NUMERICAL MODELING AND SIMULATION OF FISCHER...

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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

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© 2011 Tae-Seok Lee

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To my beloved wife and son

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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

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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

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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

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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

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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

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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

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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



7-7 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


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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

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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

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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.

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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

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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,

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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

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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.

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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.

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.

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

qq

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


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


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


H2/CO = 1.5 and different mass fluxes, F/Fbase = 0.25, 0.5, 0.75, and 1.

108


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


H2/CO = 2.2 and different mass fluxes, F/Fbase = 0.5, 0.75, and 1.

109


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


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


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


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


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


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


oC, syngas mass flux F= Fbase and different H2/CO ratios of 2.0, 2.5, 3.0, and 3.5.

113


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


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


oC, syngas mass flux F= 0.5Fbase and different H2/CO ratios of 1.5, 2.0, 2.5, and 3.0..

115


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


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

qq

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

qq

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

qq

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

qq

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

qq

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


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


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


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)


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)


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


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)


189


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)


190


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


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)


192


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)


193


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


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)


195


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)


196


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


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)


198


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)


199


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


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)


201


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)


202


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


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)


204


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)


205


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


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)


207


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)


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


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


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)


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)


213


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)


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


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)


215


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)


216


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)



217


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)


218


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)


219


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)



220


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)


221


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)


222


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


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


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)


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)


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


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)


228


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)


229


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


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)


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


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


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


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


location; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2 for various wall temperature conditions.

237


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


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


wall temperature; WHSVCO = 10 [1/hr], Tin = 485 K, Pout = 20 bar and H2/CO = 2.

239


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


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


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


location; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2 for various outlet pressure conditions.

241


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


[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


outlet pressure; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and H2/CO = 2.

243


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


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


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


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


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


[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


hydrogen to carbon monoxide feed ratio; WHSVCO = 10 [1/hr], Tin = 485 K, Twall = 500 K, and Pout = 20 bar.

247


8 9 10 11 12 13 14 15

Ln(W

n/n

)

-7.0

-6.5

-6.0

-5.5

-5.0


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

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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.

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