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1 NUMERICAL MODELING AND SIMULATION OF FISCHER TROPSCH PACKED BED REACTOR AND ITS THERMAL MANAGEMENT By TAE SEOK LEE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011
2 2011 Tae Seok Lee
3 To my beloved wife and son
4 ACKNOWLEDGMENTS This research project would not have been possible without the support of many people. The author wishes to express his gratitude to his supervisor, Dr. Chung who was abundantly helpful and offered invaluable assistance, support and guidance. Deepest gratitude are also due to the members of the supervisory committee, Dr. Sherif, Dr. Ingley and Dr. Hage lin Weaver without whose knowledge and assistance this study would not have been successful. Special thanks also to Dr. Weaver for invaluable guidance and college Dr. Colmyer for providing experimental data. The author would also like to convey thanks to the Department and Faculty for providing the financial means and laboratory facilities. The author wishes to express his love and gratitude to his beloved families; for their understanding and endless love, through the duration of his studies.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ ........ 17 1.1 Energy Crisis and Renewable Energy Source ................................ .................. 17 1.2 Research Objectives ................................ ................................ ......................... 19 2 BACKGROUND AND LITERATURE REVIEW ................................ ........................... 21 2. 1 Fischer Tropsch Catalysis ................................ ................................ ................ 21 2. 2 Reaction Mechanism ................................ ................................ ........................ 23 2. 2 .1 General Catalytic Surface Reaction Mechanism ................................ ..... 23 2. 2 .2 Carbide Mechanism ................................ ................................ ................. 24 2. 2 .3 Enolic Mechanism ................................ ................................ ................... 25 2. 2 .4 Direct (CO) Insertion Mechanism ................................ ............................ 26 2. 2 .5 Combined E nol/carbide Mechanism ................................ ........................ 27 2. 3 Intrinsic Kinetics ................................ ................................ ................................ 27 2. 3 .1 Iron Based Catalysts ................................ ................................ ............... 28 2. 3 .2 Cobalt Based Catalysts ................................ ................................ ........... 32 2.4 Products Distribution and Selectivity ................................ ................................ 36 2.4.1 Influence of P rocess O peration C ondition on the S electivity ................... 36 2.4.2 Product Selectivity Model ................................ ................................ ........ 37 2.5 Fischer Tropsch Reactors and Reactor Modeling ................................ ............. 38 2.5.1 Fluidized Bed Reactor ................................ ................................ ............. 38 2.5.2 Slu rry Phase Reactor ................................ ................................ .............. 39 2.5.3 Fixed Bed Reactor ................................ ................................ ................... 40 2.5.4 Fixed Bed Reactor Modeling ................................ ................................ ... 41 3 MATHEMATICAL MODELING OF PACKED BED FISCHER TROPSCH REACTOR ................................ ................................ ................................ .............. 50 3.1 Gas L iquid Hydrodynamics system ................................ ................................ ... 50 3.1. 1 Multi Phase Flow Model ................................ ................................ .......... 50 3.1.2 Assumption ................................ ................................ .............................. 52
6 3.1. 3 Continuity ................................ ................................ ................................ 53 3.1. 4 Momentum ................................ ................................ .............................. 53 3.1. 5 Energy Equation ................................ ................................ ...................... 55 3.1. 6 Volume Fraction Equation for the Liquid Phase ................................ ...... 55 3.1. 7 Species Transport Equation ................................ ................................ .... 55 3.2 Fischer Tropsch Reaction Kinetics and Mass Transfer Limitation .................... 56 3.2.1 Internal Diffusion through Amorphous Porous Catalyst and Overall Reaction Rates ................................ ................................ .............................. 56 3.2.2 Similarity between Heat Transfer with Fins and Catalytic Chemical Reaction ................................ ................................ ................................ ........ 57 3.2.3 Intrinsic Kinetics and Intraparticle Mass Transfer Limitation .................... 61 3.2.4 Product Distribution with Carbon Number Independent Ch ain Growth Probability ................................ ................................ ................................ ..... 63 3.2.5 Product Distribution Accomplished with Carbon Number Dependent Chain Growth Probability ................................ ................................ ............... 65 4 NUM ERICAL SOLUTION METHOD AND VALIDATIONS ................................ ......... 73 4.1 Numerical Solution by FLUENT ................................ ................................ ........ 73 4. 2 Model Validation Works ................................ ................................ .................... 75 4. 2 .1 Validation of Products Distribution ................................ ........................... 75 4. 2 .2 Validation of Reactor Model ................................ ................................ .... 77 5 INDUSTRIAL SCALE PACKED BED REACTOR MODELING ................................ .. 86 5.1 Macro Scale Reactor Description ................................ ................................ ..... 86 5.2 Base Line Case Simulation Results ................................ ................................ .. 87 5.3 FT Chemical Reactor Thermal Characteristics ................................ ................. 89 5.4 Thermal Management Analysis ................................ ................................ ........ 95 5.5 Results Analysis Summary ................................ ................................ ............... 96 6 EXPERIMENTAL VERIFICATION OF FISCHER TROPSCH CHEMICAL KINETICS MODEL ................................ ................................ ............................... 117 6 .1 General Method of Kinetics Data Analysis ................................ ...................... 117 6 2 Experimental Data from a Cobalt C atalyst B ased P acked B ed R eactor ......... 118 6 3 Chemical Kinetics Coefficients ................................ ................................ ........ 119 6.3.1 Constant Pressure Packed Bed Reactor Modeling ............................... 119 6.3.2 General Carbon Number Dependent Chain Growth Probability ............ 123 6.3.3 Coefficients of Chemical Reaction Kinetics ................................ ........... 126 6 4 Generalization of Selectivity ................................ ................................ ............ 129 6.4.1 Conceptual I dea for G eneralization of S electivity ................................ .. 129 6.4.2 Hydrogen to Carbon Monoxide Molar Ratio Effect on Selectivity .......... 132 6.4.3 Temperature Effects on Selectivity ................................ ........................ 133 6.4.4 General Selectivity ................................ ................................ ................. 135 6 5 Results Discussion and Contribution of Current Work ................................ .... 136
7 7 NUMERICAL SIMULATIONS FOR MESO AND MICRO SCALE REACTORS ..... 165 7 .1 General Advantage of a Micro Scale Reactor ................................ ................. 165 7.2 Meso S cale C hannel FLUENT Modeling ................................ ........................ 165 7.2.1 Meso Scale Reactor Geome try ................................ ............................. 165 7.2.2 WHSV CO and W all T emperature E ffect ................................ .................. 167 7.2.3 Outlet Pressure Effect ................................ ................................ ........... 169 7.2.4 Inlet H ydrogen to C arbon M onoxide R atio E ffect ................................ .. 170 7.3 Micro S cale C hannel FLUENT Modeling ................................ ........................ 172 7.3.1 Micro Scale Reactor Geometry ................................ ............................. 172 7.3.2 Mass F lux E ffect on C onversion and P roduct D istribution ..................... 173 7.3.3 Temperature E ffect on C onversion and P roduct D istribution ................. 176 7.3.4 Pressure E ffects on S yngas C onversion and P roducts D istribution ...... 178 7.3.5 Hydrogen to C arbon M onoxide M olar R atio E ffect on C onversion and P roducts D istribution ................................ ................................ ................... 178 7 4 Results Discussion and Contribution of Current Work ................................ .... 180 LIST OF REFERENCES ................................ ................................ ............................. 248 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 253
8 LIST OF TABLES Table page 2 1 Reaction rate equations for overall synthesis gas consumption rates ................ 43 2 2 Selectivity control in Fischer Tropsch synthesis by process conditions and catalyst modifications (Van der Laan and Beenackers, 1999). ........................... 44 3 1 Similarity between fin in heat transfer and catalyst reaction ............................... 68 4 1 Methodology comparison ................................ ................................ ................... 80 5 1 Physical properties and operating conditions for the baseline case. .................. 98 5 2 Calculated conversion values for selected opera ting conditions. ....................... 99 6 1 Experimental operating conditions and measurement data of carbon monoxide conversion and product selectivities up to C8. ................................ 138 6 2 The best fit results and corresponding chain growth probabilities for cases of T=205 o C. ................................ ................................ ................................ .......... 139 6 3 The best fit results; slope of the linearization A n for Eq. ( 6 32 ) ........................ 140 6 4 The best fit results; slope of the linearization, ( E n /R), for Eq. ( 6 35 ) .............. 140 6 5 Effective coefficients for carbon number dependent chain growth probability relative percent difference on carbon number dependent chain growth probability, and their standard deviations. ................................ ................ 141 7 1 Reactor channel geometry and dimensions f or both meso and micro scale reactors. ................................ ................................ ................................ ........... 182 7 2 Simulation input conditions for the meso scale channel reactor ....................... 183 7 3 Inlet mo lar and mass fractions for various hydrogen to carbon monoxide input ratios ................................ ................................ ................................ ........ 184 7 4 Simulation input conditions for micro scale channel reactor ............................. 185
9 LIST OF F IGURES Figure page 2 1 Schematics of carbide mechanism. ................................ ................................ .... 45 2 2 Schematics of Enolic mechanism. ................................ ................................ ...... 46 2 3 Schematics of Direct Insertion mechanism. ................................ ........................ 47 2 4 Schematics of Combined enol/carbide mechanism. ................................ ........... 48 2 5 Hydrocarbon selectivity as function of the chain growth probability factor calculated using ASF. ................................ ................................ ......................... 49 3 1 Concentration profile for simplest case, 1 st order reaction for various values of Thiele modulus ................................ ................................ ............................... 69 3 2 Effectiveness factor for 1 st order reaction within the spherical catalyst as a function of Thiele modulus. ................................ ................................ ................. 70 3 3 Effectiveness factor for pseudo kinetics instead of LH kinetics as a function of size and temperature. ................................ ................................ ......................... 71 3 4 Catalyst surface chemistry and Chain growth sch eme. ................................ ...... 72 4 1 Computational domain and outside coolant flow path. ................................ ....... 81 4 2 Product distribution comparison with experimental resul ts by Elbashir and Roberts; Non ASF distribution, logarithm of normalized hydrocarbon product weight fraction versus carbon number. ................................ ............................... 82 4 3 Temperature profile comparison with results by Jess and Kern (2009) ............. 83 4 4 Syngas conversion comparison with results by Jess and Kern (2009) .............. 84 4 5 D etailed temperature profile between maximum safe case and temperature runaway case ................................ ................................ ................................ ..... 85 5 1 Schematics for packed bed reactor ................................ ................................ .. 10 0 5 2 Pressure and temperature profile for baseline case; pure syngas mass flux 3.3 kg/m 2 s, H 2 /CO = 2, inlet and coolant temperature 214 o C .......................... 101 5 3 Temperature contours at three downstream locations for the baseline case; pure syngas with mass flux of 3.3 kg/m 2 s,H 2 /CO = 2,and syngas inlet and coolant temperature at 214 o C. ................................ ................................ ......... 102
10 5 4 Mass fraction profiles at the centerline in the gaseous phase for the baseline case ................................ ................................ ................................ .................. 103 5 5 Contour plots for CO molar fractions at three downstream locations, z=2, z=3, z=6 ................................ ................................ ................................ ................... 104 5 6 Contour plots for H2O molar fractions at three downstream locations, z=2, z=3, z=6. ................................ ................................ ................................ ........... 105 5 7 Reactor bed temperature profiles for inlet and coolant temperature of 214 o C, H 2 /CO = 2.0 a nd different mass fluxes, F/F base =0.5, 0.75, 1, 1.25, and 1.5. ..... 106 5 8 Reactor bed temperature profiles for inlet and coolant temperature of 214 o C, H 2 /CO = 1.5 and different mass fluxes, F/F base = 0.25, 0.5, 0.75, and 1. .......... 107 5 9 Reactor bed temperature profiles for inlet and coolant temperature of 214 o C, H 2 /CO = 2.2 and different mass fluxes, F/F base = 0.5, 0.75, and 1 ................... 108 5 10 Reactor bed temperature profiles for inlet and coolant temperature of 214 o C, H 2 /CO = 2.5 and different mass fluxes, F/F base = 0.25, 0.5, 0.75, and 1 .......... 109 5 11 Reactor bed temperature profiles for inlet and coolant temperature of 214 o C, syngas mass flux F= F base and different H 2 /CO ratios of 1.5, 1.7, 2.0, 2.2, 2.5, and 3.0. ................................ ................................ ................................ ............ 110 5 1 2 Reactor bed temperature profiles for inlet and coolant temperature of 210 o C, syngas mass flux F= F base and different H 2 /CO ratios of 1.5, 1.7, 2.0, 2.4, 2.5, and 3.0. ................................ ................................ ................................ ............ 111 5 1 3 Reactor bed temperature profiles for inlet and coolant temperature of 205 o C, syngas mass flux F= F base and different H 2 /CO ratios of 2.0, 2.5, 3.0, and 3.5. 112 5 1 4 Reactor bed temp erature profiles for inlet and coolant temperature of 214 o C, syngas mass flux F= 0.5F base and different H 2 /CO ratios of 1.5, 2.0, 2.2, 2.3, 2.5, and 3.0. ................................ ................................ ................................ ...... 113 5 1 5 Reactor bed temperature prof iles for inlet and coolant temperature of 210 o C, syngas mass flux F= 0.5F base and different H 2 /CO ratios of 1.5, 2.0, 2.5, and 3.0. ................................ ................................ ................................ .................. 114 5 1 6 Reactor bed temperature profiles for inlet and c oolant temperature of 205 o C, syngas mass flux F= 0.5F base and different H 2 /CO ratios of 1.5, 2.0, 2.5, and 3.0 ................................ ................................ ................................ ................... 115 5 1 7 Thermal viability map for a FT reactor. ................................ ............................. 116 6 1 Selectivity towards hydrocarbons for different temperatures (P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm) ................................ ................................ .... 142
11 6 2 Selectivity towards hydrocarbons fo r different hydrogen to carbon monoxide feed ratios (P=20 bar, T = 205 o C, V = 62.5 sccm with 10%vol N 2 ) .................. 143 6 3 Product distribution and ASF plot for carbon number 3~7 (P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm) ................................ ................................ .... 144 6 4 Product distribution and ASF plot for carbon number 3~7 (P=20 bar, T = 205 o C, V = 62.5 sccm with 10%vol N 2 ) ................................ ................................ ... 145 6 5 F inding appropriate value for sum of the selectivity divided its carbon number which makes sum of the squares of the deviation minimu m; (T=205 o C, P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm) ................................ ............................. 146 6 6 Selectivity comparison between experiment and simulation and chain growth probability used in the simulation; (T=205 o C, P=20 b ar, H 2 /CO =3, V = 62.5 sccm with 10%vol N 2 ) ................................ ................................ ....................... 147 6 7 Selectivity comparison between experiment and simulation and chain growth probability used in the simulation; (T=240 o C, P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm) ................................ ................................ ................................ ..... 148 6 8 Contour plots for determining appropriate kinetic coefficients .......................... 149 6 9 Contour plots for determining appropriate activation energy and hea t of adsorption ................................ ................................ ................................ ......... 152 6 10 Carbon mo noxide conversion comparison between experimental measurements and simulation with fitting coefficients. ................................ ..... 154 6 11 Carbon monoxide conversion profiles in evaluation of comparison with experime ntal work. ................................ ................................ ........................... 155 6 12 Hydrogen conversion profiles in evaluation of comparison with experimental work. ................................ ................................ ................................ ................. 156 6 13 Total number of mole reduction profiles in evaluation of comparison with experimental work. ................................ ................................ ........................... 157 6 14 C arbon number dependent chain growth probability evaluated for fitting work of the experiment ................................ ................................ .............................. 158 6 15 Linearization of general chain growth probability using Equation ( 6 32 ) ........... 160 6 16 Linearization of general chain growth probability using Equation ( 6 35 ) ........... 162 6 17 Threshold energy from the fitting results and its averaged value. ..................... 164 7 1 Schematic of slit like Meso and Micro scale channels and computational domain. ................................ ................................ ................................ ............. 186
12 7 2 M ass fra ction in gaseous phase as a function of axial distance at the center of channel; WHSV CO =0.5, T in = 485K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures ................................ ................................ ................. 187 7 3 M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures ................................ ................................ ............................. 190 7 4 M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 10, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures ................................ ................................ ................. 193 7 5 M ass fraction in gaseous phase as a function of axial dista nce at the center of channel; WHSV CO = 100, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures ................................ ................................ ................. 196 7 6 M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1000, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures ................................ ................................ ................. 199 7 7 M ass fraction in gaseous phase as a function of axial distance at the center of channel; T wall = 540 K, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various mass flow ................................ ................................ ................................ ......... 202 7 8 M ass fraction in gaseous phase as a function of axial distance at the center of channel; T wall = 600 K, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various mass flow ................................ ................................ ................................ ......... 205 7 9 CO and H 2 exit conversion as a function of w all temperature; WHSV CO = 1, T in = 485 K, P out = 20 bar and H 2 /CO = 2. ................................ ......................... 208 7 10 E xit conversion as a function of wall temperature; T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various inlet mass flows ................................ ...................... 209 7 11 E xit conversion as a function of weight hourly space velocity of carbon monoxide, WHSV CO [1/hr]; T in = 485 K, P out = 20 bar and H 2 /CO = 2 for selected wall temperatures ................................ ................................ ............... 211 7 12 M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1, T wall = 520 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions ................................ ................................ ....... 213 7 13 M as s fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 10, T wall = 600 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions ................................ ................................ ....... 216
13 7 14 M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 100, T wall = 600 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions ................................ ................................ ....... 219 7 15 M ass fraction comparison between different WHSVCOs for several outlet pressure cases. T wall = 600 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions ................................ ................................ .......................... 222 7 16 Reactants exit conversions as a function of exit pressure; T in = 485 K, and H 2 /CO = 2 for various inlet mass flows ................................ ............................. 225 7 17 M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1, T wall = 540 K, T in = 485 K, and P = 20 bar for various H 2 /CO conditions ................................ ................................ .................. 226 7 18 C onversion as a function of ax ial distance at the center of channel; WHSV CO = 1, T wall = 540 K, T in = 485 K, and P = 20 bar for various H 2 /CO conditions .... 229 7 19 CO and H 2 exit conversion as a function of inlet H 2 /CO conditions; WHSV CO = 1, T wall = 540 K, T in = 485 K, and P out = 20 bar. ................................ ............. 231 7 20 Mass fraction for gaseous phase profiles as a function of d ownstream location; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2 for various WHSV CO conditions. ................................ ................................ ......................... 232 7 21 Syngas conversion as a function of downstream location; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2 for various WHSV CO conditions ................ 233 7 22 Syngas exit conversion and liquid phase exit mass fraction as a function of weight hourly space velocity for carbon monoxide, WHSV CO ; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2. ................................ .............................. 234 7 23 WHSV CO effect on hydroca rbon distribution at the exit; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2. ................................ ................................ 235 7 24 Mass fraction for gaseous phase profiles as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperature conditions. ................................ ................................ 236 7 25 Syngas conversion as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperature conditions ................................ ................................ ................................ ......... 237 7 26 Syngas exit conversion and liquid phas e exit mass fraction as a function of wall temperature; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2. ................................ ................................ ................................ ................... 238
14 7 27 Wall temperature effect on hydrocarbon distribution at th e exit; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2. ................................ ............... 239 7 28 Mass fraction for gaseous phase profiles as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and H 2 /CO = 2 for various outlet pressure conditions. ................................ ................................ ... 240 7 29 Syngas conversion as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 50 0 K, and H 2 /CO = 2 for various outlet pressure conditions ................................ ................................ ................................ ......... 241 7 30 Syngas exit conversion and liquid phase exit mass fracti on as a function of outlet pressure; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and H 2 /CO = 2. ................................ ................................ ................................ ...................... 242 7 31 Outlet pressure effect on hydrocarbon distribution at the exit; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K and H 2 /CO = 2. ................................ ............... 243 7 32 Mass fraction for gaseous phase profiles as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and P out = 20 bar for various hydrogen to carbon monoxide feed ratio conditions. ............................ 244 7 33 Syngas conversion as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T w all = 500 K, and P out = 20 bar for various hydrogen to carbon monoxide feed ratio conditions ................................ ............................. 245 7 34 Syngas exit conversio n and liquid phase exit mass fraction as a function of hydrogen to carbon monoxide feed ratio; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and P out = 20 bar. ................................ ................................ ........ 246 7 35 Hydrogen to c arbon monoxide feed ratio effect on hydrocarbon distribution at the exit; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K and P out = 20 bar. ....... 247
15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NUMERICAL MODELING AND SIMULATION OF FISCHER TROPSCH PACKED BED REACTOR AND ITS THERMAL MANAGEMENT By Tae Seok Lee December 2011 Chair: Jacob N. C hung Major: Mechanical Engineering A mathematical modeling and numerical simulation study has been carried out for the Fischer Tropsch packed bed reactor with a comprehensive product distribution model based on a novel carbon number dependent chain growt h model and stoichiometric relation ship between the syngas and hydrocarbon s Fischer Tropsch synthesis involves a three phase phenomenon; gaseous phase syngas, water vapor and light hydrocarbons, liquid phase heavy hydrocarbon, solid phase wax produc ts and catalyst. A porous media model has been used for the two phase flow through an isotropic packed bed of spherical catalyst pellets. An Eulerian multiphase continuum model has been applied to describe the gas liquid flow through porous media. Heteroge neous catalytic chemical reactions convert syngas into hydrocarbons and water. Intra particle mass transfer limitation has also been considered in this model. In the macro scale simulation major attention has been paid to reactor temperature profiles beca use thermal management is highly importan t for the current exothermic catalytic reaction. C atalytic chemical kinetics and selectivity analysis for a novel cobalt catalyst developed by our collaborator in the Chemical E ngineering department has been
16 conduc ted. With the kinetics coefficients provided in this work, accurate reactor performance predictions might be expected for the scale up or commercialization utilizing this novel catalyst. In the thermal management, this type of analysis would yield more acc urate and precise predictions in order to understand the heat transfer effect. A m athematical function form for the chain growth probability has been proposed and verified Although this functional form is only valid for a particular catalyst used, this wo rk might help understand the complex nature of the catalytic surface reactions. The meso and micro scale reactors share many system performance characteristics with those of the macro scale reactor. However, f irst notable difference is that the temperature runaway has not been observed for comparable conditions that give rise to thermal instability in the macro scale reactor. Due to low reactor temperature s resulted by higher heat transfer, catalytic reaction might not be activated in the low temperature re gion. Therefore, catalytic reaction requires somewhat higher reactor temperature condition and is sensitive to heat transfer conditions
17 CHAPTER 1 INTRODUCTION 1.1 Energy Crisis and Renewable Energy Source As the world faces significant energy supply an d security challenges stemming from our dependence on petroleum and oil, the need for sustainable alternatives has been receiving great attention. To achieve energy security and independence in the near future, and in the long run to prepare for the post o il energy needs, the recent US NSF DOE Workshop report (Huber, 2007), concluded that liquid biofuels produced from lignocellulosic biomass can significantly reduce our dependence on oil, create new jobs, improve rural economics, reduce greenhouse emission s, and ensure energy security. Further the report emphasized that the key bottleneck for lignocellulosic derived biofuels is the lack of technology for the efficient conversion of biomass into liquid fuels. As a result, new technologies are needed to repla ce fossil fuels with renewable energy resources. Reliable estimates of renewable and sustainable lignocellulosic forest and agricultural biomass and municipal solid waste (mostly biomass) tonnage in the US (Huber, 2007) range from 1.5 to 2 billion dry tons per year so that these biomass resources could contribute ten times more to our primary energy supply (PES) than it currently does. Another forecast claims that all forms of biomass, and municipal solid waste have the potential to supply up to 60% of the total U.S. energy needs. The easiest way to wean ourselves off oil and petroleum is probably not the replacement of internal combustion engine by electrical motor s and batter ies It might be an eventual goal but it is definitely not the solution for the near term future. Alternate
18 fuel s that could be used in existing internal combustion engine with/ without modification will allow us to have a transition period for finding the solution for long term future energy needs Here are some candidates for the alternative fuels ; clean diesels, biodiesel, synthetic diesel, E85, CNG, and hydrogen. Each alternative has its own advantages and disadvantages. Among them, synthetic diesel is one of best prospects as an alternative fuel that is made by catalytic chemic al reaction from a variety of feedstock; natural gas, coal, biomass and even from municipal waste (Deng et al., 2008; Ross et al., 2008; Hanaoka et al., 2010). Synthetic diesel is usually sulfur free depending on the feedstock or requiring the feedstock to have a pre cleaning procedure. Also the synthetic diesel generally has higher energy content than the petroleum diesel. Comparing with other alternative fuels, synthetic diesel is superior to others with the following reasons: There is no necessity to bui ld new oil refineries or modify existing one for clean diesel. Current infrastructure and vehicles can be used without modification. No specialized additional equipment is necessary unlike the E85 powered vehicles. Because of its wide range feedstock avail ability synthetic diesel could be free from problem s with the edible material feedstock which is the main problem for bioethanol fuel The feedstock material is gasified into synthesis gas which after purification is converted by the Fischer Tropsch proce ss to synthetic diesel. In a scientific paper published by the US National Academy of Sciences (Hill et al., cycle accounting, ethanol from corn grain and biodiesel from soybeans, ethanol yields 25% more energy than the energy invested in its production, whereas biodiesel yields 93% more. Compared with ethanol, biodiesel releases just 1.0%, 8.3%, and 13% of the agricultural nitrogen,
19 phosphorus, and pesticide pollutants, respectively, per net ener gy gain. Relative to the fossil fuels they displace, greenhouse gas emissions are reduced 12% by the production and combustion of ethanol and 41% by biodiesel. Biodiesel also releases less air pollutants per net energy gain than ethanol. Neither biofuel ca n replace much petroleum without impacting food supplies. Transportation biofuels such as synfuel hydrocarbons or cellulosic ethanol, if produced from low input biomass grown on agriculturally marginal land or from waste biomass, could provide much greater supplies and environmental benefits than food Therefore, a very promising route to liquid fuels, in particular bio diesel, is non food based woody biomass gasification to synthesis gas (syngas: CO + H2) followed by the Fischer Tropsch p rocess to convert the syngas to hydrocarbon products. The so produced bio diesel is nearly free of sulfur and nitrogen containing compounds, which reduces undesirable emissions of pollutants. It is also virtually free of aromatic with a very high cetane, i.e. a very high quality fuel. According to the U.S. Department of Energy and the Department of Agricultu re, biodiesel yields 280 % more energy than petroleum diesel fuel, while producing 47 % lower exhaust emissions. Biodiesel is much environmentally frien dly than petroleum diesel, as harmless as table salt and as biodegradable as sugar. Furthermore, since the bio diesel is produced from biomass, 1. 2 Research Objectives The main o bjective s of this study are listed below : 1. Develop a comprehensive chemical kinetics model for the Fischer Tropsch catalytic reactions. 2. Build a thermal fluid management numerical model that incorporates the F T chemical kinetics model for the simulations o f packed bed reactors. This combined
20 numerical simulation model will include multi phase flow s non ASF distribution s individual product production rate s intraparticle diffusion as well as intrinsic kinetics. 3. Use the numerical simulation model to predict the performances of micro scale, meso scale and macro scale F T reactors and suggest the scale up principles.
21 CHAPTER 2 BACKGROUND AND LITER ATURE REVIEW Fischer Tropsch technology can be briefly defined as the means used to convert synthesis gas es containing hydrogen and carbon monoxide to hydrocarbon products. The hydrocarbons include oxygenated hydrocarbons such as alcohols. However, the sole production of an oxygenated hydrocarbon such as methanol is excluded (Steynberg and Dry, 2004). This technology had been named after two German chemists, the original inventors Franz Fischer an d Hans Tropsch (Fischer and Tropsch, 1926 and 1930). They were working for Kaiser Wilhelm Institute for Coal Research in Mlheim, Ruhr (Steynberg and Dry, 2004). Although numerous researches have worked on the Fischer Tropsch synthesis during the past seve ral decades, the fundamental understanding of the catalytic surface reaction mechanism is still not totally known and many questions remain In this chapter, the previous works including characteristic of Fischer Tropsch catalysis, intrinsic kinetics, reac tion mechanism, selectivity of products and selectivity models, and reactor modeling are reviewed. The current re se a r ch in reactor modeling for a fixed bed Fischer Tropsch Synthesis is highlighted as well. 2.1 Fischer Tropsch Catalysis The most common Fi scher Tropsch catalysts are group VIII metals; Co, Ru, and Fe. Franz Fischer and Hans Tropsch were working to produce hydrocarbon molecules from which fuels and chemicals could be made, using coal derived gas es in the 1920s. The cobalt medium pressure synt hesis was invented by Fischer and Pichler and the cobalt catalyst that Otto Roelen developed became the standard FT catalyst s in Germany. Fischer and Pichler also invented the iron medium pressure synthesis which
22 is commercialized by the Ruhrchemie and Lur gi companies and established at Sasol in South Africa in 1955. These are all example s of what is now termed as the low temperature Fischer Tropsch (LTFT) technology. Another typical type of FT synthesis usually operated in a fluidized bed reactor is the so called high temperature Fischer Tropsch technology was developed by Hydrocarbon Research. However, due to the fact that abundant crude oil was available and natural gas was close to markets where it could be sold at high prices, Gas To Liquid ( GTL ) applic ations were not economically viable either in the U.S and elsewhere. Brief general characteristic s of each metal are reviewed here. Iron catalysts are favored because of their low costs in comparison to other catalysts. Comparing with other catalysts, how ever, iron catalysts have a high water gas shift reaction activity and high selectivity to olefins ( K lbel and Ralek, 1980 ; Jager and Espinoza, 1995 ) The main advantage using Cobalt catalyst is its high selectivity for linear alkanes (Rao et al., 1992). O ther advantages of cobalt catalysts are the followings; high productivity at a high syngas conversion rate and no inhibition effect from water molecules (van Berge and Everson, 1997). Its drawbacks are the high cost and low water gas shift activity. Ruthen ium is very active but expensive, relatively it cost s about 31,000 times more than iron. Ruthenium produces mostly methane at a relatively low pressure condition ( below 100 bars), whereas at low temperatures and high pressures, it is selective toward high molecular weight waxes (van der Laan and Beenackers, 1999).
23 2. 2 Reaction Mechanism 2. 2 .1 General Catalytic Surface Reaction Mechanism The nature of the surface species and the detailed mechanistic sequence by which the reaction proceeds over the catalys t have been the subject of much study and discussion Over the years, several apparently different mechanisms have been developed, but common to them all has been the concept that polymerization reaction, a stepwise chain growth process is involved. This assumption is strongly supported by the fact that the carbon number product distributions calculated solely on probabilities of chain growth matched the experimentally observed results obtained in different reactor types and sizes over widely varying proce ss conditions and with different catalysts ( Dry, 1996 ). As a polymerization reaction, FTS mechanism proposed in the literature will have following common steps ( Adesina 1996) 1. reactant adsorption on the catalytic active site 2. generation of the chain initiat or 3. chain growth (or propagation) 4. chain termination 5. product desorption from the catalyst 6. re adsorption and further reaction (optional ) It is generally assumed that not a single reaction pathway exists on the catalyst surface during the FTS, but that a num ber of parallel operating pathways will exist. Numerous reaction mechanisms have been proposed depending on creating chain initiator and chain growth. Although its chain initiator formation and chain propagation manners are different from each other, all t he mechanism s share hydrocarbon product desorption, beta dehydrogenation for the olefin, and hydrogenation for the paraffin products. The most of proposed mechanisms remain within four categories, namely; the surface carbide, enolic intermediate, CO insert ion and alkoxy intermediate mechanisms.
24 Wojciechowski (1988) has inferred that any FT mechanism must have the following characteristics: 1. Adsorption of all species on the catalyst surface onto one set of sites resulting in the decomposition of H2 and CO to hydrogen atoms, adsorbed C and O respectively. The interaction between these surface species leads to the formation of CHx, OH, etc. 2. The monomeric species for oligomerisation is CH2 and its formation from adsorbed C and H is the rate determining step for C O hydrogenation kinetics. 3. The growing radical on the surface is immobile except for C1 C4 species. Chain growth proceeds only with a monomer near the growing chain and can either be formed next to it or migrate via surface diffusion among appropriate set of sites. 4. Surface chain growth can produce spontaneous 1 2 shift attachments leading to branched hydrocarbons. 5. The termination event and hence product type is determined by the type of occupant on the site adjacent to a growing radical. This occupant may be an appropriate termination function such as hydrogen atom, adsorbed OH or even an empty site. If, however, termination occurs after the growing chain has undergone one or more successive 1 2 shifts, internal functional groups will arise yielding alke nes, 2 alcohols, etc. 6. All classical distributions consist of product species that are primary and each has its own chain length distribution of the Anderson Schulz Flory (ASF) plot. This distribution is the property of a collocation grouping of growth, mon omer and termination sites which constitutes a growth location for that molecular species. The locations are stable in composition and continue to produce only one type of molecule at a given set of reaction conditions. 7. S ystem temperature, total pressur e and the H2/CO ratio are fundamental governing factors which affect both kinetics and product distribution. 2. 2 .2 Carbide M echanism The earliest mechanism proposed by Fischer (1926) and later refined by Craxford and Rideal (1939) involved surface carbid es (Dry, 1996). This carbide mechanism (also known as alkyl mechanism) is the most widely accepted mechanism for chain growth in FTS. Figure 2 1 shows the reaction pathways for this mechanism. Chain initiation takes
25 place via dissociative CO chemisorptions by which adsorbed carbon and adsorbed oxygen are formed. Adsorbed oxygen is removed from the surface by reacting with surface hydrogen producing the most abundant product, water molecule. Surface carbon is subsequently hydrogenated yielding in a successi ve reaction CH, CH 2 and CH 3 intermediate species. CH 2 intermediate species is regarded as the monomer, building block, and the CH 3 intermediate species as the chain initiator in this mechanism. The chain initiator is thought to take consecutive addition of the monomer for growing or polymerizing named CH 2 insertion. Product formation, also known as chain termination, is generally thought as the desorption of the surface complex species. Desorption of the straight or branched surface alkyl could yield eith er paraffins or olefins th r ough hydrogenation or hydrogen elimination, respectively. Both have been identified as primary products in the FTS by a large number of previous studies. 2. 2 .3 Enolic M echanism Carbide mechanism is mostly focusing on explai ning how hydrocarbon is produced. This mechanism is lack of explanation for oxygenated products, such as alcohol. To account for the formation of oxygenated products, Storch et al. (1951) proposed a alternative reaction mechanism involving hydroxyl carbene s, =CH(OH). In this reaction mechanism, chemisorbed CO is hydrogenated to a hydroxylated (enol) species. In this mechanism, there is no distinct differentiation between chain initiator and monomer. Figure 2 2 shows formation of initiator and monomer interm ediate species. Chain growth occurs through cond ensation with water elimination between two enolic species. Intermediate species are all enolic molecules so chain termination by desorption process could only yield oxygenated products; simple desorption giv es
26 aldehydes and hydrogenation of the enolic species produces alcohol. To account for the formation of the most abundant hydrocarbon, this mechanism requires another chain termination process. Alternative termination of the chain growth is thought as the c hain breaking into olefins and surface monomer itself. According to this reaction mechanism n paraffins are only formed secondarily by hydrogenation of primarily formed olefins. 2. 2 .4 Direct (CO) I nsertion M echanism The direct insertion mechanism which was originally proposed by Sternberg and Wender (1959) and Roginski (1965), was fully developed by Pichler and Schulz (1970). The mechanism is based on the known CO insertion from coordination chemistry and homogeneous catalysis (Steynberg and Dry, 2004). Chain initiator is the same with the carbide mechanism and adsorbed methyl species, but formation of the chain initiator differs from the carbide mechanism at the time of the oxygen removal. Monomer is chemisorbed CO itself and is inserted directly in a m etal alkyl bond leading to a surface acyl species which is well known in homogeneous catalysis (George et al., 1995). The removal of oxygen atom from acyl leads to the chain growth process. With this mechanism, it is possible to explain termination process for both linear hydrocarbons and oxygenated. After a successful CO addition to existing chain, the final surface intermediate is identical with the one from the carbide mechanism. Therefore, formation of n paraffins and/or olefins is identical to those proposed in the carbide mechanism. In addition to this, during the progress of elimination of oxygen, enolic intermediate could form oxygenated products; aldehydes by dehydrogenation and alcohols by hydrogenation. Figure 2 3 shows detailed reaction pathways for this mechanism. This mechanism is also known as the
27 2. 2 .5 Combined E nol/carbide M echanism This proposed mechanism combines both carbide mechanism and enol mechanism. Basically, chain growth occurs through CH 2 insertion so that monomer is surface m ethylene species However, enolic intermediate complex is involved to form a monomer by hydrogenation of the hydroxylated enolic CO H 2 complex. So, this mechanism is also possible to form not only hydrocarb on but also oxygenated products like a direct CO insertion mechanism. Therefore, c hain termination process could be shared with direct insertion mechanism. Reaction pathway to fo rm a monomer is illustrated in F igure 2 4. Generally C/C bond formation thro ugh CH 2 addition is thought to be the main step of chain growth, but CO addition is not completely ruled out and could be another possibility 2. 3 Intrinsic Kinetics From a classical definition of the catalyst, it is the most important feature for the ca talyst to change reaction rate, either accelerated or decelerated. This important feature can only be measured by an experiment. The major problem in describing the FT reaction kinetics is the complexity of its reaction mechanism and the large number of s pecies involved. Literature on the kinetics and selectivity of the Fischer Tropsch synthesis can be divided into two classes. Most studies aim ed at catalyst improvement and postulate d empirical power law kinetics for the carbon monoxide and hydrogen conver sion rates and a simple polymerization reaction following an Anderson Schulz Flory (ASF) distribution for the total hydrocarbon product yield. This distribution describes the entire product range by a single parameter, the probability of the addition
28 of a carbon intermediate (monomer) to a chain. Relatively few studies aim ed at understanding the reaction mechanisms. Some autho rs derived Langmuir Hinshelwood Hougen Watson (LHHW) rate expressions for the reactant consumption and quantitative formulations to d escribe the product distribution of linear and branched paraffins and olefins, and alcohols. Most kinetic expressions have been developed empirically fitting the data to a power law relationship. This is a powerful technique to gain some insight in the act ual processes taking place on the catalyst surface, but hardly adequate for scale up. Reviews of intrinsic kinetics expression for iron catalysts are given by Huff and Satterfield (1984), Zimmerman and Bukur (1990), and Van Der Laan and Beenackers (1999). 2. 3 1 Iron B ased Catalysts In general, the F T reaction rate increases with the H 2 partial pressure and decreases with the partial pressure of water. The general polynomial kinetic expression is easy to fit experimental data so numerous kinetic expressio ns for polynomial fitting have been investigated. Some of polynomial kinetic expressions are tabulated in Table 2 1 for both iron and cobalt catalysts. From T able 2 1, it can be deduced that hydrogen concentration has affected more than the carbon monoxide and in fact, carbon monoxide merely affects FT kinetics under certain condition s The c arbon monoxide term could be neglected then the F T kinetics becomes the first order dependence as observed by Anderson (1956), Dry et al. (1972) and Jess et al. (199 8 ) ( 2 1 )
29 Anderson (1956) reported that the first order rate expression fits the data well up to the syngas conversion of 60% and found water inhibition at higher conversion. So, Anderson included water inhibition term to fit the experimental data as follow s ( 2 2 ) Mathematically, Equation (2 2) reduces to Equation (2 1) when water concentration is low so the water partial pressure term could be negligible, P CO >> P H2O From the physical point of view, mathematical analysis seems to be true. In the beginning of the process, there will be no water so water inhibition term could be zero. As F T synthesis goes on, water vapor concentration will be i ncreased considering it is the main product of the F T synthesis. Finally, water retards the reaction rate by competing with carbon monoxide for available surface adsorption site. Dry (1976) and Huff and Satterfield (1984) derived the same rate expression from the enolic theory. In this derivation, they assumed rate determining step is the reaction of a molecule of H 2 competing with H 2 O, CO 2 and H 2 for the adsorption sites. Dry (1976) and Huff and Satterfield (1984) made an important assumption here, strong adsorption of CO and water relative to H 2 and CO 2 Dry (1976) reported 63 kJ/mol of activation energy for an iron catalyst used in a fixed bed. Atwood and Bennett (1979) r eported an activation energy of 85 kJ/mol, and an adsorption enthalpy of 8.8 kJ/mol, by fitt ing their data using Eq. (2 2) for fused nitrided ammonia synthesis catalyst. Shen et al. (1994) used
3 0 the same rate expression to describe the kinetics on a precip itated commercial Fe/Cu/K catalyst. They observed an activation energy of 56 kJ/mol which is relatively low for most F T synthesis catalyst s and an adsorption enthalpy of 60 kJ/mol. Anderson (1956) reported that the adsorption constant appearing in Eq. ( 2 2) varied with feed composition. Huff and Satterfield (1984) proposed a rate equation that included a linear decrease in the adsorption parameter in Eq. (2 2) with hydrogen pressure using both carbide and combined enol/carbide theory. ( 2 3 ) They assumed that absorbed intermediates are directly associated with molecular hyd rogen s on both carbide and enol/carbide mechanisms. In their mechanism for the carbide theory, they assumed that the rate determining step is when the absorbed dissociated carbon atom reacts with molecular hydrogen in gas phase and the absorbed carbon atom is the most abundant surface intermediate. In their model for combined enol/carbide theory, they used an assumption made by Vannice (1976) that the final hydrogenation of the CO H 2 complex is the slowest step in the sequence of elementary reactions. Also they assumed that the absorbed CO H 2 and H 2 O are the most abundant surface intermediates and they saturate the surface to eliminate other absorbed species in fractional coverage of absorbed CO H 2 Mathematically, the rate Equation (2 3) becomes identical w ith Eq. (2 2) if water molecule adsorption constant in Eq. (2 2) is inversely proportional to the hydrogen partial pressure. The distinguishing characteristic between Eq. (2 2) and (2 3) therefore is whether water adsorption constant is independent of hydr ogen concentration or inversely proportional to it. So, it can be
31 deduced that the rate expression Eq. (2 3) is a more general idea. Huff and Satterfield (1984) observed their experimental data gave a better fit using Eq. (2 3) and 83 kJ/mol of activation energy for fused iron catalyst. Nettelhoff et al. (1985) fitted their experimental data using both eqs. (2 2) and (2 3). They reported both rate expressions agreed reasonably well for their catalyst, precipitated, unpromoted iron catalyst at 270 o C. They a lso mentioned that Eq. (2 2) yielded a slightly better result. Deckwer et al. (1986) observed that rate expression (2 3) was not able to describe kinetic results at the low H 2 /CO feed ratio regime for potassium promoted iron catalyst. Shen et al. (1994) a ccomplished their experimental analysis using rate Eq. (2 3) and published an activation energy of 56 kJ/mol and an adsorption enthalpy of 62 kJ/mol for precipitated commercial Fe/Cu/K catalyst. Carbon dioxide also can retard the F T synthesis process by competing available catalytic surface with carbon monoxide but its effect is generally not as strong as the water molecule. However, carbon dioxide inhibition term may become significant if water gas shift reaction alters carbon monoxide into carbon dioxi de so carbon dioxide concentration is high enough. This situation may occur when low H 2 /CO feed ratios are employed and/or the catalyst has high WGS activity (Zimmerman and Bukur, 1990). From enol mechanism, Ledakowicz et al. (1985) derived a rate equation including carbon dioxide inhibition term assuming competitive chemisorptions of both CO and CO 2 with hydrogenation of adsorbed CO as the rate determining step and modifying Langmuir isotherm expression. Their reaction rate expression is given as follow s ( 2 4 )
32 They examined their high WGS activity and precipitated catalyst ( 100 Re/1.3 K), and reported an adsorption constant for CO 2 of 0.115 which is insensitive to temperature and 103 kJ/mol of activation energy. Nettelhoff et al. (1985) observed no water inhibition term and 81 kJ/mol of activation energy for high WGS activity commercial fused iron ammonia synthesis catalyst (BASF S6 10). Generalized rate expression concerning both water and CO 2 inhibitions proposed by Ledakowicz et al. (1985) is as follow s ( 2 5 ) However, Yates and Satterfield (1989) demonstrated co feeding of CO 2 to the feed gas and showed that CO 2 is relatively inert. All Pro posed rate expressions were developed with the assumption that the rate determining step is the reaction of undissociated hydrogen with a carbon intermediate The rate equations are valid only for the specific catalysts with Water Gas Shift reaction activi ty and for the process conditions used to develop the expressions. 2. 3 2 Cobalt B ased C atalysts The Fischer Tropsch synthesis reaction rate expressions for cobalt based catalysts are very limited and have different forms than iron based catalysts. The mo st distinguished characteristic is the rate determining step which involves a bimolecular surface reaction resulting in a quadratic denominator in the rate form. Furthermore, water molecule inhibition term merely appears in kinetic expression ( van der Laan and Beenackers 1999) It is another distinguished feature that no carbon dioxide formed due to low or no activity for Water Gas Shift reaction. In kinetic s studies for cobalt based
33 catalyst, polynomial kinetic expression has been reported to fit several experimental results but surely a less number of studies is reported. Several general polynomial kinetic expressions for cobalt catalyst are tabulated in Table 2 1 along with iron catalyst kinetics. Unlike iron based catal ytic kinetics, reaction order for the carbon monoxide is negative, suggesting inhibition by adsorbed CO. Sarup and Wojciechowski (1989) derived six different rate expressions for the formation of the building block, CH 2 monomer, based on both the carbide mechanism and enolic mechanism by assuming various rate determining steps. ( 2 6 ) They compared six model s with their experimental data (Sarup and Wojciechowski, 1988) obtained in a Berty internally recycled reactor using Co/Kieselguhr at 190 o C for P H2 ranging from 0.07 to 0.68 and P CO between 0.03 and 0.93 MPa. Two models, one based on the hydrogenation of s urface carbon and the other on a hydrogen assisted dissociation of carbon monoxide as the rate limiting steps were both able to provide a satisfactory fit to the experimental rate data. ( 2 7 ) and ( 2 8 ) In the first model, Eq. (2 7), rate determining steps are assumed following the surface reactions
34 ( 2 9 ) and ( 2 10 ) where s denotes active site of the catalyst and Cs is absorbed carbon atom on the active site. Equation (2 9) is the first hydrogenation of adsorbed carbon atom and Eq. (2 10) is the first hydrogenation of adsorbed oxygen atom. Using these rate determining steps, they did not actually derived the rate expression, Eq. (2 7) which is a further simplified version. They dropped P CO term in their original derivation as shown in Eq. (2 11) due to a comparatively small adsorption constant value difference in 4 orders of magnitude at 190 o C. ( 2 11 ) In the second model, Eq. (2 8), the slowest step is assumed as the hydrogenation of adsorbed CO to form adsorbed formyl shown below ( 2 12 ) Among their 6 models, Equation s (2 7) and (2 8) were not the best fit to their experimental results. Their best fit model was rejected by original authors, because one of the adsorption coefficients, not stated by authors, was negative, representing a physically unrealistic situation. The f ollowing rate expression is the rejected model by Sarup and Wojciechowski ( 2 13 )
35 Yates and Satterfield (1991) made further simplification of these rate expressions developed by Sarup and Wojciechowski, including Eq. (2 13) which was rejected by original authors. Simplification had been made to have 2 unknown kinetic parameters instead of numerous parameters so that the kinetic analysis could be convenien t and easy. However it should be reasonable. This can be accomplished b y assuming one intermediate absorbed chemical species is predominant, which is justified by nonreacting, single component adsorption data on cobalt surfaces (Vannice 1976). In the case of eqs. (2 8) and (2 13), it was assumed that CO was the predominant ab sorbed species which is also made by Rautavuoma and van der Baan (1981) for their own rate expression. Unlike this, in the case of Eq. (2 11), it is assumed that dissociated CO as a predominant species instead of undissociated CO and this was implicitly ma de by original authors, Sarup and Wojciechowski. Yates and Satterfield reported Langmuire Hinshelwood type equation of the following form was found to best represent the results, which was rejected by Sarup and Wojciechowski ( 2 14 ) In comparison to iron catalysts, the kinetic research on cobalt catalysts is more comprehensive The situation on cobalt catalysts is easier due to the absence of the WGS reaction and less different catalytic sites. However, we conclude that the development of FT kinetics expression for both iron and cobalt catalysts still requires additional resear ch.
36 2. 4 Products Distribution and Selectivity In general, products of FTS have varieties of mixture of organic species, mostly hydrocarbon (n paraffins and olefins) and oxygenates. Wojciechowski (1988), Anderson (1984) and van der Laan and Beenackers (1999) summarized the products characteristics of FTS. 1. The carbon number distributions for hydrocarbons gives the highest concentration for methane and d ecreases monotonically for higher carbon numbers, although around C3 C4, often a local maximum is obse rved. Products distribution from result of Donnelly et al. (1988) for iron catalyst is good example. 2. Concerning branched chemical species, Anderson (1988) found that monomethyl substituted hydrocarbons are predominant and non e of quaternary branched hydro carbon products were formed. 3. Concerning olefins, it is reported that low carbon number olefins are more produced than paraffins for certain iron catalyst and those olefins are mostly olefins. Usually, ethene selectivity is lower than propene and olefin selectivity asymptotically decreases with increasing carbon number. Especially for cobalt catalyst, olefin content is low in comparison with other catalysts. 4. Chain growth parameter for linear paraffins seems to be changed, while olefin chain growth parame ter remains constant (Donnelly, 1989). 5. Alcohols productions also decrease with carbon number, except methanol (Donnelly, 1989). 2.4.1 Influence of P rocess O peration C ondition on the S electivity Fischer Tropsch product selectivity affected by temperature, partial pressure of hydrogen and carbon monoxide, and flow rate is briefly reviewed in this section. Table 2 2 shows the gene r al influence of different parameters on the selectivity (van der Laan and and Beenackers, 1999). It is reported that increasing o perating temperature of FTS results in a shift toward products with a lower carbon number for most of catalysts (Donnelly and Satterfield, 1989; Dry, 1981; Dictor and Bell, 1986). For the influence of temperature on the olefin selectivity, contradictory re sults reported; Anderson (1956),
37 Dictor and Bell (1986) and Donnelly and Satterfield (1989) reported an increase of the olefin selectivity on potassium promoted precipitated iron catalysts with increasing temperature, while Dictor and Bell (1986) observed inconsistent trend, decreasing of the olefin selectivity with increasing temperature, for unalkalized iron oxide powders. Generally, product selectivity shifts to heavier products and to more oxygernates with increasing total pressure. Dictor and Bell (19 86) observed lighter hydrocarbons and lower olefin content produced by increasing H 2 /CO ratios. Donnelly and Satterfield (1989) also reported the same tendency; decreasing olefin to paraffin ratio by increasing H 2 /Co ratio. Bukur et al. (1990), Iglesia et al. (1991) and Kuipers et al. (1996) investigated the influence of the space velocity of the syngas on FTS selectivity. All the reported works has consistency; the increase of the olefin selectivity and decrease of the conversion with increasing space velo city. 2.4.2 Product Selectivity Model According to Anderson (1956), carbon number independent chain growth probability could be explaining the distribution of n paraffins which is given by follow ( 2 15 ) where n is carbon number, m n is the mole fraction of a hydrocarbon containing chain length n, and is chain growth prob ability which is not affected by carbon number n. Equation (2 15) is well known Anderson Schulz Flory (ASF) distribution equation. Chain growth pro b ability, is defined by ( 2 16 )
38 where R g and R t are the rate of chain growth and termination, respectively. Chain growth pro b ability determines the product distribution of FT products. It is shown in F igure 2 5 that hydrocarbon selectivity as function of the chain growth pro b ability factor calculated using ASF distribution equation, Eq. (2 15). In derivation of ASF distribution, it is crucial assumption that chain growth pro b ability does not depend on carbon number. However, deviations from ASF distribution are reported in the literatures. 2. 5 Fischer Tropsch Reactors and Reactor M odeling There are four types of Fischer Tropsch reactor s in commercial applic ations at the present ( Steyberg and Dry, 2004) ; circulating fluidized bed reactor, standard fluidized bed reactor, fixed bed reactor, and slurry phase reactor. This section includes a brief review of the characteristics of each type of reactor and detailed fixed bed reactor modeling. 2.5.1 Fluidized B ed R eactor The most distinguishing characteristic of fluidized bed is the fact that it is mainly operated on high temperature F T processes for the production of light alkenes rather than wax. Fluidized bed re actor is very attractive for FTS due to its excellent heat transfer and temperature equalization characteristics. Therefore, it could be said that f luid ized bed reactors have an inherent advantage with higher heat transfer coefficients which is important d ue to the large amount of heat that must be removed from the F T reactors to control their temperature s Comparing with fixed bed reactor, another advantage for fluidized bed is the fact that it is free from intra particle diffusion limitation. However flu idization may be hampered by particle agglomeration due to heavy product deposition on the catalyst pore. So it is concluded that fluidized bed reactors are not
39 suitable for producing liquid phase products (gasoline and/or diesel) because liquid phase prod uct s may cause catalyst agglomeration and loss of fluidization. Fluidized bed systems are categorized as HTFT (High Temperature Fischer Tropsch) reactors and a notable distinguished feature between HTFT and LTFT (Low Temperature Fischer Tropsch) reactors is the absence of liquid phase in HTFT reactors. Fixed bed and slurry phase systems categorized as LTFT reactors are appropriate for producing liquid phase products. 2.5.2 Slurry P hase R eactor The slurry phase reactor is defined as a three phase bubble c olumn reactor utilizing the catalyst as a fine solids suspension in liquid. The slurry reactor system was considered to be suitable for the production of wax at low temperature FT operation s since the liquid wax itself would be the medium in which the fine ly divided catalyst is suspended. Additional separation system is required since catalysts are suspended in the product phase. The main difference on the catalyst is the size comparing with fixed bed system. Catalyst particle s for fixed bed system ha ve a l ower size limitation by pressure drop while catalyst particles for slurry phase reactor ha ve a upper size limitation by suspended phase. The rate of the F T reaction is pore diffusion limited even at low temperatures and hence the smaller the catalyst part icle the higher the observed activity. For the high temperature F T operation, the suspension medium is thermally unstable, so a high temperature slurry phase operation is therefore not practical or viable. For a low temperature F T system in a slurry reac tor is regarded by many authors as the most efficient pr ocess for F T diesel production Notable advantages over a fixed bed reactor are low pressure drop, low catalyst loading,
40 easiness to achieve an isothermal condition, and less cost for the same capaci ty. D isadvantages are more sensitive to catalyst poisoning due to low loading, and requir ing additional separation device (due to this it took long time for commercialization). I n the slurry phase reactor, it is possible to use smaller catalyst pellet s tha n a fixed bed reactor. 2.5.3 Fixed B ed R eactor F ine catalyst particles cause a huge pressure drop. The bigger particles are relatively free from large pressure drop s but there is an intra particle mass transfer limitation. The most common fixed bed react or is a shell and tubes reactor. To achieve high conversion, it is a common p ractice to recycle a portion of the reactor exit gas. High pressure operation due to narrow and long tube s fine catalyst pellets, and high operating gas velocities will increase gas compression costs and also could cause disintegration of weal catalyst pellets. Catalyst loading and sometimes unloading will be difficult for narrow and long tubes. F T synthesis reactions are exothermic so heat removal is also an important factor. Reactor design considering only kinetics aspect may have hot spot causing catalyst deactivation called sintering. Although these drawbacks of a fixed bed reactor it is widely used for F T process studies such as catalyst development, kinetics measurement, catalyst deactivation studies and so on. Despite of these drawbacks, fixed bed reactor has some benefits, easiness of its operation, no need for additional separation device, and easiness and predictable scale up for large scale reactor s Fischer Tropsch f ixed bed reactor, being one of the most compet itive reactor technologies, occupies a special position in FTS industrial practices,
41 as persuasively exemplified by the large scale commercial operations of Sasol and Shell ( Wang et al. 2003 ) 2.5.4 Fixed B e d R eactor M odeling A bundant experimental and modeling research efforts concerning slurry phase FT reactors are available elsewhere (Jess et al., 1999, Troshko A.A. Zdravistch F., 2009 and Wu et al., 2010 ) In contrast to slurry phase FT reactors, the l iterature on packed bed reactor modeling and design is very limited. Atwood and Benett (1979) developed a 1 dimensional plug flow, heterogeneous model to investigate paramet ric effects on commercial reactors. A 2 dimensional plug flow, pseudo homogeneous m odel without intraparticle diffusion limitations had been developed by Bub et al (1980) Jess et al. (1999) developed a 2 dimentional, pseudo homogeneous model for nitrogen rich syngas. A 1 dimensional, heterogeneous model to account for intraparticle dif fusion limitations had been developed by Wang et al. (2003) De Swart (1997) developed a 1 dimensional, heterogeneous model for packed bed reactors with cobalt catalyst. Jess and Kern (2009) further developed a 2 dimensional, pseudo homogeneous model with a pore diffusion limitation for a fixed bed reactor for both iron and cobalt catalysts, utilizing boiling water as the coolant. More recently, Wu et al. (2010) proposed a more comprehensive model. A two dimensional pseudo homogeneous reactor model is appli ed for fixed bed FTS reactor. They incorporated lumped CO consumption kinetic equation and carbon chain growth probability model into the reactor model. However, none of these previous works has considered product distribution s and/or individual product pr oduction rate s All these studies were developed with a lumped kinetics model for syngas. Lumped kinetics model has some inherent drawback. It cannot
42 predict the exact amount of released heat by the exothermic reactions as well as the stoichiometric consum ption ratio of hydrogen to carbon monoxide. For example, these are entirely different cases when producing one mole of n decane or ten moles of methane from ten moles of carbon monoxide and enough hydrogen (technically speaking, 156 kJ and 206 kJ of heat w ill be released per CO mole consumed and 21 moles or 30 moles of hydrogen will be required to produc e one mole of n decane or ten moles of methane, respectively ). Th ese complicated FT reactions cannot be represented by one single equation; ( 2 17 ) Moreover, none of these previous studies included the 2 dimensional flow of two phases. FTS converts syngas (hydrogen and carbon monoxide gases) into hydrocarbon and water in both gaseous and liquid phases (sometimes including solid but it is definitely the unwanted phase). Mostly wanted products are synthe tic gasoline and/or diesel ( this is why FTS had been invented). Both products are in the liquid phase definitely under the room condition and might be under certain operating condition s
43 Table 2 1 Reaction rate equations for overall synthesis gas consumption rates Catalyst Reactor type T [oC] P [MPa] H 2 /CO Rate expression Act. E [kJ/mol] Reference Iron Fixed bed N/A N/A N/A 88 Brtz (1949) 250 320 2.2 4.2 2.0 79 (est) Hall et al. (1952) Reduced and nitrided iron Fixed b ed N/A N/A N/A 84 Anderson (1956) Fixed b ed 225 255 2.2 0.25 2.0 71 100 Anderson et al. (1964) Fixed b ed 225 265 1.0 1.8 1.2 7.2 71 Dry et al. (1972) 15% Fe/Al 2 O 3 Fix ed b ed 220 255 0.1 3.0 88 4 Vannice (1976) 100 Fe/5 Cu/4.2 K/25 SiO2 Gradientless 249 289 0.3 2.0 N/A Bub and Baerns (1980) Iron N/A N/A N/A N/A Lox et al. (1993) Iron Fixed b ed 250 2.5 N/A Jess et al. (199 8 ) Co/CuO/Al 2 O 3 Fixed b ed 185 200 1.7 55 1.0 3.0 Yang et al. (1979) Co/La 2 O 3 /Al 2 O 3 Berty 215 5.2 8.4 2.0 Pannell et al. (1980) Co/B /Al 2 O 3 Berty 170 195 1.0 2.0 0.25 4.0 Wang (1987) Co/TiO 2 Fixed b ed 200 8 16 1 4 Zennaro et al. (2000)
44 Table 2 2. Selectivity control in Fischer Tropsch synthesis by process conditions and catalys t modifications (Van der Laan and Beenackers, 1999). Parameter Chain length Chain branching Olefin selectivity Alcohol selectivity Carbon deposition Methane selectivity Temperature Pressure H 2 /CO Conversion Space velocity Note: Increase with increasing parameter: Decrease with increasing parameter: Complex relation:
45 Figure 2 1 Schematics of carbide mechanism
46 Figure 2 2 Schematics of E nolic mechanism
47 Figure 2 3 Schematics of Direct Insertion mechanism
48 Figure 2 4 Schematics of Combined enol/carbide mechanism
49 Figure 2 5 Hydrocarbon selectivity as function of the chain growth probability factor calculated using ASF.
50 CHAPTER 3 MATHEMATICAL MOD ELING OF PACKED BED FISCHER TROPSCH REACTOR 3 .1 Gas L iquid Hydrodynamics system 3. 1 1 Multi P hase F low Model Multiphase flow is a simultaneous stream of m aterials with different states or phases (i.e. gas, liquid or solid). However, it is also considered a s a multiphase flow when m aterials with different chemical properties but in the same state or phase (i.e. liquid liquid systems such as oil droplets in water). Multiphase flow regimes can be grouped into four categories: gas liquid or liquid liquid flows; gas solid flows; liquid solid flows; and three phase flows. Some examples are given below, Bubbly flow: discrete gaseous bubbles in a continuous liquid. Droplet flow: discrete fluid droplets in a continuous gas. Slug flow: large bubbles in a continuous l iquid. Stratified and free surface flow: immiscible fluids separated by a clearly defined interface. Annular flow: continuous liquid along walls, gas in core. Particle laden flow: discrete solid particles in a continuous fluid. Pneumatic transport Fluidize d bed Slurry flow Hydrotransport Advances in computational fluid mechanics have provided the basis for further insight s into the dynamics of multiphase flows. Currently there are two approaches for the numerical calculation of multiphase flows: the Euler Lagrange approach (discussed below) and the Euler Euler approach In the Euler Euler approach, the different phases are treated mathematically as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phas e volume fraction is introduced. These volume fractions are assumed to be continuous functions of space
51 and time and their sum is equal to one. Conservation equations for each phase are derived to obtain a set of equations, which have similar structure for all phases. The closure of t hese equations is by providing constitutive relations that are obtained from empirical information, or, in the case of granular flows, by an application of kinetic theory. Among three different Euler Euler approach es the volume of fluid (VOF) model, the mixture model, and the Eulerian model, we have applied the so called Mixture model to packed bed for FTS. The mixture model is a simplified multiphase model that can be used in different ways. It can be used to model multi phase flows where the phases move at different velocities, but a local equilibrium over short spatial length scales is assume d It can be used to model homogeneous multiphase flows with a very strong coupling and phases moving at the same velocity and last ly, the mixture models are used to calculate non Newtonian viscosity. The mixture model can model n phases (fluid or particulate) by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary pha ses, and algebraic expressions for the relative velocities. Typical applications include sedimentation, cyclone separators, particle laden flows with a low loading, and bubbly flows where the gas volume fraction remains low. The mixture model is a good sub stitute for the full Eulerian multiphase model in several cases. A full multiphase model may not be feasible when there is a wide distribution of the particulate phase or when the interphase laws are unknown or their reliability can be questioned. A simple r model like the mixture model can perform as well as a full multiphase model while solving a smaller number of variables than the full multiphase model. The mixture model allows
52 you to select granular phases and calculates all properties of the granular p hases. This is applicable for liquid solid flows. The mixture model solves the continuity equation for the mixture, the momentum equation for the mixture, the energy equation for the mixture, and the volume fraction equation for the secondary phases, as we ll as algebraic expressions for the relative velocities if the phases are moving at different velocities (ANSYS FLUENT 12.0 Theory Guide, 2009) 3 1 2 Assumption The Fischer Tropsch synthesis and main assumptions of this model are the following: (1) The fl ow field inside the tube is an axisymmetric and two dimensional steady flow where catalyst pellets are packed inside and coolant flows outside the tube; (2) Steady state operation has been assumed, i.e., there will not be change over the time including cat alytic activ ity, selectivity and stability; (3) The two phase flow is composed of gaseous (syngas, water vapor and light hydrocarbon products) and liquid (heavier hydrocarbon) components ; (4) Solid hydrocarbon s in the form of wax ha ve been neglected; (5) N o VLE (vapor liquid equilibrium) is assumed as the liquid phase contains only heavier hydrocarbons with small mass fractions ; (6) Packed bed is assumed stati sti cally uniform; no channeling with isotropic hydrodynamic properties; (7) The production of o xyge nates (alcohols and etc ) is neglected due to their small amount s comparing with hydrocarbons; and (8) Concerning the chemical kinetic expression, it is assumed that the syngas consumption rate is governed by lumped kinetics from the semi empirical Langmui r Hinshelwood Hougen Watson ( LHHW ) model given by Yate s and Satterfiel d (1991)
53 3 1 3 Continuity In the FTS, syngas is converted mainly to hydrocarbons in both gaseous and liquid phases. As mentioned in the assumption section, solid wax production has bee n neglected Among several flow regimes possible for gas liquid flow s the droplet flow is most likely to take place that is described as discrete fluid droplets in a continuous gas phase. For the numerical modeling, the mixture model one of the Euler Eu ler approach es (Volume of Fluids model, mixture model, and Eulerian model) which consider each phase as an interpenetrating continu um has been applied for droplet flow s This mixture model is a good alternative for the full Eulerian multiphase model as a simplified one because it solves each transport equation for the mixture and the volume fraction of the secondary phases (Ishii and Hibiki, 2006 and ANSYS FLUENT 12.0 Theory Guide, 2009) The continuity equations for the gaseous and liquid phases are shown below; ( 3 1 ) where m is the mixture density defined as m G G + L L G and L are the volume fraction s of the gas and liquid phase s, respectively and v m is the mass averaged velocity defined as, ( 3 2 ) 3 1 4 Momentum Similar to the continuity equation the momentum equation f or the general mixture model is accomplish ed by using mixture prope rties (density and viscosity) and mass
54 averaged velocity defined in previous section It is considered that the primary phase and dispersed phase do flow at the same velocities which could be happening in typical multi phase phenomena. However, as the mult iphase mixture flows over the packed bed, the momentum equation needs to be modified as follows, ( 3 3 ) where S M denotes a momentum source or sink term due t o the packed bed. In this study, we have ad o pted a p orous model as a momentum sink term for the packed bed. A g eneral momentum sink term for the homogeneous porous media m odel is given by ( 3 4 ) where S M,i is the source or sink term (dependin g on sign) for the i th momentum equation, | v m | is the magnitude of the mixture velocity m is viscosity of the mixture, m is density of the mixture is the permeability of the porous medium and is the inertial resistance factor The momentum sink te rm is composed of two parts: a viscous loss flow velocity). These parameters are evaluated using a semi empirical correlation, the Ergun Equation (Ergun, 1928) ( 3 5 ) The permeability and inertial loss coefficient can be obtained from re lating Equation s (3 4) and (3 5) and given below (ANSYS FLUENT 12.0 Theory Guide) ( 3 6 )
55 where D p is catalyst particle diameter, is packed bed porosity. 3 1 5 Energy E quation The c onservation of energy for the mixture model is given below ( 3 7 ) where m is mixture thermal conductivity, S E is volumetric heat source from the reaction, and E k is defined as follow ( 3 8 ) where h k is the enthalpy for phase k. 3 1 6 Volume Fraction Equation f or t he Liquid P hase Th e volume fraction equation for liquid phase can be obtained from the mass conservation for liquid phase (continuity equation) as follow ( 3 9 ) where denotes j th reaction, and means stoichiometric coefficient and molecular weight of the i th specie s in j th reaction, respectively. The sign convention for stoichiometric coefficient is positive for products and negative for reactants. 3 1 7 Species Transport Equation Species transport equation inside q phase is given by ( 3 10 )
56 where Y i is the mass fraction of i th chemical species, J k, i means diffusion flux of i th sp ecies due to both concentration and temperature gradients. N 1 species transport equations will be solved if N is the total number of species inside the k phase. Nth equation for k phase will be the sum of total mass fraction s in q phase and it is unity, i .e., 3 2 Fischer Tropsch Reaction Kinetics and Mass Transfer Limitation 3. 2 1 Internal Diffusion through A morphous P orous C atalyst and O verall R eaction R ates In the heterogeneous catalytic reaction, intrinsic reaction kinetics is fast. Sometimes, it is faster than mass transfer rate. Seemingly, mass transfer is delaying the overall process. The heterogeneous catalytic reaction is assumed as a sequence of basic steps as the following : 1. External diffusion of the reactant; from th e bulk phase to the external surface of the catalyst. 2. Internal diffusion of the reactant; th r ough pore to the catalytic active sites. 3. Adsorption of the reactant; onto the active site. 4. Surface reaction; 5. Desorption of the product; from the active site. 6. Inte rnal diffusion of the product; th r ough the pore from the active site to the external surface of the catalyst. 7. External diffusion of the product; from the external surface of the catalyst to the bulk phase. The overall rate of reaction is equal to the rat e of the slowest step in the process When the diffusion steps (1, 2, 6, and 7 in the above basic steps) are very fast
57 compared with the reaction steps (3, 4, and 5), the concentrations in the immediate vicinity of the active sites are indistinguishable fr om those in the bulk fluid. In this situation, the transport or diffusion steps do not affect the overall rate of the reaction. In other situations, if the reaction steps are very fast compared with the diffusion steps, mass transport does affect the react ion rate. 3. 2 2 Similarity between H eat T ransfer with Fins and C ataly tic Chemical R eaction For the physical phenomena as well as analytic methods, there are analogies between heat transfer through a finned surface and chemical reaction with catalyst. In other words, a catalyst can be regarded as providing extended surfaces. Distinctions between finned surface heat transfer and amorphous porous catalytic surface re action are tabulated below. In T able 3 1, we point out the similarities and also provide simp lest governing equations and typical solutions for both finned heat transfer and heterogeneous catalytic reactions. For the sake of simplicity, a 1D uniform cross sectional fin and a spherical catalyst pellet have been considered. The energy equation for t he finned surface can be obtained from a conservation of energy by simply balancing conduction and convection for the differential element. In T able 3 1, steady state balance is given. The first term is conduction and the second term is convection from the fin surface. Similarly, chemical species equation can be obtained by balancing the diffusion inside the pore and surface reaction at the wall. The first 2 terms are molecular diffusion terms inside the pores of the catalyst but molecular diffusivity canno t be applied due to the random shapes of the pores. Generally, catalyst pores are amorphous with various cross sectional areas and tortuous paths that interconnect each other and etc. It will be a tremendous job to describe diffusion within all pores
58 indiv idually. Consequently, it is more convenient to define an effective diffusion coefficient so as to describe the average diffusion process taking place inside the spherical catalyst. An effective diffusivity is define as follows, ( 3 11 ) where D b is bulk diffusivity, p is catalyst porosity (void volume over catalyst volum e), is tortuosity defined as the ratio of actual distance a molecule travels between two points to the shortest distance between those two points, and c is the constriction factor accounting for the variation in the cross sectional area. So, this effect ive diffusivity is applied to the chemical species balancing equation. The last term in the chemical species equation is the surface reaction term corresponding to the convection term in the finned surface heat transfer case. In this wall consumption term heterogeneous catalytic chemical reaction is distinguished from cooling makes the differential equation linear so in its dimensionless form it is a linear, homogeneous, s econd order differential equation, while the surface reaction term in a chemical species balance makes a differential equation non linear even in this simple example case. If we applied an intrinsic chemical kinetics here for a comprehensive analysis, it w ill be more non linear. Only the first order chemical kinetics makes the balance equation linear. A typical solution has been obtained by assuming a first order kinetics to understand the characteristics of a heterogeneous porous catalytic reaction. We wil l further expand this to a comprehensive analysis later to model the actual phenomenon.
59 From the heat transfer background knowledge, we are aware of the fact that a different parameter m results in a different temperature profile. The Thiele modulus, dime nsionless parameter n serves the same role. The subscript n denotes its polynomial reaction order. The physical meaning of the Thiele modulus is the ratio of the surface reaction rate to the diffusion rate through the pore. When the Thiele modulus is lar ge, internal diffusion is rate limiting; when this parameter is small, the surface reacti on limits the overall rate. In F igure 3 1 the concentration profile s are depicted for the several different values of the first order kinetic Thiele modulus. T wo orde rs of magnitude differences make totally different pictures. Large values of the Thiele modulus indicate instantaneous surface reaction. Reactant chemical species is consumed near the catalyst external surface, and consequently almost never penetrates towa rd the core of the catalyst. In other words, active sites, usually a precious metal, near the center of the catalyst would be wasted because a reactant chemical species would never reach the center portion of the catalyst pellet. Small values of the Thiele modulus indicate that surface reaction is much slower than the internal diffusion so reactant species diffuse well into the center, and consequently its concentration remains relatively high. This relationship between the concentration and the Thiele modu lus is well illustrated in F igure 3 1 for the simplest 1 st order kinetics. The main purpose of porous catalyst utilization is taking the benefits of an extended surface area. As we mentioned in the previous paragraph, an extended surface area, however, is not completely utilized for certain circumstances. Definitely, it is associated with the Thiele modulus. Though, Thiele modulus itself is not enough to assess the performance of a porous catalyst. Mathematically, Thiele modulus could
60 have a value rangin g from zero to infinity and those ranges are not good enough to indicate the relative importance of diffusion and reaction limitations. An assessment of this matter may be made by evaluating the effectiveness factor which is defined as the ratio of actual overall rate of reaction to the rate of reaction that would result if the entire interior surface were exposed to the external condition. This term is analogous to the fin efficiency but is called effectiveness factor. A logical definition of the internal effectiveness factor is ( 3 12 ) For the 1 st order catalytic reactio n through the spherical pellet, a relationship between the effectiveness and the Thiele modulus is depicted in F igure 3 2 From F igure 3 2 we deduce that as the pellet size becomes very small, the Thiele modulus decreases, so that the effectiveness factor approaches unity and the reaction is surface reaction limited. On the other hand, when the Thiele modulus is large, the effectiveness factor becomes very small, and the overall reaction is diffusion limited within the catalyst. So far, we have related th e finned heat transfer to the catalytic surface reaction as an extended surface concept. And all the catalytic reactions are assumed 1 st order kinetics which is straightforward to get an analytic solution for the concentration profile within the catalyst. Next section, we will discuss intrinsic kinetics for FTS and how to apply mass transfer limitation for non linear kinetics.
61 3.2. 3 Intrinsic K inetics and I ntraparticle M ass T ransfer L imitation Describing the FT reaction kinetics is very complex due to its complicated reaction mechanism s and a large number of chemicals involved. Besides those problems, kinetic studies are of difficulty considering F T catalyst activity depends on its preparation method, metal loading, and support ( Martin Martinez and Vannic e 1991, Iglesia et al. 1992, and Ribeiro et al. 1997 ) F T kinetic studies can be categorized in to 3 different approaches; ( 1 ) Mechanistic proposals consisting of sequence of elementary reactions among surface absorbents and/or intermediates. ( 2 ) Empiric al expressions of general power law kinetics and ( 3 ) Semi empirical kinetic expression based on FT mechanism. In this study, we have accommodated a widely accepted well known semi empirical Langmuir Hinshelwood equation for kinetic s expression proposed by Yates and Satterfield (1991) ( 3 13 ) We have picked Jess and Kern s (2009) kinetic s coefficient s among numerous sets of rate constants and adsorption coefficient s available ( Maretto and Krishna 1999, Hamelicnk et al. 2004, and Philippe et al. 2009) ( 3 14 ) ( 3 15 ) Now, we will discuss how we apply effectiveness and Thiele modulus on our highly non linear Langmuir Hinshelwood type surface kinetics such as F T intrinsic kinetics.
62 We may assume Langmuir Hins helwood type reaction rate as a pseudo first order reaction rate for the hydrogen, then pseudo reaction rate and pseudo first order rate constant are as follow s ( 3 16 ) With a pseudo reaction rate, simplified effectiveness factor and Thiele modulus are given by ( 3 17 ) where, H H2 is Henry coefficient, D eff,H2,l is effective diffusion of the dissolved hydrogen in the liquid filled porous catalyst defiend by ( 3 18 ) Effectiveness factor is plotted as a function of temperature for several particle sizes in the F igure 3 3 E ffectiveness factors for pseudo kinetics decrease with increasing either particle size or temperature. It is obvious that the lower effe ctiveness factor for the larger particle by intuition. Concerning the temperature, effectiveness dependency on the temperature is higher for the larger particle. As temperature increasing, reaction constant following Arrhenius equation increases in exponen tial manner. Diffusion coefficient is not keeping up with exponentially growing reaction constant. Consequently, effectiveness is decreasing when temperature arise, so that overall reaction is inhibited by internal diffusion. Considering only the reaction kinetics,
63 the smallest catalyst is the better. However, large pressure drop is caused by packed bed of fine particle FLUENT is equipped to evaluate neither effectiveness factor nor general Thiele modulus. Therefore, C/C++ code has been written for effecti veness and Thiele modulus as a UDF (User Defined Function). 3.2. 4 Product D istribution with Carbon Number Independent Chain Growth Probability The l umped kinetic model only can describe the consumption for one of the reactants, either CO or H 2 It require s an additional approach to model the product distribution and the other reactant consumption. Here we ad o pted the well known general chain growth probability model which become s the s implest product distribution, ASF distribution, when chain growth proba bility does not depend on the number of carbon s in the products. A s toichiometric relationship between reactants and products can make it eas ier to combine the lumped kinetic model for CO consumption with the general chain growth probability model. A g ener al linear alkanes synthesis chemical reaction is shown in Eq. ( 3 19 ) ( 3 19 ) This linear alkanes production reaction shows that hydrogen to carbon monoxide ratio is 2 + ( 1/n ) to produce linear alkanes. The maximum ratio is 3 for methane production and the minimum value is 2 for producing CH 2 radical. Initially, this ratio drops quickly and approaches to 2 in an asymptotic manner with respect to increasing carbon number and this is exactly due to the mathematical nature of 1/n. T herefore, hydrogen consumption and/or actual hydrogen to carbon monoxide consumption ratio are depending on the product distribution. (For example, 10 moles of methane, 2 mole
64 of n pentane and 1 mole of n decane can be produced from 10 moles of carbon mono xide but 30 moles of hydrogen, 22 moles of hydrogen and 21 moles of hydrogen are required, respectively.) Catalyst surface chemistry and chain growth probability based on carbide mechanism of FTS are shown in Figure 3 4 At the steady state, a species bal ance for the absorbed carbon number n yields ( 3 20 ) Desorption rate could be interpreted as the hydrocarbon production rate assuming no side reactions among gaseous phase s So that hydrocarbon production ratio of n carbon number to n 1 carbon number can be written as follow, ( 3 21 ) where n is chain growth probability of n carbon containing absorbed intermediate defining ( 3 22 ) For carbon number independent chain growth probability (in another word, consta nt chain growth probability), Equation ( 3 21 ) becomes the well known ASF distribution as follow s ( 3 23 ) ( 3 24 )
65 3.2.5 Product Distribution Accomplished with Carbon Number Dependent Chain Growth Probability T he total CO consumption rate is definitely related to the hydrocarbon production rates. I t is important to note that hydrocarbon production rate is based on molar change of hydrocarbon, while carbon monoxide consumption rate is definitely based on molar change of CO in general. S toichiometric information is required for relating molar change o f hydrocarbon with molar change of CO. Also, hydrocarbon production from the CO could be considered as a parallel reaction of the carbon monoxide. So total carbon monoxide consumption rate is equivalent to the summation of each production rate considering stoichiometr ic condition ( 3 25 ) Assuming a constant chain growth prob ability, n carbon hydrocarbon production rate could be expressed using the total CO consumption (lumped kinetics for FT) ( 3 26 ) A s ignificant deviations from the ASF distribution are reported in the literatures. To achieve our objective of building a comprehensive 2D heterogeneous CFD simulation, we have derived each hydrocar bon production rate with a general chain growth probability instead of a carbon number independent constant chain growth probability as a non ASF distribution model. From Equation ( 3 21 ) successive substitutions relate any hydrocarbon desorption rate to methane production rate as follows, ( 3 27 )
66 where the common term, r 1 /(1 1 ), could be interpreted as a chain initiation process which is forming an absorbed methyl from the building block, CH 2 by adding a hydrogen atom. ( 3 28 ) Individual hydrocarbon production rate, hence, can be written as follow s using the chain initiation rate ( 3 29 ) M easurement of chain initiation rate, however, could be extreme ly challenging Without forming a carbon dioxide, which is a reaso nable assumption for the cobalt catalyst all the absorbed carbon monoxide is dissociated and the dissociated carbon successively gains a hydrogen atom to form a monomer, CH 2 in the carbide mechanism. And then this monomer or building block should face tw o possibilities in its evolving process toward forming hydrocarbon; initiation and chain growth with pre existing absorbed alkyl group. Therefore, chain initiation rate and all chain growth reaction rates should be balanced with the carbon monoxide consump tion rate. In terms of symbols, the relationship between CO consumption rate and chain initiation rate is ( 3 30 )
67 Combining Equation s ( 3 29 ) and ( 3 30 ) yields the specific hydrocarbon production rate that relat es to the CO consumption rate using an individually assigned chain growth probability ( 3 31 )
68 Table 3 1 Similarity between fin in heat transfer and catalyst reaction Finned surface Amorphous porous c atalyst What is transferred? Heat Chemical spec ies Through where? Solid material Meandering p ore Driving force Temperature g rad. Concentration g rad. At the wall Convection removes heat Chem. r xn removes reactant Extended surface Generally well defined Complex(constriction, tortuosity) Coordin ates Cartesian Spherical Steady balance Dimensionless form Dimensionless Typical solution C ondition Adiabatic tip 1 st order kinetic
69 Figure 3 1 Concentration profile for simplest case, 1 st order reaction, for various values of Thiele modulus
70 Figure 3 2 Effectiveness factor for 1 st order reaction within the spherical catalyst as a function of Thiele modulus.
71 Figure 3 3 Effectiveness factor for pseudo kinetics instead of LH kinetics as a function of size and temperature.
72 Figure 3 4 Catalyst surface chemistry and C hain growth scheme.
73 CHAPTER 4 NUMERICAL SOLUTION M ETHOD AND VALIDATION S 4 1 Numerical Solution by FLUENT As outlined in previous Chapter 3 t he synthesis process of Fischer Tropsch catalytic chemical reactions is complicated because that the soph isticated heterogeneous catalytic reactions are intensively coupled with a two phase flow in a packed bed together with simultaneous heat and mass transfer Therefore, solving this process accurately by numerical computations is a very challenging task A numerical simulation of this process including the entire system infrastructure can provide some guidance to the design, scale up and optimization of a FT reactor. A numerical simulation of the Fischer Tropsch reactor has been accomplished using a commerci al thermal hydraulic code FLUENT (ANSYS FLUENT 12) For the past several years, FLUENT has been widely accepted as the main computational software package for the numerical simulation of thermal hydraulic transport phenomena. For example, FLUENT was used for the numerical study of ignition/combustion process of pulverized coal ( Jovanovic et al. 2011). Jin and Shaw (2010) perform ed a c omputational modeling of n heptane droplet combustion in an air diluents environment under reduced gravity using the FLUENT package. Chein et al. (2010) predicted the hydrogen production in an ammonia decomposition chemical reactor using the F LUENT software. Ho et al. (2011) used the FLUENT software to simulat e the two phase flow in a falling film microreactor The discretizati on method in FLUENT is b ased on a Finite Volume Method (FVM) FLUENT can faithfully discretize the governing equations and constitutive equations with corresponding initial and boundary conditions described in Chapter 3 a nd then solve the resulting simulta neous
74 equations with the maximum possible accuracy. It can handle the two phase flow th r ough a porous media and the heterogeneous chemical reaction in the packed bed reactor The GAMBIT 2.4.6 package was used for grid generation. F ig ure 4 1 shows the schem atic of a typical grid system for a packed bed Fischer Tropsch reactor employed by the current numerical simulation Since the reactor is cylindrical and packed with isot r opic spherical catalyst beads the computational domain was assigned as a two dimensi onal axisymmetric cylinder Therefore, quadrilateral computational cells were generated by the GAMBIT as shown in Figure 4 1 A p ressure based solver employing the SIMPLE algorithm was used for the pressure velocity coupling scheme (Patankar, 1980). As des cribed in the previous Chapter the Eulerian mixtu re model was applied for the two phase flow th r ough a porous media. Laminar flow is assumed due to very small length scales in the pathway s created among small spherical catalyst pellets. As we assume no va por liquid equilibrium the gaseous phase consists of carbon monoxide hydrogen, water vapor light hydrocarbon up to C6 while heavier hydrocarbons, from C7 to C15, make up the liquid phase. FT synthesis reactions are treated as interaction s between the tw o phases in the presence of the fixes bed of catalyst pellets However, FLUENT does not have built in reaction kinetics such as Eq. ( 3 13 ) as well as Eq. ( 3 31 ) Therefore, i mplementation of the FT synthesis reaction s with rate s given by Eqs. ( 3 13 ) and ( 3 31 ) has been accomplished by using a UDF (user defined function) in FLUENT (ANSYS FLUENT UDF Manual, 2009). Our UDF als o provides intra particle mass transfer limitation defined previously by Eq ( 3 17 ) as w ell as the FT synthesis kinetics discussed i n Chapter 3 I n order to a chieve higher accuracy results, a second order upwind discretization scheme was applied except for the volume fraction where the
75 QUICK scheme was applied (Versteeg and Malalasekera, 1995; Ferziger and Peri 2002). The synth esis gas ( s yngas), a mixture of mainly carbon monoxide and hydrogen, is pumped in to the inlet of the packed bed reactor. A packed bed of catalyst pellets is assumed as a porous material. The fluid flow is described by a porous media mode l All materials gas species, liquid species, and solid catalyst are assigned appropriate properties from the literature as well as from the FLUENT database. The properties of the gas species density, viscosity, ther mal conductivity, specific heat are allowed to vary with the ir respective temperature s The thermodynamics properties of the gas phase mixture are calculated from their pure substance properties and local composition s ; ideal gas law for density and ideal gas mixing law for viscosity, thermal conductivity, and mixing law for specific heat. A large scale numerical simulation requires huge computational resources S ince we are dealing with multiphase flow s and heat transfer with complex chemical reactions involving many chemical species so grid independence study was performed considering computational resource effectiveness aspect s Grid refinement has been performed until smaller grid s do not significantly improve the accuracy. 4 2 Model Validation Works 4 2 1 Validation of Products Distribut ion Two independent comparisons have been conducted to validate ou r model. The first validation has been made by comparing products distribution with experimental work done by Elbashir and Roberts (2005) In their study, hydrocarbon product distributions a re provided both supercritical fluid and conventional gas phase Fischer
76 Tropsch synthesis over a 15% Co/Al 2 O 3 in a high pressure fixed bed reactor system. The sample analyzed in determining the product distribution was collected after the activity and the selectivity of the cobalt catalyst showed steady performance. Their typical result for conventional FTS product distribution is shown in F igure 4 2 The operating condition for presented case is for 50 sccm/min syngas flow rate over one gram (screened to 1 00 150 m) of the catalyst a reaction temperature of 250 o C, syngas partial pressure of 20 bar, and H 2 /CO feed ratio of 2. Non ASF distribution, represented by nonlinear plots of the logarithm of the normalized weight percentage versus carbon number, was r eported. According to Elbashir and Roberts, the range of deviation from the standard ASF distributions (linear behavior) in the conventional FTS reaction is limited to the light hydrocarbon (below C5) product region. As is typical, the methane selectivity is underestimated, while selectivity for other light hydrocarbons is overestimated by the standard ASF model. However, the distribution for higher hydrocarbon (above C5) follows well the standard ASF distribution with a chain growth provability of 0.80 ( El bashir and Roberts 2005) Keeping mind in log scale y axis, enormous underestimation of methane selectivity could be happen using standard ASF. Although the authors have analyzed distribution for hydrocarbons above C5 follows well the standard ASF, we hav e assigned carbon number dependent chain growth pro b ability based on production rates of each hydrocarbon from carbon number 1 to 7 as follow, ( 4 1 )
77 FLUENT model result for validation is also illustrated on F igure 4 2 along with experimental data As mentioned in the previous model description section, the total number of pr oducts (hydrocarbon) is confined to C15 due to limitation on computing power. But evaluation of each product production rate, eq ( 4 1 ) is based on carbon num ber 30. With individual chain growth probability, our FLUENT model can predict more accurately 4 2 2 Validation of Reactor Model Second validation work had been conducted for comparing temperature profile with simplified 2D pseudo homogeneous model deve loped by Jess and Kern (2009) They have simulated multi tubular Fischer Tropsch reactor based on both 1D and 2D pseudo homogeneous model taking into account the intrinsic kinetics of two commercial iron and cobalt catalysts, intraparticle mass transfer li mitations, and the radial heat transfer within the fixed bed and to the cooling medium. We have compared our temperature profile result with their 2 D cobalt simulation result which is illustrated in F igure 4 3 From the influence of the cooling temperatur e on the axial temperature profiles in the multi tubular packed bed reactor we can deduce that tendencies between simplified 2 D model and comprehensive model are similar but 2 D model predicts a little bit higher temperature than comprehensive model. The percent deviation for the peak temperatures from simulation Jess and Kern (2009) are 1.05%, 1.43%, 2.53% and 5.70% for 200 o C, 205 o C, 210 o C, 214 o C case respectively. The differences in maximum temperature are increasing with cooling temperature but the temp erature runaway happen at the same coolant temperature conditions, 215 o C. Syngas conversions are
78 also compared in the F igure 4 4 In the simplified 2 D model, carbon monoxide and hydrogen conversions are the same because H 2 /CO feeding ratio and consumption ratio are identical while H 2 /CO consumption ratio is variable in comprehensive model so that CO and H 2 conversions are different in our comprehensive model. Figure 4 4 shows conversion for 2 D pseudo homogeneous model is somewhere between carbon monoxide conversion and hydrogen conversion in our comprehensive model. Likewise the maximum temperature difference, the deviation for the conversion is increasing with coolant temperature. It is obvious that conversion differences between pseudo homogeneous 2D mod el and our comprehensive model is affected by coolant temperature since chemical reaction rates are strongly affected by the temperature. Difference in methodology is tabulated in Table 4 1 The most important terms to predict temperature profile might be heat of reactions, composition and properties. As described in the background section, it is totally different cases for producing one mole of n dodecane and ten moles of methane from ten moles of carbon monoxide from the aspect of amount of released heat per CO. We have developed 15 individual hydrocarbon production rates based on general chain growth probability, stoichiometry and intrinsic consumption rate for reactant. It is relatively simple to have reaction heat of those hydrocarbon production reactio ns. Also our mixture heat capacity is depending on mixture composition rather than evaluated for representative fixed condition. With individual reaction rates, mixture heat capacity and heat of reactions instead of lumped heat of reaction given in Equatio n (2 16 ), we believe that one can predict more accurate amount of released heat from the FTS. It is shown in F igure 4 5 that more detailed temperature profile between maximum safe case and temperature runaway case for the
79 comprehensive model. Based on two independent c omparison s we believe that our model and the methodology are realistic and correctly implemented.
80 Table 4 1 Methodology comparison Jess and Kern (2009) This study Dimention 2D Axisymmetric 2D Kinetics Intrinsic kinetic for syngas Intr insic kinetic for syngas Product distribution N/A Based on general chain growth probability and stoichiometry Heat of reaction Lumped heat of reaction Specified all individual heat of reactions Phase Pseudo homogeneous Heterogeneous Physical properties Representative Function of composition Intrapaticle Mass transfer considered Mass transfer considered Mometurm eq. Does not considered Porous material correction Pressure concentration N/A Ideal gas
81 Figure 4 1 Computat ional domain and outside coolant flow path.
82 Figure 4 2 Product distribution comparison with experimental results by Elbashir and Roberts; Non ASF distribution, logarithm of normalized hydrocarbon product weight fraction versus carbon number.
83 Fi gure 4 3 Temperature profile comparison with results by Jess and Kern (2009)
84 Figure 4 4 Syngas conversion comparison with results by Jess and Kern (2009)
85 Figure 4 5 D etailed temperature profile between maximum safe case and temperature run away case
86 CHAPTER 5 INDUSTRIAL SCALE PAC KED BED REACTOR MODELING 5 .1 Macro Scale Reactor Description The process of Fischer Tropsch catalytic chemical reactions is complicated because it involves intensively coupled multiphase flow and sophisticated heterogeneous catalytic reactions. Therefore, modeling this process accurately is a ver y challenging mission. A numerical simulation of this process including the whole system analysis can provide some guidance to the design, scale up and optimization of the F T reactor. A numerical simulation of the Fischer Tropsch reactor has been accompli shed using a commercial code FLUENT which can handle the multi phase flow as well as the homogeneous and heterogeneous chemical reactions based on a Finite Volume Method (FVM). Figure 5 1 shows the schematic of a packed bed Fischer Tropsch reactor. The sy nthesis gas (Syngas), a mixture of mainly carbon monoxide and hydrogen, is injected to the inlet of the packed bed reactor. A packed bed of catalyst pellets is assumed as a porous material. The fluid flow is described by a porous media model. All materials (gas species, liquid species, and solid catalyst) are assigned appropriate properties from the literature as well as from the FLUENT database. The properties of the gas species (density, viscosity, thermal conductivity, specific heat capacity) are allowed to vary with the local gaseous phase temperature. The properties of the mixture are calculated from its local composition and available FLUENT laws (ideal gas law for density and mass weighted mixing law for viscosity, thermal conductivity, and specific h eat capacity).
87 5 2 Base Line Case Simulation Results For the scale up and optimization of the syngas to liquid hydrocarbon system, modeling and simulation are the first step of the process. As a result, the basic performance characteristics of the cobalt catalytic packed bed reactor are examined under various system parameters. To facilitate a parametric study, the baseline case identical to the one used in the second verification study above is adopted here as a benchmark. Physical properties and operat ing condition s for the baseline case are tabulated in Table 5 1 Using the baseline case, the effects of varying the inlet H 2 /CO molar ratio, inlet and coolant temperature, and inlet mass flux on the packed bed reactor performance are compu ted. Detailed si mulation results for the baseline case are illustrated on F ig ure s 5 2 through 5 4. F igure 5 2 shows the reactor bed centerline s tatic pressure and temperature profiles along the axial direction. As shown in F igure 5 2, the pressure is linearly decreasing a nd temperature is rapidly increasing in the beginning and asymptotic ally decreasing after the peak point. The two dimensional temperature contour s are depicted in F igure 5 3 for the axisymmetric FT chemical reactor where the abscissa represents the axial c oordinate and the ordinate represents the radial coordinate For the temperature profiles, we selected three relatively upstream locations (z = 0.5, 1.5, and 2.5 m) because that most heat transfer interactions take place there. For the upstream region, the flow is heated up by the heat released from the exothermic catalytic chemical reaction where the reactants concentration s are the highest. Some portion of the released heat is removed by the coolant flowing outside of the packed bed tubes, while the rest of released heat facilitates the temperature increase of the reactor bulk flow. This causes the reactants to becom e more reactive that accelerates
88 the catalytic reaction pro ce ss. Basically the reactor bed temperature increases from 225 o C to 244 o C between z =0.5 m and 2.5 m in the axial direction due to the exothermic reaction. Also the temperature gradients in the radial direction represent the driving force for the heat loss to the outside coolant through the wall and the heat loss rate increases as we proc eed downstream due to the increase in the temperature difference between the reactor bed and the external coolant. At a certain point downstream, the flow temperature reaches the peak point and then starts decreasing due to increased convection heat loss t o the outside coolant and also due to lowered heat release rate from the chemical reaction because of the exhaustion of reactants. In F ig ure 5 4 the axial mass fraction profiles at the centerline for the gaseous phase are depicted in two different vertica l scales ( linear scale and log scale). As seen in Figure 5 4 the hydrogen and carbon monoxide mass fractions decrease linearly in the axial direction. The profiles of mass fractions for water and methane are also linear and so are the other hydrocarbons ( C2 to C6). It is also noted that for this baseline case, the outlet mass fraction of gaseous phase (all gaseous species combined) is 0.8961 and the rest is mass fraction for liquid phase that is 0.1039. The most abundant chemical species in the liquid phas e, n Heptane, possesses a mass fraction of 0.1567 in the liquid phase, therefore the mass fraction of n Heptane in the total flow at the outlet is only 0.01629 (=0.15670.1039). This example further justified the assumption of no vapor liquid equilibrium d ue to small amount of liquid phase components. More specifically, the carbon monoxide and water mass fraction contour plots are provided in Figure s 5 5 and 5 6 for the baseline case. Three downstream locations of z=2, 3, and 6 m are chosen. As shown in th e F igures 5 5 and 5 6 carbon monoxide
89 mass fraction decreases along the axial direction, while water m ass fraction increases with the axial direction. Unlike the temperature profiles in Figure 5 3 two dimensional molar contour profiles do not change the gradients significantly in the radial direction. The reason for this is due to the fact that heat is also removed radially by the ext ernal coolant but the mass (or chemical species) cannot be removed through the wall 5. 3 FT Chemical Reactor Thermal Chara cteristics Since the two phase mixture flow temperature distribution play s a crucial role in the performance of an exothermic Fischer Tropsch catalytic reactor from the aspects of re activity, selectivity, and stability w e have conducted a parametric study from the point of view of thermal management to assess the effects of syngas mass flow rate, syngas inlet and coolant temperature s and H 2 /CO feed molar ratio on the FT reactor internal temperature distributions As a background, it should be pointed out that the temperature profile in the reactor bed mainly depends on the balance between the heat generated by the exothermic reaction and the heat removed by both the internal convection and the external coolant. The exothermic heat release is basically a function of the syngas inlet H 2 /CO molar ratio. The convective loss is primarily a function of the two phase mass flow rate and the heat loss to the external coolant is a function of the bed temperature, the coolant temperature and the heat transfer coeffi cient between the tube outer surface and the coolant temperature. In the current analysis, the heat transfer coefficient is a fixed value of 364 W/m 2 K, therefore the heat loss to the external coolant is only varying with the coolant temperature, T C which i s equal to the syngas inlet temperature, T in As a
90 result, in the following thermal management study, only syngas inlet H 2 /CO molar ratio, syngas gas inlet mass flux and syngas inlet temperature (identical to the coolant temperature) will be varied. In Fi gure 5 7 the focus is on the effects of different syngas inlet mass fluxes while keeping all other system parameters equal to those of the baseline case. Five different syngas inlet mass fluxes ( F/F base = 0.5, 0.75, 1.0, 1.25, and 1.5 ; where F base denotes baseline case mass flux of 3.3 kg/m 2 sec ) are evaluated and their effects on the axial temperature profiles are given. Comparing with Figure 5 2 (b) of the b aseline case which is the Case F/F base =1 if the syngas mass flux is increased over that of the bas eline case (Cases F/F base = 1.25 and 1.5) the F T catalytic reaction becomes much more intense so that all the reactants are consumed in the first one third of the reactor and the temperature runaway takes place which is not a thermally viable case for the production of synthesis hydrocarbons If the syngas inlet mass flux is decreased below that of the baseline case (Cases F/F base = 0.5 and 0.75) the maximum reactor temperature is reduced and the position where the maximum temperature occurs is moved to a more upstream location and the conversion s of hydrogen and carbon monoxide to hydrocarbons are increased due to a prolonged residence time The percent c arbon monoxide and hydrogen final conversions are tabulated in Table 5 2 It can be seen that the perce nt conversions for both hydrogen and carbon dioxide increase with increasing H 2 /CO inlet molar ratio and inlet syngas temperature but decrease with increasing syngas mass flux. F ig ures 5 8 and 5 9 show how the syngas mass flux affects the temperature profi le for different hydrogen to carbon monoxide inlet molar ratios. The system conditions used in these F igures 5 8 and 5 9 are the same as
91 those in Figure 5 7 except the hydrogen to carbon monoxide inlet ratio (H 2 /CO=1.5 in Figure 5 8 and H 2 /CO=2.2 in Figure 5 9) When the syngas mass flux is increased, for all the hydrogen to carbon monoxide ratio s the peak temperature ascends, and its location is moved f urther downstream So the flow exit temperature keeps a continuously increasing trend with an increasing mass flux A h igher mass flux case also corresponds to a higher mass flow rate and a higher bulk velocity as we use a constant flow cross sectional area. This higher mass flux not only pushes the peak temperature further downstream but also makes the resi dence time shorter. Due to the shortened residence time, a higher mass flux case always results in a lower conversion of syngas despite a higher bed temperature ( Conversions are tabulate d in Table 5 2 ). Al though the syngas conversion is low er but the rat e of total amount of syngas converted into hydrocarbon is higher for the higher mass flux case. For example, with the coolant temperature at 214 o C and H 2 /C O molar ratio at 1.5 let us compare two different syngas mass fluxes of F/F base = 0.25 and 1. Base d on Table 5 2 the co nversion for carbon monoxide, X CO = 23.97% for F/F base =1 and X CO =55.03% for F/F base =0.2 5 that gives the F/F base =1 case a rate of total amount of syngas conversion which is 1.74 times higher than that of the F/F base =0.25 case As shown in Figure 5 9, when the hydrogen to carbon monoxide feed ratio increases to 2.2 while maintaining all other conditions the same, then the cases F/F base = 0.75 and 1.0 result in the runaway of the reactor bed temperature that is considered thermally unviabl e The thermally viable case, F/F base = 0.5 that yields 70.61% CO and 76.26% H 2 conversion s respectively, reaches the maximum bed temperature of 244 o C and converts 17.2% input syngas into liquid products. Fig ure 5 10 shows the case of hydrogen to carbon
92 monoxide feed molar ratio further increased to 2.5. In this case, even with the lowest mass flux case, F/F base = 0.25, the reactor becom es thermally unviable Since for the lower mass flux case the flow carries lower momentum when pass ing through the poro us bed so if the heat released by the F T reaction is accumulated rather than removed due to the lower flow rate the reactor bed temperature will be increased and this accelerates the exothermic reactions further that results in the temperature runaway In the actual experiment, this temperature runaway behavior may not be observed ; instead the deactivation of the catalyst would take place because the catalyst activity will be affected by the temperature which is not considered in most simulation s The lo ss of catalytic activity due to high temperature is known as the deactivation of catalyst. The catalytic deactivation caused by high temperature s is also called catalyst sintering (also known as thermal degradation). The t emperature runaway behavior in the simulation is still useful in providing a thermal management limiting condition for design consideration. If the heat released in a chemical reaction can be adequately removed then the run away temperature rise can be avoided so that a higher hydrogen to carbon monoxide feed ratio can be operated safely for a higher conversion However, too much heat removal makes the reactor stay at relatively low er temperature s in which the F T reaction also cannot be activated. This is why the thermal management is impo rtant on an exothermic catalytic reaction. Enhancing the heat removal can be obtained by either increas ing the heat transfer coefficient or increas ing the temperature gradient using lower c oolant temperatures. In this study, we only considered different co olant temperatures, but used a constant heat transfer coefficient Fig ures 5 11 through 13
93 show how syngas inlet and coolant temperatures affect the reactor temperature profile as well as the conversions. In Figure 5 11 react or temperature profiles for va rious H 2 /CO ratios with F/F base = 1.0 and syngas inlet and coolant temperature of 214 o C are depicted. Among these, the baseline case (H 2 /CO = 2) has the best performance among the thermally viable cases and the higher hydrogen to carbon monoxide feed rati os become thermally un viable It is not shown here but the case of H 2 /CO = 2.1 also yields the temperature runaway behavior. The higher the H 2 /CO ratio gives the faster temperature rise. The t emperature dependency on the H 2 /CO ratio can be explained by its intrinsic kinetics behavior with respect to hydrogen and carbon monoxide concentration s Intrinsic kinetics of FT synt hesis Eq. ( 3 13 ) is directly proporti onal to the hydrogen molar fraction but the carbon monoxide dependency is more complex than the hydrogen. Carbon monoxide acts as an inhibitor when its concentration is relatively high. When the carbon monoxide adsorption term in the denominator is greater than unity, 1<< KC CO then the entire denominator term could be approximated as ( KC CO ) 2 In this case, FT synthesis intrinsic kinetics is inverse ly proportional to the carbon monoxide concentration which is a typical characteristic of the Langmuir Hinshel wood kinetics. As we increas e the hydrogen to carbon monoxide molar ratio at the inlet the syngas consumption rate would be accelerated as a result of the increased hydrogen concentration so that more heat will be released, the reactor temperature will be higher and finally the exit conversion will be raised. By reducing the coolant temperature to 210 o C, the catalytic packed bed become s thermally viable up to H 2 /CO = 2.4 which is shown in Figure 5 12 However as mentioned previous ly the bed temperature r emains lower resulting in low syngas conversions. We found that the performance for hydrogen
94 to carbon monoxide feed ratio of 2.0 with a coolant temperature of 214 o C is similar to that of hydrogen to carbon monoxide feed ratio of 2.4 with 210 o C coolant tem perature. For the coolant temperature of 210 o C and H 2 /CO of 2.4, the CO conversion is 42.15% the H 2 conversion is 41.74% and the mass converted into liquid phase is 10.13%. If the coolant temperature drops further then even higher H 2 /CO ratio can be therm ally viable The results for coolant temperature of 205 o C are illustrated in Figure 5 13 where the case of H 2 /CO ratio as high as 3 is still thermally viable In the case of H 2 /CO = 3.3, its temperature suddenly rise s at almost half of the reactor length. Next, results are obtained using the same coolant temperatures as those in Figure s 5 11 through 1 3 but the syngas inlet mass flux value is reduced by half. Temperature profiles depicted in Figure 5 14 are obtained under the same conditions as those in Figu re 5 11 except the syngas mass flux. The temperature profile s illustrated in Figure 5 14 are very similar to those in Figure 5 11 except that the maximum H 2 /CO ratio for a thermally viable application is 2.2 instead of 2 in Figure 5 11 Also, the downstrea m location where the peak temperature occurs is closer to the inlet for lower mass fl ux case. As discussed previously, syngas conversion is higher for lower mass fl ux as a result of relatively long er residence time. For example, CO conversions are 42.18% f or H 2 /CO = 2.0 in Figure 5 11 and 70.61% for H 2 /CO = 2.2 in Figure 5 14 as provide d in Table 5 2 The half synga s mass flux version of Figure 5 12 is depicted on Figure 5 15 Similar findings can be seen as those in the coolant temperature of 214 o C case. T emperature profiles for the 205 o C coolant temperature case with the half mass flux are plotted in Figure 5 16 No cases are found to be thermally un viable for H 2 /CO ratios in the range from 1.5 to 3.0.
95 5 4 Thermal Management Analysis As discussed above, it is apparent that the reactor bed temperature profile and its thermal management hold the key for the optimal FT reactor design. We have prepared a thermal viability map given in Figure 5 17 t o summarize the thermal management strategy. The thermal viab ility map is developed using the three integral parameters: syngas inlet mass flux, F, syngas inlet and coolant temperature, and hydrogen to carbon monoxide feed ratio, For each data point with the sp ecific F and it represents the maximum value that the FT reactor is thermally viable (no reactor bed temperature run away). For example, the point with F/F base = 1 and the max imum without a reactor bed temperature runaway is 2. In other words, any point in the area under a specific curve represents a thermally viable case for the coolant temperature corresponding to that curve. Therefore each curve ca n be considered as the critical threshold boundary for thermal viability. In general, the critical value increases with decreasing coolant temperature and decreasing syngas mass flux, F. It is worth mentioning that for the case of = 205 o C and the lowest syngas mass flux, F/F base = 0.25, the reactor could function without a thermal runaway for hydrogen to carbon monoxide feed ratio, to reach as high as 3.9 For this particular cas e with a relatively high critical value, the limiting chemical species, carbon monoxide, is totally consumed within one third of the reactor length from the entrance and the bed temperature has reached its maximum point at this lo cation. After
96 the depletion of the limiting chemical species, the bed temperature will stop rising and stabilize due to no more heat release. However, this point may not be the ideal operating condition because the rest of the reactor is unutilized. This map just provides the thermal viability, however, for the ideal operating condition, the thermal viability should be considered together with reactant conversion and product selectivity. 5 5 Results Analysis Summary An axisymmetric two dimensional multi ph ase heterogeneous numerical model embedded in the FLUENT code has been developed to simulate a fixed packed bed tub u lar Fischer Tropsch reactor. The detailed chemical kinetics for producing linear paraffin in both gaseous and liquid phase s has been d erived based on carbide mechanism chain grow th probability and stoichiometry for a non ASF distribution. The fluid transport is modeled as a two phase flow going through a packed bed of porous material consisting of solid catalyst particles. An Eulerian Eulerian mixture model has been used for the two phase flow simulation together with the porous material assumed as momentum sinks in the fixed bed reactor. Mass transfer th r ough the catalyst pellet pore s is also considered by means of the general Thiele modulus. Two comparisons have been made to validate ou r model. First, the p roducts distribution predicted for a non ASF distribution gives a satisfactory agreement between the current model predictions and the experiment results. The second comparison with a simpli fied model on the packed bed temperature variations and thermal management not only validated the current model but also proved that a comprehensive model is more useful and important when assessing the thermal viability of the reactor
97 The thermal charac teristics of a FT chemical reactor ha s been investigated focusing on the effects of syngas mass flux, syngas inlet and coolant temperature s and H 2 /CO feed molar ratio on the reactor temperature profile. The simulation results indicate the following findin gs : ( 1 ) An increased syngas mass flow rate results in a shorter residence time that causes a lower conversion, a higher peak temperature, and the location of peak temperature to move more downstream ; ( 2 ) A higher hydrogen to carbon monoxide feed molar rat io make s the high syngas flow rate thermally unstable ; and ( 3 ) T emperature effect is obvious that a lower syngas inlet/coolant temperature will quench the reactions so that higher mass flow rate or higher H 2 /CO ratio can be thermally viable Among the mass flux range from 0.825 to 4.95 kg/m 2 sec, inlet/coolant temperature range from 205 o C to 214 o C, and H 2 /CO feed ratio range from 1.5 to 3.0, we have found that the case of F = 1.65 kg/m 2 sec, = 2.2, and is th e o ptimum operating condition which gives the high est syngas conversion but no reactor bed temperature runaway.
98 Table 5 1 Physical properties and operating condition s for the baseline case. Reactor type Tubes and Shell, focused on a single tube Catalys t shape S pherical Catalyst Cobalt based Internal diameter of single tube 4.6 [cm] Length of tube 12 [m] Catalyst mean diameter 3 [mm] Catalyst density 1063 [kg/m 3 ] Packed bed porosity 0.66 Outlet pressure 20 [bar] Inlet and coolant temperature 214 [ o C] Syngas inlet m ass flux 3.3 [kg/m 2 sec] I nlet H 2 /CO molar ratio 2 Overall heat transfer coefficient 364 [W/m 2 K]
99 Table 5 2. C alculated conversion values for s elected operating conditions. Operating conditions Results T in/coolant [ o C] F / F base H 2 /CO X CO [%] X H2 [%] 205 0.5 1.5 22.6 5 35.8 1 205 0.5 2.0 33.2 5 39.4 9 205 0.5 2.5 47.16 44.8 3 205 0.5 3.0 67.18 53.2 3 205 1.0 2.0 18.7 4 22.2 6 205 1.0 2.5 26.7 6 25.43 205 1.0 3 38.90 30.8 2 210 0.5 1.5 30.81 48.76 210 0.5 2.0 46.54 55.28 210 0.5 2.5 69.70 66.25 210 1.0 1.5 18.2 6 28.9 2 210 1.0 1.7 21.87 30.56 210 1.0 2.0 28.3 9 33.72 210 1.0 2.4 42.15 41.7 4 214 0.25 1.5 55.03 85.7 9 214 0.5 1.5 37.8 8 59.95 214 0.5 2.0 58.5 8 69.5 8 214 0.5 2.2 70.61 76.26 214 0.75 1.5 29.09 46.06 214 0.75 2.0 47. 16 56.0 3 214 1.0 1.5 23.97 37.96 214 1.0 1.7 29.3 5 41.01 214 1.0 2.0 42.18 50.11
100 Figure 5 1 Schematics for packed bed reactor ; (a) axisymmetric cylindrical packed bed FT reactor and (b) external coolant flow configur ation.
101 Figure 5 2 Pressure and temperature profile for baseline case; pure syngas mass flux 3.3 kg/m 2 s, H 2 /CO = 2, inlet and coolant temperature 214 o C (a) pressure and (b) temperature.
102 Figure 5 3 Temperature contour s at three downstream locat ions for the baseline case; pure syngas with mass flux of 3.3 kg/m 2 s,H 2 /CO = 2, and syngas inlet and coolant temperature at 214 o C.
103 Figure 5 4 Mass fraction profiles at the centerline in the gaseous phase for the baseline case, (a) CO, H 2 H 2 O and C H 4 and (b) all hydrocarbons in log scale; pure syngas mass flux of 3.3 kg/m 2 s, H 2 /CO = 2, inlet and coolant temperature 214 o C.
104 Figure 5 5 Contour plots for CO molar fractions at three downstream locations, z=2, z=3, z=6
105 Figure 5 6 Contour plots for H 2 O molar fractions at three downstream locations, z=2, z=3, z=6
106 Figure 5 7 Reactor bed t emperature profile s for inlet and coolant temperature of 214 o C, H 2 /CO = 2.0 and different mass flux es, F/F base =0.5, 0.75, 1, 1.25, and 1.5.
107 Fig ure 5 8 Reactor bed t emperature profile s for inlet and coolant temperature of 214 o C, H 2 /CO = 1.5 and different mass flux es, F/F base = 0.25, 0.5, 0.75, and 1.
108 Figure 5 9 Reactor bed t emperature profile s for inlet and coolant temperature of 214 o C H 2 /CO = 2.2 and different mass flux es, F/F base = 0.5, 0.75, and 1
109 Figure 5 10 Reactor bed t emperature profile s for inlet and coolant temperature of 214 o C, H 2 /CO = 2.5 and different mass flux es, F/F base = 0.25, 0.5, 0.75, and 1
110 Figure 5 11 Reactor bed t emperature profile s for inlet and coolant temperature of 214 o C, syngas mass flux F = F base and different H 2 /CO ratios of 1.5, 1.7, 2.0, 2.2, 2.5, and 3.0.
111 Figure 5 1 2 Reactor bed t emperature profile s for inlet and coolant temperatu re of 210 o C, syngas mass flux F = F base and different H 2 /CO ratios of 1.5, 1.7, 2.0, 2.4, 2.5, and 3.0.
112 Figure 5 1 3 Reactor bed t emperature profile s for inlet and coolant temperature of 205 o C, syngas mass flux F = F base and different H 2 /CO ratios o f 2.0, 2.5, 3.0, and 3.5.
113 Figure 5 1 4 Reactor bed t emperature profile s for inlet and coolant temperature of 214 o C, syngas mass flux F = 0.5F base and different H 2 /CO ratios of 1.5, 2.0, 2.2, 2.3, 2.5, and 3.0.
114 Figure 5 1 5 Reactor bed t emperatur e profile s for inlet and coolant temperature of 210 o C, syngas mass flux F = 0.5F base and different H 2 /CO ratios of 1.5, 2.0, 2.5, and 3.0.
115 Figure 5 1 6 Reactor bed t emperature profile s for inlet and coolant temperature of 205 o C, syngas mass flux F = 0.5F base and different H 2 /CO ratios of 1.5, 2.0, 2.5, and 3.0
116 Figure 5 1 7 Thermal viability map for a FT reactor
117 CHAP TER 6 EXPERIMENTAL VERIFIC ATION OF FISCHER TROPSCH CHEMICAL KIN ETICS MODEL 6 .1 General Method of Kineti cs Data Analysis Experimental data from ideal reactors: In the process of developing kinetic s expression of any chemical reaction either it is a catalyt ic or n on catalytic reaction; a rate expression must be validated against experimental data. The experimental work for the kinetic s data should be performed in a reactor that behaves as an ideal reactor. Ideal reactors could be categorized according to the reactant feed type; batch reactors or continuous reactors. Continuous reactors could also be classified according to the mixing type; complete mixing and non mixing. The c ontinuously stirred tank reactor (CSTR) is a complete mixing continuous feed ideal r eactor, while the plug flow reactor (PFR) is a non mixing continuous feed ideal reactor. Under the steady state condition in the ideal CSTR, there are no spatial gradient s of any properties, so pressure, temperature and concentration are identical everywhe re which makes the reaction rate uniform at every location inside the reactor. This type of reactor could be used for either homogeneous or heterogeneous catalytic reaction. The main advantage of the CSTR for kinetic s measurement is that the value of the r eaction rate could be directly evaluated for a given operating condition. This direct ly measured values, however, does not mean easiness for kinetic s measurement. It requires a data set analysis based on a hypothetical form of the reaction rate that requir e s intuition and experiences. On the other hand, the non mixing ideal reactor, PFR, requires an analytic integral of the hypothetical reaction rate form throughout the reactor to obtain the reaction rate under given operating conditions. The f luid flow pat tern in the ideal PFR reactor is considered
118 as a potential flow where viscosity does not exist so the no velocity gradient with respect to perpendicular to flow direction is formed which makes the complete non mixing assumption valid. A p a cked bed reactor could be categorized as an ideal PFR. Although analyzing kinetics in a PFR requires the integral of the reaction rate form, a certain type of the PFR do es not require that process. It is called the differential PFR operated at a very low conversion, so th at the average value is a good approximation instead of the integration method A d ifferential PFR has the advantage in the kineti cs study of heterogeneous catalytic reactions. This condition might be achieved under either a low loading of the catalyst or a low space time of the reactant for the heterogeneous catalytic reaction. 6 2 Experimental Data from a Cobalt C atalyst B ased P acked B ed R eactor Experimental work has been performed by a Chemical Engineering d epartment graduate student, Mr. Robert Colmy er under the supervision of Dr. Helena Hagelin Weaver. The e xperimental operating conditions and the measure d data are provided by Colmyer (2011) and t abulated in Table 6 1. For more information concerning the experimental work, please refer to his doctora l dissertation entitled Fischer Tropsch Synthesis: Using Nanoparticle Oxides As Supports for Fischer Tropsch Catalysts From the tabulated data, selectivi ty data has been plotted in F igure s 6 1 and 6 2.
119 6 3 Chemical Kinetics Coefficients 6 3 1 Constant Pressure Pa ck ed Bed Reactor Modeling As stated in the previous section, performing an experimental data analysis for an integral type of plug flow or packed bed reactors is usually more difficult than for those of CSTRs because all variables are chang ing along the axial direction even though the radial direction variation is neglected. From the experimental results obtained from chemical engineering department (Colmyer, 2011) show that differential plug flow reactor assumption is not valid for their experi mental setup since relatively high conversion of carbon monoxide has been observed through short length of the packed bed height. Therefore, d ifferential plug flow ideal reactor model is not applicable for experimental system used in Colmyer (2011). As a r esult, a one dimensional constant pressure packed bed catalytic chemical reactor modeling has been formulated below for the purpose of verifying the Fischer Tropsch chemical kinetics model developed in Chapter 3 by the experimental data obtained by Colmyer (2011) The f ollowing assumptions and idealization have been made for simplicity. One dimensional and Steady state Cylindrical Reactor with a packed bed of uniform and spherical catalyst pellets The gases are considered as i deal gas es Isotropic packed bed with a plug flow Maas/species transport by concentration gradients is neglected. Isothermal system Isobaric and no pressure gradient due to a very short length of the packed bed All species are in gaseous phase ( no liquid nor solid products) The carbon n umber up to 30 O nly paraffin products are considered ( n either olefins nor alcohols) Nitrogen is completely inert
120 With the above assumptions, mole balance of each chemical species could be written as follow s ( 6 1 ) where F i denotes the molar flow rate of the chemical species i W is the weight of the catalyst and r i is the species i reaction rate per unit mass of catalyst which has the unit s of [mol/kg cat sec]. T his equation is also called the design equation for a packed bed reactor Combining the design equation with the reaction rate expression and with the stoichiometry i nformation will lead to a successful analysis. For the chemical kinetic s part, the open literature work from Yates and Satterfield (1991) has been adopted for the kinetic s expression shown in the previous chapter as E q. (2 14). From the previous chapter, a rigorous relationship between each product production rate and lumped carbon monoxide kinetic s has been developed based on stoichiometry and parallel reactions for carbon monoxide. The p roduction rate for each individual hydrocarbon is given below ( 6 2 ) where r n is the production rate for the hydrocarbon with a carbon numbe r n, n is carbon number dependent chain growth probability. Combining the reactor design equations with the rate expression based on stoichiometry yields the system of differential equations for the hydrocarbon products below,
121 ( 6 3 ) where P CO and P H 2 are the partial pressure s of the carbon monoxide and hydrogen respectively defined as ( 6 4 ) where y CO and y H2 are the mole fractions of the CO a nd H 2 respectively. Although this model assumes an isobaric condition th r oughout the packed bed so the t otal pressure remains constant. However, the total number of mole s is changing throughout the entire packed bed based on which products are formed and h ow much syngas is consumed so that the syngas partial pressure is varying throughout the bed. Eq ( 6 3 ) denotes the formation rate of the hydrocarbon with car bon number n. In this analysis a total of 30 hydrocarbon species (the highest carbon number is 30) normal paraffins, have been involved for better accuracy of the model calculation s The molar balance for c arbon monoxide is shown below, ( 6 5 ) For Eq. (6 5), two different forms of kinetic e xpression could be applied for the carbon monoxide consumption rate, r CO as shown next. As described in the previous chapter, the total carbon monoxide consumption rate should be balanced with the sum of the carbon monoxide consumption rate for each individual hydrocarbon and this relation ship is given in Eq. (3 25). Recall this equation here below,
122 ( 6 6 ) whe re the total carbon monoxide consumption rate is given by the empirical based form as ( 6 7 ) If considering appropriate stoichiometry, the sum of all individual carbon monoxide consumption rates right hand side in Eq. ( 6 6 ) is as follows, ( 6 8 ) Analytically these two equations, Eqs. ( 6 7 ) and ( 6 8 ) should be identical, however there could be small devia tion s in the implementation of numerical methods because numerical methods have their own inevitable errors; truncation (methodological) error and round off (machine) error. In the implementation of the calculations for the total carbon monoxide consumptio n rate, Eq. ( 6 8 ) has been applied for the carbon monoxide mole balance equation rather than Eq. ( 6 7 ) for better accuracy. Therefore, the carbon monoxide balance equation is given below ( 6 9 ) Likewise, for hydrogen, water vapor, and nitrogen their chemical balances are derived based on each individual hydrocarbon formation chemical reaction as follow s,
123 ( 6 10 ) ( 6 11 ) ( 6 12 ) So, a total of 34 ODEs for chemical species, n paraffins with 1~30 carbon number s CO, H 2 H 2 O, and N 2 have been developed and the system of differential equations is numerically solved by the 4th order Runge Kutta metho d with appropriate initial conditions as shown below, ( 6 13 ) 6.3.2 G eneral Carbon Number Dependent Chain Growth Probability As shown in Fig ure s 6 1 and 6 2, experimental product selectivities up to carbon number 8 look so complicated and disordered that hardly any parameters could represent them. From the intuition based o n a basic understanding of the nature of Fischer Tropsch synthesis, it may be possible by introducing individual chain growth probability as shown later in this chapter. In this analysis, the highest carbon number is 7. One can relate the chain growth prob ability with the hydrocarbon selectivity as follow s
124 ( 6 14 ) where S n is the selectivity for the hydrocarbon with a carbon number n, n is the specific carbon number dependent chain growth probability for the hydrocarbon with a carbon number n. The term, represents the amo unt of moles of hydrocarbons produced From the above relationship between hydrocarbon selectivity and specific chain growth probability, Eq (6 14) can be rewritten as follow s ( 6 15 ) From the chain growth prob ability for carbon number n, then the n+1 chain growth probability can be evaluated in a straightforward method Starting from carbon number 1, all the chain growth probabilities can be obtained by successive substitution as follows, ( 6 16 ) ( 6 17 ) ( 6 18 )
125 From E qs. ( 6 16 ) to ( 6 18 ) it is shown that the specific carbon number dependent chain growth probabilities can be expressed in terms of the corresponding hydrocarbon selectivity, all the lower carbon number chain growth probabilities and one unknown quantity carbon spec ific hydrocarbon produced So, an appropriate evaluation of this unknown quantity would ensure the simulation results to represent the actual experimental result s well Unfortunately, only a limited range of selectivity data is available from the experiments. However, selectivities for C3+ hydrocarbons show a good agreement with the ASF distribution as shown in Fig ure s 6 3 and 6 4. This could be interpreted as that the chain growth probabilit ies for the heav ier hydrocarbon s (C8+ ) are not depending on the carbon number. As a result, those heavier hydrocarbons c ould be considered to hold constant value chain growth probabilit ies So, it is assumed here that the chain growth probabilities for C8+ hydrocarbons are all equal to a cons tant which is the averaged value of C3~7. By this way, it is possible to assess the appropriate value for the carbon specific hydrocarbon produced by applying the least square sum method. For the implementation of the least square sum method to find out th e appropriate value for the carbon specific hydrocarbon produced, following relationship has been considered, ( 6 19 ) As shown in Eq. ( 6 19 ) SUM min is the carbon specific hydrocarbon produced if FT synthesis only produce s up to C7 and for the current case, it is calculated from actual experimental data. The value of the second term on the right hand side of Eq. (6 19) is estimated by minimizing the square sum of the deviations between the experimental
126 date and the model predictio ns for the C1 C7 sectivities. Figure 6 5 shows one sample calculation for Run number four in Table 6 1. The best fit results are tabulated in Table 6 2 for cases of runs from 17 to 22 In the determination for the best fit, accuracy tolerance of the fitti ng value has been set as 510 6 The products distribution comparisons with individual chain growth probabilities estimated with the best fitting result s have been illustrated on Fig ure s 6 6 and 6 7 for Runs 20 and 14, respectively, listed in Table 6 1 In both F igure s 6 6 and 6 7 individual chain growth probabilities values have been showed together with selectivity comparison. As shown in the compar ison F igures 6 6 and 6 7 selectivity fitting has been accomplished with high accuracy and precision. 6 .3.3 Coefficients of Chemical Reaction Kinetics In the previous section, non ASF type product distribution fitting has been performed by finding the carbon number dependent chain growth probability using the least square sum method for carbon specific hyd rocarbon produced In that calculation process, reaction kinetics does not matter. They were assigned as moderate value s because it does not matter how fast the syngas is consum ed but rather w hich hydrocarbon will be formed is more important. In this section it is, however, that how to find the kinetic coefficients is described. As stated previously, syngas consumption rate is assumed to be expressed by the LH type as given in E q. ( 6 7 ) where two unknown parameters, k reaction rate constant and K CO CO adsorption constant, will be fitted.
127 Although these are called constants but they are function s of temperature. The r eaction rate constant is governed by the Arrhenius equation as follow s, ( 6 20 ) wher e k o is the pre exponent factor, E A is the activation energy, R is the gas constant, and T is the absolute temperature. Adsorption constant is equilibrium constant; therefore it obeys the ( 6 21 ) which could be rewritten as a similar form of Arrhenius equation as follow s, ( 6 22 ) where A is the pre exponent factor, H ad is the heat of adsorption for carbon monoxide molecul e s on a catalyst surface. According to general thermodynamics, adsorption heat for the chemisorption is always exothermic, H ad < 0. With this kinetic expression s the Least Square fitting work might be difficult because this system has four unknowns to be determined, k o E A A, and H ad If kinetic constants are specified for a given temperature with a good accuracy and precision then the number of unknowns would be reduce d by half and the computational task for the Least Square fitting will be reduced dra matically. So coefficients fitting has been accomplished for a fixed temperature case, T=220 o C, since this temperature is in the middle of its range. Non linear regression calculation with a high accuracy requirement might take lots of computational resou rces due to solving a system of ODEs with very fine step size s for
128 both k and K CO So using the stepwise domain narrowing technique for the possible range has been performed for better accuracy with relatively low computer resources instead of solving the whole range with fine increment s for both k and K CO At f irst, w ide possible ranges for both k and K CO were chosen ; they are from 10 5 to 10 3 for both k and K CO C ontour plotting result s are shown in Figure 6 8 (a) where the color represents the value of s um of square deviation s between experiment data and model and the location for the minimum sum value has been marked In the second run, the possible ranges are narrowed to near the previous minimum value region and the newly calculated minimum sum locatio n is depicted in Figure 6 8 (b). In the final run, the best fitting results could be achieved that gives k = 1.05 10 4 and K CO = 0.0455 with tolerances of 5 10 7 and 2.5 10 4 for k and K CO at the given temperate, T = 220 o C, respectively. It is also illustrated in the contour graph given in Figure 6 8 (c) for the final run. After obtaining the kinetic coefficients at a single reactor temperature with high accuracy, the activation energy and heat of adsorption have also been fitted with exactly the sam e method for a given temperature range of 180 o C ~ 245 o C. In the first trial, possible ranges are assigned from 10 to 100 [kJ/mol] for the activation energy and from 50 to 150 [kJ/mol] for the heat of CO adsorption on the catalyst surface, respectively. A two dimensional non linear regression has been performed and the calculation results are shown in Figure 6 9 (a). T he values which result in the smallest deviations are obtained and they are E A = 42.4 and H ad = 118 [kJ/mol]. Also the locations have be en marked on the contour plot. For the better accuracy, second trial has been performed with the range narrowed and step size of 0.1 kJ/mol for both E A and H ad and the best fit values are obtained as 43.2 and 116 kJ/mol for E A and H ad respectively. The
129 contour plot and the location for the minimum deviations are also given in Figure 6 9 (b). With the best fit results of E A = 43.2 and H ad = 116 [kJ/mol], carbon monoxide conversion behavior over the whole operating temperature range has been plotted in F ig ure 6 10 together with the experimental measurements for comparison. From this F igure 6 10 it can be concluded that the implementation of the reactor model, chemical kinetics and product distribution is successfully achieved. And the followings are the kinetics coefficients for this catalyst used in the experiment, ( 6 23 ) ( 6 24 ) where the units are mol/(kg cat sec bar 2 ) and (1/bar) for k and K CO respectively. With the above coefficients and all the chain growth probability values obtained in the previous section, the carbon monoxide and hydrogen conversion profiles as a function of the packed bed space time, o defined as the catalyst loading divided by its inlet volume flow rate with the standard units of cubic centimeters per second, have been illustrated in Fig ure s 6 11 and 6 12. The total number of mole reduction profile is depicted in Figure 6 13. 6 4 Generalization of Selectivity 6.4.1 Conceptual I dea for G eneralization of S electivity In the previous sections, both selectivity and kinetic s coefficients have been fitted using the kinetics model with very high accuracy and precision The k inetic s coefficients
130 are, however, fitted into pres cribed function al forms (Eqns. 6 23 and 6 24) while the selectivities are fitted only by some individual value s which demonstrates a good agreement with the measurement results. However, no general trend or functional form has been deduced yet for the sel ectivity. Even though the syngas consumption rate can be predicted with a good agreement with the experimental data for a given range of reactor operational conditions, however, the product selectivity can not be predict ed unless a functional form that pro vides the general characteristics has been deduced. So, in this section, finding a general trend on the chain growth probability has been attempted. All of the 147 chain growth probabilities calculated from the 21 experimental runs (a set of 7 selectivitie s for every experimental run) which have been used for finding the kinetic coefficients are plotted in Figure 6 14. The t emperature effect on the chain growth probability is shown in Figure 6 14 (a) and the hydrogen to carbon monoxide molar ratio effect is illustrated in Figure 6 14 (b). From F igure 6 14 it is difficult to deduce any general trends according to the following functional dependence form for the chain growth probability ( 6 25 ) The chain growth probability theoretically depend s on the n (product carbon number ) ( H 2 /CO molar ratio) and T (reaction temperature ). The separation of variables method is applied assuming those independent variables (n, T, ) effects are independent each other. So it is assumed that the general chain growth probability consists of thre e independent functions which are only depending on one variable each; carbon number dependency function, temperature dependency function,
131 and hydrogen to carbon monoxid e ratio dependency function. Since a general tendency of how the chain growth probability varies with the reaction temperature and hydrogen to carbon monoxide molar ratio is known that is decreas es with increasing T and FT product chain length decreases with increasing both reaction temperature and hydrogen to carbon monoxide molar ratio. Therefore, the chain growth probability is assumed to possess the follow ing functional form, ( 6 26 ) w here C 1 and C 2 are constants to be determined is a function only depending on the c arbon number n and representing the carbon number effect on the chain growth probability, and are functions to represent the temperature effect and hydrogen to carbon monoxide effect on the chain growth probability and are only depending on temperature and hydrogen to carbon monoxide ratio respectively. For simplicity, arbitrary constants, C 1 and C 2 are fixed as unity here. ( 6 27 ) The c arbon number effect has been assign ed as a coefficient instead of a function. So each chain growth probability corresponding to a certain carbon number has its own coefficients. By doing t his way, carbon number dependency could be eliminated but a series of chain growth probabilit ies each is still a function of T and are required as shown below,
132 ( 6 28 ) In Eq. (6 28), is the carbon number specific chain growth probability. R ewriting Eq. ( 6 28 ) yields a convenient form below for further development. ( 6 29 ) 6.4.2 Hydrogen to Carbon Monoxide Molar Ratio Effect on Selectivity Hydrogen to carbon monoxide molar ratio effect on selectivity, i.e. chain growth probability, could be simpli fied from E q. ( 6 29 ) as follow s, ( 6 30 ) where the subscript T means evaluated under an isothermal condition, is the coefficient relating to the temperature effect, The e xperimental measurements on th e selectivity for different hydrogen to carbon monoxide ratios under a uniform temperature, Figure 6 2, have been converted to corresponding chain growth probabilities as shown in Figure 6 14 (b). Next, the dependence on the hydrogen to carbon monoxide rat io is explored first. After several try outs, the following form has been selected for the H / C function ( 6 31 ) Substituting the above in Eqn. (6 30), the following is obtained, ( 6 32 )
133 where It is noted that E q. ( 6 32 ) represents a linear relationship if is a constant. In Figure 6 15 E q. ( 6 32 ) has been used to fit the experimental data for carbon numbers from C1 to C7 and also for C8+. The purp ose is to find out whether a linear relationship proposed in Eq. (6 32) is a good fit. With only two data points (for n = 3and 6) excluded due to obvious inconsistency, the linear trend is indeed a good assumption according to Figure 6 15 For references, the are tabulated in Table 6 3. It is noted the general profile for shows a similar trend to that of the selectivity data shown in Figure 6 6. 6.4.3 Temperature Effects on Selectivity In the same man ner, the temperature effect could be evaluated using the follow ing proposed relationship, ( 6 33 ) where the subscript denotes the condition of constant hydrogen to carbon monoxide molar ratio. Strictly speaking, it is almost impossible to maintain the condition of constant hydrogen to carbon monoxide molar ratio over the ent ire reactor length since the hydrogen and carbon monoxide consumption rates are affected by the selectivity that is changing with axial location In other words, hydrogen and carbon monoxide consumption rates along the reactor depend on which kind of produ ct will form In the experimental work, hydrogen to carbon monoxide molar ratio has been fixed at the feed as two Based on the general kinetics theory, t he function al form describing the temperature effect has been proposed as the Boltzmann distribution as follow s,
134 ( 6 34 ) where E is threshold energy and R is the universal g as constant. With this exponential form, lineariz ed curve fitting using the model with the experimental data has been performed and the results are depicted in Figure 6 1 6 A total of 16 experimental sets are available for this analysis that indicates more data points than those available in the effect analysis discussed above. Substituting Eq. (6 34) into Eq. (6 33), and taking a natural logarithm yields Eq. (6 35) below, ( 6 35 ) Eq. (6 35) is then used to fit the experimental data and the results are given in Figure 6 16. As seen in Figure 6 16, in order to fit the experimental data with consistency, 17 data points out of the total 112 are excluded. These excluded data points identified by the triangular shape are mainly from the low temperature region with a low syngas conversion. Since more data p oints are excluded in the evaluation of the temperature effect, it seems that the actual FT process is more sensitive to the reactor temperature. In addition to this, two excluded data points for the hydrogen to carbon monoxide effect analysis in the previ ous section were also from the low hydrogen to carbon monoxide region that is again associated with a low syngas conversion. It is therefore also noted that data measurement in low conversion cases might include more uncertainties due to small intrinsic qu antitative values. Unlike with the previous hydrogen to carbon monoxide effect, t he slope of the linear curve fit (E n /R) in Figure 6 16 do es have a physical meaning here so they are calculated and tabulated in Table 6
135 4. From each slope in Figure 6 16, the threshold energy has been evaluated and plotted against the carbon number in Figure 6 17 together with the averaged value. The averaged value for the threshold energy is = 27.0142 [kJ/mol] with a standard deviation of 4.7264 [kJ/ mol] It is concluded that the averaged value is a good representative for the threshold energy over the entire carbon range, to that the averaged value has been selected for Eq. ( 6 34 ) for the overall FT synthesis and the general selectivity evaluation in the next section 6.4.4 General Selectivity From previous sections, the hydrogen to carbon monoxide molar ratio effect, E q. ( 6 31 ) and the temperature effect, E q. ( 6 34 ) with the averaged value for the threshold en ergy are substituted into the general chain growth probability E q. ( 6 28 ) to obtain the following equation, ( 6 36 ) This expression is the carbon number dependent chain growth probabilit y including the reactor temperature and hy drogen to carbon monoxide ratio effects for a particular catalyst. First it is noted that with a given n from the experimental selectivity a C n can be solved for using Eq. (6 36). In the actual application of Eq. (6 36), we need to find a single represen tative C n for each carbon number. This single coefficient, is called an effective C n that is obtained by averaging all twenty one solved from the experimental data set for a particular carbon number. In Table 6 5, is
136 listed for all the carbon numbers. Table 6 5 also provides the standard deviation values for all the values. In addition to this, carbon number dependent chain growth probabilities are also compared between experimental ly derived values, using Eq. (6 15) and calculated values, using Eq. ( 6 36 ) with and actual reactor temperature and hydrogen to carbon monoxide input molar ratio. It is noted that for each carbon number, we have twenty one values for each and Re lati ve percent difference on chain growth probability for a particular carbon number under a specific system condition is defined below, ( 6 3 7 ) An averaged value for all twenty one is also given in Table 6 5 with the corresponding standard deviations. It is worth noting fro m Table 6 5 that the standard deviations are quite large for some carbon numbers that is basically caused by the relatively substantial data scattering. 6 5 Results Discussion and Contribution of Current Work In this chapter, catalytic chemical kinetics and selectivity analysis for a novel cobalt catalyst developed by our collaborator in the Chemical E ngineering department has been conducted. First, a semi empirical expression is considered as a matching expression for this novel catalyst, from the least square fitting results. With the kinetics coefficients provided in this work, accurate reactor performance predictions might be expected for the scale up or commercialization utilizing this novel catalyst. Second, this
137 kind of analysis is very limited for accommodating both chemical kinetics and selectivity at the same time with high accuracy. In the thermal management, this type of analysis would yield more accurate and precise predictions in order to understand the heat transfer effect. Third, it provide s a general trend of chain growth probability with respect to reactor temperature as well as hydrogen to carbon monoxide molar ratio effects. A m athematical function form for the chain growth probability has been proposed and verified Although this functio nal form is only valid for a particular catalyst used, this work might help understand the complex nature of the catalytic surface reactions.
138 Table 6 1. Experimental operating condition s and measurement data of carbon monoxide conversion and product sel ectivities up to C8. Run T [ o C] P [bar] H 2 /CO [ ] N 2 % [vol%] V [sccm] X CO [% ] Selectivity [%] C1 C2 C3 C4 C5 C6 C7 C8 C8+ CO 1 180 20 2 10 62.5 3.339 8.534 0 2.7075 2.4512 0 0.1917 0 0 85.7688 0 2 190 20 2 10 62.5 5.211 12.5266 0 6.6992 6.3967 3 .409 1.7558 0.4229 0 68.7898 0 3 200 20 2 10 62.5 8.317 12.0568 1.8708 6.357 5.8732 4.7829 3.561 2.1813 0.1366 63.317 0 4 205 20 2 10 62.5 5.007859 16.2909 2.9705 6.3237 5.2151 2.0769 1.3377 0.984 1.5996 64.8013 0 5 210 20 2 10 62.5 25.023 8.4987 1.37 4 .2942 3.9753 3.3794 2.7429 1.802 0.5688 73.7365 0.2009 6 215 20 2 10 62.5 22.7326 12.4064 1.9184 4.0085 5.0519 4.2248 3.5519 2.4689 1.18419 65.5111 0.858 7 220 20 2 10 62.5 27.6297 13.4043 2.1662 5.2151 5.0964 4.0824 3.1174 2.1746 1.5232 63.4597 1.2839 8 220 20 2 10 62.5 29.5377 9.8105 1.6383 2.7345 4.4671 3.6539 2.703 1.4373 1.1147 71.8645 0.5761 9 225 20 2 10 62.5 29.865 12.8 2.0012 4.4009 4.9515 4.0852 3.2647 2.1361 1.4385 63.7249 1.1969 10 230 20 2 10 62.5 32.707 13.9619 2.1403 4.5928 5.2801 4.428 3.582 2.3369 1.3924 60.06 2.2256 11 230 20 2 10 62.5 44.5599 11.259 1.8937 4.3153 4.5136 3.767 2.5581 1.1611 0.5648 68.7586 1.2088 12 235 20 2 10 62.5 40.479 15.2204 2.3111 5.1343 5.1902 4.3118 3.1722 1.7989 1.0193 57.3704 4.4713 13 240 20 2 10 62.5 48. 1666 16.2394 2.4565 5.1281 5.3516 4.4507 3.1878 1.5895 0.7333 53.8929 6.9702 14 240 20 2 10 62.5 51.905 15.7638 2.4683 5.0366 5.0606 4.1 2.7401 1.3708 0.5222 57.7393 5.1983 15 245 20 2 10 62.5 52.295 17.2178 2.7313 5.3464 5.2368 4.1509 2.7296 1.488 0.643 6 49.3489 11.1058 16 245 20 2 10 62.5 60.5144 17.0679 2.5165 4.9939 4.6879 3.494 2.516 1.2858 0.7176 51.1297 11.5908 17 205 20 0.5 10 62.5 2.10851 9.7071 0 6.4934 0 0 6.5288 0 6.2191 80.3419 0 18 205 20 1 10 62.5 1.82841 10.0552 0 4.6641 2.6834 0 0 0.57 87 6.4437 82.0188 0 19 205 20 2 10 62.5 5.007859 16.2909 2.9705 6.3237 5.2151 2.0769 1.3377 0.984 1.5996 64.8013 0 20 205 20 3 10 62.5 4.718933 20.6755 3.6832 7.1072 6.0976 2.2231 1.8576 1.1774 2.4037 57.1784 0 21 205 20 5 10 62.5 13.72128 27.4504 4.66 07 6.3452 6.8678 3.3429 2.7534 2.0425 1.1012 46.5371 0 22 205 20 10 10 62.5 56.04576 39.3139 5.3531 8.3832 5.9318 4.3326 3.2469 1.6329 0.9859 31.8056 0 identical with run number 4.
139 Table 6 2. The best fit results and corresponding chain growth probab ilities for cases of T=205 o C. H 2 /CO = 0.5 H 2 /CO = 1.0 H 2 /CO = 2.0 0.18799 0.19205 0.26809 1 0.4836 0.4764 0.3923 2 1.0000 1.0000 0.8588 3 0.7619 0.8301 0.7666 4 1.0000 0.9117 0.8117 5 1.0000 1.0000 0.9261 6 0.8429 1.0000 0.9572 7 1.0000 0.9881 0.9718 8+ 0.9210 0.9460 0.8867 H 2 /CO = 3.0 H 2 /CO = 5.0 H 2 /CO = 10.0 0.31697 0.38722 0.50616 1 0.3477 0.2911 0.2233 2 0.8329 0.7933 0.7632 3 0.7419 0.7634 0.6760 4 0.7762 0.7485 0.7457 5 0.9159 0.8691 0.8007 6 0.9361 0.8967 0.8446 7 0.9629 0.9267 0.9207 8+ 0.8666 0.8409 0.7975
140 Table 6 3. The best fit results; slope of the linearization A n for Eq. ( 6 32 ) C arbon number 1 2 3 4 A n 1.2049 1.0609 10 2 2.4221 10 2 1.5040 10 2 C arbon number 5 6 7 8+ A n 5.5352 10 3 3.0439 10 3 8.0285 10 4 6.7084 10 3 Table 6 4. The best fit results; slope of the linearization, ( E n /R), for Eq. ( 6 35 ) C ar bon number 1 2 3 4 S lope ( E n /R) 2905.1 3108.2 3590.5 4117.2 C arbon number 5 6 7 8+ S lope ( E n /R) 2734.4 2586.7 3698.3 5148.9
141 Table 6 5. Effective coefficients for carbon number dependent chain growth probability relative percent difference on carbon number dependent chain growth probability, and their standard deviations. Carbon number 1 2 3 4 5 6 7 8+ 746.81 63.59 131.65 102.44 67.17 52.53 23.23 68.19 Std. Dev. 225.78 21.44 75.74 35.60 16.20 45.48 9.43 20.96 14.24 3.88 7.09 4.27 2.46 2.95 1.48 2.32 Std. Dev. 6.42 2.48 3.81 2.71 2.19 3.02 0.77 1.45
142 Figure 6 1, Selectivity towards hydroca rbons for different temperatures (P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm)
143 Figure 6 2, Selectivity towards hydrocarbons for different hydrogen to carbon monoxide feed ratios (P=20 bar, T = 205 o C, V = 62.5 sccm wit h 10%vol N 2 )
144 Figure 6 3. Product distribution and ASF plot for carbon number 3~7 (P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm); (a) T = 200 o C, (b) T = 220 o C, (c) T = 235 o C, and (d) T = 245 o C
145 Figure 6 4, Product distribution and ASF plot for carbon number 3~7 (P=20 bar, T = 205 o C, V = 62.5 sccm with 10%vol N 2 ); (a) H 2 /CO = 2 and (b) H 2 /CO = 10
146 Figure 6 5. F inding appropriate value for su m of the selectivity divided its carbon number which makes sum of the squares of the deviation minimum; (T=205 o C, P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm)
147 Figure 6 6. Selectivity comparison between experiment and simulation and chain growth probability used in the simulation; (T=205 o C, P=20 bar, H 2 /CO =3, V = 62.5 sccm with 10%vol N 2 )
148 Figure 6 7. Selectivity comparison between experiment and simulation and chain growth probab ility used in the simulation; (T=240 o C, P=20 bar, H 2 /CO/N 2 = 6:3:1, V = 62.5 sccm)
149 (a) Figure 6 8. Contour plots for determining appropriate kinetic coefficients ; (a) First try out (b) Second try out and (c) Final calculation
150 (b) Figure 6 8. C ontined
151 (c) Figure 6 8. Continued.
152 (a) Figure 6 9. Contour plots for determining appropriate activation energy and hea t of adsorption ; (a) First try out and (b) Final calculation
153 Figure 6 9. Continued
154 Figure 6 10. Carbon monoxide conversion comparison between experimental measurements and simulation with fitting coefficients.
155 Figure 6 11. Carbon monoxide conversion profiles in evaluation of comparison wi th experimental work.
156 Figure 6 12. Hydrogen conversion profiles in evaluation of comparison with experimental work.
157 Figure 6 13. Total number of mole reduction profiles in eval uation of comparison with experimental work.
158 (a) Figure 6 14. C arbon number dependent chain growth probability evaluated for fitting work of the experiment ; (a) Temperature dependency and (b) Hydrogen to carbon monox ide dependency
159 (b) Figure 6 14. Continued
160 (a) Figure 6 15. Linearization of general chain growth probability using Equation ( 6 32 ) ; (a) 1 ~ 4 and (b) 5 ~ 7 and 8+
161 (b) Figure 6 15. Continued.
162 (a) Figure 6 16. Linearization of general chain g rowth probability using Equation ( 6 35 ) ; (a) 1 ~ 4 and (b) 5 ~ 7 and 8+
163 (b) Figure 6 16. Continued.
164 Figure 6 17. Threshold energy from the fitting results and its averaged value.
165 CHAPTER 7 NUMERICAL SIMULATION S FOR MESO AND MICRO SCALE REACTORS 7 .1 General Advantage of a Micro Scale Reactor Meso and micro scale reactors: For a strongly exothermic reaction such as the FT synthesis, temperature control is of critical importance in minimizing the methanation reaction and prolonging the catalyst life. In the previous chapter, a typical single tube from the industrial scale shell and tubes reactor has been modeled for numerical simulation and verif ications. Meso and Micro scale reactors usually offer better heat transfer performance than macro systems because they have not only larger surface area per volume but also less thermal resistance due to small length scales. So in this chapter, numerical simulations for Meso and Micro scale packed bed FT reactors are reported. 7.2 Meso S cale C hannel FLUENT Modeling 7.2.1 Meso Scale Reactor Geometry The meso scale reactor used in this study is a slit like rectangular channel with a large aspect ratio (= channel width/height). Th e schematic is given in Figure 7 1. A two dimensional model has been developed since the end effects for the width are significantly small compared to the one caused by the very narrow height. The channel geometry and system dimen sions have been tabulated in Table 7 1. As provided in the T able 7 1 the mass flux effect, wall temperature effect, outlet pressure effect, and hydrogen to carbon monoxide feed molar ratio effect have been considered. It is more useful to analyze and comp are reactor performance if the reactor size could be normalized since a bigger reactor can load more catalyst and handle a higher mass flow
166 rate or flux. So, it is more meaningful to introduce the concept of residence time instead of the mass flux or mass flow rate. Also the space velocity is useful for analyzing and comparing the reactor performance. In the FT synthesis, the reactor performance could be affected by hydrogen to carbon monoxide feed molar ratio as well as the total mass feed rate. In this w ork, WHSV (weight hourly space velocity) has been defined only for the carbon monoxide component. The definition for WHS CO is given below, ( 7 1 ) where is carbon monoxide feed mass flow rate and m cat is total mass of catalyst loaded in the reactor. A simple mathematical manipulation gives the relati on between WHSV CO and syngas feed mass flux which is convenient for the FLUENT input as follows, ( 7 2 ) where bulk is catalytic bed bulk density, L is length of the reactor, and Y CO is inlet mass fraction for the carbon monoxide (Y CO =0.875 for H 2 /CO = 2). It is important to note that t he kinetic s expression and coefficients as well as the chain growth probability values from previous Macro scale shell and tube packed bed reactor have been applied exactly in the Meso scale rectangular channel packed bed reactor modeling. Table 7 2 shows successful ly converged cases and their operating conditions, in other words, input parameters in the simulations. Cases 1~18 from the table show wall temperature effects as well as mass flow rate effects on syngas consumption rates as the carbon monoxide and hydroge n mass fractions are changing. The pressure effect on the syngas consum ption rate is illustrated in Figures 7 12
167 through 7 16 using Cases 19~30. Finally, inlet hydrogen to carbon monoxide feed molar ratio effect on syngas mass fraction is shown in Figures 7 17 through 7 19 using Cases 31 to 36. For all cases, only mass fractions of carbon monoxide, hydrogen and water vapor representing the reactants are illustrated as a function of normalized axial distance. Temperature profiles are not shown here as there is no temperature gradient within the channel. A uniform temperature distribution in the reactor except a short length from the inlet has been observed for the steady state solution. Unlike previous industrial scale simulations, the temperature runaway ca se is not observed for the meso scale simulation. The temperature is almost uniform so that the reaction is not that intense comparing to the large scale simulation. In the previous large scale simulation case, the released heat was not transferred effecti vely so that the reactor temperature has increased sharply once the thermal runaway condition is reached. This initial increased temperature level causes not only an accelerating chemical reaction but also an increasing heat transfer toward outside. In the meso scale calculation, no temperature runaway has been observed. Actually meso scale is more manageable under high temperatures, in other words a meso scale reactor requires a higher temperature boundary condition to initiate reaction comparing to macro scale results. Therefore, the meso scale is thermally more viable than the macro scale. 7.2.2 WHSV CO and W all T emperature E ffect Figures 7 2 through 7 6 show carbon monoxide, hydrogen and water vapor mass fractions in the gaseous phase at the center line of the channel for different WHSV CO values of WHSV CO = 0.5, WHSV CO = 1, WHSV CO = 10, WHSV CO = 100, and WHSV CO = 1000, respectively. Each plot contains several family curves for different wall
168 temperature conditions. In these simulation cases, the highest CO conversion obtained is 84.6% for WHSV CO = 0.5, T wall = 540K, P = 20 bar, and H 2 /CO = 2. Since a sudden temperature increase or thermal runaway is not observed for the meso scale reactor, the higher wall temperature case yields the higher syngas convers ion. Syngas consumption rate increases considerably as the wall temperature is increas ed regardless of the syngas mass flow rate Syngas consumption is more sensitive to wall temperature for the low WHSV CO case. For the fixed outlet pressure case the inle t pressure is depending on the total mass flow rate, i n other words, on the WHSV CO Increasing WHSV CO for a given outlet pressure will result in a higher inlet pressure which might cause more chemical reaction inside the reactor. Even though it is a porous bed reactor, gaseous pressure drop is not that significant, actually the pressure is almost constant. However, increasing WHSV CO yields less residence time so the reactant s do not ha ve enough time to react. This will result in more conversion into hydroca rbon for the low WHSV CO case. Therefore, low WHSV CO cases ha ve more reactive time under the same temperature s as well as more sensitive to the wall temperature. This is clearly shown in Fig ures 7 2 through 7 6. In addition to this, two comparisons are show n in Fig ures 7 7 and 7 8. All five different WHSV CO cases are illustrated in Figure 7 7 with a wall temperature of 540K and outlet pressure of 20 bar. With a higher temperature, mass flow effects for the higher WHSV CO cases are more obvious than the low WH SV CO cases but no data is available for low WHSV CO cases for the 600K condition. Syngas exit conversions are shown as a function of wall temperature in F igures 7 9 and 7 10 Temperature dependency for both carbon monoxide and hydrogen conversions is depict ed in Figure 7 9 for WHSV CO =1, H 2 /CO =
169 2 and P = 20 bar case. In the case illustrated in Figure 7 9, there is not much difference between CO and H 2 conversions but this model is still distinguished from those who use a constant CO and H 2 consumption ratio As the reactor temperature increas es differences between CO and H 2 conversions become more distinct. The sysgas mass flow rate and wall temperature effects on the exit syngas conversion are illustrated in Fig ure s 7 10 and 7 11. 7.2.3 Outlet Pressure Ef fect Pressure effects on syngas conversion are shown in Fig ures 7 12 through 7 16. Carbon monoxide, hydrogen and water vapor mass fractions at the centerline of the channel are shown for various simulation conditions. In Figure 7 12, (a) carbon monoxide, (b) hydrogen and (c) water vapor mass fractions in gaseous phase for pressure ranging from 10 to 40 bars are depicted for WHSV CO = 1, T = 520K and H 2 /CO = 2. For both CO and H 2 their mass fraction s drop smoothly from their inlet value s of 0.875 for CO and 0.125 for H 2 along the axial distance. The e xit carbon monoxide mass fraction decreases as the exit pressure increases except for the case with an outlet pressure of 40 bar. It is reminded that this is the mass fraction not the quantitative value The a ct ual amount for the outlet pressure of 40 bar is less than that of 30 bar exit pressure because the gas phase mass fraction for the 40 bar exit pressure case is smaller than that of the 30 bar exit pressure case. A similar plot is illustrated in Figure 7 13 for a higher mass flow rate and higher wall temperature case (WHSV CO = 10 and T= 600K). However, it is not observed that the reverse on the exit carbon monoxide and hydrogen mass fractions between 30 bar and 40 bar. The e xit carbon monoxide and hydrogen m ass fractions decrease monotonously with an increasing exit pressure. The p ressure effect on syngas consumption is noticeable in this case due to a relatively high
170 temperature and low WHSV CO The p ressure effect on syngas consumption for a higher mass flow case is depicted in Figure 7 14; WHSV CO = 100 and the same conditions as those in Figure 7 13. In spite of a high wall temperature, the syngas consumption is not that noticeable due to a high WHSV CO The e xit carbon monoxide mass fraction is in a similar magnitude as that in the Figure 7 12 case. In this case no reverse on the exit syngas mass fractions is obtained for any of the various pressure cases. The e xit syngas mass fractions in the gaseous phase decrease monotonously with the exit pressure. A d ire ct comparison between different mass flow rate cases is shown in Figure 7 15. It is clearly shown that the mass flow rate could make the pressure effect more remarkable; the same pressure increase will make more noticeable syngas consumption change than wi th the low mass flow case. This is clearly illustrated in Figure 7 16. H ow the pressure effect could be amplified by manipulating with the syngas mass flow rates 7.2.4 Inlet H ydrogen to C arbon M onoxide R atio E ffect In the previous section, It has been s hown the weight hourly space velocity WHSV CO (in essence, the mass flux), reactor temperature and pressure effects on the syngas consumption. But, those effects are relatively well understood because previous researches had already considered those effect s but without individual hydrocarbon production rate s However, how does the syngas consumption depend on the hydrogen to carbon monoxide input molar ratio is our unique contribution since we have developed individual hydrocarbon production rates based on the stoichiometric relation between syngas and products using the carbon number dependent chain growth probability. Figure 7 17 shows how the syngas mass fraction at the centerline of the
171 reactor is affected by the hydrogen to carbon monoxide input molar ratio for the conditions of WHSV CO = 1, T = 540K, and P = 20 bar. Unlike the previous syngas mass fraction, the inlet values of carbon monoxide mass fraction or hydrogen mass fraction are not same due to varying hydrogen to carbon monoxide input molar rati o Inlet molar as well as mass fractions are tabulated in Table 7 3 for several hydrogen to carbon monoxide input molar ratios Special caution is needed because not only the inlet mass fraction but also the inlet syngas mass flux is not constant in spite of a constant WHSV CO This is because weight hourly space velocity is based on only the carbon monoxide species. As shown in the mass flux WHSV CO relation, Eq. ( 7 2 ) the syngs mass flux will be changed if the CO mass fraction is changed for a constant WHSV CO A constant WHSV CO means that the mass flow of CO will be constant for any cases shown in Figure 7 17. Therefore, CO mass flow rates used in Figure 7 17 a re the same but the total mass flow rates are all different. At a glance of Figure 7 17, one could deduce that a higher H 2 /CO ratio yields more syngas consumption. Actually that is true but it cannot be verified before the syngas conversion comparison is m ade So, the reactor centerline CO conversions are presented as a function of the axial distance in fig. 7 18. Under the given condition s of WHSV CO = 1, T = 540K, and P = 20 bar, the exit CO conversion is increasing with increasing H 2 /CO input molar ratio up to H 2 /CO = 4. The r eactants exit conversions as a function of H 2 /CO input molar ratio are illustrated in Figure 7 19. H ydrogen is the limiting species in the low H 2 /CO input molar ratio region and the carbon monoxide is the limiting species in the highe r H 2 /CO input molar ratio region. And the CO conversion overtakes the hydrogen conversion at around H 2 /CO = 2.4 where the hydrogen conversion starts to flatten out
172 7.3 Micro S cale C hannel FLUENT Modeling 7.3.1 Micro Scale Reactor Geometry Micro scale s imulation s ha ve also been carried out using the ANSYS FLUENT software package The m icro scale reactor is also taken as a slit like large aspect ratio rectangular channel. The reactor geometry and dimensions are also tabulated in Table 7 1 together with th e meso scale reactor. However, the micro scale numerical simulation is quite differen t from the previous macro and meso scale simulation s in the approach of chemical kinetics. Since a different set of comprehensive kinetics and selectivity accomplished wi th the carbon number dependent chain growth probability as a function of reactor temperature and hydrogen to carbon monoxide input molar ratio have been developed in Chapter 6 those are implemented for representing a novel FT catalyst instead of using kin etics coefficient and fixed carbon number in dependent chain growth probability from the open literatures. The following summarizes the major components of chemical kinetics reaction coefficients and chain growth probability, Eqs.(6 7), (6 23), (6 24), and (6 39), that were developed in Ch. 6 and are used in the micro scale simulations. ( 7 3 ) ( 7 4 ) ( 7 5 )
173 ( 7 6 ) Also it is noticeable that the intraparticle mass transfer has been neglected due to the small size of the catalyst length scale. Therefore a w hole new UDF (user defined functi on) must be written to include the above for the FLUENT simulation Reactor working conditions, in other words input parameters for FLUENT ha ve been tabulated in Table 7 4. 7.3.2 Mass F lux E ffect on C onversion and P roduct D istribution The m ass flux eff ect s on both syngas conversion and product distribution ha ve been studied here. As described previously, the mas flux has been converted into weight hourly space velocity to exclude specific reactor size and catalyst loading effects. Unlike the meso scale simulation, syngas conversion has been evaluated and illustrated instead of the syngas mass fraction. By doing this, a more explicit comparison could be accomplished since the conversion expresses a fractional consumption of the reactant, while the mass fr action denotes the remained reactant fraction within the gaseous phase whose mass fraction is also decreas ing The c onventional reactant conversion expression is shown in the previous chapter but is recall ed here, ( 7 7 ) ANSYS FLUENT calculat ion is based on the mass basis. So, the molar flow rate of carbon monoxide could be wr it t e n as follow s ( 7 8 )
174 where Y CO is the carbon monoxide mass fraction inside the gaseous phase, M W,CO is the molecular weight of the carbon monoxide, G and m are densit ies for the gaseous phase and the mixture phase respectively, G is the gaseous phase volume fraction, and is the mixture mass fl ow rate. After plug ging Eq. ( 7 8 ) into the definition of conversion, Eq. ( 7 7 ) and simplification we have the carbon monoxide conversion as follows, ( 7 9 ) With a pure syngas inlet condition, Eq. ( 7 9 ) could be further simplified as ( 7 10 ) where the term ( G G )/ m has its own physical meaning, which is gaseous mass fraction. This is why the conversion ex presses is more rigorous than the mass fraction itself. If the mass of a reactant phase does not change over the flow length (this condition is possible when reactants and products are in the same phase), then the reactant mass fraction and its conversion reveal the same. If reactants and products are not in the same phase, then the reactant mass fraction does not indicate the extent of the reaction progress. Also, hydrogen conversion is defined like the carbon monoxide, ( 7 11 ) Figure 7 20 shows the change of the gaseous phase mass fraction, defined as Y gas = ( G G )/ m along the micro scale reactor channel for different WHSV CO cases, which are run s number 1~3 listed in Table 7 4. Since solid products are neglected here, the rest is in the liquid phase as higher hydrocarbons. Figure 7 20 clearly shows more
175 liquid phase could b e acquired from the low WHSV CO case which means a longer residence time. Syngas conversion is illustrated in Figure 7 21 for (a) carbon monoxide and ( b ) hydrogen. Like the previous macro and meso scale simulation s the hydrogen conversion is slightly gre ater than that of the carbon monoxide. This means, again, hydrogen to carbon monoxide consumption molar ratio is not 2. Hydrogen is the limiting chemical species. Similar with the previous simulation s the total amount of converted syngas is larger for hig her WHSV CO cases although the fractional conversion is lower. The e xit syngas conversion against WHSV CO has been plotted together with the liquid phase exit mass fraction in Figure 7 22. As shown in Figure 7 22, liquid mass fraction has the same tendency w ith syngas conversion. This is obvious as the more conversion of the reactants, syngas, will result in forming more liquid products. In addition to this, the difference between hydrogen conversion and carbon monoxide conversion is getting larger with high er conversion. This is also the same tendency with previous simulations. Products distributions are depicted in Figure 7 23. Unlike the previous simulation s individual carbon number dependent chain growth probability in a function al form, Eq. (6 39), has been applied here. In previous simulation s individual carbon number dependent chain growth probability has been assigned as a fixed value irrelevant of the operating condition s although a comprehensive model for the chain growth probability has been devel oped. After the comprehensive analysis for product selectivity in C hapter 6, individual carbon number dependent chain growth probability as a function of temperature and hydrogen to carbon monoxide input molar ratio has been ad o pted in the micro channel si mulation. In E q (6 39), individual carbon number dependent chain growth probability equation neither mass flow effect nor WHSV CO effect has been
176 considered. However, the deviation between carbon monoxide and hydrogen consumption ratio and hydrogen to car bon monoxide feed molar ratio causes differences in the chain growth probability. Therefore, a slight difference in the product distribution has been observed here in Figure 7 23. 7.3.3 Temperature E ffect on C onversion and P roduct D istribution The t emper ature effect s on both syngas conversion and product distribution ha ve been studied here. A t otal of five different cases, tabulated in Ta ble 7 4 a s run number s 4~8, ha ve been simulated for the same operating conditions; WHSV CO = 10 [1/hr], T in = 485 K, P ou t = 20 bar, and H 2 /CO = 2. First, the gaseous phase mass fraction along axial distance of the reactor has been plotted in Figure 7 24. In the mass flux result analysis, a decreasing WHSV CO (or mass flux) yields a longer residence time which causes more rea ction to occur. So, the gaseous phase mass fraction decreases with decreasing mass flow (or WHSV CO ). Every single reaction is accelerated with increasing reactor temperature. So, the accelerated reaction rate will result in further decrease of gaseous phas e mass fraction since all the reactants (H 2 and CO) exist in the gaseous phase. This is well represented in Fig 7 24 for the reactor entrance region. As depicted in Figure 7 24, the gaseous phase mass fraction drops significantly for the higher reactor tem perature case in the beginning. But it will be flatte ned over the rest of the reactor and the gaseous phase exit mass fraction is not proportional to the operating temperature which is also illustrated in Figure 7 26 as a liquid phase mass fraction. This i s due to the extinction of the reactant chemical species. As shown in Figure 7 25, the limiting chemical species, hydrogen in this case, is depleted almost one fifth from the reactor inlet for both T wall = 540 K and 560 K. This is why the gaseous phase mas s
177 fraction does not change for those two cases. Reactants conversion can explain why the gaseous phase mass fraction does not change over the reactor length But another question might be brought up here; why is the final exit gaseous phase mass fraction n ot inversely proportional to the reactor temperature. Like previous section, the exit conversion and liquid phase mass fraction are depicted in Figure 7 26. Unlike the previous mass flux effect, temperature effects on syngas conversion and exit liquid phas e mass fraction are different. As shown in Figure 7 26, syngas conversion increase s with the reactor temperature, this is the nature of the reaction rate and Arrhenius expression; all the reactions are accelerated with a higher temperature so more reactant s are consume d However, products distribution is not directly proportional to the temperature. As provided in Figure 7 27 for the product s distribution, lower carbon number hydrocarbons favor higher reactor temperature, while heavier hydrocarbons prefer l ower reactor temperature. For carbon number s 1~3, higher reactor temperature cases result in higher selectivit ies For the mid ranged hydrocarbons, in this particular case carbon number s 4~6, all the selectivity values remain the same regardless of the rea ctor temperature. And for higher hydrocarbon s C7+, the higher temperature cases produce less hydrocarbons. This temperature effect on product selectivity makes the liquid phase exit mass fraction to behave in a non linear manner with respect to temperatur e. To summarize, in the wall temperature of 560 K cases, the syngas is consume d very fast but is converted into lighter hydrocarbon s mainly. This is why the liquid phase exit mass fraction is dropped after the peak point.
178 7 .3.4 Pressure E ffect s on S yng as C onversion and P roduct s D istribution The p ressure effect s on both syngas conversion and product s distribution ha ve been studied. The g aseous phase mass fraction profiles along the flow direction for different pressure cases are plotted in Figure 7 28. F or this pressure range no significant difference has been observed. Syngas conversion is depicted in Figure 7 29 but again not much difference among the different pressure cases is found. Although differences are small, the exit conversion and liquid phas e exit mass fraction are found to be proportional to the outlet pressure which is illustrated in Figure 7 30. Product s distribution s are all identical in this pressure range. 7.3. 5 Hydrogen to C arbon M onoxide M olar R atio E ffect on C onversion and P roduct s D istribution As provided in the Tab le 7 4 7 different hydrogen to carbon monoxide feed molar ratio cases are examined here. Varying the hydrogen to carbon monoxide molar ratio could be accomplished in two different ways. 1. Fix the total syngas mass flow rate and change both carbon monoxide and hydrogen species flow rates In this case the total flow is constant but chemical species flow rates are all different from each other. 2. Fixed one component flow rate, e.g. constant CO flow rate, and change hydr ogen flow rates corresponding to the hydrogen to carbon monoxide molar ratio. In this case, total syngas flow rates will be varying with respect to hydrogen to carbon monoxide molar ratio. In this simulation work, the second method is chosen. For a ll 8 cas es, every input parameter is identical except the hydrogen flow rate. Gaseous phase mass fractions for 8 different H 2 /CO ratios are plotted in Figure 7 32. Similarly with the temperature effect, the gaseous phase mass fraction drops quickly with increasing hydrogen to carbon
179 monoxide molar ratio at the inlet But for higher hydrogen to carbon monoxide molar ratio cases, H 2 /CO greater than 3 in this simulation, the gaseous phase mass fraction levels out after the middle section of the reactor. The reason for this is exactly the same with the temperature effect on conversion and syngas mass fraction. The limiting chemical species is exhausted. The limiting chemical species is depending on hydrogen to carbon monoxide molar ratio. In this level off case, the car bon monoxide is the limiting chemical species due to a high hydrogen to carbon monoxide molar ratio. Also this is confirmed by the syngas conversion profile illustrated in Figure 7 33. As shown in Figure 7 33, the carbon monoxide conversion s for higher hyd rogen to carbon monoxide cases reach almost unity which means a complete depletion of carbon monoxide. Comparing carbon monoxide conversion with that of hydrogen, carbon monoxide conversion is found to be widely spread ranging from 0.2 to 1.0 for the exit value, while those for hydrogen are close together regardless of the hydrogen to carbon monoxide molar ratio. This can be more clearly seen in Figure 7 34, the exit conversion plot as a function of the hydrogen to carbon monoxide molar ratio. This can be e xplained with limiting chemical species. For lower hydrogen to carbon monoxide molar ratio cases, the hydrogen is the limiting chemical species so hydrogen conversion is generally higher than that of carbon monoxide. While for higher hydrogen to carbon mon oxide molar ratio cases, there are abundant hydrogen molecules so the carbon monoxide is the limiting chemical species. In Figure 7 34, the hydrogen exit conversion intersects with the carbon monoxide exit conversion around hydrogen to carbon monoxide mola r ratio of 2.4. At this intersection point, the hydrogen to carbon monoxide feed molar ratio and the consumption ratio are identical. Considering the selectivity affected by the
180 hydrogen to carbon monoxide molar ratio, the selectivity suppresses the flatte ning of hydrogen conversion over hydrogen to carbon monoxide molar ratio. As shown in Figure 7 35, methane is favored by the high hydrogen to carbon monoxide molar ratio case while higher hydrocarbons are preferred in low hydrogen to carbon monoxide molar ratio case 7 4 Results Discussion and Contribution of Current Work In this chapter, the FT reactor performance has been studied for two different reactor scale s in order to characterize reactor performance with respect to various operating conditions. T hermal management is a very important element in the process of a FT synthesis reactor. Meso and Micro scale reactors usually offer better heat transfer performance than the macro systems because they not only have a larger surface area per volume but als o less thermal resistance to heat transfer due to small length scales. So in this chapter, numerical simulations for Meso and Micro scale packed bed FT reactors have been performed. Both the meso and micro systems have the same slit like channel geometry h owever the system scales are on the order of 10 3 m and 10 4 m for the meso and micro reactor channels, respectively. Additionally, the micro scale numerical simulation is quite different from the previous macro and meso scale simulations in the appro ach of chemical kinetics. Since a different set of comprehensive kinetics and selectivity accomplished with the carbon number dependent chain growth probability as a function of reactor temperature and hydrogen to carbon monoxide input molar ratio have bee n developed in Chapter 6, those are implemented for representing a novel FT catalyst instead of using kinetics coefficient and fixed carbon number in dependent chain growth probability from the open literatures.
181 The meso and micro scale reactors share many system performance characteristics with those of the macro scale reactor. However, f irst notable difference is that the temperature runaway has not been observed (both meso and micro scale s ) for comparable conditions that give rise to thermal instability in the macro scale reactor. As every coin has two sides, the small scale reactors, however, are also involv ed with inherent disadvantage. Due to low reactor temperature s resulted by higher heat transfer, catalytic reaction might not be activated in the l ow temperature region. Therefore, catalytic reaction requires somewhat higher reactor temperature condition and is sensitive to heat transfer conditions General findings on the reactor performance are as follow s : a higher syngas mass flow rate yields low er conversion due to less residence time. Increasing operating temperature gives higher conversion and the temperature dependency is exponential. A h igher system pressure is favored due to the general nature of chemical reaction with decreasing total numb er of mole s of reactants following the reaction. An i ncreasing hydrogen to carbon monoxide molar ratio yields higher conversion due to that the reaction rate is directly proportional to the hydrogen mole fraction. Considering selectivity, the reactor opera ting condition should be carefully considered. In the micro scale analysis using individual carbon number dependent chain growth probability, the liquid phase selectivity has a complex trend especially with respect to reactor temperature and hydrogen to ca rbon monoxide feed molar ratio. A h igher syngas conversion does not guarantee a higher yield on liquid phase or higher hydrocarbon s in other words wanted products.
182 Table 7 1. Reactor channel geometry and dimensions for both meso and micro scale reac tors Meso Micro Reactor shape R ectangular channel R ectangular channel S mallest length C hannel height Channel height Aspect ratio (W/H) 12.5 37.5 Width 1.27 10 2 m 7.620 10 3 m (0.3 ) Height 1.016 10 3 m 2.124 10 4 m (0.008 ) Length 1.778 10 2 m 4.064 10 2 m (1.6 ) P article diameter 200 m 2 m
183 Table 7 2. Simulation input conditions for the meso scale channel reactor Run # WHSV CO Tin [K] Twall [K] Pout [bar] H 2 /CO 01 0.5 485 500 20 2 02 0.5 485 510 20 2 03 0.5 485 520 20 2 04 0.5 485 530 20 2 05 0.5 485 540 20 2 06 1 485 500 20 2 07 1 485 520 20 2 08 1 485 540 20 2 09 1 485 550 20 2 10 10 485 500 20 2 11 10 485 540 20 2 12 10 485 600 20 2 13 100 485 500 20 2 14 100 485 540 20 2 15 100 485 600 20 2 16 1000 485 500 20 2 17 1000 485 540 20 2 18 1000 485 600 20 2 19 1 485 520 10 2 20 1 485 520 15 2 21 1 485 520 30 2 22 1 485 520 40 2 23 10 485 600 10 2 24 10 485 600 15 2 25 10 485 600 30 2 26 10 485 600 40 2 27 100 485 600 10 2 28 100 485 600 15 2 29 100 485 60 0 30 2 30 100 485 600 40 2 31 1 485 540 20 1 32 1 485 540 20 1.5 33 1 485 540 20 2 .5 34 1 485 540 20 3 35 1 485 540 20 3.5 36 1 485 540 20 4
184 Table 7 3. Inlet molar and mass fractions for various hydrogen to carbon monoxide input ratios H 2 /CO y CO y H2 Y CO Y H2 1.0 0.5 0.5 0.93333 0.06667 1.5 0.4 0.6 0.90323 0.09677 2.0 0.33333 0.66667 0.875 0.125 2.5 0.28571 0.71429 0.84848 0.15152 3.0 0.25 0.75 0.82353 0.17647 3.5 0.22222 0.77778 0.8 0.2 4.0 0.2 0.8 0.77778 0.22222
185 Table 7 4. Simulatio n input conditions for micro scale channel reactor Run # WHSV CO Tin [K] Twall [K] Pout [bar] H2/CO 01 1 485 500 20 2 02 10 485 500 20 2 03 100 485 500 20 2 04 10 485 480 20 2 05 10 485 500 20 2 06 10 485 520 20 2 07 10 485 540 20 2 08 10 485 560 2 0 2 09 10 485 500 10 2 10 10 485 500 20 2 11 10 485 500 30 2 12 10 485 500 20 1 13 10 485 500 20 1.5 14 10 485 500 20 2 15 10 485 500 20 2 .5 16 10 485 500 20 3 17 10 485 500 20 3.5 18 10 485 500 20 4 : the same condition with run number 02.
186 Figure 7 1. Schematic of slit like Meso and Micro scale channel s and computational domain.
187 (a) Figure 7 2. M ass fraction in gaseous phase as a function of axial distance at the cen ter of channel; WHSV CO =0.5, T in = 485K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures ; (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
188 (b) Figure 7 2. Continued.
189 (c) Figure 7 2. Continued.
190 (a) Figure 7 3. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1, T in = 485 K, P out = 20 bar and H 2 /CO = 2 fo r various wall temperatures ; (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
191 (b) Figure 7 3. Continued.
192 (c) Figure 7 3. Continued.
193 (a) Figure 7 4. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 10, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction
194 (b) Figure 7 4. Continued.
195 (c) Figure 7 4. Continued.
196 (a) Figure 7 5. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 100, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
197 (b) Figure 7 5. Continued.
198 (c) Figure 7 5. Continued.
199 (a) Figure 7 6. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1000, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperatures (a) CO mass fraction and (b) H 2 mass fraction and (c) H 2 O mass fraction
200 (b) Figure 7 6. Continued.
201 (c) Figure 7 6. Continued.
202 (a) Figure 7 7. M ass fraction in gaseous phase as a function of axial distance at the center of channel; T wall = 540 K, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various mass flow (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
203 (b) Figure 7 7. Continued.
204 (c) Figure 7 7. Continued.
205 (a) Figure 7 8. M ass fraction in gaseous phase as a function of axial distance at the center of channel; T wall = 600 K, T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various mass flow (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
206 (b) Figure 7 8. Continued.
207 (c) Figure 7 8. Continued.
208 Figure 7 9. CO and H 2 exit conversion as a function of wall temperature; WHSV CO = 1, T in = 485 K, P out = 20 bar and H 2 /CO = 2.
209 (a) Figure 7 10. E xit conversion as a function of wall temperature; T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various inlet mass flows (a) CO conversion and (b) H 2 conversio n
210 (b) Figure 7 10. Continued.
211 (a) Figure 7 11. E xit conversion as a function of weight hourly space velocity of carbon monoxide, WHSV CO [1/hr]; T in = 485 K, P out = 20 bar and H 2 /CO = 2 for selected wall temperatures (a) CO conversion and (b) H 2 conversion
212 (b) Figure 7 11. Continued.
213 (a) Figure 7 12. M ass fraction in gaseous phase as a func tion of axial distance at the center of channel; WHSV CO = 1, T wall = 520 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction
214 (b) Figure 7 12. Continued.
215 (c) Figure 7 12. Continued.
216 (a) Figure 7 13. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 10, T wall = 600 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
217 (b) Figure 7 13. Continued.
218 (c) Figure 7 13. Continued.
219 (a) Figure 7 14. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 100, T wall = 600 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
220 (b) Figure 7 14. Continued.
221 (c) Figure 7 14. Continued.
222 (a) Figure 7 15. M ass fraction comparison between different WHSVCOs for several outlet pressure cases. T wall = 600 K, T in = 485 K, and H 2 /CO = 2 for various exit pressure conditions (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
223 (b) Figure 7 15. Continued.
2 24 (c) Figure 7 15. Continued.
225 Figure 7 16. Reactants exit conversions as a function of exit pressure; T in = 485 K, and H 2 /CO = 2 for various inlet mass flows
226 (a) Figure 7 17. M ass fraction in gaseous phase as a function of axial distance at the center of channel; WHSV CO = 1, T wall = 540 K, T in = 485 K, and P = 20 bar for various H 2 /CO conditions (a) CO mass fraction (b) H 2 mass fraction and (c) H 2 O mass fraction.
227 (b) Figure 7 17. Continued.
228 (c) Figure 7 17. Con tinued.
229 (a) Figure 7 18. C onversion as a function of axial distance at the center of channel; WHSV CO = 1, T wall = 540 K, T in = 485 K, and P = 20 bar for various H 2 /CO conditions (a) CO conversion and (b) H 2 conver sion.
230 (b) Figure 7 18. Continued.
231 Figure 7 19. CO and H 2 exit conversion as a function of inlet H 2 /CO conditions; WHSV CO = 1, T wall = 540 K, T in = 485 K, and P out = 20 bar
232 Figure 7 20. Mass fraction for gaseous phase profiles as a function of downstream location; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2 for various WHSV CO conditions.
233 Figure 7 21. Syngas conversion as a function of downstream location; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2 for various WHSV CO conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
234 Figure 7 22. Syngas exit conversion and liquid phase exit mass fraction as a function of weight hourly space velocity for carbon monoxide, WHSV CO ; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2.
235 Figure 7 23. WHSV CO effect on hydrocarbon distribution at the exit; T in = 485 K, T wall = 500 K, P out = 20 bar and H 2 /CO = 2.
236 Figure 7 24. Mass fraction for gaseous phase profiles as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2 for various wall temperature conditions.
237 Figure 7 25. Syngas conversion as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 b ar and H 2 /CO = 2 for various wall temperature conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
238 Figure 7 26. Syngas exit conversion and liquid phase exit mass fraction as a function of wall tempe rature; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2.
239 Figure 7 27. Wall temperature effect on hydrocarbon distribution at the exit; WHSV CO = 10 [1/hr], T in = 485 K, P out = 20 bar and H 2 /CO = 2.
240 Figure 7 28. Mass fraction for gaseous phase profiles as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and H 2 /CO = 2 for various outlet pressure conditions.
241 Figure 7 29. Syngas conversion as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and H 2 /CO = 2 for various outlet pressure conditions (a) carbon monoxide conversion and (b) hydrogen conversion.
242 Figure 7 30. Syngas exit conversion and liquid phase exit mass fraction as a function of outlet pressure; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and H 2 /CO = 2.
243 Figure 7 31. Outle t pressure effect on hydrocarbon distribution at the exit; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K and H 2 /CO = 2.
244 Figure 7 32. Mass fraction for gaseous phase profiles as a function of downstream location; WH SV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and P out = 20 bar for various hydrogen to carbon monoxide feed ratio conditions.
245 Figure 7 33. Syngas conversion as a function of downstream location; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and P out = 20 bar for various hydrogen to carbon monoxide feed ratio conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
246 Figure 7 34. Syngas exit conversion and liquid p hase exit mass fraction as a function of hydrogen to carbon monoxide feed ratio; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K, and P out = 20 bar.
247 Figure 7 35. Hydrogen to carbon monoxide feed ratio effect on hydro carbon distribution at the exit; WHSV CO = 10 [1/hr], T in = 485 K, T wall = 500 K and P out = 20 bar.
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253 BIOGRAPHICAL SKETCH Tae Seok Lee was born in 1977 in Seoul, Republic of Korea. He matriculated in Department of Chemical Engineering, University of Seoul, Kor ea in 1996. After completing his sophomore, he had joined Korea Military Service as a Field Artillery for 26 months. Tae Seok won the bronze medal in Transport Phenomena national competition held by Korea Institute of Chemical Engineering, KIChE in his sen ior year and 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 had joined Department of Mechanical and Aerosp ace Engineering at University of Florida in fall 2005 as a graduate student. He got his Master of Engineering with thesis titled PROCESS DESIGN AND OPTIMIZATION OF SOLID OXIDE FUEL CELLS AND PRE REFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS in December 2 008