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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. Hagelin-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.
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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 Enol/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 Process Operation Condition on the Selectivity ................... 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 Slurry 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-Liquid 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 Chain Growth Probability ..................................................................................................... 63
3.2.5 Product Distribution Accomplished with Carbon Number Dependent Chain Growth Probability............................................................................... 65
4 NUMERICAL 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 Catalyst Based Packed-Bed Reactor ......... 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 Idea for Generalization of Selectivity .................................. 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-Scale Channel FLUENT Modeling ........................................................ 165
7.2.1 Meso-Scale Reactor Geometry ............................................................. 165
7.2.2 WHSVCO and Wall Temperature Effect .................................................. 167
7.2.3 Outlet Pressure Effect ........................................................................... 169
7.2.4 Inlet Hydrogen to Carbon Monoxide Ratio Effect .................................. 170
7.3 Micro-Scale Channel FLUENT Modeling ........................................................ 172
7.3.1 Micro-Scale Reactor Geometry ............................................................. 172
7.3.2 Mass Flux Effect on Conversion and Product Distribution ..................... 173
7.3.3 Temperature Effect on Conversion and Product Distribution ................. 176
7.3.4 Pressure Effects on Syngas Conversion and Products Distribution ...... 178
7.3.5 Hydrogen to Carbon Monoxide Molar Ratio Effect on Conversion and Products Distribution ................................................................................... 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 operating 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=205oC. .......................................................................................................... 139
6-3 The best fit results; slope of the linearization An for Eq. (6-32). ........................ 140
6-4 The best fit results; slope of the linearization, (En/R), for Eq. (6-35). .............. 140
6-5 Effective coefficients for carbon number dependent chain growth probability
,n EffC , relative percent difference on carbon number dependent chain growth
probability, n and their standard deviations. ................................................ 141
7-1 Reactor channel geometry and dimensions for both meso- and micro- scale reactors. ........................................................................................................... 182
7-2 Simulation input conditions for the meso-scale channel reactor ....................... 183
7-3 Inlet molar 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 FIGURES
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, 1st order reaction, for various values of Thiele modulus ............................................................................................... 69
3-2 Effectiveness factor for 1st 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 scheme. ...................................... 72
4-1 Computational domain and outside coolant flow path. ....................................... 81
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. ............................................................... 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 Detailed temperature profile between maximum safe case and temperature runaway case ..................................................................................................... 85
5-1 Schematics for packed bed reactor .................................................................. 100
5-2 Pressure and temperature profile for baseline case; pure syngas mass flux 3.3 kg/m2s, H2/CO = 2, inlet and coolant temperature 214 oC .......................... 101
5-3 Temperature contours at three downstream locations for the baseline case; pure syngas with mass flux of 3.3 kg/m2s,H2/CO = 2,and syngas inlet and coolant temperature at 214 oC. ......................................................................... 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 oC, H2/CO = 2.0 and different mass fluxes, F/Fbase=0.5, 0.75, 1, 1.25, and 1.5. ..... 106
5-8 Reactor bed temperature profiles for inlet and coolant temperature of 214 oC, H2/CO = 1.5 and different mass fluxes, F/Fbase = 0.25, 0.5, 0.75, and 1. .......... 107
5-9 Reactor bed temperature profiles for inlet and coolant temperature of 214 oC, H2/CO = 2.2 and different mass fluxes, F/Fbase = 0.5, 0.75, and 1. ................... 108
5-10 Reactor bed temperature profiles for inlet and coolant temperature of 214 oC, H2/CO = 2.5 and different mass fluxes, F/Fbase = 0.25, 0.5, 0.75, and 1. .......... 109
5-11 Reactor bed temperature profiles for inlet and coolant temperature of 214 oC, syngas mass flux F= Fbase and different H2/CO ratios of 1.5, 1.7, 2.0, 2.2, 2.5, and 3.0. ............................................................................................................ 110
5-12 Reactor bed temperature profiles for inlet and coolant temperature of 210 oC, syngas mass flux F= Fbase and different H2/CO ratios of 1.5, 1.7, 2.0, 2.4, 2.5, and 3.0. ............................................................................................................ 111
5-13 Reactor bed temperature profiles for inlet and coolant temperature of 205 oC, syngas mass flux F= Fbase and different H2/CO ratios of 2.0, 2.5, 3.0, and 3.5. 112
5-14 Reactor bed temperature profiles for inlet and coolant temperature of 214oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.2, 2.3, 2.5, and 3.0....................................................................................................... 113
5-15 Reactor bed temperature profiles for inlet and coolant temperature of 210 oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.5, and 3.0.. .................................................................................................................. 114
5-16 Reactor bed temperature profiles for inlet and coolant temperature of 205 oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.5, and 3.0. ................................................................................................................... 115
5-17 Thermal viability map for a FT reactor. ............................................................. 116
6-1 Selectivity towards hydrocarbons for different temperatures (P=20 bar, H2/CO/N2 = 6:3:1, V = 62.5 sccm) .................................................................... 142
11
6-2 Selectivity towards hydrocarbons for different hydrogen to carbon monoxide feed ratios (P=20 bar, T = 205 oC, V = 62.5 sccm with 10%vol N2) .................. 143
6-3 Product distribution and ASF plot for carbon number 3~7 (P=20 bar, H2/CO/N2 = 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 oC, V = 62.5 sccm with 10%vol N2) ................................................................... 145
6-5 Finding appropriate value for sum of the selectivity divided its carbon number which makes sum of the squares of the deviation minimum; (T=205 oC, P=20 bar, H2/CO/N2 = 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=205oC, P=20 bar, H2/CO =3, V = 62.5 sccm with 10%vol N2) ....................................................................................... 147
6-7 Selectivity comparison between experiment and simulation and chain growth probability used in the simulation; (T=240 oC, P=20 bar, H2/CO/N2 = 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 heat of adsorption ......................................................................................................... 152
6-10 Carbon monoxide conversion comparison between experimental measurements and simulation with fitting coefficients. ..................................... 154
6-11 Carbon monoxide conversion profiles in evaluation of comparison with experimental 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 Carbon 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
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7-2 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO =0.5, Tin = 485K, Pout = 20 bar and H2/CO = 2 for various wall temperatures ................................................................................. 187
7-3 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 1, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures ............................................................................................. 190
7-4 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 10, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures ................................................................................. 193
7-5 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 100, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures ................................................................................. 196
7-6 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 1000, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures ................................................................................. 199
7-7 Mass fraction in gaseous phase as a function of axial distance at the center of channel; Twall = 540 K, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various mass flow ......................................................................................................... 202
7-8 Mass fraction in gaseous phase as a function of axial distance at the center of channel; Twall = 600 K, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various mass flow ......................................................................................................... 205
7-9 CO and H2 exit conversion as a function of wall temperature; WHSVCO = 1, Tin = 485 K, Pout = 20 bar and H2/CO = 2. ......................................................... 208
7-10 Exit conversion as a function of wall temperature; Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various inlet mass flows ...................................................... 209
7-11 Exit conversion as a function of weight hourly space velocity of carbon monoxide, WHSVCO [1/hr]; Tin = 485 K, Pout = 20 bar and H2/CO = 2 for selected wall temperatures ............................................................................... 211
7-12 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 1, Twall = 520 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions ....................................................................... 213
7-13 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 10, Twall = 600 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions ....................................................................... 216
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7-14 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 100, Twall = 600 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions ....................................................................... 219
7-15 Mass fraction comparison between different WHSVCOs for several outlet pressure cases. Twall = 600 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions .......................................................................................... 222
7-16 Reactants exit conversions as a function of exit pressure; Tin = 485 K, and H2/CO = 2 for various inlet mass flows ............................................................. 225
7-17 Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 1, Twall = 540 K, Tin = 485 K, and P = 20 bar for various H2/CO conditions.................................................................................. 226
7-18 Conversion as a function of axial distance at the center of channel; WHSVCO = 1, Twall = 540 K, Tin = 485 K, and P = 20 bar for various H2/CO conditions .... 229
7-19 CO and H2 exit conversion as a function of inlet H2/CO conditions; WHSVCO = 1, Twall = 540 K, Tin = 485 K, and Pout = 20 bar. ............................................. 231
7-20 Mass fraction for gaseous phase profiles as a function of downstream location; Tin = 485 K, Twall = 500 K, Pout = 20 bar and H2/CO = 2 for various WHSVCO conditions. ......................................................................................... 232
7-21 Syngas conversion as a function of downstream location; Tin = 485 K, Twall = 500 K, Pout = 20 bar and H2/CO = 2 for various WHSVCO conditions ................ 233
7-22 Syngas exit conversion and liquid phase exit mass fraction as a function of weight hourly space velocity for carbon monoxide, WHSVCO; Tin = 485 K, Twall = 500 K, Pout = 20 bar and H2/CO = 2. .............................................................. 234
7-23 WHSVCO effect on hydrocarbon distribution at the exit; Tin = 485 K, Twall = 500 K, Pout = 20 bar and H2/CO = 2. ................................................................. 235
7-24 Mass fraction for gaseous phase profiles as a function of downstream location; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperature conditions. ................................................................ 236
7-25 Syngas conversion as a function of downstream location; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperature conditions ......................................................................................................... 237
7-26 Syngas exit conversion and liquid phase exit mass fraction as a function of wall temperature; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2. ................................................................................................................... 238
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7-27 Wall temperature effect on hydrocarbon distribution at the exit; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2. ............................................... 239
7-28 Mass fraction for gaseous phase profiles as a function of downstream location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2 for various outlet pressure conditions. ................................................................... 240
7-29 Syngas conversion as a function of downstream location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2 for various outlet pressure conditions ......................................................................................................... 241
7-30 Syngas exit conversion and liquid phase exit mass fraction as a function of outlet pressure; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2. ...................................................................................................................... 242
7-31 Outlet pressure effect on hydrocarbon distribution at the exit; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K and H2/CO = 2. ............................................... 243
7-32 Mass fraction for gaseous phase profiles as a function of downstream location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar for various hydrogen to carbon monoxide feed ratio conditions. ............................ 244
7-33 Syngas conversion as a function of downstream location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar for various hydrogen to carbon monoxide feed ratio conditions ............................................................. 245
7-34 Syngas exit conversion and liquid phase exit mass fraction as a function of hydrogen to carbon monoxide feed ratio; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar. ........................................................................ 246
7-35 Hydrogen to carbon monoxide feed ratio effect on hydrocarbon distribution at the exit; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K and Pout = 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. Chung 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 growth model and
stoichiometric relationship between the syngas and hydrocarbons. Fischer-Tropsch
synthesis involves a three-phase phenomenon; gaseous phase – syngas, water vapor
and light hydrocarbons, liquid phase – heavy hydrocarbon, solid phase – wax products
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.
Heterogeneous 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 because thermal-management is highly important for the current exothermic
catalytic reaction.
Catalytic chemical kinetics and selectivity analysis for a novel cobalt catalyst
developed by our collaborator in the Chemical Engineering department has been
16
conducted. 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 accurate and precise predictions in order to understand the heat transfer effect. A
mathematical 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
work 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, first 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
temperatures resulted by higher heat transfer, catalytic reaction might not be activated
in the low temperature region. 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 and 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-oil 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 emissions, 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 replace 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 motors and batteries. It might
be an eventual goal but it is definitely not the solution for the near-term future. Alternate
18
fuels 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 chemical 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 build 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 availability, synthetic diesel could be free
from problems 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 process to synthetic diesel.
In a scientific paper published by the US National Academy of Sciences (Hill et al.,
2006), the authors reported the following : “ Through a life-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 energy 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 can 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-based biofuels”.
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 process 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 Agriculture, biodiesel yields 280% more energy than
petroleum diesel fuel, while producing 47% lower exhaust emissions. Biodiesel is much
environmentally friendly than petroleum diesel, as harmless as table salt and as
biodegradable as sugar. Furthermore, since the bio-diesel is produced from biomass,
which consumes CO2 during growth, the result is a “carbon neutral” process.
1.2 Research Objectives
The main objectives 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 of packed-bed reactors. This combined
20
numerical simulation model will include multi-phase flows, non-ASF distributions, individual product production rates, 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 LITERATURE REVIEW
Fischer-Tropsch technology can be briefly defined as the means used to convert
synthesis gases 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 and Hans Tropsch (Fischer and Tropsch,
1926 and 1930). They were working for Kaiser Wilhelm Institute for Coal Research in
Mülheim, Ruhr (Steynberg and Dry, 2004). Although numerous researches have worked
on the Fischer-Tropsch synthesis during the past several 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, reaction mechanism, selectivity of products
and selectivity models, and reactor modeling are reviewed. The current research in
reactor modeling for a fixed bed Fischer-Tropsch Synthesis is highlighted as well.
2.1 Fischer-Tropsch Catalysis
The most common Fischer-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 gases in the 1920s.
The cobalt medium pressure synthesis was invented by Fischer and Pichler and the
cobalt catalyst that Otto Roelen developed became the standard FT catalysts in
Germany. Fischer and Pichler also invented the iron medium pressure synthesis which
22
is commercialized by the Ruhrchemie and Lurgi companies and established at Sasol in
South Africa in 1955. These are all examples 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) applications were not economically
viable either in the U.S and elsewhere.
Brief general characteristics of each metal are reviewed here. Iron catalysts are
favored because of their low costs in comparison to other catalysts. Comparing with
other catalysts, however, iron catalysts have a high water-gas shift reaction activity and
high selectivity to olefins (Kölbel and Ralek, 1980; Jager and Espinoza, 1995). The main
advantage using Cobalt catalyst is its high selectivity for linear alkanes (Rao et al.,
1992). Other 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.
Ruthenium is very active but expensive, relatively it costs 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 catalyst 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 process 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 initiator 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 number 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 the mechanisms 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-insertion 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 CO 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 -alkenes, 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, monomer 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. System temperature, total pressure and the H2/CO ratio are fundamental governing factors which affect both kinetics and product distribution.
2.2.2 Carbide Mechanism
The earliest mechanism proposed by Fischer (1926) and later refined by Craxford
and Rideal (1939) involved surface carbides (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 successive reaction CH, CH2, and
CH3 intermediate species. CH2 intermediate species is regarded as the monomer,
building block, and the CH3 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 CH2 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 either paraffins or α-olefins through
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 Mechanism
Carbide mechanism is mostly focusing on explaining 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 carbenes, =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 intermediate
species. Chain growth occurs through condensation 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 gives
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 chain
breaking into α-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) Insertion Mechanism
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 metal-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 α-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 ‘alkyl migration.’
27
2.2.5 Combined Enol/carbide Mechanism
This proposed mechanism combines both carbide mechanism and enol
mechanism. Basically, chain growth occurs through CH2 insertion so that monomer is
surface methylene species. However, enolic intermediate complex is involved to form a
monomer by hydrogenation of the hydroxylated enolic CO-H2 complex. So, this
mechanism is also possible to form not only hydrocarbon but also oxygenated products
like a direct CO insertion mechanism. Therefore, chain termination process could be
shared with direct insertion mechanism. Reaction pathway to form a monomer is
illustrated in Figure 2-4.
Generally C/C bond formation through CH2 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
catalyst 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
species involved. Literature on the kinetics and selectivity of the Fischer-Tropsch
synthesis can be divided into two classes. Most studies aimed at catalyst improvement
and postulated empirical power-law kinetics for the carbon monoxide and hydrogen
conversion 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 aimed at
understanding the reaction mechanisms. Some authors derived Langmuir-Hinshelwood-
Hougen-Watson (LHHW) rate expressions for the reactant consumption and
quantitative formulations to describe 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 actual 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-Based Catalysts
In general, the F-T reaction rate increases with the H2 partial pressure and
decreases with the partial pressure of water. The general polynomial kinetic expression
is easy to fit experimental data so numerous kinetic expressions for polynomial fitting
have been investigated. Some of polynomial kinetic expressions are tabulated in Table
2-1 for both iron and cobalt catalysts. From Table 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 conditions. The carbon 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. (1998).
2FT Hr kP (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 follows,
2
2
exp
exp
H CO
FT
CO H O
Ao
ado
kP Pr
P aP
Ek k
RT
Ha a
RT
(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, PCO >> PH2O.
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 increased 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 H2
with a chemisorbed CO molecule. From Langmuir’s adsorption theory, CO molecule is
competing with H2O, CO2, and H2 for the adsorption sites. Dry (1976) and Huff and
Satterfield (1984) made an important assumption here, strong adsorption of CO and
water relative to H2 and CO2. Dry (1976) reported 63 kJ/mol of activation energy for an
iron catalyst used in a fixed-bed. Atwood and Bennett (1979) reported an activation
energy of 85 kJ/mol, and an adsorption enthalpy of 8.8 kJ/mol, by fitting their data
using Eq. (2-2) for fused nitrided ammonia synthesis catalyst. Shen et al. (1994) used
30
the same rate expression to describe the kinetics on a precipitated commercial Fe/Cu/K
catalyst. They observed an activation energy of 56 kJ/mol which is relatively low for
most F-T synthesis catalysts 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 2 2
2 2 22
2
2
' '
H CO H CO H CO
FT
CO H O CO H H OCO H O
H
kP P kP P kP Pr
aP aP P P a PP P
P
(2-3)
They assumed that absorbed intermediates are directly associated with molecular
hydrogens 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-H2 complex is the slowest step in the sequence of elementary
reactions. Also they assumed that the absorbed CO-H2 and H2O are the most abundant
surface intermediates and they saturate the surface to eliminate other absorbed species
in fractional coverage of absorbed CO-H2. Mathematically, the rate Equation (2-3)
becomes identical with 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 hydrogen 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
270oC. They also 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 H2/CO feed ratio regime for potassium-promoted iron catalyst. Shen et al. (1994)
accomplished 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 dioxide so carbon dioxide
concentration is high enough. This situation may occur when low H2/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
CO2, with hydrogenation of adsorbed CO as the rate determining step and modifying
Langmuir isotherm expression. Their reaction rate expression is given as follows
2
2
H CO
FT
CO CO
kP Pr
P aP
(2-4)
32
They examined their high WGS activity and precipitated catalyst (100 Re/1.3 K),
and reported an adsorption constant for CO2 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 CO2 inhibitions proposed
by Ledakowicz et al. (1985) is as follows,
2
2 2
H CO
FT
CO H O CO
kP Pr
P aP bP
(2-5)
However, Yates and Satterfield (1989) demonstrated co-feeding of CO2 to the feed
gas and showed that CO2 is relatively inert.
All Proposed 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
activity and for the process conditions used to develop the expressions.
2.3.2 Cobalt-Based Catalysts
The Fischer-Tropsch synthesis reaction rate expressions for cobalt based
catalysts are very limited and have different forms than iron based catalysts. The most
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 kinetics 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 catalytic 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, CH2 monomer, based on both the carbide mechanism
and enolic mechanism by assuming various rate determining steps.
2
2
2
1
1
a b
H CO
FTn
c d
i H CO
i
kP Pr
K P P
(2-6)
They compared six models with their experimental data (Sarup and Wojciechowski,
1988) obtained in a Berty internally recycled reactor using Co/Kieselguhr at 190oC for
PH2 ranging from 0.07 to 0.68 and PCO between 0.03 and 0.93 MPa. Two models, one
based on the hydrogenation of surface 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
2
1 2 1 2
21 2 1 2
1 21
H CO
CO
CO H
kP Pr
K P K P
(2-7)
and
2
2
1 2
21 2
1 21
H CO
CO
CO H
kP Pr
K P K P
(2-8)
In the first model, Eq. (2-7), rate determining steps are assumed following the
surface reactions
34
1CK
Cs Hs CHs s (2-9)
and
1OK
Os Hs HOs s (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 PCO 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 190oC.
2
2
1 2 1 2
21 2 1 2
1 2 31
H CO
CO
CO H CO
kP Pr
K P K P K P
(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
1OHK
OCs Hs HOCs s (2-12)
Among their 6 models, Equations (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 following rate expression is the rejected model by
Sarup and Wojciechowski
2
2 2
21 2 1 2
1 2 31
H CO
CO
CO H CO H
kP Pr
K P K P K P P
(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 convenient and
easy. However it should be reasonable. This can be accomplished by 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
absorbed 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 made
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
2
1
H CO
CO
CO
kP Pr
KP
(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 research.
36
2.4 Products Distribution and Selectivity
In general, products of FTS have varieties of mixture of organic species, mostly
hydrocarbon (n-paraffins and α-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 decreases monotonically for higher carbon numbers, although around C3-C4, often a local maximum is observed. 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 none of quaternary branched hydrocarbon 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 α-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 parameter remains constant (Donnelly, 1989).
5. Alcohols productions also decrease with carbon number, except methanol (Donnelly, 1989).
2.4.1 Influence of Process Operation Condition on the Selectivity
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 general influence of different parameters on the selectivity (van der Laan
and and Beenackers, 1999). It is reported that increasing operating 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 results 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 (1986) observed lighter hydrocarbons and
lower olefin content produced by increasing H2/CO ratios. Donnelly and Satterfield
(1989) also reported the same tendency; decreasing olefin-to-paraffin ratio by
increasing H2/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 velocity.
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
1(1 ) n
nm (2-15)
where n is carbon number, mn is the mole fraction of a hydrocarbon containing chain
length n, and α is chain growth probability which is not affected by carbon number n.
Equation (2-15) is well known Anderson-Schulz-Flory (ASF) distribution equation. Chain
growth probability, α, is defined by
g
g t
R
R R
(2-16)
38
where Rg and Rt are the rate of chain growth and termination, respectively. Chain
growth probability determines the product distribution of FT products. It is shown in
Figure 2-5 that hydrocarbon selectivity as function of the chain growth probability factor
calculated using ASF distribution equation, Eq. (2-15). In derivation of ASF distribution,
it is crucial assumption that chain growth probability does not depend on carbon number.
However, deviations from ASF distribution are reported in the literatures.
2.5 Fischer-Tropsch Reactors and Reactor Modeling
There are four types of Fischer-Tropsch reactors in commercial applications 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 Bed Reactor
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 reactor is very attractive for FTS due to its excellent heat
transfer and temperature equalization characteristics. Therefore, it could be said that
fluidized bed reactors have an inherent advantage with higher heat transfer coefficients
which is important due to the large amount of heat that must be removed from the F-T
reactors to control their temperatures. Comparing with fixed bed reactor, another
advantage for fluidized bed is the fact that it is free from intra-particle diffusion limitation.
However fluidization 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 products 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 Phase Reactor
The slurry phase reactor is defined as a three phase bubble column 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 operations
since the liquid wax itself would be the medium in which the finely 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 particles for fixed bed system have a lower size limitation by
pressure drop while catalyst particles for slurry phase reactor have 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 particle 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 reactor is regarded by
many authors as the most efficient process 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 capacity.
Disadvantages are more sensitive to catalyst poisoning due to low loading, and
requiring additional separation device (due to this it took long time for
commercialization). In the slurry phase reactor, it is possible to use smaller catalyst
pellets than a fixed bed reactor.
2.5.3 Fixed Bed Reactor
Fine catalyst particles cause a huge pressure drop. The bigger particles are
relatively free from large pressure drops but there is an intra-particle mass transfer
limitation. The most common fixed bed reactor is a shell-and-tubes reactor. To achieve
high conversion, it is a common practice to recycle a portion of the reactor exit gas.
High pressure operation due to narrow and long tubes, 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 reactors. Fischer-Tropsch fixed bed reactor, being one of the most
competitive 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 Bed Reactor Modeling
Abundant 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 literature on packed-
bed reactor modeling and design is very limited. Atwood and Benett (1979) developed a
1-dimensional plug flow, heterogeneous model to investigate parametric effects on
commercial reactors. A 2-dimensional plug flow, pseudo-homogeneous model 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 diffusion
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
applied 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 distributions and/or individual
product production rates. 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 consumption 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 will be released per CO mole consumed and 21
moles or 30 moles of hydrogen will be required to produce one mole of n-decane or ten
moles of methane, respectively). These complicated FT reactions cannot be
represented by one single equation;
2 2 2 2982 152oCO H CH H O H kJ mol (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 synthetic 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 conditions.
43
Table 2-1. Reaction rate equations for overall synthesis gas consumption rates
Catalyst Reactor type
T [oC] P [MPa] H2/CO Rate expression Act. E [kJ/mol]
Reference
Iron Fixed-bed N/A N/A N/A 2
2
HC H COR aP P 88 Brötz (1949)
250 - 320
2.2 – 4.2 2.0 2H CO totalR aP 79 (est) Hall et al. (1952)
Reduced and nitrided iron
Fixed-bed N/A N/A N/A 2 2H CO HR aP 84 Anderson (1956)
Fixed-bed 225 - 255
2.2 0.25 – 2.0 2 2
0.66 0.34
H CO H COR aP P 71-100 Anderson et al. (1964)
Fixed-bed 225-265
1.0-1.8 1.2-7.2 2 2H CO HR aP 71 Dry et al. (1972)
15% Fe/Al2O3 Fixed-bed 220-255
0.1 3.0 2
1.1 0.1 0.1 0.1
HC H COR aP P 88 4 Vannice (1976)
100 Fe/5 Cu/4.2 K/25 SiO2
Gradientless 249-289
0.3-2.0 N/A 2
i im n
i i H COR a P P Bub and Baerns (1980)
Iron N/A N/A N/A N/A 2
m n
CO H COR aP P Lox et al. (1993)
Iron Fixed-bed 250 2.5 N/A 2CO HR aP Jess et al. (1998)
Co/CuO/Al2O3 Fixed-bed 185-200
1.7-55 1.0-3.0 2 2
0.5
H CO H COR aP P
Yang et al. (1979)
Co/La2O3/Al2O3 Berty 215 5.2-8.4 2.0 2 2
0.55 0.33
H CO H COR aP P
Pannell et al. (1980)
Co/B/Al2O3 Berty 170-195
1.0-2.0 0.25-4.0 2
0.68 0.5
CO H COR aP P Wang (1987)
Co/TiO2 Fixed-bed 200 8-16 1-4 2
0.74 0.24
CO H COR aP P Zennaro et al. (2000)
44
Table 2-2. Selectivity control in Fischer-Tropsch synthesis by process conditions and catalyst modifications (Van der Laan and Beenackers, 1999).
Parameter Chain length
Chain branching
Olefin selectivity
Alcohol selectivity
Carbon deposition
Methane selectivity
Temperature
Pressure
H2/CO
Conversion
Space velocity
Note: Increase with increasing parameter: . Decrease with increasing parameter: .
Complex relation: .
45
CO
|
COC
|
O
|
H
|
H
|
H2
H
|
C
|
C
|
H
|
H2
|
C
|
H
|
C
|
H
|
CO
|
COC
|
O
|
H
|
H
|
H2
H
|
C
|
C
|
H
|
H2
|
C
|
H
|
C
|
H
|
Figure 2-1. Schematics of carbide mechanism.
46
CO
|
CO
C
|
H2
HO CH3
C
|
HO H
C
|
HO H
H2
H2O
C
|
HO H
Figure 2-2. Schematics of Enolic mechanism.
47
H
|
H
|
H2
H
|
C=O
|H
|
CO H3
|
C
|
-H2O
+2H2
H3
|
C
|
CO CH3
|
C=O
|
Figure 2-3. Schematics of Direct Insertion mechanism.
48
CO
|
COC
|
H2HO H
C
|
HO H
H2
CH2
|
H2O
CO
|
COC
|
H2HO H
C
|
HO H
H2
CH2
|
H2O
Figure 2-4. Schematics of Combined enol/carbide mechanism.
49
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
C16+
C10-15
C5-9
C2-4
C1
We
igh
t fr
actio
n,
Wt
[-]
chain growth probability,
Figure 2-5. Hydrocarbon selectivity as function of the chain growth probability factor calculated using ASF.
50
CHAPTER 3 MATHEMATICAL MODELING OF PACKED-BED FISCHER-TROPSCH REACTOR
3.1 Gas-Liquid Hydrodynamics system
3.1.1 Multi-Phase Flow Model
Multiphase flow is a simultaneous stream of materials with different states or
phases (i.e. gas, liquid or solid). However, it is also considered as a multiphase flow
when materials 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 liquid.
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
Fluidized bed
Slurry flow
Hydrotransport
Advances in computational fluid mechanics have provided the basis for further
insights 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 phase 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 these 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 approaches – 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 multiphase flows where the
phases move at different velocities, but a local equilibrium over short spatial length
scales is assumed. It can be used to model homogeneous multiphase flows with a very
strong coupling and phases moving at the same velocity and lastly, 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 phases, 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 substitute 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 simpler 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 phases. 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 well 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 flow 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 catalytic activity, 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 hydrocarbons in the form of wax have
been neglected; (5) No VLE (vapor-liquid equilibrium) is assumed as the liquid phase
contains only heavier hydrocarbons with small mass fractions; (6) Packed-bed is
assumed statistically uniform; no channeling with isotropic hydrodynamic properties; (7)
The production of oxygenates (alcohols and etc.) is neglected due to their small
amounts 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 Langmuir-Hinshelwood-Hougen-Watson (LHHW) model
given by Yates and Satterfield (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 been
neglected. Among several flow regimes possible for gas-liquid flows, 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-Euler
approaches (Volume of Fluids model, mixture model, and Eulerian model) which
consider each phase as an interpenetrating continuum, has been applied for droplet
flows. 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;
0m m mvt
(3-1)
where ρm is the mixture density defined as ρm ≡GρG+LρL. G and L are the volume
fractions of the gas and liquid phases, respectively and vm is the mass-averaged
velocity defined as,
k k k
km
m
v
v
(3-2)
3.1.4 Momentum
Similar to the continuity equation, the momentum equation for the general mixture
model is accomplished by using mixture properties (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 multiphase mixture flows over the packed-
bed, the momentum equation needs to be modified as follows,
m m m m m m Mv v v p St
(3-3)
where SM denotes a momentum source or sink term due to the packed-bed. In this
study, we have adopted a porous model as a momentum sink term for the packed-bed.
A general momentum sink term for the homogeneous porous media model is given by
, , ,
2
mM i m i m m iS v v v
(3-4)
where SM,i is the source or sink term (depending on sign) for the i-th momentum
equation, |vm| 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 term is composed of two parts: a viscous loss
term (dominant in laminar flow, Darcy’s law) and an inertial loss term (dominant at high
flow velocity). These parameters are evaluated using a semi-empirical correlation, the
Ergun Equation (Ergun, 1928).
2 2
2 3 3
1 7 1150
4
o o
p p
p v v
L D D
(3-5)
The permeability and inertial loss coefficient can be obtained from relating Equations (3-
4) and (3-5) and given below (ANSYS FLUENT 12.0 Theory Guide)
2 3
2 3
17,
150 21
p
p
D
D
(3-6)
55
where Dp is catalyst particle diameter, is packed-bed porosity.
3.1.5 Energy Equation
The conservation of energy for the mixture model is given below,
k k k k k k k m E
k k
E v E p T St
(3-7)
where m is mixture thermal conductivity, SE is volumetric heat source from the reaction,
and Ek is defined as follow
2
Gaseous phase2
Liquid phaseL
k GG
G
h
E vph
(3-8)
where hk is the enthalpy for phase k.
3.1.6 Volume Fraction Equation for the Liquid Phase
The volume fraction equation for liquid phase can be obtained from the mass
conservation for liquid phase (continuity equation) as follow
,
L phase
L L L L m j ji W ji
j i
v Mt
(3-9)
where j denotes j-th reaction,
ji and ,W jiM means stoichiometric coefficient and
molecular weight of the i-th species 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
, , , ,k k k i k k k k i k k i j ji W ji
j
Y v Y J Mt
(3-10)
56
where Yi is the mass fraction of i-th chemical species, Jk,i means diffusion flux of i-th
species 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 fractions in q phase and it is unity, i.e.,
, 1k i
i
Y .
3.2 Fischer-Tropsch Reaction Kinetics and Mass Transfer Limitation
3.2.1 Internal Diffusion through Amorphous Porous Catalyst and Overall Reaction Rates
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 the bulk phase to the external surface of the catalyst.
2. Internal diffusion of the reactant; through 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. Internal diffusion of the product; through 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 rate 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 from 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 reaction rate.
3.2.2 Similarity between Heat Transfer with Fins and Catalytic Chemical Reaction
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 reaction
are tabulated below. In Table 3-1, we point out the similarities and also provide simplest
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 the finned surface can be obtained from a conservation of energy by simply
balancing conduction and convection for the differential element. In Table 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 cannot
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
individually. 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,
p c
e
DD
(3-11)
where Db is bulk diffusivity, p is catalyst porosity (void volume over catalyst volume),
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 effective
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
the finned heat transfer. The convection term which is based on the Newton’s law of
cooling makes the differential equation linear so in its dimensionless form it is a linear,
homogeneous, second-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 will 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 will 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,
dimensionless 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 large, internal diffusion is rate-limiting; when this parameter is small, the
surface reaction limits the overall rate. In Figure 3-1, the concentration profiles are
depicted for the several different values of the first order kinetic Thiele modulus. Two
orders 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 toward 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 modulus is well illustrated in Figure 3-1 for the simplest 1st 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 ranging 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
ACat
As
r
r
(3-12)
For the 1st order catalytic reaction through the spherical pellet, a relationship
between the effectiveness and the Thiele modulus is depicted in Figure 3-2. From
Figure 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 the finned heat transfer to the catalytic surface reaction as
an extended surface concept. And all the catalytic reactions are assumed 1st 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 Kinetics and Intraparticle Mass Transfer Limitation
Describing the FT reaction kinetics is very complex due to its complicated reaction
mechanisms 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 Vannice 1991, Iglesia et al.
1992, and Ribeiro et al. 1997). F-T kinetic studies can be categorized into 3 different
approaches; (1) Mechanistic proposals consisting of sequence of elementary reactions
among surface absorbents and/or intermediates. (2) Empirical 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 kinetics expression proposed by Yates and
Satterfield (1991).
2
21
H CO
FT
CO
kC Cr
KC
(3-13)
We have picked Jess and Kern’s (2009) kinetics coefficients among numerous
sets of rate constants and adsorption coefficients available (Maretto and Krishna 1999,
Hamelicnk et al. 2004, and Philippe et al. 2009).
637, 400
0.4expseccat
mk
RT kg mol
(3-14)
3
9 68,5005 10 exp
mK
RT mol
(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-Hinshelwood 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 follows,
2 2 and
1
COFT pseudo H pseudo
CO
aP RTr k C k
bP
(3-16)
With a pseudo reaction rate, simplified effectiveness factor and Thiele modulus are
given by
,FT eff FTr r (3-17)
tanhpore
, 2
2, , ,
pseudo p Hp
p ext eff H l
k HV
A D RT
where, HH2 is Henry coefficient, Deff,H2,l is effective diffusion of the dissolved hydrogen in
the liquid-filled porous catalyst defiend by
2 2, , , ,
p
eff H l mol H l
p
D D
(3-18)
Effectiveness factor is plotted as a function of temperature for several particle
sizes in the Figure 3-3. Effectiveness factors for pseudo kinetics decrease with
increasing either particle size or temperature. It is obvious that the lower effectiveness
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 exponential
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 effectiveness and
Thiele modulus as a UDF (User Defined Function).
3.2.4 Product Distribution with Carbon Number Independent Chain Growth Probability
The lumped kinetic model only can describe the consumption for one of the
reactants, either CO or H2. It requires an additional approach to model the product
distribution and the other reactant consumption. Here we adopted the well-known
general chain growth probability model which becomes the simplest product distribution,
ASF distribution, when chain growth probability does not depend on the number of
carbons in the products. A stoichiometric relationship between reactants and products
can make it easier to combine the lumped kinetic model for CO consumption with the
general chain growth probability model. A general linear-alkanes synthesis chemical
reaction is shown in Eq. (3-19)
2 2 2 2
1 12 n nCO H C H H O
n n
(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 CH2 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. Therefore,
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
monoxide 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 balance for
the absorbed carbon number n yields,
chain growth, 1 desorption, chain growth,n n nr r r (3-20)
Desorption rate could be interpreted as the hydrocarbon production rate assuming
no side reactions among gaseous phases. So that hydrocarbon production ratio of n
carbon number to n-1 carbon number can be written as follow,
desorption, 1 chain growth, 2
1
1 desorption, 1 1 chain growth, 2 1
1 1
1 1
n n n n nnn
n n n n n
r rr
r r r
(3-21)
where αn is chain growth probability of n-carbon containing absorbed intermediate
defining
chain growth, chain growth, chain growth,
chain consumption, desorption, chain growth, chain growth, 1
n n n
n
n n n n
r r r
r r r r
(3-22)
For carbon number independent chain growth probability (in another word,
constant chain growth probability), Equation (3-21) becomes the well-known ASF
distribution as follows,
2 1
1 2 1
n
n n nr r r r
(3-23)
2 1
1 1 2 1 and n
n n n n nr r r r r r
(3-24)
65
3.2.5 Product Distribution Accomplished with Carbon Number Dependent Chain Growth Probability
The total CO consumption rate is definitely related to the hydrocarbon production
rates. It 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. Stoichiometric information is required for relating molar
change of 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 stoichiometric condition.
1 2 32 3CO FT i
i
r r r r r i r (3-25)
Assuming a constant chain growth probability, n-carbon hydrocarbon production
rate could be expressed using the total CO consumption (lumped kinetics for FT)
21 1
1 1n n
n FTr r r (3-26)
A significant 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 hydrocarbon 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,
12 2 1
1
11
rr
13 3 2 1
1
11
rr
(3-27)
66
11 2 1
1
11
n n n n
rr
where the common term, r1/(1α1), could be interpreted as a chain initiation
process which is forming an absorbed methyl from the building block, CH2, by adding a
hydrogen atom.
1
11ini
rr
(3-28)
Individual hydrocarbon production rate, hence, can be written as follows using the
chain initiation rate
1
1 2 11
1 1n
n n n n ini n k inik
r r r
(3-29)
Measurement of chain initiation rate, however, could be extremely challenging.
Without forming a carbon dioxide, which is a reasonable 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, CH2, in the carbide
mechanism. And then this monomer or building block should face two 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 consumption rate. In terms
of symbols, the relationship between CO consumption rate and chain initiation rate is
, 1 1 2 1 2 31
1 1
1N N k
CO ini chain growth i ini ini ini ini ini ii
i k
r r r r r r r r
(3-30)
67
Combining Equations (3-29) and (3-30) yields the specific hydrocarbon production
rate that relates to the CO consumption rate using an individually assigned chain growth
probability
1
1
11
1
1
n
n k COk
n N p
p
r
r
(3-31)
68
Table 3-1. Similarity between fin in heat transfer and catalyst reaction
Finned surface Amorphous porous catalyst
What is transferred?
Heat Chemical species
Through where? Solid material Meandering pore
Driving force Temperature grad. Concentration grad.
At the wall Convection removes heat Chem. rxn removes reactant
Extended surface Generally well defined Complex(constriction, tortuosity)
Coordinates Cartesian Spherical
Steady balance 2
20
c
d T hPT T
dx kA
2
2
20nnA A
A
e
kd C dCC
dr r dr D
Dimensionless form
22
20
dm
dx
22
2
20n
n
d d
d d
Dimensionless 2
c
hPm
kA
2 12
n
n Asn
e
k R C
D
Typical solution cosh
coshb
m L x
mL
1
1
sinh1
sinh
A
As
C
C
Condition Adiabatic tip 1st order kinetic
69
Normalized radial direction in spherical catalyst, r/R
0.0 0.2 0.4 0.6 0.8 1.0
Norm
aliz
ed c
oncentr
ation b
y s
urf
ace c
oncentr
ation,
CA/C
AS
0.0
0.2
0.4
0.6
0.8
1.0 = 0.1
= 0.5
= 1
= 2
= 5
= 10
Figure 3-1. Concentration profile for simplest case, 1st order reaction, for various values
of Thiele modulus
70
Figure 3-2. Effectiveness factor for 1st order reaction within the spherical catalyst as a
function of Thiele modulus.
71
180 190 200 210 220 230 240 250 260 2700.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Temperature [oC]
Effectiveness facto
r,
po
re
Dp = 200 m
Dp = 100 m
Dp = 50 m
Dp = 300 m
Dp = 400 m
Dp = 500 m
Figure 3-3. Effectiveness factor for pseudo kinetics instead of LH kinetics as a function
of size and temperature.
72
C1* C2* C3* C4* … Cn*CH2*C*
COCH4
C2H6C3H8
C4H8CnH(2n+2)
Catalyst
surface
Gas or
Liquid
α α α α
Cn*
rchain growth, n1 rchain growth, n
rdesorption, n
Figure 3-4. Catalyst surface chemistry and Chain growth scheme.
73
CHAPTER 4 NUMERICAL SOLUTION METHOD AND VALIDATIONS
4.1 Numerical Solution by FLUENT
As outlined in previous Chapter 3, the synthesis process of Fischer-Tropsch
catalytic chemical reactions is complicated because that the sophisticated
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 commercial 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) performed a computational 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 FLUENT software. Ho et al. (2011) used the FLUENT software to
simulate the two-phase flow in a falling film microreactor. The discretization method in
FLUENT is based 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 and then solve the resulting simultaneous
74
equations with the maximum possible accuracy. It can handle the two-phase flow
through a porous media and the heterogeneous chemical reaction in the packed-bed
reactor. The GAMBIT 2.4.6 package was used for grid generation. Figure 4-1 shows the
schematic 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
isotropic spherical catalyst beads, the computational domain was assigned as a two-
dimensional axisymmetric cylinder. Therefore, quadrilateral computational cells were
generated by the GAMBIT as shown in Figure 4-1. A pressure-based solver employing
the SIMPLE algorithm was used for the pressure velocity coupling scheme (Patankar,
1980). As described in the previous Chapter, the Eulerian mixture model was applied for
the two-phase flow through a porous media. Laminar flow is assumed due to very small
length scales in the pathways created among small spherical catalyst pellets. As we
assume no vapor-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 interactions
between the two 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, implementation of the FT synthesis reactions with rates 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 also provides intra-particle mass
transfer limitation defined previously by Eq. (3-17) as well as the FT synthesis kinetics
discussed in Chapter 3. In order to achieve 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 Perić,
2002). The synthesis gas (syngas), a mixture of mainly carbon monoxide and hydrogen,
is pumped into 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, are allowed to
vary with their respective temperatures. The thermodynamics properties of the gas
phase mixture are calculated from their pure substance properties and local
compositions; 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. Since we are dealing with multiphase flows and
heat transfer with complex chemical reactions involving many chemical species, so grid
independence study was performed considering computational resource effectiveness
aspects. Grid refinement has been performed until smaller grids do not significantly
improve the accuracy.
4.2 Model Validation Works
4.2.1 Validation of Products Distribution
Two independent comparisons have been conducted to validate our 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 are provided both supercritical fluid and conventional gas-phase Fischer-
76
Tropsch synthesis over a 15% Co/Al2O3 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 Figure 4-2. The
operating condition for presented case is for 50 sccm/min syngas flow rate over one
gram (screened to 100-150 m) of the catalyst, a reaction temperature of 250oC,
syngas partial pressure of 20 bar, and H2/CO feed ratio of 2. Non-ASF distribution,
represented by nonlinear plots of the logarithm of the normalized weight percentage
versus carbon number, was reported. 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 (Elbashir 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 have assigned carbon-number dependent chain growth
probability based on production rates of each hydrocarbon from carbon number 1 to 7
as follow,
0.292 1
0.0317 1.0362 2 7
0.8 8)
n
n
n n
n
(4-1)
77
FLUENT model result for validation is also illustrated on Figure 4-2 along with
experimental data. As mentioned in the previous model description section, the total
number of products (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
number 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 developed 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 limitations, 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
Figure 4-3. From the influence of the cooling temperature 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 200oC, 205oC, 210oC, 214oC case respectively. The differences in maximum
temperature are increasing with cooling temperature but the temperature runaway
happen at the same coolant temperature conditions, 215oC. Syngas conversions are
78
also compared in the Figure 4-4. In the simplified 2-D model, carbon monoxide and
hydrogen conversions are the same because H2/CO feeding ratio and consumption
ratio are identical while H2/CO consumption ratio is variable in comprehensive model so
that CO and H2 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 model 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 reactions. 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 Equation (2-16), we believe that one can predict more accurate
amount of released heat from the FTS. It is shown in Figure 4-5 that more detailed
temperature profile between maximum safe case and temperature runaway case for the
79
comprehensive model. Based on two independent comparisons, 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 Intrinsic 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
Computational domain(quadrilateral mesh)
Axisymmetric
Packed-bed of spherical catalyst
C L
Coolant flow
Synga
s
zr
FT Products & unreacted syngas
Figure 4-1. Computational domain and outside coolant flow path.
82
Carbon number (in the products hydrocarbon)
ln(W
n/n
)
0 5 10 15 20 25 30-12
-10
-8
-6
-4
-2
0
Literature
FLUENT
Standard ASF
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
Axial distance, z [m]
Tem
pera
ture
@cen
terl
ine,T
CL
[oC
]
0 2 4 6 8 10 12200
250
300
350
400
Jess and Kern
This work
214o
C
200o
C
210o
C
215o
C
205o
C
Figure 4-3. Temperature profile comparison with results by Jess and Kern (2009).
84
inlet and coolant temperature, Tin/cool
[oC]
Co
nvers
ion
,X
i[%
]
200 205 210 2150
20
40
60
XCO
XH2
XJess and Kern
Figure 4-4. Syngas conversion comparison with results by Jess and Kern (2009).
85
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[o]
0 2 4 6 8 10 12
220
240
260
280
300
mass flux =3.3 kg/m2s
H2/CO = 2.0
Tin/cool
= 215oC
Tin/cool
= 214.5oC
Tin/cool
= 214.3oC
Tin/cool
= 214.2oC
Tin/cool
= 214.1oC
Tin/cool
= 214oC
Figure 4-5. Detailed temperature profile between maximum safe case and temperature
runaway case
86
CHAPTER 5 INDUSTRIAL SCALE PACKED-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 very
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 accomplished
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 synthesis 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 heat 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 operating conditions for the baseline case are
tabulated in Table 5-1. Using the baseline case, the effects of varying the inlet H2/CO
molar ratio, inlet and coolant temperature, and inlet mass flux on the packed-bed
reactor performance are computed. Detailed simulation results for the baseline case are
illustrated on Figures 5-2 through 5-4. Figure 5-2 shows the reactor bed centerline static
pressure and temperature profiles along the axial direction. As shown in Figure 5-2, the
pressure is linearly decreasing and temperature is rapidly increasing in the beginning
and asymptotically decreasing after the peak point. The two-dimensional temperature
contours are depicted in Figure 5-3 for the axisymmetric FT chemical reactor where the
abscissa represents the axial coordinate 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 concentrations 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 become more reactive that accelerates
88
the catalytic reaction process. Basically the reactor bed temperature increases from
225oC to 244oC 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 proceed 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 to the outside coolant and also due to lowered heat release rate
from the chemical reaction because of the exhaustion of reactants.
In Figure 5-4, the axial mass fraction profiles at the centerline for the gaseous
phase are depicted in two different vertical 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 phase, 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 (=0.1567×0.1039). This example further justified the assumption
of no vapor-liquid equilibrium due to small amount of liquid phase components.
More specifically, the carbon monoxide and water mass fraction contour plots are
provided in Figures 5-5 and 5-6 for the baseline case. Three downstream locations of
z=2, 3, and 6 m are chosen. As shown in the Figures 5-5 and 5-6, carbon monoxide
89
mass fraction decreases along the axial direction, while water mass 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 external
coolant but the mass (or chemical species) cannot be removed through the wall.
5.3 FT Chemical Reactor Thermal Characteristics
Since the two-phase mixture flow temperature distribution plays a crucial role in
the performance of an exothermic Fischer-Tropsch catalytic reactor from the aspects of
reactivity, selectivity, and stability, we 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 temperatures, and H2/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
H2/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 coefficient between the tube outer surface
and the coolant temperature. In the current analysis, the heat transfer coefficient is a
fixed value of 364 W/m2K, therefore the heat loss to the external coolant is only varying
with the coolant temperature, TC which is equal to the syngas inlet temperature, Tin. As a
90
result, in the following thermal management study, only syngas inlet H2/CO molar ratio,
syngas gas inlet mass flux and syngas inlet temperature (identical to the coolant
temperature) will be varied.
In Figure 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/Fbase = 0.5, 0.75, 1.0, 1.25, and 1.5; where Fbase denotes
baseline case mass flux of 3.3 kg/m2sec) are evaluated and their effects on the axial
temperature profiles are given. Comparing with Figure 5-2 (b) of the baseline case
which is the Case F/Fbase=1, if the syngas mass flux is increased over that of the
baseline case (Cases F/Fbase= 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/Fbase= 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 conversions of hydrogen and carbon
monoxide to hydrocarbons are increased due to a prolonged residence time. The
percent carbon monoxide and hydrogen final conversions are tabulated in Table 5-2. It
can be seen that the percent conversions for both hydrogen and carbon dioxide
increase with increasing H2/CO inlet molar ratio and inlet syngas temperature but
decrease with increasing syngas mass flux. Figures 5-8 and 5-9 show how the syngas
mass flux affects the temperature profile for different hydrogen to carbon monoxide inlet
molar ratios. The system conditions used in these Figures 5-8 and 5-9 are the same as
91
those in Figure 5-7 except the hydrogen to carbon monoxide inlet ratio (H2/CO=1.5 in
Figure 5-8 and H2/CO=2.2 in Figure 5-9). When the syngas mass flux is increased, for
all the hydrogen to carbon monoxide ratios, the peak temperature ascends, and its
location is moved further downstream. So the flow exit temperature keeps a
continuously increasing trend with an increasing mass flux. A higher 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 residence 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 tabulated in Table 5-2).
Although the syngas conversion is lower, but the rate of total amount of syngas
converted into hydrocarbon is higher for the higher mass flux case. For example, with
the coolant temperature at 214 oC and H2/CO molar ratio at 1.5 let us compare two
different syngas mass fluxes of F/Fbase = 0.25 and 1. Based on Table 5-2, the
conversion for carbon monoxide, XCO = 23.97% for F/Fbase=1 and XCO=55.03% for
F/Fbase =0.25 that gives the F/Fbase=1 case a rate of total amount of syngas conversion
which is 1.74 times higher than that of the F/Fbase=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/Fbase = 0.75 and 1.0 result in the runaway
of the reactor bed temperature that is considered thermally unviable. The thermally
viable case, F/Fbase = 0.5, that yields 70.61% CO and 76.26% H2 conversions,
respectively, reaches the maximum bed temperature of 244oC and converts 17.2%
input syngas into liquid products. Figure 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/Fbase = 0.25, the reactor becomes thermally unviable. Since for the
lower mass flux case, the flow carries lower momentum when passing through the
porous 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 simulations. The
loss of catalytic activity due to high temperature is known as the deactivation of catalyst.
The catalytic deactivation caused by high temperatures is also called catalyst sintering
(also known as thermal degradation). The temperature 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 lower temperatures in which the F-T
reaction also cannot be activated. This is why the thermal management is important on
an exothermic catalytic reaction. Enhancing the heat removal can be obtained by either
increasing the heat transfer coefficient or increasing the temperature gradient using
lower coolant temperatures. In this study, we only considered different coolant
temperatures, but used a constant heat transfer coefficient. Figures 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, reactor temperature profiles for various
H2/CO ratios with F/Fbase = 1.0 and syngas inlet and coolant temperature of 214oC are
depicted. Among these, the baseline case (H2/CO = 2) has the best performance
among the thermally viable cases and the higher hydrogen to carbon monoxide feed
ratios become thermally unviable. It is not shown here but the case of H2/CO = 2.1 also
yields the temperature runaway behavior. The higher the H2/CO ratio gives the faster
temperature rise. The temperature dependency on the H2/CO ratio can be explained by
its intrinsic kinetics behavior with respect to hydrogen and carbon monoxide
concentrations. Intrinsic kinetics of FT synthesis, Eq. (3-13), is directly proportional 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<< KCCO, then the entire denominator term could be approximated as (KCCO)2. In
this case, FT synthesis intrinsic kinetics is inversely proportional to the carbon monoxide
concentration which is a typical characteristic of the Langmuir-Hinshelwood kinetics. As
we increase 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
210oC, the catalytic packed-bed becomes thermally viable up to H2/CO = 2.4 which is
shown in Figure 5-12. However, as mentioned previously, the bed temperature remains
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 214oC is similar to
that of hydrogen to carbon monoxide feed ratio of 2.4 with 210oC coolant temperature.
For the coolant temperature of 210oC and H2/CO of 2.4, the CO conversion is 42.15%,
the H2 conversion is 41.74% and the mass converted into liquid phase is 10.13%. If the
coolant temperature drops further then even higher H2/CO ratio can be thermally viable.
The results for coolant temperature of 205oC are illustrated in Figure 5-13 where the
case of H2/CO ratio as high as 3 is still thermally viable. In the case of H2/CO = 3.3, its
temperature suddenly rises at almost half of the reactor length.
Next, results are obtained using the same coolant temperatures as those in
Figures 5-11 through 13 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 Figure 5-11 except the syngas mass flux. The temperature profiles illustrated in
Figure 5-14 are very similar to those in Figure 5-11 except that the maximum H2/CO
ratio for a thermally viable application is 2.2 instead of 2 in Figure 5-11. Also, the
downstream location where the peak temperature occurs is closer to the inlet for lower
mass flux case. As discussed previously, syngas conversion is higher for lower mass
flux as a result of relatively longer residence time. For example, CO conversions are
42.18% for H2/CO = 2.0 in Figure 5-11 and 70.61% for H2/CO = 2.2 in Figure 5-14 as
provided in Table 5-2. The half syngas 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 214oC
case. Temperature profiles for the 205oC coolant temperature case with the half mass
flux are plotted in Figure 5-16. No cases are found to be thermally unviable for H2/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 to summarize the thermal management
strategy.
The thermal viability map is developed using the three integral parameters: syngas
inlet mass flux, F, syngas inlet and coolant temperature, in cT T , and hydrogen to
carbon monoxide feed ratio, 2 /H CO . For each data point with the specific F and cT , it
represents the maximum 2 /H CO value that the FT reactor is thermally viable (no reactor
bed temperature run away). For example, the point with F/Fbase = 1 and 214o
cT C the
maximum 2 /H co 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 can be
considered as the critical threshold boundary for thermal viability. In general, the critical
2 /H CO value increases with decreasing coolant temperature and decreasing syngas
mass flux, F. It is worth mentioning that for the case of in cT T = 205oC and the lowest
syngas mass flux, F/Fbase = 0.25, the reactor could function without a thermal runaway
for hydrogen to carbon monoxide feed ratio,2 /H CO to reach as high as 3.9. For this
particular case with a relatively high critical 2 /H CO 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 location. 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-phase heterogeneous numerical model
embedded in the FLUENT code has been developed to simulate a fixed packed-bed
tubular Fischer-Tropsch reactor. The detailed chemical kinetics for producing linear-
paraffin in both gaseous and liquid phases has been derived based on carbide
mechanism chain growth 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 through the catalyst pellet
pores is also considered by means of the general Thiele modulus. Two comparisons
have been made to validate our model. First, the products 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 simplified 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 characteristics of a FT chemical reactor has been investigated
focusing on the effects of syngas mass flux, syngas inlet and coolant temperatures, and
H2/CO feed molar ratio on the reactor temperature profile. The simulation results
indicate the following findings : (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 ratio makes the high syngas flow rate thermally unstable;
and (3) Temperature effect is obvious that a lower syngas inlet/coolant temperature will
quench the reactions so that higher mass flow rate or higher H2/CO ratio can be
thermally viable. Among the mass flux range from 0.825 to 4.95 kg/m2sec, inlet/coolant
temperature range from 205oC to 214oC, and H2/CO feed ratio range from 1.5 to 3.0, we
have found that the case of F = 1.65 kg/m2sec, 2 /H CO = 2.2, and 214o
cT C is the
optimum operating condition which gives the highest syngas conversion but no reactor
bed temperature runaway.
98
Table 5-1. Physical properties and operating conditions for the baseline case.
Reactor type Tubes-and-Shell, focused on a single tube
Catalyst shape Spherical
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/m3]
Packed-bed porosity 0.66
Outlet pressure 20 [bar]
Inlet and coolant temperature 214 [oC]
Syngas inlet mass flux 3.3 [kg/m2sec]
Inlet H2/CO molar ratio 2
Overall heat transfer coefficient 364 [W/m2K]
99
Table 5-2. Calculated conversion values for selected operating conditions.
Operating conditions Results
Tin/coolant [oC] F / Fbase H2/CO XCO [%] XH2 [%]
205 0.5 1.5 22.65 35.81
205 0.5 2.0 33.25 39.49
205 0.5 2.5 47.16 44.83
205 0.5 3.0 67.18 53.23
205 1.0 2.0 18.74 22.26
205 1.0 2.5 26.76 25.43
205 1.0 3 38.90 30.82
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 18.26 28.92
210 1.0 1.7 21.87 30.56
210 1.0 2.0 28.39 33.72
210 1.0 2.4 42.15 41.74
214 0.25 1.5 55.03 85.79
214 0.5 1.5 37.88 59.95
214 0.5 2.0 58.58 69.58
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 56.03
214 1.0 1.5 23.97 37.96
214 1.0 1.7 29.35 41.01
214 1.0 2.0 42.18 50.11
100
Catalyst pellet
Cylindrical
Packed bed
F-T Reactor
F-T Reactants
CO & H2
Tin, F and θH2/CO
F-T Products
mainly
hydrocarbon
z = Lz = 0
z = z z = z + z
D
Coolant
TC
Packed bed tube
(a)
(b)
Figure 5-1. Schematics for packed bed reactor; (a) axisymmetric cylindrical packed-bed FT reactor and (b) external coolant flow configuration.
101
P
ressu
re,P
[bar]
0 0.2 0.4 0.6 0.8 1
20
20.5
21
21.5
22
22.5
23
23.5
24
(a)
normalized axial distance, Z [-]
Tem
pera
ture
,T
[K]
0 0.2 0.4 0.6 0.8 1485
490
495
500
505
510
515
520
525
(b)
Figure 5-2. Pressure and temperature profile for baseline case; pure syngas mass flux
3.3 kg/m2s, H2/CO = 2, inlet and coolant temperature 214 oC, (a) pressure and (b) temperature.
102
Figure 5-3. Temperature contours at three downstream locations for the baseline case;
pure syngas with mass flux of 3.3 kg/m2s,H2/CO = 2,and syngas inlet and coolant temperature at 214 oC.
103
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
CO
H2O
H2
CH4
(a)
gaseo
us
ph
ase,[-
]
Normalized axial distance, Z [-]0 0.2 0.4 0.6 0.8 1
10-5
10-4
10-3
10-2
10-1
CH4
C6H
14
C5H
12
C4H
10
C3H
8
C2H
6(b)
Mass
fractio
nin
gaseo
us
ph
ase,[-
]
Figure 5-4. Mass fraction profiles at the centerline in the gaseous phase for the baseline
case, (a) CO, H2, H2O and CH4, and (b) all hydrocarbons in log scale; pure syngas mass flux of 3.3 kg/m2s, H2/CO = 2, inlet and coolant temperature 214 oC.
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 H2O molar fractions at three downstream locations, z=2,
z=3, z=6.
106
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
Tin/cool
= 214oC
H2/CO = 2.0
F/Fbase
= 1.25
F/Fbase
= 0.5
F/Fbase
= 0.75
F/Fbase
= 1
F/Fbase
= 1.5
Figure 5-7. Reactor bed temperature profiles for inlet and coolant temperature of 214 oC,
H2/CO = 2.0 and different mass fluxes, F/Fbase=0.5, 0.75, 1, 1.25, and 1.5.
107
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12210
212
214
216
218
220
222
224
226
228
230
Tin/cool
= 214oC
H2/CO = 1.5
F/Fbase
= 0.25
F/Fbase
= 1
F/Fbase
= 0.5
F/Fbase
= 0.75
Figure 5-8. Reactor bed temperature profiles for inlet and coolant temperature of 214 oC,
H2/CO = 1.5 and different mass fluxes, F/Fbase = 0.25, 0.5, 0.75, and 1.
108
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
Tin/cool
= 214oC
H2/CO = 2.2
F/Fbase
= 0.5
F/Fbase
= 0.75
F/Fbase
= 1
Figure 5-9. Reactor bed temperature profiles for inlet and coolant temperature of 214 oC,
H2/CO = 2.2 and different mass fluxes, F/Fbase = 0.5, 0.75, and 1.
109
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
320
340
360
380
400
420
440
Tin/cool
= 214oC
H2/CO = 2.5
F/Fbase
= 0.5
F/Fbase
= 0.75
F/Fbase
= 0.25
F/Fbase
= 1
Figure 5-10. Reactor bed temperature profiles for inlet and coolant temperature of 214
oC, H2/CO = 2.5 and different mass fluxes, F/Fbase = 0.25, 0.5, 0.75, and 1.
110
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
Tin/cool
= 214oC
F/Fbase
= 1
H2/CO = 2.5
H2/CO = 2.2
H2/CO = 3.0
H2/CO = 2.0
H2/CO = 1.7
H2/CO = 1.5
Figure 5-11. Reactor bed temperature profiles for inlet and coolant temperature of 214
oC, syngas mass flux F= Fbase and different H2/CO ratios of 1.5, 1.7, 2.0, 2.2, 2.5, and 3.0.
111
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
Tin/cool
= 210oC
F/Fbase
= 1H
2/CO = 2.5
H2/CO = 2.4
H2/CO = 3.0
H2/CO = 2.0
H2/CO = 1.7
H2/CO = 1.5
Figure 5-12. Reactor bed temperature profiles for inlet and coolant temperature of 210
oC, syngas mass flux F= Fbase and different H2/CO ratios of 1.5, 1.7, 2.0, 2.4, 2.5, and 3.0.
112
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
Tin/cool
= 205oC
F/Fbase
= 1
H2/CO = 2.5
H2/CO = 3.3
H2/CO = 3.0
H2/CO = 2.0
Figure 5-13. Reactor bed temperature profiles for inlet and coolant temperature of 205
oC, syngas mass flux F= Fbase and different H2/CO ratios of 2.0, 2.5, 3.0, and 3.5.
113
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
Tin/cool
= 214oC
F/Fbase
= 0.5
H2/CO = 2.2
H2/CO = 2.3
H2/CO = 3.0
H2/CO = 2.5
H2/CO = 2.0
H2/CO = 1.5
Figure 5-14. Reactor bed temperature profiles for inlet and coolant temperature of
214oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.2, 2.3, 2.5, and 3.0.
114
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
220
240
260
280
300
H2/CO = 2.0
H2/CO = 1.5
H2/CO = 2.5
H2/CO = 3.0
Tin/cool
= 210oC
F/Fbase
= 0.5
Figure 5-15. Reactor bed temperature profiles for inlet and coolant temperature of 210
oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.5, and 3.0..
115
Axial distance, Z [m]
Tem
pera
ture
@C
L,T
CL
[oC
]
0 2 4 6 8 10 12200
205
210
215
220
225
230
H2/CO = 3.0
Tin/cool
= 205oC
F/Fbase
= 0.5
H2/CO = 1.5
H2/CO = 2.5
H2/CO = 2.0
Figure 5-16. Reactor bed temperature profiles for inlet and coolant temperature of 205
oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.5, and 3.0.
116
Mass flux ratio, F/Fbase
0.25 0.50 0.75 1.00
Hydro
gen to c
arb
on m
onoxid
e m
ola
r fe
ed r
atio,
H2/C
O
1.5
2.0
2.5
3.0
3.5
4.0 Tin
and TC= 214
oC
Tin
and TC= 210
oC
Tin
and TC= 205
oC
Figure 5-17. Thermal viability map for a FT reactor.
117
CHAPTER 6 EXPERIMENTAL VERIFICATION OF FISCHER-TROPSCH CHEMICAL KINETICS
MODEL
6.1 General Method of Kinetics Data Analysis
Experimental data from ideal reactors: In the process of developing kinetics
expression of any chemical reaction, either it is a catalytic or non-catalytic reaction; a
rate expression must be validated against experimental data. The experimental work for
the kinetics 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 continuously stirred tank reactor
(CSTR) is a complete mixing continuous feed ideal reactor, 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 gradients of any properties, so pressure,
temperature and concentration are identical everywhere 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 kinetics measurement is that the value of the reaction rate could be directly
evaluated for a given operating condition. This directly measured values, however, does
not mean easiness for kinetics measurement. It requires a data set analysis based on a
hypothetical form of the reaction rate that requires 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 fluid flow pattern 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 packed-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 does not require that process. It is called the differential PFR
operated at a very low conversion, so that the average value is a good approximation
instead of the integration method. A differential PFR has the advantage in the kinetics
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 Catalyst Based Packed-Bed Reactor
Experimental work has been performed by a Chemical Engineering department
graduate student, Mr. Robert Colmyer under the supervision of Dr. Helena Hagelin-
Weaver. The experimental operating conditions and the measured data are provided by
Colmyer (2011) and tabulated in Table 6-1. For more information concerning the
experimental work, please refer to his doctoral dissertation entitled “Fischer-Tropsch
Synthesis: Using Nanoparticle Oxides As Supports for Fischer-Tropsch Catalysts”.
From the tabulated data, selectivity data has been plotted in Figures 6-1 and 6-2.
119
6.3 Chemical Kinetics Coefficients
6.3.1 Constant Pressure Packed-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 changing 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 experimental setup since relatively high
conversion of carbon monoxide has been observed through short length of the packed-
bed height. Therefore, differential plug-flow ideal reactor model is not applicable for
experimental system used in Colmyer (2011). As a result, 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 following
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 ideal gases
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 number up to 30
Only paraffin products are considered (neither olefins nor alcohols)
Nitrogen is completely inert
120
With the above assumptions, mole balance of each chemical species could be
written as follows,
0ii
dFr
dW (6-1)
where Fi denotes the molar flow rate of the chemical species i, W is the weight of the
catalyst and ri is the species i reaction rate per unit mass of catalyst which has the units
of [mol/kgcatsec]. This 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 information will lead to a successful analysis. For the chemical kinetics
part, the open-literature work from Yates and Satterfield (1991) has been adopted for
the kinetics expression shown in the previous chapter as Eq. (2-14). From the previous
chapter, a rigorous relationship between each product production rate and lumped
carbon monoxide kinetics has been developed based on stoichiometry and parallel
reactions for carbon monoxide. The production rate for each individual hydrocarbon is
given below,
1
1
11
1
1
n
n k COk
n N p
p
r
r
(6-2)
where rn is the production rate for the hydrocarbon with a carbon number 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
2
1
1
2
11
1
11
n
n
n kkHC CO H
n N p
CO COq
qp
dF kP Pr
dW K P
(6-3)
where PCO and PH2 are the partial pressures of the carbon monoxide and hydrogen
respectively defined as,
2 2
CO CO t
H H t
P y P
P y P
(6-4)
where yCO and yH2 are the mole fractions of the CO and H2 respectively. Although this
model assumes an isobaric condition throughout the packed-bed so the total pressure
remains constant. However, the total number of moles is changing throughout the entire
packed bed based on which products are formed and how 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 carbon 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 calculations. The molar balance for carbon
monoxide is shown below,
COCO
dFr
dW (6-5)
For Eq. (6-5), two different forms of kinetic expression could be applied for the
carbon monoxide consumption rate, rCO 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
relationship is given in Eq. (3-25). Recall this equation here below,
122
1, 2, 3, 1 2 32 3CO CO CO CO n
n
r r r r r r r n r (6-6)
where the total carbon monoxide consumption rate is given by the empirical based form
as,
2
21
CO H
CO
CO CO
kP Pr
K P
(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,
2
1
1
21 1
11
1
11
n
n kN Nk CO H
n N pn n CO CO
p
nkP P
nrK P
(6-8)
Analytically these two equations, Eqs. (6-7) and (6-8), should be identical,
however there could be small deviations 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 consumption 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,
2
1
1
21 1
11
1
11
n
n kN Nk CO HCO
CO n N pn n CO CO
p
nkP PdF
r nrdW K P
(6-9)
Likewise, for hydrogen, water vapor, and nitrogen, their chemical balances are
derived based on each individual hydrocarbon formation chemical reaction as follows,
123
2 2
2
1
1
21 1
11
1
2 1 2 111
n
n kN NkH CO H
H n N pn n CO CO
p
dF kP Pr n r n
dW K P
(6-10)
2 2
2
1
1
21 1
11
1
11
n
n kN NkH O CO H
H O n N pn n CO CO
p
ndF kP P
r nrdW K P
(6-11)
2
20
N
N
dFr
dW (6-12)
So, a total of 34 ODEs for chemical species, n-paraffins with 1~30 carbon
numbers, CO, H2, H2O, and N2, have been developed and the system of differential
equations is numerically solved by the 4th order Runge-Kutta method with appropriate
initial conditions as shown below,
2 2 2 2 2, , ,0, , , 0, @ 0
nHC CO CO o H H o H O N N oF F F F F F F F W (6-13)
6.3.2 General Carbon Number Dependent Chain Growth Probability
As shown in Figures 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 on 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 probability with the hydrocarbon selectivity as follows,
124
1
1
1
1n
nn k
km
m
S n
S m
(6-14)
where Sn 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, 1
m
m
S
m
, represents the amount of moles of hydrocarbons produced
per mole of carbon monoxide consumed, that will be called “carbon specific
hydrocarbon produced” from this point on. From the above relationship between
hydrocarbon selectivity and specific chain growth probability, Eq. (6-14) can be rewritten
as follows,
1
11
1 nn n
k m
mk
S n
S m
(6-15)
From the chain growth probability 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,
11
1
11
m
m
S
S m
(6-16)
22
1
1
21
m
m
S
S m
(6-17)
33
1 2
1
31
m
m
S
S m
(6-18)
125
From Eqs. (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 specific hydrocarbon produced, 1
m
m
S m
. So, an appropriate
evaluation of this unknown quantity would ensure the simulation results to represent the
actual experimental results 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 Figures 6-3 and 6-4. This could
be interpreted as that the chain growth probabilities for the heavier hydrocarbons (C8+)
are not depending on the carbon number. As a result, those heavier hydrocarbons could
be considered to hold constant value chain growth probabilities. So, it is assumed here
that the chain growth probabilities for C8+ hydrocarbons are all equal to a constant
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
the appropriate value for the carbon specific hydrocarbon produced, following
relationship has been considered,
7
min
1 1 8 8
m m m m
m m m m
S S S SSUM
m m m m
(6-19)
As shown in Eq. (6-19), SUMmin is the carbon specific hydrocarbon produced if FT
synthesis only produces 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 predictions 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 fitting value has been set as ±5×106. The products distribution
comparisons with individual chain growth probabilities estimated with the best fitting
results have been illustrated on Figures 6-6 and 6-7 for Runs 20 and 14, respectively,
listed in Table 6-1. In both Figures 6-6 and 6-7, individual chain growth probabilities
values have been showed together with selectivity comparison. As shown in the
comparison Figures 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 hydrocarbon produced, 1
m
m
S
m
. In that
calculation process, reaction kinetics does not matter. They were assigned as moderate
values because it does not matter how fast the syngas is consumed, but rather which
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 Eq. (6-7) where two unknown
parameters, k – reaction rate constant and KCO – CO adsorption constant, will be fitted.
127
Although these are called constants but they are functions of temperature. The reaction
rate constant is governed by the Arrhenius equation as follows,
exp Ao
Ek k
RT
(6-20)
where ko is the pre-exponent factor, EA is the activation energy, R is the gas constant,
and T is the absolute temperature. Adsorption constant is equilibrium constant;
therefore it obeys the van’t Hoff’s equation,
ln
1CO adK H
RT
(6-21)
which could be rewritten as a similar form of Arrhenius equation as follows,
exp adCO
HK A
RT
(6-22)
where A is the pre-exponent factor, Had is the heat of adsorption for carbon
monoxide molecules on a catalyst surface. According to general thermodynamics,
adsorption heat for the chemisorption is always exothermic, Had < 0. With this kinetic
expressions, the Least Square fitting work might be difficult because this system has
four unknowns to be determined, ko, EA, A, and Had. If kinetic constants are specified
for a given temperature with a good accuracy and precision then the number of
unknowns would be reduced by half and the computational task for the Least Square
fitting will be reduced dramatically. So coefficients fitting has been accomplished for a
fixed temperature case, T=220oC, since this temperature is in the middle of its range.
Non-linear regression calculation with a high accuracy requirement might take lots of
computational resources due to solving a system of ODEs with very fine step sizes for
128
both k and KCO. 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 increments for both k and KCO. At first, wide
possible ranges for both k and KCO were chosen; they are from 105 to 103 for both k
and KCO. Contour plotting results are shown in Figure 6-8 (a) where the color represents
the value of sum of square deviations 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 location is depicted in Figure 6-8 (b). In the final run, the best
fitting results could be achieved that gives k = 1.05 × 104 and KCO = 0.0455 with
tolerances of ±5 × 107 and ±2.5× 104 for k and KCO at the given temperate, T = 220oC,
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 same method for a given temperature range of 180 oC ~ 245 oC. 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). The values which result in the smallest deviations are
obtained and they are EA = 42.4 and Had = 118 [kJ/mol]. Also the locations have been
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 EA and Had and the best
fit values are obtained as 43.2 and 116 kJ/mol for EA and Had 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 EA = 43.2 and Had = 116 [kJ/mol], carbon monoxide
conversion behavior over the whole operating temperature range has been plotted in
Figure 6-10 together with the experimental measurements for comparison. From this
Figure 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,
4 1 11.05 10 exp 3.9547exp
493.15
A AE Ek
R T RT
(6-23)
141 10.0455exp 2.3486 10 exp
493.15
ad adCO
H HK
R T RT
(6-24)
where the units are mol/(kgcat sec bar2) and (1/bar) for k and KCO, 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 Figures 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 Idea for Generalization of Selectivity
In the previous sections, both selectivity and kinetics coefficients have been fitted
using the kinetics model with very high accuracy and precision. The kinetics coefficients
130
are, however, fitted into prescribed functional forms (Eqns. 6-23 and 6-24), while the
selectivities are fitted only by some individual values which demonstrates a good
agreement with the measurement results. However, no general trend or functional form
has been deduced yet for the selectivity. 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 cannot be predicted
unless a functional form that provides 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 selectivities for every experimental run) which have been used for
finding the kinetic coefficients are plotted in Figure 6-14. The temperature 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 Figure 6-14, it is
difficult to deduce any general trends according to the following functional dependence
form for the chain growth probability.
2
, , H COfn n T (6-25)
The chain growth probability theoretically depends on the n (product carbon
number), 2H CO (H2/CO molar ratio) and T (reaction temperature). The separation of
variables method is applied assuming those independent variables (n, T, 2H CO ) effects
are independent each other. So it is assumed that the general chain growth probability
consists of three independent functions which are only depending on one variable each;
n - carbon number dependency function, T - temperature dependency function,
131
and 2H CO - hydrogen to carbon monoxide 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
decreases with increasing T and 2H CO . 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 following functional
form,
2
2
1
2
, , H CO
H CO
Cn T
C n T
(6-26)
where C1 and C2 are constants to be determined, is a function only depending on the
carbon 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, C1 and C2, are fixed as unity here.
2
2
1, ,
2H CO
H CO
n Tn T
(6-27)
The carbon number effect has been assigned as a coefficient instead of a function. So
each chain growth probability corresponding to a certain carbon number has its own
coefficients. By doing this way, carbon number dependency could be eliminated but a
series of chain growth probabilities, each is still a function of T and 2H CO , are required
as shown below,
132
2
2
1,
1n H CO
n H CO
TC T
(6-28)
In Eq. (6-28), n is the carbon number specific chain growth probability. Rewriting Eq.
(6-28) yields a convenient form below for further development.
2
1 nn H CO
n
C T
(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 simplified from Eq. (6-29) as follows,
2
1 nn H CO
n T
A
(6-30)
where the subscript T means evaluated under an isothermal condition, nA is the
coefficient relating to the temperature effect, . The experimental measurements on the
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 ratio is
explored first. After several try-outs, the following form has been selected for the H/C
function, .
2
2
0.5
H
H CO
CO
p
p
(6-31)
Substituting the above in Eqn. (6-30), the following is obtained,
2
2
1 Hnn
n COT
pA
p
(6-32)
133
where 2
n nA A . It is noted that Eq. (6-32) represents a linear relationship if nA is a
constant. In Figure 6-15, Eq. (6-32) has been used to fit the experimental data for
carbon numbers from C1 to C7 and also for C8+. The purpose 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 nA s are tabulated in Table 6-3.
It is noted the general profile for nA , 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 manner, the temperature effect could be evaluated using the following
proposed relationship,
1 n
n
n
B T
(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 entire 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 product 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, the functional form describing the
temperature effect has been proposed as the Boltzmann distribution as follows,
134
expE
RT
(6-34)
where E is threshold energy and R is the universal gas constant. With this exponential
form, linearized curve fitting using the model with the experimental data has been
performed and the results are depicted in Figure 6-16. A total of 16 experimental sets
are available for this analysis that indicates more data points than those available in the
2H CO effect analysis discussed above. Substituting Eq. (6-34) into Eq. (6-33), and
taking a natural logarithm yields Eq. (6-35) below,
1 1
ln lnn nn
n
EB
R T
(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 points 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 previous 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 quantitative values. Unlike with the previous
hydrogen to carbon monoxide effect, the slope of the linear curve fit (En/R) in Figure 6-
16 does 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 nE = 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, Eq.
(6-31), and the temperature effect, Eq. (6-34) with the averaged value for the threshold
energy are substituted into the general chain growth probability, Eq. (6-28), to obtain the
following equation,
2
2
10.5
, 1 expH n
n H CO n
CO
p ET C
p RT
(6-36)
This expression is the carbon number dependent chain growth probability
including the reactor temperature and hydrogen to carbon monoxide ratio effects for a
particular catalyst. First it is noted that with a given n from the experimental selectivity,
a Cn can be solved for using Eq. (6-36). In the actual application of Eq. (6-36), we need
to find a single representative Cn for each carbon number. This single coefficient,
,n EffC is called an effective Cn that is obtained by averaging all twenty one solved nC s
from the experimental data set for a particular carbon number. In Table 6-5, ,n EffC is
136
listed for all the carbon numbers. Table 6-5 also provides the standard deviation values
for all the ,n EffC values. In addition to this, carbon number dependent chain growth
probabilities are also compared between experimentally derived values, , exp.fitn using
Eq. (6-15) and calculated values, , funcn using Eq. (6-36) with
,n EffC 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 , exp.fitn and , funcn
.
Relative percent difference on chain growth probability for a particular carbon number
under a specific system condition is defined below,
, exp.fit , func
, exp.fit
% 100n n
n
n
(6-37)
An averaged value for all twenty one n s , n , is also given in Table 6-5 with the
corresponding standard deviations. It is worth noting from 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 Engineering 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 provides a general trend of chain growth probability with respect
to reactor temperature as well as hydrogen to carbon monoxide molar ratio effects. A
mathematical 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
work might help understand the complex nature of the catalytic surface reactions.
138
Table 6-1. Experimental operating conditions and measurement data of carbon monoxide conversion and product selectivities up to C8.
Run T
[oC]
P [bar]
H2/CO [-]
N2 % [vol%]
V [sccm]
XCO
[%]
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 0.6436 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 0.5787 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 4.6607 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 probabilities for cases of T=205oC.
H2/CO = 0.5 H2/CO = 1.0 H2/CO = 2.0
m
m
S m 0.18799 0.19205 0.26809
α1 0.4836 0.4764 0.3923
α2 1.0000 1.0000 0.8588
α3 0.7619 0.8301 0.7666
α4 1.0000 0.9117 0.8117
α5 1.0000 1.0000 0.9261
α6 0.8429 1.0000 0.9572
α7 1.0000 0.9881 0.9718
α8+ 0.9210 0.9460 0.8867
H2/CO = 3.0 H2/CO = 5.0 H2/CO = 10.0
m
m
S m 0.31697 0.38722 0.50616
α1 0.3477 0.2911 0.2233
α2 0.8329 0.7933 0.7632
α3 0.7419 0.7634 0.6760
α4 0.7762 0.7485 0.7457
α5 0.9159 0.8691 0.8007
α6 0.9361 0.8967 0.8446
α7 0.9629 0.9267 0.9207
α8+ 0.8666 0.8409 0.7975
140
Table 6-3. The best fit results; slope of the linearization An for Eq. (6-32).
Carbon number
1 2 3 4
An 1.2049 1.0609 × 102 2.4221 × 102 1.5040 × 102
Carbon number
5 6 7 8+
An 5.5352 × 103 3.0439 × 103 8.0285 × 104 6.7084 × 103
Table 6-4. The best fit results; slope of the linearization, (En/R), for Eq. (6-35).
Carbon number
1 2 3 4
Slope (En/R) -2905.1 -3108.2 -3590.5 -4117.2
Carbon number
5 6 7 8+
Slope (En/R) -2734.4 -2586.7 -3698.3 -5148.9
141
Table 6-5. Effective coefficients for carbon number dependent chain growth probability
,n EffC , relative percent difference on carbon number dependent chain growth
probability, n and their standard deviations.
Carbon
number 1 2 3 4 5 6 7 8+
,n EffC 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
n 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
%
Sele
ctivity
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
180oC
190oC
200oC
205oC
% S
ele
ctivity
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
210oC
215oC
220oC case1
220oC case2
Carbon number, n
1 2 3 4 5 6 7
% S
ele
ctivity
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
225oC
230oC case1
230oC case2
235oC
Carbon number, n
1 2 3 4 5 6 7%
Sele
ctivity
0.0
2.5
5.0
7.5
10.0
12.5
15.0
17.5
240oC case1
240oC case2
245oC case1
245oC case2
Figure 6-1, Selectivity towards hydrocarbons for different temperatures (P=20 bar,
H2/CO/N2 = 6:3:1, V = 62.5 sccm)
143
Carbon number, n
1 2 3 4 5 6 7
% S
ele
ctivity
0
10
20
30
40H2/CO = 0.5
H2/CO = 1
H2/CO = 2
H2/CO = 3
H2/CO = 5
H2/CO = 10
Figure 6-2, Selectivity towards hydrocarbons for different hydrogen to carbon monoxide
feed ratios (P=20 bar, T = 205 oC, V = 62.5 sccm with 10%vol N2)
144
ln (
Sn/n
)
-6
-5
-4
-3
-2
-1
ln (
Sn/n
)
-6
-5
-4
-3
-2
-1
Carbon number, n
1 2 3 4 5 6 7
ln (
Sn/n
)
-7
-6
-5
-4
-3
-2
-1
Carbon number, n
1 2 3 4 5 6 7ln
(S
n/n
)-7
-6
-5
-4
-3
-2
-1
(a) T = 200 oC (b) T = 220 oC
(C) T = 235 oC (d) T = 245 oC case2
Figure 6-3. Product distribution and ASF plot for carbon number 3~7 (P=20 bar,
H2/CO/N2 = 6:3:1, V = 62.5 sccm); (a) T = 200 oC, (b) T = 220 oC, (c) T = 235 oC, and (d) T = 245 oC
145
ln (
Sn/n
)
-7
-6
-5
-4
-3
-2
-1
Carbon number, n
0 1 2 3 4 5 6 7 8
ln (
Sn/n
)
-7
-6
-5
-4
-3
-2
-1
0
(a) H2/CO = 2
(b) H2/CO = 10
Figure 6-4, Product distribution and ASF plot for carbon number 3~7 (P=20 bar, T = 205
oC, V = 62.5 sccm with 10%vol N2); (a) H2/CO = 2 and (b) H2/CO = 10
146
sum of the selectivity divided its carbon number, (Sn/n)
0.2 0.3 0.4 0.5 0.6 0.7
sum
of th
e s
quare
s o
f th
e d
evia
tions
betw
een m
easure
d a
nd c
acula
ted v
alu
es
0.00
0.02
0.04
0.06
0.08
0.2675 0.2680 0.2685 0.2690
0
2e-6
4e-6
6e-6
8e-6
Minimum
Figure 6-5. Finding appropriate value for sum of the selectivity divided its carbon number which makes sum of the squares of the deviation minimum; (T=205 oC, P=20 bar, H2/CO/N2 = 6:3:1, V = 62.5 sccm)
147
S
ele
ctivity
0.00
0.05
0.10
0.15
0.20
0.25
Experimental result
Model
Carbon number, n
0 1 2 3 4 5 6 7 8
Chain
gro
wth
pro
babili
ty
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 6-6. Selectivity comparison between experiment and simulation and chain growth
probability used in the simulation; (T=205oC, P=20 bar, H2/CO =3, V = 62.5 sccm with 10%vol N2)
148
S
ele
ctivity
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Experimental result
Model
Carbon number, n
0 1 2 3 4 5 6 7 8
Chain
gro
wth
pro
babili
ty
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Figure 6-7. Selectivity comparison between experiment and simulation and chain growth
probability used in the simulation; (T=240 oC, P=20 bar, H2/CO/N2 = 6:3:1, V = 62.5 sccm)
149
k
KC
O
10-4
10-2
100
102
10-5
10-4
10-3
10-2
10-1
100
101
102
103
-5
0
5
10
15
20
25
30
(a)
Figure 6-8. Contour plots for determining appropriate kinetic coefficients; (a) First try-out, (b) Second try-out and (c) Final calculation.
150
k
KC
O
1 2 3 4 5 6 7 8 9 10
x 10-4
0.1
0.2
0.3
0.4
0.5
0.6
-6.5
-6
-5.5
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
(b)
Figure 6-8. Contined.
151
k
KC
O
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x 10-4
0.05
0.1
0.15
-6.5
-6
-5.5
-5
-4.5
-4
-3.5
-3
-2.5
-2
(c)
Figure 6-8. Continued.
152
EA
-
Ha
d
10 20 30 40 50 60 70 80 90 10050
60
70
80
90
100
110
120
130
140
150
(a)
Figure 6-9. Contour plots for determining appropriate activation energy and heat of adsorption; (a) First try-out and (b) Final calculation.
153
Activation Energy, EA [kJ/mol]
Head o
f adsorp
tion, -
Ha
d [kJ/m
ol]
38 39 40 41 42 43 44 45 46114
115
116
117
118
119
120
121
122
Figure 6-9. Continued.
154
Temperature, T [oC]
170 180 190 200 210 220 230 240 250
CO
Convers
ion, X
CO [-]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Experiment
Model
Figure 6-10. Carbon monoxide conversion comparison between experimental
measurements and simulation with fitting coefficients.
155
Packed-bed space time, o [g.sec/ccSTP]
0.0 0.2 0.4 0.6 0.8
CO
convers
ion, X
CO [-]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
T = 245 oC
T = 240 oC
T = 235 oC
T = 230 oC
T = 225 oC
T = 220 oC
T = 215 oC
T = 210 oC
T = 205 oC
T = 200 oC
T = 190 oC
T = 180 oC
Figure 6-11. Carbon monoxide conversion profiles in evaluation of comparison with
experimental work.
156
Packed-bed space time, o [g.sec/ccSTP]
0.0 0.2 0.4 0.6 0.8
H2 c
onvers
ion, X
H2
[-]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
T = 245 oC
T = 240 oC
T = 235 oC
T = 230 oC
T = 225 oC
T = 220 oC
T = 215 oC
T = 210 oC
T = 205 oC
T = 200 oC
T = 190 oC
T = 180 oC
Figure 6-12. Hydrogen conversion profiles in evaluation of comparison with
experimental work.
157
Packed-bed space time, o [g.sec/ccSTP]
0.0 0.2 0.4 0.6 0.8
Tota
l num
ber
of
mole
reduction, F
tota
l/ F
tota
l,o [-]
0.6
0.7
0.8
0.9
1.0
T = 180 oC
T = 190 oC
T = 200 oC
T = 205 oC
T = 210 oC
T = 215 oC
T = 220 oC
T = 225 oC
T = 230 oC
T = 235 oC
T = 240 oC
T = 245 oC
Figure 6-13. Total number of mole reduction profiles in evaluation of comparison with
experimental work.
158
Carbon number, n
1 2 3 4 5 6 7 8
Ch
ain
gro
wth
pro
ba
bili
ty,
n [
-]
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
T = 180 oC
T = 190 oC
T = 200 oC
T = 205 oC
T = 210 oC
T = 215 oC
T = 220 oC (1)
T = 220 oC (2)
T = 225 oC
T = 230 oC (1)
T = 230 oC (2)
T = 235 oC
T = 240 oC (1)
T = 240 oC (2)
T = 245 oC (1)
T = 245 oC (2)
(a)
Figure 6-14. Carbon number dependent chain growth probability evaluated for fitting work of the experiment; (a) Temperature dependency and (b) Hydrogen to carbon monoxide dependency.
159
Carbon number, n
1 2 3 4 5 6 7 8
Ch
ain
gro
wth
pro
ba
bili
ty,
n [
-]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
H2/CO = 0.5
H2/CO = 1
H2/CO = 2
H2/CO = 3
H2/CO = 5
H2/CO = 10
(b)
Figure 6-14. Continued.
160
[(
1-
n)/
n]2
0
2
4
6
8
10
12
14
[(1-
n)/
n]2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
H2/CO
0 1 2 3 4 5 6 7 8 9 10
[(1-
n)/
n]2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
H2/CO
0 1 2 3 4 5 6 7 8 9 10
[(1-
n)/
n]2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
n=1, 1 n=2, 2
n=3, 3 n=4, 4
excluded
(a)
Figure 6-15. Linearization of general chain growth probability using Equation (6-32); (a) α1 ~ α4 and (b) α5 ~ α7 and α8+.
161
[(1-
n)/
n]2
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
[(1-
n)/
n]2
0.00
0.01
0.02
0.03
0.04
H2/CO
0 1 2 3 4 5 6 7 8 9 10
[(1-
n)/
n]2
0.000
0.002
0.004
0.006
0.008
0.010
H2/CO
0 1 2 3 4 5 6 7 8 9 10
[(1-
n)/
n]2
0.00
0.02
0.04
0.06
0.08
n=5, 5 n=6, 6
n=7,7n=8+, 8+
excluded
(b) Figure 6-15. Continued.
162
ln [
(1-
n)/
n
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
ln [
(1-
n)/
n
-3.2
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
Inverse temperature, 1000/T [1/K]
1.9 2.0 2.1 2.2
ln [
(1-
n)/
n
-2.8
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
1.9 2.0 2.1 2.2
ln [
(1-
n)/
n
-3.0
-2.8
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
-1.4
n=1, 1n=2, 2
n=3, 3n=4, 4
excluded data points
(a)
Figure 6-16. Linearization of general chain growth probability using Equation (6-35); (a) α1 ~ α4 and (b) α5 ~ α7 and α8+.
163
ln [
(1-
n)/
n
-2.6
-2.4
-2.2
-2.0
-1.8
-1.6
ln [
(1-
n)/
n
-6
-5
-4
-3
-2
-1
Inverse temperature, 1000/T [1/K]
1.9 2.0 2.1 2.2
ln [
(1-
n)/
n
-4.5
-4.0
-3.5
-3.0
-2.5
1.9 2.0 2.1 2.2
ln [
(1-
n)/
n
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
n=5, 5 n=6, 6
n=7, 7n=8+, 8+
excluded data points
(b)
Figure 6-16. Continued.
164
Carbon number, n
0 1 2 3 4 5 6 7 8
Thre
shold
energ
y,
E [
kJ/m
ol]
15
20
25
30
35
40
average valueE
avg = 27.01 [kJ/mol]
std = 4.73 [kJ/mol]
Figure 6-17. Threshold energy from the fitting results and its averaged value.
165
CHAPTER 7 NUMERICAL SIMULATIONS 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 verifications. 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-Scale Channel 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). The 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 dimensions have been tabulated in Table 7-1. As provided in the
Table 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 compare 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 work, WHSV (weight hourly space velocity) has been defined only for
the carbon monoxide component. The definition for WHSCO is given below,
1WHSV COCO
cat
m
hrm
(7-1)
where COm is carbon monoxide feed mass flow rate and mcat is total mass of catalyst
loaded in the reactor. A simple mathematical manipulation gives the relation between
WHSVCO and syngas feed mass flux, syngasm which is convenient for the FLUENT input
as follows,
"
WHSV
3600
bulk CO
Syngas
CO
Lm
Y
(7-2)
where bulk is catalytic bed bulk density, L is length of the reactor, and YCO is inlet
mass fraction for the carbon monoxide (YCO =0.875 for H2/CO = 2).
It is important to note that the kinetics 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 successfully 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 hydrogen mass fractions are changing.
The pressure effect on the syngas consumption 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 case 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 effectively 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 WHSVCO and Wall Temperature Effect
Figures 7-2 through 7-6 show carbon monoxide, hydrogen and water vapor mass
fractions in the gaseous phase at the centerline of the channel for different WHSVCO
values of WHSVCO = 0.5, WHSVCO = 1, WHSVCO = 10, WHSVCO = 100, and WHSVCO =
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 WHSVCO = 0.5, Twall = 540K, P = 20 bar, and H2/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 conversion. Syngas
consumption rate increases considerably as the wall temperature is increased
regardless of the syngas mass flow rate. Syngas consumption is more sensitive to wall
temperature for the low WHSVCO case. For the fixed outlet pressure case, the inlet
pressure is depending on the total mass flow rate, in other words, on the WHSVCO.
Increasing WHSVCO 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 WHSVCO yields less residence time so the
reactants do not have enough time to react. This will result in more conversion into
hydrocarbon for the low WHSVCO case. Therefore, low WHSVCO cases have more
reactive time under the same temperatures as well as more sensitive to the wall
temperature. This is clearly shown in Figures 7-2 through 7-6. In addition to this, two
comparisons are shown in Figures 7-7 and 7-8. All five different WHSVCO 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 WHSVCO cases are more
obvious than the low WHSVCO cases but no data is available for low WHSVCO cases for
the 600K condition. Syngas exit conversions are shown as a function of wall
temperature in Figures 7-9 and 7-10. Temperature dependency for both carbon
monoxide and hydrogen conversions is depicted in Figure 7-9 for WHSVCO =1, H2/CO =
169
2 and P = 20 bar case. In the case illustrated in Figure 7-9, there is not much difference
between CO and H2 conversions but this model is still distinguished from those who use
a constant CO and H2 consumption ratio. As the reactor temperature increases,
differences between CO and H2 conversions become more distinct. The sysgas mass
flow rate and wall temperature effects on the exit syngas conversion are illustrated in
Figures 7-10 and 7-11.
7.2.3 Outlet Pressure Effect
Pressure effects on syngas conversion are shown in Figures 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 WHSVCO = 1, T = 520K and H2/CO
= 2. For both CO and H2, their mass fractions drop smoothly from their inlet values of
0.875 for CO and 0.125 for H2 along the axial distance. The exit 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 actual 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 (WHSVCO = 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 exit carbon monoxide and
hydrogen mass fractions decrease monotonously with an increasing exit pressure. The
pressure effect on syngas consumption is noticeable in this case due to a relatively high
170
temperature and low WHSVCO. The pressure effect on syngas consumption for a higher
mass flow case is depicted in Figure 7-14; WHSVCO = 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 WHSVCO. The exit 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 exit
syngas mass fractions in the gaseous phase decrease monotonously with the exit
pressure. A direct 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 with the low mass flow case. This is clearly illustrated in
Figure 7-16. How the pressure effect could be amplified by manipulating with the
syngas mass flow rates.
7.2.4 Inlet Hydrogen to Carbon Monoxide Ratio Effect
In the previous section, It has been shown the weight-hourly-space-velocity,
WHSVCO (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 effects but without individual hydrocarbon
production rates. 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 WHSVCO = 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 ratio. 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
WHSVCO. This is because weight-hourly-space-velocity is based on only the carbon
monoxide species. As shown in the mass flux-WHSVCO relation, Eq. (7-2), the syngs
mass flux will be changed if the CO mass fraction is changed for a constant WHSVCO. A
constant WHSVCO 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 are the same
but the total mass flow rates are all different. At a glance of Figure 7-17, one could
deduce that a higher H2/CO ratio yields more syngas consumption. Actually that is true
but it cannot be verified before the syngas conversion comparison is made. So, the
reactor centerline CO conversions are presented as a function of the axial distance in
fig. 7-18. Under the given conditions of WHSVCO = 1, T = 540K, and P = 20 bar, the exit
CO conversion is increasing with increasing H2/CO input molar ratio up to H2/CO = 4.
The reactants exit conversions as a function of H2/CO input molar ratio are illustrated in
Figure 7-19. Hydrogen is the limiting species in the low H2/CO input molar ratio region
and the carbon monoxide is the limiting species in the higher H2/CO input molar ratio
region. And the CO conversion overtakes the hydrogen conversion at around H2/CO =
2.4 where the hydrogen conversion starts to flatten out.
172
7.3 Micro-Scale Channel FLUENT Modeling
7.3.1 Micro-Scale Reactor Geometry
Micro-scale simulations have also been carried out using the ANSYS-FLUENT
software package. The micro-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 the meso-scale reactor. However, the micro-scale numerical
simulation is quite different from the previous macro- and meso-scale simulations in the
approach 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 been developed in Chapter 6, those are implemented for representing a novel FT
catalyst instead of using kinetics coefficient and fixed carbon number independent 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.
2
2sec1
CO H
CO
catCO CO
kP P molr
kgK P
(7-3)
2
43,2003.9547exp
seccat
molk
RT kg bar
(7-4)
14 116,000 12.3486 10 expCOK
RT bar
(7-5)
173
2
10.5
27,014.2, 1 exp
H
n n
CO
pT HC C
p RT
(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 whole new UDF (user-defined-
function) must be written to include the above for the FLUENT simulation. Reactor
working conditions, in other words - input parameters for FLUENT, have been tabulated
in Table 7-4.
7.3.2 Mass Flux Effect on Conversion and Product Distribution
The mass flux effects on both syngas conversion and product distribution have
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 fraction denotes the remained reactant fraction within the gaseous
phase whose mass fraction is also decreasing. The conventional reactant conversion
expression is shown in the previous chapter but is recalled here,
,
,
CO in CO
CO
CO in
N NX
N
(7-7)
ANSYS FLUENT calculation is based on the mass basis. So, the molar flow rate of
carbon monoxide could be written as follows,
,
CO GCO G
W CO m
YN m
M
(7-8)
174
where YCO is the carbon monoxide mass fraction inside the gaseous phase, MW,CO is
the molecular weight of the carbon monoxide, G and m are densities for the gaseous
phase and the mixture phase, respectively, G is the gaseous phase volume fraction,
and m is the mixture mass flow rate. After plugging Eq. (7-8) into the definition of
conversion, Eq. (7-7), and simplification, we have the carbon monoxide conversion as
follows,
,
, , ,
1m inCO G G
CO
CO in G in m G in
YX
Y
(7-9)
With a pure syngas inlet condition, Eq. (7-9) could be further simplified as,
,
1 CO GCO G
CO in m
YX
Y
(7-10)
where the term (GG)/m has its own physical meaning, which is gaseous mass
fraction. This is why the conversion expresses 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,
2
2
2 ,
1H G
H G
H in m
YX
Y
(7-11)
Figure 7-20 shows the change of the gaseous phase mass fraction, defined as
Ygas = (GG)/ m, along the micro-scale reactor channel for different WHSVCO cases,
which are runs 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 be acquired from the low WHSVCO 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 simulations, the hydrogen
conversion is slightly greater 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 simulations, the total amount of converted
syngas is larger for higher WHSVCO cases although the fractional conversion is lower.
The exit syngas conversion against WHSVCO 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 with 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 higher conversion. This is also the same tendency with previous simulations.
Products distributions are depicted in Figure 7-23. Unlike the previous simulations,
individual carbon number dependent chain growth probability in a functional form, Eq.
(6-39), has been applied here. In previous simulations, individual carbon number
dependent chain growth probability has been assigned as a fixed value irrelevant of the
operating conditions although a comprehensive model for the chain growth probability
has been developed. After the comprehensive analysis for product selectivity in Chapter
6, individual carbon number dependent chain growth probability as a function of
temperature and hydrogen to carbon monoxide input molar ratio has been adopted in
the micro-channel simulation. In Eq. (6-39), individual carbon number dependent chain
growth probability equation, neither mass flow effect nor WHSVCO effect has been
176
considered. However, the deviation between carbon monoxide and hydrogen
consumption ratio and hydrogen to carbon 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 Effect on Conversion and Product Distribution
The temperature effects on both syngas conversion and product distribution have
been studied here. A total of five different cases, tabulated in Table 7-4 as run numbers
4~8, have been simulated for the same operating conditions; WHSVCO = 10 [1/hr], Tin =
485 K, Pout = 20 bar, and H2/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 WHSVCO (or mass flux) yields a longer residence time which causes more
reaction to occur. So, the gaseous phase mass fraction decreases with decreasing
mass flow (or WHSVCO). Every single reaction is accelerated with increasing reactor
temperature. So, the accelerated reaction rate will result in further decrease of gaseous
phase mass fraction since all the reactants (H2 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
temperature case in the beginning. But it will be flattened 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
is 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 Twall = 540 K and 560 K. This is why the gaseous phase mass
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
not 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
phase mass fraction are different. As shown in Figure 7-26, syngas conversion
increases 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 reactants are consumed. However, products distribution is not directly proportional
to the temperature. As provided in Figure 7-27 for the products distribution, lower
carbon number hydrocarbons favor higher reactor temperature, while heavier
hydrocarbons prefer lower reactor temperature. For carbon numbers 1~3, higher reactor
temperature cases result in higher selectivities. For the mid-ranged hydrocarbons, in
this particular case carbon numbers 4~6, all the selectivity values remain the same
regardless of the reactor temperature. And for higher hydrocarbons, 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 temperature. To summarize, in the wall temperature of 560 K cases, the
syngas is consumed very fast, but is converted into lighter hydrocarbons, mainly. This is
why the liquid phase exit mass fraction is dropped after the peak point.
178
7.3.4 Pressure Effects on Syngas Conversion and Products Distribution
The pressure effects on both syngas conversion and products distribution have
been studied. The gaseous phase mass fraction profiles along the flow direction for
different pressure cases are plotted in Figure 7-28. For 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 phase exit mass fraction are found
to be proportional to the outlet pressure which is illustrated in Figure 7-30. Products
distributions are all identical in this pressure range.
7.3.5 Hydrogen to Carbon Monoxide Molar Ratio Effect on Conversion and Products Distribution
As provided in the Table 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 hydrogen 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 all 8 cases, every input
parameter is identical except the hydrogen flow rate. Gaseous phase mass fractions for
8 different H2/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, H2/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 carbon 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 conversions for higher hydrogen 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 explained 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 monoxide
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 molar
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 flattening 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 scales in order to characterize reactor performance with respect to various
operating conditions. Thermal 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 also 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,
however, 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 approach
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 been
developed in Chapter 6, those are implemented for representing a novel FT catalyst
instead of using kinetics coefficient and fixed carbon number independent 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, first notable difference is
that the temperature runaway has not been observed (both meso- and micro- scales)
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 involved with
inherent disadvantage. Due to low reactor temperatures resulted by higher heat transfer,
catalytic reaction might not be activated in the low 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
follows : a higher syngas mass flow rate yields lower conversion due to less residence
time. Increasing operating temperature gives higher conversion and the temperature
dependency is exponential. A higher system pressure is favored due to the general
nature of chemical reaction with decreasing total number of moles of reactants following
the reaction. An increasing 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 operating 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 carbon monoxide feed molar ratio. A
higher syngas conversion does not guarantee a higher yield on liquid phase or higher
hydrocarbons, in other words wanted-products.
182
Table 7-1. Reactor channel geometry and dimensions for both meso- and micro- scale reactors.
Meso Micro
Reactor shape Rectangular channel Rectangular channel
Smallest length Channel height Channel height
Aspect ratio (W/H) 12.5 37.5
Width 1.27 102
m 7.620 103
m (0.3”)
Height 1.016 103
m 2.124 104
m (0.008”)
Length 1.778 102
m 4.064 102
m (1.6”)
Particle diameter 200 m 2 m
183
Table 7-2. Simulation input conditions for the meso-scale channel reactor
Run # WHSVCO Tin [K] Twall [K] Pout [bar] H2/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
29 100 485 600 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
H2/CO yCO yH2 YCO YH2
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. Simulation input conditions for micro-scale channel reactor
Run # WHSVCO 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 20 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
Syngas
Hydrocarbon
and water
L
L
HW
2D computation domain
Catalyst pellet
2D computation domain
F-T Reactants
CO & H2 F-T Products
mainly
hydrocarbonz = 0
Figure 7-1. Schematic of slit-like Meso- and Micro- scale channels and computational
domain.
187
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
ma
ss f
raction
in
ga
se
ou
s p
ha
se
[-]
0.4
0.5
0.6
0.7
0.8
0.9
Twall
= 500 K
Twall
= 510 K
Twall
= 520 K
Twall
= 530 K
Twall
= 540 K
WHSVCO
= 0.5/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(a) Figure 7-2. Mass fraction in gaseous phase as a function of axial distance at the center
of channel; WHSVCO =0.5, Tin = 485K, Pout = 20 bar and H2/CO = 2 for various wall temperatures; (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
188
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
Twall
= 500 K
Twall
= 510 K
Twall
= 520 K
Twall
= 530 K
Twall
= 540 K
WHSVCO
= 0.5/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(b)
Figure 7-2. Continued.
189
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.0
0.1
0.2
0.3
0.4
0.5
Twall
= 540 K
Twall
= 530 K
Twall
= 520 K
Twall
= 510 K
Twall
= 500 K
WHSVCO
= 0.5/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(c)
Figure 7-2. Continued.
190
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Twall
= 500 K
Twall
= 520 K
Twall
= 540 K
Twall
= 550 K
WHSVCO
= 1.0/hr
Tin = 485 k
Pout
= 20 bar
H2/CO = 2
(a)
Figure 7-3. Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 1, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures; (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
191
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.07
0.08
0.09
0.10
0.11
0.12
0.13
Twall
= 500 K
Twall
= 520 K
Twall
= 540 K
Twall
= 550 K
WHSVCO
= 1.0/hr
Tin = 485 k
Pout
= 20 bar
H2/CO = 2
(b)
Figure 7-3. Continued.
192
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.05
0.10
0.15
0.20
0.25
Twall
= 550 K
Twall
= 540 K
Twall
= 520 K
Twall
= 500 K
WHSVCO
= 1.0/hr
Tin = 485 k
Pout
= 20 bar
H2/CO = 2
(c)
Figure 7-3. Continued.
193
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
Twall
= 500 K
Twall
= 540 K
Twall
= 600 KWHSVCO
= 10/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(a)
Figure 7-4. Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 10, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
194
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.095
0.100
0.105
0.110
0.115
0.120
0.125
0.130
Twall
= 540 K
Twall
= 500 K
Twall
= 600 K
WHSVCO
= 10/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(b)
Figure 7-4. Continued.
195
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
WHSVCO
= 10/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(c)
Figure 7-4. Continued.
196
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.83
0.84
0.85
0.86
0.87
0.88
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
WHSVCO
= 100/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(a)
Figure 7-5. Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 100, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
197
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.118
0.119
0.120
0.121
0.122
0.123
0.124
0.125
0.126
Twall
= 540 K
Twall
= 500 K
Twall
= 600 KWHSV
CO = 100/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(b)
Figure 7-5. Continued.
198
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass f
raction in g
aseous p
hase [
-]
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
WHSVCO
= 100/hr
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(c)
Figure 7-5. Continued.
199
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass fra
ction in g
aseous p
ha
se [
-]
0.871
0.872
0.873
0.874
0.875
0.876
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
(a)
Figure 7-6. Mass fraction in gaseous phase as a function of axial distance at the center of channel; WHSVCO = 1000, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperatures, (a) CO mass fraction, and (b) H2 mass fraction, and (c) H2O mass fraction.
200
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.1242
0.1244
0.1246
0.1248
0.1250
Twall
= 540 K
Twall
= 500 K
Twall
= 600 K
(b)
Figure 7-6. Continued.
201
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
(c)
Figure 7-6. Continued.
202
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
ma
ss f
raction
in
ga
se
ou
s p
ha
se
[-]
0.4
0.5
0.6
0.7
0.8
0.9
WHSVCO
= 103 [1/hr]
WHSVCO
= 102 [1/hr]
WHSVCO
= 10 [1/hr]
WHSVCO
= 1.0 [1/hr]
WHSVCO
= 0.5 [1/hr]
(a)
Figure 7-7. Mass fraction in gaseous phase as a function of axial distance at the center of channel; Twall = 540 K, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various mass flow, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
203
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.05
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
WHSVCO
= 103 [1/hr]
WHSVCO
= 102 [1/hr]
WHSVCO
= 10 [1/hr]
WHSVCO
= 1.0 [1/hr]
WHSVCO
= 0.5 [1/hr]
(b)
Figure 7-7. Continued.
204
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.0
0.1
0.2
0.3
0.4
0.5
WHSVCO
= 0.5 [1/hr]
WHSVCO
= 1.0 [1/hr]
WHSVCO
= 10 [1/hr]
WHSVCO
= 102 [1/hr]
WHSVCO
= 103 [1/hr]
(c)
Figure 7-7. Continued.
205
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
WHSVCO
= 103 [1/hr]
WHSVCO
= 102 [1/hr]
WHSVCO
= 10 [1/hr]
Tin = 485 K
Twall
= 600 K
H2/CO = 2
Pout
= 20 bar
(a)
Figure 7-8. Mass fraction in gaseous phase as a function of axial distance at the center
of channel; Twall = 600 K, Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various mass flow, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
206
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.095
0.100
0.105
0.110
0.115
0.120
0.125
0.130
WHSVCO
= 103 [1/hr]
WHSVCO
= 102 [1/hr]
WHSVCO
= 10 [1/hr]
Tin = 485 K
Twall
= 600 K
H2/CO = 2
Pout
= 20 bar
(b)
Figure 7-8. Continued.
207
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Tin = 485 K
Twall
= 600 K
H2/CO = 2
Pout
= 20 bar
WHSVCO
= 103 [1/hr]
WHSVCO
= 102 [1/hr]
WHSVCO
= 10 [1/hr]
(c)
Figure 7-8. Continued.
208
Wall temperature, Twall [K]
500 510 520 530 540 550
Reacta
nt %
convers
ion @
exit, X
CO o
r X
H2 [%
]
10
20
30
40
50
60
70
WHSVCO
= 1
Tin = 485 K
H2/CO = 2
Pout
= 20 bar
COH
2
Figure 7-9. CO and H2 exit conversion as a function of wall temperature; WHSVCO = 1,
Tin = 485 K, Pout = 20 bar and H2/CO = 2.
209
Wall temperature, Twall [K]
500 520 540 560 580 600
Carb
on m
onoxid
e %
convers
ion @
exit, X
CO [%
]
0.01
0.1
1
10
100
Tin = 485 K
H2/CO = 2
Pout
= 20 bar
WHSVCO
= 1
WHSVCO
= 10
WHSVCO
= 100
WHSVCO
= 1000
WHSVCO
= 0.5
(a)
Figure 7-10. Exit conversion as a function of wall temperature; Tin = 485 K, Pout = 20 bar
and H2/CO = 2 for various inlet mass flows, (a) CO conversion and (b) H2 conversion.
210
Wall temperature, Twall [K]
500 520 540 560 580 600
Hydro
gen %
convers
ion @
exit, X
H2 [%
]
0.01
0.1
1
10
100
Tin = 485 K
H2/CO = 2
Pout
= 20 bar
WHSVCO
= 1
WHSVCO
= 10
WHSVCO
= 100
WHSVCO
= 1000
WHSVCO
= 0.5
(b)
Figure 7-10. Continued.
211
WHSVCO [1/hr]
1 10 100 1000
Carb
on m
onoxid
e %
convers
ion @
exit, X
CO [%
]
0.01
0.1
1
10
100
Tin = 485 K
H2/CO = 2
Pout
= 20 bar
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
(a)
Figure 7-11. Exit conversion as a function of weight hourly space velocity of carbon
monoxide, WHSVCO [1/hr]; Tin = 485 K, Pout = 20 bar and H2/CO = 2 for selected wall temperatures, (a) CO conversion and (b) H2 conversion.
212
WHSVCO [1/hr]
1 10 100 1000
Hydro
gen %
convers
ion @
exit, X
H2 [%
]
0.01
0.1
1
10
100
Tin = 485 K
H2/CO = 2
Pout
= 20 bar
Twall
= 500 K
Twall
= 540 K
Twall
= 600 K
(b)
Figure 7-11. Continued.
213
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.78
0.80
0.82
0.84
0.86
0.88
Pout
= 10 bar
Pout
= 15 bar
Pout
= 20 bar
Pout
= 30 bar
Pout
= 40 bar
WHSVCO
= 1
Twall
= 520 K
H2/CO = 2
Tin = 485 K
(a)
Figure 7-12. Mass fraction in gaseous phase as a function of axial distance at the center
of channel; WHSVCO = 1, Twall = 520 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
214
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.110
0.112
0.114
0.116
0.118
0.120
0.122
0.124
0.126
Pout
= 10 bar
Pout
= 15 bar
Pout
= 20 bar
Pout
= 30 bar
Pout
= 40 bar
WHSVCO
= 1
Twall
= 520 K
H2/CO = 2
Tin = 485 K
(b)
Figure 7-12. Continued.
215
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Pout
= 40 bar
Pout
= 30 bar
Pout
= 20 bar
Pout
= 15 bar
Pout
= 10 bar
WHSVCO
= 1
Twall
= 520 K
H2/CO = 2
Tin = 485 K
(c)
Figure 7-12. Continued.
216
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
Pout
= 10 bar
Pout
= 15 bar
Pout
= 20 bar
Pout
= 30 bar
Pout
= 40 bar
WHSVCO
= 10
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(a)
Figure 7-13. Mass fraction in gaseous phase as a function of axial distance at the center
of channel; WHSVCO = 10, Twall = 600 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
217
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.07
0.08
0.09
0.10
0.11
0.12
0.13
Pout
= 10 bar
Pout
= 15 bar
Pout
= 20 bar
Pout
= 30 bar
Pout
= 40 bar
WHSVCO
= 10
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(b)
Figure 7-13. Continued.
218
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.05
0.10
0.15
0.20
0.25
Pout
= 40 bar
Pout
= 30 bar
Pout
= 20 bar
Pout
= 15 bar
Pout
= 10 bar
WHSVCO
= 10
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(c)
Figure 7-13. Continued.
219
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass f
raction in g
aseous p
hase [
-]
0.80
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
Pout
= 10 bar
Pout
= 15 bar
Pout
= 20 bar
Pout
= 30 bar
Pout
= 40 bar
WHSVCO
= 100
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(a)
Figure 7-14. Mass fraction in gaseous phase as a function of axial distance at the center
of channel; WHSVCO = 100, Twall = 600 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
220
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.112
0.114
0.116
0.118
0.120
0.122
0.124
0.126
Pout
= 10 bar
Pout
= 15 bar
Pout
= 20 bar
Pout
= 30 bar
Pout
= 40 bar
WHSVCO
= 100
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(b)
Figure 7-14. Continued.
221
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Pout
= 40 bar
Pout
= 30 bar
Pout
= 20 bar
Pout
= 15 bar
Pout
= 10 bar
WHSVCO
= 100
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(c)
Figure 7-14. Continued.
222
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
mass fra
ction in g
aseous p
hase [-]
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
WHSVCO
= 100
WHSVCO
= 10
Pout
= 10 bar
P
out = 20 bar
P
out = 40 bar
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(a)
Figure 7-15. Mass fraction comparison between different WHSVCOs for several outlet
pressure cases. Twall = 600 K, Tin = 485 K, and H2/CO = 2 for various exit pressure conditions, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
223
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.07
0.08
0.09
0.10
0.11
0.12
0.13
WHSVCO
= 100
WHSVCO
= 10
Pout
= 10 bar
Pout
= 20 bar
Pout
= 40 bar
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(b) Figure 7-15. Continued.
224
Dimensionless axial distance [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.05
0.10
0.15
0.20
0.25
WHSVCO
= 100
WHSVCO
= 10
Pout
= 40 bar
Pout
= 20 bar
Pout
= 10 bar
Twall
= 600 K
H2/CO = 2
Tin = 485 K
(c)
Figure 7-15. Continued.
225
15
20
25
30
35
40
45
XCO
XH2
Outlet gauge pressure, Pout [bar]
10 15 20 25 30 35 40
Reacta
nt %
convers
ion, X
CO o
r X
CO
[%]
0
10
20
30
40
50
60
WHSVCO
= 1
WHSVCO
= 10
WHSVCO
= 100
Twall
= 600 K
H2/CO = 2
Tin = 485 K
Twall
= 520 K
H2/CO = 2
Tin = 485 K
Figure 7-16. Reactants exit conversions as a function of exit pressure; Tin = 485 K, and
H2/CO = 2 for various inlet mass flows
226
Dimensionless axial distance, Z [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
ma
ss f
raction
in
ga
se
ou
s p
ha
se
[-]
0.4
0.5
0.6
0.7
0.8
0.9
1.0
H2/CO = 1.0
H2/CO = 1.5
H2/CO = 2.0
H2/CO = 2.5
H2/CO = 3.0
H2/CO = 3.5
H2/CO = 4.0
WHSVCO
= 1
Twall
= 540 K
Pout
= 20 bar
Tin = 485 K
(a)
Figure 7-17. Mass fraction in gaseous phase as a function of axial distance at the center
of channel; WHSVCO = 1, Twall = 540 K, Tin = 485 K, and P = 20 bar for various H2/CO conditions, (a) CO mass fraction, (b) H2 mass fraction, and (c) H2O mass fraction.
227
Dimensionless axial distance, Z [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 m
ass fra
ction in g
aseous p
hase [-]
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
H2/CO = 1.0
H2/CO = 1.5
H2/CO = 2.0
H2/CO = 2.5
H2/CO = 3.0
H2/CO = 3.5
H2/CO = 4.0
WHSVCO
= 1
Twall
= 540 K
Pout
= 20 bar
Tin = 485 K
(b)
Figure 7-17. Continued.
228
Dimensionless axial distance, Z [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2O
mass fra
ction in g
aseous p
hase [-]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
H2/CO = 4.0
H2/CO = 3.5
H2/CO = 3.0
H2/CO = 2.5
H2/CO = 2.0
H2/CO = 1.5
H2/CO = 1.0
WHSVCO
= 1
Twall
= 540 K
Pout
= 20 bar
Tin = 485 K
(c)
Figure 7-17. Continued.
229
Dimensionless axial distance, Z [-]
0.0 0.2 0.4 0.6 0.8 1.0
CO
convers
ion, X
CO [-]
0.0
0.2
0.4
0.6
0.8
1.0
H2/CO = 4.0
H2/CO = 3.5
H2/CO = 3.0
H2/CO = 2.5
H2/CO = 2.0
H2/CO = 1.5
H2/CO = 1.0
WHSVCO
= 1
Twall
= 540 K
Pout
= 20 bar
Tin = 485 K
(a)
Figure 7-18. Conversion as a function of axial distance at the center of channel;
WHSVCO = 1, Twall = 540 K, Tin = 485 K, and P = 20 bar for various H2/CO conditions, (a) CO conversion and (b) H2 conversion.
230
Dimensionless axial distance, Z [-]
0.0 0.2 0.4 0.6 0.8 1.0
H2 c
onvers
ion, X
H2 [-]
0.0
0.2
0.4
0.6
0.8
H2/CO = 4.0
H2/CO = 3.5
H2/CO = 3.0
H2/CO = 2.5
H2/CO = 2.0
H2/CO = 1.5
H2/CO = 1.0
WHSVCO
= 1
Twall
= 540 K
Pout
= 20 bar
Tin = 485 K
(b)
Figure 7-18. Continued.
231
Hydrogen to carbon monoxide feed ratio, HC [-]
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Reacta
nt
% c
onvers
ion @
exit,
XC
O &
XH
2 [
%]
20
30
40
50
60
70
80
XCO
XH2
WHSVCO
= 1
Twall
= 540 K
Pout
= 20 bar
Tin = 485 K
Figure 7-19. CO and H2 exit conversion as a function of inlet H2/CO conditions;
WHSVCO = 1, Twall = 540 K, Tin = 485 K, and Pout = 20 bar.
232
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
Gaseous p
hase m
ass fra
ction, Y
gas [-]
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
Tin = 485 K
Twall
= 500 K
Pout
= 20 bar
H2/CO = 2
WHSVCO
= 100
WHSVCO
= 10
WHSVCO
= 1
Figure 7-20. Mass fraction for gaseous phase profiles as a function of downstream
location; Tin = 485 K, Twall = 500 K, Pout = 20 bar and H2/CO = 2 for various WHSVCO conditions.
233
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
Syng
as c
onvers
ion
, X
CO o
r X
H2 [-]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Tin = 485 K
Twall
= 500 K
Pout
= 20 bar
H2/CO = 2
WHSVCO
= 100
WHSVCO
= 10
WHSVCO
= 1
WHSVCO
= 1
WHSVCO
= 10
WHSVCO
= 100
(a) XCO
(b) XH2
Figure 7-21. Syngas conversion as a function of downstream location; Tin = 485 K, Twall
= 500 K, Pout = 20 bar and H2/CO = 2 for various WHSVCO conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
234
WHSVCO [1/hr]
0 20 40 60 80 100Liq
uid
phase m
ass f
raction
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Exit c
onvers
ion,
XC
O a
nd X
H2 [
-]
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Tin = 485 K
Twall
= 500 K
Pout
= 20 bar
H2/CO = 2
XCO
XH2
Figure 7-22. Syngas exit conversion and liquid phase exit mass fraction as a function of
weight hourly space velocity for carbon monoxide, WHSVCO; Tin = 485 K, Twall = 500 K, Pout = 20 bar and H2/CO = 2.
235
carbon number, n [-]
8 9 10 11 12 13 14 15
Ln(W
n/n
)
-6.0
-5.8
-5.6
-5.4
-5.2
-5.0
-4.8
carbon number, n [-]
1 2 3 4 5 6 7
-6
-5
-4
-3
-2
-1
WHSVCO
= 1 [1/hr]
WHSVCO
= 10 [1/hr]
WHSVCO
= 100 [1/hr]
Figure 7-23. WHSVCO effect on hydrocarbon distribution at the exit; Tin = 485 K, Twall =
500 K, Pout = 20 bar and H2/CO = 2.
236
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
Gaseous p
hase m
ass fra
ction, Y
gas [-]
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
WHSVCO
= 10
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
Twall
= 480 K
Twall
= 500 K
Twall
= 520 K
Twall
= 540 K
Twall
= 560 K
Figure 7-24. Mass fraction for gaseous phase profiles as a function of downstream
location; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperature conditions.
237
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Syngas c
onvers
ion, X
CO o
r X
H2 [-]
0.0
0.2
0.4
0.6
0.8
1.0
Twall
= 480 K
Twall
= 500 K
Twall
= 520 K
Twall
= 540 K
Twall
= 560 K
WHSVCO
= 10
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(a) XCO
(b) XH2
Figure 7-25. Syngas conversion as a function of downstream location; WHSVCO = 10
[1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperature conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
238
Wall temperature, Twall [K]
480 500 520 540 560Liq
uid
phase m
ass f
raction
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Exit c
onvers
ion,
XC
O a
nd X
H2 [
-]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
WHSVCO
= 10 [1/hr]
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
XCO
XH2
Figure 7-26. Syngas exit conversion and liquid phase exit mass fraction as a function of
wall temperature; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2.
239
carbon number, n [-]
8 9 10 11 12 13 14 15
Ln(W
n/n
)
-6.6
-6.4
-6.2
-6.0
-5.8
-5.6
-5.4
-5.2
-5.0
-4.8
carbon number, n [-]
1 2 3 4 5 6 7
-6
-5
-4
-3
-2
-1
0
Twall
= 480 K
Twall
= 500 K
Twall
= 520 K
Twall
= 540 K
Twall
= 560 K
Figure 7-27. Wall temperature effect on hydrocarbon distribution at the exit; WHSVCO =
10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2.
240
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
Gaseous p
hase m
ass fra
ction, Y
gas [-]
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00 WHSVCO
= 10 [1/hr]
Tin = 485 K
Twall
= 500 K
H2/CO = 2
Pout
= 10 bar
Pout
= 20 bar
Pout
= 30 bar
Figure 7-28. Mass fraction for gaseous phase profiles as a function of downstream
location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2 for various outlet pressure conditions.
241
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
Syng
as c
onvers
ion
, X
CO o
r X
H2 [
-]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Pout
= 10 bar
Pout
= 20 bar
Pout
= 30 bar
(a) XCO
(b) XH2
WHSVCO
= 10 [1/hr]
Tin = 485 K
Twall
= 500 K
H2/CO = 2
Figure 7-29. Syngas conversion as a function of downstream location; WHSVCO = 10
[1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2 for various outlet pressure conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
242
Outlet pressure, Pout [bar]
5 10 15 20 25 30 35
Liq
uid
phase m
ass fra
ction
0.116
0.117
0.118
0.119
0.120
0.121
0.122
0.123
0.124
Exit c
onvers
ion, X
CO a
nd X
H2 [-]
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
WHSVCO
= 10 [1/hr]
Tin = 485 K
Twall
= 500 K
H2/CO = 2
XCO
XH2
Figure 7-30. Syngas exit conversion and liquid phase exit mass fraction as a function of
outlet pressure; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2.
243
carbon number, n [-]
8 9 10 11 12 13 14 15
Ln(W
n/n
)
-6.0
-5.8
-5.6
-5.4
-5.2
-5.0
-4.8
carbon number, n [-]
1 2 3 4 5 6 7
-6
-5
-4
-3
-2
-1
Pout
= 10 bar
Pout
= 20 bar
Pout
= 30 bar
Figure 7-31. Outlet pressure effect on hydrocarbon distribution at the exit; WHSVCO = 10
[1/hr], Tin = 485 K, Twall = 500 K and H2/CO = 2.
244
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
Gaseous p
hase m
ass fra
ction, Y
gas [-]
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
H2/CO = 1
H2/CO = 1.5
H2/CO = 2
H2/CO = 2.5
H2/CO = 3
H2/CO = 3.5
H2/CO = 4
WHSVCO
= 10
Tin = 485 K
Twall
= 500 K
Pout
= 20 bar
Figure 7-32. Mass fraction for gaseous phase profiles as a function of downstream
location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar for various hydrogen to carbon monoxide feed ratio conditions.
245
Dimensionless axial distance, z [-]
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Syngas c
onvers
ion, X
CO o
r X
H2 [-]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
H2/CO = 1
H2/CO = 1.5
H2/CO = 2
H2/CO = 2.5
H2/CO = 3
H2/CO = 3.5
H2/CO = 4
WHSVCO
= 10
Tin = 485 K
Pout
= 20 bar
H2/CO = 2
(a) XCO
(b) XH2
Figure 7-33. Syngas conversion as a function of downstream location; WHSVCO = 10
[1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar for various hydrogen to carbon monoxide feed ratio conditions, (a) carbon monoxide conversion and (b) hydrogen conversion.
246
Hydrogen to carbon monoxide feed ratio, H2/CO [-]
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5Liq
uid
phase m
ass f
raction
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Exit c
onvers
ion,
XC
O a
nd X
H2 [
-]
0.0
0.2
0.4
0.6
0.8
1.0
1.2
WHSVCO
= 10 [1/hr]
Tin = 485 K
Twall
= 500 K
Pout
= 20 bar
XCO
XH2
Figure 7-34. Syngas exit conversion and liquid phase exit mass fraction as a function of
hydrogen to carbon monoxide feed ratio; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar.
247
carbon number, n [-]
8 9 10 11 12 13 14 15
Ln(W
n/n
)
-7.0
-6.5
-6.0
-5.5
-5.0
carbon number, n [-]
1 2 3 4 5 6 7
-6
-5
-4
-3
-2
-1
0
H2/CO = 1
H2/CO = 1.5
H2/CO = 2
H2/CO = 2.5
H2/CO = 3
H2/CO = 3.5
H2/CO = 4
Figure 7-35. Hydrogen to carbon monoxide feed ratio effect on hydrocarbon distribution
at the exit; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K and Pout = 20 bar.
248
LIST OF REFERENCES
Adesina, A. A., 1996. Appl. Catal. A: General 138, 345-367. Anderson, R. B., 1956. Catalysts for the Fischer-tropsch Synthesis Vol. 4. Van Nostrand
Reinhold, New York. Anderson, R. B., 1984. The Fischer-Tropsch synthesis, Academic Press, New York. Anderson, R. B., Karn, F. S., Shultz, J. F., 1964. U.S. Bur. Mines Bull. 614. ANSYS Inc., 2009. ANSYS FLUENT Theory Guide Version 12.0 ANSYS Inc., 2009. ANSYS FLUENT UDF Manual Version 12.0. Atwood, H. E., Bennett, C. O., 1979. Ind. Eng. Chem. Process Des. Dev. 18, 163. Brötz, W., 1949. Z. Elektrochem. 5, 301. Bub, G., Baerns, M., 1980. Chem. Eng. Sci. 35, 348-355. Bukur, D. B., Patel, S. A., Lang, X., 1990. Appl. catal. A 61, 329. Chein, R.Y., Chen, Y.C., Chang, C.S., Chung, J.N., 2010. Numerical modeling of
hydrogen production from ammonia decomposition for fuel cell applications. Int. J Hydrogen Energy 35, 589-597.
Craxford, S. R., Rideal, E., 1939. Brennstoff-Chem. 20, 263. Deckwer, W.-D., Kokunn, R., Sanders, E., Ledakowicz, S., 1986. Ind. Eng. Chem.
Process Des. Dev. 25, 643. De Swart, J. W. A., 1996. Ph. D. Thesis, University of Amsterdam, Netherlands. Dictor, R. A., Bell, A. T., 1986. J. Catal., 97, 121. Donnelly, T. J., Satterfield, C. N., 1989. Appl. Catal. A 52, 93. Donnelly, T. J., Yates, I. C., Satterfield, C. N., 1988. Energy Fuels 2, 734. Dry, M. E., 1976. Ind. Eng. Chem. Prod. Res. Dev. 15, 282-286. Dry, M. E., 1981. Catalysis-Science and Technology (Aderson, J. R. and Boudart, M.
eds.), Springer-Verlag, New York. Dry, M. E., 1996. Applied Catalysis A: General 138, 319-344.
249
Dry, M. E., Shingles, T., Boshoff, L. J., 1972. J. Catal. 25, 99. Elbashir, N. O., Roberts, C. B., 2005. Ind. Eng. Chem. Res., 44, 505-521. Ergun, S., 1952. Chem. Engr. Prog., 48, 89-94. Ferziger, J. H., Perić , M., 2002. Computational Methods for Fluid Dynamics, 3rd ed.,
Springer. Fischer, F., Trosch, H., 1926. Brennstoff-Chem. 7, 97. Fischer, F., Trosch, H., 1930. Brennstoff-Chem. 11, 489. George, R., Andersen, J.-A. M., Moss, J. R., 1995. J. Organomet. Chem. 505, 131. Hall, C. C., Gall, D., Smith, S. L., 1952. J. Inst. Pet. 38, 845. Hamelicnk, C. N., Faaij, A. P.C., den Uil, H., Boerrigter, H., 2004. Energy 29, 1743-1771. Hill, J., Nelson, E., Tilman, D., Polasky, S., Tiffany, D., 2006. Proceedings of the
National Academy of Sciences, 103, 11206-11210. Ho, C.D., Chang, H., Chen, H.J., Chang, C.L., Li, H.H., Chang, Y.Y., 2011. CFD
simulation of the two-phase flow for a falling film micro reactor. International Journal of Heat and Mass Transfer 54, 3740-3748.
Huber, G. W., 2007. “Workshop report “Breaking the Chemical and Engineering Barriers
to Lignocellulosic Biofuels : A Researh Roadmap for Making Lignocellulosic Biofuels a Practical Reality”, Sponsored by NSF, DOE and American Chemical Society, June 25-26, 2007 Washington, D.C.
Huff Jr., G. A., Satterfield, C. N., 1984. Ind. Eng. Chem. Process Des. Dev. 23, 696. Iglesia, E., Reyes, S. C., Madon, R. J., 1991. J. Catal. 129, 238. Iglesia, E., Soled, S.L., Fiato, R.A., 1992. J. Catal., 137, 212. Ishii, M., Hibiki, T., 2006. Thermo-Fluid Dynamics of Two-Phase Flow, Springer, New-
York. Jager, B., Espinoza, R., 1995. Catal. Today, 23, 17. Jess, A., Kern, C., 2009. Chem. Eng. Technol. 32, 1164-1175. Jess, A., Popp, R., Hedden, K., 1998. OIL GAS European Magazine 24, 34-43.
250
Jess, A., Popp, R., Hedden, K., 1999. Applied catalysis A: General 186, 321-342. Jin, Y., Shaw, B.D., 2010. Computational modeling of n-heptane droplet combustion in
air-diluentsenvironments under reduced-gravity. International Journal of Heat and Mass Transfer 53, 5782-5791.
Jovanovic, R.,Milewska, A., Swiatkowski, B., Goanta, A., Spliethoff, H., 2011. Numerical
investigation of influence of homogeneous/heterogeneousignition/combustion mechanisms on ignition point position during pulverizedcoal combustion in oxygen enriched and recycled flue gases atmosphere. International Journal of Heat and Mass Transfer 54, 921–931.
Kölbel, H., Ralek, M., 1980. Catal. Rev.-Sci. Eng., 21, 225. Kuipers, E. W., Scheper, C., Wilson, J. H., Oosterbeek, H., 1996. J. Catal. 158, 288. Ledakowicz, S., Nettelhoff, H., Kokuun, R., Deckwer, W.-D., 1985. Ind. Eng. Chem.
Process Des. Dev. 24, 1043-1049. Lox, E. S., Froment, G. F., 1993. Ind. Eng. Chem. Res. 32, 71-82. Maretto, C., Krishna, R., 1999. Catalysis Today 52, 279-289. Martin-Martinez , J.M., Vannice, M.A., 1991. Ind. Eng. Chem. Res., 30, 2263. Nettelhoff, H., Kokuun, R., Ledakowicz, S., Deckwer, W.-D., 1985. Ger. Chem. Eng. 8,
177-185. Pangarkar, K., Schildhauer, T. J., Ruud van Ommen, J., Nijenhuis, J., Moulijn, J. A.,
Kapteijn, F., 2009. Catalysis Today, 147S, S2-S9. Pannell, R. B., Kibby, C. L., Kobylinski, T. P., 1980. In Proceeding of the 7th
International congress on catalysis, Tokyo, 447-459. Patankar, S. V., 1980. Numerical Heat Transfer and Fluid Flow, Hemisphere,
Washington, DC. Philippe, R., Lacroix, M., Dreibine, L., Pham-Huu, C., Edouard, D., Savin, S., Luck, F.,
Schweich, D., 2009. Catalysis Today 147S, S305-S312. Pichler, H., Schulz, H., 1970. Chem.-Ing. Techn. 42, 1162. Rao, V. U. S., Stiegel, G. J., Cinquegrane, G. J., Srivastave, R. D., 1992. Fuel Process.
Technol., 30, 83. Rautavuoma, A. O. I., van der Baan, H. S., 1981. Appl. Catal. 1, 247-272.
251
Ribeiro, F.H., Schach von Wittenau , A.E., Bartholemew, C.H., Somorjai, G.A., 1997.
Catal. Rev.-Sci. Eng., 39, 49. Roginski, S., 1965. Proc. 3rd Congr. on Catalysis, Amsterdam, 939. Sarup, B, Wojciechowski, B. W., 1988. The Canadian Journal of chemical Engineering
66, 831-842. Sarup, B, Wojciechowski, B. W., 1989. The Canadian Journal of chemical Engineering
67, 62-74. Shen, W. J., Zhou, J. L., Zhang, B. J., 1994. J. Nat. Gas Chem. 4, 385. Sternberg, A., Wender, J., 1959. Proc. Intern. Conf. Coordination Chem., The Chemical
Society, London, 53. Steyberg, A. P., Dry, M. E., 2004. Studies in surface science and catalysis Vol. 152;
Fischer-Tropsch Technology. Elsevier, New York. Storch, H. H., Golumbic, N., Anderson, R. B., 1951. The Fischer-Tropsch and Related
Synthesis, John Wiley & Sons, New York. Troshko, A.A., Zdravistch, F., 2009. CFD modeling of slurry bubble column reactors for
Fisher–Tropsch synthesis. Chemical Engineering Science, 64 (5), 892-903. Van Berge, P. J., Everson, R. C., 1997. Stud. Surf. Sci. Catal., 107, 207. Van Der Laan, G. P. Beenackers, A. A. C. M., 1999. Kinetics and Selectivity of the
Fischer-Tropsch Synthesis: a Literature Review, Catal. Rev.-Sci. Eng. 41, 255. Vannice, M. A., 1976. Catal. Rev. Sci. Eng. 14, 153-191. Versteeg, H. K., Malalasekera, W., 1995. An introduction to Computational Fluid
Dynamics The Finite Volume Method, Longman, Essex, England. Wang, J., 1987. Ph. D. Thesis, Bringham Young University, Provo, UT. Wang, Y.-N., Xu, Y.-Y., Li, Y.-W., Zhao, Y.-L., Zhang, B.-J., 2003. Chemical
Engineering Science 58, 867-875. Wojciechowski, B. W., 1988. Cat. Rev. Sci. Eng. 30, 629. Wu, J., Zhang, H., Ying, W., Fang, D., 2010. Chemical Engineering Technology 33,
1083-1092.
252
Yang, C. H., Massoth, F. E., Oblad, A. G., 1979. Adv. Chem. Ser. 178, 35-46. Yates, I. C., Satterfield, C. N., 1989. Ind. Eng. Chem. Res. 28, 9-12. Yates, I. C., Satterfield, C. N., 1991. Energy & Fuels 5, 168-173. Zennaro, R., Tagliabue, M., Bartholomew, C., 2000. Catal. Today 58, 309-319. Zimmerman, W. H., Bukur, D. B., 1990. Reaction Kinetics Over Iron Catalysts used for
the Fischer-Tropsch synthesis, The Canadian Journal of chemical engineering. 68, 292.
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, Korea 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 senior 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
Aerospace 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 2008.