Reci rculation and CO2 Capture..........31 Recycle Ratio and Water Management...........................................................................32 Energy Balance and Efficiency Results without Recirculation and CO2 Capture..........32 Carbon Dioxide Capture Effects.....................................................................................34 Recirculation Effects.......................................................................................................35 Optimization................................................................................................................... ........35 4 SUMMARY AND CONCLUSION.......................................................................................60

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6 LIST OF REFERENCES............................................................................................................. ..62 BIOGRAPHICAL SKETCH.........................................................................................................63

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7 LIST OF TABLES Table page 1-1 Types of fuel cells, their characteristics.............................................................................15 2-1 Critical and reduced te mperature and pressure..................................................................28 2-2 Heat capacities of gase s in the ideal-gas state...................................................................29 2-3 Coefficients for dodecane heat ca pacity in the ideal-gas state..........................................30 3-1 Overall molar balance results.............................................................................................5 7 3-2 Dependency on CO2 adsorption percentage a nd recirculation ratio..................................58 3-3 Maximum overall efficiencies for given SC and TSOFC with corresponding recirculation ratio and CO2 capture percent.......................................................................59

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8 LIST OF FIGURES Figure page 2-1 Process flow diagram....................................................................................................... ..26 2-2 Effect of number of transfer units, NTU, on the effectiveness, with several heat capacity ratios, Cr, for crossflow and both fluids mixed heat exchanger..........................27 3-1 Reaction equilibrium results for steam reforming and water-gas shift reaction for several steam to carbon ratios............................................................................................37 3-2 Produced hydrogen per consumed energy.........................................................................38 3-3 Effect of SOFC temperature on fuel cons umption rate with different steam to carbon ratio, where no CO2 capture and no recirculation..............................................................40 3-4 Effect of SOFC temperature on oxygen c onsumption rate with different steam to carbon ratio, where no CO2 capture and no recirculation..................................................41 3-5 AOG recycle percent versus SOFC temper ature with different steam to carbon ratio, where no CO2 capture and no recirculation.......................................................................42 3-6 Effect of SOFC temperature on additional heat transferred rate for pre-reformer unit with different steam to carbon ratio, where no CO2 capture and no recirculation.............43 3-7 Effect of SOFC temperature on detailed additional heat tran sferred rate for prereformer unit with S/C =4, where no CO2 capture and no recirculation............................44 3-8 Effect of SOFC temperature on efficien cy based on LHV with different steam to carbon ratio, where no CO2 capture and no recirculation..................................................45 3-9 Effect of SOFC temperature on fuel cons umption rate with different steam to carbon ratios and several CO2 adsorption percents, where no recirculation.................................46 3-10 Carbon dioxide capture effects on the de pleted fuel consumption fraction for the several steam to carbon ratios where no recirculation......................................................47 3-11 Effect of SOFC temperature on fuel cons umption rate with different steam to carbon ratio and several recirc ulation ratio, where no CO2 adsorption.........................................48 3-12 Recirculation effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no CO2 adsorption........................................................................49 3-13 Efficiency based on LHV of fuel.......................................................................................50 3-14 Effects of SOFC temperature a nd SC on maximum system efficiency.............................56

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9 Abstract of Thesis Presen ted 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 OPTI MIZATION OF SOLID OXIDE FUEL CELLS AND PREREFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS By Tae Seok Lee December 2008 Chair: Jacob N. Chung Major: Mechanical Engineering We conducted optimization for a flow process consisting of a typica l direct internal reforming Solid Oxide Fuel Cell (SOFC) util izing synthesis gas (s yngas) produced through steam reforming of the liquid hydrocarbon inside th e external reforming unit. The anode off gas recycling system and after-burne r 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 fo r minimum fuel and oxygen consumption rates corresponding to the temperatures of pre-reformer and SOFC, th e steam to carbon ratio inside the pre-reformer, recircula tion ratio, and rate of CO2 capture. Studies on the reforming chemical reactions and chemical equilibria ar e presented. The results include CO2 adsorption in the adsorbent bed as well as recirculation. For the molar balance study, we provided dodecane consumption rate and overall molar balance re sults. With the energy balance analysis, the temperature distributions in the system are cal culated by means of solving energy balance for each device. However, energy is not perfectly bala nced. 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, wh ich makes heat balanced without newly introduced heat effect

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10 on pre-reformer, is named as self-energy bala nced operating temperat ure. 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 outpu t divided by the lower heating value rate of fuel input. Considering net power output, produced elect rical work should reimburse insufficient heat on the pre-reformer. It is also provided optimal case operating parameters. Thermodynamic efficiency is mainly affected by CO2 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, r ecommend operating conditions are SC =2, 800 oC SOFC temperature, 550 oC Pre-Reformer temperature, 0.35 r ecirculation ratio and 25% carbon dioxide adsorption yielding the highest efficiency as 74.79%.

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11 CHAPTER 1 INTRODUCTION AND BACKGROUND Steam Reforming Reaction The catalytic conversion of hydrocarbons with wa ter steam is one of the most widely used industrial methods for production of hydrogen-co ntaining gases. The first industrial steam reformer was installed at Baton Rouge by Standa rd Oil of New Jersey and commissioned in 1930. Steam reforming is an essential process in the manufacture of synt hesis gas (syngas) and hydrogen from hydrocarbons [1, 2]. Solid-Oxide Fuel Cells A fuel cell is an electrochemical energy c onversion device that c onverts chemical energy of fuel directly into electri city, 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 therm odynamic limitations of heat engines such as the Carnot efficiency. A fuel cell is similar to a batter y 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 th e batteries. Because of this, batteries may be discharged, whereas fuel ce lls 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 ch aracteristics of the main fuel cell types. Solid oxide fuel cells (SOFCs) have an electr olyte that is a solid, non-porous metal oxide. The cell is constructed w ith two porous electrodes that sandwi ch an electrolyte. Air (or oxygen)

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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 th e cell where they contact the anod e. 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 11223344MMMM (1-1) where | i| is a stoichiometric coefficient, positiv e sign for a product and negative sign for a reactant, and Mi stands for a chemical species i. As the reaction represented by Eq. (1-1) progresses, the changes in the numbers of moles of species Mi, dni, are in direct proportion to the stoichiometric numbers Introducing variable called the extent of reac tion or progress variable, it is possible to represent an amount of reacti on. The general relation co nnecting the differential change dni with d is therefore: or i ii idn dndd (1-2) Integration of Eq. (1-2) from an initial un-reacted state to a st ate reached after an arbitrary amount of reaction gives: or i ion iiiioi nodndnn (1-3) The molar fractions of the species i, yi, are as follows:

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13 iioi i iioi iiinn y nn (1-4) Equation (1-4) represents molar fraction of the ith 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 gene ral equation analogous to Eq. (1-3) is as follow: ,iijj jdnd (1-5) where i,j denotes the stoichiometric number of species i in reaction j. The number of moles of ith 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 unreacted state to a state reached after an arbitrary amount of reaction gives: iioijj jnn (1-6) Therefore, molar fraction of the i-th species in progress of multireaction can be expressed as follow ioijj j i i i ioijj i ijin n y n n (1-7) Chemical Reaction Equilibrium and Equilibrium Constant Consider a closed system containing an arbi trary number of species and comprised of an arbitrary number of phases in which the temper ature and pressure are uniform. Combining the first law with the second law of the thermodynamics yields ,0 or 0tttt TPdUPdVTdSdG (1-8)

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14 where superscript t denotes total properties of the system. This equation (1-8) represents that all irreversible processes occurring at constant temperature and pressu re proceed in such a direction as to cause a decrease in the Gibbs energy of the system. For the single-phase, open system, mixt ure, the total Gibbs energy (nG or Gt) 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 ii idnGnVdPnSdTdn (1-9) where i is the chemical potential of sp ecies i in the mixture defined by ,, j i i P TnnG n (1-10) Substituting Eq. (1-2) into Eq. (1-9) gives ii idnGnVdPnSdTd (1-11) The right hand side of Eq.(1-11), is an exact differential expression; whence, t ii i TP TPG nG (1-12) Considering Eq. (1-8), a criterion of chem ical reaction equilibrium is therefore: 0ii i (1-13) By assuming the equilibrium mixture behave s as an ideal gas, Eq. (1-13) becomes expii ii io ii i i oo iG PP yK PRTP (1-14) This expression is also the definition of the equilibrium constant, K [5, 6].

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15 Table 1-1. Types of fuel cells, their characteristics PEFC AFC PAFC MCFC SOFC Electrolyte Hydrated Polymeric Ion Exchange Membranes Mobilized or Immobilized Potassium Hydroxide in asbestos matrix Immobilized Liquid Phosphoric Acid in SiC Immobilized Liquid Molten Carbonate in LiAlO2 Porovskites (Ceramics) Electrodes Carbon Transition metals Carbon Nickel and Nickel Oxide Perovskite and perovskite / metal cermet Catalyst Platinum Platinum Platinum Electrode material Electrode material Interconnect Carbon or metal Metal Graphite Stainless steel or Nickel Nickel, ceramic, or steel Operating Temperature 40 – 80 C 65 – 220 C 205 C 650 C 600–1000 C Charge Carrier H+ OH H+ CO3 2 O2 External Reformer HC Yes Yes Yes No, for some fuels No, for some fuels and cell designs External shift conversion of CO to H2 Yes, plus purification to remove trace CO Yes, plus purification to remove CO and CO2 Yes No No Prime Cell Components Carbon-based Carbon-based Graphitebased Stainlessbased Ceramic Product Water Management Evaporative Evaporative Evaporative Gaseous Product Gaseous Product Product Heat Management Process Gas + Liquid Cooling Medium Process Gas + Electrolyte Circulation Process Gas + Liquid cooling medium or steam generation Internal Reforming + Process Gas Internal Reforming + Process Gas

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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 recirc ulated direct internal reforming SOFC, prereforming unit, recuperator, carbon dioxide adso rbent, 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 wh ich produces electrical power in a SOFC. With appropriate AOG recycle, it is poss ible 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 compre ssor is required for this AOG circulation system. From thermodynamics point of view, high temperature compressing process requires more work than low temperature comp ression. Therefore, AOG should be cooled down before the compressing process. After compresse d, 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-bur ner could be used to heat up mixture of fuel and recycled AOG or oxygen flows by passing through fuel pre-he ater 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 le tter denotes temperature. Theref ore, streams 1a and 1b are the same molar composition but in different temperature.

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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 ch emical 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 mo lar balance or chemical equilibrium. This means pressure effect is ignored on equilibrium constant. Complete combustion occurs at th e after-burner. So, it is assume d 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 r eaction is converted into electrical work instead of taking into account voltage losses consisting of activ ation, ohmic (or resistive), and concentration polarization. Thermodynamic Properties of Chemical Species Justification for Ideal Gas Assumption As mentioned in assumption section, all gases are assumed as the ideal gases. This condition should be justified before evaluating th ermodynamic properties of chemical species. It is well-known that all gases and vapors appr oach ideal-gas behavior under the low density condition. At higher densities the behavior may de viate substantially from the ideal-gas equation of state. By introducing compressibility fact or, Z, this ambiguousness, low density, condition could be cleared. Compressibility factors Z fo r different chemical sp ecies exhibit similar behavior when correlated as a f unction of reduced temperature, Tr, and reduced pressure, Pr.

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18 Critical temperature and pressure as well as redu ced temperature and pressure data are provided in Table 2-1. Reduced temperatures in the Table 2-1 are evaluated at the lowest temperature, T2b, in the process flow diagram. If the pressure is very low (that is, Pr << 1), the ideal-gas model can be assumed with good accuracy, regardless of the temperature. Furthermore, at high temperatures (that is, Tr > 2), the ideal-gas model can be assumed with good accu racy to reduced pressures as high as four or five [5, 6]. As shown in Tabl e 2-1, reduced pressures are significantly small, Pr ~ 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, 22 PC ABTCTDT R (2-1) where either C or D is zero, depending on the su bstance considered and T is in Kelvin. Equation (2-1) is applied for Hydrogen, Water vapor, Methane, Carbon Monoxi de and Carbon Dioxide. The coefficients are presented in the Table 2-2 [5 ]. This empirical relationship is valid from room temperature (298.15 K) to Tmax presented in Table 2-2. Heat Capacity for Fuel (n-Dodecane) The specific heat of dodecane is interpolated into 3rd order polynomial, Eq. (2-2), using data achieved by Lemmon and Huber [7 ] and Span and Wagner [8]. 23 PC ABTCTDT R (2-2) Interpolation result is presented in Table 2-3.

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19 Molar Balance Chemical Equilibrium at the Pre-Reformer As shown in Fig. 2-1, pre-reformer unit consis ts of external reformer and after-burner. Preheated mixture of fuel and recycled AOG is pa ssing through reforming cha nnel 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]. 4223CHHOCOH (2-3) 222COHOHCO (2-4) 422224CHHOCOH (2-5) Reforming reactions (2-3) and (2-5) are str ongly endothermic, so the forward reaction is favored by high temperature, while the water-ga s 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 he at of AOG from SOFC and combustion heat from the after-burner. Let the extents of reacti on, which are defined as Eq. (1-5), be R1, R2, and R3 for chemical equilibrium reactions (2-3), (2-4), and (2-5), respectively. Then equilibrium molar fractions are expressed as follows; 2 2,123 132 22oHORRR HO oRRF y F (2-6) 4 4,13 1322oCHRR CH oRRF y F (2-7) 2 2,123 1334 22oHRRR H oRRF y F (2-8)

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20 ,12 1322oCORR CO oRRF y F (2-9) 2 2,23 1322oCORR CO oRRF y F (2-10) where, Fo and Fo,i denote inlet total molar flow rate, label 3b, and inlet molar flow rate of i component, respectively. Once exte nts of reaction are obtained, evaluation of the equilibrium molar fraction is straightforward. Therefore, one needs three equations to be solved simultaneously to find R1, R2 and R3 under equilibrium condition. These are the chemical equilibrium equations corresponding to the steam reforming and water-gas shift reaction, as following; 2 422 3 1 1expHCO R R o CHHOyy G p KT pyyRT (2-11) 22 20 2 2expHCO R R o HOCOyy G p KT pyyRT (2-12) 22 242 4 3 3 2expHCO R R o HOCHyy G p KT pyyRT (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 ener gy 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 fo r methane, Eq. (2-3), water-gas shift reaction,

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21 Eq.(2-4), and electrochemical reac tion, Eq.(2-14), occur simultane ously at the direct internal reforming SOFC. 2221 2 HOHO (2-14) The extent of reaction for electrochemical reaction, S3, can be expressed using molar balance, definition of molar fracti on, and recirculation ratio [11]. 2,12 33 1oHSS SUF rrU (2-15) Here, r is the recirculation ratio, U is fuel utilization, Si is reaction coordina tes for i-th reaction at the SOFC, respectively. Also, Fo denotes inlet of SOFC anode label 5. With the above assumptions and Eq. (2-15), molar fractions for all th e species at the exit of the anode of fuel cell are given as below : 4 4,1 12oCHS CH oSF y F (2-16) 2 2 2,12 ,12 13 1 2oHSS oHOSS HO oSF FU rrU y F (2-17) 2 2,12 13 11 21oHSS H oSF rU y FrrU (2-18) ,12 12oCOSS CO oSF y F (2-19) 2 2,2 12oCOS CO oSF y F (2-20)

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22 Here, S1 and S2 are only unknowns. Likewise chemical e quilibrium 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 fo r AOG recycle system is determination of the recycle ratio. The amount of recycl ed AOG is manipulated to mainta in the desired SC value. The AOG recycle ratio is defined as recycl ed AOG to pre-recycled AOG, Rc = F2/F1. The steam to carbon ratio is defined as; 2 42, 2, HO CHfF SC FFNC (2-21) where, Ff and NC denote molar flow rate of fuel a nd 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 241,1,01f HOCHSCFNC Rc FSCF (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 mean s amount of excess steam available before recycling. The range of recycle AOG is between 0 a nd 1. It is obvious that recycle ratio is always greater than zero because operato r manipulates recycle ratio to regulate SC and SC is greater than zero. Mathematically it, however, could be gr eater than 1. This means shortage of the water content in AOG. In this case, recycle ratio should be set as unity, i.e. to tal 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-r eacted hydrogen as well as carbon monoxide which can be utilized through the after-burner.

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23 Energy Balance With the energy balance analysis, the temperat ure of the each stream and capacity of the cooler can be calculated. Basically, it is assume d 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 temperat ures are assumed equa l to their operating temperature. This means TSOFC = T1a = To3 and TPRE = T1b = T4 = Ta1. Concerning AOG compressor work, low temperature is favored. In this work, temperature of the AOG compressor is fixed (T2b = Tcomp=150 oC). The temperature of the feedst ock, fuel and oxygen, is assumed room temperature, Tf = To1 = T0 (= 298.15 K). The molar com position and temperature are unchanged at the splitter where recycle ratio is determined, T1c = T2a = Tv. Now, temperature of 10 streams out of 18 streams is pres et so unknown stream temperatures, T1c, T2c, T3a, T3b, T5, To2, Ta2, and Ta3, should be evaluated with applying a ppropriate energy balance equations. However, 6 devices are availa ble for applying first law of thermodynamics (adsorbent, condenser, cooler, injector, preheater, and recuperator). Unknow n 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 -NTU method to the heat exchanger, i.e. pre-heat er 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 T1c and T2c applying -NTU method to recuperator. Once the temperature of injector outlet obtained, it is st raightforward to compute both outlet temperature of the pre-heater, T3b and Ta2, by applying -NTU method. Temperature of stream leaving adsorbent, T5, and injector, T3a, and cooler duty could be com puted by applying the first law of thermodynamics to adsorbent, injector, and cooler respectively. Now, temp eratures of departing

PAGE 24

24 from the pre-heater for oxygen, or condenser, ar e 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 sensib le heat to heat up oxygen flow, pre-heater should be replaced with condenser. For recuperator and fuel pre-heater, applied -NTU method is as follow (crossflow, both fluids mixed); 1 1exp1expr rNTU CNTU NTU NTUCNTU (2-23) where, =q/qmax=q/Cmin(Th,i-Tc,i), Cr=Cmin/Cmax, and NTU=AUo/Cmin. It is assumed NTU as 4 despite of small overall heat transfer coefficient, Uo, for gases. This may be possible by means of increasing total surface area, A, replenishing hi gh conductivity porous material into the flow channels. The effect of number of tran sfer units, NTU, on the effectiveness, 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 en thalpy difference, specific heats for ideal gas mixture are integrated with respect to temperatur e. Regarding the reaction, heat of reaction for occurring reactions for SOFC, external reformer, CO2 adsorbent, and after-burner is taking into account as well as sensible heat. In this work, th e value of heat of adso rption is used literature value, 17000 J/mol [13]. It is assumed that heat of combustion from the after-burner is completely transferred into external reformer to provide heat of refo rming reaction which is strongly endothermic. AOG recycle ra tio, however, is controlled to maintain desired SC ratio not to supply enough heat into the external reformer. This may cause energy imbalance on the

PAGE 25

25 external reformer. To make energy balanced, addi tional 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.

PAGE 26

26 Figure 2-1. Process flow diagram

PAGE 27

27 012345 0.0 0.2 0.4 0.6 0.8 1.0 Cr = 1.0 Cr = 0.8 Cr = 0.6 Cr = 0.4 Cr = 0.2 Cr = 0 Effectiveness, No. of transfer Units, NTU Figure 2-2. Effect of nu mber of transfer units, NTU, on the effectiveness, with several heat capacity ratios, Cr, for crossflow and both fluids mixed heat exchanger

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28 Table 2-1. Critical and reduced temperature and pressure Substance Formula Critical Temperature (K) Critical Pressure (MPa) Reduced Temperature Reduced Pressure Hydrogen H2 33.2 1.30 1.2745 101 7.7942 10-2 Methane CH4 190.4 4.60 2.2224 100 2.2027 10-2 Water H2O 647.3 22.12 6.5372 10-1 4.5807 10-3 Carbon monoxide CO 132.9 3.50 3.1840 100 2.8950 10-2 Carbon Dioxide CO2 304.1 7.38 1.3915 100 1.3730 10-2 Dodecanea) C12H26 658.2 1.80 6.4289 10-1 5.6292 10-2 From Ref. [5] a) Critical temperature a nd pressure data are from NIST chemistry webbook.

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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 H2 3000 3.249 0.422 0 0.083 Methane CH4 1500 1.702 9.081 2.164 0 Water H2O 2000 3.470 1.450 0 0.121 Carbon monoxide CO 2500 3.376 0.557 0 0.031 Carbon Dioxide CO2 2000 5.457 1.045 0 1.157

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30 Table 2-3. Coefficients for dodecane h eat capacity in the ideal-gas state Substance Formula A B C D Dodecane C12H26 3.5966 0.1558 1.0259 10 4 2.6471 10 8

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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 me thane and water vapor. The dry molar fraction is plotted versus reaction temperature with severa l 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 CO2 Capture A parametric study is performed to find the optimal operating condition such as temperature of SOFC, SC ratio recirculation ratio, and CO2 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 CO2 capture. Regardless of SC ratio, required fuel and oxygen rates increase with increasing SOFC operating temperature.

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32 On the other hand, fuel and oxygen consumption rate s 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. Appare nt reaction is as follow taking into account adsorbed carbon dioxide; 1226222218.51312CHxOHOCOxO (3-1) Several overall molar balance result s are provided in Table 3-1. Recycle Ratio and Water Management Figure 3-5 shows AOG recycle percentage, i.e. F2a/F1c 100. As mentioned in molar balance section, AOG recycle percen tage 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 do ubled SC ratio. AOG recycle percent is independent with SOFC temperat ure despite of the fact that fuel requirement increases with SOFC temperature. This m eans AOG water content increases with SOFC temperature so it is possible to maintain SC rati o though fuel flow rate is increased with SOFC temperature. Also, Fig 3-5 shows that AOG has e nough water content to adjust SC ratio up to 5 by recycling. Therefore, water is self sufficient, in other words th ere is no necessity to add water with fuel. Energy Balance and Efficiency Results without Recirculation and CO2 Capture As mentioned in energy balance section, un-re cycled 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 reformi ng reaction. Heat, however, is imbalanced on prereformer unit. To make energy ba lanced, another heat effect, QPRE, is introduced on pre-reformer

PAGE 33

33 unit. The amount of this newly introduced heat effect is dependent upon SOFC temperature. This could be either heat surplus or insufficient he at depending on SOFC te mperature. Figure 3-6 shows energy balance results for th e external reformer. The negative QPRE means heat is rejected from the external reformer, heat surplus, while the positive QPRE means heat from AOG and after-burner is insufficient for heat of reformi ng 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 favor ed in efficiency point of view In Figure 3-7, detailed heat analysis is presented for SC = 4. Shaded region named | HAOG| represents heat transferred from sensible heat of AOG stream and under the shaded region denotes heat transferred from the afterburner, |QAB|. The magnitude of heat require ment for reforming reactions, | HPRE|, is decreased slightly with SOFC temperature. The magnitude of transferred heat from the after-burner increases with SOFC temperature due to increas ing of carbon monoxide c ontent into the afterburner. The major reason of changing from insu fficient heat region to excess heat region is sensible heat of AOG. Tw o different efficiencies, LHV and Th, are evaluated. The first efficiency, LHV, is based on lower heating value of fuel, while the second efficiency, Th, is based on total enthalpy change of Eq. (3-1). Seemi ngly, apparent chemical reaction, Eq. (3-1), is similar to combustion process. In this work, e fficiency based on lower heating value is used despite of water condensing. De finition of efficiency considering heat imbalance for Prereformer unit is as follows; 0 0elect PRE f LHV electPRE PRE fW Q FLHV WQ Q FLHV (3-2)

PAGE 34

34 In insufficient heat case, heat deficiency at the pre-reformer unit is subtracted from SOFC electrical work. Figure 3-8 demons trates how the efficiency cha nges 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 unde rstand 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 QPRE, 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 dioxi de 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 chan nel inlet gases consis t of all 5 chemical components. After the equilibrium achieved inside the external reformer, outlet of reforming channel contains unreacted methane. This unrea cted methane is undergone reforming reaction, Eq. (2-3), in SOFC. Both intern al reforming and WGS reactions are limited by equilibrium. If it is possible to manipulate both fo rward reactions getting over the equilibrium, fuel consumption rate will decrease. With regard to concentr ation under constant temperature and pressure condition, there are two ways getting over th e equilibrium; to remove product of forward reaction, and to add more reactant of forward re action. The first concept is ineffective to steam

PAGE 35

35 reforming reaction, Eq. (2-3), because products, CO and H2, are already consuming by WGS and electrochemical reactions. For WGS reaction, CO2 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 ca n be achieved by recirculation of AOG back into anode inlet due to high water content of AOG. Carbon dioxide captu re effects on fuel consumption rate are illustrated in Fig. 3-9 for several SC ratios. For th e comparison, decreased fuel consumption rate due to CO2 capture is expressed in a fracti on to the fuel consumption rate for the same condition, expect CO2 capture. These reduced fractions are depicted in Fig. 3-10. Fuel consumption rate is definitely decreased with CO2 capture but decreased amount is not directly proportional to CO2 capture. From the Fig. 3-10, it is found that CO2 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 calculat ed 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. 3-12. Fuel consumption rate decreases with increasing recirculation ratio. In this simulation, recirc ulation ratio is limited up to 0.5 because current density is affected by recirculat ion 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 CO2 capture rate and recirculation ratio. Total 4620 cases of parame tric studies had been conducted

PAGE 36

36 concerning efficiency with variations of SC, TSOFC, CO2 capture and recirculation ratio. Parameters for optimization are as follows; SC: 2, 3, 4, and 5 TSOFC: 600, 700, 800, 900 and 1000 C CO2 capture: 21 cases (0 ~ 100 %) Recirculation ratio: 11 cases (0 ~ 0.5) Concerning maximum efficiency, these parametr ic studies could be classified 6 unique types according to dependency on CO2 adsorption and recirculation; a) high CO2 adsorption and low recirculation b) moderate CO2 adsorption and low recirculation c) low CO2 adsorption and low recirculation d) low CO2 adsorption and high recirculation e) moderate CO2 adsorption and high recirculation f) high CO2 adsorption and high recirculation Distribution map for those 6 categ ories is provided in the Tabl e 3-2. Representative overall efficiencies of the each category, depending on CO2 capture and recirculat ion ratio at given SC and TSOFC, are illustrated in Figure 3-13. Among a ll 4620 cases, 20 maximum efficiencies for given SC and TSOFC are presented in the Table 3-3 and Fi gure 3-14. Data in the Table 3-3 and Figure 3-14 is representation of the highe st efficiency with given SC and TSOFC. In the Table 3-3, carbon dioxide capture and recircul ation effects appear in oppos ite manner although they have a common tendency for dependency on SC and te mperature. Low temperature cases prefer maximum CO2 capture and no recirculation, whil e maximum recirculation and low CO2 capture are preferred in high temperature.

PAGE 37

37 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 350400450500550600650700750 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 350400450500550600650700750 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (d) (c) (b) (a) S/C = 5 S/C = 4 S/C = 3 S/C = 2 H2 CH4 CO CO2 molar fraction, yi,DRY [-] molar fraction, yi,DRY [-] molar fraction, yi,DRY [-] Temperature [oC] molar fraction, yi,DRY [-] Figure 3-1. Reaction equilibrium results for steam reforming and water-gas shift reaction for several steam to carbon ratios

PAGE 38

38 300350400450500550600650700750800 5 6 7 8 9 10 11 12 TR = 25 oC Hydrogen output / requ ired heat [mmol/kJ]Pre-Reformer Temperature, [oC] S/C = 2 S/C = 3 S/C = 4 S/C = 5 A Figure 3-2. Produced hydroge n per consumed energy A) TR = 25 C, B) TR = 100 C

PAGE 39

39 300350400450500550600650700750800 5 6 7 8 9 10 11 12 TR = 100 oC Hydrogen output / required heat [mmol/kJ]Pre-Reformer Temperature, [oC] S/C = 2 S/C = 3 S/C = 4 S/C = 5 B Figure 3-2. Continued

PAGE 40

40 6006507007508008509009501000 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture r = 0 S/C = 5 S/C = 4 S/C = 3 S/C = 2 Dodecane consumption rate for 1 kW operation [g/min]SOFC Temperature, TS [oC] Figure 3-3. Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio, where no CO2 capture and no recirculation

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41 6006507007508008509009501000 5.8 6.0 6.2 6.4 6.6 6.8 7.0 7.2 7.4 TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture r = 0 S/C = 5 S/C = 4 S/C = 3 S/C = 2 Oxygen consumption rate fo r 1 kW operation [g/min]SOFC Temperature, TS [oC] Figure 3-4. Effect of SOFC temperature on oxyg en consumption rate with different steam to carbon ratio, where no CO2 capture and no recirculation

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42 6006507007508008509009501000 66 68 70 72 74 76 78 80 82 84 TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture r = 0 S/C = 5 S/C = 4 S/C = 3 S/C = 2 AOG Recycle percent [%]SOFC Temperature, TS [oC] Figure 3-5. AOG recycle percent versus SOFC te mperature with different steam to carbon ratio, where no CO2 capture and no recirculation

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43 6006507007508008509009501000 -300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300 surplus Heat region insufficient Heat region TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture r = 0 S/C = 5 S/C = 4 S/C = 3 S/C = 2 QPRE [Watt]SOFC Temperature, TS [oC] Figure 3-6. Effect of SOFC te mperature on additional heat transf erred rate for pre-reformer unit with different steam to carbon ratio, where no CO2 capture and no recirculation

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44 6006507007508008509009501000 0 100 200 300 400 500 600 |HAOG|+|QAB| Insufficient Heat Excess Heat |HPRE| | H AOG | |Q AB | SOFC temperature, TS [oC] TPR = 550 oC U = 0.85FC = 0.85 S/C = 4 no CO2 capture r = 0 Rate of required and transferred heat [Watt] Figure 3-7. Effect of SOFC temperature on deta iled additional heat tr ansferred rate for prereformer unit with S/C =4, where no CO2 capture and no recirculation

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45 6006507007508008509009501000 57 60 63 66 69 72 75 78 81 TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture r = 0 S/C = 2 S/C = 3 S/C = 4 S/C = 5 LHV [%]SOFC Temperature, TS [oC] Figure 3-8. Effect of SOFC temperature on e fficiency based on LHV with different steam to carbon ratio, where no CO2 capture and no recirculation

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46 6006507007508008509009501000 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 Line color S/C = 2 S/C = 3.5 S/C = 5 CO2 capture 0 % 50 % 100 % TPR = 550 oC U = 0.85FC = 0.85 r = 0 Dodecane consumpt ion rate [g/min]SOFC Temperature, TS [oC] Figure 3-9. Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratios and several CO2 adsorption percents, where no recirculation

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47 6006507007508008509009501000 0.94 0.96 0.98 1.00 Line color S/C = 2 S/C = 3.5 S/C = 5 CO2 capture 50 % 100 % TPR = 550 oC U = 0.85FC = 0.85 r = 0 Dodecane consumption rate ratio to no CO2 captureSOFC Temperature, TS [oC] Figure 3-10. Carbon dioxide capture effects on th e depleted fuel consumption fraction for the several steam to carbon rati os, where no recirculation

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48 6006507007508008509009501000 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 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 = 0.5 TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture Dodecane consumpt ion rate [g/min]SOFC Temperature, TS [oC] Figure 3-11. Effect of SOFC temperature on fu el consumption rate with different steam to carbon ratio and several recirc ulation ratio, where no CO2 adsorption

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49 6006507007508008509009501000 0.94 0.96 0.98 1.00 Line color S/C = 2 S/C = 3.5 S/C = 5 recirculation ratio, r 0.25 0.5 TPR = 550 oC U = 0.85FC = 0.85 no CO2 capture Dodecane consumption rate ratio to no recirculationSOFC Temperature, TS [oC] Figure 3-12. Recirculation effects on the deplet ed fuel consumption fraction for the several steam to carbon ratios, where no CO2 adsorption

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50 70.23 70.77 71.32 71.86 72.41 69.68 69.14 72.95 68.59 0.00.10.20.30.40.5 0 20 40 60 80 100 Recirculation ratio, r [-]CO2 Adsorption percent [%] 67.50 68.05 68.59 69.14 69.68 70.23 70.77 71.32 71.86 72.41 72.95 73.50 Figure 3-13. Efficiency based on LHV of fuel; A) S/C = 2, TSOFC=600 oC (example (a), low temperature region), B) S/C = 3, TSOFC=700 oC (example (b), low or moderate temperature region), C) S/C = 4, TSOFC=800 C (example (c), moderate temperature and medium to high S/C region), D) S/C = 5, TSOFC=900 oC (example (d), moderate or high temperature and high S/C region), E) S/C = 5, TSOFC=1000 oC (example (e), high temperature and high S/C re gion), and F) S/C = 2, TSOFC=900 oC (example (f), high temperature and low S/C region)

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51 69.77 69.41 69.05 68.68 68.32 70.14 67.95 67.59 0.00.10.20.30.40.5 0 20 40 60 80 100 Recirculation ratio, r [-]CO2 Adsorption percent [%] 66.50 66.86 67.23 67.59 67.95 68.32 68.68 69.05 69.41 69.77 70.14 70.50 B Figure 3-13. Continued

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52 72.73 72.09 71.45 70.82 70.18 69.55 68.91 68.27 67.6 4 0.00.10.20.30.40.5 0 20 40 60 80 100 Recirculation ratio, r [-]CO2 Adsorption percent [%] 67.00 67.64 68.27 68.91 69.55 70.18 70.82 71.45 72.09 72.73 73.36 74.00 C Figure 3-13. Continued

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53 72.82 73.55 73.55 72.82 72.09 71.36 70.64 69.91 69.18 68.45 74.27 0.00.10.20.30.40.5 0 20 40 60 80 100 Recirculation ratio, r [-]CO2 Adsorption percent [%] 67.00 67.73 68.45 69.18 69.91 70.64 71.36 72.09 72.82 73.55 74.27 75.00 D Figure 3-13. Continued

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54 70.09 70.45 70.82 71.18 71.55 71.91 72.27 71.91 71.55 71.18 72.64 70.82 0.00.10.20.30.40.5 0 20 40 60 80 100 Recirculation ratio, r [-]CO2 Adsorption percent [%] 69.00 69.36 69.73 70.09 70.45 70.82 71.18 71.55 71.91 72.27 72.64 73.00 E Figure 3-13. Continued

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55 69.50 70.00 70.50 71.00 71.50 72.00 72.50 73.00 73.5 0 0.00.10.20.30.40.5 0 20 40 60 80 100 Recirculation ratio, r [-]CO2 Adsorption percent [%] 68.50 69.00 69.50 70.00 70.50 71.00 71.50 72.00 72.50 73.00 73.50 74.00 F Figure 3-13. Continued

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56 73.20 72.27 71.33 70.40 69.47 68.53 67.60 73.20 66.67 74.13 74.136006507007508008509009501000 2.0 2.5 3.0 3.5 4.0 4.5 5.0 SOFC temperature, TS [oC]Steam to carbon ratio, S/C 62.00 62.93 63.87 64.80 65.73 66.67 67.60 68.53 69.47 70.40 71.33 72.27 73.20 74.13 75.07 76.00 Figure 3-14. Effects of SOFC temperatur e and SC on maximum system efficiency

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57 Table 3-1. Overall molar balance results Input Output CO2/C12H26 S/C TSOFC [oC] C12H26 [mmol/sec] O2/C12H26 H2O/C12H26 O2/C12H26 total adsorbed output 2 700 0.1783 18.88 13.00 0.38 12.00 0.00 12.00 3 700 0.1748 18.79 13.00 0.29 12.00 0.00 12.00 4 700 0.1727 18.74 13.00 0.24 12.00 0.00 12.00 2 900 0.1942 18.99 13.00 0.49 12.00 0.00 12.00 3 900 0.1895 18.89 13.00 0.39 12.00 0.00 12.00 4 900 0.1865 18.82 13.00 0.32 12.00 0.00 12.00 2 700 0.1752 18.80 13.00 0.30 12.00 6.79 5.21 3 700 0.1721 18.72 13.00 0.22 12.00 8.05 3.95 4 700 0.1703 18.68 13.00 0.18 12.00 8.87 3.13 2 900 0.1881 18.85 13.00 0.35 12.00 6.72 5.28 3 900 0.1839 18.76 13.00 0.26 12.00 8.00 4.00 4 900 0.1815 18.70 13.00 0.20 12.00 8.84 3.16

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58 Table 3-2. Dependency on CO2 adsorption percentage and recirculation ratio TSOFC S/C 600 oC 700 oC 800 oC 900 oC 1000 oC 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)

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59 Table 3-3. Maximum overall e fficiencies for given SC and TSOFC with corresponding recirculation ratio and CO2 capture percent TSOFC S/C 600 oC 700 oC 800 oC 900 oC 1000 oC 5 62.20 % r = 0.0 C = 100 % 64.96 % r = 0.0 C = 35 % 72.51 % r = 0.0 C = 0 % 74.63 % r = 0.5 C = 5 % 72.96 % r = 0.5 C = 50 % 4 65.15 % r = 0.0 C = 100 % 67.30 % r = 0.0 C = 40 % 73.67 % r = 0.0 C = 0 % 74.18 % r = 0.5 C = 5 % 72.65 % r = 0.5 C = 55 % 3 68.76 % r = 0.0 C = 100 % 70.34 % r = 0.0 C = 40 % 74.18 % r = 0.05 C = 10 % 74.01 % r = 0.5 C = 20 % 72.37 % r = 0.5 C = 85 % 2 73.23 % r = 0.0 C = 100 % 74.40 % r = 0.0 C = 30 % 74.79 % r = 0.35 C = 25 % 73.89 % r = 0.5 C = 80 % 71.62 % r = 0.5 C = 100 %

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60 CHAPTER 4 SUMMARY AND CONCLUSION In this thermodynamics and chemical equili brium model of 1 kW SOFC system utilizing liquid hydrocarbon, the individual effect of each parameter is analyzed. n-Dodecane, saturated hydrocarbon containing 12 carbons, is selected for simulation as a re presentation of diesel fuel. Appropriate thermodynamic properties of chemical species are applied. Especially, heat capacity of n-Dodecane is obtained from interpolat ion of previous literature value. From not only chemical equi librium results but also ener gy efficiency point of view, optimum pre-reformer temperature is suggest ed. AOG recycle ratio and water management analysis are considered. Water is self-sufficient by means of r ecycling AOG up to SC 5, so there is no necessity to add water with fuel. The e ffects of SOFC temperat ure and steam to carbon ratio on fuel and oxygen consumption rates are presented. Fuel and oxygen consumption rates show similar inclination. From the molar (or mass) balance point of view, low SOFC temperature and high SC are preferred. Overa ll species balance is considered, so overall chemical reaction equation is indicated. It looks like combustion reaction of fuel. Also, overall chemical species balance result is presented. Ca rbon dioxide capture and r ecirculation effects are examined on purpose to produce more hydrogen than chemical equilibrium limitation under given SOFC temper ature condition. CO2 capture and recirculation effects on fuel consumption rate have the similar tendency. The higher temper ature and the smaller SC yield the less fuel consumption. Concerning energy balance, heat is imbalanced on pre-reformer unit. To make energy balanced, another heat effect, QPRE, is introduced on pre-reformer unit. The amount of this newly introduced heat effect is dependent upon SOFC temperature. This c ould be either heat surplus or insufficient heat depending on SO FC temperature. The temperature, which makes heat balanced

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61 without newly introduced heat effect on pre-re former, is named as self-energy balanced operating temperature. It is possi ble to obtain the maximum effici ency operating SOFC with this self-energy balanced operating temperature. The higher temperature operation yields the more fuel consumption. Lower temperature operation give s heat insufficiency on the pre-reformer unit. Therefore, produced electrical wo rk should reimburse this insuffi cient heat on the pre-reformer. Parametric study is conducted for 4620 cases 4 cases of SC ratio, 5 cases of SOFC temperature, 21 cases of CO2 capture percentage, and 11 cases of recirculation ratio. Parametric study results are classified into 6 uniqu e types according to dependency on CO2 capture and recirculation ratio. It is also categorized by dependency on SC ratio and SOFC temperature. Distribution map for 6 categorie s over SC and SOFC temperature is presented. Also, the maximum efficiencies depending on r ecirculation ratio as well as CO2 capture are presented for given SC and SOFC temperature. In the maximu m efficiency table, car bon dioxide capture and recirculation effects appear in opposite ma nner although they have a common tendency for dependency on SC and temperature. Low temperature cases prefer maximum CO2 capture and no recirculation, while maximum recirculation and low CO2 capture are preferred in high temperature. Among these maximum efficiencies, SC =2 and 800 oC SOFC temperature case under 0.35 recirculation ratio and 25% carbon dioxide adsorption yields the highest efficiency as 74.79%.

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62 LIST OF REFERENCES 1. Rostrup-Nielsen, J.R., 1984, Catalytic Steam Reforming Springer-Verlag, Berlin, Heidelberg, Germany. 2. Imperial Chemical Industries, 1970, Catalyst handbook: with special reference to unit processes in ammonia and hydrogen manufacture Wolfe Scientific Books, London, UK. 3. EG&G Technical Services, Inc., 2004, Fuel Cell Handbook (Seventh Edition), U.S. Department of Energy, Morgantown, West Virginia. 4. Barbir, F., 2005, PEM Fuel Cells: Theory and Practice Elsevier Academic Press, London, UK. 5. Smith, J.M., Van Ness, H.C., and Abbott, M.M., Introduction to Chem ical Engineering Thermodynamics McGraw-Hill, New York, NY. 6. Sonntag, R.E., and Van Wylen, G.J., 1991, Introduction to Thermodynamics Classical and Statistical John Wiley & Sons, Hoboken, NJ. 7. Lemmon, E.W., and Huber, M.L., 2004, “T hermodynamic Properties of n-Dodecane,” Energy & Fuels, 18, pp. 960-967. 8. Span, R., Wagner, W., 2003, “Equations of State for Technica l Applications. I. Simultaneously Optimized Functional Forms for Nonpolar and Polar Fluids,” International Journal of Thermophysics, 24, pp. 1-39. 9. Xu, J., and Froment, G.F., 1989, “Methane Steam Reforming, Methanation and WaterGas Shift: I. Intrinsic Kinetics,” AIChE Journal, 35(1), pp. 88-96. 10. Chapra, S.C, and Canale, R.P., 1998, Numerical Methods for Engineers: with programming and software applications McGraw-Hill, New York, NY. 11. Colpan, C.O., Dincer, I., and Hamdulla hpur, F., 2007, “Thermodynamic Modeling of Direct Internal Reforming Solid Oxide Fuel Cells Operating with Syngas,” International Journal of Hydrogen Energy, 32(7), pp. 787-795. 12. Kays, W.M., and London, A.L., 1984, Compact Heat Exchangers McGraw-Hill, New York, NY. 13. Ding, Y., and Alpay, E., 2000, “Adsorptio n-enhanced steam-methane reforming,” Chemical Engineering Science, 55, pp. 3929-3940.

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BIOGRAPHICAL SKETCH Tae Seok Lee was born in 1977, in Seoul, Re public of Korea. He matriculated in Department of Chemical Engineering, University of Seoul, Korea in 1996. After completing his sophomore, he had joined Korea Military Servic e as a Field Artillery for 26 months. After completing his military duty, Tae Seok went back to University. In his senior year, Tae Seok won the bronze medal in the Transport Phenomena national competition held by Korea Institute of Chemical Engineering, KIChE. And he had earned his B.S. in Chemical Engineering, University of Seoul in 2003. After graduating, he worked at Korea Institute of Science and Technology, KIST, as a commissioned research scientist. Tae Seok joined Department of Mechanical and Aerospace Engineering at Univer sity of Florida in Fall 2005 as a graduate student. Upon graduation he plans to pursue Ph.D. in the same research area.