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UBC Theses and Dissertations

The effects of Co particle size on the deactivation of Co/Al₂O₃ and Re-Co/Al₂O₃ catalysts in the Fischer-Tropsch… Ghasvareh, Pooneh 2017

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  The effects of Co particle size on the deactivation of Co/Al2O3 and Re-Co/Al2O3 catalysts in the Fischer-Tropsch synthesis by  Pooneh Ghasvareh                                   M.Sc., University of Tehran, 2009 B.Sc., Iran University of Science and Technology, 2005  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   February 2017  © Pooneh Ghasvareh, 2017 ii  Abstract  To assess the effect of Co particle size on the deactivation of Co catalysts during Fischer-Tropsch (FT) synthesis, a series of Co/Al2O3 and Re-Co/Al2O3 FT catalysts with varying Co particle size, were tested in a continuous flow, stirred tank reactor operated at 220C, 2.1MPa and a H2/CO = 2/1 synthesis gas for periods up to 190 h time-on-stream (TOS). At the chosen operating conditions, carbon deposition was the main cause of catalyst deactivation and the initial rate of carbon deposition per active Co site increased with increased Co particle size (dCo=2– 22 nm) when measured at approximately the same CO conversion level.  Results showed that catalyst stability was dependent upon the Co particle size, degree-of-reduction (DOR) of the catalyst precursor and the CO conversion. The initial rate of carbon deposition increased with increase in CO conversion, when CO conversion ≤ 40%, for a particular catalyst, whereas at high concentrations of H2O and CO2 in the reactor (CO conversions> 60%), the initial rate of carbon deposition decreased with increased CO conversion. Furthermore, Co/Al2O3 catalysts with small Co particles (dCo = 2 nm and dCo = 1 nm) were activated with TOS during the FT synthesis. These catalysts had a low DOR (≤3%) and were reduced further when exposed to the synthesis gas.  Comparison between the extent of catalyst deactivation for the Co/Al2O3 and Re-Co/Al2O3 model catalysts and a commercial Co/P-Al2O3 catalyst (Co catalyst on a P modified Al2O3 support), showed that the Co/P-Al2O3 catalyst was more stable during ~160 TOS due to a reduced carbon deposition rate. However, when the catalyst was operated over a range of process conditions (i.e, temperature, pressure and H2/CO ratio) for extended operating periods (up to iii  1200 h), the CH4 selectivity increased at TOS > 400 h and when the catalyst was exposed to high temperature (T≥ 230 ºC) and a PH2O/PH2 ratio > 0.5. The change in CH4 selectivity was shown to be dependent on the high 𝑃𝐻2𝑂 in the reactor which resulted in Co oxidation and hence a change in product selectivity.                      iv  Preface  This Ph.D. thesis consists of eight chapters. The Ph.D. study was conducted by Pooneh Ghasvareh under the direct supervision of Professor Kevin Smith in the Department of Chemical and Biological Engineering at UBC. The catalyst preparation, catalyst characterization, catalyst testing, data collection, data analysis, data interpretation, literature review, and dissertation preparation was done by Pooneh Ghasvareh under the supervision of Professor Kevin Smith.   The reactor set-up was installed by Dr. Hooman Rezaei under the supervision of Professor Kevin Smith. The Matlab program files of Chapter 7 were written with the assistance of Dr.Farnaz Sotoodeh, under the supervision of Professor Kevin Smith. TEM images were produced by Bradford Ross in the Department of Botany at UBC. XPS measurements were performed by Dr. Ken Wong and TOF-SIMS analysis was conducted by John Kim Kyong Tae in the Department of Material Engineering at UBC. Approximately half of the Co catalysts that were synthesized in the presence of ethylene glycol, were prepared with the assistance of Hivio Fabiono (a visiting undergraduate student) under the supervision and guidance of Pooneh Ghasvareh.  Pooneh Ghasvareh has published data from Chapter 5 and 6 in Energy and Fuels, DOI: 10.1021/acs.energyfuels.6b01981. Pooneh Ghasvareh, K.J.Smith “Effects of Co particle size on the stability of Co/Al2O3 and Re-Co/Al2O3 catalysts in a slurry phase Fischer-Tropsch reactor”. Data analysis, data collection, catalyst testing and characterization were done by Pooneh Ghasvareh.   v  Pooneh Ghasvareh presented data from Chapter 7 at the 23 rd North American Catalysis Society meeting (Louisville, Kentucky, US), 2013 in a poster titled “Kinetics of deactivation of a Co/Al2O3 catalyst in Fischer-Tropsch synthesis’’. The catalyst testing, data collection and analysis was done by Pooneh Ghasvareh. Dr. Hooman Rezaei prepared the set-up and assisted Pooneh Ghasvareh to perform the experiments at the early stages. Dr. Farnaz Sotoodeh assisted Pooneh Ghasvareh to develop the Matlab files for kinetic modelling.   Data from Chapters 4 and 5 were presented at the 23rd Canadian Symposium on Catalysis (Edmonton, AB, Canada), 2014 in a paper titled “Deactivation of Co/Al2O3 Catalysts during Fischer-Tropsch Synthesis”. Hivio Fabiano prepared a series of Co/Al2O3 catalysts under the supervision and guidance of Pooneh Ghasvareh. The catalyst testing, data analysis, data collection and catalyst characterization was done by Pooneh Ghasvareh.   Pooneh Ghasvareh presented data from Chapters 4 and 6 at the 24th North American Catalysis Society meeting (Pittsburgh, PA, US), 2015 in a poster titled “Effect of Co particle size on deactivation of Co/Al2O3 Catalysts in the Fischer-Tropsch Synthesis”. Data analysis, data collection, catalyst testing and characterization were done by Pooneh Ghasvareh.        vi  Table of Contents   Abstract…………………. .............................................................................................................. ii Preface………………………………………………………………………………………..…..iv Table of Contents ........................................................................................................................... vi List of Tables …………………………………………………………………………………...xii List of Figures …………………………………………………………………………………xviii List of Abbreviations and Acronyms ......................................................................................... xviii List of Symbols ......................................................................................................................... xxvii Acknowledgements .................................................................................................................. xxviii Dedication….. ……………………………………………………………..................................xxx Chapter 1. Introduction ............................................................................................................. 1 1.1 Background ..................................................................................................................... 1 1.2 Thesis objectives ............................................................................................................. 5 1.3 Approach ......................................................................................................................... 6 1.4 Thesis layout ................................................................................................................... 7 Chapter 2. Literature review ................................................................................................... 10 2.1 Introduction ................................................................................................................... 10 2.2 Catalyst preparation and methods to control the metal particle size ............................ 10 2.2.1 Controlling Co particle size on Al2O3 support by impregnation .............................. 11 2.2.2 Controlling Co particle size on Al2O3 support by the micelle method ..................... 13 2.3 Reduction of Co/Al2O3 catalysts ................................................................................... 15 vii  2.3.1 Effect of promoter in the reduction of the Co/Al2O3 catalyst ................................... 17 2.4 Effect of Co particle size on FT activity and product selectivity ................................. 18 2.5 Catalyst deactivation mechanisms ................................................................................ 22 2.5.1 Formation of Co-support compounds ....................................................................... 22 2.5.2 Formation of carbon species ..................................................................................... 26 2.5.3 Formation of Co-oxide and the effect of H2O .......................................................... 30 2.5.4 Sintering and aggregation ......................................................................................... 34 2.5.5 Summary and conclusions ........................................................................................ 38 Chapter 3. Experimental methods .......................................................................................... 42 3.1 Introduction ................................................................................................................... 42 3.2 Catalyst preparation ...................................................................................................... 42 3.2.1 Wax extraction of the used catalysts ......................................................................... 43 3.3 Catalyst characterization methods ................................................................................ 44 3.3.1 Thermogravimetric analysis (TGA) .......................................................................... 44 3.3.2 Temperature programmed reduction and CO pulse chemisorption .......................... 44 3.3.3 Temperature programmed hydrogenation (TPH) ..................................................... 45 3.3.4 CH analysis ............................................................................................................... 46 3.3.5 X-ray powder diffraction (XRD) .............................................................................. 46 3.3.6 X-ray photoelectron spectroscopy (XPS) ................................................................. 47 3.3.7 Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) ............................ 48 3.3.8 Brunauer-Emmett-Teller (BET) surface area ........................................................... 48 3.3.9 Transmission electron microscopy (TEM) ............................................................... 49 viii  3.4 Laboratory-scale FT synthesis unit ............................................................................... 50 3.5 Analytical and calculation procedures .......................................................................... 54 3.6 Mass transfer effects ..................................................................................................... 57 Chapter 4. Properties of the Co/Al2O3 and Re-Co/Al2O3 catalysts ........................................ 61 4.1 Introduction ................................................................................................................... 61 4.2 Characterization of the fresh catalysts .......................................................................... 62 4.2.1 TGA analysis to estimate the required calcination temperature ............................... 62 4.2.2 CH analysis to confirm the decomposition of carbon during catalyst preparation ... 63 4.2.3 XRD analysis to measure Co and Co3O4 crystallite size on fresh catalysts after calcination and reduction ...................................................................................................... 64 4.2.4 TPR of Co/Al2O3 and Re-Co/Al2O3 catalysts to measure DOR ............................... 72 4.2.5 Metal dispersion and Co particle size measurement by CO chemisorption ............. 86 4.2.6 BET analysis to measure surface area of the fresh catalysts .................................... 91 4.2.7 TEM analysis to investigate the effect of EG on Co clusters ................................... 92 4.3 Conclusion .................................................................................................................... 93 Chapter 5. Stability, selectivity and activity of Co/Al2O3 and Re-Co/Al2O3 catalysts .......... 95 5.1 Introduction ................................................................................................................... 95 5.2 Experimental conditions ............................................................................................... 96 5.2.1 Limitations ................................................................................................................ 97 5.3 Co/Al2O3 and Re-Co/Al2O3 catalyst stability and selectivity tests ............................... 99 5.3.1 Selectivity and stability of the Co/Al2O3 catalysts with TOS ................................... 99 5.3.2 Selectivity and stability of the Re-Co/Al2O3 catalysts with TOS ........................... 108 ix  5.4 Effect of Co particle size on the initial activity of the Co/Al2O3 and Re-Co/Al2O3 catalysts………………………………………………………………………………..……..116 5.5 Conclusions ................................................................................................................. 120 Chapter 6. Deactivation of Co catalysts ............................................................................... 122 6.1 Introduction ................................................................................................................. 122 6.2 Challenges and limitations .......................................................................................... 123 6.3 Characterization of the used catalysts ......................................................................... 124 6.3.1 Identification of Co or Co3O4 particle growth ........................................................ 124 6.3.2 Identification of the changes in catalyst surface area ............................................. 127 6.3.3 Identification of carbon species .............................................................................. 129 6.4 Quantifying the extent of catalyst deactivation using an activity factor ..................... 135 6.4.1 Effect of carbon deposition on deactivation of the catalysts .................................. 138 6.5 Catalyst regeneration in hydrogen flow ...................................................................... 142 6.6 Conclusions ................................................................................................................. 144 Chapter 7. Long-term deactivation of a commercial Co catalyst in FT synthesis ................ 145 7.1 Introduction ................................................................................................................. 145 7.1.1 Comparison between activity, stability and selectivity of Re-Co/Al2O3, Co/Al2O3 and Co/P-Al2O3 catalysts .................................................................................................... 145 7.2 Effect of process conditions on long term stability of the Co/P-Al2O3 catalyst ......... 151 7.3 Kinetic modeling ......................................................................................................... 160 7.4 Conclusions ................................................................................................................. 161 x  Chapter 8. Conclusions and recommendations for future work ........................................... 162 8.1 Conclusions ................................................................................................................. 162 8.2 Recommendations for future work ............................................................................. 165 8.2.1 Preparing the catalysts with the same DOR ............................................................ 165     8.2.2    Regeneration of the deactivatedcatalysts ................................................................ 166 8.3.1 Applying the effect of process conditions on activity factor in long-term deactivation study ……………………………………………………………………………………..166 References …………………………………………………………………………………..167 Appendices …………………………………………………………………………………..182 Appendix A : Catalyst preparation ......................................................................................... 182 Appendix B : F-T unit start-up and shut-down procedure ...................................................... 184 Appendix C : Unit components and operating conditions ...................................................... 190 Appendix D : Calibration ........................................................................................................ 195 Appendix E : GC method files ................................................................................................ 200 Appendix F : Data processing procedure ................................................................................ 212 Appendix G : Internal diffusion calculations .......................................................................... 225 Appendix H : Use of XRD to determine Co particle size ....................................................... 226 Appendix I : Error in XRD analysis ....................................................................................... 230 Appendix J : Comparison between Co3O4 particle size measured by XRD, TEM and CO chemisorption .......................................................................................................................... 233 Appendix K : Experimental results for the Co/Al2O3 catalysts .............................................. 238 Appendix L : Experimental results for the Re-Co/Al2O3 catalysts ......................................... 266 Appendix M : Residence time of the entire reactor system .................................................... 276 xi  Appendix N : Effect of Co particle size on TOFFT at t=48 h .................................................. 278 Appendix O : MS analysis and relative intensity of the peaks ............................................... 280 Appendix P : Estimated parameters for the empirical models ................................................ 284 Appendix Q : Kinetic models ................................................................................................. 291                   xii  List of Tables  Table 3.1. FT unit specification and operating conditions ......................................................... 52 Table 4.1. CH analysis of calcined precursors (16 h calcination at 300 ºC) .............................. 64 Table 4.2. CH analysis of reduced catalysts .............................................................................. 64 Table 4.3. Comparison between Co3O4 particle size before and after reduction and Co particle size after reduction for different catalysts using XRD.................................................................. 72 Table 4.4. Comparison between Co particle size and DOR for Re-Co/Al2O3 and Co/Al2O3 catalysts, particle sizes are measured by CO chemisorption ........................................................ 85 Table 4.5. Comparison between the Co size measurement by CO chemisorption and XRD .... 87 Table 4.6. Surface area and pore diameter of the reduced fresh catalysts prior to the FT reaction, the Co particle size was measured by CO chemisorption .............................................. 92 Table 5.1. Effect of Co particle size on activity of the Re-Co/Al2O3 and Co/Al2O3 catalysts at time t* ……………………………………………………………………………………..119 Table 6.1. Co and Co3O4 particle sizes before and after the reaction for Co/Al2O3 catalysts. The stated average CO conversion is calculated from t~48 h to t~190 of TOS ................................ 126 Table 6.2. BET surface area (m2/g) and average pore diameter (nm) before and after the reaction for Co/Al2O3 and Re- Co/Al2O3 catalysts with deactivation ........................................ 128 Table 6.3. Forms and reactivity of carbon species in TPH profile of used FT catalysts ......... 130 Table 6.4.  Co/Al ratio obtained with XPS for Co/Al2O3 and Re-Co/Al2O3 catalysts.............. 135 Table 6.5. Empirical models fitted to catalyst deactivation [82] ............................................. 137 Table 6.6. Example calculations for TOF0C (initial rate of carbon deposition) ....................... 141 Table 6.7. CO chemisorption on fresh catalyst versus CO chemisorption on used Co/Al2O3 and Re-Co/Al2O3 catalysts after reduction in hydrogen .................................................................... 143 xiii  Table 7.1. Comparison of initial CO and C TOFs, deactivation rates and carbon deposition on Co/Al2O3, Re-Co/Al2O3 and Co/P-Al2O3 catalysts ..................................................................... 149 Table 7.2. Comparison between properties of Re-Co/Al2O3, Co/Al2O3 and Co/P-Al2O3 catalysts ……………………………………………………………………………………..149 Table 7.3. Comparison between selectivity of the Re-Co/Al2O3, Co/Al2O3 and Co/P-Al2O3 catalysts at the same range of CO conversion (the stated average conversion is calculated from t~48 h to t~160 h of TOS) ........................................................................................................... 150 Table 7.4. Operating conditions used for stability experiments over the Co/P-Al2O3  catalyst ……………………………………………………………………………………..151 Table 7.5. Operating conditions used for experiments to collect kinetic data over the Co/P-Al2O3 catalyst. ............................................................................................................................. 152 Table 7.6. Catalyst stability as reflected in average values and standard deviations of CO conversion and product distributions, measured at 220 C, 21.4 bar, GHSV = 0.06  mol/(g.h), H2/CO = 2/1 over the period of 1200 h TOS, related to Run1, Run2 and Run3 ........................ 158 Table 7.7. Estimated kinetic parameters for the power law CH4 formation rate 1) corrected data 2) measured data ......................................................................................................................... 160 Table D.1. The composition of gas mixtures used for calibration of GC 2014 and GC 2010.. 197 Table F.1. The composition of the inlet gas to the CSTR reactor within 24.5 h ...................... 213 Table F.2. Outlet gas measured by GC equipped with TCD .................................................... 214 Table F.3. The measured and calculated compounds at the reactor outlet............................... 215 Table F.4. Measured mass of (CH2)n at the outlet, calculated mass of H2O in traps and CH2 in hot condenser and FID ................................................................................................................ 216 Table F.5. Iterative calculation to measure the amount of HC in FID ..................................... 217 Table F.6. Mass of hydrocarbons measured in liquid analysis ................................................ 219 xiv  Table F.7. Cumulative mass of hydrocarbons produced within ~24 h in hot and cold condensers as well as the outlet of the unit.................................................................................................... 221 Table F.8. Overall mass and carbon balance and comparison between theoretical and actual values for ~24h ........................................................................................................................... 223 Table F.9. Rate of formation and consumption of different compounds ................................. 224 Table H.1.  Parameters of the Gaussian curve fitted to the subtracted peak at 2ϴ ~52 ° ......... 227 Table H.2. Parameters of the Gaussian curve fitted to the de-convoluted peak at 2ϴ~52 ° ..... 228 Table H.3. Parameters of the Gaussian curve fitted to the de-convoluted peak at 2ϴ~52 ° ..... 229 Table I.1. Parameters of the Gaussian curve fitted to the subtracted peak at 2ϴ~43 ° ........... 231 Table J.1.  Calculated parameters for the de-convoluted peaks ............................................... 234 Table K.1. Experimental condition and summary of results of RUN14EXP1 with 5Co/Al2O3(0) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g 238 Table K.2. Experimental condition and summary of results of RUN16EXP1, with 20Co/Al2O3(0.6) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g .................................................................................................................. 240 Table K.3. Experimental condition and summary of results for RUN17EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g .................................................................................................................. 242 Table K.4. Experimental condition and summary of results of RUN18EXP1, with 5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g .................................................................................................................. 244 Table K.5. Experimental condition and summary of results of RUN19EXP1, with 5Co/Al2O3(0.9) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g .................................................................................................................. 246 xv  Table K.6. Experimental condition and summary of results of RUN20EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g .................................................................................................................. 248 Table K.7. Experimental condition and summary of results for RUN21EXP1, with 5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.01 mol/ h.g .................................................................................................................. 250 Table K.8. Experimental condition and summary of results for RUN22EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.08 mol/ h.g .................................................................................................................. 252 Table K.9. Experimental condition and summary of results for RUN24EXP1, with 20Co/Al2O3(0.6) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.18 mol/ h.g .................................................................................................................. 254 Table K.10. Experimental condition and summary of results for RUN25EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.16 mol/ h.g .................................................................................................................. 256 Table K.11. Experimental condition and summary of results for RUN26EXP1, with 5Co/Al2O3(0.9) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.01 mol/ h.g .................................................................................................................. 258 Table K.12. Experimental condition and summary of results for RUN27EXP1, with 5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=230 °C, P=20 bar and H2/CO=2, GHSV=0.02 mol/ h.g .................................................................................................................. 260 Table K.13. Experimental condition and summary of results for RUN30EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.07 mol/ h.g .................................................................................................................. 262 xvi  Table K.14. Experimental condition and summary of results for RUN32EXP1, with 5Co/Al2O3(0.9) catalyst,  tested in CSTR reactor at T=245 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g .................................................................................................................. 264 Table L.1. Experimental condition and summary of results for RUN33EXP1, with 0.5Re-5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.05 mol/ h.g .................................................................................................................. 266 Table L.2. Experimental condition and summary of results for RUN34EXP1, with 0.3Re-3Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.05 mol/ h.g .................................................................................................................. 268 Table L.3. Experimental condition and summary of results for RUN35EXP1, with 1.2Re-12Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.05 mol/ h.g .................................................................................................................. 270 Table L.4. Experimental condition and summary of results for RUN36EXP1, , with 1.2Re-12Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.08 mol/ h.g .................................................................................................................. 272 Table L.5 Experimental condition and summary of results for RUN37EXP1, with 1.2Re-12Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.12 mol/ h.g .................................................................................................................. 274 Table N.1. Effect of Co particle size on activity of the Re-Co/Al2O3 and Co/Al2O3 catalysts at time t*=48 h ................................................................................................................................ 278 Table O.1. The expected relative intensity of the peaks for different compounds in MS ........ 280 Table P.1. Estimated parameters for the empirical models (Co/Al2O3 catalysts with deactivation), Co particle size is measured with CO chemisorption .......................................... 284 xvii  Table P.2. Estimated parameters for the empirical models (Re-Co/Al2O3 catalysts), Co particle size is measured with CO chemisorption .................................................................................... 285 Table Q.1. Estimated kinetic parameters for CO consumption rate by fitting the measured data to different kinetic models. ......................................................................................................... 292 Table Q.2. Estimated kinetic parameters for activity-corrected CH4 formation rate by fitting the measured data to different kinetic models. ................................................................................. 295 Table Q.3. Best fitted kinetic parameters for the formation rate of various C2+ components .. 298 Table Q.4. Estimated power law parameters for ASF α-values ................................................ 298           xviii  List of Figures  Figure 2.1. Effect of water mass fraction of impregnation solvent on Co3O4 crystallite size after calcination. Reproduced with permission from [86], Copyright © 2008 Elsevier Inc. ................ 12 Figure 2.2. Thermodynamic equilibrium constants for cobalt oxidation reactions: (──) thermodynamic equilibrium requirement for Co+Al2O3+H2O⇆CoAl2O4+H2, (...) thermodynamic equilibrium requirement for Co+H2O⇆CoO+H2, (---) thermodynamic equilibrium Constant for 3Co+4H2O⇆Co3O4+4H2. Reproduced with permission from [125], Copyright © 2000 Elsevier Inc. ………………………………………………………………………………………23 Figure 2.3. Stability region of spherical β-Co (fcc) and Co(II)O at 493 ºK in H2O/H2 atmosphere (…..) β-Co ±15%. Reproduced with permission from [79], Copyright © 2005 Elsevier Inc. ..... 31 Figure 3.1. Fischer-Tropsch Process Flow Diagram ................................................................... 53 Figure 3.2. Stirred reactor and analytical facility ........................................................................ 54 Figure 3.3. Product sample collection and analysis ...................................................................... 57 Figure 3.4. Effect of stirrer speed on the CO conversion and rates of CO consumption, CH4 formation and C2-C4 formation. Operating conditions: 220 C, 21.4 bar, GHSV = 0.06 (mol/g.h), H2/CO = 2/1. ................................................................................................................................. 59 Figure 3.5. Effect of stirrer speed on the hot gas product composition as determined by FID analysis. Operating conditions: 220 C, 21.4 bar, GHSV= 0.06 (mol/g.h), H2/CO = 2 ............... 60 Figure 4.1. TGA profile of: (A) Al2O3 support impregnated with a mixture of EG and water (R=0.9), (B) 5Co/Al2O3(0) dried precursor, (C) 5Co/Al2O3(0.9) dried precursor ........................ 63 Figure 4.2. XRD spectrum of: A) 15Co/Al2O3 (0.1) after reduction, B) 15Co/Al2O3(0.1) calcined precursor, C) Al2O3 support............................................................................................ 65 xix  Figure 4.3. Relative intensity of the peaks in powder diffraction files: Al2O3: PDF 00-029-0063, Co3O4: PDF 00-043-1003, Co: PDF 00-015-0806 ....................................................................... 66 Figure 4.4. XRD spectrum (subtracted from the support) of calcined 5Co/Al2O3, A) without EG (R=0), B) with EG (R=0.6) with no detectable Co3O4 ................................................................. 68 Figure 4.5. XRD spectrum (subtracted from the support) of calcined 10Co/Al2O3, A) without glycol (R=0), B) with glycol (R=0.1), C) with glycol (R=0.6)..................................................... 69 Figure 4.6. XRD spectrum (subtracted from the support) of calcined 15Co/Al2O3 .................... 70 Figure 4.7. XRD spectrum (subtracted from the support) of calcined 20Co/Al2O3, A) without EG (R=0), B) with EG (R=0.2), C) with EG (R=0.6), D) with EG (R=0.9) ................................ 71 Figure 4.8. Relative intensity of the H2 and H2O peaks at the outlet of the fixed bed reactor during the reduction of 15Co/Al2O3 (0.6) ..................................................................................... 74 Figure 4.9. Relative intensity of CO2, CO and CH4 at the outlet of the fixed bed reactor during the reduction of 15Co/Al2O3(0.6) ................................................................................................. 75 Figure 4.10. TPR profile of catalysts with different Co loadings, without EG in impregnation solution (R=0) ............................................................................................................................... 79 Figure 4.11. TPR profile of catalysts with different Co loadings, with EG in impregnation solution (R=0.9) ............................................................................................................................ 80 Figure 4.12. TPR profile of catalysts with different Co loadings, with EG in impregnation solution (R=0.7) ............................................................................................................................ 81 Figure 4.13. TPR profile of 10Co/Al2O3 with different amount of EG (different R) .................... 82 Figure 4.14. Effect of adding promoter on the reduction of 5Co/Al2O3 (0.7), promoted catalyst contains 0.5wt% Re ...................................................................................................................... 84 Figure 4.15. Effect of adding promoter on the reduction of 3Co/Al2O3(0.9), promoted catalyst contains 0.3wt% Re ...................................................................................................................... 85 xx  Figure 4.16. Co particle size of Co/Al2O3 catalysts as determined from CO chemisorption versus the mass fraction of EG (R) in the impregnation solution, at different Co loadings .................... 90 Figure 4.17. Co particle size versus DOR for 20, 15, 10, 5 and 3wt% Co/Al2O3 and 3, 5, 8 and 12 wt% Re-Co/Al2O3 with different weight fractions of EG ............................................................. 91 Figure 4.18. TEM images of 20Co/Al2O3(0)(left), 20Co/Al2O3(0.6) (right) ................................ 93 Figure 5.1. CO conversion versus TOS for Co/Al2O3 catalysts operated at T=220 ºC, P=20 bar and H2/CO=2 with varied GHSVs .............................................................................................. 101 Figure 5.2. The CO2 selectivity (mol%) versus time on stream for small and large Co particles, Average conversion 20±6% measured at T=220 oC, P=20 bar and H2/CO=2 ........................... 102 Figure 5.3. Product selectivity and CO conversion of 15Co/Al2O3(0.1) catalyst with dCo=10 nm during FT synthesis reaction conditions of T=220 ºC, P=20 bar and H2/CO=2 ......................... 104 Figure 5.4. Product selectivity and CO conversion of 5Co/Al2O3(0.7) catalyst with dCo= 2 nm during FT synthesis reaction conditions of T=220 oC, P=20 bar and H2/CO=2 ......................... 105 Figure 5.5. Product selectivity and CO conversion of  5Co/Al2O3(0.9) catalyst with dCo =1 nm during FT synthesis reaction conditions of T=220 oC, P=20 bar and H2/CO=2 ......................... 106 Figure 5.6. Effect of Co particle size (nm) on CH4 and C5+ selectivity (wt%) measured at average CO conversion 20±6% and T=220 oC, P=20 bar and H2/CO=2 ................................... 108 Figure 5.7. CO conversion for Re-Co/Al2O3 catalysts with different Co particle sizes. Operating condition is T=220 ºC, P=20 bar, H2/CO=2 ............................................................................... 110 Figure 5.8. CH4 and C5+ selectivity for Re-Co/Al2O3 catalysts with different Co particle sizes. Operating condition is T=220 ºC, P=20 bar, H2/CO=2 at an average CO conversion of 32±8% (shown by the dashed line) ......................................................................................................... 111 Figure 5.9. (A) CO2 selectivity(%) versus TOS; (B) PH2O/PH2 versus TOS; and  (C) CO conversion versus TOS for Re-Co/Al2O3  with dCo=11 nm at different GHSVs ........................ 114 xxi  Figure 5.10. Product selectivity for Re-Co/Al2O3 catalysts (average conversion 32±8%) and Co/Al2O3 catalysts (average conversion 20±6%) with different Co particle size A) CH4 selectivity B) C5+ selectivity ....................................................................................................... 115 Figure 5.11. TOF0FT versus Co particle size. For the Re-Co/Al2O3 catalysts the CO conversion is between 34 to 72% and for the Co/Al2O3 catalysts the CO conversion is between 1 to 63%. Error bars represent four data points for 15Co/Al2O3(0.1) catalyst and two data points for 1.2Re-12Co/Al2O3(0) catalyst at varied CO conversions as reported in Table 5.1 ............................... 120 Figure 6.1. Reduction in BET surface area (%) versus C content (wt%) of used catalysts. ..... 129 Figure 6.2. TPH profile for used catalysts, Solid line: 20Co/Al2O3 (0.6) catalyst with dCo=13 nm at average CO conversion of 35%, Solid line: 5Co/Al2O3(0.7) catalyst with dCo=2 nm at average CO conversion of 17% ................................................................................................................ 132 Figure 6.3. TOF-SIMS maps of C, Co, Al for the dewaxed used 0.3Re-3Co/Al2O3(0.9) catalyst. The areas with high concentration of elements appear with brightest color (Yellow) ............... 133 Figure 6.4.  TOF-SIMS maps of C, Co, Al for the dewaxed used 15Co/Al2O3(0.1) catalyst. The areas with high concentration of elements appear with brightest color (Yellow) ...................... 134 Figure 6.5. TOFC versus dCo for Re-Co/Al2O3 and Co/Al2O3 catalysts with different Co particle sizes. All the experiments were conducted at 220 ºC and 2.1 MPa ............................................ 142 Figure 7.1. CO conversion versus TOS for 1.2Re-12Co/Al2O3(0),15Co/Al2O3(0.1) and 20Co/P-Al2O3  catalysts. Operating conditions: 220 ºC, ~20 bar and H2/CO=2 ...................................... 147 Figure 7.2. α(𝜑) versus 𝜑 for 15Co/Al2O3(0.1), 1.2Re-12Co/Al2O3(0) and 20Co/P-Al2O3 catalysts and the fitted reciprocal power model for catalyst deactivation. Operating conditions: 220 ºC, ~20 bar and H2/CO=2, with GHSV of 0.04, 0.12 and 0.06 mol/g.h, respectively. ........ 148 Figure 7.3. Process conditions as a function of TOS for the kinetic experiments (Run1 and Run 2) …………………………………………………………………………………….153 xxii  Figure 7.4. Process conditions as a function of TOS for the kinetic experiments (Run 3) ....... 154 Figure 7.5. Catalyst stability as reflected in CO conversion and product distribution measured at standard set of operating conditions (220 C, 21.4 bar, GHSV=0.06 mol/(g.h), H2/C=2/1). Solid line is time averaged value. ......................................................................................................... 157 Figure 7.6. Catalyst stability as reflected in FTS α-value measured at standard set of operating conditions: 220 C, 21.4 bar, GHSV = 0.06 mol/(g.h), H2/CO = 2/1. Solid line is time-averaged value ……………………………………………………………………………………..158 Figure 7.7. CH4 formation rate measured and corrected by applying activity factor at the standard conditions as a function of TOS.  Reaction conditions: 220 C, 21.4 bar, GHSV = 0.06 mol/(g.h), H2/CO = 2/1. .............................................................................................................. 159 Figure D.1. Calibration of MFC for N2, H2, CO and gas mixture for GC 2014 calibration ...... 196 Figure D.2. The LN(RF) versus carbon number and the fitted line ........................................... 198 Figure D.3. RF value versus carbon number in D-2887 calibration mix, used for liquid calibration ................................................................................................................................... 199 Figure F.1. Hydrocarbon distribution according to ASF equation (α=0.76) ............................. 222 Figure H.1. XRD profile of 5Co/Al2O3(0) catalyst and Normalized Al2O3 support from 2ϴ =50 ° to 2ϴ=60 ° ……………………………………………………………………………………..226 Figure H.2.  Subtracted peak at 2ϴ ~52 ° and the Gaussian curve fitted to the peak……….….225 Figure H.3. Deconvolution of the peaks in XRD profile of 5Co/Al2O3(0) catalyst, at 2ϴ =52° and 2ϴ=54° ……………………………………………………………………………………..228 Figure H.4. Deconvolution of the peaks in XRD profile of 1.2Re-12Co/Al2O3(0) catalyst, at 2ϴ =52° and 2ϴ =54 ° ...................................................................................................................... 229 Figure I.1. Gaussian fitted curve to measure Co3O4 particle size on 20Co/Al2O3(0.6) ............ 232 xxiii  Figure J.1. The full XRD spectra of reduced 0.3Re-3Co/Al2O3(0.9), Co particles were oxidized when exposed to air .................................................................................................................... 233 Figure J.2.  XRD spectra of the 0.3Re-3Co/Al2O3(0.9) to calculate Co3O4 particle size ........... 234 Figure J.3.  TEM image of fresh 0.3Re-3Co/Al2O3(0.9), Co particles were oxidized when exposed to air .............................................................................................................................. 236 Figure J.4.  Log normal distribution of Co3O4 particle size for 0.3Re-3Co/Al2O3(0.9). ……………………………………………………………………………………..237 Figure N.1.  TOFFT ( at t=48) versus Co particle size. For the Re-Co/Al2O3 catalysts the CO conversion is between 32 to 61% and for the Co/Al2O3 catalysts the CO conversion is between 3 to 43%. Error bars represent four data points for 15Co/Al2O3(0.1) catalyst and two data points for 1.2Re-12Co/Al2O3(0) catalyst at varied CO conversions as reported in Table N.1.............. 279 Figure O.1.  CO2 outlet flow rate versus TOS for 20Co/Al2O3(0.6) ......................................... .282 Figure O.2. CO outlet flow rate versus TOS for 20Co/Al2O3(0.6) ............................................. 282 Figure P.1. Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS....................................................................................... 286 Figure P.2.  Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS....................................................................................... 287 Figure P.3.  Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS....................................................................................... 288 Figure P.4.  Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS....................................................................................... 289 Figure P.5.  Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS....................................................................................... 290 xxiv  Figure Q.1.  Parity plot for rate of CO consumption applied to the power law model. Parameter values as reported in Table Q.1. .................................................................................................. 293 Figure Q.2.  Parity plot comparison of the fitted modified Schulz model to the measured CH4 formation rate: with and without the activity factor for Run2 and Run3.................................... 294 Figure Q.3.  Illustrative ASF plots to determine the α-value as a function of operating conditions. ……………………………………………………………………………………..299                   xxv  List of Abbreviations and Acronyms  ASF Anderson-Schulz-Flory distribution amu Atomic mass unit BET Brunauer-Emmett-Teller surface area analysis BJH Barrett-Joyner-Halenda pore size and volume analysis CH Elemental analysis of C and H CMC Critical micelle concentration point CNF Carbon Nano-Fiber CSTR Continuous Stirred Tank Reactor DOR Degree of reduction EDTA Ethylene diamine tetra acetic acid EG Ethylene glycol EXAFS Extended X-Ray Absorption Fine Structure fcc Face-centered cubic FID Flame Ionization Detector FT Fischer-Tropsch FTIR Fourier Transform Infrared Spectroscopy  FWHM Full Width at Half Maximum intensity GC Gas Chromatograph MFC Mass Flow Controller GHSV Gas Hourly Space Velocity (mol/ (g.h)) MS Mass Spectrometry MSI Metal-Support interaction xxvi  MW Molecular Weight PDF Powder Diffraction Files R Mass fraction of EG in the impregnation solution (-) STEM Scanning Transmission Electron Microscope STP Standard condition for temperature and pressure TCD Thermal Conductivity Detector TEM Transmission Electron Microscopy TGA Thermo Gravimetric Analysis TOF-SIMS Time-of-Flight Secondary Ion Mass Spectrometry TOF Turnover frequency TOS Time-On-Stream TPH Temperature Programmed Hydrogenation TPO Temperature Programmed Oxidation TPR Temperature Programmed Reduction TPSR Temperature Programmed Surface Reactions WGS Water-gas shift reaction XANES X-ray Absorption Near Edge Structure XPS X-ray Photoelectron Spectroscopy XRD X-ray Powder Diffraction       xxvii  List of Symbols  d Catalyst particle size (nm) D Metal dispersion (%) dCo Co crystallite size (nm) 𝐹𝑖𝑛 Total inlet flowrate (mol/s) 𝐹𝑖𝑛𝐶𝑂 CO inlet flowrate (mol/s) 𝐹𝑜𝑢𝑡𝐶𝑂  CO outlet flowrate (mol/s) kd Deactivation constant (-) Mcat Mass of the catalyst (g) NCO CO uptake (µmol/g) n Number of carbon atoms in hydrocarbons (-) Pi Partial pressure of compound i (bar) −𝑟𝐴(𝑡) Rate of formation/consumption of compound A at time t (mol/(g.s)) −𝑟𝐶𝑂(𝑡) Total rate of the reaction at time t (mol/(g. s)) −𝑟𝐶0 Initial rate of carbon deposition (mol/(g. s)) t* Time at which the deactivation starts (h) Wn Weight fraction of hydrocarbon (-) wt Weight percentage (%) α The rate of chain propagation to the rate of chain termination (-) α(t) Activity factor at time t (-) θ Bragg angle (radians) 𝜑 (t-t*)/𝜏 dimensionless time (-) 𝜏 Residence time of gas in the reactor (h) λ Wave length (nm)  xxviii  Acknowledgements  First and foremost, I wish to thank my PhD supervisor, Professor Kevin J Smith. He has been a tremendous mentor to me since I began to work at Catalysis Group. Dr. Smith encouraged me during my research, contributed his time, provided a great and peaceful environment in our research group and suggested brilliant ideas throughout my research. He has been an excellent example of a successful professor who has dedicated his life to scientific work.   My thesis committee, Professor Tony Bi and Professor Naoko Ellis, guided me through these years. Thank you for providing valuable suggestions and comments regarding my PhD thesis.   I would like to thank all the staff at the department of Chemical and Biological Engineering (CHBE) including Lori Tanaka, Helsa Leong, Amber Lee, Salman Zafar, Joan Dean, Richard Ryoo, Dough Yuen and all the workshop staff.   I am also grateful for the financial support provided by the Natural Sciences and Engineering Research Council of Canada and the Korea Gas Corporation (KOGAS).    Thank you my colleagues in Catalysis Group for your friendship and collaboration (Dr. Hooman Rezaei, Dr. Farnaz Sotoodeh, Dr. Victoria Whiffen, Dr. Shahrzad Jooya Ardakani, Dr. Shahin Goodarznia, Dr. Ross Kukrard, Dr. Ramin Gholami Shahrestani, Mina Alyani, Ali Alzaid, Alexander Imbault, Lucie Solnickova, Xu Zhao, Majed Alamoudi, Haiyan Wang, Shida Liu, Chujie Zhu and Hamad Almohamadi).  xxix  A special thanks to my parents, Mehdi and Ezat, without their moral support and patience, I could not finish this work. I would also like to thank my brother, Pooya, and all of my friends who supported me, encouraged me and stayed by my side throughout this difficult but exciting journey. xxx    Dedication     To my parents  For their endless love and support  1  Chapter 1. Introduction 1.1 Background  The Fischer–Tropsch (FT) reaction converts synthesis gas to a range of hydrocarbons. The desired products are long chain hydrocarbons or waxes [1, 2]. The stoichiometry of the reaction can be expressed as: 𝑛𝐶𝑂 + (2𝑛 + 1)𝐻2 → 𝐶𝑛𝐻2𝑛+2 + 𝑛𝐻2𝑂 1.1 𝑛𝐶𝑂 + 2𝑛𝐻2 → 𝐶𝑛𝐻2𝑛 + 𝑛𝐻2𝑂 1.2 The synthesis gas feed to a Fischer-Tropsch reactor is a mixture of CO and H2 which may be produced by steam reforming of CH4 [3-5], gasification of coal [6, 7] or gasification of biomass [6, 8-10]. It has been estimated that the reserves of CH4 and coal exceed those of crude oil by a factor of 1.5 and 25 [11], respectively, and  the production of fuel and chemicals from natural gas and coal is of interest when the price of crude oil rises or reserves are reduced [12, 13]. The fuels derived from the FT synthesis are high quality since they have low sulphur and aromatic content.   The FT reaction is catalyzed by several metals including Fe, Co and Ru [14-16] with Fe and Co currently used in industrial practise [11, 16, 17]. The FT reaction occurs through a CO-insertion, chain propagation reaction mechanism [18-21]. Consequently, the FT product distribution is well described by the Anderson-Schulz-Flory (ASF) distribution [17, 22, 23], assuming a 2  stepwise growth mechanism of C1 species [23], in which the weight fraction of each hydrocarbon is described by the α-value that defines the rate of chain propagation to the rate of chain termination.  𝑊𝑛 = 𝑛 × (1 − 𝛼)2 × 𝛼𝑛−1                                                  1.3 where n is the number of carbon atoms in a hydrocarbon, Wn is the weight fraction of hydrocarbon with carbon number n and α is the probability of chain growth. If α is independent of hydrocarbon chain length, the following equation results:  𝑙𝑛 (𝑊𝑛𝑛) = 𝑛 × 𝑙𝑛𝛼 + 𝑙𝑛((1 − 𝛼)2/𝛼)                 1.4  By plotting ln(Wn/n) versus n, a straight line of slope ln(α) results.  However, it is also well established that this simple model of chain propagation has significant deviations at low carbon numbers, in part because of re-incorporation of olefinic hydrocarbons in the growing chain [24, 25].  Several side reactions may occur during the FT process, such as the water-gas shift reaction (WGS) and the Boudouard reaction [26, 27].  𝐶𝑂 + 𝐻2𝑂 → 𝐶𝑂2 + 𝐻2             WGS 1.5 2 𝐶𝑂 → 𝐶 + 𝐶𝑂2                        Boudouard 1.6 In particular, the Boudouard reaction is an undesired reaction, which leads to the formation of carbon on the surface of the catalyst that can cause catalyst deactivation.  3  Although Co catalysts are more expensive than Fe, they have a higher yield of straight-chain alkanes [28, 29] and they have low WGS activity [17, 30] compared to Fe. They are also more resistant to attrition, and therefore are more suitable for slurry phase reactors [14].   Co catalysts lose up to 30-50% of their activity and hydrocarbon productivity within 9-12 months of operation in a typical FT reactor [31]. The cost of Co and noble metals (used as promoters) is high [32]. Therefore, it is essential to understand the fundamental causes of catalyst deactivation to extend the catalyst lifetime and make the FT process economically more feasible [32] .   Poisoning [33-35], sintering [36-41], carbon deposition [33, 42-46], catalyst re-oxidation [47, 48] and formation of Co support compounds [49-52] in the presence of H2O, are the main causes of catalyst deactivation in the FT synthesis. One of the main reasons for catalyst poisoning is the presence of sulphur compounds, which may be present in synthesis gas derived from natural gas or coal. The effect of sulphur compounds has been well studied and is not the focus of the present study [34, 35].   Sintering is a consequence of metal crystallite migration or atomic migration [53-55] and generally takes place at high temperature and in the presence of H2O [54, 56]. It is reported that sintering is more severe during FT synthesis with a H2/CO=1, compared to higher H2/CO ratios [41, 57, 58] and only occurs when the Co catalyst is exposed to a combination of high CO and high H2O partial pressures [58]. Sintering of smaller Co particles is more probable than larger ones because surface diffusion is more rapid for smaller crystallites [59, 60]. However, the 4  metal-support interaction (MSI) may reduce sintering [61, 62]. Smaller Co particles can have a stronger MSI than larger particles since they have a higher percentage of edge atoms [63-65]. In addition, the interaction of a metal cluster with an oxide support is low whereas a metal oxide can interact strongly with an oxide support, meaning that the degree of reduction (DOR) of the catalyst may also impact sintering [66]. Hence, the Co crystallite size and the degree of reduction impact the diffusion of Co particles and the MSI, both of which can affect sintering.  Formation of Co-support compounds may also occur as a result of diffusion of Co particles into the support. Co3O4 and -alumina have isotropic crystal structures, which assists in the migration of cobalt ions from the Co3O4 phase into the support during oxidative treatments. Spinel compounds such as CoAl2O4 result, which in H2 can only be reduced at temperatures > 800 C [37]. Smaller Co particles with higher surface diffusion rates in the presence of H2O are more prone to form Co aluminate compounds [50]. Hence, it may be expected that fresh Co on Al2O3 catalysts prepared via the traditional impregnation, calcination and reduction route will contain some amount of cobalt aluminate. More recently, however, Moodley et al. [67] reported that cobalt aluminate formation during FT synthesis under realistic operating conditions is not a major catalyst deactivation mechanism and that even at high H2O partial pressures (𝑃𝐻2𝑂 = 10 bar, 𝑃𝐻2𝑂/𝑃𝐻2  = 2.2), only about 10% cobalt aluminate is formed.  Carbon deposition is another possible mechanism of deactivation of FT catalysts [31, 32, 68-70]. Since the FT product selectivity and activity of Co catalysts is dependent on Co particle size [42, 71-76], it is likely that the rate of carbon deposition and catalyst deactivation will also depend on Co particle size. The number of active sites on the surface depends on DOR and Co crystallite 5  size, so that the number of active Co sites deactivated by carbon or non-reactive heavy hydrocarbons will also depend on the Co particle size.   Re-oxidation of Co catalysts has also been reported as a likely deactivation mechanism in FT synthesis, because the product H2O is a strong oxidizing agent that can oxidize Co particles [40, 77, 78]. Smaller Co particles (dCo< 5 nm) are more prone to oxidation than larger Co particles at 𝑃𝐻2𝑂/𝑃𝐻2  > 1-1.5 [79-81]. 1.2 Thesis objectives   From the above summary, it is clear that many of the reported catalyst deactivation mechanisms in the FT synthesis are related to the catalyst metal particle size.  However, a study of the effect of Co particle size on the deactivation of Co-based FT catalysts has not, to the author’s knowledge, been reported in the literature. Hence, in the present study the deactivation rate of several Co/Al2O3 and Re-Co/Al2O3 catalysts, prepared so that the Co particle size varied over a wide range (~1 to 22 nm), is reported. The FT catalyst activity was measured over a period of 120-190 h time-on-stream (TOS) using a slurry phase FT reactor. By combining the activity data with the used catalyst property data, the effect of Co particle size on the different catalyst deactivation mechanisms in the FT synthesis, is elucidated.   The deactivation of the Co/Al2O3 and Re-Co/Al2O3 model catalysts is also compared to that of a Co/P-Al2O3 catalyst, supplied as a representative commercial catalyst by one of the project supporters. The impact of long-term (up to 1200 h TOS) catalyst deactivation of the Co/P-Al2O3 6  catalyst was investigated as process conditions (e.g. temperature, pressure, H2/CO ratio) were varied with TOS. The catalyst deactivation as the operating conditions vary is more complex than that observed on the model catalysts and has a significant impact on the rate of CH4 production and selectivity during the FT synthesis. An empirical approach to dealing with the impact of deactivation is incorporated into a kinetic analysis of the CH4 formation rate measured for this catalyst over a period of 1200 h TOS.  1.3 Approach  To determine the relationship between Co particle size and catalyst deactivation, a series of Co/Al2O3 and Re-Co/Al2O3 catalysts with different particle sizes, were prepared. The Co particle size was controlled by using ethylene glycol as the impregnating solvent and Re was used to increase the DOR of the Co precursors. The activities and selectivities of the catalysts were compared to each other. The catalysts were analyzed for their long-term stability under FT reaction conditions. The change in the properties of the examined catalysts was investigated by comparing the structure of the fresh and used catalysts using relevant characterization techniques.   The activities and selectivities of the catalysts were measured in a continuous, slurry-phase, stirred reactor (CSTR) under controlled pressure and temperature. A CSTR is beneficial in this case since the rate of the reaction can be measured explicitly from the concentration of reactants and products; whereas, in a fixed bed reactor the conversion must be measured at different residence times to obtain an estimate of the reaction rate [82, 83]. Since the Co loading and DOR 7  of the tested catalysts was different, operation at the same reaction conditions resulted in different CO conversions. To properly assess and compare the catalysts, deactivation rates were measured at similar CO conversion levels so that the catalysts in the completely back-mixed reactor were exposed to similar concentrations of reactants and products. Similar CO conversion levels were obtained by changing the mass of the catalyst in the slurry phase reactor and hence the gas hourly space velocity (GHSV) was varied from 0.01 to 0.18 (mol/g.h). The experiments were continued for 5-7 days until the CO conversion reached an approximately constant value and the mass of liquid sample collected was equal for two consecutive days. The extent of deactivation was measured by empirical equations fitted to the CO consumption rate measured as a function of time-on-stream (TOS). The properties of the fresh and used catalysts were examined with relevant techniques to reveal the reasons for catalyst deactivation.  To investigate the effect of process conditions on the long-term stability of the commercial Co/P-Al2O3 catalyst, kinetic data were collected using the CSTR reactor operated over a range of temperatures (210 – 230 ºC), pressure (14.6 – 21 bar) and H2/CO feed gas ratios (1/1 – 3/1) continuously for a 1200 h period. One experiment was repeated periodically during the 1200 h at a standard set of conditions (220 oC, 21 bar, H2/CO = 2) to compare the activity and selectivity of the catalyst with TOS and to determine the long-term deactivation behaviour of the catalyst. 1.4 Thesis layout  Chapter 2 provides a detailed review of the literature most relevant to this study.  8  The methods for catalyst preparation, catalyst characterization and catalyst deactivation tests are described in Chapter 3.  Chapter 4 reports on the properties of the Co/Al2O3 and Re-Co/Al2O3 catalysts with different Co loadings. The Co particle size of the catalysts was measured using different characterization techniques. The DOR for all the catalysts was calculated after temperature programmed reduction. The fresh catalysts were analyzed to measure the amount of residual carbon from ethylene glycol (EG) present in the catalyst after calcination and reduction.   Chapter 5 reports on the catalysts stabilities and selectivities as measured in the CSTR reactor. Changes in CO conversion and product selectivity were measured with TOS. In addition, experiments were conducted at different GHSVs by changing the amount of catalyst in the reactor. Therefore, the effect of different CO conversion levels on product selectivity was determined. Furthermore, the effect of Co particle size on the activity and selectivity of the catalysts is reported at similar CO conversion level.  In Chapter 6 the extent of catalyst deactivation is analyzed. The used catalysts were wax extracted and recovered from the reactor. The extent of deactivation of the catalysts was measured by fitting empirical deactivation models to the changes in CO consumption rate with TOS. Then, the used catalysts were analyzed using various characterization methods to determine the changes in catalyst properties that occurred during the reaction. Subsequently, the main deactivation mechanisms were identified and the effect of Co particle size on the deactivation process was determined. 9   In Chapter 7, the stabilities of the Re-Co/Al2O3 and Co/Al2O3 catalysts are compared to the commercial Co/P-Al2O3 catalyst. This  catalyst was tested in the CSTR reactor for over 1200 h at different pressures, temperatures and H2/CO ratios to investigate the effect of process conditions on the long-term deactivation of the FT Co catalyst. The change in CH4 selectivity with TOS was modeled using an activity factor and hence related to the operating conditions.  In Chapter 8, conclusions from the study are drawn and recommendations for future work are presented.                10  Chapter 2. Literature review 2.1 Introduction  In this chapter, the effect of Co particle size on the activity and selectivity of supported Co catalysts is reviewed. In addition, the catalyst preparation methods reported in the literature that aim to control Co particle size on Al2O3 supports, are described. Subsequently, the deactivation mechanisms of supported Co catalysts are discussed based on several detailed studies. The effect of Co particle size on the deactivation of Co-based FT catalysts has not been studied specifically in the literature. However, the focus in Section 2.5 is to link the reported deactivation mechanisms to process conditions and Co particle size if the Co size is known.  2.2  Catalyst preparation and methods to control the metal particle size  One of the principal challenges of this research was producing a well dispersed catalyst with small Co particle size. The purpose of this section is to identify a simple method to control the size of Co particles on an Al2O3 support in FT synthesis. Generally the synthesis of Co particles with dCo<10 nm supported on γ-Al2O3 is a challenge, and few papers have reported Co particles in this size range which are reviewed in detail in Sections 2.2.1 and 2.2.2.  11  2.2.1 Controlling Co particle size on Al2O3 support by impregnation   The most common method to prepare Co based catalysts for FT synthesis is by impregnation, in which the dry support is contacted with a Co salt solution (precursor). The incipient wetness impregnation takes place when all the pores of the support are filled with Co salt solution and there is no additional moisture above this level [14].    It has been shown that the choice of solvent can affect the Co particle size and its distribution on the support [75, 84-86]. Different catalysts were prepared on 𝛾- and 𝛼-Al2O3 with different precursors containing water, ethylene glycol (EG), diethylene glycol or a mixture of all three [86]. Glycol can act as a surfactant and increase the wettability of the support [86]. The samples which were prepared by adding glycol with relatively high concentration had better dispersed Co3O4 particles compared to the samples with lower EG. The size of the Co3O4 particle after calcination was not related to the Co loading at high concentrations of EG (𝑚 𝐻2𝑂𝑚 𝐻2𝑂+𝑚 𝐸𝐺< 0.8); whereas, at lower concentrations of EG, increased loading increased the Co3O4 size, as shown in Figure 2.1 [86]. Adding organic solvent reduced the size of aggregates and enhanced the distribution of Co compared to the samples which were prepared just with water [86].  The Co metal particle size was measured using the H2 chemisorption data and considering the DOR of Co obtained by oxygen titration. While the Co3O4 particle sizes changed from 3.4 nm to 17 nm, the Co metal particle size was in the range of 3.1 to 18 nm after reduction in H2 at 350 ºC for 16 h [86, 87].   12     Figure 2.1. Effect of water mass fraction of impregnation solvent on Co3O4 crystallite size after calcination. Reproduced with permission from [86], Copyright © 2008 Elsevier Inc.   The effect of adding ammonium Co-citrate and Co-EDTA precursor instead of Co-nitrate has also been studied on 2.5 and 5wt% Co on Al2O3 catalysts prepared by impregnation [85]. Catalysts prepared by Co-citrate had smaller Co oxide particles compared to those prepared by Co-EDTA and Co-nitrate. To prepare ammonium Co citrate, Co nitrate was dissolved in water and KOH solution to form a Co(OH)2 precipitate. The precipitate was then centrifuged, washed with water and dissolved in acetic acid. Then 25% NH4OH was added to the solution to form ammonium Co citrate. The prepared Co oxide on Al2O3 catalysts had 3.9 nm particle size and consequently a very low DOR as well as low activity [85]. The aforementioned preparation method was also used in preliminary work for this study. The Co oxide particle size was decreased from 22 nm to 13 nm for 5w% Co/Al2O3 catalyst prepared with Co nitrate solution 13  and ammonium Co citrate solution, respectively. Nevertheless, a Co oxide particle size of 15 nm was still large for the purpose of the experiments, confirming that controlling the size of metallic Co while dCo≤10 nm, is a difficult task.   Pore size distribution of the support can also affect the size of Co particles. It has been reported that larger Co3O4 particles are prone to form on the 𝛾-Al2O3 with larger pores [86, 88-91]. Thirteen different catalysts were prepared by impregnation using exactly the same procedure but thirteen different 𝛾-Al2O3 supports with varying pore size. The Co loading for all catalysts was 20wt% and they were promoted with 0.5wt% Rh. The study showed that the Co particle size clearly increased from 12 nm to 21 nm with increase in pore diameter from 5.7 nm to 21 nm, with small Co particles formed in the narrow pores and large Co particles formed in the wide pores [88]. In the present study, a 𝛾-Al2O3 with the average pore diameter of 10 nm was used as a support for all the prepared catalysts. 2.2.2 Controlling Co particle size on Al2O3 support by the micelle method  A micro emulsion is a mixture of water, oil and a stabilizer (surfactant, a molecule with both polar and nonpolar ends). Micelles or reverse micelles will form when the concentration of the stabilizer reaches the critical micelle concentration (CMC) point due to hydrophobic and hydrophilic interactions. By adjusting the ratio of stabilizer, water and oil, Co particle sizes with the range of 5-50 nm can be produced [14, 92-96]. The preparation method usually consists of preparing two micro emulsions, one which encapsulates the metal salt, and the other which 14  encapsulates the reducing agent such as N2H4. Reduction takes place by mixing the two micro emulsions and is controlled by the inter micelle exchange rate [14, 92-96].   The preparation of Co face-centered cubic (fcc) particles on Al2O3 using the reverse micelle method was reported by Fischer et al. [92]. Co3O4 particles of 3-10 nm that did not extensively sinter during the reduction were obtained [92]. Berol 050 was used as surfactant in n-hexane. Co-nitrate solutions with different concentrations were added drop wise to the mixture which was stirred at 800 rpm for 2 h. The ratio of water to surfactant was varied to affect the size of the reverse micelles. Co precipitation was achieved by adding NH3 solution. Finally, the micelles were broken by adding acetone to the system. The resulting green precipitate was washed with acetone after micelle breakage and calcined in air. The Co3O4 powder obtained was re-dispersed in distilled water and mixed with the Al2O3 support. However, re-dispersion of Co3O4 powder in water might result in the aggregation of the particles and no method was mentioned to prevent this aggregation.  To conclude, the most common method of synthesis of supported Co particles in FT catalysts is by impregnation. By using an organic solvent the wettability of the support increases resulting in smaller Co particles. Also, using a narrow pore size Al2O3 assists in the production of smaller Co particles. Although, the micelle method yields small Co particles, it is a complicated procedure, and is mainly suitable for production of small quantities of catalysts. For example to produce 18 gram of 5wt% Co/Al2O3 catalyst, about 500 mL of hexane and 23 mL of surfactant are required. In addition, the procedure to remove the remaining surfactant and n-hexane is complicated and additional characterization techniques are required to confirm the elimination of residual 15  chemicals. Consequently, the impregnation method with a mixture of an organic solvent (EG) and water was chosen in this study for the sake of simplicity.  2.3  Reduction of Co/Al2O3 catalysts  Since metallic Co is the active phase in the FT synthesis, the last step in catalyst preparation is reduction of the Co oxide or other Co complexes to metallic Co, in a flow of H2 at elevated temperature. In laboratory studies the reduction is done while increasing temperature at a fixed rate. In this way the reduction process can be monitored by measuring the H2 consumption during the reaction. This process is called temperature programmed reduction (TPR) and is described in detail in Section 3.3.2. Different assumptions have to be made to assign reduction steps to TPR profiles. As a result, there are a variety of proposals for the reduction of Co/Al2O3 catalysts [97]. In order to understand the TPR profiles observed in Section 4.2.4, the proposed steps reported in the literature are reviewed here.     The support type can influence the reducibility of Co species. Co species on high interacting supports such as Al2O3 reduce at higher temperatures compared to low interacting supports such as silica [14, 98]. For catalysts with a Co loading of 15-25% which were calcined at low temperatures (≈350 ºC), two reduction peaks were observed, a sharp peak at ≈ 350 ºC and a broad peak extending up to 800 ºC, in which the area ratio of the second peak to the first one is 3:1. This has led to the explanation of the two step reduction involving gas solid reactions as follows [97].  16  Co3O4+H2→3CoO+H2O 2.1 3CoO+3H2→3Co+3H2O 2.2 For 10wt% Co/Al2O3 catalyst, calcined at 300 ºC for five hours, two different peaks were observed in the TPR profile [98]. The TPR was performed with a gas mixture of 6.5 vol% H2-Ar at a flow rate of 180 mL/min. The first peak was at 324 ºC and the second peak was at 382 ºC with a tail extending to 727 ºC.  The first peak was assigned to the reduction of Co oxide surface compounds which do not interact with the support and the second peak was assigned to the reduction of mixed oxides of the type xCoO.yAl2O3.  In another study [99], 15wt% Co/Al2O3 catalyst was calcined for 6 h at 350 ºC and reduced in 10%H2/Ar at a flow of 30 mL/min. Three different peaks were observed. One small peak at about 260 ºC, two major peaks at temperatures between 280-380 ºC and 380-750 ºC. The first peak was attributed the presence of residual Co nitrate solution [88, 99]. The second peak was ascribed to reduction of Co3O4 to CoO and the third peak was assigned to the reaction of CoO with H2 to form metallic Co [99].    Three reduction peaks were also observed on a 8 wt% Co/Al2O3 catalyst prepared by slurry phase impregnation and calcined at low heating rate of 0.4 ºC/min with an air space velocity of 1.02 m3air/kg Co(NO3)2.6H2O/h [100]. The TPR pattern was explained as follows for the three step reduction process: 3 CoO(OH)+0.5 H2→ Co3O4+2H2O 2.3 17  Co3O4+ H2→3CoO+ H2O 2.4 3CoO+3 H2→3Co+3H2O 2.5 It was also postulated that the CoO(OH) production increased with dicreased local concentrations of water and NOx [100]. In all of the proposed TPR mechanisms the peak extending up to 800 0C is assigned to the reduction of CoO+H2 Co+H2O.Therefore, in the present study the DOR was calculated based on H2 uptake of the 3rd  peak in the TPR profile as will be discussed in Sections 4.2.4 and 4.2.5. 2.3.1 Effect of promoter in the reduction of the Co/Al2O3 catalyst  The fraction of unreduced Co is large (>70%) on Co/Al2O3 catalysts with low Co loadings (<10-15wt%) when reduced at low temperatures (e.g. 350-400 ºC) [101]. The particles are mostly in the form of CoO (60-80%) and CoAl2O4, which only reduces at very high temperatures (>700 ºC) [101]. Also, approximately 30-60 wt% of CoO remains unreduced in catalysts with higher Co loadings (15-30 wt%) [102, 103]. It was reported that adding 1wt% Re to 20wt% Co/Al2O3 catalyst increased the Co dispersion and also the DOR of the promoted catalyst by approximately 30% compared to the Co/Al2O3 catalyst with the same Co loading [52]. Conventional promoters such as Pt and Ru can decrease the reduction temperature in both steps (reduction of Co3O4 and CoO); whereas, Re promotes the second reduction step only [101, 104, 105]. By adding a noble metal promoter, the particle size measured by CO chemisorption is slightly decreased, due to the fact that the promoters assist the reduction of smaller Co particles [104].   18   In addition, Re, Ru and Pt were used as promoters of a 25% Co/Al2O3 catalyst and the effect of co-deposition versus sequential deposition of promoters was compared [106]. It was found that all the 25% Co/Al2O3 co-deposited catalysts had smaller Co particles compared to sequentially deposited catalysts. Although, sequentially deposited catalysts required higher reduction temperatures they had higher DOR compared to co-deposited catalysts.  To conclude, in the present study, the DOR of catalysts with low Co loadings were improved by adding Re promoter to the impregnation solution with co-deposition method to obtain well-dispersed Co particles with high DOR.  2.4  Effect of Co particle size on FT activity and product selectivity  In this Section, the effect of Co particle size on the activity and selectivity of supported Co catalysts will be briefly reviewed. Although the focus of this study is mainly deactivation of Co catalysts, differences in activity and the product selectivity among different catalysts is also expected to influence the deactivation rate of the catalyst. For instance, a change in product selectivity may also change the rate of carbon deposition.  Furthermore, the associated increase in H2O production may increase the probability of sintering [54, 56].  The activity and selectivity of 12, 20, 30 wt% Co on σ- and θ-Al2O3 (medium pore) with 2-14 nm Co particle sizes, has been reported in a fixed bed reactor at 20 bar, 210 oC, H2/CO=1 and the CO conversion of 45-50% [87]. Generally, the C5+ selectivity for Co catalyst on σ-Al2O3 was 19  higher than θ-Al2O3. It was postulated that by increasing the Lewis acidity of the support (γ>θ>σ>α-Al2O3), the C5+ selectivity decreases. The C5+ selectivity increased with increased Co particle size from 2 nm to 9-10 nm. For Co particle sizes above 10 nm the C5+ selectivity decreased to almost a common value for both supports, suggesting that the influence of support is reduced with increased particle size. Consequently, the selectivity to CH4 passed through a minimum at a Co particles size of 9-10 nm. In contrast to other reports using Co catalysts on SiO2 [107] and carbon nanofiber [108], no clear relation between the particle size and turnover frequency (TOF) was observed for Co particles supported on Al2O3 support [87]. It was proposed that the change in the DOR of the catalysts during the FT reaction makes it difficult to measure the TOF with ex situ methods [87].  For catalysts with small Co particle size, numerous studies have reported a decrease in TOF with a decrease in Co particle size (dCo <10 nm) [42, 71-76, 109, 110] while other researches have not detected the same  effect of Co particle size on TOF using catalysts with similar Co particle sizes [111-117]. Therefore, Bezemer et al. [108] conducted experiments that were more systematic by measuring the activity of Co catalysts with Co particle size range of 2.6-27 nm on a carbon nano-fiber (CNF) support, in a fixed bed reactor. Unlike the catalysts on oxide supports, the Co catalysts on CNF, were highly reduced (CoO was <3% ) [108, 118] and hence the change in DOR due to exposure to synthesis gas was minimized. The results showed that for the Co particles larger than 6-8 nm the CO consumption TOF was constant (10-2 s-1). However, for smaller Co particles, TOF for CO consumption decreased with decreased particle size to 10-3 s-1. Although the TOF was almost constant for 8 and 16 nm Co particles, C5+ selectivity shifted towards heavier hydrocarbons as Co particle size increased [108]. Also, EXAFS analysis showed 20  a decrease in coordination number of Co atoms when the Co/CNF catalyst was exposed to synthesis gas. Co crystals were reconstructed from hemispherical to face centered particles under reaction conditions, resulting in a decrease in the coordination number of the Co atoms [108]. The FT reaction consists of several intermediate reactions steps such as association, dissociation and insertion and each of these reactions require a specific active site. It was proposed that in order to stabilize the active sites which are responsible for chain growth in the FT reaction, a minimum Co particle size is needed [108, 119, 120]. As small Co particle catalysts have a lower fraction of active sites for responsible for chain growth, their selectivity to CH4 is higher. Also, the higher paraffin to olefin ratio in small Co particles agrees well with their higher hydrogenation activity and lower chain growth probability [108].  Structure sensitivity of a series of Co/Al2O3 catalysts (Co particle size in the range of 3-10 nm), was tested in a fixed bed reactor with CO conversion < 10%, H2/CO=2 and 190 ºC [119]. Note that these catalysts had very high DOR which was not dependent on crystallite size [92]. TOF for both fresh and used catalysts increased with increased Co particle size, which was in agreement with several other reports [71-74, 76, 109, 110]. In this study, the decrease in activity of the catalysts from 1 to 25 h of TOS did not change the selectivity of the products. However, there was a slight increase in average CH4 selectivity and decrease in average C5+ selectivity with increased Co particle size [119].  The CH4 selectivity for these catalysts was 50-100% higher compared to the literature [119]. Since water inhibits CH4 formation rate [121], it was proposed that low partial pressure of water due to the low CO conversion resulted in an increase in CH4 selectivity [119].   21  Selectivity and activity results for Co catalysts in the range of 5.6-11 nm on ITQ-2 support was compared to a catalyst with very low dispersion and a Co particle size of 141 nm supported on SiO2 [107]. The experiments were conducted in a fixed bed reactor at conversion levels of 10±2 %, CO/H2/Ar=3/6/1, 20 bar and 220 oC. The catalysts were highly reducible with DOR of 87-100%. It was found that the TOF decreased with decreased Co particle size from 11 to 5.6 nm, but was constant for both 11 and 141 nm catalysts. However, C5+ selectivity increased from 61.6 to 78.9 wt%, even at constant TOF. This is probably due to the different intrinsic activities of small and large Co particles. There was also no correlation between the CO2 selectivity and particle size. It is known that the presence of Co oxide promotes the water gas shift reaction [77, 122, 123]. Accordingly, the low selectivity towards CO2 for all the catalysts was due to the high DOR for these catalysts.  Steady State Isotopic Transient Kinetic Analysis (SSITKA) was applied to understand the relation between metal particle size in FT synthesis and the reaction intermediate surface coverage of Co particles [65]. The trend of TOF versus particle size was the same as the trend reported elsewhere [42, 71-76, 108-110]. Based on the experiment, it was found that the fraction of irreversibly chemisorbed CO increased linearly with the fraction of unsaturated Co sites. In other words, concentrated valence electrons on the low coordination number atoms led to stronger CO bonds [65]. The cubo-octahedral model shows that the fraction of atoms with low coordination number is meaningfully higher on small Co particles [107]. Consequently, metal atoms with low coordination number may bond irreversibly with CO which results in partial blockage of surface Co atoms and hence a decrease in TOF on the catalysts with small Co particles [65].  22   To conclude, Co crystals have different shapes and sizes and consequently different amounts of Co atoms on corners, edges and terraces. The ability of these sites to associate or dissociate a specific bond or to release the products is different [124]. The FT reaction consists of several intermediate reactions. However, on catalysts with small Co particle size the desired ensemble of active sites is not stable or optimum in order to combine these reactions [108, 119]. Consequently on Co particles with dCo<10 nm the general trend is decreased TOF with decreased Co particle size [42, 71-76, 109, 110]. 2.5 Catalyst deactivation mechanisms 2.5.1 Formation of Co-support compounds   A thermodynamic evaluation has been conducted to determine if the formation of Co oxides and Co-support species from metallic Co are favoured at realistic FT conditions [125]. Generally, the range of PH2/PH2O at industrially relevant conditions varies from 0.86 to 2. These values are higher than the equilibrium constants for  𝐶𝑜 + 𝐻2𝑂 ↔ 𝐶𝑜𝑂 + 𝐻2 and 𝐶𝑜 + 4 𝐻2𝑂 ↔ 𝐶𝑜3𝑂4 +4𝐻2 but lower than the equilibrium constant for Co+Al2O3+H2O↔CoAl2O4+H2. As a result, under FT conditions, oxidation of metallic Co to Co-oxides is not spontaneous; whereas, formation of CoAl2O4 cannot be ruled out by thermodynamic calculations based on equilibrium constants, as shown in Figure 2.2 [125]. It is noteworthy that the thermodynamic evaluations have been conducted for bulk phase thermodynamics, which might be different in the presence 23  of metal-support and metal-metal oxide interactions at high Co dispersions and in the presence of synthesis gas (See Section 2.5.3). There are some studies, which show the formation of Co-support species is possible at FT conditions.      Figure 2.2. Thermodynamic equilibrium constants for cobalt oxidation reactions: (──) thermodynamic equilibrium requirement for Co+Al2O3+H2O⇆CoAl2O4+H2, (...) thermodynamic equilibrium requirement for Co+H2O⇆CoO+H2, (---) thermodynamic equilibrium constant for 3Co+4H2O⇆Co3O4+4H2. Reproduced with permission from [125], Copyright © 2000 Elsevier Inc.   Since the range of H2/CO ratio varies from 0.5-1.5 to 1.7-3 for synthesis gas derived from coal and natural gas, respectively, the deactivation of Co/SiO2 catalyst in a down flow fixed bed reactor at 210 °C, 2.0 MPa and SV=1000 h− 1 with H2/CO=1,2 and 3 was investigated [41]. As the H2/CO ratio increased, the deactivation rate also increased. TPR results showed the formation of Co silicates or hydro silicates on the used catalysts, which are only reducible at high temperatures (T>800 °C) and were not detectable on the fresh catalyst. The amount of Co silicates/hydro silicates increased at high H2 partial pressures, although XRD was not capable of 24  detecting these species, probably due to their high dispersion. As the amount of H2O in the outlet gas was almost constant for all experiments, it was concluded that high partial pressure of H2 led to the reduction of Co particles, thus the metallic Co interacted with SiO2 under hydrothermal conditions and formed Co silicates [41]. Results from H2 chemisorption and FTIR analysis of the used catalysts in the presence of CO indicated that the amount of active metallic Co was decreased with increased H2/CO ratio, which is compatible with the formation of Co-support compounds. Consequently, it was postulated that at higher H2/CO ratios, deactivation was mainly caused by the formation of Co silicate species, while for H2/CO=1, sintering was the cause of deactivation [41]. However, no other evidence for sintering except kinetic data and the power order of deactivation was provided, because XRD could not be used for analysis of highly dispersed Co crystallites.    The formation of Co support species during the FT reaction at realistic commercial operating conditions (T=230 °C, P=20 bar and H2 + CO conversion between 50 and 70% with feed gas composition of 50–60 vol.% H2 and 30–40 vol% CO) has been studied for 20 wt% Co supported on 𝛾-Al2O3, with an average Co particle size of 6 nm. External H2O was injected into the feed [67]. Catalyst samples were collected periodically from the reactor operated at industrially relevant conditions with 𝑃𝐻2𝑂=4-6 bar. At these conditions, the formation of Co aluminate was not significant. By adding external H2O to the system the formation of Co aluminate increased slightly (at H2O partial pressure of 10 bar); however, the used catalyst still underwent reduction when compared to the fresh catalyst. The results implied that the amount of CoOx decreased, but the amount of CoAl2O4 increased with H2O addition. As a result, it was concluded that the formation of Co and support species did not change the total activity of the catalyst significantly 25  and the main deactivation mechanism was either sintering or carbon deposition. It was also postulated that the small amount of Co aluminate formation was the result of diffusion of small CoO particles (2-3 nm) to the Al2O3 support. Some of the small CoO particles sintered during the reaction and the resulting larger particles have lower interaction with the support and could reduce in the FT environment [67].  The effect of water on deactivation of 0.5wt% Pt and 15wt % Co on Al2O3 support with Co particle size of 5.6 nm in FT synthesis has been investigated in a CSTR reactor at T=210 0C, P=2 MPa and H2/CO=2 [50]. The results showed that below 25% water addition (PH2O/PH2 ≤0.6) the observed deactivation was reversible and due to the kinetic effects. However, above this level, the deactivation was irreversible. Examination of the used catalysts by XANES analysis indicated a sharp peak on the used catalyst that was assigned to Co aluminate and was not observed in CoOx compounds. This confirms that some Co was transformed to a tetrahedraly coordinated environment and formed Co aluminate.   Un-promoted, Ru promoted and Pt promoted 15wt% Co/Al2O3 catalysts (with Co particle size of 5.9, 5.7 and 5.6 nm, respectively) were tested in a CSTR reactor at P=1.8 MP, T=220 0C and H2/CO=2 to investigate the catalyst deactivation mechanism during FT process [49]. Comparison between XANES analysis of calcined and used catalysts suggested the formation of Co aluminate compounds. EXAFS analysis also showed sintering of Co particles. It was suggested that addition of Ru and Pt results in the reduction of small Co particles. Since the behaviour of these small Co particles deviate strongly from the bulk Co, hence the formation of Co aluminate, Co oxide and sintering is more probable on the promoted catalysts [49]. In 26  addition at initial stages of FT synthesis, these catalysts are more active (due to more active sites) and produce more water. Therefore, the higher deactivation rate on the promoted catalysts was assigned to highly reduced small Co particles present on these catalysts [49].   Re-promoted and un-promoted 20 wt% Co/Al2O3 catalysts with Co particle sizes of ~10 nm were tested in a quartz capillary in situ cell for FT synthesis at T=220 0C, 18 bar, H2/CO = 2.1 and with CO conversion >50% [52]. During the initial deactivation stages, the promoted catalyst showed a transformation of Co to Co2+ tetrahedraly coordinated, which is a part of the CoAl2O4 structure. No significant change in Co particle size or concentration of Co was observed [52]. 2.5.2 Formation of carbon species   As mentioned in Section 2.4, Co particle size affects FT product selectivity and activity of the catalyst [42, 71-75, 109, 110]. Consequently, the change in the selectivity might influence the carbon deposition rate and stability of the catalysts. For instance, a higher selectivity towards heavier hydrocarbons will affect the rate of non-reactive high molecular weight hydrocarbon deposition on the surface of the catalyst that can block the pores. Also, highly dispersed Co particles which are mainly within the pores of the support, might deactivate more easily if the deactivation is caused by pore blockage by carbonaceous materials. In addition, changes in Co particle size and DOR will change the amount of available active sites on the surface. As a result, depending on the percentage of active sites covered by carbon deposits, the extent of deactivation may vary. Hence, we expect that a change in particle size might influence the rate of deactivation caused by carbon deposition on the surface of the catalyst.   27   The formation of un-reactive carbon in the presence of H2 on the surface of both Co and the support in a Pt-Co/Al2O3 catalyst with 20wt% Co loading has been observed [68]. The FT experiment was performed in a 100-barrel/day slurry bubble column reactor, and the catalyst was examined after six months of operation at commercial FT conditions (T=230 °C, P=20 bar, H2 + CO conversion between 50 and 70%, feed gas composition of 50–60 vol.% H2 and 30–40 vol.% CO). The Co particle size was not reported in the study. The catalysts were wax extracted in an inert atmosphere after the experiment. TPH and TPO showed an increased amount of inactive polymeric carbon formation on the surface of the catalyst as TOS increased. Finally, the catalyst with polymeric carbon deposits was regenerated by oxidation at 300 °C, which resulted in significantly lower polymeric carbon content. The catalysts were then re-reduced and used in a lab-scale CSTR reactor. The regenerated catalyst showed 90% recovered activity.   Other studies have also shown the formation of polymeric carbon on the surface of the catalyst.   For instance, a comparison between the deactivation behaviour of Ru and Pt promoted as well as un-promoted Co-based catalysts on a P modified Al2O3 support (P-Al2O3) has been reported, both in CSTR and fixed bed reactors [126]. The Co particle size of these catalysts was 18.2, 14.7 and 15 nm for the un-promoted, Ru- and Pt-promoted catalysts, respectively. Ru-Co/P-Al2O3 (Ru- promoted Co based catalyst on P-Al2O3 support) had the highest activity in the fixed bed reactor that was attributed to the higher reducibility and homogenous dispersion of Co particles on this catalyst. However, this catalyst acted differently in the slurry phase reactor, having a lower conversion compared to the Pt-promoted catalyst. The lower activity was ascribed to the 28  formation of larger catalyst “lumps” containing heavy hydrocarbons. The size of the catalyst agglomerate was almost two times larger for Ru-Co/P-Al2O3. The used catalysts were characterized by TPSR, XRD and Raman spectroscopy and formation of high amounts of polymeric carbon was confirmed for the Ru-Co/P-Al2O3. While the Co particle size did not change significantly for the promoted catalysts, the un-promoted catalyst showed a considerable increase in Co particle size [126].  The formation of high molecular weight products and blockage of support pores was suggested as one of the main deactivation mechanism of Co/SiO2 catalysts during CO hydrogenation [46]. Catalysts were prepared from either carbonyl or nitrate solution. Carbonyl prepared catalysts (Co(CO)/SiO2) had higher dispersion and the Co particles were mainly inside the pores compared to the nitrate prepared catalyst (Co(N)/SiO2) which had lower dispersion and the Co particles were mainly on the external surface. The experiments were conducted in a fixed bed reactor at P=5 bar, T=235-290 oC and Ar:CO:H2 3:1:3. The initial activity of Co(CO)/SiO2 was higher as a result of higher dispersion but the deactivation rate was also higher compared to Co(N)/SiO2. The spent catalysts were characterized and carbon content of the used catalysts was measured. The amount of carbon on the Co(CO)/SiO2 was higher and the carbon was mainly in the form of C15-C30 paraffins,C10-C20 alcohols and C10-C20 ketones. It was suggested that the high molecular weight hydrocarbons blocked the pores of Co(CO)/SiO2 and reduced the catalyst activity; whereas, for the Co(N)/SiO2 catalyst, Co particles were more accessible to the reacting gas as they were mainly on the external surface, consequently pore blockage could not affect their activity significantly [46].    29  Co2C species have also been detected by XRD on the surface of used promoted and un-promoted Co catalyst supported on Al2O3 [127]. The catalysts were tested in a CSTR reactor stirred at 750 rpm and operated at T=220 oC and H2:CO= 2:1.  However, the main deactivation mechanism was suggested to be Co re-oxidation and sintering [49]. In addition, in situ XRD indicated the formation of Co2C species on the surface of Co/Al2O3 with 25wt% Co loading after 8-10 hrs of operation in a fixed bed reactor, although the initial deactivation was assigned to Co sintering [127].  A 25 wt% Co on Al2O3/SiO2 support promoted with 0.25 wt% Pt was tested in a fixed bed reactor for 800 h at T=230 0C, P=20 bar and at different partial pressures of CO and H2 [31].  Deactivation increased as the H2/CO ratio decreased at constant PCO, due to the formation of less hydrogenated polymeric carbon. Also, deactivation increased with increased H2/CO ratio at constant PH2, which was attributed to the formation of more hydrogenated polymeric carbon. There was no sintering of Co particles detected by XRD. Also, formation of Co oxide and Co aluminate was inhibited by conducting the experiments at low CO conversion levels (16-23 %) [31].  To summarize, formation of polymeric carbon has been proved at realistic FT conditions [31, 68, 128], although there have been no studies on the effect of Co particle size on the formation of polymeric carbon and deactivation of the catalyst. In addition, blockage of the pores by high molecular weight materials has been reported as a deactivation mechanism by carbon on Co catalysts in CO hydrogenation [46]. Carbon in the form of Co2C can also cause an activity loss during FT reaction [127]. 30  2.5.3 Formation of Co-oxide and the effect of H2O   During FT synthesis the following reactions take place, in which CO reacts with H2 on the Co surface and forms hydrocarbons (CH2). Subsequently, the surface oxygen is removed while reacting with H2: CO+H2+Co ↔ CoO+ CH2         2.6 CoO+H2↔ Co+H2O 2.7 Accordingly, regeneration of CoO is only possible if the state containing Co and water is energetically favoured over the state containing CoO and H2. It has been theoretically demonstrated that the oxidation of spherical Co crystallites smaller than 4-5 nm is thermodynamically possible under FT conditions with 𝑃𝐻2𝑂/𝑃𝐻2= 1-1.5. The total surface energy of the system in the presence of water and H2 was calculated by considering the effect of Co crystallite diameter. Taking into account that Co crystallites smaller than 100 nm are mainly stable and in the form of β-Co (fcc), Figure 2.3 indicates the stability region calculated for β-Co (fcc) with ± 15% variation in surface energy [79].  31   Figure 2.3. Stability region of spherical β-Co (fcc) and Co(II)O at 493 ºK in H2O/H2 atmosphere (…..) β-Co ±15%. Reproduced with permission from [79], Copyright © 2005 Elsevier Inc.  In an experiment conducted in a slurry phase reactor using Pt-Co/Al2O3 catalyst with 20 wt% Co loadings and 6 nm Co particle size at industrial condition (T=230 °C, P=20 bar, H2 + CO conversion between 50 and 70%, feed gas composition of (50 vol.% H2 and 25 vol.%) [129], fresh and spent wax coated catalysts were analyzed by XRD, XANES and magnetic measurements. All these techniques demonstrated that the spent catalyst contained less Co oxide than the fresh catalyst, which means that under FT reaction conditions, the catalyst had been reduced, therefore the observed deactivation was not a consequence of oxidation. Although, the main reason for deactivation was not investigated in this work, the reason for reduction of the catalyst was probably related to the high partial pressure of H2 or presence of CO or sintering that caused larger crystallites that have a higher tendency towards reduction [129]. In addition, it has been shown that for selected literature data, in which the oxidation state of Co was measured directly, the oxidation state of Co is related to Co particle size and 𝑃𝐻2𝑂/𝑃𝐻2 in the system and is in agreement with the theoretical values shown in Figure 2.3 [79]. 32   A highly dispersed Co catalyst was prepared on potassium-exchanged zeolite (KL) with a 1 nm Co particle size measured by XANES and the DOR of 75% for the fresh catalyst. The catalyst was tested in a CSTR reactor at industrially relevant conditions (T= 220 °C, P=1.8 MPa, H2/CO ratio of 1.95 (v/v) and 1.0–3.0 NL/(g.h) space velocities) [130]. Upon exposure to syngas, the Co-Co coordination number decreased while Co-O coordination number increased, indicating that a significant oxidation had occurred (67% oxidized). The initial 𝑃𝐻2𝑂/𝑃𝐻2 that caused the oxidation was unknown, because by the time the conversion was measured the oxidation had already occurred and the CO conversion had dropped significantly [130].    The deactivation mechanism of Ru-Co/γ-Al2O3 in a tubular fixed bed reactor has also been studied [40]. The metallic Co particle size was about 20 nm. The amount of 𝑃𝐻2𝑂 (⁄ 𝑃𝐻2 + 𝑃𝐶𝑂) during 1000 h of FT reaction at T=220 °C and P=20 bar was measured. In this experiment the 𝑃𝐻2𝑂 (⁄ 𝑃𝐻2 + 𝑃𝐶𝑂) dropped from 1.3 to 0.8 ( 𝑃𝐻2𝑂/𝑃𝐻2 from 1.95 to 1.2) in the first 250 h period; however, it only decreased from 0.8 to 0.7 ( 𝑃𝐻2𝑂/𝑃𝐻2 from 1.2 to 1.0) in the next 750 h. The catalysts were examined by XRD, TPR, BET, H2 chemisorption as well as carbon content measurements. When the 𝑃𝐻2𝑂 (⁄ 𝑃𝐻2 + 𝑃𝐶𝑂) was above 0.75 ( 𝑃𝐻2𝑂/𝑃𝐻2 > 1.1), the decrease in CO conversion versus time was zero order in CO conversion. The deactivation was attributed to oxidation of metallic Co and Co-support interaction. At 𝑃𝐻2𝑂 (⁄ 𝑃𝐻2 + 𝑃𝐶𝑂) below 0.75, the deactivation rate was fitted with a power-law rate expression. The main deactivation mechanism was postulated to be sintering in this operating window [40]. According to TPR results, the H2O induced Co oxide can be regenerated by reduction at 270-275 °C. In addition, a more resistant form of Co oxide with high interaction between Al2O3 can be regenerated at 400 °C, and Co-33  aluminates will be regenerated only above 800 °C [40]. The used catalyst was regenerated at these three temperatures. As a result, after the first regeneration step, 69.9% of the catalyst activity was recovered, 21.9% of the catalyst activity was recovered in the second step of regeneration, and 7.2% of the total activity was not recovered after the third step of regeneration. Therefore, it was concluded that the main deactivation mechanism was Co oxidation [40].   Some studies have tried to quantify deactivation at a variety of operating conditions. For example, the effect of H2O on the deactivation of Pt promoted Co/Al2O3 catalyst (dCo= 5.6 nm) operated at T=180 0C, P=2.93 MPa has been studied by increasing the CO conversion with decreasing space velocity (SV) to change the H2O partial pressure and by adding external H2O to the system [77]. In the first step, at SV > 2 L (STP)/ (g.h) and consequently low partial pressure of water, the deactivation rate based on CO conversion was low (0.3 % per day); however, by decreasing the space velocity to lower values (CO conversion > 50%, 𝑃𝐻2𝑂/𝑃𝐻2  >0.45) the water partial pressure as well as the deactivation rate increased. In the second step, specific amounts (3.0-30%vol) of H2O were added to the system. By adding a small amount of water (H2O/H2=0.3-0.6) the deactivation was reversible and due to kinetic effects. However, adding 28 vol% H2O (𝑃𝐻2𝑂/𝑃𝐻2 >0.59) resulted in permanent deactivation, probably due to the oxidation of Co. During this period, CO2 selectivity was also increased from 4% to 11%, which is evidence for Co oxidation. This is because Co oxides are known to be active in the water-gas shift reaction [77, 122, 123]. In this study, characterization techniques needed to investigate the catalyst oxidation state were not used and the work was mainly focused on the kinetic effects.  34  Some studies have investigated the effect of catalyst properties on the deactivation mechanism. For instance, the effect of H2O on six Co-based catalysts with three different supports (TiO2, 𝛼-Al2O3 and 𝛾-Al2O3) has been investigated in a fixed bed reactor [78]. In all cases, H2O had a positive kinetic effect on the FT rate, while the partial pressure of syngas was kept constant. However, for the narrow pore catalyst with 12 wt% Co on  𝛾-Al2O3 support and 12 nm Co particle size, CO conversion decreased upon exposure to H2O, which was assigned to oxidation of Co. The amount of H2O added was chosen so that 𝑃𝐻2𝑂/𝑃𝐻2 represented 50-75% conversion in a CSTR reactor. The TPR tests on the used catalyst demonstrated a significant H2 uptake at high temperature after exposing to FT conditions, which was not apparent before the experiment and was not observed on Co catalysts on other supports. This increase in H2 uptake may be the result of formation of Co-support compounds or formation of Co oxides, which are well dispersed on the support, and lead to deactivation.    2.5.4 Sintering and aggregation  Sintering refers to either a loss of catalyst surface area due to crystallite growth or loss of support surface area due to support collapse (which may result in loss in active sites when pores of the support collapse and block the active phase). In this study we refer to sintering as a crystallite growth. There are three main mechanisms for growth of crystallites known as particle or crystallite migration, atomic migration (Ostwald ripening) and vapour transport (at very high temperatures) [56]. The driving force for sintering is minimization of the surface energy of Co particles which results in formation of more stable large Co particles [131, 132]. Also an increase in mobility of atoms can assist sintering [131, 132]. Mobility of atoms increases in the 35  presence of water [132, 133] and with an increase in temperature. At the Hütting temperature (T=0.3 T melting in ºK), the atoms on defects start to move and at the Tamman temperature (T=0.5 T melting in ºK) the atoms in the bulk exhibit mobility [58, 131]. For Co catalysts these temperatures are 253 and 604 ºC, respectively [58].  Sintering of the metals of supported catalysts depends on several parameters such as temperature, reaction atmosphere, support, promoter and metal. Stability of metal crystallites towards sintering is related to their tendency to dissociate [66, 134, 135]. Therefore, the size and the shape of the crystallites can affect sintering rate. The bond energy of metal atoms to a metal crystallite decreases with decreasing particle size. Indeed the melting temperature of a micro cluster is well below that of the bulk material [66]. Also, surface diffusion is more rapid for smaller aggregates [59, 60]. In addition, the metal and support interaction (MSI), has a major impact on the extent of sintering [61, 62].  When the MSI is large, crystallite migration is less likely. Generally the interaction of metal clusters with an oxide support is weak; whereas, metal oxides can interact strongly with the oxide support [66]. In conclusion, both the crystallite size and MSI can affect the sintering of metal particles.   Furthermore, the effect of adding promoters to Co/Al2O3 catalysts has been reported in the literature [101]. It has been suggested that catalyst promotion facilitates the reduction of small Co particles (dCo < 2-4.4 nm). Small Co particles are more prone to oxidation at high CO conversions and can go through a complex sintering process,which involves the coalescence of CoO particles, re-reduction and sintering of the particles [101].    36  In situ XRD was used to investigate the deactivation of two 25wt% Co/Al2O3 catalysts promoted with 0.1wt% Pt. The catalysts were prepared and calcined at 300 and 500 oC and tested in a fixed bed reactor at industrially relevant conditions (T =220 0C, P = 20 bar, H2/CO = 2), with the conversion below 50% [127]. STEM images indicated the formation of 5-10 nm spherical Co particles. The in situ XRD demonstrated fcc and hcp Co crystallites as well as Al2O3, nevertheless there was no CoO on the surface. The fcc Co crystallites were dominant on the surface and within the first 6 h of the reaction, the size of the fcc Co particles increased from 6 nm to 10 nm. The degree of sintering was less for the catalyst prepared with the higher calcination temperature (Co size increase from 5.3 to 6.5 nm). There was no indication of oxidation or reduction during the process, and the size increase in fcc Co particles stopped after 6-7 hours. As a result, the initial deactivation of the catalyst was assigned to Co sintering [127].  A mechanistic model was developed for sintering of Co based catalysts in the first 400 min of the FT reaction by Sadeqzadeh et al. [132]. A three step mechanism for sintering was proposed, consisting of formation of an intermediate oxide layer on the Co nanoparticles which results in lowering the surface energy and increasing the diffusion rate of the particles. Consequently, particle migration results in collision and formation of larger particles and reduction of the oxide layer in the presence of H2. The proposed mechanism was implemented in a fixed bed unsteady state reactor model. The effect of water on sintering is also applied to the model in which α the ASF constant equals 0.9, and the particle surface is assumed to be either CoO or Co for simplicity. The sintering model accurately represents the deactivation of Co particles for the first 100 min of the reaction for Co particle sizes larger than 6 nm. It was suggested that other deactivation mechanisms must also take place along with sintering after 100 min [132].  37   The effect of changing the H2/CO ratio and temperature on the deactivation mechanism of a Pt-Co/Al2O3 catalyst was investigated in a mini-fixed bed reactor [57]. It was suggested that both the operating temperature and the H2/CO ratio, can affect the stability of Al2O3 supported Co catalysts significantly. At 220 ºC and H2/CO=1, deactivation was attributed to sintering in the presence of water; whereas, at 220 ºC and H2/CO=2-4 surface oxidation of Co also played a role in the deactivation of the catalyst. At higher temperature (240 ºC), the initial deactivation profile was assigned to sintering. However, long-term deactivation was proposed to be the effect of either carbon deposition or Co oxidation. The deactivation profiles were best fitted to a model that assumes sintering and carbon deposition occur simultaneously during the reaction [57].   An in situ magnetometer was used to study the deactivation mechanism of a Pt-Co/Al2O3 catalyst as a function of process conditions in a fixed bed reactor [58]. Co crystallites were in the range of 3-15 nm, with maximum abundance of 6 nm. CO conversion was < 15% and water partial pressure was increased by external injection. The process conditions were changed widely, by fixing PH2O and changing CO/syngas ratio and vice versa. In addition, a mixture of water and H2 (without CO) was used as a feed for comparison. It was found that sintering can occur both at high PCO and high PH2O. Nevertheless, no sintering was observed with a mixture of H2 and water at 230 ºC and the sintering process only started when CO was exposed to the catalyst. Therefore, it was proposed that sintering occurred via formation of sub carbonyl groups which may lower the activation energy for Co migration. Also, formation of a hydroxylated support weakened the Co-support interaction which facilitated sintering [58].  38  Intra-particle spacing is also reported to have an effect on deactivation of Co/SiO2 catalysts [136]. A series of Pt promoted and un-promoted Co catalysts were prepared with ~9 nm Co particle size. The size of aggregates (single crystallite domains consisting of multiple nano-crystals) were controlled by the drying process during the catalyst synthesis. It was found that the maximum spacing could be obtained when drying at 100 oC and in a flow of N2. The aggregate sizes were between 13-80 nm. The catalyst with smallest aggregates indicated 25% higher initial activity compared to the one with the largest aggregates. However, the C5+ selectivity was higher for larger aggregates. Although no particle growth was observed, macroscopic migration of Co towards the outside of the catalyst grain was detected by SEM. Subsequently, aggregates as large as 300 nm were formed. The larger the initial size of the aggregates, the greater the migration that occurred. Consequently, the catalysts with the large aggregates demonstrated a higher deactivation rate as a result of sintering on the external surface [136]. 2.5.5 Summary and conclusions  Co catalysts used in the FT synthesis are relatively expensive and deactivate during several months of operation. Therefore, to improve the economics of the FT synthesis using Co catalysts, it is necessary to extend their operating life and understand the mechanisms of catalyst deactivation. The main deactivation mechanisms reported in the literature are formation of Co-support and Co-oxide compounds, carbon deposition, sintering and aggregation.  39  Generally, formation of carbonaceous materials and polymeric carbon formation is expected in the FT synthesis [31, 68, 128]. The hydrogen resistant carbon may cover the Co and the support [68], large catalyst aggregates containing heavy hydrocarbons may form [126], the support pores may be blocked [46] or Co2C species may form during the reaction [49]. However, the effect of Co particle size on carbon deposition has not been studied. The change in Co particle size might change the carbon deposition rate. Also, the number of available active sites varies with Co particle size and Co loading, which might also affect the percentage of active sites covered by carbon. Therefore, it is expected that a change in Co particle size might also change the rate of deactivation due to carbon deposition.  There are discrepancies in attributing the deactivation mechanism of the FT synthesis to the formation of Co-support species. From a thermodynamic analysis of bulk phase formation [125] the formation of metal-support compounds is possible. Also, an increase in Co-support compounds has been observed in experiments that have been conducted at the same partial pressure of H2O as the outlet gas, but with different H2 partial pressure [41]. It is postulated that a high partial pressure of H2 leads to reduction of Co oxide particles. Consequently, reduced Co interacts with the support in presence of H2O to form Co-support compounds [41]. It has been shown that, even by increasing the amount of H2O up to 10 bar, the formation of Co-support compounds is not sufficient to cause severe deactivation [67]. Generally, the formation of Co-support compounds cannot be ruled out in FT synthesis, but there is debate about the extent of deactivation that can be caused by this mechanism. Also, the effect of particle size in the formation of Co-support compounds has not been studied, although, the formation of Co- support compounds is expected to be more probable when Co particle size is smaller [49, 81]. 40   The effect of Co particle size and relative partial pressure of H2O and H2 on the oxidation state of bulk Co (fcc) has been theoretically calculated [79]. However, there are some literature data that are not in agreement with these calculations.  For instance, it has been reported that 20 nm Co particles at  𝑃𝐻2𝑂/𝑃𝐻2~1.1 [40], 12 nm Co particles at 𝑃𝐻2𝑂/𝑃𝐻2~1 − 1.5 [77] and 5.6 nm Co particles at 𝑃𝐻2𝑂/𝑃𝐻2~0.59 [78] were oxidized in FT synthesis even though the Co particles were relatively large and 𝑃𝐻2𝑂/𝑃𝐻2 was below the theoretical value that can cause oxidation. Therefore, there are some discrepancies in the literature about the possibility of formation of Co oxide species with different Co particle sizes at realistic FT conditions.     Sintering of Co particles was observed during the FT reaction in the presence of H2O in some reports, especially within the first hours of the reaction [53, 132]. It is reported that sintering is more severe during FT synthesis with a H2/CO = 1 [41, 57, 58]. Sintering of smaller metal particles is more probable than larger ones because surface diffusion is more rapid for smaller crystallites [59, 60]. Therefore, it is important to investigate the effect of different parameters such as the initial Co particle size on sintering in a FT reaction.  Reviewing the published works on catalyst deactivation in the FT synthesis reveals that there is no clear conclusion on the effect of Co particle size on catalyst deactivation mechanisms during FT synthesis. Hence to determine the effect of Co particle size and process conditions on the deactivation of the FT Co catalysts, it is required to synthesize Co/Al2O3 catalysts with controlled Co particle sizes and to characterize them before and after reaction. Also, in order to understand the deactivation mechanism, it is necessary to know the effect of Co particle size on 41  the activity and selectivity of the catalysts. Therefore, the following chapters of the present study are focused on catalyst preparation and characterization, testing the catalysts in a FT reactor and measuring the activity, selectivity and stability of the catalysts in FT synthesis. These data are used to investigate the deactivation mechanism by characterizing the used catalysts. Finally, the deactivation of the model Co/Al2O3 and Re-Co/Al2O3 catalysts is compared to a commercial Co/P-Al2O3 catalyst and the effect of process conditions (e.g temperature, pressure and H2/CO ratio) on long-term deactivation of the Co/P-Al2O3 catalyst is investigated for up to 1200 h TOS.               42  Chapter 3. Experimental methods 3.1 Introduction  This chapter focuses on the methods used to conduct the FT experiments, including the catalyst preparation. Methods used to characterize the fresh and used catalysts are also described and the experimental set-up and operating procedure used to assess the catalyst activity, selectivity and stability are presented. 3.2 Catalyst preparation   The Co/Al2O3 and Re-Co/Al2O3 catalysts were prepared by a modified incipient wetness impregnation method in which the Co particle size is controlled by using a water-ethylene glycol impregnating solution [86]. Accordingly, the required amount of Co(NO3)2.6H2O (Sigma Aldrich  98%) was dissolved in aqueous - ethylene glycol (EG) (Sigma Aldrich reagent plus 99%), with the EG weight fraction varied from 0 to 0.90. The solution was added drop-wise to 2.5 g of the γ-Al2O3 (Sasol 99%, pore volume 0.525 ml/g) support that was sieved before use to provide particles with diameters (d) in the size range 90≤ d≤ 150 µm. The impregnated support was aged for ~ 2 h, dried in stagnant air at 110 ºC for 3 h and calcined in a 30 mL(STP)/min flow of air at 300 ºC for 16 h. The catalysts were subsequently reduced in 9.5 vol% H2 in Ar, by heating at a ramp rate of 5 ºC/min from room temperature to 600 ºC, with the final temperature held for 30 min. After cooling to room temperature, the catalysts were transferred to the reactor in 30 mL of squalane under Ar flow to limit exposure to air. The Re-Co/Al2O3 catalysts were 43  prepared similarly, except that a perrhenic acid solution (HReO4) (Sigma Aldrich 75-80 wt% in H2O) was added to the Co(NO3)2.6H2O and water-EG solution, so that the Re:Co molar ratio was set to 0.03125 for all catalysts. The catalysts were prepared with Co loadings of 5 to 20 wt %, with varying amounts of EG in the impregnating solution.  Herein the catalysts are identified as nCo/Al2O3(R) or mRe-nCo/Al2O3(R) where n is the Co loading (wt%), m is the Re loading (wt%) and R is the mass fraction of EG in the impregnating solution. The details of calculations for catalyst preparation are explained in Appendix A. 3.2.1 Wax extraction of the used catalysts  The catalysts that had been used in the slurry phase FT reactor were covered with wax that must be removed before characterization. The catalysts were washed with methylene dichloride (CH2Cl2) and then transferred to glass micro fiber filters in order to be washed using a Soxhlet extractor. The extractor was filled with CH2Cl2 and heated to 80 ºC. The samples were placed inside the extractor for two hours. The washed samples were then dried in stagnant air and heated to 350 oC degree in vacuum (66 Pa). The samples were then used for further characterization.  44  3.3 Catalyst characterization methods 3.3.1 Thermogravimetric analysis (TGA)  Thermogravimetric analysis (TGA) is a method to measure weight loss (or gain) of a sample as a function of temperature in a controlled flow of gas such as N2 or air [137]. In this study, TGA was done using a TGA-50 thermo gravimetric analyzer (Shimadzu, Japan) to estimate the calcination temperature required for catalyst preparation. Samples of 7-14 mg were analyzed in an air flow of 30 mL (STP)/min at a ramp rate of 10 ºC/min up to 950 ºC and the samples remained at the maximum temperature for 30 minutes. The weight change of the sample was recorded online during the experiment. 3.3.2 Temperature programmed reduction and CO pulse chemisorption   Temperature programmed reduction (TPR) measures the H2 consumed in the reduction of the Co oxide precursor as a function of temperature. From the reaction stoichiometry, the amount of Co oxide reduced to Co can be measured when the total H2 consumption is known. Therefore, the approximate degree of reduction (DOR) can be determined in percentage [137].  𝐷𝑂𝑅 = (𝑛𝐶𝑜0/𝑛𝐶𝑜) × 100 3.1 where 𝑛𝐶𝑜0 is the moles of reduced Co per gram of catalyst and  𝑛𝐶𝑜 is the theoretical moles of Co loaded on the support. A Micromeritics Autochem II 2920 was used for TPR analysis of the catalysts. TPR was done in a10%H2/Ar flow at 50 mL(STP)/min and the sample was heated at a 45  ramp rate of 5 ºC/min up to 600 ºC. The catalysts remained a 600 ºC for 30 min before cooling to 55 ºC. Prior to reduction the catalysts were pre-treated in 50 ml (STP)/min Ar and heated to 120 ºC at a rate of 10 ºC/min and then held at this temperature for 45 min. The purpose of the pretreatment step was to remove adsorbed moisture from the system.   CO pulse chemisorption was done in the same unit after the reduction with H2, to measure the dispersion of metallic Co. After the reduction step, 50 mL(STP)/min of He was used to flush the samples and remove the moisture produced during the reduction. The samples were cooled to 55 ºC and prepared for CO pulse chemisorption. CO pulses were injected repeatedly until the response from the thermal conductivity detector (TCD) showed no further CO uptake after consecutive injections. The amount of CO absorbed was subsequently used to measure the Co dispersion of the catalysts as described in Section 4.2.5. 3.3.3 Temperature programmed hydrogenation (TPH)  In order to identify the carbon species deposited on the used catalysts, TPH of the wax extracted catalysts was conducted in a stainless steel fixed bed reactor and a flow of 17 %H2/He at 36 mL(STP)/min. The reactor was heated at a ramp rate of 5 ºC/min from room temperature to 600 ºC followed by holding at this final temperature for 30 min. The outlet gas from the reactor was connected to a VG ProLab quadrupole mass spectrometer (MS). All the peaks were normalized to the intensity of He (the reference gas).  46  3.3.4 CH analysis  Elemental C and H analysis was performed on the calcined and reduced catalysts as well as the used catalyst. The samples were analyzed with a Perkin-Elmer 2400 Series 2 CHNS/O analyzer. Prior to analysis, the samples were crushed with a mortar and pestle. Samples of 1.5-2.5 mg were loaded into tin capsules and injected into the combustion column of the unit. The samples were then introduced to the oxygen environment with excess oxygen and burned at 975 ºC. The combustion gases passed through the reduction tube at 500 ºC and mixed in the mixing chamber before passing through the packed column and the TCD using He as the reference gas. Consequently, the weight percentage of C and H were determined by calibration. 3.3.5 X-ray powder diffraction (XRD)  XRD can be used for qualitative and quantitative analysis of crystalline materials larger than 5 nm which diffract X-rays when their amounts are greater than 1 wt%. Crystal structures contain planes formed by repetitive arrangement of atoms, which diffract X-rays that interfere constructively at critical angles, dependent upon the various planes of the crystal. Therefore, each crystalline component of the material being analyzed has its own unique diffraction pattern [137, 138].   XRD patterns of the calcined and reduced/passivated catalysts, the used catalysts and the Al2O3 support were collected using a Bruker D8 Focus (LynxEye detector) with a Co Kα X-ray source of wavelength 1.7902 Å. The data were obtained between 2𝛳 =10 to 80º. The reduced catalysts 47  were coated with squalane to prevent oxidation during analysis. The phase identification was conducted after subtraction of the background (the details of analysis are provided in Section 4.2.3). Powder diffraction files (PDF) were used for reference. Crystallite size (dCo) estimates were made using the Scherrer equation, dCo =K λ/( βcos 𝛳) 3.2 where λ is the wavelength of radiation in nm, β is the peak full width at half maximum intensity (FWHM) in radians, 𝛳 is the Bragg angle of the  diffraction peak in radians and K is a dimensionless number close to the unity. The accuracy of the K value depends on the method used for determination of the peak width along with the shape and size distribution of the crystallites [139]. For the particles with cubic, tetrahedral and octahedral crystallites, using different methods to measure peak width, the average K value is ~0.9 [139].  3.3.6 X-ray photoelectron spectroscopy (XPS)  XPS is a surface analysis method in which the surface is bombarded with X-ray photons. The emitted core photoelectrons can be measured as a function of electron energy which is specific for each element and oxidation state. The depth of the analysis is 0.1-2 nm [137].  A Leybold Max200 X-ray photoelectron spectrometer (XPS) was used for surface analysis of the fresh and used catalysts. Al Kα was used as the photon source generated at 15 kV and 20 mA. A pass energy of 192 eV for the survey scan and 48 eV for the narrow scan analysis was used. The Co/Al atom ratio was determined from the analysis for all the samples. Co was in the oxide form 48  for all the reduced fresh and used catalysts, indicating that the surface Co was oxidized during sample handling prior to the XPS analysis. 3.3.7 Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS)  TOF-SIMS is a highly surface sensitive analytical method, capable of determining the chemical composition of the uppermost monolayer of a solid (the average depth of analysis is 1 nm) and provides distribution maps of the mass of interest (spatial resolution of less than 400 nm).   TOF-SIMS uses a focused pulsed particle beam that penetrates into the solid and transfers its kinetic energy to the surface particles. The secondary emitted particles are then accelerated to the flight path. Hence, the basic principal of TOF-SIMS is based on secondary ion analysis of the compounds entering the flight path in the shortest possible time interval by a time-of-flight mass spectrometer [140]. In this study, a PHIL trift v nano TOF with Au+ as a source particle beam, was used to produce mapping images of the Al, Co and C formed on the used catalyst surface. The samples were wax extracted prior to analysis with the procedure described in Section 3.2.1. 3.3.8 Brunauer-Emmett-Teller (BET) surface area  Brunauer-Emmett-Teller (BET) is the most common procedure for determining the surface area of catalysts and is based on adsorption and condensation of liquid N2 at 77 K using a static 49  vacuum procedure. By estimating the number of molecules adsorbed in a monolayer, internal surface area can be determined. Each absorbed molecule occupies an area of the surface comparable to its cross sectional area (for N2 0.162 nm2). The BET equation relates the volume adsorbed at a given partial pressure and the volume adsorbed at monolayer coverage [137].  BET analysis was conducted on the used and fresh Co/Al2O3 and Re-Co/Al2O3 catalysts. Surface areas were measured by N2 adsorption using a Micromeritics ASAP 2020 analyzer. Prior to N2 adsorption the samples were degassed at 350 ºC in vacuum (66 Pa) for 2 h to remove any moisture or adsorbed compounds. 3.3.9 Transmission electron microscopy (TEM)  Transmission electron microscopy (TEM) determines the micro-structure and micro-texture of electron transparent samples [137]. A FEI Tecnai TEM is a 200kV LaB6 filament TEM, capable of 1.4 Å point-to-point resolution, used to analyze the focused and transmitted electrons through a thin transparent film of sample to form a high-resolution image of the specimen. The catalyst samples were crushed with a pestle and mortar for 20 minutes and dispersed in ethanol by 30 minutes sonication. The samples were put aside for 10 minutes so that the larger particles settle.  A few drops of the dispersion were then placed on carbon coated Cu grids and dried under a fume hood for at least 24 h, before being analysed. 50  3.4 Laboratory-scale FT synthesis unit  The process flow diagram of the FT reactor unit is shown in Figure 3.1. A picture of the stirred reactor and the analytical facilities are shown in Figure 3.2. The reactor consists of a 300 ml slurry phase stirred autoclave in which the synthesis gas contacts with the catalyst and heavy (C30+) liquid hydrocarbons under forced mixing (700 rpm) and controlled pressure and temperature. The products from the reactor are directed through a heated line (120 C) to the hot gas condenser held at ~120 °C. The outlet from the hot condenser is also equipped with heating tapes to avoid condensation. The gases leaving the hot condenser pass through a back-pressure regulator and the depressurized gas then passes through an automated sampling valve connected to a gas chromatograph (GC) equipped with a capillary column and a flame ionization detector (FID) to analyze the products. The hot gases leaving the GC sampling valve are subsequently directed to a cold condenser, held at < 2 ºC, to condense any remaining hydrocarbons. The gases leaving the cold condenser are analyzed by a second GC equipped with a TCD.  Liquid products are recovered periodically (once every 24 h) from both the hot condenser and the cold condenser and preserved in a fridge (2 ºC) for analysis. The unit operating conditions are summarized in Table 3.1. Details of the reactor start-up and shut-down procedure are provided in Appendix B. The details of the unit components are given in Appendix C.  Prior to each experiment the mass flow controllers (MFC) were calibrated for all feed gases (H2, CO and N2) as well as the calibration mixture. The calibration for both GCs was checked before 51  each experiment by injecting the calibration mixture through the reactor feed line with three different dilutions to the GCs. Calibration details are provided in Appendix D.   The unit is operated continuously at the specified operating condition. Typically the catalyst sample is reduced ex-situ and transferred to the reactor in 30 mL of squalane under Ar flow to avoid exposure to air.  The catalyst is then placed in the reactor by adding 65 ml more squalane which acts as the initial slurry phase in the reactor. After purging with N2 to remove trace amounts of air, the feed is passed through the reactor overnight to completely purge the system with the feed gas (H2 ~33 mL(STP)/min, CO~16.5 mL(STP)/min and N2~ 20 mL(STP)/min). The feed is injected in to the GC(TCD) prior to the reaction in order to measure the mole percentage of H2, CO and N2 in the feed and the measured amounts are double checked with the desired flows obtained from the MFCs for the feed gases. Subsequently, the reactor is pressurized gradually up to ~ 21 bars over a period of 5 to 6 h. The reactor is then heated to the desired temperature within 30 minutes. Subsequently, the data storage is begun and the GC(FID) and the GC(TCD) are set up to analyze the exit gases every 3 and 1 h, respectively.         52  Table 3.1. FT unit specification and operating conditions  Reactor Volume 300 mL total, 95 mL liquid phase Catalyst particle size  90-150 m Catalyst/Liquid ratio ~ 1.5/100 w/w to 24.5/100 w/w Pressure ~ 20 bar, Max allowed pressure is 220 bar Temperature 210 – 230 C, Max allowed temperature is 450 C Gas hourly space velocity ~0.01 to 0.16  (mol/g.h) Hot condenser used for wax and heavy hydrocarbons collection during the reaction Operating pressure ~ 20 bar Operating temperature ~120 °C Condenser volume 150 mL Cold condenser used for collecting lighter hydrocarbons that leave hot section and to separate permanent gases (H2, CO, CO2, N2, C1 – C4) Operating pressure 1 bar Operating temperature ~ 2 °C Condenser volume 150 mL 53  Bypass valveLCBypass lineFFFFSpeed ControllerTemperature ControllerElectronic BoxVentControl and Read outPGPTTCMFCMFCMFCMFMH2BPRFilterHot Condenser Cold CondenserSlurry Phase ReactorGC,FIDGC,TCDElectronic LineHeated LineCON2 Figure 3.1. Fischer-Tropsch Process Flow Diagram    54    Figure 3.2. Stirred reactor and analytical facility 3.5 Analytical and calculation procedures  To measure the activity of the catalysts as a function of operating conditions the rate of formation of all the products must be determined. A mixed flow reactor has a uniform composition profile. Therefore, the design equation becomes [83]: −𝑟𝐴(𝑡) =𝐹𝐴0  −  𝐹𝐴𝑜𝑢𝑡𝑊 3.3 GC(FID) FT reactor Hot condenser Liquid N2 Cryogenic liquid N2 Inlet line GC(FID) GC(TCD) Control box CSTR reactor Stirrer rotor Pressure gauge   55 where 𝑟𝐴(𝑡) is the consumption rate of compound A (mol/g.s), 𝐹𝐴0   is the initial flow rate of compound A (mol/s), 𝐹𝐴𝑜𝑢𝑡 is the exit flow rate of compound A (mol/s) and W is the mass of catalyst in the reactor (g).  Hence each run gives directly the value of the consumption rate of reactants with the known composition of the exit fluid. The CO conversion in percentage can be defined as follows: 𝐶𝑂 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 % = 100 × (1 −𝐹𝐶𝑂𝑜𝑢𝑡𝐹𝐶𝑂𝑖𝑛 ) = 100 × (𝐹𝑖𝑛 × 𝑦𝐶𝑂𝑖𝑛 − 𝐹𝑜𝑢𝑡 × 𝑦𝐶𝑂𝑜𝑢𝑡𝐹𝑖𝑛 × 𝑦𝐶𝑂𝑖𝑛)    3.4  In which, 𝐹𝐶𝑂𝑖𝑛  is the inlet molar flow of CO (mol/s), 𝐹𝐶𝑂𝑜𝑢𝑡 is the outlet molar flow of CO (mol/s), 𝐹𝑖𝑛  is the total inlet flowrate (mol/s), 𝑦𝐶𝑂𝑖𝑛  is the mole fraction of CO in inlet stream, 𝐹𝑜𝑢𝑡 is the total outlet flowrate (mol/s) and 𝑦𝐶𝑂𝑜𝑢𝑡  is the mole fraction of CO in the outlet stream.   The hydrocarbon product selectivity is reported based on the wt% of hydrocarbons in the outlet stream, excluding CO, N2, H2 and CO2. The CO2 selectivity (mol%) is reported based on the moles of CO2 produced per mole of CO consumed. The selectivities were calculated in approximately 24 h intervals between two liquid sample collections from the hot and cold condensers as follows: 𝑆𝑛 =𝑀𝑛∑ 𝑀𝑛∞𝑛=1× 100 3.5 𝑆𝐶𝑂2 =𝑛𝐶𝑂2𝑛𝐶𝑂𝑖𝑛 − 𝑛𝐶𝑂𝑜𝑢𝑡× 100 3.6  where 𝑆𝑛 is the selectivity to a hydrocarbon with n carbon atoms in the FT hydrocarbon products (wt%), 𝑀𝑛 is the cumulative hydrocarbon mass with carbon number n collected within a period of approximately 24 h (g), 𝑆𝐶𝑂2 is the CO2 selectivity (mol%), 𝑛𝐶𝑂2is the cumulative   56 CO2 moles in the outlet stream after a period of  approximately 24 h, 𝑛𝐶𝑂𝑖𝑛  is the cumulative moles of CO in the inlet stream and 𝑛𝐶𝑂𝑜𝑢𝑡 is cumulative moles of CO in the outlet stream, both after a period of approximately 24 h.   In the present work, both gas and liquid phase products were measured using several different analytical methods. As shown in Figure 3.3, several samples were generated during each experiment.  Both liquid and gas phase products and unreacted synthesis gas passed through the hot condenser, held at 120 C, that collected the high boiling liquid products. The products were removed from the hot condenser in 24 h periods and analyzed off-line by GC(FID) (the sample collected from the hot condenser was dissolved in CS2 prior to injection to the FID column). The uncondensed vapour from the hot condenser then passed to the on-line sampling valve connected to the GC(FID) that quantified the C1–C18 hydrocarbons present in this vapour stream. The vapour stream was analyzed periodically in 3-4 h intervals. The vapour stream from the GC(FID) then passed to a second condenser held at < 2 C, to remove water and light hydrocarbons, before passing to the GC(TCD) used to quantify the unreacted CO and light gas products including CO2, CH4, C2H6, C2H4, C3H8 and C3H6. N2 added to the feed gas as an inert was also analyzed by GC(TCD) and used to determine the exit gas flowrate. Details of the GC settings are given in Appendix E.   The gas analysis data were time averaged over the 24 h period so that it could be combined with the liquid analysis. The mass balance calculations were based on the cumulative gas and liquid analysis over the 24 hour period of each liquid sample.      57  Figure 3.3. Product sample collection and analysis  The measured gas and liquid sample analysis was used to perform an overall mass balance and carbon balance on the unit. Note that the mass balance for all experiments reported herein was within ±5%, and the carbon balance was within ±5%. CO conversion and stoichiometry of the reaction were used to determine the H2 and H2O produced. A detailed calculation procedure of the data analysis related to one experiment is provided in Appendix F.   3.6 Mass transfer effects  Mass transfer effects are known to be important in the FT synthesis [141-143].  In laboratory scale tests, in which intrinsic activities need to be measured, both internal and external mass transfer effects need to be minimized.  In slurry-phase FT synthesis, internal diffusion effects can be minimized by using small catalyst particles.  In laboratory scale units, external mass transfer can be minimized by operating at high stirrer speeds.   In the present work, internal diffusion effects were minimized by using an average catalyst particle size of 90-150 m for all the kinetic measurements. It is reported that in slurry phase FT Reactor Hot Condenser GC (FID) Feed Hot Condenser Liquid Cold Condenser Liquid Outlet Cold Condenser GC (TCD)   58 reactors the internal mass transfer inside the pores is insignificant when the average particle size is less than 150 m [141, 144]. The Weisz–Prater Criterion [145] was also used to confirm that there was no internal diffusion limitation associated with the measured rate data, as described in Appendix G. External diffusion effects were minimized by operating at a stirrer speed of 700 rpm. Experiments conducted to determine the effect of increased stirrer speed (up to 1000 rpm) were completed to ensure that external diffusion effects were not important.  The experiments were conducted at 220 C, 20.7 bar and a gas hourly space velocity (GHSV) of 0.06 (mol/g.h).  The CO conversion, CH4 and C2-C4 formation rates, measured over a period of 260 h as the stirrer speed was increased are summarized in Figure 3.4. Similarly, the hydrocarbon product distribution as measured in the gas leaving the hot condenser is shown in Figure 3.5.  Together, these data show that there was no significant effect of increased stirrer speed on the measured rate of reaction or product distribution after initial stabilization period, from which it can be concluded that external diffusion effects were not important at the chosen operating conditions.   59 0 50 100 150 200 250 3003035404550551E-81E-71E-61E-51000 rpm900 rpm800 rpm CO Conv (%)TOS (h)700 rpm  Reaction rate (mol/( g cat. sec)) CH4C2-C4 CO consumption Figure 3.4. Effect of stirrer speed on the CO conversion and rates of CO consumption, CH4 formation and C2-C4 formation. Operating conditions: 220 C, 21.4 bar, GHSV = 0.06 (mol/g.h), H2/CO = 2/1.    60  Figure 3.5. Effect of stirrer speed on the hot gas product composition as determined by FID analysis. Operating conditions: 220 C, 21.4 bar, GHSV= 0.06 (mol/g.h), H2/CO = 2          0 2 4 6 8 10 12 14 16 181E-30.010.1110100 700 rpm 800 rpm 900 rpm 1000 rpm  Wn/nCarbon number  61 Chapter 4. Properties of the Co/Al2O3 and Re-Co/Al2O3 catalysts 4.1 Introduction  After catalyst preparation by incipient wetness impregnation as described in Section 3.2, the fresh catalysts were characterized before testing at FT reaction conditions in the CSTR reactor. One of the main purposes of the catalyst characterization was to confirm the size of the Co particles on the support surface. Since each characterization technique has some limitations, it is important to use different methods simultaneously. Although addition of EG to the impregnation solution and its effect on particle size are known [86], some questions about the catalyst properties prepared by this method remain, such as the amount of residual carbon on the catalyst after the reduction step and the state of the crystallites on the surface. The DOR of the Co particles was determined by TPR for both Re-Co/Al2O3 and Co/Al2O3 catalysts. Particle size measurements were conducted on both calcined and reduced catalysts, providing complementary data to the literature [86]. In this chapter the characterization and surface properties of the Re-Co/Al2O3 and Co/Al2O3 catalysts are presented and discussed.     62 4.2 Characterization of the fresh catalysts  4.2.1 TGA analysis to estimate the required calcination temperature  TGA analysis was conducted on the impregnated support in order to ensure that the chosen calcination temperature was sufficient to decompose and remove the EG and nitrate from the catalyst after drying and calcination. High calcination temperatures promote sintering of crystallites and result in larger Co3O4 particles, but the calcination temperature must be sufficient to convert the precursor to metal oxide. The experiment was done using 8.52 mg of 5Co/Al2O3(0.9) dried precursor according to the procedure described in Section 3.3.1. The aforementioned sample was chosen because it had the largest amount of EG among the prepared samples. The sample was dried at 110 ºC for 3 h in stagnant air prior to TGA analysis. In addition, 13.12 mg of 5Co/Al2O3(0) dried precursor which was dried for 2 h at 60 ºC and for 2 h at 120 ºC, and 11.52 mg of the Al2O3 support, impregnated with EG (R=0.9) without Co nitrate, were also analyzed.   The TGA profiles in Figure 4.1 (A,C), indicate that the calcination temperature of 300 ºC is sufficient for the decomposition of all the residual compounds on the catalysts prepared with a mixture of water and EG. But the peak for the sample prepared from water alone, Figure 4.1 (B), extends up to 500 ºC indicating that higher calcination temperature is required for this sample.   Comparing the sample that contains only EG and Al2O3, Figure 4.1(A), to that of the 5Co/Al2O3(0.9) dried precursor, Figure 4.1(C), suggests that the first peak is the result of EG   63 evaporation from the support; whereas, the second broad peak in Figure 4.1(C, B) results from complexes of Co, which were not detected in the sample without Co, as shown in Figure 4.1 (A). 0 200 400 600 800 1000-0.015-0.010-0.0050.000-0.015-0.010-0.0050.000-0.015-0.010-0.0050.000 Temperature (oC)C Rate of weight loss (mg/sec)B  A Figure 4.1. TGA profile of: (A) Al2O3 support impregnated with a mixture of EG and water (R=0.9), (B) 5Co/Al2O3(0) dried precursor , (C) 5Co/Al2O3(0.9) dried precorsor   4.2.2 CH analysis to confirm the decomposition of carbon during catalyst preparation  The C and H content of the fresh catalysts and the calcined precursors were determined using a CH analyzer. The amount of C detected after 16 h calcination at 300 ºC was ≤ 0.3 wt% as shown in Table ‎4.1 for all the samples analyzed. The amount of C detected after reduction at 600 ºC was ≤ 0.1 wt% as shown in Table ‎4.2. The analytical range that can be measured by CH analyzer is ~0.1 wt% for C. Therefore, the difference between the amount of C on the calcined sample and the reduced sample is ≤ 0.2 wt %. Hence, it is expected that the amount of C that hydrogenates   64 during the reduction must be negligible and the H2 consumption measured during reduction of the catalyst is mostly due to the reduction of Co compounds by H2 and not hydrogenation of residual carbon. Further analysis in Section 4.2.4 confirms that during the TPR of the catalyst the H2 is mostly used to reduce the Co oxide compounds. Table 4.1. CH analysis of calcined precursors (16 h calcination at 300 ºC)              Table 4.2. CH analysis of reduced catalysts  Sample C, wt% H, wt% 10Co/Al2O3(0.7) 0.1 0 20Co/Al2O3 (0.6) 0.1 0 4.2.3 XRD analysis to measure Co and Co3O4 crystallite size on fresh catalysts after calcination and reduction   Figure 4.2 shows the measured XRD spectra of the 15Co/Al2O3(0.1) catalyst after reduction (A), the same catalyst after calcination (B), and the Al2O3 support without Co (C). The calcined catalyst contains both Co3O4 and Al2O3 compounds; whereas, the reduced catalyst also has Co. Sample C, wt% H, wt% 5Co/Al2O3(0.7)  0.2 0.5 5Co/Al2O3 (0.6)  0.2 0.7 10Co/Al2O3 (0.9)  0.3 0.6 10Co/Al2O3 (0.7) 0.2 0.6 10Co/Al2O3 (0.6) 0.2 0.6   65 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 8505001000150001000200030004000050010001500 2THETA C) IntensityB)  A) Al2O3 Co3O4 Co Figure 4.2. XRD spectrum of: A) 15Co/Al2O3 (0.1) after reduction, B) 15Co/Al2O3(0.1) calcined precorsor, C) Al2O3 support  The diffraction peaks for  γ-Al2O3, Co3O4 and Co are shown in Figure 4.3. There is significant overlap among the peaks making it difficult to de-convolute all of the peaks observed in the XRD profiles measured for each sample. At 2𝛳~53.5 o the Al2O3 peak has a relative intensity of ~ 0.8 whereas at 2𝛳~53 o the intensity of the Co3O4 is 0.2 (the difference between the intensity of the peaks for γ-Al2O3 and Co3O4 is highest at 2𝛳 ~53 o). Hence, it is assumed the peak that was observed in the calcined precursors and reduced catalysts at 2𝛳 ~53 o, is mostly the result of    66 20 30 40 50 60 70 800.00.20.40.60.81.0  Relative intensity2THETA Al2O3 Co3O4 Co Figure 4.3. Relative intensity of the peaks in powder diffraction files: Al2O3: PDF 00-029-0063, Co3O4: PDF 00-043-1003, Co: PDF 00-015-0806  Al2O3 diffraction. For Co/Al2O3 catalysts the peak at 2𝛳~53 o assigned to Al2O3 and the peak at 2𝛳 =52 o assigned to metallic Co are not merged completely and are separable. Consequently, for both the calcined and reduced Co/Al2O3 catalysts, the peak at 2𝛳 ~53 o was normalized to the intensity of the peak for pure Al2O3 at the same angle. The subtraction of the normalized calcined and reduced catalyst diffraction profiles from the Al2O3 support spectrum yields the peaks for Co3O4 and Co without Al2O3. At 2𝛳 =43 o and 2𝛳 =52 o the peak for Co3O4 and Co had maximum intensity, respectively, and these peaks were chosen to measure the particle size using the Scherrer equation. For the Re-Co/Al2O3 catalyst the peak at 2𝛳~53 o assigned to Al2O3 and the peak at 2𝛳 =52 o assigned to metallic Co are almost merged completely and only a small shoulder at 2𝛳 =52 o is visible. Therefore, the peak at 2𝛳~53 o cannot be normalized to the intensity of the peak for pure Al2O3. Hence, for the Re-Co/Al2O3 catalysts the peaks at 2𝛳=52 o   67 and 2𝛳~53 o are de-convoluted. The details of these two methods for measuring Co and Co3O4 particle sizes and comparison between these methods are provided in Appendix H.  Figures 4.4 through 4.7, indicate the effect of adding EG to the impregnation solution versus intensity of the peaks measured by XRD (subtracted from the Al2O3 support) of calcined catalysts. The width of the peak at 2𝛳=43 o increases as more EG is added to the impregnation solution, indicative of a smaller Co3O4 particle size. Figure 4.7 shows that there is no noticeable difference between the width of the peaks when R<0.6 (for 10-15wt% Co loadings the same trend was observed although it is not shown here), and by the Scherrer equation, the Co3O4 particle size is <4 nm. In Figure 4.4 (B), the subtracted spectrum from Al2O3 does not show any peak, indicating that Co oxide particles are too small to be detected by XRD.  After reducing the catalysts, they were transferred into a beaker filled with squalane under Ar  flow to prevent oxidation. The squalane coated catalysts were then washed with CH2Cl2 and analyzed by XRD. The Co metal particles were only visible on the surface of the 15Co/Al2O3(0.1), 20Co/Al2O3(0.6) and 5Co/Al2O3(0), as measured in Table ‎4.3, probably because small Co particles are not detectable by XRD and oxidize much faster than large Co particles. Hence, catalysts with small Co particles might oxidize even when they are coated with a layer of squalane and therefore only Co oxide is visible on these samples.    68 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 8505001000150020000500100015002000R=0.6 Intensity2ThetaB     ACo3O4R=0 Figure 4.4. XRD spectrum (subtracted from the support) of calcined 5Co/Al2O3, A) without EG (R=0), B) with EG (R=0.6) with no detectable Co3O4    69 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85010002000300001000200030000100020003000R=0.6 2Theta   CR=0.1 Intensity   B     A Co3O4R=0 Figure 4.5. XRD spectrum (subtracted from the support) of calcined 10Co/Al2O3, A) without glycol (R=0), B) with glycol (R=0.1), C) with glycol (R=0.6)          70 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85010002000300040000100020003000400001000200030004000R=0.7 2ThetaCR=0.1 IntensityB     A Co3O4R=0  Figure 4.6. XRD spectrum (subtracted from the support) of calcined 15Co/Al2O3  A) without EG (R=0), B) with EG (R=0.1), C) with EG (R=0.7)    71 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 850200040006000020004000600002000400060000200040006000R=0.9 2THETADR=0.6  CR=0.2 IntensityB     ACo3O4R=0 Figure 4.7. XRD spectrum (subtracted from the support) of calcined 20Co/Al2O3, A) without EG (R=0), B) with EG (R=0.2), C) with EG (R=0.6), D) with EG (R=0.9)  Table 4.3 reports the Co and Co3O4 particle sizes of the calcined precursor and reduced catalysts. The crystallite size was measured after fitting a Gaussian curve to the peaks at 2𝛳=52 º and 2𝛳=43 º, respectively, to determine line broadening. Hence Equation 3.2 was used to estimate crystallite size.The error in the size measurement reported hereafter reflects the error in the fitted curve. If 𝛳 has an error of 𝛿𝛳 and 𝛽 has an error of 𝛿𝛽 the total error (z) for dCo can be calculated as described in Appendix I. In theory, Co particle size after reduction should be   72 smaller than the Co3O4 particle size [88], but Table ‎4.3 shows that Co particles of the reduced catalysts are larger than or the same size as the Co3O4 particles of the calcined precursor. Consequently, the Co particles must have sintered during the reduction step. The average particle size of the Co3O4 particles that remained after reduction decreased, since larger Co3O4 particles are reduced to Co and smaller ones remain in the oxide form. The average Co size increased compared to Co3O4 particle size due to sintering and consequently the equation  𝑑𝐶𝑜 = 0.75 ×𝑑𝐶𝑜3𝑂4[88] cannot be used to measure metallic Co size of the reduced catalyst from the Co3O4 particle sizes of the calcined precursor.  Table 4.3. Comparison between Co3O4 particle size before and after reduction and Co particle size after reduction for different catalysts using XRD  Catalyst Co3O4 size of calcined precursor* (nm) Co3O4 size after reduction* (nm) Co size after reduction* (nm) 20Co/Al2O3(0.6) 5±0.1 3±0.1 12±0.7 15Co/Al2O3 (0.1) 9±0.2 5±0.2 9±0.8 5Co/Al2O3(0) 12±0.2 8±1.1 21±0.8 * The error in the size measurement reported here reflects the error in the fitted curve as described in Appendix I 4.2.4 TPR of Co/Al2O3 and Re-Co/Al2O3 catalysts to measure DOR  The H2 consumption observed during TPR using a Micrometrics Autochem II 2920 was assumed to be the result of the reduction of Co oxide compounds to metallic Co. In order to prove that the observed peaks were not related to the reaction of other surface compounds such as EG, an experiment was conducted in which 1.27 g of 15Co/Al2O3(0.6)  was loaded into the fixed bed reactor. The catalyst was reduced with 50 mL(STP)/min of 10% H2/He at a ramp rate of 5   73 ºC/min up to 600 ºC. The reactor outlet line was connected to a MS to analyze the outlet gases after the reduction. All the intensities of the peaks were normalized to the intensity of inert He. According to Figure 4.8 at ~100 oC the first H2O peak was detected, which is related to the amount of absorbed water on the surface of the catalyst. As the temperature increased a second, third and fourth H2O peak was also observed, and at the same time, H2 was consumed, suggesting that the reduction of Co oxide species in the presence of H2 to form metallic Co and water had occurred. The H2 consumption peaks occur at approximately 200, 300 and 600 ºC (peaks 1 through 3).  As can be seen in Figure 4.9, apart from H2O, some other compounds such as CO2, CO and CH4 were also observed in the product gas.  From about 1420 µmol H2/gcat consumed during this TPH experiment, only 45 µmol CH4 /gcat was produced, showing that most of the H2 consumption was the result of Co oxide reduction and only small amounts (~3.2%) of the remaining carbon reacts with H2 at ~450 ºC to form CH4. Accordingly, about 20 µmol of CO2 and CO were produced/gcat, which is probably the result of reaction of H2O with the remaining carbon from EG on the catalyst during the thermal treatment.  These results indicate that below 300 ºC, some carbon from EG is present on the catalyst, which is removed in the form of CO and CO2, and at 450 ºC, CH4 was also observed in the outlet. Nevertheless, the intensity of the signals for H2O were much more significant compared to other compounds. In addition, the temperatures at which the H2 consumption occurred at around 150 ºC, 300 ºC and 600 ºC were quite similar to the temperatures that H2O production occurred. This indicates that most of the H2 consumption was due to the reduction of Co oxide to Co.   74 0 50 100 15002004006000.400.450.500.550.000.050.100.15 Temp (C)Time (min) Temp Relative Intensity H212 3   H2O1234 Figure 4.8. Relative intensity of the H2 and H2O peaks at the outlet of the fixed bed reactor during the reduction of 15Co/Al2O3 (0.6)    75 -20 0 20 40 60 80 100 120 140 160 18002004006000.0030.0040.0050.0060.0070.0080.0000.0020.0040.0060.0080.0000.0020.0040.0060.008 Temp (C)Time (min) Temp  CO Relative Intensity  CO2   CH4 Figure 4.9. Relative intensity of CO2, CO and CH4 at the outlet of the fixed bed reactor during the reduction of 15Co/Al2O3(0.6)  After ensuring that H2 uptake in the TPH profile is mainly related to reduction of Co oxide compounds, TPR of Co/Al2O3 catalysts was done using a Micrometrics Autochem II 2920 unit based on the procedure described in Section 3.3.2. The peaks observed can be assigned to reduction of various species of Co oxide as described in Section 2.3.  Figure 4.10  indicates the TPR profile of catalysts with different Co loadings when there is no EG in the impregnation solution. According to Section 4.2.4, the peaks are observed at similar temperatures to the H2   76 consumption peaks reported in Figure 4.8. In order to compare the amount of H2 consumed during the TPR for the catalysts with different Co loadings, the H2 consumption rate is divided by the mass of Co on each sample to obtain a measure of the H2 consumption per gram of Co (by integrating the area under the TPR profile versus time).  The amount of H2 consumed per gram of Co assigned to the first peak increases as the Co loading decreases (Figure 4.10). As a result, the first peak at ~180 ºC was not due to the remaining nitrate solution, as proposed in [88] since the area of the first peak should be almost constant in that case (moles of nitrate per moles of Co is constant). However, it is believed that the first peak is the result of the reduction of CoO(OH) compounds. It has been postulated that the production of CoO(OH) increases with low local concentrations of water and NOx [100], which is in agreement with the profile observed in Figure 4.10. The amount of nitrate solution for the preparation of the catalyst decreased with decreased Co loading. Consequently, less NOx would be produced during calcination and hence the amount of CoO(OH) increases and the area of the first peak rises per gram of Co.   The amount of H2 consumed per gram of Co in the second peak does not change significantly. Since the second peak is assigned to the reduction of Co3O4, it suggests that the amount of Co3O4  particles reduced to CoO per gram of Co is almost the same for all loadings of Co, excluding the 3wt% catalyst.   Figures 4.11 and 4.12 present the TPR profiles of the Co/Al2O3 catalysts prepared using EG in the impregnation solution. As shown in Figures 4.11 and 4.12, the same 3 reduction peaks were   77 observed for these catalysts. The H2 consumption rate per gram of Co follows the same trend as in Figure 4.10. For some of the catalysts, an extra peak was observed before the last peak, which might be the result of reduction of larger CoO particles with lower interaction with the support. Also, there is a small peak observed at 100 ºC for some of the catalysts. According to Section 4.2.4 and Figure 4.9, small amounts of CO2 might be produced during thermal treatment of the catalyst at ~100 C, which is the result of the reaction of surface oxygen with the residual C from EG. This peak may also be the result of adsorbed water on the surface of the catalyst, but in all cases the area under the curve associated with this peak is relatively small.  Figure 4.13 depicts the total H2 consumption rate per gram of Co during the reduction of 10Co/Al2O3 catalyst prepared using different amounts of EG in the impregnation solution. The total H2 consumption decreases as the amount of EG increases from R=0 to R=0.9. This decline is due to the formation of smaller Co oxide particles on the catalyst surface as R increases, which have stronger interaction with the Al2O3 support and thus, are less likely to reduce. In addition, the last peak which is assigned to the reduction of CoO, moves towards higher temperatures as the amount of EG increases. The reduction at higher temperatures is similarly the result of the formation of smaller CoO particles (See Section 4.2.5) with higher interaction with the support that are less reducible.   According to the stoichiometry of Co oxide reduction, the total amount of H2 uptake for the reduction of CoO in moles, should be 3 times higher than the amount of H2 uptake for the reduction of Co3O4 to CoO (see Equation 2.1-2.2 and Equation 2.3-2.5 for the two different proposed mechanisms of reduction of Co compounds reported in Section 2.3). However, it has   78 been observed that the ratio of the area of the third to second peak decreases from 2.5 for 10-15 wt% Co loading on Al2O3 to 2 for 5wt% Co loading on Al2O3 and 1 for 3 wt% Co loading on Al2O3.  The decrease in DOR of CoO to metallic Co for lower loadings of Co, agrees well with the effect of particle size on the reducibility of the catalyst. If, as expected, the CoO particle size decreases with Co loading and since smaller Co oxide particles are more resistant to reduction [79], a lower percentage of smaller CoO particles would reduce to Co compared to larger Co particles. By measuring the H2 consumption assigned to the third reduction peak in the TPR profile (shown in Figures 4.10 through 4.12), using the stoichiometry of the reduction reaction (CoO+H2→Co+H2O) the amount of  reduced Co can be quantified. As 𝑛𝐶𝑜0 in Equation 3.1 equals 𝑛𝐻2 (the moles of H2 consumed per gram of catalyst in the reduction of CoO species, mol/g) the following equation is obtained: 𝐷𝑂𝑅 = (𝑛𝐻2 𝑛𝐶𝑜) × 100  ⁄   4.1 Where 𝑛𝐶𝑜 is the moles of Co loaded on the catalyst per gram of catalyst (mol/g).    79 0 100 200 300 400 500 600048120481204812010203040 Temperature (°C) 15 wt%123 H2 consumption rate per gram of Co, mL(STP)/(min. g) 10 wt%123  5 wt%1 23   3 wt%123 Figure 4.10. TPR profile of catalysts with different Co loadings, without EG in impregnation solution (R=0)    80 0 100 200 300 400 500 6000246024602460246 Temperature (°C) 15 wt%12 3 H2 consumption rate  per gram of Co, mL(STP)/(min. g) 10 wt%12 3  5 wt%123   3 wt%1,2 3 Figure 4.11. TPR profile of catalysts with different Co loadings, with EG in impregnation solution (R=0.9)   81 0 100 200 300 400 500 6000246024602460246 Temperature (°C) 15 wt%123 H2 consumption rate per gram of Co, mL(STP)/(min. g) 10 wt%12 3  5 tw%1,23   3 wt%1,23 Figure 4.12. TPR profile of catalysts with different Co loadings, with EG in impregnation solution (R=0.7)    82 0 200 400 6000510051005100510 Temperature (°C)R=0.91 23 H2 consumption rate per gram of Co, mL(STP)/(min. g)R=0.712 3 R=0.61 233  R=012 Figure 4.13. TPR profile of 10Co/Al2O3 with different amount of EG (different R)   Co catalysts promoted with Re were also prepared as described in Section 3.2, based on the fact that Re improves the reducibility of Co/Al2O3 catalysts as reviewed in Section 2.3.1. Figure 4.14 indicates that by adding 0.5 wt% Re to the 5Co/Al2O3(0.7) catalyst, the first H2 reduction peak does not change in terms of area and reduction temperature; whereas, the area of the second peak is much larger for the 0.5Re-5Co/Al2O3(0.7) catalyst versus the 5Co/Al2O3(0.7) catalyst. In addition, the reduction temperature decreases from 600 ºC to about 400 ºC, indicating that the   83 reducibility increased significantly. It is known that the reduction of the peaks at lower temperature is not affected by Re promoter, as the Re oxide itself reduces at approximately 300 ºC [104]. Above 300 ºC, presumably the spillover of H2 from the metallic promoter facilitates the reduction of CoO [103, 105, 146-148]. Figure 4.15 for the 0.3Re-3Co/Al2O3(0.9) catalyst, shows the same trend as in Figure 4.14.  Peak 2 and peak 3 are assigned to the reduction of CoO on the surface with low and high interaction with the support, respectively. For 0.3Re-3Co/Al2O3(0.9) catalyst, the CoO particles reduce at lower temperatures and the H2 consumption peak assigned to reduction of CoO has a much larger area compared to the 3Co/Al2O3(0.9) catalyst. The comparison between the DOR of the two different Co/Al2O3 and Re-Co/Al2O3 catalysts is reported in Table ‎4.4, which also reports the Co particle size measured by CO chemisorption for these catalysts (see Section 4.2.5, for Co particle size measurement with CO chemisorption). The small Co particle size measured by CO chemisorption for the 5Co/Al2O3(0.9) catalyst (dCo~ 1nm) is the result of partially reduced Co oxide crystallites with DOR ≤ 3%. The size measured for Co3O4 crystallites with XRD for this catalyst after calcination was 4±0.4 nm.       84 0 50 100 150 2000.000.020.040.060.080.100.000.020.040200400600 H2 consumption rate (mL(STP)/minTime (Min)0.5Re-5Co/Al2O3(0.7)122   5Co/Al2O3(0.7)1  Temp (oC) Figure 4.14. Effect of adding promoter on the reduction of 5Co/Al2O3 (0.7), promoted catalyst contains 0.5wt% Re    85 0 50 100 150 2000.000.020.040.060.080.000.010.020.030.040200400600 H2 consumption rate , mL(STP)/minTime (Min)0.3Re-3Co/Al2O(0.9)123 3Co/Al2O3(0.9)123  Temp(oC) Figure 4.15. Effect of adding promoter on the reduction of 3Co/Al2O3(0.9), promoted catalyst contains 0.3wt% Re Table 4.4. Comparison between Co particle size and DOR for Re-Co/Al2O3 and Co/Al2O3 catalysts, particle sizes are measured by CO chemisorption   Co/Al2O3 Re-Co/Al2O3 Catalyst DOR (%)  dCo (nm) DOR (%)  dCo(nm) 5Co/Al2O3 (0.7) 2 2 64 5 3Co/Al2O3 (0.9) 3 1 55 2   86 4.2.5 Metal dispersion and Co particle size measurement by CO chemisorption   Metal dispersion was measured by CO pulse chemisorption after the reduction of the catalysts, using a Micromeritics Autochem II 2920, as described in Section 3.3.2. The dispersion can be calculated by the following equation, 𝐷 =𝑁𝐶𝑂 × 𝑀𝑊 × 𝜎𝑤𝑡/100× 100 4.2 D is the metal dispersion (%), 𝑁𝐶𝑂 is the number of moles of CO adsorbed per gram of catalyst (mol/g), MW is the molecular weight of the metal, wt is the weight percent loading of metal on the catalyst and σ is the stoichiometric number of CO adsorption on the metal, which is defined below. When Co particles are only partially reduced the Co size is estimated accounting for DOR with the following equation reported in [86]. 𝑑Co = 96/D×DOR 4.3 where dCo  is the Co particle size in nm, D is the Co dispersion (%) and DOR is the degree of reduction.  σ in Equation 4.2 varies according to the different types of adsorption of the CO molecule on metal, with σ=1, 2 and 0.5 for linear, bridge and twin type adsorption, respectively. Various CO adsorption models have been reported for supported Co catalysts [149, 150], resulting in different σ values [151] in the rage of 0.9 to 2.5 for Co/Al2O3 catalysts prepared by different methods and with various Co loadings [102]. However, σ=2 was assumed when estimating the Co particle size [152]. Assuming σ=2 for supported Co catalysts is also in accordance with standard methodologies, used by manufacturers of CO chemisorption units (see for example application note CAT-APP-002 from Micrometrics). Because of the complexity of the adsorption   87 stoichiometry on supported Co catalysts, in this study the Co particle size measured by CO chemisorption using σ=2 is compared to the Co particle size measurements made  by other available methods to ensure the reliability of the assumption. Therefore, the size of large Co particles measured by CO chemisorption is compared with the Co crystallite size estimated from XRD, as shown in Table 4.5. The results show a reasonable agreement between each method. The data indicate that the Co occurs as individual crystallites accessible to CO, supported on the Al2O3. It is worth mentioning that Co particle sizes meaured by XRD and CO chemisorption are mean values. However, a distribution of Co particle sizes must be present on the support, with the XRD unable to quantify particles of size less than about 5 nm. Table 4.5. Comparison between the Co size measurement by CO chemisorption and XRD  catalyst dCo measured by CO chemisorption (nm) dCo measured by XRD* (nm) 5Co/Al2O3(0) 22 21±0.8 20Co/Al2O3(0.6) 13 12±0.7 15Co/Al2O3(0.1) 10 9±0.8 1.2Re-12Co/Al2O3(0) 11 8±0.7 * The error in the size measurement reported here reflects the error in the fitted curve as described in Appendix I.  To further support the chosen σ value, the 0.3Re-3Co/Al2O3(0.9) catalyst was reduced and passivated according to the procedure described in Section 3.3.2. The catalyst was analysed by XRD and no metallic Co particle was detected indicating that the Co particles were oxidized during the passivation process. However, the Co3O4 particle size measured by XRD was 3±0.6 nm. In addition, the Co oxide particle size of the same catalyst was measured by TEM,   88 considering 125 particles from 9 different images (Note that the TEM images of all the other catalysts in this study did not have a reasonable contrast to conduct Co particle size measurments, as will be shown in Section 4.2.7). Subsequently, the average Co3O4 particle size of 3.5 nm was calculated by TEM for this particular catalyst, which was consistent with the XRD calculation. The Co particle size of the same catalyst measured by CO pulse chemisorption and σ=2 was 2 nm (2.8 nm if it was in Co3O4 form) which is agreement with the other two methods. The details of the calculations are provided in Appendix J.  Figure 4.16 shows the effect of adding EG to the impregnation solution on the Co particle size of the Co/Al2O3 catalysts. For the 5-20 wt% Co/Al2O3 catalysts, without EG (R=0), the Co particle size measured by CO chemisorption was dCo>20 nm and the large size is probably due to agglomeration of Co particles during the reduction at 600 ºC. For the 3Co/Al2O3(0) catalyst, the Co particle size is < 2 nm, likely a consequence of a strong MSI and low DOR that limits the agglomeration of the Co particles. By adding EG to the impregnation solution, the Co particles for 5-15 wt% Co/Al2O3 catalysts decrease in size. However, EG does not affect the 3Co/Al2O3 catalysts, which already has small particles. The effect of EG is believed to be the result of increased wettability of the Co salt solution [86], which results in better distribution throughout the support.   Finally, Figure 4.17  shows a general trend that larger Co particles correspond to increased DOR of the calcined precursor, which is consistent with the higher reducibility of larger Co particles [49, 81] because of a reduced MSI. Also, the Re-Co/Al2O3 catalysts have a higher DOR   89 compared to the Co/Al2O3, while showing the same trend of increased reducibility with increased Co particle size.   90 0.0 0.2 0.4 0.6 0.8 1.0051015202530   3Co/Al2O3 5Co/Al2O3 10Co/Al2O3 15Co/Al2O3Co Particle size(nm)R Figure 4.16. Co particle size of Co/Al2O3 catalysts as determined from CO chemisorption versus the mass fraction of EG (R) in the impregnation solution, at different Co loadings   91 0 10 20 300102030405060708090 Co/Al2O3 Re-Co/Al2O3  DOR (%)Co Particle size (nm) Figure 4.17. Co particle size versus DOR for 20, 15, 10, 5 and 3wt% Co/Al2O3 and 3, 5, 8 and 12 wt% Re-Co/Al2O3 with different weight fractions of EG 4.2.6 BET analysis to measure surface area of the fresh catalysts   Brunauer-Emmett-Teller (BET) analysis was conducted on the reduced, fresh Co/Al2O3 catalysts to measure the surface area. The Barrett-Joyner-Halenda (BJH) desorption method was used to measure the average pore diameter of the catalyst. Table 4.6 indicates that for the Re-Co/Al2O3 and Co/Al2O3 catalysts, surface area decreases with increasing Co loading, consistent with the blockage of pores by Co particles. From the average pore diameter it appears that some of the Co particles are larger than 10 nm (the average pore diameter of the support) and hence must be located outside the pores.   92 Table 4.6. Surface area and pore diameter of the reduced fresh catalysts prior to the FT reaction, the Co particle size was measured by CO chemisorption  Catalyst dCo,  Surface area  Average pore diameter  nm m2/g nm Co/Al 2O3 20Co/Al2O3(0.6) 13 155 8 15 Co/Al2O3(0.1) 10 161 9 5 Co/Al2O3(0.7) 2 170 9 5 Co/Al2O3(0.9) 1 186 9 5 Co/Al2O3(0) 22 186 8 Re-Co/Al 2O3 0.3Re-3Co/Al2O3(0.9) 2 185 9 0.5Re-5 Co/Al2O3(0.7) 5 152 11 1.2Re-12Co/Al2O3(0) 11 123 11  Al2O3 support … 198 10 4.2.7 TEM analysis to investigate the effect of EG on Co clusters    TEM analysis of passivated Co/Al2O3 catalysts was conducted as described in Section 3.3.9. The contrast between partially oxidized Co after passivation and the Al2O3 support was subtle. Consequently, Image J software was used to increase the contrast. However, most pictures were not suitable for measuring Co particle size because of the low contrast between the particles and the support.     93 Figure 4.18 indicates the qualitative effect of adding EG to the impregnation solution on the 20Co/Al2O3 catalyst. It is quite obvious that adding EG prevents the agglomoration of Co particles and results in smaller clusters, where by adding EG (R=0.6), the cluster size decreased to about 10 nm compared to the 25 nm cluster size of the 20Co/Al2O3 catalyst without EG(R=0).            4.3 Conclusion  A series of Re-Co/Al2O3 and Co/Al2O3 catalysts with 3-20 wt% Co loading were prepared. For the Co/Al2O3 catalysts, the characterization data show varying DOR and Co particle size in the range of 2 to 71% and ~1 nm to 26 nm, respectively. For the Re-Co/Al2O3 catalysts, DOR and Co particle size was in the range of 55 to 85% and 2 to 11 nm, respectively. Addition of EG reduced the size of Co particles and increased their dispersion. Moreover, the reduced catalysts Figure 4.18. TEM images of 20Co/Al2O3(0)(left), 20Co/Al2O3(0.6) (right)    94 have slightly larger Co particles compared to Co3O4 particle size in the calcined precursor, due to sintering during thermal hydrogenation.   It was confirmed that above a calcination temperature of 300 oC, there is no further weight change in the calcined precursor. The residual carbon on the surface of the catalysts (after calcination) hydrogenates during the reduction step at 600 oC. Nevertheless, the H2 uptake measured during the reduction step was mostly due to reaction of H2 with Co oxide compounds and only a small amount of H2 (~5%) was consumed to hydrogenate the residual carbon on the surface of the catalyst during TPR.  In addition, some amount of CoO(OH) was formed on the calcined precursor, which increased with decreased amount of NOx during calcination. Moreover, as the Co oxide particle size decreased, the ratio of H2 uptake for reduction of Co3O4 to CoO and H2 uptake for reduction of CoO to Co, decreased. Accordingly, it was confirmed that small Co oxide particles have high MSI and are difficult to reduce.  Finally, from the BET surface area and pore diameter of all the fresh catalysts, it is clear that the large Co particles (dCo>10 nm) are mostly located outside the pores of the support. TEM was also conducted on the Co/Al2O3 catalysts but the contrast between the metal particles and the support was low, making it impossible to measure the Co particle size for most catalysts by TEM.    95 Chapter 5. Stability, selectivity and activity of Co/Al2O3 and Re-Co/Al2O3 catalysts  5.1 Introduction  The rate of catalyst deactivation is affected by the CO conversion level and selectivity of the catalyst. For instance, higher conversion leads to more H2O production in the reactor, which could influence the sintering of Co particles [55, 66, 132]. Higher selectivity towards heavier hydrocarbons might cause more hydrocarbon deposition on the surface and lead to loss of active sites because of hydrocarbon coverage. The impact of CO conversion and product selectivity is particularly important when assessing catalysts in a back-mixed CSTR since then all of the catalyst is exposed to the reactants and products measured at the reactor exit. As the prepared catalysts have different Co loadings and DOR, operating the catalyst at the same reaction conditions will result in different CO conversion levels at the reactor exit, which will in turn impact the catalyst deactivation rate. Hence, to determine the effects of Co particle size on the catalyst deactivation rate, the catalyst assessment must be done at similar CO conversions. The main purpose of this part of the study was to determine the effect of CO conversion on product selectivity and stability of the FT catalysts for each of the available Co particle sizes as a function of TOS and to investigate the effect of Co particle size on activity and selectivity of the catalysts at similar CO conversion levels.  The effect of Co particle size on catalyst activity and product selectivity was reviewed in Section 2.4. Literature data show that small Co particles (dCo< 6-8 nm [108], dCo<9-10 nm [87] or dCo<11 nm [107]) have higher CH4 selectivity than large Co particles. C5+ selectivity is reported to be   96 constant or shifted slightly towards heavier hydrocarbons as Co particle size increases for Co catalysts supported on  carbon nanofibers or zeolites [107, 108]; whereas, for Co/Al2O3, the C5+ selectivity decreases to a common value for large Co particles [87]. Also, the TOF is lower for Co particle sizes in the range of dCo< 6-8 nm [108] or dCo<11 nm [107] compared to larger Co particle sizes [152]. For Co/Al2O3 catalysts, no relation between Co particle size and TOF (measured based on ex situ H2 chemisorption) was observed, since the DOR of the catalysts changed during the FT reaction [87].   As the catalysts used in this study have variable Co loadings and DOR, it is important to understand the effect of CO conversion on the stability and selectivity of the catalysts with TOS, measured at different CO conversion levels. The study is more complicated for Co/Al2O3 in which high interaction between Co oxides and support results in low DOR, especially for small Co oxide particles.  5.2 Experimental conditions  The catalysts were assessed in the slurry phase Fisher-Tropsch reactor described in Section 3.4. All the experiments were conducted for a continuous period of 120 to 190 h TOS at 21 bar, 220 ºC and H2/CO=2. The experiments were stopped once the average CO conversion reached a steady value for a period of approximately 48 h and the mass of the liquid samples collected from the hot and cold condensers was constant over the same 48 h period. In order to control the CO conversion, the mass of catalyst inside the slurry liquid was changed so that the gas hourly space velocity (GHSV) for different experiments varied from 0.01 to 0.18 mol/(g.h). The GHSV   97 was calculated as  𝐹𝑖𝑛 × 3600/𝑀𝑐𝑎𝑡 , where Fin is the total inlet flow rate in mol/s and Mcat  is the mass of catalyst in grams. 5.2.1 Limitations  The Co/Al2O3 catalysts prepared for this study had Co loadings of 5-20 wt%, whereas the Re-Co/Al2O3 catalysts had Co loadings of 3-12 wt%.  The DOR also varied among the catalysts. Consequently, when the catalysts were assessed for FT performance at the same reaction conditions, the CO conversions were significantly different. To obtain similar CO conversion for all catalysts, the feed flow rate or the mass of the catalyst (i.e. the GHSV) was adjusted. The feed mass flow controllers (MFC) used in the experimental set-up described in Section 3.4 were limited to a minimum total flow rate of 70 mL(STP)/min. Also, the maximum mass of catalyst that has been reported in similar FT slurry reactors that ensures adequate catalyst agitation is 25/100 wt/wt catalyst in the slurry. Based on these limits, it was not possible to operate at high CO conversion with catalysts with low Co loading and low DOR. Alternatively, increasing the reactor temperature above a certain level (~240 ºC) resulted in significant evaporation of the squalane and a loss in the slurry liquid level in the reactor. Consequently, the comparison between activity, selectivity and deactivation rate for different catalysts has been done at different CO conversions, although as far as possible the data within a similar CO conversion level were selected for comparison. Otherwise, the effect of the variation in CO conversion has been assessed prior to drawing conclusions.    98 The total mass balance for all experiments reported herein was within ±5%. The mass balance was very dependent on the mass of liquid collected from the condensers, which was dependent on the liquid yield. At low liquid yield the system volume was such that at least a 48 h period was needed to obtain a representative sample.  In addition, the liquid collected from the hot condenser contained some amount of squalane, used initially to disperse the catalyst in the slurry phase. The level of the squalane in the reactor at start-up is chosen so that it is exactly below the liquid collector. Therefore, as reaction proceeds and hydrocarbons are produced, a mixture of products and squalane flows through the exit line. Consequently, some liquid products remain inside the reactor. To account for the products inside the reactor, the mass distribution of the hydrocarbon products collected in the hot condenser was reported as the wt% of all hydrocarbon products (without squalane) measured by GC (FID) based on the total mass of liquid collected from the hot condenser. The mass fraction of each hydrocarbon product was then multiplied by total mass of hydrocarbon produced based on CO conversion of the reaction and reaction stoichiometry. Hence, the total mass of each compound produced during the reaction was obtained. The details of the calculations are provided in Appendix F. The carbon balance with this calculation method is within ±4%. A summary of the spreadsheets containing the experimental conditions, selectivity of the products, consumption and formation rate of different compounds, as well as mass and carbon balances, is reported in Appendix K and L.     99 5.3 Co/Al2O3 and Re-Co/Al2O3 catalyst stability and selectivity tests  5.3.1 Selectivity and stability of the Co/Al2O3 catalysts with TOS  To obtain data at similar CO conversion level, a series of tests with the same catalyst but operated at different GHSVs was conducted at 20 bar, 220 ºC and H2/CO=2.  These tests provided insight into the effect of CO conversion on the stability and selectivity of the catalysts as a function of TOS.  Figure 5.1 shows the CO conversion versus TOS for the Co/Al2O3 catalysts. In all cases, the CO conversion with TOS reaches a maximum and then declines except for the 5Co/Al2O3(0.7) and  5Co/Al2O3(0.9) catalysts with dCo=3 nm and dCo=1 nm, respectively. Also, for most of the catalysts the CO conversion increases rapidly within about the first 10 h TOS before continuously decreasing in activity for the period of the experiment. A part of this initial behaviour is ascribed to the initial hydrodynamic response of the reactor system which is approximately 8 h (the details of the calculation are provided in Appendix M). The maximum in CO conversion, followed by a decline over longer periods of time has been observed in other studies. Fischer et al. [119] and Welker [153] reported a maximum in CO conversion after 30-50 min TOS in a system with a hydrodynamic response time of about 10 min, and the system reached steady-state after approximately 10 h [119]. Several studies have shown that freshly reduced Co catalysts undergo a slow reduction or reconstruction after exposure to synthesis gas at elevated temperatures and pressures [52, 119, 153-159]. This reconstruction is likely caused by adsorption of carbon species and CO which results in formation of Co islands [52, 154-157].   100 In the case of the 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalysts with small Co particles (dCo=2 nm and dCo=1 nm) and low DOR, Figure 5.1 (A), CoOx was continuously reduced in the presence of synthesis gas during 180 h of TOS. For 15Co/Al2O3(0.1) catalyst with a higher degree of reduction (61%), a longer TOS is required  to achieve the same level of reduction as the GHSV increases, Figure 5.1 (B, C, D), and hence the maximum CO conversion occurs at longer times. Welker [153] and Fischer et al. [119] showed that by exposing the catalyst to CO at pressure between 1-3.3 bar and temperature between 170-190 ºC for about 1-2 h before the reaction the maximum initial activity decreased noticeably, which supports the idea that the maximum initial activity of the catalyst is the result of reconstruction of freshly reduced catalyst when exposed to synthesis gas.   Figure 5.1 (B,C,D) also compares the effect of changing GHSV on the CO conversion for the 15Co/Al2O3(0.1) catalyst with dCo=10 nm. At lower GHSV the deactivation that occurs after maximum CO conversion is more significant compared to that observed at higher GHSV. The reason for this lower deactivation rate will be discussed in Chapter 6.   101 0 20 40 60 80 100 120 140 160 180 200 2200102030204060010200204002040600102030F Time-on-stream (h)15Co/Al2O3(0.1), GHSV=0.04 mol/g.hE 20Co/Al2O3(0.6), GHSV=0.04 mol/g.hD CO conversion (%)15Co/Al2O3(0.1), GHSV=0.08 mol/g.hC 5Co/Al2O3(0), GHSV=0.04 mol/g.hB  15Co/Al2O3(0.1), GHSV=0.16 mol/g.h  5Co/Al2O3(0.9), GHSV=0.01 mol/g.h 5Co/A2O3(0.7), GHSV=0.01 mol/g.hA Figure 5.1. CO conversion versus TOS for Co/Al2O3 catalysts operated at T=220 ºC, P=20 bar and H2/CO=2 with varied GHSVs  Previous studies report that the presence of CoOx during FT synthesis promotes the WGS reaction and therefore results in an increase in CO2 selectivity [77, 122, 123]. Figure 5.2 indicates that the CO2 selectivity is higher for catalysts with smaller Co particles (dCo =2 nm and dCo=1 B   102 nm) compared to larger Co particles (dCo≥10 nm) at approximately the same CO conversion level, consistent with the lower DOR and hence the presence of CoOx species in the case of small Co particles. As the CO conversion increases with TOS for the 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalysts, Figure 5.1 (A), the CO2 selectivity declines with TOS, suggesting that the CoOx particles are being reduced to metallic Co during the reaction. An increase in the DOR of the 6 nm Co particles on Pt-Co/Al2O3 catalyst has been reported previously [160], in which XANES analysis showed an increase in the DOR of the catalyst during the first 2-3 days of the experiment from 53% to 89% [160]. An increase in DOR during FT reaction has also been reported elsewhere [67, 135, 152]. 0 40 80 120 160 200024681012  5Co/Al2O3(0), 22 nm 20Co/Al2O3(0.6), 13 nm  15Co/Al2O3(0.1), 10 nm 5Co/Al2O3(0.7), 2 nm 5Co/Al2O3(0.9), 1 nmCO2 Selectivity, mol%TOS, h Figure 5.2. The CO2 selectivity (mol%) versus time on stream for small and large Co particles, Average conversion 20±6% measured at T=220 oC, P=20 bar and H2/CO=2    103 Figure ‎5.3 (A,B) present the selectivity to products for the 15Co/Al2O3(0.1) catalysts with dCo=10 nm at different GHSVs. Note that, each data point is the average selectivity determined over a period of approximately 24 h. Figure ‎5.3 (C) shows similar data for the CO conversion with TOS, in which each point is the average CO conversion over a period of approximately 24 h. These data show that as the GHSV increases for the 15Co/Al2O3(0.1) catalyst, the CO conversion decreases and subsequently C5+ selectivity decreases and CH4 selectivity increases. Figures 5.4 and 5.5 also show the change in CH4 and C5+ selectivity with TOS for 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalysts with dCo=2 nm and dCo=1nm at two different GHSVs, confirming that a decrease in CO conversion due to an increase in GHSV, results in an increase in CH4 selectivity and a decrease in C5+ selectivity.  The change in product selectivity at varied CO conversion levels is due to the change in partial pressure of reactants and produced water that influences the formation rate of the products. Therefore, to investigate the effect of Co particle size on product selectivity it is necessary to consider the selectivity of the products within approximately the same CO conversion level.  Accordingly, Figure 5.6 indicates that at similar CO conversion level the CH4 selectivity on the Co/Al2O3 catalyst with small Co particles (dCo=2 nm and dCo=1 nm) is greater than on larger Co particles (dCo≥ 10 nm). Furthermore, the C5+ selectivity is lower on smaller Co particles (dCo=2 nm and dCo=1 nm) compared to larger Co particles (dCo ≥10 nm).    104 0510152060708090100 50 100 150 20002040608010  CH4(wt%)A C5+(wt%)B CO conversion (%)TOS (h)GHSV=0.04 mol/g.hGHSV=0.08 mol/g.hGHSV=0.16 mol/g.hC   Figure 5.3. Product selectivity and CO conversion of 15Co/Al2O3(0.1) catalyst with dCo=10 nm during FT synthesis reaction conditions of T=220 ºC, P=20 bar and H2/CO=2    105 0 80 16005101520250204060800102030 CO conversion (%)Time (h) GHSV=0.01 mol/g.h GHSV=0.04 mol/g.hC C5+(wt%)B  CH4 (wt%)A  Figure 5.4. Product selectivity and CO conversion of 5Co/Al2O3(0.7) catalyst with dCo= 2 nm during FT synthesis reaction conditions of T=220 oC, P=20 bar and H2/CO=2   106 0 80 16005101520250204060800204060 CO conversion (%)TOS (h) GHSV=0.01 mol/g.h GHSV=0.04 mol/g.h C C5+(wt%)B  CH4(wt%)A  It is clear that by increasing the Co particle size the CH4 selectivity decreases to a certain level and upon further increase in Co particle size, the CH4 selectivity stabilizes.  The higher CH4 selectivity for smaller Co particles indicates that the number of essential sites for polymerization of hydrocarbons is lower on small Co particles [65, 108, 119]. Active sites have different levels of activity, which depend on the number of adjacent coordinatively unsaturated Co atoms. It Figure 5.5. Product selectivity and CO conversion of  5Co/Al2O3(0.9) catalyst with dCo =1 nm during FT synthesis reaction conditions of T=220 oC, P=20 bar and H2/CO=2    107 seems that in the FT synthesis a minimum ensemble of active sites is required to combine all the intermediate reaction steps [65, 108, 119].   For Co catalysts supported on σ-Al2O3 and 𝜃-Al2O3, it has been reported that CH4 selectivity decreases with increasing Co particle size up to 8-9 nm and then remains constant or increases. Also, the C5+ selectivity increases with increase in Co particle size up to 8-9 nm and then decreases or remains constant [87]. For Co catalysts supported on carbon nanofiber it has been shown that CH4 selectivity decreases by increasing the Co particle size up to 5 to 6 nm and then remains constant; whereas, C5+ selectivity increases with increasing Co particle size, even for larger Co particles (above 5-6 nm). Accordingly C5+ selectivity increased from 76 to 84 wt % at 210 °C by increasing the particle size from 5 to 15 nm [108], which is consistent with an increase in C5+   selectivity for 4.8-17.5 nm Co particles on γ-Al2O3 support reported elsewhere [161]. In Figure 5.6, there is a gap between 2 to 10 nm particle sizes, so it is not clear at what particle size the CH4 selectivity starts to decrease or C5+ selectivity increases with Co particle size. However, the trend of change in CH4 and C5+ selectivity with Co particle size is consistent with that reported in the literature [87, 107, 108, 161] as described above.    108 0 5 10 15 20 250102030CH4 selectivity: 5Co/Al2O3(0) 20Co/Al2O3(0.6) 15Co/Al2O3(0.1) 5Co/Al2O3(0.7) 5Co/Al2O3(0.9) CH4 selectivity (wt%)dCo(nm)606570758085C5+ selectivity:5Co/Al2O3(0)20Co/Al2O3(0.6) 15Co/Al2O3(0.1)5Co/Al2O3(0.7) 5Co/Al2O3(0.9)C5+ selectivity (wt%) Figure 5.6. Effect of Co particle size (nm) on CH4 and C5+ selectivity (wt%) measured at average CO conversion 20±6% and T=220 oC, P=20 bar and H2/CO=2 5.3.2 Selectivity and stability of the Re-Co/Al2O3 catalysts with TOS  For the 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalysts with small Co particles (dCo=2 nm and dCo =1 nm), the DOR is low (< 3%) and hence their behaviour in FT synthesis with TOS was quite different compared to catalysts with a higher DOR. The small Co particles were reduced in the FT environment and hence their activity increased with TOS. However, the CO conversion for these catalysts was still low even after an increase in DOR. Therefore, a series of Re-Co/Al2O3 catalysts was prepared to improve the DOR [103, 105]. The DOR of the Re-Co/Al2O3 with dCo=2, 5 and 11 nm was 55, 64 and 85%, respectively.   109 Figure 5.7 presents the CO conversion of the Re-Co/Al2O3 catalysts with TOS. The CO conversion reaches a maximum value within about the first 10 h TOS before decreasing for all catalysts. As discussed before, the initial behaviour of the catalysts in the reactor is partially the result of the dynamic response time of the system and partially because of some reconstruction of freshly reduced catalysts after exposure to synthesis gas. Figure ‎5.8 shows the catalysts with dCo=2, 5 and 11 nm at similar average CO conversion of 32±8 % (The stated average CO conversion is calculated from t~ 48 h to t~190 h of TOS). As the conversion decreases with TOS the water partial pressure also decreases, which results in an increase in CH4 selectivity and a decrease in C5+ selectivity. In addition, Figure ‎5.8 shows that at similar CO conversion level the CH4 selectivity for smaller Co particles (dCo=2 and 5 nm) is higher compared to 11 nm Co particles; whereas, the C5+ selectivity is higher for the 11 nm Co particle catalyst compared to smaller Co particles. As discussed in Section 5.3.1, on large Co particles, an increase in the number of active sites responsible for chain growth results in higher C5+ selectivity compared to small Co particles.     110 0 20 40 60 80 100 120 140 160 180 20002550751000255075100025507510002550751000255075100 Time (h)1.2Re-12Co/Al2O3(0), GHSV=0.05 mol/g.hF 1.2Re-12Co/Al2O3(0), GHSV=0.08 mol/g.hDE CO conversion (%)1.2Re-12Co/Al2O3(0), GHSV=0.12 mol/g.hC 0.5Re-5Co/Al2O3(0.7), GHSV=0.05 mol/g.hB  0.3Re-3Co/Al2O3(0.9), GHSV=0.05 mol/g.hA Figure 5.7. CO conversion for Re-Co/Al2O3 catalysts with different Co particle sizes. Operating condition is T=220 ºC, P=20 bar, H2/CO=2     111 0 80 160 2400204060801002406080100510152025 CO conversion (%)TOS (h) 0.3Re-3Co/Al2O3(0.9), dCo=2 nm 0.5Re-5Co/Al2O3(0.7), dCo=5 nm 1.2Re-12Co/Al2O3(0), dCo=11 nm C5+ (wt%)  CH4 (wt%)  Figure ‎5.9 (A) compares the CO2 selectivity of the Re-Co/Al2O3 catalyst, with Co particle size of 11 nm, at different CO conversions. The CO2 selectivity is high (average 18.1 mol%) when the average CO conversion is 82%, compared to an average CO2 selectivity of 3.2 and 2.2 (mol%) at Figure 5.8. CH4 and C5+ selectivity for Re-Co/Al2O3 catalysts with different Co particle sizes. Operating condition is T=220 ºC, P=20 bar, H2/CO=2 at an average CO conversion of 32±8% (shown by the dashed line)   112 lower average CO conversions (60% and 40%), respectively. Also, the average CH4 selectivity at 82% CO conversion is 17 wt% whereas for lower conversions it is below 9 wt%. Consequently, it is apparent that at high CO conversion (~82%) the WGS reaction has been promoted significantly and the product selectivity has changed. The high partial pressure of H2O in the system can cause the surface oxidation of Co and increase the rate of the WGS reaction [162, 163]; whereas, the high partial pressure of H2 favours the reduction of the catalysts. Consequently, the PH2O/PH2 ratio is a reasonable parameter to measure the probability of oxidation of metallic Co to CoO. Figure ‎5.9 (B) shows that the average PH2O/PH2 is two times higher when the average CO conversion is 82%, compared to lower average CO conversion of 60%. This significantly high average PH2O/PH2 can oxidize the smaller particles and increase the rate of the WGS reaction. Van Steen et al. [79] showed that spherical Co crystallites of size <4-5 nm oxidize at PH2O/PH2 = 1-1.5 in FT synthesis. Oxidation of Co catalysts with 12 nm Co particles at 𝑃𝐻2𝑂/𝑃𝐻2≥0.35 [78] and of 5.6 nm Co particles at 𝑃𝐻2𝑂/𝑃𝐻2>0.59 [77] have been reported elsewhere, which resulted in an increase in CO2 selectivity to about 6 mol%. Therefore, according to the literature data, the oxidation of Co particles is possible at all three conversions (40, 60 and 82% of Figure ‎5.9), considering that PH2O/PH2>0.57 when CO conversion is maximum during the reaction for all three experiments. For the catalyst with average CO conversion of 82%, PH2O/PH2 was above 1 with TOS throughout the experiment, which resulted in a significant change in both CO2 and hydrocarbon selectivity.  Figure ‎5.9 (B) shows that PH2O/PH2 increases to a maximum value of 2.7 with TOS, which means that theoretically, Co particles of approximately 6 nm can oxidize at this condition according to the profile shown in Figure 2.3. Note that in this study the average Co particle size is 11 nm measured by CO   113 chemisorption and 8±0.7 nm measured by XRD, although a range of Co particle sizes is likely to be present on the surface, in which smaller Co particles are more prone to oxidation.    Figure ‎5.10 demonstrates the effect of Co particle size on the selectivity of the Re-Co/Al2O3 and Co/Al2O3 catalysts measured in the CSTR at approximately the same CO conversion. Comparison between the CH4 selectivity of the Re-Co/Al2O3 catalyst and the Co/Al2O3 catalyst shows that there is no significant effect of adding Re promoter on the CH4 selectivity, although the average CO conversion for the Re-Co/Al2O3catalysts was higher than the Co/Al2O3 catalyst.  The C5+ selectivity is not significantly affected by adding the Re-promoter either, especially for large Co particles (dCo≥10 nm). Nevertheless, the average C5+ selectivity for the 0.3Re-3Co/Al2O3(0.9) with dCo=2 nm is 65%, which is lower than the average C5+ selectivity (~73 %) for the 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalyst with small Co particle (dCo=2nm and dCo =1 nm).         114 0 70 1400204060801001230510152025 CO conversion (%)Time (h) Average conv=82%, GHSV=0.05 mol/g.h  Average conv=60%, GHSV=0.08 mol/g.h Average conv=40%, GHSV=0.12 mol/g.hC PH2O/PH2B  CO2 selectivity (mol %)A  Figure 5.9. (A) CO2 selectivity(%) versus TOS; (B) PH2O/PH2 versus TOS; and  (C) CO conversion versus TOS for Re-Co/Al2O3  with dCo=11 nm at different GHSVs   115 0 5 10 15 20 25051015202530 5Co/Al2O3(0)  20Co/Al2O3(0.6)  15Co/Al2O3(0.1)  5Co/Al2O3(0.9)  5Co/Al2O3(0.7)  0.3Re-3Co/Al2O3(0.9)   0.5Re-5Co/Al2O3(0.7)   1.2Re-12Co/Al2O3(0)  CH4 selectivity (wt%)dCo (nm)A 0 5 10 15 20 255060708090100 5Co/Al2O3(0)  20Co/Al2O3(0.6) 15Co/Al2O3(0.1) 5Co/Al2O3(0.9) 5Co/Al2O3(0.7) 0.3Re-3Co/Al2O3(0.9)  0.5Re-5Co/Al2O3(0.7) 1.2Re-12Co/Al2O3(0)  C5+ (wt%)dCo(nm)B  Figure 5.10. Product selectivity for Re-Co/Al2O3 catalysts (average conversion 32±8%) and Co/Al2O3 catalysts (average conversion 20±6%) with different Co particle size A) CH4 selectivity B) C5+ selectivity    116 5.4 Effect of Co particle size on the initial activity of the Co/Al2O3 and Re-Co/Al2O3 catalysts  The catalyst turn-over frequency (TOF) for a particular reaction is defined as the number of moles of reactant converted per mole of active catalytic sites per unit of time.  In the case of the FT synthesis, with the number of active sites determined by CO uptake, the catalyst total TOF is calculated as follows: 𝑇𝑂𝐹𝐶𝑂 =−𝑟𝐶𝑂(𝑡)𝑁𝐶𝑂 × 𝜎× 106 5.1  where 𝑁𝐶𝑂 is the CO uptake obtained according to the methodology described in Section 3.3.2 and measured for the fresh catalyst in µmol of CO per gram of catalyst. σ is the stoichiometry number and is equal to 2, assuming bridge type CO adsorption on Co. −𝑟𝐶𝑂(𝑡) is defined as the total CO consumption rate, measured as the moles of CO converted per gram of catalyst per second, calculated directly from the CSTR design equation as: −𝑟𝐶𝑂(𝑡) = 𝐹𝑖𝑛𝐶𝑂𝑋𝐶𝑂𝑊 5.2  where 𝐹𝑖𝑛𝐶𝑂 is the CO molar flowrate at the inlet (mol/s), W is the catalyst mass (g) and 𝑋𝐶𝑂 is the CO conversion.  Taking in to account the CO consumed in the WGS reaction, the amount of CO consumed to produce FT products is given by the total amount of CO consumed minus the total amount of CO2 produced during the reaction. Hence, the TOF for the CO converted to FT products is given by: 𝑇𝑂𝐹𝐹𝑇 =  𝑇𝑂𝐹𝐶𝑂 − 𝑇𝑂𝐹𝐶𝑂2  5.3   117 The 𝑇𝑂𝐹𝐶𝑂0  (the initial total CO TOF) was calculated based on the rate of the reaction, −𝑟𝐶𝑂(𝑡), at time t*. The definition of t* is usually taken as the time at which the reaction rate is maximum. However, as reported by others and shown in Figures 5.1 and 5.7, as a result of the unsteady-state behaviour of the reactor system following the introduction of synthesis gas, t* has been defined differently in various studies to exclude the initial system hydrodynamic response and the catalyst stabilization period [31, 119, 153]. According to the hydrodynamic response of the system (approximately 8 h, see Appendix M) and the initial catalyst reconstruction following introduction of the synthesis gas, the initial catalyst stabilization period is set at approximately 10 h for all the catalysts, except for the experiments with the 15Co/Al2O3(0.1) catalyst at high GHSVs (0.16 and 0.08 mol/g.h), Figure 5.1 (C,D). For these catalysts the initial stabilization period occurred at much longer times (11≤t*≤45 h) because of slow reduction or reconstruction of Co particles in the FT environment, as already discussed in Section 5.3.1. For these catalysts t* was chosen as the time at maximum CO conversion.   With the above assumptions, Table 5.1 shows the calculated initial turn over frequencies at time t*, based on the total CO consumption (𝑇𝑂𝐹𝐶𝑂0 ), CO consumption to CO2 (𝑇𝑂𝐹𝐶𝑂20  ) and CO consumption to FT products (𝑇𝑂𝐹 𝐹𝑇0 ). Figure ‎5.11 plots 𝑇𝑂𝐹𝐹𝑇0  versus Co particle size for the Re-Co/Al2O3 and Co/Al2O3 catalysts with the dotted trend lines reflecting data reported in the literature [107, 108]. The data indicate that 𝑇𝑂𝐹𝐹𝑇0  over the Co/Al2O3 catalysts is lower for the small Co particles (dCo=1 nm and dCo=2 nm) compared to the large Co particles (dCo ≥10 nm).  A similar trend is observed for the 𝑇𝑂𝐹𝐹𝑇0  over the Re-Co/Al2O3 catalysts. Figure ‎5.11 shows some scatter in part because the CO conversions are not in the same range for all catalysts. Since the rate of reaction has been measured in a completely back-mixed reactor, the products may impact   118 the rate of the reaction and hence the 𝑇𝑂𝐹𝐹𝑇0 . Also, note that NCO in Equation 5.1 was measured on the freshly reduced catalysts and may be impacted by the change in DOR. However, most of the catalysts, Figures 5.1 and 5.7 show maximum CO conversion after relatively short reaction times and so the impact of the DOR changes are thought to be relatively small. Despite the uncertainties, the trend of activity observed in this study is similar to the trends observed elsewhere [107, 108], in which TOF is lower for Co particle sizes in the range of dCo< 6-8 nm [108] or dCo<11 nm [107] compared to larger Co catalysts. The lower 𝑇𝑂𝐹𝐹𝑇0  of small Co particles is because different surface sites are exposed to the FT environment since the fraction and type of the surface atoms change with Co particle size [107, 108, 164] (e.g small Co particles have higher fraction of atoms with low coordination numbers [124]). Also, in a FT reaction a minimum ensemble of active sites are required to combine all the intermediate steps [107, 108, 164]. Figure ‎5.11 does not contain the data for the 1.2Re-12Co/Al2O3(0) catalyst at high CO conversion ( 95%) at time t*. As reported in Table 5.1, 1.2Re-12Co/Al2O3(0) catalyst has low 𝑇𝑂𝐹𝐹𝑇0   at high CO conversion (95%), which is likely the result of surface oxidation of Co particles at high partial pressure of water, which leads to a reduction in the number of active Co sites on the surface.  Due to the uncertainty in choosing the time t*, the TOF calculations were repeated based on the CO conversion measured after 48 h TOS for all the experiments (Appendix N). The results are in agreement with the trend observed in Figure ‎5.11. Note that the 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalysts with (dCo=1 and 2 nm) were continuously reduced with TOS, Figure 5.1 (A), however their TOFs were significantly lower compared to catalysts with large Co particles (dCo≥ 10 nm) throughout the experiment.    119 Table 5.1. Effect of Co particle size on activity of the Re-Co/Al2O3 and Co/Al2O3 catalysts at time t*   Catalyst dCo (nm) CO conv at time t* (%) NCO (µmol/g) TOF0CO  (s-1) 𝑇𝑂𝐹𝐶𝑂20  (s-1) TOF0FT (s-1) Co/Al 2O3 5Co/Al2O3(0) 22 14 14 1.6E-02 8.6E-05 1.6E-02 20Co/Al2O3(0.6) 13 63 51 1.8E-02 1.7E-04 1.8E-02 15Co/Al2O3(0.1) 10 60 70 1.3E-02 2.1E-04 1.3E-02 15Co/Al2O3(0.1) 10 40 70 1.5E-02 1.1E-04 1.5E-02 15Co/Al2O3(0.1) 10 43 70 1.5E-02 1.5E-04 1.5E-02 15Co/Al2O3(0.1) 10 26 70 1.2E-02 1.3E-04 1.2E-02 5Co/Al2O3(0.7) 2 12 7 1.3E-03 8.0E-05 1.2E-03 5Co/Al2O3(0.7) 2 1 7 5.4E-04 7.7E-05 4.7E-04 5Co/Al2O3 (0.9) 1 12 10 1.1E-03 2.4E-05 1.1E-03 5Co/Al2O3 (0.9) 1 3 10 6.9E-04 8.4E-05 6.1E-04  1.2Re-12Co/Al2O3(0) 11 95 75 2.1E-02 4.6E-03 1.6E-02 Re-Co/Al 2O3 1.2Re-12Co/Al2O3(0) 11 72 75 2.8E-02 2.5E-03 2.6E-02 1.2Re-12Co/Al2O3(0) 11 56 75 3.0E-02 2.3E-03 2.8E-02 0.5Re-5Co/Al2O3(0.7) 5 41 56     1.1E-02 6.4E-04 9.9E-03 0.3Re-3Co/Al2O3(0.9) 2 34 62 8.1E-03 1.7E-04 7.9E-03   120 0 5 10 15 20 250.0000.0050.0100.0150.0200.0250.030   5Co/Al2O3(0) 20Co/Al2O3(0.6) 15Co/Al2O3(0.1) 5Co/Al2O3(0.7) 5Co/Al2O3(0.9) 1.2Re-12Co/Al2O3(0) 0.5Re-5Co/Al2O3(0.7) 0.3Re-3Co/Al2O3(0.9) TOF0FT, S-1dCo, nm Figure 5.11. TOF0FT versus Co particle size. For the Re-Co/Al2O3 catalysts the CO conversion is between 34 to 72% and for the Co/Al2O3 catalysts the CO conversion is between 1 to 63%. Error bars represent four data points for 15Co/Al2O3(0.1) catalyst and two data points for 1.2Re-12Co/Al2O3(0) and 5Co/Al2O3(0.9) catalysts at varied CO conversions as reported in Table 5.1 5.5 Conclusions  The effect of CO conversion level on stability and selectivity of the Co/Al2O3 and Re-Co/Al2O3 catalysts was studied in this chapter.By decreasing the GHSV for a specific catalyst and increasing the CO conversion up to approximately 60%, the CH4 selectivity decreases. Several studies on the effect of water in FT synthesis also show that the C5+ selectivity increases and CH4 selectivity decreases with increased CO conversion or water concentration in the system using Co/Al2O3 catalysts, consistent with the observations of this study [165-168]. However, for the   121 1.2Re-12Co/Al2O3(0) catalyst at high average CO conversion of 82%, the average CH4 selectivity increases to 20wt% compared to average CH4 selectivity of 6wt% and 10wt% at average CO conversions of 60% and 40%, respectively. The increase in CH4 selectivity is presumably due to PH2O/PH2>1, which results in surface oxidation of Co particles. Also, the average CO2 selectivity increases significantly to 17.9 (mol%) at high average CO conversion (82%) compared to lower average conversion of 60% and 40%, in which the average CO2 selectivity was 3.2 and 2.2 (mol%), respectively.  The significant increase in CO2 selectivity also confirms the surface oxidation of Co particles at high partial pressure of water, which promotes the water gas shift reaction.  Comparing the CH4 and C5+ selectivity for the Co/Al2O3 with different Co particle sizes at 20±6% CO conversion and for the Re-Co/Al2O3 catalyst at 32±8% CO conversion, indicates that the average CH4 selectivity decreased and the average C5+ selectivity increased with increased Co particle size (up to dCo ~ 10 nm). The higher CH4 selectivity of small Co particles (dCo ≤5 nm) compared to large ones (dCo ≥10 nm) is related to a lower amount of essential sites for polymerization of hydrocarbons on small Co particles compared to large Co particles [65, 108, 119].   The activities of the catalysts were also compared by measuring the initial catalyst activity, 𝑇𝑂𝐹𝐹𝑇0  at time t*. The trend between observed 𝑇𝑂𝐹𝐹𝑇0  and Co particle size was similar to the reported data in the literature [42, 71-76, 109, 110], which showed increased 𝑇𝑂𝐹𝐹𝑇0  with increased Co particle size up to approximately dCo< 6-8 nm [108] or dCo<11 nm [107] and above this Co particle size the activity remains constant.    122 Chapter 6. Deactivation of Co catalysts  6.1 Introduction  The main deactivation mechanisms of FT catalysts reported in the literature were reviewed in Section 2.5. Deactivation by the formation of Co support compounds, formation of carbon species, formation of Co oxides and sintering or aggregation are all deactivation mechanisms that can occur on Co catalysts [1]. Practically, all the catalyst deactivation mechanisms can be affected by metal particle size and metal-support interactions. For example, small Co particles are prone to oxidation upon exposure to relatively high temperature and high partial pressure of water, which can be present in the FT reaction environment [79]. Co particle size can also affect the rate of carbon deposition on the surface of the catalyst depending on the mechanism of carbon formation. Specific sites that promote carbon deposition might be favoured on Co particles of a particular size. For instance, as discussed in Chapter 5, small Co particles (dCo≤5 nm) are more selective towards CH4 formation, in other words there are fewer sites for chain growth on the Co surface, resulting in more carbon that hydrogenates with sufficient dissociated hydrogen [108]. Consequently, it is expected that on large Co particles the formation of long chain hydrocarbons is more probable which may result in the formation of hydrogen resistant polymeric carbon as well. Also, the number of active Co sites covered by carbon may depend on Co particle size. Sintering is also strongly dependant on the particle size and MSI [61, 62, 66]. The melting temperature of a nanocluster is well below that of the bulk material and surface diffusion is faster for smaller particle sizes [59, 60]. However, a high interaction between metal and support can reduce crystallite migration [66]. Also, during FT reaction unreducible Co-  123 support compounds at high partial pressure of water can be formed which lead to catalyst deactivation, in which small Co particles have more tendency to form Co-support compounds because of their high interaction with the support [49, 67, 80, 81].  The purpose of this chapter is to determine the effect of Co particle size on the deactivation of the Co/Al2O3 catalysts in FT synthesis and to identify the deactivation mechanisms by characterization of the used catalysts. The rate of deactivation has also been quantified by fitting different empirical activity models to the measured rates as a function of TOS. 6.2 Challenges and limitations   Characterization of the used catalysts recovered from the FT synthesis done in a slurry phase reactor is challenging. After the reaction, the used catalyst is suspended in product wax, which is usually solid at ambient temperature. To recover the catalyst from the heavy hydrocarbons, the wax was melted and the catalyst was allowed to settle by gravity, and then the liquid wax was removed. The separated catalyst was then washed with CH2Cl2, to remove any remaining wax on the surface of the catalyst. Since the FT catalysts are in a reduced state during reaction, once removed from the reactor and exposed to ambient air they rapidly re-oxidise unless special precautions are taken to limit oxygen exposure. The layer of wax on the surface of the catalyst can limit oxidation of the metallic Co. For example, XRD analysis of the wax-covered used Co/Al2O3 and Re-Co/Al2O3 catalysts with dCo≥10 nm, showed the presence of metallic Co. However, since small Co particles are more prone to oxidation, metallic Co was not detectable on the wax covered used Co/Al2O3 and Re-Co/Al2O3 catalysts with small Co particle size.   124 Consequently, ex situ measurement of the DOR after the reaction, to identify the degree of reduction of the catalyst following exposure to synthesis gas for extended reaction periods, was not possible. The re-oxidation of the Co also makes TEM analysis of the used catalysts less effective because of the reduced contrast that exists between the Al2O3 support and CoO particles.  Determining the amount of carbon (in graphitic and amorphous forms) deposited on the surface of the used catalysts is also a challenge due to the presence of waxy hydrocarbons on the catalyst surface and inside the pores of the catalyst/support. To address this issue, a standard method of wax extraction, as described in Section 3.2.1 was used prior to elemental analysis of the used catalyst.  6.3 Characterization of the used catalysts  6.3.1 Identification of Co or Co3O4 particle growth  The Co and Co3O4 particle sizes of the catalysts are shown in Table ‎6.1. Although XRD is not a suitable method for detecting well dispersed Co particles, the catalysts with small Co particles (dCo≤5 nm) were characterized to determine if there was significant growth in metallic Co after reaction. For the 5Co/Al2O3(0.9), the 5Co/Al2O3(0.7), the 0.3Re-3Co/Al2O3(0.9) and the 0.5Re-5Co/Al2O3(0.7) catalyst with small Co particles, no peak assigned to metallic Co was observed before and after the reaction, indicating that the Co particle size was either too small to be   125 detected by XRD or the Co particles were oxidized after exposure to air. Considering the error in the measurements, there was no significant Co crystallite growth observed for the Co/Al2O3 and Re-Co/Al2O3 with large Co particles (dCo≥10 nm) that was detectable by XRD. In addition, for the Re-Co/Al2O3 and Co/Al2O3 catalysts with dCo≤5 nm, there was no Co oxide particle growth observed, confirming that there was no significant particle sintering during FT synthesis, under the reaction condition of this study.                    126  Table 6.1. Co and Co3O4 particle sizes before and after the reaction for Co/Al2O3 catalysts. The stated average CO conversion is calculated from t~48 h to t~190 of TOS  Catalyst, Co particle size from CO chemisorption Average CO conversion (%) Fresh catalyst by XRD Used catalyst by XRD Co (nm) Co3O4 (nm) Co (nm) Co3O4 (nm) 5Co/Al2O3(0), 22 nm 14 21±0.8 8±1.1 23±0.7 7±2.8 20 Co/Al2O3 (0.6), 13 nm 35 12±0.7 3±0.1 11±0.6 4±0.2 15Co/Al2O3(0.1), 10 nm 41 9±0.8 5±0.2 10±0.4 5±0.4 15Co/Al2O3(0.1), 10 nm 36 9±0.8 5±0.2 12±1.6 4±0.1 15Co/Al2O3(0.1), 10 nm 33 9±0.8 5±0.2 13±1.6 4±0.3 15Co/Al2O3(0.1), 10 nm 30 9±0.8 5±0.2 12±1.5 4±0.3 15Co/Al2O3(0.1), 10 nm 25 9±0.8 5±0.2 11±0.6 5±0.5 5Co/Al2O3(0.7), 2 nm 17 NA 2±0.3 NA 3±0.5 5Co/Al2O3 (0.7), 2 nm 4 NA 2±0.3 NA 3±0.2 5Co/Al2O3 (0.9), 1 nm 21 NA 4±0.5 NA 3±0.3 5Co/Al2O3 (0.9), 1 nm 4 NA 4±0.5 NA 5±0.5 0.3Re-3Co/Al2O3(0.9), 2 nm 24 NA 3±0.1 NA 4±0.0 0.5Re-%Co/Al2O3 (0.7), 5 nm 30 NA 3±0.7 NA 3±0.0 1.2Re-12Co/Al2O3(0), 11 nm 82 8±0.7 4±0.0 9±1.5 3±0.0 1.2Re-12Co/Al2O3(0), 11 nm 60 8±0.7 4±0.0 8±1.0 4±0.5       127 6.3.2 Identification of the changes in catalyst surface area  The wax on the used catalysts was removed with CH2Cl2 in a Soxhelet extractor, at 80 ºC for 2 h. The washed samples were then degassed and analyzed in a Micromeritics ASAP 2020 analyzer as described in Section 3.3.8. The BET surface area, pore diameter and the amount of carbon deposited on the used catalysts measured by CH analysis, as described in Section 3.3.4, are reported in Table ‎6.2 for the catalysts that showed deactivation during FT synthesis. For the 15Co/Al2O3(0.1) catalysts with dCo=10 nm, the BET surface area of the used catalysts decreased with increase in CO conversion. The decrease in BET surface area may be the result of water, which promotes sintering of the support, or because of carbon deposition in the pores of the support. The total C content of the used catalyst is plotted versus the reduction in BET surface area in Figure 6.1 (excluding the 1.2Re-12Co/Al2O3(0) catalyst with 82% CO conversion that showed a negative change in BET surface area). As shown in Figure 6.1 there is a general increased loss in the used catalyst BET surface area with increased C content of the used catalyst.  Furthermore, the small change in BET surface area of the Re-Co/Al2O3 catalyst operated at high CO conversion (Table ‎6.2; corresponding to high amounts of water in the system), suggests that the reduction in BET surface area is not the result of sintering of the support. Similarly, the significant decrease in BET surface area of the 5Co/Al2O3(0) catalyst occurs despite a low CO conversion (14%) and water content (PH2O/PH2< 0.09) in the reactor; whereas, the carbon content of the used catalyst is high (4.7 C wt%). Hence carbon deposition appears to be the main cause of the reduced BET surface area of the used catalysts at the reaction conditions of this study.   128 Table 6.2. BET surface area (m2/g) average pore diameter (nm) before and after the reaction for Co/Al2O3 and Re- Co/Al2O3 catalysts with deactivation,     Fresh Used  Catalyst/ Co particles measured by CO chemisorption Ave CO Conv (%) SBET m2/g Average pore diameter, (nm) SBET m2/g, dpore,  (nm) C, wt% Reduction in Surface area (%) 5Co/Al2O3(0), 22 nm 14 186 8 126 9 4.7 32.5 20Co/Al2O3(0.6), 13 nm 35 155 8 101 8 6.5 34.7 15Co/Al2O3(0.1), 10 nm 37 161 8 112 7 7.6 30.5 15Co/Al2O3(0.1), 10 nm 30 161 8 157 7 4.4 2.3 15Co/Al2O3(0.1), 10 nm 25 161 8 157 7 2.7 2.3 0.5Re-5Co/Al2O3(0.7), 5 nm 30 152 11 141 10 4.9 7.2 0.3eRe-3Co/Al2O3 (0.9), 2 nm 24 185 9 163 10 3.4 11.9 1.2Re-12Co/Al2O3(0), 11 nm 82 123 11 135 8 4.1 -9.7 1.2Re-12Co/Al2O3(0), 11 nm 60 123 11 111 9 5.9 9.7 1.2Re-12Co/Al2O3(0), 11 nm 40 123 11 109 … 6.0 11.4   129  Figure 6.1. Reduction in BET surface area (%) versus C content (wt%) of used catalysts. 6.3.3 Identification of carbon species  The nature of carbon deposits that resulted in the reduction in BET surface area is examined in this section. The temperature at which different surface carbon species, deposited on Co catalysts, are hydrogenated/reacted in H2, has been used in the literature to identify the type of carbon (see Table ‎6.3). In addition, by using the reference carbon species it was found that during hydrogenation of amorphous carbon on metallic Co, two CH4 peaks at 275 ºC and 430 ºC 0 5 10 15 20 25 30 3502468101214   5Co/Al2O3(0)  15Co/Al2O3(0.1)  20Co/Al2O3(0.6) 0.3Re3Co/Al2O3(0.9)  0.5Re5Co/Al2O3(0.7)  1.2Re12Co/Al2O3(0)Carbon content, wt%Reduction in SBET, %  130 were generated and during hydrogenation of graphene or graphite compounds one sharp peak at 550 ºC was detected [70].  Table 6.3. Forms and reactivity of carbon species in TPH profile of used FT catalysts  Hydrogenation temperature ( ºC) Possible carbon type Ref 250 Surface carbide species (atomic carbon), residual wax/hydrocarbons, bulk Co carbide  [68] 330 Residual wax in small pores of the support [68] 420-455 Polymeric or amorphous carbon on Co or support [68, 169] 550-650 Graphitic or crystalline films (semi-ordered) [70, 169] 700-750 Graphitic or crystalline films (moderately ordered sheets) [70, 169]  Temperature programmed hydrogenation (TPH) was conducted in a fixed bed reactor on two different used catalysts of the present study as described in Section 3.3.3, to examine the form of the deposited carbon. Firstly, the 20Co/Al2O3(0.6) catalyst with dCo=13 nm was removed from the CSTR reactor after 161 h operating at an average CO conversion of 35% and analyzed. A second 5Co/Al2O3(0.7) catalyst with dCo=2 nm after operating for 185 h at an average CO conversion of 17% was also analyzed. CH analysis of these catalysts with dCo=13 nm and dCo=2 nm showed 6.5 wt% and 2.8 wt% carbon content, respectively.   Because of the overlap of the mass fragments from the hydrocarbons in the TPH product streams (See Table O.1 in Appendix O), a precise quantitative analysis of the TPH products other than CH4 is difficult. Figure 6.2 indicates the intensity of several mass numbers exiting from the reactor. Some amount of CO2 and CO is present in the outlet gas, likely the result of carbon   131 reacting with the oxygen from oxide compounds on the catalyst surface. The quantitative analysis of the outlet gas indicates that for the 20Co/Al2O3(0.6) and the 5Co/Al2O3(0.7) catalysts, the  maximum amount of (CO+CO2)  is 10 mol% and 7 mol %, respectively (this calculation was made according to the initial amount of C on the catalyst as measured with the CH analyzer as described in Appendix O). Therefore at least 90 mol% of the outlet gas for the 20Co/Al2O3(0.6) catalyst and 93 mol % of the outlet gas for the 5Co/Al2O3(0.7) catalyst consists of hydrocarbons such as CH4, C2H4, C2H6 and C3H8. For the 5Co/Al2O3(0.7) catalyst with an average CO conversion of 17%, CH4 (amu15 and amu16) has two broad peaks at approximately 450 ºC and 550 ºC; whereas, the 20Co/Al2O3(0.6) catalyst with an average CO conversion of 35% has an additional sharp peak at 600 ºC which has maximum intensity. In addition, mass 26 and mass 27 (an overlap of C2H4, C2H6 and C3H8) have an additional peak at 550-600 ºC during the hydrogenation of the 20Co/Al2O3(0.6) catalyst.   As reported in the literature [68, 70, 169], during hydrogenation amorphous or polymeric carbon hydrogenates at 420-455 ºC showing a broad peak; whereas, semi-ordered graphitic carbon hydrogenates at 550 ºC to 650 ºC, showing a sharp peak. Hence, the carbon on the surface of the 5Co/Al2O3(0.7) catalyst generated at lower CO conversion is mainly in the form of amorphous or polymeric carbon; whereas, the carbon deposited on the surface of the 20Co/Al2O3(0.6) catalyst at higher CO conversion, is in the form of amorphous and polymeric carbon and semi-ordered graphite. Moreover, the wt% of H measured by CH analysis of all the used catalysts was approximately zero (<0.05 wt%). Hence, the measured C content of the used catalyst is not the result of residual high molecular weight hydrocarbons from the liquid product, which confirms the carbon is  rather in the form of graphitic, amorphous or polymeric carbon deposition on the   132 catalyst surface.These carbon species are all un-reactive under Fischer-Tropsch conditions. Weststrate et al. [159] proposed a mechanism for graphene formation during low temperature FT synthesis at  227 ºC in which step edges and defects play a significant role in the formation of graphene nuclei. Subsequently, the growth occurs by addition of C2Hx compounds.  0 200 400 600 8000.000.010.020.000.010.020.030.0000.0010.0020.0000.0030.0060.0000.0150.0300.0450.0000.0020.0040.0000.0030.0060.009 Temp(0C)amu 15 amu 16 amu 26 Reletive Intensityamu 27 amu 28 amu 29  amu 44 Figure 6.2. TPH profile for used catalysts, Solid line: 20Co/Al2O3 (0.6) catalyst with dCo=13 nm at average CO conversion of 35%, dotted line: 5Co/Al2O3(0.7) catalyst with dCo=2 nm at average CO conversion of 17%    133 TOF-SIMIS was used to locate the hard to remove carbon distribution on the 0.3Re-3Co/Al2O3(0.9) catalyst operated at average CO conversion of 24% and the 15Co/Al2O3(0.1) catalyst operated at average CO conversion of 33% . The catalysts were dewaxed by the procedure described in Section 3.2.1 after removal from the reactor.   Figure 6.3. TOF-SIMS maps of C, Co, Al for the dewaxed used 0.3Re-3Co/Al2O3(0.9) catalyst. The areas with high concentration of elements appear with brightest color (Yellow)   Total Ion Co C Al   100 m   134    Figure 6.4.  TOF-SIMS maps of C, Co, Al for the dewaxed used 15Co/Al2O3(0.1) catalyst. The areas with high concentration of elements appear with brightest color (Yellow)  Figure 6.3 and Figure 6.4 indicate that the hard to remove carbon is distributed both on the Co and the support. Furthermore, Table 6.4 compares the Co/Al ratio for a series of fresh and used Co/Al2O3 and Re-Co/Al2O3 catalysts as determined by XPS analysis. Presumably, if carbon is mostly deposit on the Co surface, the Co/Al ratio should decrease with increased amount of Total Ion Co C Al  100 m   135 carbon, as the Co signal will be suppressed. However, the Co/Al ratio did not change with a specific trend, confirming that the carbon is not selectively deposited on the Co. Table 6.4.  Co/Al ratio obtained with XPS for Co/Al2O3 and Re-Co/Al2O3 catalysts  Catalyst TOS Avg. CO conv. Fresh catalyst by XPS Used catalyst by XPS h % Co/Ala Co/Ala 5Co/Al2O3(0) 145 14 0.04 0.04 15Co/Al2O3(0.1) 165 33 0.08 0.10  137 25 0.08 0.16 20Co/Al2O3(0.6) 162 35 0.12 0.10 0.3Re-3Co/Al2O3(0.9) 190 24 0.02 0.02 0.5Re-5Co/Al2O3(0.7) 190 30 0.04 0.05 1.2Re-12Co/Al2O3(0) 233 82 0.05 0.08  139 60 0.05 0.05  166 40 0.05 0.07 a The error in the analysis is ±20% 6.4 Quantifying the extent of catalyst deactivation using an activity factor  As discussed in Chapter 5, the 5Co/Al2O3(0.7) and 5Co/Al2O3(0.9) catalysts with dCo = 2 nm and dCo =1 nm did not deactivate in the reactor after ~160 h of operation, but rather were activated with TOS. The activation is assumed  to be due to further reduction of these catalysts with a low DOR, after exposure to the syngas [135, 160]. Demonstrating that the DOR increased during the FT reaction is difficult because of the re-oxidation of the catalysts during their recovery from the   136 reactor. However, an increase in reduction has been reported by in situ methods in a fixed bed reactor [135, 160].   For the Re-Co/Al2O3 and the Co/Al2O3 catalysts with large Co particles (dCo ≥ 10 nm) and for the Re-Co/Al2O3 catalysts with small Co particles (dCo=5 nm and dCo=2 nm), catalyst deactivation was observed.  The results discussed in Sections 6.3.1 – 6.3.3 suggest that carbon deposition was the primary cause of the catalyst deactivation. The extent of catalyst deactivation is quantified using the activity factor defined as: 𝛼(𝑡) = −𝑟𝐶𝑂(𝑡)/−𝑟𝐶𝑂(𝑡∗) 6.1 where α(t) is the activity factor at time t, −𝑟𝐶𝑂(𝑡) (mol/(g.s)) is the total rate of CO consumption at time t and −𝑟𝐶𝑂(𝑡∗) (mol/(g.s)) is the initial rate of reaction at time t* chosen as discussed in Section 5.4, and −𝑟𝐶𝑂(𝑡) is the measured rate from the CSTR design Equation 5.2. Note that t* was chosen to exclude the initial system response from the longer term catalyst deactivation. Table 6.5 summarizes empirical models from the literature that correlate the activity factor with different deactivation rate orders and examples of the corresponding dominant deactivation mechanisms.  The models are written in terms of a dimensionless time variable 𝜑 = (𝑡 − 𝑡∗)/𝜏 where 𝜏 is the residence time of the gas in the reactor ( = 0.8 h for all the experiments, see Appendix M for gas residence time inside the reactor) and kd is the dimensionless deactivation rate constant. The models predict that the activity goes to zero at  𝑡 → ∞ and the same assumption has been made in deactivation models reported for the FT synthesis previously [40, 41, 62, 170, 171]. Since the models in the present study were used to quantify the deactivation rate in the time span of t=t* to t = 200 h, it was not necessary to add a limiting activity as was done in [172, 173].   137  The models of Table 6.5 were fitted to the activity profiles of the Co/Al2O3 catalysts (See Appendix P, Figures P.1 through P.5) with dCo= 22, 13 and 10 nm and Re-Co/Al2O3 catalysts with dCo=11, 5 and 2 nm. Note that the reciprocal power model has two variables defined by n and kd. By fixing the value n in the reciprocal power model, kd can be used as a direct measure of deactivation rate with which to compare the different catalysts.  Table 6.5. Empirical models fitted to catalyst deactivation [82]  Functional form of activity Integral form of activity Deactivation order Dominant deactivation mechanism Linear α (𝜑)=1-(kd 𝜑)** 0 Poisoning Exponential α (𝜑)= exp(-kd𝜑) 1 Poisoning Hyperbolic 1/ α (𝜑)=1+kd 𝜑 2 Sintering Reciprocal Power 1/α (𝜑) = 1+kd 𝜑n n Coking or Fouling ** Linear model is only valid for 0 ≤ 𝜑≤ 1/kd, where α is in the range of 0 to 1 The estimated parameter values are reported in Appendix P (Tables P.1 and P.2). The reciprocal power model with n = 0.5 and consistent with a deactivation mechanism associated with catalyst fouling or coking, i.e. 𝛼(𝜑) = 1 (1 + 𝑘𝑑𝜑0.5)⁄  had the best fit to the catalyst activity profiles, although for the 1.2Re-12Co/Al2O3(0) catalyst operated at an average CO conversion of 82%, the fit was poor, likely because  of oxidation of Co particles in  the presence of high concentrations of H2O and CO2, as is discussed in Section 5.3.2. For the cracking of light east Texas gas oil at 398 oC, in which deactivation was due to coke deposition, an n value of 0.5 in deactivation rate was also reported [174], in agreement with the value used here and reported   138 elsewhere [175]. The kd values of the reciprocal power model for the Co/Al2O3 and Re-Co/Al2O3 catalysts are summarized in Table 6.6.   6.4.1  Effect of carbon deposition on deactivation of the catalysts  As reported in Section 6.4, the reciprocal power model representing the coking or fouling of the catalysts, had the best fit to the deactivation profile of the catalysts. Assuming that coke formation occurs in parallel with the FT synthesis reaction [175-177], then the rate of coke formation with TOS can be written as: −𝑟𝐶 = 𝑟𝐶0  × 𝛼𝐶(𝜑)   6.2 where 𝑟𝐶 is the the rate of coke formation per gram of catalyst (mol/g.s), 𝑟𝐶0 is the initial rate of coke formation (mol/g.s) and 𝛼𝐶(𝜑) is the coke formation activity factor that captures the rate of deactivation of the coke formation reaction. Assuming that the activity factor of the CO consumption to FT products (α(𝜑)) is the same for the coke formation reaction [175], i.e.  𝛼𝐶(𝜑) =  α(𝜑) then the total amount of carbon deposited on the catalyst is easily calculated by integration of the equation: 𝐶𝑐 = 𝑟𝐶0τ ∫11+𝑘𝑑𝜑1/2𝜑0 𝑑𝜑  6.3 in which Cc is the total amount of carbon deposited on the catalyst in mol/g, as measured by C elemental analysis of the used catalyst. Integration of Equation 6.3 allows the initial rate of carbon deposition to be calculated as follows: 𝑟𝐶0 = 𝐶𝑐 × 𝑘𝑑2 [2𝜏(𝑘𝑑 × 𝜑0.5 − ln(1 + 𝑘𝑑 × 𝜑0.5))⁄ ]  6.4   139 The procedure to calculate 𝑟𝐶0 is reported in Table 6.6 and the initial coke formation rate per active Co site (i.e. the initial carbon deposition turnover frequency, 𝑇𝑂𝐹𝐶0) is readily determined from the CO uptake data. Hence, Figure 6.5 shows that the initial rate of carbon deposition per active Co site (𝑇𝑂𝐹𝐶0), measured at approximately the same CO conversion level such that the gas composition within the reactor is approximately the same, increases approximately linearly (correlation coefficient of R2=0.87) with increased Co particle size. Note that the data of Figure 6.5 are restricted to carbon deposition rates measured at average CO conversions of 14-40% and excludes the data obtained on the 1.2Re-12Co/Al2O3(0) catalyst at high CO conversion of 60 and 82% because high partial pressure of H2O and CO2 decreases the carbon deposition rate. At lower CO conversions, the effect of change in CO2 and H2O partial pressure is less significant. Furthermore, an average value for 𝑇𝑂𝐹𝐶0  is reported for the 15Co/Al2O3(0.1) catalyst, based on the carbon deposition rates measured at CO conversions of 25-37%. The calculated 𝑇𝑂𝐹𝐶0 values for this catalyst suggest that the initial rate of carbon deposition increases with CO conversion (Table 6.6). At higher CO conversions (≥ 60%), 𝑇𝑂𝐹𝐶0 decreased with increased CO conversion on the 1.2Re-12Co/Al2O3(0) catalyst. An increase in the amount of CO2 produced as a result of the WGS reaction can decrease the amount of carbon deposited by the reverse Boudouard reaction: C + CO2  2CO. Alternatively, the high amount of water present under these conditions may remove C by steam gasification.  The 𝑇𝑂𝐹𝐶0 can also be compared to the initial total CO consumption rate per active site,𝑇𝑂𝐹𝐶𝑂0 , as measured at time t*. The comparison shows (Table 6.6) that the carbon deposition rate is at least 2-orders of magnitude slower than the total CO consumption rate. Also, note that 𝑇𝑂𝐹𝐹𝑇0 ~ 𝑇𝑂𝐹𝐶𝑂0  due to the low rate of CO2 production, see Table 5.1. Hence, although 𝑇𝑂𝐹𝐶𝑂0  includes   140 the rate of carbon deposition, the error in assuming that the CO consumption rate represents the conversion of CO by the WGS and FT reactions that occur in parallel to the carbon deposition reaction, is minimal.   Table 6.6 shows that for Re-Co/Al2O3 catalyst with dCo=11 nm, unlike the Co/Al2O3 catalysts, kd of the reciprocal power model (or overall rate of deactivation) is low at high average CO conversion of 82%. Hence, for this catalyst, Co oxidation increased but carbon deposition and overall rate of deactivation decreased. This suggests that the overall deactivation rate is affected mainly by the amount of carbon deposition rather than oxidation state of Co particles. It is worth mentioning that a lower deactivation rate at high average CO conversion (82%) for the Re-Co/Al2O3 catalyst with large Co particles (dCo=11 nm) is not necessarily an ideal operating case, since oxidation of the Co particles also affects the selectivity of the catalyst. As mentioned in Section 5.3.2 at 82% CO conversion, a severe increase in CO2 and CH4 selectivity was observed compared to lower CO conversions (40% and 60%), which is not favourable.     141 Table 6.6. Example calculations for TOF0C (initial rate of carbon deposition)  Catalyst dCo NCO CO conv. C Cc 𝜑 kd 𝑟𝐶0 𝑇𝑂𝐹𝐶0 𝑇𝑂𝐹𝐶𝑂0   nm mol/g % wt% mol/gcat (t-t*)/  mol/g.h s-1 s-1 5Co/Al2O3(0) 22 13.96 14 4.7 3.9E-03 168.8 1.4E-02 3.2E-05 3.2E-04 1.6E-02 20Co/Al2O3(0.6) 13 51.34 35 6.5 5.4E-03 188.8 8.6E-02 6.2E-05 1.7E-04 1.8E-02 15Co/Al2O3(0.1) 10 70.30 37 7.6 6.3E-03 228.8 5.7E-02 5.3E-05 1.1E-04 1.3E-02 15Co/Al2O3(0.1) 10 70.30 30 4.4 3.7E-03 175.0 3.2E-02 3.4E-05 6.7E-05 1.5E-02 15Co/Al2O3(0.1) 10 70.30 25 2.7 2.3E-03 117.5 8.9E-03 2.5E-05 5.0E-05 1.5E-02 15Co/Al2O3(0.1) 10 70.30 33 4.6 3.8E-03 150.0 3.5E-02 4.0E-05 7.9E-05 1.2E-02 0.5Re-5Co/Al2O3(0.7) 5 56.44 30 4.9 4.1E-03 225.0 3.5E-02 3.0E-05 7.5E-05 1.1E-02 0.3Re-3Co/Al2O3(0.9) 2 61.65 24 3.4 2.8E-03 225.0 4.0E-02 2.2E-05 4.9E-05 8.1E-03 1.2Re-12Co/Al2O3(0) 11 74.63 82 4.1 3.4E-03 280.0 1.2E-02 1.7E-05 3.2E-05 2.1E-02 1.2Re-12Co/Al2O3(0) 11 74.63 60 5.9 4.9E-03 195.0 2.2E-02 3.8E-05 7.0E-05 2.8E-02 1.2Re-12Co/Al2O3(0) 11 74.63 40 6.0 5.0E-03 161.3 3.6E-02 5.0E-05 9.4E-05 3.0E-02    142 0 5 10 15 20 255.0x10-51.0x10-41.5x10-42.0x10-42.5x10-43.0x10-43.5x10-44.0x10-4   5Co/Al2O3(0)  20Co/Al2O3(0.6)  15Co/Al2O3(0.1)  0.5Re-5Co/Al2O3(0.7) 0.3Re-3Co/Al2O3(0.9) 1.2Re-12Co/Al2O3(0) TOF0 C, s-1dCo, nm Figure 6.5. 𝑻𝑶𝑭𝑪𝟎 versus dCo for Re-Co/Al2O3 and Co/Al2O3 catalysts with different Co particle sizes. All the experiments were conducted at 220 º C and 2.1 MPa. The error bar represents four data points for 15Co/Al2O3(0.1) catalyst at varied CO conversions as reported in Table 6.6 6.5 Catalyst regeneration in hydrogen flow  The wax extracted used catalysts were re-reduced in 30 mL(STP)/min of 10% H2/Ar at a ramp rate of 5 ºC/min up to 600 ºC (the same reduction procedure used for the fresh catalysts). Subsequently, CO chemisorption was conducted on the re-reduced used catalyst. More than 80% of carbon on the catalyst surface hydrogenates after re-reduction at 600 0C (See Table 6.6 and Table 6.7 for carbon contents of used and hydrogenated used catalysts, respectively). However,    143 the amount of CO uptake reduced considerably after re-reduction compared to the fresh catalyst. This suggests that the Co particles were sintered during the regeneration process. Table 6.7. CO chemisorption on fresh catalyst versus CO chemisorption on used Co/Al2O3 and Re-Co/Al2O3 catalysts after reduction in hydrogen  Catalyst dCo , nm Average conversion % Fresh catalyst Used catalyst after re-reduction Reduction in CO uptake  CO uptake µmol/g CO uptake µmol/g C wt% % 15Co/Al2O3(0.1) 10 37 70 34 0.9 51 1.2Re-12Co/Al2O3(0) 11 60 74 44 1.0 41 1.2Re-12Co/Al2O3(0) 11 40 74 52 1.0 30 0.5Re-5Co/Al2O3(0.7) 5 30 61 23 0.7 62 0.3Re-3Co/Al2O3(0.9) 2 24 56 21 0.4 63  Saib et al. reported that oxidation in a controlled environment is an essential step in re-dispersion of sintered Co particles. The reduction after oxidation results in multi nucleation on the oxide shells and hence re-dispersion of Co [178, 179]. There is no common method for regeneration of FT catalysts. Several regeneration procedures have been reported in the literature including oxidation, reduction, combination of oxidation and reduction, solvent extraction and steam reduction [180]. However, there is little information on long-term behaviour of regenerated catalysts [163].  In the present study, the hydrogenation of wax extracted Co catalysts at 600 0C resulted in significant growth in Co particle size after regeneration. Therefore, further studies are required to find a proper regeneration method, which results in re-dispersion of sintered Co particles.    144 6.6 Conclusions   Deactivation of Co catalysts used for FT synthesis is dependent on Co particle size, DOR and CO conversion. At the conditions of the present study, carbon deposition was the main cause of catalyst deactivation. There was no significant Co sintering observed and it was found that the initial rate of carbon deposition per active Co site increased with increased Co particle size (dCo = 2 – 22 nm) when measured at approximately the same CO conversion (< 40%).  On the 15Co/Al2O3(0.1) catalyst the rate of carbon deposition increased with CO conversion when CO conversion was ≤40%. However, for the 1.2Re12Co/Al2O3(0) catalyst, the rate of carbon deposition decreased with increased CO conversion at high CO conversions (≥60%) due to high concentrations of H2O and CO2 in the reactor. The Co catalysts that had both a low DOR and small Co particles were activated during the first 200 h TOS of FT synthesis, and the activation is attributed to increased reduction of CoOx species present in these catalysts, by the synthesis gas.          145 Chapter 7. Long-term deactivation of a commercial Co catalyst in FT synthesis 7.1 Introduction  In previous chapters, the stability of a series of model Co/Al2O3 and Re-Co/Al2O3 catalysts was assessed for the FT synthesis. Commercial Co/Al2O3 catalysts differ from the model catalysts in that they typically incorporate property promoters such as K and P. In this chapter, the stability of a Co/P-Al2O3 catalyst, provided by the project sponsor as a representative commercial catalyst, is assessed and compared to the Co/Al2O3 and Re-Co/Al2O3 model catalysts.  The commercial Co/P-Al2O3 catalyst was also assessed over a longer TOS period (~1200 h) as reactor conditions were varied so as to obtain FT kinetic data. A common strategy used to account for catalyst deactivation under these circumstances is to periodically repeat one set of operating conditions so as to monitor the extent of catalyst deactivation. In this study three long-term experiments were conducted in this way and the data analyzed to examine the catalyst deactivation. The deactivation behaviours that were identified for these longer TOS experiments are compared to those identified on the model catalysts. 7.1.1 Comparison between activity, stability and selectivity of Re-Co/Al2O3, Co/Al2O3 and Co/P-Al2O3 catalysts  Figure ‎7.1 shows the CO conversion versus TOS for the 1.2Re-12Co/Al2O3(0), 15Co/Al2O3(0.1) and 20Co/P-Al2O3 catalysts operated at standard FT conditions of 220 ºC, H2/Co=2 and ~20 bar    146 at GHSV of 0.12, 0.04 and 0.06 mol/g.h, respectively. For all three catalysts the CO conversion reaches a maximum value with TOS and decreases to almost the same final value (32%). As described in Section 5.3.1, the initial behaviour of the catalyst is attributed to the dynamic response of the system and reconstruction of the catalysts after exposure to synthesis gas and hence the deactivation of the catalysts is quantified after about 10 h TOS.  Figure ‎7.2 compares the stability of the catalysts based on the activity factor, defined by Equation 6.1, and  indicates that for the 15Co/Al2O3(0.1) and 1.2Re-12Co/Al2O3(0) catalysts, α(𝜑) decreased to 0.55 and 0.60 after 160 h TOS and 191 h TOS, respectively. However, for the 20Co/P-Al2O3 catalyst α(𝜑) decreased to 0.83 after 259 h of TOS. Also, the reciprocal power model with n=0.5, α(Ɵ)=1/(1+kd×Ɵ0.5), assigned to coking or fouling of the catalysts, fitted well to all the catalysts activity data.   The calculated kd values are reported in Table ‎7.1 showing that the 20Co/P-Al2O3 catalyst is the most stable among the three, with the lower kd value. Accordingly, the measured amount of carbon after 259 h TOS is relatively low (4.5 wt%) compared to 15Co/Al2O3(0.1) and 1.2Re-12Co/Al2O3(0) catalysts with 7.6 and 6.0 wt% carbon content, which is the result of a lower initial carbon deposition rate, TOF0C, for this catalyst. Furthermore, the amount of H measured by CH analysis for the 20Co/P-Al2O3 catalyst was relatively high (0.65 wt%), suggesting that unlike the 1.2Re-12Co/Al2O3(0), 15Co/Al2O3(0.1) catalysts, the carbon is in a more hydrogenated form. The change in carbon deposition rate and type of deposited carbon is suggestive of the effect of the P modified Al2O3 support on the carbon formation, but further study is required to clearly understand this effect.    147  Table ‎7.1 also compares the initial CO turnover frequency at t=t*, calculated based on the CO uptake measured on the fresh catalyst. The results show that 1.2Re-12Co/Al2O3(0) is the most active catalyst among the three and the activity of the 15Co/Al2O3(0.1) and 20Co/P-Al2O3 is approximately the same initially. 0 20 40 60 80 100 120 140 160 180 200 220 240 260020406002040600204060 TOS (h) 20Co/P-Al2O3               GHSV=0.06= mol/g.h CO conversion (%)  1.2Re-12Co/Al2O3(0)          GHSV=0.12 mol/g.h   15Co/Al2O3(0.1)          GHSV=0.04 mol/g.h Figure 7.1. CO conversion versus TOS for 1.2Re-12Co/Al2O3(0),15Co/Al2O3(0.1) and 20Co/P-Al2O3  catalysts. Operating conditions: 220 ºC, ~20 bar and H2/CO=2     148 0 20 40 60 80 100 120 140 160 180 200 220 2400.40.60.81.00.40.60.81.00.40.60.81.0  20Co/P-Al2O3 Modeled  1.2Re-12Co/Al2O3(0) Modeled   15Co/Al2O3(0.1) Modeled Figure 7.2. α(𝝋) versus 𝝋 for 15Co/Al2O3(0.1), 1.2Re-12Co/Al2O3(0) and 20Co/P-Al2O3 catalysts and the fitted reciprocal power model for catalyst deactivation. Operating conditions: 220 ºC, ~20 bar and H2/CO=2, with GHSV of 0.04,0.12 and 0.06 mol/g.h, respectively.  Table ‎7.2 compares the properties of  the 15Co/Al2O3(0.1), 1.2Re-12Co/Al2O3(0) and 20Co/P-Al2O3 catalysts. The high DOR of the 20Co/P-Al2O3 catalyst indicates that P enhanced the reducibility of Co particles and hence increased the CO uptake of the fresh catalyst. Co particle size measured by XRD does not show a significant growth in Co size for the 15Co/Al2O3(0.1) before and after the reaction, 1.2Re-12Co/Al2O3(0) and the 20Co/P-Al2O3 catalysts, taking account of the error in the analysis.  However, the change in BET surface area due to C    149 deposition is lower for the 20Co/P-Al2O3 compared to the 15Co/Al2O3(0.1) and 1.2Re-12Co/Al2O3(0) catalysts, consistent with a lower carbon deposition rate.  Table 7.1. Comparison of initial CO and C TOFs, deactivation rates and carbon deposition on Co/Al2O3, Re-Co/Al2O3 and Co/P-Al2O3 catalysts  Catalyst TOS TOF0CO kd C H TOF0C  h s-1  wt% wt% s-1 1.2Re-12Co/Al2O3(0) 166 3.0E-02 3.6E-02±4.8E-03 6.0 0.03 9.4E-05 15Co/Al2O3(0) 191 1.3E-02 5.7E-02±2.8E-04 7.6 0.05 1.1E-04 20Co/P-Al2O3 159 9.0E-03   2.1E-02±3.3E-04 4.5 0.65 2.0E-05  Table 7.2. Comparison between properties of Re-Co/Al2O3, Co/Al2O3 and Co/P-Al2O3 catalysts   Fresh Used Catalyst SBET  DOR  NCO  dCo   SBET  dCo    m2/g % µmol/g nm m2/g nm 1.2Re-12Co/Al2O3(0) 123 85 70 8±1 109 8±2 15Co/Al2O3(0.1) 161 61 75 9±1 112 12±2 20Co/P-Al2O3 105 90 130 9±1 96 12±1  Table ‎7.3 compares the average product selectivity, 𝛼 − 𝑣𝑎𝑙𝑢𝑒𝑠  of the ASF distribution, average CO conversion of the Co/Al2O3, Re-Co/Al2O3 and Co/P-Al2O3 catalysts. The CO conversion and product selectivity were measured at the standard experimental condition (220 ºC, ~20 bar and H2/CO=2) for all three catalysts. For the Co/P-Al2O3 catalyst, the average CH4 and C5+ selectivity within ~160 h of TOS is 11±1% and 88±1%, respectively, which is slightly higher than the Re-   150 Co/Al2O3 and Co/Al2O3 catalysts. The Co/P-Al2O3 catalyst is more stable in terms of product selectivity within ~160 of TOS compared to Re-Co/Al2O3 and Co/Al2O3 catalysts (See Table ‎7.3, the lowest variation in CH4 and C5+ selectivity with TOS occurred for the Co/P-Al2O3 catalyst).   According to the reported results, although Re-Co/Al2O3 has the highest activity among the three catalysts, in terms of stability in CO conversion and CH4 selectivity it is the least stable catalyst. Since the focus of this study was Co catalyst deactivation in FT synthesis, the most stable catalyst in terms of CO conversion and product selectivity was chosen to investigate the stability of the catalysts at longer periods of TOS.  Table 7.3. Comparison between selectivity of the Re-Co/Al2O3, Co/Al2O3 and Co/P-Al2O3 catalysts at the same range of CO conversion (the stated average conversion is calculated from t~48 h to t~160 h of TOS)  Catalyst CO conv  GHSV CH4  selectivity a  CH4 C5+  selectivity a  C5+  𝛼  % mol/g.h Ave± Std. Dev %Dev Ave± Std. Dev %Dev  1.2Re-12Co/Al2O3(0) 40 0.12 9±2 20 83±2 3 0.84 15Co/Al2O3(0.1) 37 0.04 8±1 12 79±3 4 0.89 20Co/P-Al2O3  32 0.06 11±1 8 88±1 2 0.76 a Time averaged values and standard deviations are based on analysis of samples taken every 24 h over 160 h of TOS       151 7.2 Effect of process conditions on long term stability of the Co/P-Al2O3 catalyst  To determine the effect of process conditions on stability of the catalyst, a set of data were obtained over a wide range of operating conditions over extended periods of continuous operation of the reactor as reported in Table ‎7.4. Typically, the chosen process conditions were maintained for a minimum period of about 75 hours during which the gas and liquid products were analysed and the rates of reaction determined.  Periodically, during each experiment, the process conditions were re-set to a standard condition to monitor the catalyst deactivation as a function of TOS.  The standard set of process conditions were chosen as 220 C, 21.4 bar, GHSV = 0.06 mol/(g.h), H2/CO = 2/1.  The conditions of each of the experiments are shown in Table ‎7.5. Note that the experiments were done in three sets (referred to herein as Run 1, Run 2 and Run 3), in which a fresh catalyst was loaded in the reactor at the beginning of each run. The change in process conditions as a function of TOS for each run is presented in Figures 7.3 and 7.4.  Table 7.4. Operating conditions used for stability experiments over the Co/P-Al2O3  catalyst  Run # Expt # Temperature C Pressure bar Ratio H2/CO 1 1-8 210, 220 14.6, 21.4 1, 2, 3 2 1-18 210, 220, 230 14.6, 21.4 1, 2, 3 3 1-6 210, 220, 230 14.6, 21.4 1, 2, 3     152  Table 7.5. Operating conditions used for experiments to collect kinetic data over the Co/P-Al2O3 catalyst.  Run # Expt # Temperature Pressure H2/CO   C bar Ratio 1 1 210 14.6 1 1 2 220 14.6 2 1 3 220 14.6 1 1 4 220 21.4 2 1 5 220 21.4 3 1 6 220 21.4 1 1 7 210 21.4 3 1 8 220 21.4 2 2 1 230 14.6 1 2 2 230 14.6 2 2 3 210 14.6 3 2 4 220 21.4 2 2 5 230 21.4 3 2 6 210 21.4 1 2 7 230 21.4 1 2 8 220 21.4 2 2 9 230 21.4 2 2 10 210 21.4 2 2 11 220 21.4 2 2 12 210 14.6 2 2 13 220 14.6 3 2 14 230 14.6 3 2 15 230 14.6 1 2 16 220 21.4 2 2 18 220 21.4 1 3 1 210 21.4 2 3 2 230 21.4 2 3 3 220 21.4 2 3 4 230 21.4 3 3 5 220 21.4 2 3 6 230 21.4 2       153 210215220225230Temp, oC RUN 124681012  Pressure, bar COH20 200 400 600 800 10001234  Time-on-stream, hH2O  210215220225230  Temp, oC RUN 2246810 Pressure, bar   COH20 200 400 600 800 1000 120012345  Time-on-stream, hH2O Figure 7.3. Process conditions as a function of TOS for the kinetic experiments (Run1 and Run 2)     154 205210215220225230235Temp, oC RUN 3024681012CO Pressure, bar H20 200 400 600 800 10001234567  Time-on-stream, hH2O  Figure 7.4. Process conditions as a function of TOS for the kinetic experiments (Run 3)   Figures 7.5 and 7.6 compare the results from the standard condition experiments made during the course of each of the extended TOS experiments.  Three sets of data were obtained. The time averaged values and standard deviation of each set of data measured over the duration of the repeated experiments, is summarized in Table ‎7.6. The data show that for the CO conversion, C5+ selectivity and the calculated FTS α-value, the variation as a function of time was small over a period of about 1200 h continuous operation.  Higher variations were observed for the C2-C4 fraction, especially near the end of the run.  However, the most significant variation occurred for the CH4 fraction of the hydrocarbon products, which increased significantly with TOS.    Figure ‎7.7 shows the CH4 formation rate at the standard reaction conditions with TOS. The rate of CH4 formation appeared to depend on the catalyst age, especially when the catalyst had been exposed to a high temperature (230 C) and high partial pressure of water (PH2O/PH2>0.5), as was    155 the case for Run 2 and Run 3. However, for Run 1, where the catalyst temperature was below 220 C throughout the run and partial pressure of water was low (PH2O/PH2<0.5), the CH4 formation rate did not depend on the TOS or the thermal history. These results confirm that the catalyst deactivation is very dependent on reaction conditions [31] and that carbon formation is not the only cause of change in catalyst performance with TOS under these varied operating conditions and longer TOS periods.   As described in Section 5.3.2, at high partial pressure of water (PH2O/PH2>0.5), surface oxidation of Co is possible which leads to an increase in the WGS reaction and results in an increase in CH4 and CO2 selectivity. Comparing the CO2 selectivity from the standard experiments also shows an increase from 2 to 5 (mol%) in Run 2 and an increase from 2.5 to 6.5 (mol%) in Run3, suggesting that the oxidation of Co compounds in the presence of water resulted in the change in CH4 selectivity.  According to Table 6.5, the linear empirical model for deactivation is assigned to loss in active metal sites due to poisoning. Assuming that oxidation results in a decrease in Co sites responsible for chain growth and acts as a poison, all the CH4 formation rate data of Run 2 and Run 3 were fitted to an empirical linear deactivation model that accounts for the thermal and time history of the catalyst. It was assumed that the activity of the catalyst α(i), where i refers to the i-th measurement made at a set of process operating conditions and a certain TOS, is given by an equation of the form:  𝑎(𝑖) =  𝑎(𝑖 − 1) + 𝑘𝑑(𝑡𝑖 − 𝑡𝑖−1) 7.1    156 where: 𝑘𝑑 =  𝑘𝑑0𝑒−𝐸𝑑𝑅𝑇𝑖  is the deactivation rate constant and ti is the TOS for the i-th measurement at a set of process operating conditions. The objective function used to estimate kd was defined so as to minimize the sum of squares of the errors between the measured CH4 formation rate for the i-th measurement at standard condition (T=220 0C, P=20 bar and H2/CO=2) and the CH4 formation rate calculated from the activity factor (𝑎(𝑖)) defined by Equation 7.1 for the same experiment. Hence: 𝑓(𝑜𝑏𝑗) = ∑(𝑟𝐶𝐻4𝑚 − 𝑟𝐶𝐻40 × 𝑎(𝑖))2 7.2 where  𝑟𝐶𝐻4𝑚   is the measured  CH4 formation rate at the standard condition for the i-th measurement and  𝑟𝐶𝐻4𝑜  is the initial rate of CH4 formation rate measured at the standard operating condition, without deactivation.   The estimated parameter values obtained for Run 2 were: kd = 1.07 x10-6 h-1, Ed =1699.9 kJ/mol, with an R2 = 0.79. For Run 3 the estimated parameters were: kd = 2.15 x10-3 h-1, Ed =50.15 kJ/mol, with an R2 = 0.98. The differences in the estimated parameters between Run 2 and Run 3 reflect a complex deactivation that depends not only on the thermal and time history that is accounted for in the deactivation model, but also probably water content and CO conversion history.      157 1020304050607080 Run 1  Run 2  Run 3   %CO conversion, mol%0102030405060   Product distribution - CH4 wt %0 200 400 600 800 1000 1200051015202530 %  Time-on-stream, hProduct distribution, C2-C4, wt %0 200 400 600 800 1000 120020406080100  Time-on-stream, hProduct distribution, C5+, wt % Figure 7.5. Catalyst stability as reflected in CO conversion and product distribution measured at standard set of operating conditions (220 C, 21.4 bar, GHSV=0.06 mol/(g.h), H2/C=2/1). Solid line is time averaged value.    158 200 400 600 800 1000 12000.700.750.800.850.900.951.00 Run 1 Run 2 Run 3  FTSvalueTime-on-stream, h Figure 7.6. Catalyst stability as reflected in FTS α-value measured at standard set of operating conditions: 220 C, 21.4 bar, GHSV = 0.06 mol/(g.h), H2/CO = 2/1. Solid line is time-averaged value  Table 7.6. Catalyst stability as reflected in average values and standard deviations of CO conversion and product distributions, measured at 220 C, 21.4 bar, GHSV = 0.06  mol/(g.h), H2/CO = 2/1 over the period of 1200 h TOS, related to Run1, Run2 and Run3  Parameter Average  Std. Dev %Dev CO conversion, mol % 47.6  5.1 10.7 CH4 , wt% 16.2  6.5 40.1 C2 – C4 , wt% 9.21  3.1 33.7 C5 + , wt% 74.7  8.3 11.1 α -value 0.892  0.015 1.7    159  0 200 400 600 800 1000 12002E-74E-76E-78E-71E-6 Run1, measured Run2, measured Run2, corrected Run3, measuredRun3,  corrected  Rate of CH4 formation, mol/(g.sec)Time-on-stream, h Figure 7.7. CH4 formation rate measured and corrected by applying activity factor at the standard conditions as a function of TOS.  Reaction conditions: 220 C, 21.4 bar, GHSV = 0.06 mol/(g.h), H2/CO = 2/1.  The corrected data points shown in Figure ‎7.7 are the measured CH4 formation rate a time ti divided by α(i), which indicates the rate of CH4 formation if there was no catalyst deactivation. The complete sets of CH4 formation rate (including the data from process conditions other than the standard condition) were also corrected for deactivation in the case of Run 2 and Run 3.  The corrected and measured data of CH4 formation rate were applied to a power law kinetic model.  Table ‎7.7 shows the estimated parameters using both the measured CH4 formation rate data and the data corrected for the effect of TOS.  The R2 value was significantly lower compared to R2 value when the data was corrected (or if there was no deactivation). Also the    160 power order of water (e) is much larger when the activity factor is not included (measured data) whereas the power order of CO and H2 is almost the same for both cases. Accordingly, an increase in the rate of CH4 formation is mainly influenced by the partial pressure of water, confirming that the oxidation of Co compounds in the presence of water at 230 ºC and PH2O/PH2>0.5 is the reason for the change in CH4 selectivity.   Table 7.7. Estimated kinetic parameters for the power law CH4 formation rate 1) corrected data 2) measured data   k0×10-8 Ea (kJ/mol) c d e R2 1) 𝑟 = 𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒  3.1±2.18 128±14 -0.57±0.06 0.79±0.11 0.14±0.08 0.88 2)  𝑟 = 𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒  0.49±0.66 154±26 -0.61±0.10 0.81±0.18 0.66±0.15 0.81 *  In the kinetic expressions: 𝑎 = 𝑘0 exp (−𝐸𝑎𝑅(1𝑇−1?̅?)), dimensions of k0 depend on the model, rate of the reaction is in (mol g-1 s-1) , pressures are in (psi) 7.3 Kinetic modeling  The collected experimental data were also used to obtain an empirical kinetic model for CO consumption rate and the formation rates of CH4, C2-C4, C5-C8, C9-C12 and C12+ as well as 𝛼 values. The details of the kinetic modeling and the results are reported in Appendix Q. A power law was the best model for the description of CO consumption rate and formation rates of C2+ hydrocarbons; whereas, both the power law and the Satterfield model had acceptable fits for the description of the CH4 formation rate.    161 7.4 Conclusions  The Co/P-Al2O3 catalyst was more stable than the model Co/Al2O3 and Re-Co/Al2O3 catalysts when compared for periods of ~ 160 h TOS. The stability of the catalyst corresponds to the reduced rate of carbon deposition on this catalyst. However, when the Co/P-Al2O3 catalyst was operated over a range of process conditions for a longer period (i.e TOS~1200 h), the catalyst stability changed and resulted in increased CH4 activity and selectivity with TOS. An increase in CH4 selectivity was observed after 400 h TOS when the catalyst was exposed to high temperature (T≥ 230 ºC) and high partial pressure of water (PH2O/PH2 >0.5). The change in CH4 rate was described by an empirical catalyst activity function of the form 𝑎(𝑖) =  𝑎(𝑖 − 1) + 𝑘𝑑(𝑡𝑖 −𝑡𝑖−1). Fitted power law rate equations for CH4 formation using corrected and measured data, showed that the power order of PH2O increased from 0.14±0.08 to 0.66±0.15, suggesting that the change in CH4 selectivity is the result of an increase in PH2O at high temperature (230 ºC). Accordingly, it is believed that the surface oxidation of Co compounds in the presence of water results in an increase in CH4 selectivity. An increase in CO2 selectivity was also observed which confirms the oxidation of Co compounds.       162 Chapter 8. Conclusions and recommendations for future work 8.1 Conclusions  The focus of this study was to determine the effect of Co particle size on the deactivation mechanism of Co/Al2O3 catalysts in slurry phase FT synthesis and to investigate the effect of process conditions on long-term stability of Co catalysts.   To determine the effect of Co particle size on deactivation of the Co catalysts, a series of Co/Al2O3 of Re-Co/Al2O3 catalysts with controlled Co particle size were prepared on an Al2O3 support, using the method reported by Borg et al. [86], in which EG was added to the impregnation solution in order to increase wettability.   The prepared catalysts were characterized before conducting experiments in the FT reactor. Results showed that Co3O4 particle size of the calcined precursors was reduced by adding EG to the impregnation solution. However, after reduction at 600 oC, Co particles sintered. The Co particle size measured by both XRD and CO pulse chemisorption showed reasonable agreement, and was confirmed that the amount of residual carbon on the fresh catalyst was negligible. The characterization also showed incomplete reduction of the calcined precursors and that DOR increased with Co particle size. Addition of Re to the Co/Al2O3 catalysts resulted in a significant increase in DOR.     163 Some of the prepared Co/Al2O3 and Re-Co/Al2O3 catalysts were tested in a CSTR reactor. By increasing the CO conversion level for a specific catalyst up to 60%, the CH4 selectivity increased and C5+ selectivity decreased, in agreement with the selectivity data reported in literature [165, 166, 181]. However for 1.2Re-12Co/Al2O3(0) catalyst at high average CO conversion of 82%, Co particles were oxidized at high partial pressure of water (PH2O/PH2>1), resulted in a significant increase in CO2 and CH4 selectivity.  To determine the effect of Co particle size on selectivity of Co catalysts the selectivity of the catalysts was determined at similar CO conversions. It was found that the CH4 selectivity of Re-Co/Al2O3 and Co/Al2O3 catalysts decreased with an increase in particle size (for dCo≤5 nm) and then remains constant (for dCo≥ 10 nm). However, the C5+ selectivity increased with increase in Co particle size (for dCo≤5 nm) and then remains constant (for dCo≥ 10 nm). A minimum amount of active sites are required for propagation and polymerization of hydrocarbons, and the number of these active sites is lower on small Co particles [65, 108, 119], which results in higher CH4 selectivity and lower C5+ selectivity on small Co particles. Furthermore, comparing the initial turn over frequency of the catalysts showed that, 𝑇𝑂𝐹𝐹𝑇0  was higher for larger Co particles (dCo≥ 10 nm) compared to smaller Co particles (dCo≤5 nm), in agreement with literature data [42, 71-76, 109, 110].  At the conditions of this study, carbon deposition was the main deactivation mechanism. There was no significant Co sintering observed. The initial rate of carbon deposition, 𝑇𝑂𝐹𝐶0, increased with increased Co particle size at CO conversion of  <40%. For 1.2 Re-Co/Al2O3 catalyst the rate of carbon deposition decreased with increased CO conversion (≥60%) due to high concentration    164 of CO2 and H2O in the reactor. For the catalysts with both low DOR and Co particle size, Co particles were activated with TOS due to reduction of CoOx particles in synthesis gas.  Finally, the activity, product selectivity and stability of Re-Co/Al2O3 and Co/Al2O3 catalysts were compared to a commercial Co/P-Al2O3 catalyst. The Co/P-Al2O3 catalyst was shown to be more stable than the Re-Co/Al2O3 and Co/Al2O3 catalysts in the first ~160 h of TOS and the reduced deactivation of the Co/P-Al2O3 catalyst corresponds to a slower carbon deposition rate on this catalyst.  The Co/P-Al2O3 catalyst was also tested in the CSTR reactor operated continuously for over 1200 h at various operating conditions (Temperature: 210, 220 and 230 C, H2/CO ratio: 1/1, 2/1 and 3/1 and Pressure: 14.6 and 21.4 bar). The rate of CH4 formation was shown to depend on the thermal history of the catalyst with an increase in CH4 formation rate after operation at 230 ºC and at PH2O/PH2 is >0.5. The increase in CH4 rate was described by a linear catalyst activity factor of the form 𝑎(𝑖) =  𝑎(𝑖 − 1) + 𝑘𝑑(𝑡𝑖 − 𝑡𝑖−1).  The results from the model suggests that the main reason for an increase in CH4 selectivity is an increase in PH2O when the temperature is ≥230 ºC.  At this elevated temperature PH2O/PH2 is >0.5. Therefore, it is believed that an increase in CH4 selectivity is due to surface oxidation of Co particles at high partial pressure of water.  In summary, to minimize the deactivation rate it  is desirable to prepare catalysts with small Co particle size, since as shown in the current study, the initial deactivation rate increases with increase in Co particle size. However, a minimum ensemble of active sites are required for propagation of hydrocarbons. Hence, to maintain a high C5+ selectivity, Co catalysts with    165 minimum Co particle size of ~ 10 nm  are required. Larger Co particles would not change the selectivity significantly but may result in higher carbon deposition rate. In addition, Co catalysts are sensitive to high concentrations of water (PH2O/PH2>0.5) and high temperatures (≥230 ºC). These conditions may result in severe change in product selectivity and increase the CH4 formation rate, which is not desirable. Therefore, controlling the process conditions and avoiding process upsets can extend the catalyst lifetime. 8.2 Recommendations for future work 8.2.1 Preparing the catalysts with the same DOR  In order to examine a set of catalysts with the same DOR and eliminate the effect of further reduction of partially reduced Co particles upon exposure to synthesis gas, preparation of the catalysts on a carbon support should be investigated. The lower interaction between Co particles and the carbon support results in Co particles with high DOR. However, by using Co catalysts supported on carbon, it is important to ensure that catalyst attrition does not have a significant effect in the CSTR reactor. To eliminate the attrition effect, catalyst activity experiments alternatively can be conducted in a fixed bed reactor.      166 8.2.2 Regeneration of the deactivated catalysts    As described before, the main deactivation mechanism of the Re-Co/Al2O3 and Co/Al2O3 catalysts is carbon deposition. This study showed that after re-reduction of the Co catalysts, the amount of carbon on the catalyst decreased considerably. However Co particles were sintered during the regeneration in hydrogen at 600 oC. A series of oxidation-hydrogenation processes at lower temperatures might result in carbon removal from active Co sites and re-disperse the sintered Co particles. The challenge is to recover the catalyst from the wax in the lab scale slurry phase reactor and ex situ regeneration of the catalyst. However, regeneration in a lab scale fixed bed reactor is much easier, since hydrogenation and oxidation can be conducted in-situ.  8.2.3 Applying the effect of process conditions on activity factor in long-term deactivation study  The fit for the CH4 activity factor applied in Section 7.2  is relatively low due to limited sets of data with small variations in experimental parameters. Also, the linear activity factor for CH4 formation rate was chosen for the sake of simplicity. However, the results in this study show that the partial pressure of water (which is the consequence of high temperature) has a major effect on an increase in CH4 formation rate with TOS. Since the thermal history of Run 2 and Run 3 were different, the parameters obtained for kd and Ed are not extendable to other conditions. 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To prepare 2.5 g of 0.5Re-5Co/Al2O3(0.7) catalyst the following calculation method was used: Mass of the 𝐶𝑜 (𝑔) = 0.05 × 2.5 (𝑔 𝑐𝑎𝑡𝑎𝑙) = 0.125 𝑔 Mass of the 𝑅𝑒 (𝑔) = 0.005 × 2.5 (𝑔 𝑐𝑎𝑡𝑎𝑙) = 0.0125 𝑔 The amount of Co(NO3)2.6H2O (98 % purity) needed for catalyst preparation was obtained as:  𝐶𝑜 (𝑁𝑂3)2. 6𝐻2𝑂 (𝑔) =  0.125 (𝑔 𝐶𝑜) ×𝐶𝑜 (𝑁𝑂3)2. 6𝐻2𝑂 (𝑀𝑊)𝐶𝑜(𝑀𝑊)×10.98= 0.6299 𝑔 where the molecular weight of  𝐶𝑜 (𝑁𝑂3)2. 6𝐻2𝑂 is equal to 291 g/mol and the molecular weight of Co is equal to 58.9 g/mol. The amount of HReO4 (77.5% purity) needed to promote the Co catalyst was obtained as follows. 𝐻𝑅𝑒𝑂4 (𝑔) =  0.125 (𝑔 𝑅𝑒) ×𝐻𝑅𝑒𝑂4 (𝑀𝑊)𝑅𝑒(𝑀𝑊)×10.775= 0.022 𝑔 where the molecular weight of 𝐻𝑅𝑒𝑂4 is equal to 251 g/mol and the molecular weight of Re is  equal to 186 g/mol. Since  ρHReO4 = 2.16 g/ml , the volume of Perrhenic acid required was calculated: 𝐻𝑅𝑒𝑂4(𝑚𝑙) = 0.022 𝑔 ×12.16 𝑔/𝑚𝑙 = 0.101 𝑚𝑙 As the pore volume of the support is 0.525 ml/g, the total volume of the solution needed to fill the pores of the support was: 𝐴𝑙2 𝑂3 (𝑔) = 2.5 (𝑔 𝑐𝑎𝑡𝑎𝑙) − 0.125(𝑔 𝐶𝑜) = 2. 375 (𝑔) 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛 (𝑚𝑙) = 2.375 (𝑔) × 0.525 (𝑚𝑙𝑔) = 1.247 (𝑚𝑙)    183 Volume of distilled water in the solution with 𝑅 =𝐸𝐺(𝑔)𝐻2𝑂 (𝑔)+𝐸𝐺(𝑔)= 0.7 was obtained as: 𝐻2𝑂 (𝑚𝑙) = 0.3 × 1.247 (𝑚𝑙 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛) × 𝜌𝐸𝐺(1 − 0.3) × 𝜌𝐻2𝑂 + 0.3 𝜌𝐸𝐺− 0.101( 𝑚𝑙 𝐻𝑅𝑒𝑂4) = 0.393 𝑚𝑙                  𝐸𝐺 (𝑚𝑙) = 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛 (𝑚𝑙) − 𝐻2𝑂 (𝑚𝑙) − 0.101( 𝑚𝑙 𝐻𝑅𝑒𝑂4) = 0.844 𝑚𝑙   Hence, to prepare 2.5 g of 0.5Re-5Co/Al2O3(0.7) catalyst, 0.6299 g of Co(NO3)2.6H2O  is dissolved in a mixture of 0.393 ml 𝐻2𝑂, 0.844 ml of EG and 0.101 ml of HReO4,  stirred with an ultrasonic shaker for about 5 minutes and  added dropwise to 2.375 g of  𝛾 − 𝐴𝑙2𝑂3 . The mixture is soaked for about 2 h before proceeding to the calcination step, so that the solution penetrates inside the pores. The details of calcination and reduction steps are reported in Section 3.2.                 184 Appendix B: F-T unit start-up and shut-down procedure   Start-up procedure to be performed when the unit has been shut down and completely drained and vented, before the start-up all MFCs, GC(TCD) and GC(FID)  have to be calibrated:  Check all the GC gas cylinders (Helium, Air and Hydrogen) and reaction gases (CO,H2 and N2), 1-2 days before the reactor loading to make sure there are enough gas in the cylinders. Change the GC gas cylinders if the pressure in the tanks is below 400 psi.  Turn on the heating tapes about one day before the experiment.  Turn on the cold bath and circulating water of the cold condenser and adjust the flows so that the level remains constant.  Turn on the GC with TCD about 5 hours and the GC with FID about 2 hours before the experiment. Prepare the batch files for the hot gas and permanent gas analysis for both GC-2010 and GC-2014.  Open the cooling water valve to prevent high temperature around the mixer.  Fully open the back pressure regulator.  Load the reactor with squalane and catalyst.  Close the reactor and seal it.  Put the heating jacket around the reactor and make sure it is tightened.  Check that bypass valve and gas inlet valves are in close position.  Open the feed gases (CO and H2) and Nitrogen from the main cylinder and set the outlet pressure to be around 360-370 PSI.    185  Open the ball valves for synthesis gas and Nitrogen (valves are located on the panel after MFCs)  Adjust the flow of Nitrogen to about 100 sccm from the software and wait for about 10 minutes to be sure that the purging process is complete than close the Nitrogen flow.  Adjust the flow of H2, CO and N2 to the desired value and leave the reactor for overnight to make sure the system has been purged with the feed gas.  Inject the feed to the GC 2014 for several times till the feed compounds get stable.  Perform a quick leak test with the gas detector to make sure there is no major leak.  Turn on the mixer and set the speed set point on desired value (usually 700 rpm)  Start closing the back-pressure regulator gradually to increase the system pressure until reaching a pressure of 10-20 psi less than the desired pressure.  Do a complete leak test of the high pressure zone starting from gas cylinders and finishing at back-pressure regulator. ANY LEAK should be examined and fixed.  Turn on the heater and set the target temperature to 180 °C with a high ramping rate (10°C/min)  When the reactor reached 180 °C, decrease the ramp rate to 3-5 °C/min and set the target temperature to the desired reaction temperature.  When the reactor reached the desired temperature, continue closing the back-pressure regulator until you reach the reaction pressure in the system.  Type a file name for data logging of the reactor software (left side of software screen). As soon as the reaction temperature reached the set point value, reset the MFCs' and MFM totalizer and press the start button for starting data logging.     186 Normal operation procedure   Continuously monitor the reaction and operation conditions of the reactor (i.e. pressure, temperature, mixer speed, data logging inlet gas flow rates etc.) during the day to make sure the reactor is working under stable conditions.  Check the GC gases (helium, air and hydrogen) and also feed gases (CO, H2 and N2) daily to make sure enough gas is available for next few days. If any of the cylinders is close to finish, order a new cylinder in advance.  Check the coolant liquid level in the cold condenser jacket around the cold condenser several times in a day to make sure the liquid level is stable and that the cold condenser body is all inside the cold liquid. If necessary, make the adjustment for the liquid level.  Check the coolant liquid level inside the cooling bath every 4-5 days. Due to the moisture condensation on the cold surface of cold circulating liquid, the liquid level in the cooling bath increases with time. The rate of this condensation varies with the humidity of the lab. If the liquid level is too high, remove some liquid from the bath to adjust the level.  Randomly check the GC analysis files to make sure the files are properly saved on the computer.  Make a daily back-up of the GC analysis files as well as the reactor data logging file.  Do a quick leak test of the system using a gas detector to make sure there is no leak in the system. This is very important at the first few days after the experiment has been started since heating of the system and vibrational movement of the system due to mixing could cause potential leaks.    187  In the morning, label two empty 20 mL vials for collecting the liquid samples from hot and cold condensers.  At a certain time of everyday, take the liquid samples collected in the hot and cold condensers. This should be done with great patience, especially for hot condenser liquid sample, to prevent disturbing the hydrodynamic of the reactor due to possible sudden pressure drop in the reactor.  Weight the vials and clearly record the weights in the lab notebook as well as the electronic file. Indicate the date and time of sample collection as well and experiment number.  Do the analysis of the conversion level with Matlab software (using the GC analysis done by GC-2014 that measures the exit CO concentration) to see if the reactor is in stable reaction conditions.  Shut-down procedure   Stop the reactor data logging from the reactor user interface software.  Set the reactor temperature to a temperature about 80 oC. This is to ensure the wax in the reactor will remain in the liquid phase until the shut-down is completed.  While the reactor is being cooled down, close the CO and H2 flow to the reactor and increase the N2 flowrate to 50 sccm.  Wait until the reactor temperature is down to 80 oC.  Slowly open the back-pressure regulator until the pressure in the reactor drops to atmospheric pressure.    188  Keep the high flowrate of N2 running through the system for about 3 - 4 h.   Turn off the heater of the reactor through the reactor software on the computer and remove the heating jacket from the reactor.  Turn off the mixer before the reactor temperature is below 80 oC.   While the N2 gas is running and while the reactor temperature is around 80 oC, open the reactor and lower the reactor jack. Leave the reactor on the jack for 1-2 minutes so that all the wax drippings from the reactor fittings go back to the reactor.  Before the wax is hardened, decant the wax and catalyst into a beaker for further analysis.  At this step, the wax on the internal fittings of the reactor should be solidified. Close the nitrogen flow. Nitrogen flow to the reactor when the wax is still liquid will prevent blockage of the sparger holes in the reactor.  Double check hot and cold condensers for any remained liquid samples in them.  Put both GCs on standby mode to save gas and reduce thermal stress on the injectors and detectors as well as the column.  Close the on-off valves for hydrogen, CO and nitrogen located on the reactor inlet line.  Close the main cylinder valves of the synthesis gas and nitrogen.  Turn off the cold condenser bath (refrigerator and circulating pump).  If you do not plan to use the GCs in couple of days, turn off GC-2010 from the software and then turn the unit off using the main on-off switch on the GC.  Turn the GC-2014 off from the software.  Wait until the detector temperature drops below 100 ºC and then turn off the switch.    189  Do not turn off the GC-2014 using the main on-off switch on the GC (will shut down the gas flow to TCD) until the detector temperature is below 100 ºC. Failing to do so will damage the filament of TCD.  Turn off the heating tapes wrapped around reactor inlet line, reactor head, reactor exit lines and those wrapped around hot condenser and back-pressure regulator.  Close the cooling water flowing through the cooling jacket around the reactor mixer.  Close the reactor user interface software on the computer.  Turn off the reactor heater and mixer switches as well as the main shut down switch on the sentinel controller of the reactor.                   190 Appendix C: Unit components and operating conditions  Item name Description and operating condition Liquid injection pump Liquid delivery system for pumping water into the reactor Manufacturer and model: Shimadzu, LC-20AD Max output pressure: 40 MPa Targeted operating pressure: Reaction pressure H2, CO and N2 gas regulators Gas regulators for supplying reaction and balance gases to the mass flow controllers Manufacturer and model: Praxair, PRS1451 Max inlet pressure: 7000 psi Max outlet pressure: 1000 psi Operating outlet pressure: 350 psi Check valve Check valve to prevent gas reflux due to possible pressure shock Manufacturer and model: Swagelok, SS-2C-10 Max working pressure: 3000 (206) psi(bar) at temperature range of -10 to 37 °C Operating pressure: 350 psi Mass flow controller (MFC) MFC to control the inlet flowrates Manufacturer:  Brooks instruments, Provided by Autoclave Engineering  Max inlet pressure: 1500 psi, Operating inlet pressure: ~ 350 psi at room temperature     191 Item name Description and operating condition Safety buffer Separates the gas-liquid mixture and discharges the gas to the vent in the case of a rupture-disk burst Manufacturer and model: Swagelok, 304L-HDF8-1000, 1000 mL Max working pressure: 1800 (124) psi(bar) at temperature range of -10 to 37 °C AE sentinel controller Controls reactor temperature, mixing speed, inlet flowrates and reads the exit flowrate Manufacturer and model: AE, S11111181312111 Magnedrive mixer For mixing the products inside the reactor Manufacturer and model: Autoclave Engineering (AE), Dispersimax (6blade) Power: 90 Volt DC GP motor Reactor Reactor for slurry-phase continuous FT reaction Manufacturer and model: AE, 300 mL Eze-Seal reactor, 316 SS Max operating pressure: 3300 psi at 454 °C Operating pressure: 290 psi at 220 °C (variable) Descriptions: Metal gasket seal, Tall bench stand, Manual screw jack Internal accessories: Sample tube with manual valve (to be used as outlet port), Sparge tube with manual valve, No cooling coil, Thermowell with type "K" thermocouple      192 Item name Description and operating condition Hot condenser Hot condenser for wax collection during the reaction Manufacturer and model: Swagelok, 304L-HDF4-150, 150 mL Max working pressure: 1800  psi at 37 °C,  1360 psi at 93 °C, 1230 psi at 148 °C and 1130 psi at 204 °C Normal operating pressure: Reaction pressure at ~ 140 °C Filter For filtering the gas exiting the hot condenser before entering back-pressure regulator Manufacturer and model: Swagelok, SS-2F-15 Max working pressure: 3000  psi at 37 °C,  2580 psi at 93 °C, 2330 psi at 148 °C and 2140 psi at 204 °C Operating pressure: Reaction pressure at ~ 140 °C Back-pressure regulator Back-pressure regulator (BPR) for controlling the reactor and hot condenser pressures Manufacturer and model: Tescom, 26-2363-24-229 series Max operating temperature: 200 °C, Operating temperature:  ~ 140 °C Flow switching valve GC controlled 4-way switching valve for switching the flow toward gas sampling valve of GC-2010 Manufacturer and model: Valco, N/A (provided by Mandel Scientific) Description: Nitronic 60 valve body, T-type rotor for use above 175 °C to 350 °C and 300 psi, Micro-electric actuator      193 Item name Description and operating condition Mass flow meter (MFM) MFM to measure the exit flowrate Manufacturer: Brooks instruments, Provided by Autoclave Engineering (AE) Normal operating pressure:  14.7 psi at room temperature Cold condenser Cold condenser for hydrocarbon collection and separation of permanent gases during the reaction Manufacturer and model: Swagelok, 304L-HDF4-300, 300 mL Max working pressure: 1800  psi at 37 °C,  1360 psi at 93 °C, 1230 psi at 148 °C and 1130 psi at 204 °C Normal operating conditions: 14.7 psia at 2 °C GC GC for analysis of permanent gases leaving cold condenser (CO, CO2, H2, N2, C1 -C4) Manufacturer and model: Shimadzu, GC-2014 Details: Shimadzu GC-2014 with dual AFC, Dual Inj-Pac-2014, dual differential TCD-2014 with manual detector gas control and standard temperature and pressure control valves, 20 temperature progmamming steps, logging of operation temperature profile, flow profile and heat zone temperatures are stored in 10 non-volatile memory files in the GC for easy access Accessories: 20' * 1/8" Ni column P/W Hayesep D 100/120, 6-port sampling loop (P-type, stainless steel)     194      Item name Description and operating condition GC GC for analysis gases leaving hot condenser and the liquid samples collected in hot and cold condensers Manufacturer and model: Shimadzu, GC-2010 plus Details: Shimadzu GC-2010 plus simulated distillation analyzer, Complete with FID, 1 capillary column, appropriate hardware and software to perform any of the simulated distillation ASTM methods, which are ASTM D2887, ASTN D3710, ASTM D5307, ASTM D6352 and ASTM D7169. Includes enhanced data station, GC solution software and Petro software Accessories: 1) SPL-2010 with AFC (This kit contains the SPL-2010 and AFC-2010 with all associated cables and tubing to connect to GC-2010, 2) Shimadzu FID-2010 plus with APC module, electrometer, cables and tubing to connect it to the GC-2010, 3) Auxiliary temperature controller for the GC-2010/2014. 4) Shimadzu MXT-1 SimDis Column; 5m * 0.53 mm I.D * 0.1 µm, 4) AOC-20i autoinjector with power supply for GC-2010, auto-sensing power supply. Includes mounting hardware for GC-2010 5) Shimadzu valve enclosure for two valves, 6) Valco 4-port valve, Nitronic valve body, T-type rotor for use above 175 °C up to 350 °C at 300 psi, Micro-electric actuator, 7) 6-port loop sampling, T-type    195 Appendix D: Calibration  Calibration of feed mass flow controllers  Mass flow meter calibrations were checked before each experiment for the feed gases and the calibration gas mixture. A bubble flow meter was connected to the outlet of the unit in order to measure the actual flow rates. The temperature of the room was recorded to convert the flow rates to the standard volumetric flow (mL(STP)/min).  A calibration plot was measured at 3-4 different points for each gas and each point is measured for more than three times to get an average. The calibration plots for one of the experiments are shown in Figure D.1.   Calibration of GC-2014  The standard gas mixture was used for calibration of both GC2014 and GC2010. The gas mixture was diluted with 100 and 50 mL(STP)/min of H2 to produce two more different concentrations of gas mixture for calibration. Each of these diluted gases were passed through the reactor lines for more than 1 hr and three different injections were made to ensure that the system was completely stable. The composition of the gas mixtures used for calibration is shown in Table D.1. Hence, the calibration curve was created by plotting the area under each peak versus the expected compositions for the compounds at three different dilutions.     196 0 5 10 15 20 25 30 35 40 45 50 55 6001020304050010203040500102030405001020304050 MFC set point (sccm) H2  CO Bubble flowmeter (sccm)  N2   Gas mixture Figure D.1. Calibration of MFC for N2, H2, CO and gas mixture for GC 2014 calibration          197 Table D.1. The composition of gas mixtures used for calibration of GC 2014 and GC 2010   Calibration Gas 1 2 3 Mol% Mol% Mol% Butane 4 0.69 0.38 Carbon Dioxide 8 1.379 0.75 Ethane 8 1.379 0.75 Ethylene 2 0.349 0.19 Hydrogen 25 87.10 92.96 Isobutane 2 0.349 0.19 Methane 10 1.72 0.94 Nitrogen 10 1.72 0.94 Propane 6 1.03 0.56 Carbon Monoxide 25 4.30 2.35  Calibration of GC-2010 for gas  The same gas mixtures shown in Table D.1 were also injected in GC 2010. However, there might be some compounds as heavy as C15 passing through the GC during the experiments. As a result, the calibration has been made for heavier gas compounds by using response factor (RF) as follows. 𝑅𝐹 = 𝑚𝑜𝑙, %/𝐴𝑟𝑒𝑎                               D.1 Therefore, RF for each compound is the expected mol,% of that compound divided by the area of the relevant peak. The relation between the RF value and carbon number of methane, ethane, propane and butane for one of the experiments is shown in Figure D.2. Consequently, the RF values of heavier compounds were calculated from the fitted line.    198 1 2 3 4-16.5-16.0-15.5-15.0-14.5-14.0  LN(RF)C# Figure D.2. The LN(RF) versus carbon number and the fitted line   Calibration of GC-2010 for liquid  D-2887 Calibration mix, AccuStanard Inc, consisting of 17 components was diluted with CS2, 99% Sigma Aldrich. The mixture is then injected into an FID column after several blank injections with CS2. The RF value is calculated for each compound from Equation D.1. The results are indicated in Figure D.3. For the compounds which were not present in the calibration mix, the RF value was interpolated or extrapolated based on the carbon number.    199 5 10 15 20 25 30 35 40 450123456 RF (mol%)C (#).*10-8 Figure D.3.  RF value versus carbon number in D-2887 calibration mix, used for liquid calibration              200 Appendix E: GC method Files Details of GC 2010 analysis method file for gas Analytical Line 1, Injection Port SPL1 Injection Mode : Split  Temperature : 430.0 C  Carrier Gas : He  Flow Control Mode : Velocity  Pressure : 78.6 kPa  Total Flow : 66.6 mL/min  Column Flow : 1.29 mL/min  Linear Velocity : 27.2 cm/sec  Purge Flow : 1.0 mL/min  Split Ratio : 50.0  High Pressure Injection : OFF  Carrier Gas Saver : ON  Split Ratio : 5.0  Time : 1.00  Splitter Hold : OFF  Column Oven: Initial Temperature : -10.0 C  Equilibration Time : 0.0 min  CRG : ON  Column Oven Temperature Program:    201 Total Program Time : 41.00 min   Rate(C/min) Temperature(C) Hold Time(min)  … -10.0 0.00 1 10.0 375.0 2.50 Column Information: Column Name : MTX-1  Serial Number : 1003798  Film Thickness : 0.25 um  Column Length : 30.0 m  Inner Diameter : 0.25 mm ID  Column Max Temp : 430 C  Installation Date : 2013/08/03  Detector Channel 1 GASFID: Temperature : 440.0 C  Signal Acquire : Yes  Sampling Rate : 40 msec  Stop Time : 41.00 min  Delay Time : 0.00 min  Subtract Detector : None  Makeup Gas : He  Makeup Flow : 30.0 mL/min  H2 Flow : 40.0 mL/min  Air Flow : 400.0 mL/min     202 General: Ready Check Heat Unit:  Column Oven : Yes    SPL1 : Yes    GASFID : Yes    VAL-BOX : Yes   Ready Check Detector (FTD)  Ready Check Baseline Drift       GASFID            : No Ready Check Injection Flow       SPL1 Carrier : Yes      SPL1 Purge : Yes Ready Check Add. Flow   Ready Check Detector APC Flow > GASFID Makeup : Yes     GASFID H2 : Yes    GASFID Air : Yes   External Wait : No   Prerun Program(2):   Total Program Time 1.00 min    Time Device Event Value 1 0.00 Relay Relay91(0:Pt.B/1:Pt.A) 1 2 1.00 Relay Relay91(0:Pt.B/1:Pt.A) 1    203 Time Program(3):     Total Program Time 3.50 min  Time Device Event Value 1 0.05 Relay Relay92(0:Pt.B/1:Pt.A) 1 2 0.15 Relay Relay91(0:Pt.B/1:Pt.A) 0 3 3.50 Relay Relay92(0:Pt.B/1:Pt.A) 0 Auto Flame On : Yes    Auto Flame Off : Yes    Reignite : No    Auto Zero After Ready : Yes   Additional Heater/Flow: Additional Heater(5):     VAL-BOX (200.0 C)      Details of GC 2010 analysis method file for liquid Analytical Line 1, Injection Port SPL1: Injection Mode  : Split  Temperature  : 430.0 C  Carrier Gas  : He  Flow Control Mode  : Velocity  Pressure  : 102.9 kPa  Total Flow  : 9.3 mL/min     204 Column Flow  : 1.38 mL/min  Linear Velocity  : 31.6 cm/sec  Purge Flow  : 1.0 mL/min  Split Ratio  : 5.0  High Pressure Injection : OFF  Carrier Gas Saver  : ON  Split Ratio  : 5.0  Time  : 1.00  Splitter Hold  : OFF  Column Oven: Initial Temperature  : 40.0 C  Equilibration Time  : 0.5 min  CRG  : OFF  Column Oven Temperature Program: Total Program Time : 40.00 min   Rate(C/min)  Temperature(C) Hold Time(min)  …  40.0 0.00 1 20.0  425.0 20.75 Column Information: Column Name  : MTX-1  Serial Number  : 1003798  Film Thickness  : 0.25 um  Column Length  : 30.0 m     205 Inner Diameter  : 0.25 mm ID  Column Max Temp  : 430 C  Installation Date  : 2013/08/03  Detector Channel 1 GASFID:  Temperature  : 440.0 C  Signal Acquire  : Yes  Sampling Rate  : 40 msec  Stop Time  : 40.00 min  Delay Time  : 0.00 min  Subtract Detector  : None  Makeup Gas  : He  Makeup Flow  : 30.0 mL/min  H2 Flow  : 40.0 mL/min  Air Flow  : 400.0 mL/min  General Ready Check Heat Unit:    Column Oven : Yes   SPL1 : Yes   GASFID : Yes   VAL-BOX : Yes   Ready Check Injection Flow  SPL1 Carrier    : Yes SPL1 Purge     : Yes    206 Ready Check Add. Flow  Ready Check Detector APC Flow, GASFID Makeup : Yes  GASFID H2 : Yes GASFID Air : Yes External Wait : No Auto Flame On : Yes Auto Flame Off : Yes Reignite : No Auto Zero After Ready : Yes Additional Heater/Flow: Additional Heater(5): VAL-BOX (200.0 C) Peak Integration Parameters - Channel 1: Width : 10 sec Slope   : 5 uV/min Drift : 0 uV/min T.DBL   : 1000 min Min.Area/Height : 60 counts =Integration Time Program= Enable Time(min) Event  Value 1 [Yes] 17.500 Drift= 10000000.000 2 [Yes] 17.500 Width= 1.000 3 [Yes] 17.500 T.DBL= 10.000 Quantitative Parameters - Channel 1: Quantitative Parameters:    207 Quantitative Method : External Standard Calculated by : Area  Calibration Level# : 2 Calibration Curve : Linear  Through Origin : Not through Weight Regression : None  Unit : % Identification Parameters: Window/Band: Window Window : 5 % Default Band Time : --- Identification Method : Absolute Peak Select  : All Peaks Grouping : None Correction RT  : Replace  Column Performance Parameters - Channel 1: Calc. Method : JP Column Length : 0 mm Time of Unretained Peak : Time of 1st Peak Set Time : … Calculated for Identified Peak : OFF Details of GC 2014 analysis method file for gas Analytical Line 1,Injection Port DINJ1: Temperature : 150.0 C  L.Carrier Gas : He  L.Column Flow : 25.0 mL/min  L.Flow Program:   Total Program Time : 20.00 min  Rate(mL/min) Flow(mL/min) Hold Time(min)  ------ 25.0 4.00 1 5.0 30.0 15.00    208 Column Oven:   Initial Temperature : 40.0 C  Equilibration Time : 3.0 min  Column Oven Temperature Program  Total Program Time : 20.00 min   Rate(C/min) Temperature(C) Hold Time(min)  ------ 40.0 3.00 1 20.0 200.0 9.00 L.Column Information:  Column Name : Haysep D 100/120 Serial Number : 610080490  Film Thickness : 2.00 um  Column Length : 6.2 m  Inner Diameter : 2.00 mm ID  Column Max Temp : 290 C  Installation Date : 2010/11/18  Detector Channel 1 DTCD1:  Temperature : 200.0 C  Signal Acquire : Yes  Sampling Rate : 40 msec  Stop Time : 20.00 min  Delay Time : 0.00 min  Subtract Detector : None     209 Current : 120 mA  Polarity : +  Temperature(Pre) : 200.0 C  General:    Ready Check Heat Unit:   Column Oven : Yes   DINJ1 : Yes   DTCD1 : Yes   PRETCD : Yes  Ready Check Detector (FTD)  Ready Check Baseline Drift  DTCD1 : No Ready Check Injection Flow DINJ1 Carrier    : Yes Ready Check Add. Flow Ready Check Detector APC Flow  External Wait : No    Prerun Program(1): Total Program Time 0.50 min  Time Device Event Value 1 0.50 Relay Relay91(0:Pt.B/1:Pt.A) 0 Time Program(2): Total Program Time 2.00 min    210  Time Device Event Value 1 0.20 Relay Relay91(0:Pt.B/1:Pt.A) 1 2 2.00 Relay Relay91(0:Pt.B/1:Pt.A) 0 Auto Flame On : Yes Auto Flame Off : Yes Reignite : No Auto Zero After Ready : Yes Peak Integration Parameters - Channel 1: Width : 3 sec Slope : 300 uV/min Drift : 0 uV/min T.DBL : 1000 min Min.Area/Height : 100 counts Quantitative Parameters - Channel 1 Quantitative Parameters: Quantitative Method : External Standard Calculated by : Area  Calibration Level# : 3 Calibration Curve : Linear  Through Origin : Not through Weight Regression : None  Unit : ppm Identification Parameters: Window/Band : Window Window : 5 % Default Band Time : … Identification Method Absolute Peak Select : All Peaks Grouping : None Correction RT : No Change     211 Compound Table - Channel 1: ID# Name  Type Ret.Time Conc.1 Conc.2 Conc.3  1 Nitrogen  Target 3.538 10.000 1.762  0.971  2 CO  Target 3.843 25.000 4.405  2.427  3 Methane  Target 5.548 10.000 1.762  0.971  4 CO2  Target 7.670 8.000 1.410  0.777  5 Ethelyne  Target 9.479 2.000 0.352  0.194  6 Ethane  Target 10.234 8.000 1.410  0.777  7 Propane  Target 13.621 6.000 1.057  0.583  8 I-Butane  Target 17.506 2.000 0.352  0.194  9 Butane  Target 18.693 4.000 0.705  0.388  Column Performance Parameters - Channel 1: Calc. Method : JP Column Length : 0 mm Time of Unretained Peak : Time of 1st Peak Set Time : ---              212 Appendix F: Data processing procedure  The following example illustrates the calculation methods used to convert measured flowrates and compound compositions, selectivities and reaction rates. The example data was collected using the 0.3Re-3Co/Al2O3(0.9) catalyst at  GHSV (0.045 mol/g.h)  at 220 ºC and H2/CO=2.  Step1:  The inlet gas flow rate is measured by the mass flow controllers. The actual flow rate entering the reactor is calculated by MFC calibration curves in Figure D.1. The total mass and moles of each compound entering the reactor during ~ 24 h is calculated as follows: 𝑀𝐴 =𝐹𝐴×𝑡×𝑀𝑊𝐴22414      F.1                                                 where 𝐹𝐴 is the flow rate of compound A in sccm, 𝑀𝐴 is mass of compound A entering the reactor between two liquid sample collections, t is the total time in minutes (the time between two liquid sample collections which is approximately 24 h), 𝑀𝑊𝐴 is the  molecular weight of compound A. Therefore, moles of compound A entering the reactor between two liquid sample collections, 𝑀𝑜𝑙𝐴, is calculated as follows: 𝑀𝑜𝑙𝐴 =𝑀𝐴𝑀𝑊𝐴                                                                 A sample result of inlet gas calculations is shown in Table F.1.        213 Table F.1. The composition of the inlet gas to the CSTR reactor within 24.5 h  INLET sccm mass in  moles mole fraction CO 16.1 29.7 1.1 0.23 H2 34.2 4.5 2.2 0.49 N2 19.6 36.0 1.3 0.28 TOTAL 70.0 70.2 4.6    The mol% of outlet gases (C1-C4, CO2, CO and N2) was measured every hour by the GC equipped with a TCD. The measured data was averaged over the time between collection of two consecutive liquid samples. Since N2 is an inert gas, the outlet flow rate is measured by N2 balance as follows: 𝐹𝑜𝑢𝑡 = (𝐹𝑖𝑛 × 𝑦𝑁2𝑖𝑛 )/(𝑦𝑁2𝑜𝑢𝑡  ) F.2 where 𝐹𝑜𝑢𝑡 is the total outlet flow in sccm and Fin is the total inlet flow in sccm, 𝑦𝑁2𝑖𝑛  is N2 mole fraction  at the inlet and 𝑦𝑁2𝑜𝑢𝑡  is the N2 mol fraction at the outlet . Hence, CO conversion is measured by Equation  3.4  and total moles of compound A exiting the reactor between two liquid sample collections, MoloutA, is measured as follows:     𝑀𝑜𝑙𝐴𝑜𝑢𝑡 =𝐹𝑜𝑢𝑡 × 60 × 𝑡 × 𝑛𝐴𝑜𝑢𝑡100 × 22414 F.3 A sample result of outlet gas measured by TCD is indicated in Table F.3, where 𝑛𝐴𝑜𝑢𝑡 is the average mole % of compound A, between two liquid sample collections, and t is time period between two liquid sample collections in h.       214 Table F.3. Outlet gas measured by GC equipped with TCD  Compound Average mol % Measured by TCD Methane 0.88   CO2 0.09   Ethylene 0.01   Ethane 0.05   Propane 0.14   i-Butane 0.06   Butane 0.11   Nitrogen 34.48   CO 21.35       N2 balance yields: (within 24.5 h)    Flow out 56.9 sccm CO out 0.8 moles CO conversion 24.8 % CO consumed 0.26 moles CO2 produced 0.0035 moles   Step2:  The mass of water and H2 and the total mass of hydrocarbons at the outlet were calculated from stoichiometry and CO conversion of the reaction according to the following stoichiometric equations:  n CO +2 nH2 → (CH2)n + n H2O F.4 n CO+n H2O → n CO2 + n H2 F.5 Mass of H2 (g) at outlet =[moles of H2 at inlet-2×moles of CO consumed+ moles of CO2 produced]×2 Mass of H2O (g)=[moles of CO consumed- moles of CO2 produced]×18 Mass of CH2 (g)=[moles of CO consumed]×14    215 The results are compared to the measured amount of hydrocarbons and water collected from the experiment to ensure the calculations are correct. The sample results are shown in Table F.3.  Table F.3. The measured and calculated compounds at the reactor outlet  Reactor exit grams moles  Mole fraction CO 22.31 0.80 Measured 0.18 CO2 0.15 0.00 Measured 0.00 H2 3.44 1.72 Stoichiometry  0.40 H2O 4.66 0.26 Stoichiometry 0.06 CH2 3.67 0.26 Stoichiometry 0.06 N2 36.04 1.29 Measured 0.30 Total 70.29 4.32       measured Stoichiometry Water  4.13 4.66 Hydrocarbons in Hot condenser 2.0 1.62  Step3:  The mass of (CH2)n in the outlet gas was also measured from the average TCD results by adding the measured (C1-C4) values indicated in Table F.4. The theoretical mass of water in the hot and cold condensers or H2O in traps is calculated from stoichiometry and CO conversion. Assuming that all the H2O is condensed in hot and cold condensers and the outlet gas is dry. This amount is comparable with the actual amount of water collected from both hot and cold condensers (see Table F.3). In addition, the total mass of CH2 collected in the hot condenser and going to FID can be calculated by subtracting the total mass of CH2 produced based on stoichiometry and CO conversion (reported in Table F.3) and the total mass of CH2 in the outlet gas (reported in Table F.4).      216 Table F.4. Measured mass of (CH2)n at the outlet, calculated mass of H2O in traps and CH2 in hot condenser and FID   mol % Component moles Moles CH2 Mass as CH2 CH4 0.88 0.033 0.033 0.462 C2H6 0.06 0.002 0.004 0.0671 C3H8 0.14 0.005 0.016 0.222 C4H10 0.16 0.006 0.025 0.354  Total 1.26 0.047 0.079 1.105  H2O in traps 4.66 grams CH2 in (Hot Condenser + FID) 2.57 grams   Step 4:  To measure the mass of hydrocarbons going to the GC FID, the actual GC FID flow rate is calculated by iteration. The initial guess is calculated based on conservation of C3 moles in both FID and TCD, as C3 is not condensable throughout the system (C3 is chosen because C1-C2 peaks merged together in the FID chromatograph). Hence, the initial guess for FID flow rate, FFID, is derived as follows: 𝐹𝐹𝐼𝐷 (𝑠𝑐𝑐𝑚) =𝐹𝑇𝐶𝐷(𝑠𝑐𝑐𝑚)× 𝑛𝐶3 𝑖𝑛 𝑇𝐶𝐷𝑛𝐶3 𝑖𝑛 𝐹𝐼𝐷                                                                               F.6 where 𝑛𝐶3 is the mol% of C3. In addition, the mass of water in the cold condenser based on stoichiometry and CO conversion is derived as follows: 𝑚𝐻2𝑂 (𝑠𝑡𝑜𝑖𝑐ℎ in CC) =𝑚𝐻2𝑂 (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 in CC)𝑚𝐻2𝑂 (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 in CC+HH)× 𝑚𝐻2𝑂 (𝑠𝑡𝑜𝑖𝑐ℎ)                                           F.7 where HC is the abbreviation for hot condenser and CC is the abbreviation for cold condenser and 𝑚𝐻2𝑂  is the mass of water in gram.    217  The H2O in cold condenser is equal to the mass of H2O at the FID inlet, if we assume that the outlet gas is dry. Total mass of hydrocarbons measured in the FID inlet based on the initial guess of FID inlet flowrate is used to calculate the new FID inlet flowrate. The iteration is continued until the flowrates become almost equal. A sample calculation is indicated in Table F.5. Table F.5. Iterative calculation to measure the amount of HC in FID  FID flow Sccm 56.9 Initial guess   FID flow Sccm 60.9 Final  value   FID C# Mean Mole% Comp molesmoles Moles CH2 CH2 mass C1-C2 1.5 1.2519 0.050016 0.075025 1.050345 C3 3 0.1419 0.005669 0.019841 0.277768 C4 4 0.08149 0.003254 0.013015 0.182207 C5 5 0.04449 0.001775 0.008876 0.124263 C6 6 0.02199 0.000876 0.004820 0.067479 C7 7 0.0162 0.000647 0.004526 0.063370 C8 8 0.0140 0.000559 0.004191 0.058678 C9 9 0.0141 0.000564 0.005078 0.071090 C10 10 0.0149 0.000598 0.005681 0.079527 C11 11 0.0101 0.000404 0.004441 0.062168 C12 12 0.0023 0.000094 0.001084 0.015177 C13 13 0.0001 0.000007 0.000093 0.001299 C14 14 2.2E-05 0.000001 0.000012 0.000170 C14+ 15 2.4E-05 0.000001 0.000015 0.000206 Total  1.6136 0.064465 0.146696 2.054a FID inlet grams Moles Sccm CO 22.314 0.796941 12.1514 CO2 0.155 0.003528 0.0538 H2 3.441 1.720579 26.2347 H2O 2.226 0.123678 1.8858 (CH2)n 2.054a 0.063149 0.9629 N2 36.041 1.287191 19.6266 Total 66.232  60.9 a The total hydrocarbon measured in FID is used to measure the FID inlet flow rate base on iteration       218  Step5:   The wt% of products collected from the hot condenser is measured by FID liquid analysis. To calculate mass of each compound produced during the 24 h period, the total mass of product in the hot condenser collected within 24 hours is required. As some squalane is always in the products and some amount of wax always remains inside the reactor, it is more convenient to correct the total mass of hydrocarbons in hot condenser using stoichiometric amount of hydrocarbon products based on CO conversion, according to the following equations: Actual mass of products in HC =  Collected mass in HC − Mass of squalane in HC           F.8 𝑀𝐴 = 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 𝑖𝑛 𝐻𝐶 𝑏𝑎𝑠𝑒𝑑 𝑜𝑛 𝐶𝑂 𝑐𝑜𝑛 ×𝑀𝐴 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑏𝑦 𝐹𝐼𝐷    𝐴𝑐𝑡𝑢𝑎𝑙 𝑚𝑎𝑠𝑠 of products 𝑖𝑛 𝐻𝐶                    F.9 where MA is the mass of compound A formed during 24 h. A sample analysis of hot condenser liquid is defined in Table F.6.              219 Table F.6. Mass of hydrocarbons measured in liquid analysis  #C wt (g) ,in analysed liquid wt (g), in HC Moles in HC 6 3.7E-04 3.5E-03 4.2E-05 7 5.8E-03 5.5E-02 5.6E-04 8 6.7E-03 6.4E-02 5.7E-04 9 8.5E-03 8.0E-02 6.4E-04 10 1.3E-02 1.2E-01 8.6E-04 11 1.7E-02 1.6E-01 1.1E-03 12 2.0E-02 1.9E-01 1.1E-03 13 2.0E-02 1.9E-01 1.0E-03 14 1.7E-02 1.6E-01 8.4E-04 15 1.2E-02 1.2E-01 5.6E-04 16 1.3E-02 1.2E-01 5.4E-04 17 1.0E-02 9.6E-02 4.0E-04 18 7.4E-03 7.0E-02 2.8E-04 19 6.0E-03 5.7E-02 2.1E-04 20 4.2E-03 4.0E-02 1.4E-04 21 2.9E-03 2.7E-02 9.3E-05 22 1.4E-03 1.3E-02 4.4E-05 23 8.8E-04 8.4E-03 2.6E-05 24 6.4E-04 6.1E-03 1.8E-05 25 1.3E-03 1.2E-02 3.5E-05 26 1.0E-03 9.6E-03 2.6E-05 27 7.4E-04 7.0E-03 1.9E-05 28 3.2E-04 3.0E-03 7.7E-06 29 9.6E-05 9.1E-04 2.2E-06 30 1.7E-04 1.6E-03 3.8E-06 Total 1.7E-01 1.6E+00 9.2E-03           220 Step 6:   The total moles for each hydrocarbon was obtained by combining the TCD and FID analysis for both gas and liquid within ~24 h. Consequently, the total mass of each product and its selectivity based on wt% was calculated as follows: Total mass of hydrocarbons produced in ~ 24 h=The average mass of hydrocarbon at the outlet of the unit measured by TCD in ~24 h + The mass of hydrocarbon collected in cold condenser measured by FID  gas analysis in ~24 h + the mass of hydrocarbon collected in hot condenser measured by FID liquid analysis in ~24 h. (See Figure 3.3) Table F.7 indicates the cumulative amount of hydrocarbon produced during ~ 24 h. Figure F.1 defines the ASF plot for ~ 24 h in which the probability of chain growth is obtained from the slope of linear line fitted to the experimental data.                221 Table F.7. Cumulative mass of hydrocarbons produced within ~24 h in hot and cold condensers as well as the outlet of the unit   TCD mole FID (Gas) mole FID (Liquid) mole TOTAL mole TOTAL wt wt%  Wn/N  ln(Wn/N) 1 3.3E-02   3.3E-02 5.3E-01 1.7E+01 1.7E+01 2.8E+00 2 2.4E-03   2.4E-03 7.1E-02 2.2E+00 1.1E+00 1.1E-01 3 5.3E-03 5.7E-03  5.3E-03 2.3E-01 7.3E+00 2.4E+00 8.9E-01 4 6.3E-03 3.3E-03  3.3E-03 1.9E-01 5.9E+00 1.5E+00 3.9E-01 5  1.8E-03  1.8E-03 1.2E-01 3.9E+00 7.8E-01 -2.5E-01 6  8.8E-04 4.2E-05 9.2E-04 7.7E-02 2.4E+00 4.0E-01 -9.1E-01 7  6.5E-04 5.6E-04 1.2E-03 1.2E-01 3.7E+00 5.3E-01 -6.4E-01 8  5.6E-04 5.7E-04 1.1E-03 1.3E-01 4.0E+00 4.9E-01 -7.0E-01 9  5.6E-04 6.4E-04 1.2E-03 1.5E-01 4.7E+00 5.3E-01 -6.4E-01 10  6.0E-04 8.6E-04 1.5E-03 2.0E-01 6.4E+00 6.4E-01 -4.5E-01 11  4.0E-04 1.1E-03 1.5E-03 2.2E-01 7.0E+00 6.4E-01 -4.5E-01 12  9.4E-05 1.1E-03 1.2E-03 2.1E-01 6.4E+00 5.4E-01 -6.2E-01 13  7.1E-06 1.0E-03 1.1E-03 1.9E-01 6.0E+00 4.6E-01 -7.7E-01 14  9.0E-07 8.4E-04 8.4E-04 1.7E-01 5.2E+00 3.7E-01 -1.0E+00 15  9.8E-07 5.6E-04 5.6E-04 1.2E-01 3.7E+00 2.5E-01 -1.4E+00 16   5.4E-04 5.4E-04 1.2E-01 3.8E+00 2.4E-01 -1.4E+00 17   4.0E-04 4.0E-04 9.6E-02 3.0E+00 1.8E-01 -1.7E+00 18   2.8E-04 2.8E-04 7.0E-02 2.2E+00 1.2E-01 -2.1E+00 19   2.1E-04 2.1E-04 5.7E-02 1.8E+00 9.4E-02 -2.4E+00 20   1.4E-04 1.4E-04 4.0E-02 1.2E+00 6.2E-02 -2.8E+00 21   9.3E-05 9.3E-05 2.7E-02 8.5E-01 4.1E-02 -3.2E+00 22   4.4E-05 4.4E-05 1.3E-02 4.2E-01 1.9E-02 -4.0E+00 23   2.6E-05 2.6E-05 8.4E-03 2.6E-01 1.1E-02 -4.5E+00 24   1.8E-05 1.8E-05 6.1E-03 1.9E-01 7.9E-03 -4.8E+00 25   3.5E-05 3.5E-05 1.2E-02 3.8E-01 1.5E-02 -4.2E+00 27   1.9E-05 1.9E-05 7.0E-03 2.2E-01 8.1E-03 -4.8E+00 28   7.7E-06 7.7E-06 3.0E-03 9.4E-02 3.4E-03 -5.7E+00 29   2.2E-06 2.2E-06 9.1E-04 2.8E-02 9.8E-04 -6.9E+00 30   3.8E-06 3.8E-06 1.6E-03 5.0E-02 1.7E-03 -6.4E+00 SUM     3.2E+00 1.0E+02        222 0 5 10 15 20 25 30 35-10-8-6-4-20246  Ln(Wn/N)Carbon number #Equation y = a + b*xWeight No WeightingResidual Sum of Squares12.96306Pearson's r -0.96824Adj. R-Square 0.93533Value Standard ErroLn(Wn)/NIntercept 1.88091 0.24447Slope -0.2764 0.01326 Figure F.1. Hydrocarbon distribution according to ASF equation (α=0.76)  Step 7:   The total mass and carbon balance obtained from the calculated cumulative products during ~ 24 h. The theoretical mass of water and hydrocarbons calculated in previous steps were compared with measured data. The following definitions were used to measure the system hold-up as well as mass and carbon balance. System hold up=Mass entering the system-Mass exiting the system Mass or carbon balance= (System hold up)/ Mass entering the system×100 A sample result for overall mass and carbon balance is shown in Table F.8.     223 Table F.8. Overall mass and carbon balance and comparison between theoretical and actual values for ~24h  1. Overall mass balance grams Mass In 70.19 Mass out  TCD 63.06 Water in cold condenser 1.97 Water in hot condenser 2.15 Hydrocarbon in hot condenser 2.00  Total out 69.34 Hold-Up 0.85  Mass balance 1.2% 2. Comparison between theoretical and measured Values Measured grams Water in cold condenser 1.97 Water in hot condenser 2.2 Hydrocarbon in hot condenser 2.00   Theoretical  Water in cold condenser 2.22 Water in hot condenser 2.44  Hydrocarbon in hot condenser 1.62 3. Overall Carbon balance grams In 12.7 Out  CO, CO2 9.6 Hydrocarbons 2.6 Total out 12.2 Hold-Up 0.5 Carbon balance 3.5%  Step 8:  Finally, the rate of formation or consumption of each component was calculated as follows:  𝑟𝐴 =𝑛𝐴 𝑀𝑐𝑎𝑡∗𝑡                   F.10     224 Where 𝑟𝐴 is the rate of formation or consumption of compound A in mol/g.s, nA is the moles of compound A consumed or formed during the reaction and t is the time in which compound A is consumed or formed in second. The measured rate of consumption and formation of different compounds during ~ 24 h were reported in Table F.9.  Table F.9. Rate of formation and consumption of different compounds  Carbon number Rate(mole/g.s) Compounds Rate(mole/g.s) 1 9.1E-08 CO consumption 7.3E-07 2 6.6E-09 Carbon produced 6.14E-07 3 1.5E-08 C2-C4 3.0E-08 4 9.0E-09 C5-C8 1.4E-08 5 4.9E-09 C9-C12 1.5E-08 6 2.5E-09 C12+ 1.2E-08 7 3.3E-09 H2  Consumption 1.5E-06 8 3.1E-09 H2O 7.2E-07 9 3.3E-09 CO2 9.8E-09 10 4.0E-09   11 4.0E-09   12 3.4E-09   13 2.9E-09   14 2.3E-09   15 1.6E-09   16 1.5E-09   17 1.1E-09   18 7.7E-10   19 5.9E-10   20 3.9E-10   21 2.6E-10   22 1.2E-10   23 7.2E-11   24 5.0E-11   25 9.6E-11   26 0.0E+00   27 5.1E-11   28 2.1E-11   29 6.2E-12   30 1.0E-11      225 Appendix G: Internal diffusion calculations  The Weisz–Prater criterion for internal diffusion is defined as follows [82]: 𝐶𝑤𝑝 =−𝑟𝐴 (𝑜𝑏𝑠)𝜌𝑐 𝑅2𝐷𝑒 𝐶𝐴𝑆      G.1 Where  −𝑟𝐴 (𝑜𝑏𝑠) is the  observed rate of the compound 𝐴 (mol/g.s),   𝜌𝑐 is the catalyst density (kg/m3 ), R is the particle radius (m), 𝐷𝑒 is the molecular diffusivity of solute (m2/s ). If  𝐶𝑤𝑝 ≪ 1 there is no internal diffusion limitation .  The maximum H2 consumption rate measured in this study during the FT reaction was approximately 8×10-3 (mol/kg.s). The H2 diffusivity in FT reaction condition is approximately 2.2×10-8 (m2/s) [142].  𝐶𝐴𝑆 is equal to solubility of H2 in heavy wax (C30+) which is approximately 0.1 (mol/kg wax) at 20 bar and 200 oC [145]. Density of squalane is 858 (kg/m3 ), density of the catalyst is approximately equals to the density of the support, which is 800 (kg/m3) according to the MSDS. Therefore, 𝐶𝑤𝑝 is calculated as follows: 𝐶𝑤𝑝 =8 × 10−3   × 800 × (1502× 10−6)2 2.2 × 10−6 × 0.1 × 858= 0.019 ≪ 1   Hence, internal diffusion is not a rate determination step.        226 Appendix H: Use of XRD to determine Co particle size  To measure the Co particle size by XRD, two different methods of calculations were compared. The XRD profile of the 5Co/Al2O3(0) catalyst and the Al2O3 support is shown in Figure H.1. With the first method, the XRD profile of 5Co/Al2O3(0) catalyst is subtracted from the Al2O3 support. A Gaussian curve is then fitted to the subtracted peak at 2 𝛳 ~52 °  as shown in Figure H.2.  50 55 60-2000200400600800100012001400  PSD2THETA 5Co/Al2O3(0) Support Co  Al2O3 Figure H.1. XRD profile of 5Co/Al2O3(0) catalyst and Normalized Al2O3 support from 2ϴ =50 ° to 2ϴ=60 °      227 50.0 50.5 51.0 51.5 52.0 52.5 53.0-20002004006008001000  PSD2THETA 5Co/Al2O3(0) subtracted from support   Gaussian fit Figure H.2.  Subtracted peak at 2ϴ ~52 ° and the Gaussian curve fitted to the peak   Co particle size is  measured  by Scherrer equation, using the parameter values of the Gaussian fitted curve shown in Table H.1. The details of calculations of particle size and the error in the size measurements are provided in Appendix I. The results show that dCo is 21±0.8 nm with this first method. Table H.1.  Parameters of the Gaussian curve fitted to the subtracted peak at 2𝚹 ~52 °     a See Equation I.3 for the parameters in the Gaussian curve Parameter a Value Error (±) y0 38.8 10.500 xc 51.8 0.007 w 0.4 0.015 fwhm 0.5 0.018 dCo (nm) 21 0.8    228 With the second method, the Co particle size is measured by de-convolution of the peaks at 2𝛳 ~52 ° and 2𝛳 ~ 54 °, as shown in Figure H.3. Co particle size was measured by Scherrer equation, using the parameter values of the Gaussian fitted curve shown in Table H.2. The results shows that dCo is 20±0.5 nm with the second method and is in good agreement to the first method. 50 51 52 53 54 55-20002004006008001000  PSD2THETA 5Co/Al2O3(0) FittedCurves FittedCurves Co Al2O3 Figure H.3. Deconvolution of the peaks in XRD profile of 5Co/Al2O3(0) catalyst, at 2ϴ=52° and 2ϴ=54 ° Table H.2. Parameters of the Gaussian curve fitted to the de-convoluted peak at 2ϴ~52 ° Parameter a Value Error (±) y0  33.6 6.660 xc  51.8 0.006 w  0.4 0.012 fwhm   0.5 0.014 dCo(nm) 20 0.5 a See Equation I.3 for the parameters in the Gaussian curve    229 For Re-Co/Al2O3 catalysts the peak at 2𝛳~52 ° is merged to the peak at 2𝛳 ~54 ° and has just a small shoulder. Therefor subtraction of the Al2O3 support is not possible. Alternatively, the deconvolution of the peaks is done as shown in Figure H.4. Measured Co particle size, using the parameters shown in Table H.3 obtained from the fitted Gaussian curve at 2𝛳 ~52 ° is 8±0.7nm. 50 51 52 53 54 55 56 57 58 59 60-20002004006008001000  PSD2THETA1.2Re-12Co/Al2O3(0) FittedCurves FittedCurves Co Al2O3 Figure H.4. Deconvolution of the peaks in XRD profile of 1.2Re-12Co/Al2O3(0) catalyst, at 2ϴ =52° and 2ϴ =54 ° Table H.3. Parameters of the Gaussian curve fitted to the de-convoluted peak at 2ϴ ~52°       Parameter Value Error (±) y0 7.8 6.520 xc 52.0 0.063 w 1.1 0.105 FWHM 1.3 0.123 dCo (nm) 8 0.7    230  Appendix I: Error in XRD analysis   If various quantities (i.e. 𝛳, 𝛽) are measured with small uncertainties (i.e.  𝜕𝛳, 𝜕𝛽) in which these values are used to measure some quantity like Z, then uncertainties in 𝛳 and 𝛽 cause an uncertainty in Z as follows: 𝜕𝑧2 = (𝛿𝑓(𝛽, 𝛳)𝛿𝛽)2 𝜕𝛽2 + (𝛿𝑓(𝛽, 𝛳)𝛿𝛳)2 𝜕𝛳2               I.1 For the Scherrer equation dCo=K λ/( βcos 𝜑), the uncertainty in dCo caused by 𝜕𝜑 and 𝜕𝛽 is calculated as follows: 𝜕𝑧2 = (−𝐾𝜆𝛽2𝐶𝑜𝑠𝛳)2 𝜕𝛽2 + (𝐾𝜆 sin 𝛳𝛽 cos 𝛳2)2  𝜕𝛳2               I.2 The Gaussian curve is defined by the following equation: 𝑦 = 𝑦0 +𝐴𝑤√𝜋/2 𝑒−2(𝑥−𝑥𝑐)2𝑤2        I.3 In which  𝐹𝑊𝐻𝑀 (2𝜑) = 𝛽 = √2 ∗ 𝑙𝑛2 × 𝑤 =𝑤0.849 , 𝛳 =𝑥𝑐2 ,1 degree = 0.0175 radian. As an example, for 20Co/Al2O3(0.6) catalysts, the parameters of Scherer equation and the standard errors of each parameter are reported in Table I.1 and the fitted curve to 2𝛳~43 ° assigned to Co3O4 particle size is shown in Figure I.1.   Therefore, according to the parameters reported in Figure I.1, dpCo3O4 is calculated by the Scherrer equation as follows:     231 𝑑𝑝𝐶𝑜3𝑂4 =𝐾𝜆𝛽𝑐𝑜𝑠𝛳=0.9 × 0.1792.76330.849× 0.0175 ×  𝐶𝑜𝑠(42.95 ×0.01752)= 3.0 𝑛𝑚  The error associated with the Gaussian fit with regard to the error of each parameter was calculated as follows:   𝑧 = √(−𝐾𝜆𝛽2𝐶𝑜𝑠𝛳)2 𝜕𝛽2 + (𝐾𝜆 sin 𝛳𝛽 cos2 𝛳)2  𝜕𝛳2 = √(−0.9×0.179(2.7630.849×0.0175)2×𝐶𝑜𝑠(42.95×0.0172))2× (0.13480.849× 0.017)2+ (0.9×0.179×sin (42.95×0.0172)2.7630.849×0.0175×𝐶𝑜𝑠2(42.95×0.0172) )2× (0.03372× 0.017)2=0.01  Hence, the Co3O4 particle size is 3±0.01 nm  Table I.1. Parameters of the Gaussian curve fitted to the subtracted peak at 2𝜭 ~43 °  Parameter Value Error (±) y0  -89.22 9.925 xc  42.95 0.0337 w  2.763 0.1348 fwhm   3.25 … dCo3O4(nm) 3 0.01        232 40 41 42 43 44 45 46 47-200-1000100200300400500600700800900100011001200130014001500160017001800PSD(normalized)2ThetaModel GaussianRedused  Chl-Sqr 2370.1401Adj- R Square 0.84527Value Standard ErrorPSD (Normallized) y0 -89.22076 9.92525PSD (Normallized) xc 42.95054 0.03369PSD (Normallized) A 962.59604 64.60453PSD (Normallized) w 2.76331 0.13477 Figure I.1. Gaussian fitted curve to measure Co3O4 particle size on 20Co/Al2O3(0.6)              233 Appendix J: Comparison between Co3O4 particle size measured by XRD, TEM and CO chemisorption  The unused 0.3Re-3Co/Al2O3(0.9) catalyst was examined by XRD after reduction and subsequent exposure to air. Figure J.1 shows the full XRD spectra of the catalyst. There was no Co particle identified with XRD, indicating that the Co particles were oxidized when exposed to air.  Therefore, only Co3O4 particle size is measured. 0 10 20 30 40 50 60 70 80 90-10001002003004005006007008009001000   0.3Re-3Co/Al2O3(0.9) Al2O3 Co3O4PSD2THETA Figure J.1. The full XRD spectra of reduced 0.3Re-3Co/Al2O3(0.9), Co particles were oxidized when exposed to air     234  Figure J.2.  XRD spectra of the 0.3Re-3Co/Al2O3(0.9) to calculate Co3O4 particle size  Table J.1.  Calculated parameters for the de-convoluted peaks   Peak1 Peak2 Peak3  y0 xc1 w1 A1 xc2 w2 A2 xc3 w3 A3 Value 3.1 43.1 2.9 391.653 43.5 1.5 176.9 46.2 0.7 103.0 Error 7.932 0.332 0.647 171.992 0.158 0.508 173.259 0.049 0.112 20.372  Figure J.2 shows the XRD spectra for the same catalyst, but from 2𝛳 =40 to 50 °. The two peaks at 2𝛳 ~43 ° and 43.5 ° are assigned to Co3O4 and Al2O3 compounds, respectively. The peak at 2𝛳~46 is only assigned to Al2O3 compound, since the intensity of Co3O4 peak is low at this angle. By deconvolution of the peaks the Co3O4 particle size is measured by Scherre equation as follows, (the calculated parameters are reported in Table J.1): 40 41 42 43 44 45 46 47 48 49 50-1000100200300400500600  PSD2THETA 0.3Re-3Co/Al2O3(0.9) Al2O3 Co3O4   235 𝑑𝐶𝑜3𝑂4 =𝐾𝜆𝛽𝑐𝑜𝑠 𝛳=0.9 × 0.1792.8680.849× 0.0175 ×  𝐶𝑜𝑠(43.1 ×0.01752)= 2.9 𝑛𝑚~3 𝑛𝑚  The error in the analysis is calculated as follows: 𝑧 = √(−𝐾𝜆𝛽2𝐶𝑜𝑠𝛳)2 𝜕𝛽2 + (𝐾𝜆 sin 𝛳𝛽 cos2 𝛳)2  𝜕𝛳2 = √(−0.9×0.179(2.8680.849×0.0175)2×𝐶𝑜𝑠(43.1×0.0172))2× (0.6470.849× 0.017)2+ (0.9×0.179×sin (43.1×0.0172)2.8680.849×0.0175×𝐶𝑜𝑠2(43.1×0.0172) )2× (0.33162× 0.017)2=0.6 Therefore, the Co3O4 particle size measured by XRD is 3±0.6 nm  Figure J.3 shows a TEM image of 0.3Re-3Co/Al2O3(0.9) and Figure J.4 indicates the log normal curve which was fitted to the Co3O4 particle size distribution considering 125 particles from 9 different images and shows the maximum abundance of 3.5 nm for Co3O4 particles.   The Co particle size for the same catalyst was also calculated considering the dispersion and DOR of the particles using Equation 4.2 and Equation 4.3:  𝐷 =𝜗𝑐ℎ𝑒𝑚×𝑀𝑊×𝜎𝑤𝑡/100× 100=62 (𝜇𝑚𝑜𝑙𝑔 𝑐𝑎𝑡 )×10−6×58.9×20.03× 100 = 24.3 𝑑Co = 96/D×DOR=96/24.3×0.55=2.1 nm     236 Co particle size is related to Co3O4 particle size by dCo=0.75×𝑑𝐶𝑜3𝑂4 [88]. Therefore, the Co3O4 particle size measured by CO chemisorption is equal to 2.8 nm. Hence, the Co3O4 particle size measured by XRD, TEM and CO chemisorption is 3±0.6, 3.5 and 2.8 nm, respectively.   Figure J.3. TEM image of fresh 0.3Re-3Co/Al2O3(0.9), Co particles were oxidized when exposed to air     237 2 4 6 8 1001020304050  #Dp (nm) Figure J.4. Log normal distribution of Co3O4 particle size for 0.3Re-3Co/Al2O3(0.9).   238 Appendix K: Experimental results for the Co/Al2O3 catalysts Summary of conditions and experimental results for Co/Al2O3 catalysts.  Table K.1. Experimental condition and summary of results of RUN14EXP1 with 5Co/Al2O3(0) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 2 3 4 5 6 TOS, h 44 24 26 23 28 Cumulative TOS, h 44 68 94 117 145       CO conv 14.8 14.0 14.0 13.6 13.5       Products distribution wt%      CH4 11.2 13.0 12.9 13.8 13.7 C2-C4 13.8 13.8 12.5 12.4 12.4 C5-C8 13.1 11.9 21.4 12.8 12.8 C9-C12 19.4 14.7 19.4 19.4 13.4 C12+ 42.5 46.7 50.9 47.7 42.5 CH4, mol% 9.2 11.0 11.0 11.3 11.3 CO2, mol% 0.6 0.8 0.8 0.8 0.8 CH4, C atom% 10.0 11.9 11.6 12.3 12.2 C5+ Selectivity 75.0 73.2 91.8 79.8 68.7       Alpha 0.83 0.82 0.82 0.85 0.81       CO, (mol/sec.g) 4.05E-07 3.83E-07 3.83E-07 3.71E-07 3.68E-07 CH4  3.72E-08 4.22E-08 4.21E-08 4.20E-08 4.16E-08 CO2  2.32E-09 2.91E-09 2.88E-09 2.84E-09 2.80E-09 C2-C4 f 1.56E-08 1.58E-08 1.44E-08 1.34E-08 1.28E-08 C4-C8  7.79E-09 6.99E-09 1.19E-08 7.11E-09 5.56E-09 C9-C12  6.91E-09 5.09E-09 6.10E-09 4.40E-09 4.47E-09 C12+  8.90E-09 1.01E-08 8.42E-09 9.92E-09 1.06E-08       yCO 2.1E-01 2.1E-01 2.1E-01 2.1E-01 2.122E-01 yCO2 2.1E-04 2.6E-04 2.6E-04 2.5E-04 2.512E-04 yH2 4.2E-01 4.2E-01 4.2E-01 4.2E-01 4.265E-01 yH2O 3.6E-02 3.4E-02 3.4E-02 3.3E-02 3.285E-02 YCH2 3.6E-02 3.4E-02 3.4E-02 3.3E-02 3.310E-02     239 Day 2 3 4 5 6 TOS, h 44 24 26 23 28 Cumulative TOS, h 44 68 94 117 145 PH2 126.38 127.36 127.32 127.86 127.96 PCO 62.86 63.35 63.33 63.60 63.65 PCO2 0.06 0.08 0.08 0.08 0.08 PH2O 10.90 10.25 10.27 9.92 9.86 PCH2 11.0 10.3 10.3 10.0 9.9 Overall mass balance, % 4.3 2.8 2.9 3.2 3.0 overall carbon balance,% 1.2 0.9 0.6 1.0 0.9       PH2O/PH2 0.09 0.08 0.08 0.08 0.08       CO (mol/sec.g) 8.1E-06 7.6E-06 7.6E-06 7.4E-06 7.3E-06 CH4  7.433E-07 8.4E-07 8.4E-07 8.4E-07 8.3E-07 CO2  4.643E-08 5.8E-08 5.7E-08 5.6E-08 5.5E-08 C2-C4  3.113E-07 3.1E-07 2.8E-07 2.6E-07 2.5E-07 C4-C8  1.557E-07 1.3E-07 2.3E-07 1.4E-07 1.1E-07 C9-C12  1.383E-07 1.0E-07 1.2E-07 8.7E-08 8.9E-08 C12+  1.779E-07 2.0E-07 1.6E-07 1.9E-07 2.1E-07       CO,TOF (S-1) 1.45E-02 1.37E-02 1.37E-02 1.33E-02 1.32E-02 CH4  1.33E-03 1.51E-03 1.51E-03 1.50E-03 1.49E-03 CO2  8.31E-05 1.04E-04 1.03E-04 1.02E-04 1.00E-04 C2-C4 5.57E-04 5.67E-04 5.16E-04 4.80E-04 4.60E-04 C4-C8  2.79E-04 2.50E-04 4.25E-04 2.55E-04 1.99E-04    C9-C12 2.48E-04 1.82E-04 2.18E-04 1.57E-04 1.60E-04 C12+ 3.19E-04 3.60E-04 3.02E-04 3.55E-04 3.80E-04 C5+ 8.45E-04 7.92E-04 9.45E-04 7.67E-04 7.40E-04         240 Table K.2. Experimental condition and summary of results of RUN16EXP1, with 20Co/Al2O3(0.6) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 1 2 3 4 5 6 7 TOS, h 21 27 23.5 22.45 26 22.25 19.45 Cumulative TOS, h 21 48 71.5 93.95 119.95 142.2 161.65         CO conv 48.49 42.12 37.45 34.77 32.65 31.17 30.98         Products distribution wt%        CH4 5.44 5.78 6.86 7.67 7.75 7.81 7.94 C2-C4 3.8 4.2 4.2 4.7 4.6 4.5 4.7 C5-C8 14.5 15.9 9.5 8.4 6.7 7.9 6.0 C9-C12 12.4 20.1 19.0 15.6 15.8 14.3 13.0 C12+ 63.8 54.1 60.4 63.6 65.1 65.5 58.2 CH4, mol% 4.6 4.8 5.7 6.2 6.4 6.4 6.5 CO2, mol% 1.1 0.9 0.5 0.4 0.4 0.4 0.4 CH4, C atom% 4.8 5.1 6.1 6.8 6.9 6.9 7.0 C5+ Selectivity 90.7 90.0 88.9 87.6 87.6 87.7 77.2         Alpha 0.90 0.89 0.89 0.91 0.90 0.91 0.92         CO, (mol/sec.g) 1.43E-06 1.24E-06 1.10E-06 1.02E-06 9.62E-07 9.18E-07 9.13E-07 CH4  6.61E-08 5.98E-08 6.24E-08 6.38E-08 6.12E-08 5.87E-08 5.96E-08 CO2  1.55E-08 1.09E-08 5.18E-09 4.27E-09 3.82E-09 3.53E-09 3.45E-09 C2-C4 f 1.72E-08 1.62E-08 1.45E-08 1.48E-08 1.38E-08 1.25E-08 1.34E-08 C4-C8  3.04E-08 2.92E-08 1.55E-08 1.26E-08 9.64E-09 1.08E-08 8.81E-09 C9-C12  6.61E-09 2.23E-08 1.83E-08 1.38E-08 1.32E-08 1.14E-08 1.03E-08 C12+  2.96E-08 2.90E-08 3.40E-08 3.03E-08 3.17E-08 2.82E-08 2.84E-08         yCO 1.3E-01 1.5E-01 1.6E-01 1.6E-01 1.7E-01 1.7E-01 1.7E-01 yCO2 1.4E-03 9.795E-04 4.6E-04 3.7E-04 3.3E-04 3.0E-04 3.0E-04 yH2 2.7E-01 3.0E-01 3.2E-01 3.3E-01 3.4E-01 3.5E-01 3.5E-01 yH2O 1.2E-01 1.1E-01 9.7E-02 9.0E-02 8.4E-02 8.0E-02 7.9E-02 YCH2 1.3E-01 1.1E-01 9.8E-02 9.0E-02 8.4E-02 8.0E-02 7.9E-02            241 Day 1 2 3 4 5 6 7 TOS, h 21 27 23.5 22.45 26 22.25 19.45 Cumulative TOS, h 21 48 71.5 93.95 119.95 142.2 161.65 PH2 83.30 91.94 98.04 101.53 104.26 106.14 106.38 PCO 41.66 46.05 49.18 50.93 52.30 53.25 53.37 PCO2 0.43 0.29 0.14 0.11 0.10 0.09 0.09 PH2O 38.79 33.21 29.31 27.03 25.25 24.02 23.86 PCH2 39.2 33.5 29.4 27.1 25.4 24.1 24.0 Overall mass balance, % 1.9 4.6 3.6 2.0 3.2 3.2 3.5 overall carbon balance,% 1.2 2.0 2.4 2.7 2.2 2.2 2.1         PH2O/PH2 0.47 0.36 0.30 0.27 0.24 0.23 0.22         CO (mol/sec.g) 7.1E-06 6.2E-06 5.5E-06 5.1E-06 4.8E-06 4.5E-06 4.5E-06 CH4  3.3E-07 2.9E-07 3.1E-07 3.1E-07 3.0E-07 2.9E-07 2.9E-07 CO2  7.7E-08 5.4E-08 2.5E-08 2.1E-08 1.9E-08 1.7E-08 1.7E-08 C2-C4  8.6E-08 8.1E-08 7.2E-08 7.4E-08 6.9E-08 6.2E-08 6.7E-08 C4-C8  1.5E-07 1.4E-07 7.7E-08 6.3E-08 4.8E-08 5.3E-08 4.4E-08 C9-C12  3.3E-08 1.1E-07 9.1E-08 6.8E-08 6.6E-08 5.7E-08 5.1E-08 C12+  1.4E-07 1.4E-07 1.6E-07 1.5E-07 1.5E-07 1.4E-07 1.4E-07         CO,TOF  (S-1) 1.39E-02 1.21E-02 1.07E-02 9.97E-03 9.37E-03 8.94E-03 8.89E-03 CH4  6.43E-04 5.83E-04 6.07E-04 6.21E-04 5.96E-04 5.72E-04 5.80E-04 CO2  1.51E-04 1.06E-04 5.04E-05 4.16E-05 3.72E-05 3.44E-05 3.36E-05 C2-C4 1.68E-04 1.58E-04 1.41E-04 1.44E-04 1.35E-04 1.22E-04 1.31E-04 C4-C8  2.96E-04 2.84E-04 1.51E-04 1.23E-04 9.39E-05 1.05E-04 8.58E-05       C9-C12 6.43E-05 2.17E-04 1.78E-04 1.34E-04 1.29E-04 1.11E-04 1.01E-04 C12+ 2.88E-04 2.82E-04 3.31E-04 2.95E-04 3.08E-04 2.74E-04 2.77E-04 C5+ 6.49E-04 7.84E-04 6.60E-04 5.52E-04 5.31E-04 4.90E-04 4.63E-04        242 Table K.3. Experimental condition and summary of results for RUN17EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 2 3 4 5 6 7 8 TOS, h 24.5 25.5 23.5 24.5 24.25 24 23.5 Cumulative TOS, h 45.5 71 94.5 119 143.25 167.25 190.75         CO conv 45.01 36.79 38.42 36.55 35.51 34.29 34.30         Products distribution wt%        CH4 7.04 7.04 8.71 9.45 9.68 10.05 9.59 C2-C4 3.52 4.35 3.35 2.98 3.05 3.41 3.48 C5-C8 10.99 7.43 6.22 6.95 4.26 4.86 10.64 C9-C12 22.67 18.32 15.34 16.57 14.58 12.32 12.91 C12+ 47.39 51.76 48.78 50.49 50.39 49.93 44.84 CH4, mol% 5.89 5.73 7.20 7.72 7.98 8.28 7.91 CO2, mol% 1.25 0.39 0.49 0.38 0.34 0.31 0.27 CH4, C atom% 6.23 6.23 7.72 8.38 8.59 8.92 8.50 C5+ Selectivity 81.0 77.5 70.3 74.0 69.2 67.1 68.4         Alpha 0.90 0.91 0.92 0.91 0.92 0.93 0.92         CO, (mol/sec.g) 1.28E-06 1.04E-06 1.09E-06 1.04E-06 1.0E-06 9.7E-07 9.7E-07 CH4  7.51E-08 5.97E-08 7.84E-08 8.00E-08 8.0E-08 8.0E-08 7.6E-08 CO2  1.59E-08 4.07E-09 5.31E-09 3.96E-09 3.4E-09 3.0E-09 2.6E-09 C2-C4 f 1.49E-08 1.39E-08 1.19E-08 9.93E-09 1.0E-08 1.0E-08 1.0E-08 C4-C8  2.02E-08 1.09E-08 9.78E-09 1.03E-08 6.0E-09 6.7E-09 1.4E-08 C9-C12  2.61E-08 1.66E-08 1.48E-08 1.50E-08 1.2E-08 1.0E-08 1.1E-08 C12+  3.31E-08 2.94E-08 3.08E-08 2.96E-08 2.9E-08 2.7E-08 2.5E-08         yCO 1.4E-1 1.6E-01 1.6E-01 1.6E-01 1.7E-01 1.7E-01 1.7E-01 yCO2 1.5E-3 3.8E-04 5.0E-04 3.7E-04 3.2E-04 2.8E-04 2.5E-04 yH2 2.8E-1 3.2E-01 3.1E-01 3.2E-01 3.3E-01 3.4E-01 3.4E-01 yH2O 1.210E-1 9.8E-02 1.0E-01 9.7E-02 9.4E-02 9.0E-02 9.0E-02 YCH2 1.225E-1 9.8E-02 1.0E-01 9.7E-02 9.4E-02 9.1E-02 9.1E-02         PH2 86.59 97.61 95.43 97.92 99.30 100.91 100.89 PCO 44.90 50.54 49.45 50.70 51.39 52.20 52.19 PCO2 0.46 0.11 0.15 0.11 0.10 0.08 0.07     243 Day 2 3 4 5 6 7 8 TOS, h 24.5 25.5 23.5 24.5 24.25 24 23.5 Cumulative TOS, h 45.5 71 94.5 119 143.25 167.25 190.75 PH2O 36.29 29.30 30.70 29.10 28.20 27.15 27.17 PCH2 36.8 29.4 30.8 29.2 28.3 27.2 27.2 Overall mass balance, % -2.1 -4.1 -4.3 -4.5 -4.5 -5.4 -5.3 overall carbon balance,% 1.9 2.8 2.4 2.7 2.4 2.4 2.3         PH2O/PH2 0.42 0.30 0.32 0.30 0.28 0.27 0.27         CO (mol/sec.g) 8.5E-06 6.9E-06 7.2E-06 6.9E-06 6.7E-06 6.5E-06 6.5E-06 CH4  5.0E-07 3.9E-07 5.2E-07 5.3E-07 5.3E-07 5.4E-07 5.1E-07 CO2  1.1E-07 2.7E-08 3.5E-08 2.6E-08 2.3E-08 2.0E-08 1.7E-08 C2-C4  9.9E-08 9.2E-08 7.9E-08 6.6E-08 6.7E-08 6.9E-08 7.2E-08 C4-C8  1.3E-07 7.3E-08 6.5E-08 6.8E-08 4.0E-08 4.5E-08 9.8E-08 C9-C12  1.7E-07 1.1E-07 9.8E-08 1.0E-07 8.6E-08 7.0E-08 7.4E-08 C12+  2.2E-07 1.9E-07 2.0E-07 1.9E-07 1.9E-07 1.8E-07 1.6E-07         CO,TOF (S-1) 1.0E-02 9.1E-03 7.4E-03 7.7E-03 7.4E-03 7.2E-03 6.9E-03 CH4  5.6E-04 5.3E-04 4.2E-04 5.6E-04 5.7E-04 5.7E-04 5.7E-04 CO2  1.7E-04 1.1E-04 2.9E-05 3.8E-05 2.8E-05 2.4E-05 2.1E-05 C2-C4 1.2E-04 1.1E-04 9.9E-05 8.5E-05 7.1E-05 7.2E-05 7.4E-05 C4-C8  3.0E-04 1.4E-04 7.8E-05 7.0E-05 7.3E-05 4.3E-05 4.8E-05    C9-C12 1.8E-04 1.9E-04 1.2E-04 1.0E-04 1.1E-04 9.2E-05 7.5E-05 C12+ 2.0E-04 2.4E-04 2.1E-04 2.2E-04 2.1E-04 2.1E-04 2.0E-04 C5+ 6.7E-04 5.7E-04 4.1E-04 3.9E-04 3.9E-04 3.5E-04 3.2E-04                  244 Table K.4. Experimental condition and summary of results of RUN18EXP1, with 5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 1 2 3 4 5 6 7 TOS, h 24 24 24.83 24.66 23 24 21 Cumulative TOS, h 24 48 72.83 97.49 120.49 144.49 165.49         CO conv 2.21 2.24 3.81 4.35 4.02 3.84 4.02         Products distribution wt%        CH4 28.81 32.38 26.41 25.23 31.58 24.14 37.92 C2-C4 38.77 43.68 27.49 25.03 18.42 11.73 15.79 C5-C8 6.69 6.34 4.49 4.35 3.94 4.05 4.98 C9-C12 3.53 4.44 5.63 6.45 6.84 7.19 7.11 C12+ 22.19 13.17 35.98 38.94 39.22 55.51 34.20 CH4, mol% 31.54 31.49 26.14 24.47 27.62 29.85 30.50 CO2, mol% 9.92 9.78 6.71 5.99 6.49 6.95 7.02 CH4, C atom% 26.81 30.34 24.29 23.14 29.05 21.90 35.12 C5+ Selectivity 32.4 23.9 46.1 49.7 50.0 66.8 46.3         Alpha 0.85 0.81 0.82 0.83 0.82 0.84 0.82         CO, (mol/sec.g) 6.64E-08 6.73E-08 1.14E-07 1.30E-07 1.21E-07 1.15E-07 1.21E-07 CH4  2.09E-08 2.12E-08 2.12E-08 3.19E-08 3.33E-08 3.44E-08 3.68E-08 CO2  6.58E-09 6.58E-09 6.58E-09 7.81E-09 7.83E-09 8.00E-09 8.48E-09 C2-C4 f 1.37E-08 1.35E-08 1.42E-08 1.44E-08 7.98E-09 6.30E-09 6.15E-09 C4-C8  8.93E-10 7.99E-10 9.56E-10 1.02E-09 7.76E-10 1.12E-09 9.21E-10 C9-C12  2.9E-10 3.23E-10 6.82E-10 8.69E-10 7.72E-10 1.08E-09 7.40E-10 C12+  8.2E-10 5.4E-10 2.63E-09 3.19E-09 2.70E-09 4.91E-09 2.18E-09         yCO 2.6E-01 2.6E-01 2.5E-01 2.54E-01 2.5E-01 2.5E-01 2.5E-01 yCO2 5.8E-04 5.8E-04 6.8E-04 6.92E-04 6.94E-04 7.08E-04 7.51E-04 yH2 4.5E-01 4.5E-01 4.4E-01 4.4E-01 4.4E-01 4.4E-01 4.4E-01 yH2O 5.3E-03 5.3E-03 9.4E-03 1.1E-02 9.9E-03 9.5E-03 9.9E-03 YCH2 5.8E-03 5.9E-03 1.0E-02 1.1E-02 1.1E-02 1.0E-02 1.1E-02         PH2 134.31 134.27 132.35 131.68 132.09 132.32 132.09 PCO 77.60 77.59 76.66 76.33 76.53 76.64 76.52 PCO2 0.17 0.17 0.20 0.21 0.21 0.21 0.23    245 Day 1 2 3 4 5 6 7 TOS, h 24 24 24.83 24.66 23 24 21 Cumulative TOS, h 24 48 72.83 97.49 120.49 144.49 165.49 PH2O 1.58 1.61 2.83 3.26 3.00 2.84 2.98 PCH2 1.8 1.8 3.0 3.5 3.2 3.1 3.2 Overall mass balance, % 0.6 0.2 1.0 1.1 1.0 1.0 1.0 overall carbon balance,% -0.6 -0.3 -0.5 -0.5 -0.1 -1.7 0.2         PH2O/PH2 0.01 0.01 0.02 0.02 0.02 0.02 0.02         CO (mol/sec.g) 1.33E-06 1.35E-06 2.28E-06 2.61E-06 2.41E-06 2.30E-06 2.42E-06 CH4  4.19E-07 4.24E-07 4.24E-07 6.39E-07 6.67E-07 6.87E-07 7.37E-07 CO2  1.32E-07 1.32E-07 1.32E-07 1.56E-07 1.57E-07 1.60E-07 1.70E-07 C2-C4  2.73E-07 2.69E-07 2.84E-07 2.88E-07 1.60E-07 1.26E-07 1.23E-07 C4-C8  1.79E-08 1.60E-08 1.91E-08 2.05E-08 1.55E-08 2.23E-08 1.84E-08 C9-C12  5.89E-09 6.46E-09 1.36E-08 1.74E-08 1.54E-08 2.17E-08 1.48E-08 C12+  1.65E-08 1.09E-08 5.26E-08 6.37E-08 5.41E-08 9.83E-08 4.35E-08         CO,TOF (S-1) 6.33E-04 6.42E-04 1.09E-03 1.24E-03 1.15E-03 1.10E-03 1.15E-03 CH4  2.00E-04 2.02E-04 2.02E-04 3.04E-04 3.18E-04 3.28E-04 3.51E-04 CO2  6.28E-05 6.27E-05 5.18E-06 7.45E-05 7.47E-05 7.63E-05 8.09E-05 C2-C4 1.30E-04 1.28E-04 1.35E-04 1.37E-04 7.61E-05 6.01E-05 5.86E-05 C4-C8  8.52E-06 7.62E-06 9.12E-06 9.76E-06 7.40E-06 1.06E-05 8.78E-06    C9-C12 2.81E-06 3.08E-06 6.51E-06 8.29E-06 7.37E-06 1.03E-05 7.06E-06 C12+ 7.85E-06 5.18E-06 2.51E-05 3.04E-05 2.58E-05 4.68E-05 2.07E-05 C5+ 1.92E-05 1.59E-05 4.07E-05 4.84E-05 4.05E-05 6.78E-05 3.66E-05                 246 Table K.5. Experimental condition and summary of results of RUN19EXP1, with 5Co/Al2O3(0.9) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 1 2 3 4 5 6 7 8 TOS, h 22.15 24.5 24 25 25 22.5 23.5 23.5 Cumulative TOS, h 22.15 46.65 70.65 95.65 120.65 143.15 166.65 190.15          CO conv 1.0 2.2 2.9 3.2 3.7 4.0 4.1 4.5          Products distribution wt%         CH4 58.81 54.55 53.52 47.12 43.51 40.07 38.15 36.34 C2-C4 36.69 36.31 22.70 18.93 17.09 15.78 18.31 17.02 C5-C8 2.78 3.92 4.80 4.60 4.54 4.18 4.03 3.36 C9-C12 1.72 2.47 4.18 5.06 5.71 6.00 5.96 5.84 C12+ 0.00 2.75 14.81 24.29 29.15 33.97 33.56 37.42 CH4, mol% 90.00 51.73 41.49 37.49 34.44 32.63 31.89 30.89 CO2, mol% 33.32 18.85 14.45 12.58 11.03 10.05 9.45 8.90 CH4, C atom% 56.74 52.31 50.77 44.21 40.59 37.19 35.39 33.62 C5+ Selectivity 4.5 9.1 23.8 34.0 39.4 44.2 43.5 46.6          Alpha 0.49 0.75 0.78 0.77 0.81 0.81 0.80 0.81          CO, (mol/sec.g) 2.7E-08 6.3E-08 8.3E-08 9.3E-08 1.0E-07 1.1E-07 1.2E-07 1.3E-07 CH4  2.5E-08 3.2E-08 3.4E-08 3.5E-08 3.6E-08 3.7E-08 3.7E-08 4.0E-08 CO2  9.1E-09 1.2E-08 1.2E-08 1.2E-08 1.1E-08 1.1E-08 1.1E-08 1.1E-08 C2-C4  6.5E-09 9.2E-09 5.4E-09 5.0E-09 5.1E-09 5.3E-09 6.9E-09 7.5E-09 C4-C8  2.3E-10 4.6E-10 5.7E-10 6.3E-10 7.1E-10 7.3E-10 7.2E-10 7.0E-10 C9-C12  8.3E-11 1.7E-10 2.9E-10 4.0E-10 5.1E-10 5.9E-10 6.2E-10 6.8E-10 C12+  0.E+00 1.0E-10 5.9E-10 1.2E-09 1.5E-09 2.0E-09 2.1E-09 2.6E-09          yCO 2.5E-01 2.4E-01 2.4E-01 2.4E-01 2.4E-01 2.4E-01 2.4E-01 2.4E-01 yCO2 7.9E-04 1.0E-03 1.0E-03 1.0E-03 1.0E-03 9.9E-04 9.6E-04 1.0E-03 yH2 4.5E-01 4.5E-01 4.5E-01 4.4E-01 4.4E-01 4.4E-01 4.4E-01 4.4E-01 yH2O 1.6E-03 4.4E-03 6.2E-03 7.1E-03 8.1E-03 8.9E-03 9.2E-03 1.0E-02 YCH2 2.4E-03 5.5E-03 7.2E-03 8.1E-03 9.1E-03 9.9E-03 1.0E-02 1.1E-02          PH2 136.34 134.95 134.14 133.72 133.23 132.87 132.77 132.25 PCO 73.87 73.15 72.75 72.55 72.32 72.14 72.10 71.84    247 Day 1 2 3 4 5 6 7 8 TOS, h 22.15 24.5 24 25 25 22.5 23.5 23.5 Cumulative TOS, h 22.15 46.65 70.65 95.65 120.65 143.15 166.65 190.15 PCO2 0.24 0.31 0.31 0.31 0.30 0.30 0.29 0.30 PH2O 0.48 1.33 1.85 2.13 2.44 2.68 2.76 3.08 PCH2 0.7 1.6 2.2 2.4 2.7 3.0 3.0 3.4 Overall mass balance, % -0.2 0.1 0.1 0.3 0.5 0.6 0.6 0.8 overall carbon balance,% -0.9 -0.4 0.1 0.1 0.2 0.1 0.0 0.0          PH2O/PH2 0.00 0.01 0.01 0.02 0.02 0.02 0.02 0.02          CO, mol/sec.g 5.5E-07 1.2E-06 1.6E-06 1.9E-06 2.1E-06 2.3E-06 2.3E-06 2.6E-06 CH4  4.9E-07 6.5E-07 6.8E-07 7.0E-07 7.2E-07 7.4E-07 7.4E-07 7.9E-07 CO2  1.8E-07 2.4E-07 2.4E-07 2.3E-07 2.3E-07 2.3E-07 2.2E-07 2.3E-07 C2-C4  1.3E-07 1.8E-07 1.1E-07 1.0E-07 1.0E-07 1.1E-07 1.4E-07 1.5E-07 C4-C8  4.7E-09 9.1E-09 1.1E-08 1.3E-08 1.4E-08 1.5E-08 1.4E-08 1.4E-08 C9-C12  1.6E-09 3.3E-09 5.9E-09 8.1E-09 1.0E-08 1.2E-08 1.2E-08 1.4E-08 C12+  0.E+00 2.0E-09 1.2E-08 2.4E-08 3.1E-08 4.1E-08 4.1E-08 5.2E-08          CO,TOF (S-1) 2.1E-04 4.7E-04 6.3E-04 7.0E-04 7.9E-04 8.6E-04 8.8E-04 9.7E-04 CH4  1.9E-04 2.5E-04 2.6E-04 2.6E-04 2.7E-04 2.8E-04 2.8E-04 3.0E-04 CO2  6.9E-05 8.9E-05 9.0E-05 8.8E-05 8.7E-05 8.6E-05 8.3E-05 8.7E-05 C2-C4 5.0E-05 7.0E-05 4.1E-05 3.8E-05 3.9E-05 4.0E-05 5.3E-05 5.7E-05 C4-C8  1.8E-06 3.5E-06 4.4E-06 4.8E-06 5.4E-06 5.6E-06 5.5E-06 5.3E-06    C9-C12 6.3E-07 1.3E-06 2.2E-06 3.1E-06 3.8E-06 4.5E-06 4.7E-06 5.2E-06 C12+ 0.0E+00 7.8E-07 4.5E-06 9.0E-06 1.2E-05 1.5E-05 1.6E-05 2.0E-05 C5+ 2.4E-06 5.5E-06 1.1E-05 1.7E-05 2.1E-05 2.5E-05 2.6E-05 3.0E-05             248 Table K.6. Experimental condition and summary of results of RUN20EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 1 2 3 4 5 6 TOS, h 15.25 24 24.5 23.5 25 25.25 Cumulative TOS, h 15.25 39.25 63.75 87.25 112.25 137.5        CO conv 26.1 45.5 45.0 42.3 40.3 38.3        Products distribution wt%       CH4 10.31 7.78 7.74 8.19 8.21 9.26 C2-C4 6.47 4.75 4.56 4.71 4.64 5.07 C5-C8 21.66 22.95 12.32 9.52 6.89 7.08 C9-C12 15.85 25.46 23.23 21.99 19.00 6.00 C12+ 39.07 37.34 49.70 53.00 56.62 57.80 CH4, mol% 8.71 6.58 6.38 6.74 6.97 7.58 CO2, mol% 2.29 2.59 2.13 1.65 1.38 1.23 CH4, C atom% 9.16 6.89 6.86 7.26 7.27 8.22 C5+ Selectivity 76.6 85.7 85.3 84.5 82.5 70.9        Alpha 0.87 0.85 0.86 0.87 0.88 0.85        CO, (mol/sec.g) 7.56E-07 1.32E-06 1.30E-06 1.23E-06 1.17E-06 1.11E-06 CH4  6.58E-08 8.67E-08 8.31E-08 8.26E-08 8.13E-08 8.41E-08 CO2  1.73E-08 3.41E-08 2.77E-08 2.03E-08 1.62E-08 1.36E-08 C2-C4  1.50E-08 1.93E-08 1.80E-08 1.75E-08 1.69E-08 1.69E-08 C4-C8  2.38E-08 4.36E-08 2.26E-08 1.64E-08 1.17E-08 7.33E-10 C9-C12  1.14E-08 3.14E-08 2.69E-08 2.38E-08 2.01E-08 1.91E-08 C12+  1.50E-08 2.61E-08 3.38E-08 3.46E-08 3.66E-08 3.36E-08        yCO 2.002E-01 1.555E-01 1.570E-01 1.634E-01 1.682E-01 1.728E-01 yCO2 1.617E-03 3.360E-03 2.731E-03 1.981E-03 1.572E-03 1.317E-03 yH2 3.463E-01 2.558E-01 2.581E-01 2.706E-01 2.801E-01 2.895E-01 yH2O 6.911E-02 1.266E-01 1.255E-01 1.179E-01 1.120E-01 1.061E-01 YCH2 7.072E-02 1.299E-01 1.282E-01 1.199E-01 1.135E-01 1.074E-01        PH2 103.90 76.73 77.43 81.17 84.04 86.84 PCO 60.05 46.65 47.09 49.01 50.46 51.85 PCO2 0.49 1.01 0.82 0.59 0.47 0.40 PH2O 20.73 37.97 37.64 35.37 33.59 31.83 PCH2 21.2 39.0 38.5 36.0 34.1 32.2 Overall mass balance, % -5.3 1.6 2.6 2.6 2.1 3.0 Overall carbon balance 0.7 0.9 2.2 2.3 1.1 2.5    249 Day 1 2 3 4 5 6 TOS, h 15.25 24 24.5 23.5 25 25.25 EXP Cumulative TOS, h 15.25 39.25 63.75 87.25 112.25 137.5        PH2O/PH2 0.20 0.49 0.49 0.44 0.40 0.37        CO, mol/sec.g 5.040E-06 8.788E-06 8.680E-06 8.171E-06 7.780E-06 7.399E-06 CH4  4.388E-07 5.779E-07 5.539E-07 5.507E-07 5.423E-07 5.608E-07 CO2  1.152E-07 2.272E-07 1.849E-07 1.350E-07 1.077E-07 9.076E-08 C2-C4  1.001E-07 1.287E-07 1.203E-07 1.168E-07 1.127E-07 1.130E-07 C4-C8  1.588E-07 2.905E-07 1.509E-07 1.094E-07 7.795E-08 4.885E-09 C9-C12  7.588E-08 2.090E-07 1.797E-07 1.589E-07 1.343E-07 1.274E-07 C12+  1.002E-07 1.742E-07 2.252E-07 2.307E-07 2.443E-07 2.238E-07        CO,TOF (S-1) 5.38E-03 9.38E-03 9.26E-03 8.72E-03 8.30E-03 7.89E-03 CH4  4.68E-04 6.17E-04 5.91E-04 5.87E-04 5.79E-04 5.98E-04 CO2  1.23E-04 2.42E-04 1.97E-04 1.44E-04 1.15E-04 9.68E-05 C2-C4 1.07E-04 1.37E-04 1.28E-04 1.25E-04 1.20E-04 1.21E-04 C4-C8  1.69E-04 3.10E-04 1.61E-04 1.17E-04 8.32E-05 5.21E-06    C9-C12 8.09E-05 2.23E-04 1.92E-04 1.70E-04 1.43E-04 1.36E-04 C12+ 1.07E-04 1.86E-04 2.40E-04 2.46E-04 2.61E-04 2.39E-04 C5+ 3.57E-04 7.19E-04 5.93E-04 5.32E-04 4.87E-04 3.80E-04                        250 Table K.7. Experimental condition and summary of results for RUN21EXP1, with 5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.01 mol/ h.g  Day 1 2 3 4 5 6 7 8 TOS, h 17.5 26 24 22 25.5 23.5 24.5 22 Cumulative TOS, h 17.5 43.5 67.5 89.5 115 138.5 163 185          CO conv 9.7 11.4 13.0 14.1 16.6 18.6 19.8 19.9          Products distribution wt%         CH4 21.85 22.46 21.56 21.38 19.07 18.28 17.22 17.53 C2-C4 18.93 10.21 9.54 9.91 8.34 7.95 7.51 7.66 C5-C8 23.30 9.51 11.17 12.86 9.09 10.67 8.40 8.20 C9-C12 11.33 18.26 17.57 15.68 16.39 18.99 18.15 17.65 C12+ 24.58 39.56 40.17 40.17 47.04 43.83 48.46 48.65 CH4, mol% 20.21 18.54 17.68 17.34 15.82 14.93 14.33 2.98 CO2, mol% 10.91 9.23 7.11 5.83 4.38 3.60 3.14 2.98 CH4, C atom% 9.16 20.32 19.47 19.31 17.16 16.43 15.46 15.74 C5+ Selectivity 59.2 67.3 68.9 68.7 72.5 73.5 75.0 74.5          Alpha 0.83 0.83 0.79 0.79 0.82 0.82 0.83 0.82          CO, (mol/sec.g) 6.4E-08 7.6E-08 8.7E-08 9.4E-08 1.1E-07 1.2E-07 1.3E-07 1.3E-07 CH4  1.3E-08 1.4E-08 1.5E-08 1.6E-08 1.8E-08 1.8E-08 1.9E-08 1.9E-08 CO2  7.0E-09 7.0E-09 6.2E-09 5.5E-09 4.9E-09 4.5E-09 4.1E-09 4.0E-09 C2-C4  5.1E-09 2.4E-09 2.4E-09 2.7E-09 2.8E-09 2.9E-09 3.0E-09 3.1E-09 C4-C8  2.3E-09 1.0E-09 1.4E-09 1.8E-09 1.5E-09 1.9E-09 1.6E-09 1.6E-09 C9-C12  7.6E-10 1.2E-09 1.3E-09 1.3E-09 1.6E-09 2.1E-09 2.1E-09 2.1E-09 C12+  8.3E-10 1.7E-09 2.0E-09 2.1E-09 2.8E-09 2.9E-09 3.5E-09 3.6E-09          yCO 0.220 0.216 0.213 0.211 0.206 0.202 0.200 0.200 yCO2 0.003 0.003 0.002 0.002 0.002 0.002 0.002 0.001 yH2 0.447 0.440 0.434 0.430 0.420 0.412 0.407 0.407 yH2O 0.021 0.025 0.030 0.033 0.039 0.045 0.048 0.048 YCH2 0.023 0.028 0.032 0.035 0.041 0.046 0.049 0.050          PH2 134.14 132.14 130.29 128.90 125.99 123.65 122.18 121.99 PCO 65.87 64.86 63.98 63.32 61.89 60.74 60.02 59.94 PCO2 0.77 0.77 0.68 0.61 0.54 0.50 0.46 0.44 PH2O 6.27 7.59 8.86 9.83 11.79 13.35 14.35 14.48 PCH2 7.04 8.36 9.54 10.43 12.33 13.85 14.81 14.93 Overall mass balance, % -8.23 0.76 1.92 1.44 -1.38 -1.04 -0.55 -0.12 overall carbon balance,% -1.21 -0.06 0.27 0.62 0.57 1.03 0.82 0.80             251 Day 1 2 3 4 5 6 7 8 TOS, h 17.5 26 24 22 25.5 23.5 24.5 22 Cumulative TOS, h 17.5 43.5 67.5 89.5 115 138.5 163 185 PH2O/PH2 0.05 0.06 0.07 0.08 0.09 0.11 0.12 0.12          CO, mol/sec.g 1.3E-06 1.5E-06 1.7E-06 1.9E-06 2.2E-06 2.5E-06 2.6E-06 2.7E-06 CH4  2.6E-07 2.8E-07 3.1E-07 3.3E-07 3.5E-07 3.7E-07 3.8E-07 3.9E-07 CO2  1.4E-07 1.4E-07 1.2E-07 1.1E-07 9.7E-08 8.9E-08 8.3E-08 7.9E-08 C2-C4  1.0E-07 4.8E-08 4.8E-08 5.4E-08 5.6E-08 5.8E-08 6.0E-08 6.2E-08 C4-C8  4.6E-08 2.1E-08 2.9E-08 3.5E-08 3.0E-08 3.8E-08 3.3E-08 3.2E-08 C9-C12  1.5E-08 2.5E-08 2.7E-08 2.6E-08 3.2E-08 4.15E-08 4.3E-08 4.2E-08 C12+  1.7E-08 3.3E-08 4.0E-08 4.3E-08 5.7E-08 5.83E-08 6.0E-08 7.2E-08          CO,TOF (S-1) 4.9E-04 5.8E-04 6.6E-04 7.2E-04 8.4E-04 9.4E-04 1.0E-03 1.0E-03 CH4  9.9E-05 1.1E-04 1.2E-04 1.2E-04 1.3E-04 1.4E-04 1.4E-04 1.5E-04 CO2  5.3E-05 5.3E-05 4.7E-05 4.2E-05 3.7E-05 3.4E-05 3.1E-05 3.0E-05 C2-C4 3.9E-05 1.8E-05 1.9E-05 2.1E-05 2.1E-05 2.2E-05 2.3E-05 2.3E-05 C4-C8  1.8E-05 7.9E-06 1.1E-05 1.3E-05 1.1E-05 1.4E-05 1.2E-05 1.2E-05    C9-C12 5.8E-06 9.4E-06 1.0E-05 9.8E-06 1.2E-05 1.6E-05 1.6E-05 1.6E-05 C12+ 6.3E-06 1.3E-05 1.5E-05 1.6E-05 2.1E-05 2.2E-05 2.6E-05 2.7E-05 C5+ 3.0E-05 3.0E-05 3.6E-05 3.9E-05 4.5E-05 5.2E-05 5.5E-05 5.5E-05                           252 Table K.8. Experimental condition and summary of results for RUN22EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.08 mol/ h.g  Day 1 2 3 4 5 6 7 TOS, h 19 26 22 24 25.45 24.15 22 Cumulative TOS, h 19 45 67 91 116.9 141.05 163.05         CO conv 25.1 36.9 33.2 32.3 30.4 28.2 27.6         Products distribution wt%        CH4 9.61 8.56 9.43 10.07 10.36 10.28 10.51 C2-C4 10.56 5.96 5.74 5.91 6.11 5.95 6.06 C5-C8 13.23 12.16 8.19 6.80 5.87 4.55 4.67 C9-C12 18.29 25.63 24.76 20.30 18.86 17.34 16.24 C12+ 48.32 46.33 47.59 51.64 52.74 57.16 55.86 CH4, mol% 8.47 7.26 7.97 8.55 8.70 8.77 8.94 CO2, mol% 0.83 0.76 0.62 0.59 0.61 0.63 0.63 CH4, C atom% 8.56 7.59 8.37 8.95 9.21 9.14 9.35 C5+ Selectivity 79.8 84.1 80.5 78.7 77.5 79.0 76.8         Alpha 0.83 0.87 0.89 0.90 0.91 0.90 0.91         CO, (mol/sec.g) 1.31E-06 1.93E-06 1.73E-06 1.68E-06 1.59E-06 1.47E-06 1.44E-06 CH4  1.11E-07 1.40E-07 1.38E-07 1.44E-07 1.38E-07 1.29E-07 1.29E-07 CO2  1.09E-08 1.47E-08 1.08E-08 9.96E-09 9.75E-09 9.27E-09 9.09E-09 C2-C4  5.36E-08 3.63E-08 3.06E-08 3.07E-08 2.97E-08 2.73E-08 2.71E-08 C4-C8  2.56E-08 3.37E-08 2.05E-08 1.68E-08 1.35E-08 9.96E-09 9.98E-09 C9-C12  2.35E-08 4.56E-08 3.88E-08 3.10E-08 2.68E-08 2.30E-08 2.11E-08 C12+  3.38E-08 4.80E-08 4.72E-08 4.91E-08 4.72E-08 4.74E-08 4.54E-08         yCO 0.197 0.172 0.180 0.182 0.186 0.191 0.192 yCO2 0.001 0.001 0.001 0.001 0.001 0.000 0.000 yH2 0.363 0.311 0.327 0.332 0.340 0.350 0.352 yH2O 0.066 0.100 0.089 0.086 0.081 0.075 0.073 YCH2 0.066 0.101 0.090 0.087 0.081 0.075 0.073         PH2 108.9 93.2 98.2 99.5 101.9 104.9 105.7 PCO 59.2 51.5 54.0 54.6 55.8 57.3 57.7 PCO2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 PH2O 19.7 29.9 26.7 25.9 24.3 22.4 21.9 PCH2 19.9 30.2 26.9 26.0 24.4 22.5 22.0     253 Day 1 2 3 4 5 6 7 TOS, h 19 26 22 24 25.45 24.15 22 Cumulative TOS, h 19 45 67 91 116.9 141.05 163.05 Overall mass balance, % 1.6 3.2 2.4 2.6 1.5 1.0 3.3 overall carbon balance,% 0.1 1.3 1.4 1.2 1.5 0.9 1.0         PH2O/PH2 0.18 0.32 0.27 0.26 0.24 0.21 0.21         CO, mol/sec.g 8.75E-06 1.28E-05 1.16E-05 1.12E-05 1.06E-05 9.81E-06 9.61E-06 CH4  7.41E-07 9.33E-07 9.21E-07 9.60E-07 9.22E-07 8.61E-07 8.59E-07 CO2  7.24E-08 9.78E-08 7.18E-08 6.64E-08 6.50E-08 6.18E-08 6.06E-08 C2-C4  3.58E-07 2.42E-07 2.04E-07 2.05E-07 1.98E-07 1.82E-07 1.81E-07 C4-C8  1.71E-07 2.25E-07 1.37E-07 1.12E-07 9.02E-08 6.64E-08 6.66E-08 C9-C12  1.57E-07 3.04E-07 2.59E-07 2.07E-07 1.79E-07 1.54E-07 1.41E-07 C12+  2.25E-07 3.20E-07 3.15E-07 3.27E-07 3.15E-07 3.16E-07 3.02E-07         CO,TOF(S-1) 9.33E-03 1.37E-02 1.23E-02 1.20E-02 1.13E-02 1.05E-02 1.02E-02 CH4  7.90E-04 9.96E-04 9.83E-04 1.02E-03 9.84E-04 9.18E-04 9.16E-04 CO2  7.73E-05 1.04E-04 7.66E-05 7.08E-05 6.94E-05 6.60E-05 6.46E-05 C2-C4 3.82E-04 2.58E-04 2.18E-04 2.19E-04 2.11E-04 1.94E-04 1.93E-04 C4-C8  1.82E-04 2.40E-04 1.46E-04 1.19E-04 9.62E-05 7.08E-05 7.10E-05    C9-C12 1.67E-04 3.24E-04 2.76E-04 2.20E-04 1.91E-04 1.64E-04 1.50E-04 C12+ 2.41E-04 3.41E-04 3.36E-04 3.49E-04 3.36E-04 3.37E-04 3.23E-04 C5+ 5.90E-04 9.05E-04 7.58E-04 6.89E-04 6.23E-04 5.72E-04 5.44E-04                       254 Table K.9. Experimental condition and summary of results for RUN24EXP1, with 20Co/Al2O3(0.6) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.18 mol/ h.g  Day 1 2 3 4 5 TOS, h 20 23 25.5 25 24 Cumulative TOS, h 20 43 68.5 93.5 117.5       CO conv 26.2 28.8 28.3 27.7 26.6       Products distribution wt%      CH4 8.91 9.23 9.43 9.52 9.82 C2-C4 4.94 5.13 5.21 5.32 5.44 C5-C8 42.85 4.77 4.99 4.16 4.66 C9-C12 14.53 21.58 20.26 19.43 16.39 C12+ 28.78 59.29 60.11 61.56 59.11 CH4, mol% 7.60 7.77 7.93 8.06 8.39 CO2, mol% 0.66 0.58 0.58 0.58 0.60 CH4, C atom% 7.90 8.19 8.37 8.45 8.72 C5+ Selectivity 86.2 85.6 85.4 85.2 80.2       Alpha 0.83 0.78 0.75 0.73 0.71       CO, (mol/sec.g) 3.15E-06 3.47E-06 3.41E-06 3.33837E-06 3.20165E-06 CH4  2.39E-07 2.70E-07 2.70E-07 2.69E-07 2.68E-07 CO2  2.09E-08 2.01E-08 1.97E-08 9.96E-09 1.91E-08 C2-C4  4.91E-08 5.38E-08 5.32E-08 5.39E-08 5.34E-08 C4-C8  2.56E-08 2.45E-08 2.51E-08 2.08E-08 2.24E-08 C9-C12  4.45E-08 6.61E-08 5.98E-08 5.64E-08 5.92E-08 C12+  5.71E-08 1.29E-07 1.31E-07 1.34E-07 1.263E-07       yCO 0.18499 0.17949 0.18059 0.18181 0.18413 yCO2 0.0004 0.0004 0.0004 0.00041 0.00039 yH2 0.37997 0.36902 0.37120 0.37359 0.37822 yH2O 0.06508 0.07228 0.07086 0.06929 0.06625 YCH2 0.06551 0.072710 0.07127 0.06969 0.06665  113.99 110.71 111.36 112.08 113.47 PH2 55.50 53.85 54.18 54.54 55.24 PCO 0.13 0.13 0.12 0.12 0.12    255 Day 1 2 3 4 5 TOS, h 20 23 25.5 25 24 Cumulative TOS, h 20 43 68.5 93.5 117.5 PCO2 19.53 21.69 21.26 20.79 19.88 PH2O 19.66 21.81 21.38 20.91 20.00 PCH2 1.57 3.20 2.39 2.60 1.54 Overall mass balance, % 0.83 1.29 1.31 1.13 0.86 overall carbon balance,%       0.17 0.20 0.19 0.19 0.18 PH2O/PH2       1.575E-05 1.736E-05 1.704E-05 1.669E-05 1.601E-05 CO, mol/sec.g 1.197E-06 1.350E-06 1.352E-06 1.345E-06 1.343E-06 CH4  1.047E-07 1.007E-07 9.872E-08 4.978E-08 9.552E-08 CO2  2.459E-07 2.690E-07 2.664E-07 2.696E-07 2.671E-07 C2-C4  1.281E-07 1.226E-07 1.257E-07 1.043E-07 1.121E-07 C4-C8  2.224E-07 3.307E-07 2.995E-07 2.820E-07 2.962E-07 C9-C12  2.856E-07 6.441E-07 6.533E-07 6.719E-07 6.319E-07 C12+        3.07E-02 3.38E-02 3.32E-02 3.25E-02 3.12E-02 CO,TOF×(S-1) 2.33E-03 2.63E-03 2.63E-03 2.62E-03 2.62E-03 CH4  2.04E-04 1.96E-04 1.92E-04 9.70E-05 1.86E-04 CO2  4.79E-04 5.24E-04 5.19E-04 5.25E-04 5.20E-04 C2-C4 2.49E-04 2.39E-04 2.45E-04 2.03E-04 2.18E-04 C4-C8  4.33E-04 6.44E-04 5.83E-04 5.49E-04 5.77E-04    C9-C12 5.56E-04 1.25E-03 1.27E-03 1.31E-03 1.23E-03 C12+ 1.24E-03 2.14E-03 2.10E-03 2.06E-03 2.03E-03                256 Table K.10. Experimental condition and summary of results for RUN25EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.16 mol/ h.g  Day 1 2 3 4 5 6 TOS, h 19.75 23.15 24.15 25.15 24 21 Cumulative TOS, h 19.75 42.9 67.05 92.2 116.2 137.2        CO conv 13.2 23.0 26.0 25.3 24.7 24.3        Products distribution wt%       CH4 13.57 11.31 10.81 11.18 11.50 10.99 C2-C4 11.63 7.33 6.86 6.78 6.96 6.11 C5-C8 27.33 25.06 23.29 16.63 16.48 5.01 C9-C12 17.53 21.55 22.48 17.98 18.70 19.83 C12+ 29.94 34.76 36.24 45.66 44.63 58.06 CH4, mol% 10.29 8.72 8.65 9.01 9.30 8.41 CO2, mol% 1.18 0.81 0.65 0.65 0.66 0.60 CH4, C atom% 12.15 10.07 9.62 9.95 8.72 10.84 C5+ Selectivity 74.8 81.4 82.0 80.3 79.8 82.9        Alpha 0.75 0.77 0.83 0.86 0.86 0.86        CO, (mol/sec.g) 3.1E-06 3.5E-06 3.4E-06 3.3E-06 3.2E-06 3.2E-06 CH4  2.4E-07 2.7E-07 2.7E-07 2.7E-07 2.7E-07 2.7E-07 CO2  2.1E-08 2.0E-08 2.0E-08 1.9E-08 1.9E-08 1.9E-08 C2-C4  4.9E-08 5.4E-08 5.3E-08 5.4E-08 5.3E-08 5.3E-08 C4-C8  2.0E-07 2.4E-08 2.5E-08 2.1E-08 2.2E-08 2.1E-08 C9-C12  4.4E-08 6.6E-08 6.0E-08 5.6E-08 5.9E-08 5.0E-08 C12+  5.7E-08 1.3E-07 1.3E-07 1.3E-07 1.3E-07 1.1E-07        yCO 0.185 0.179 0.181 0.182 0.184 0.185 yCO2 0.000 0.000 0.000 0.000 0.000 0.000 yH2 0.380 0.369 0.371 0.374 0.378 0.379 yH2O 0.065 0.072 0.071 0.069 0.066 0.066 YCH2 0.066 0.073 0.071 0.070 0.067 0.066        PH2 113.99 110.71 111.36 112.08 113.47 113.70 PCO 55.50 53.85 54.18 54.54 55.24 55.36 PCO2 0.13 0.13 0.12 0.12 0.12 0.12 PH2O 19.53 21.69 21.26 20.79 19.88 19.73 PCH2 19.66 21.81 21.38 20.91 20.00 19.84    257 Day 1 2 3 4 5 6 TOS, h 19.75 23.15 24.15 25.15 24 21 Cumulative TOS, h 19.75 42.9 67.05 92.2 116.2 137.2 Overall mass balance, % 1.57 3.20 2.39 2.60 1.54 1.04 overall carbon balance,% 1.87 2.89 2.45 2.22 2.12 2.76        PH2O/PH2 0.17 0.20 0.19 0.19 0.18 0.17        CO, mol/sec.g 2.1E-05 2.3E-05 2.3E-05 2.2E-05 2.1E-05 2.1E-05 CH4  1.6E-06 1.8E-06 1.8E-06 1.8E-06 1.8E-06 1.8E-06 CO2  1.4E-07 1.3E-07 1.3E-07 1.3E-07 1.3E-07 1.2E-07 C2-C4  3.3E-07 3.6E-07 3.5E-07 3.6E-07 3.6E-07 3.5E-07 C4-C8  1.3E-06 1.6E-07 1.7E-07 1.4E-07 1.5E-07 1.4E-07 C9-C12  3.0E-07 4.4E-07 4.0E-07 3.8E-07 3.9E-07 3.3E-07 C12+  3.8E-07 8.6E-07 8.7E-07 9.0E-07 8.4E-07 7.4E-07        CO,TOF(S-1) 2.2E-02 2.5E-02 2.4E-02 2.4E-02 2.3E-02 2.3E-02 CH4  1.7E-03 1.9E-03 1.9E-03 1.9E-03 1.9E-03 1.9E-03 CO2  1.5E-04 1.4E-04 1.4E-04 1.4E-04 1.4E-04 1.3E-04 C2-C4 3.5E-04 3.8E-04 3.8E-04 3.8E-04 3.8E-04 3.8E-04 C4-C8  1.4E-03 1.7E-04 1.8E-04 1.5E-04 1.6E-04 1.5E-04    C9-C12 3.2E-04 4.7E-04 4.3E-04 4.0E-04 4.2E-04 3.5E-04 C5+ 4.1E-04 9.2E-04 9.3E-04 9.6E-04 9.0E-04 7.9E-04                    258 Table K.11. Experimental condition and summary of results for RUN26EXP1, with 5Co/Al2O3(0.9) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.01 mol/ h.g  Day 1 2 3 4 5 6 7 8 TOS, h 19.75 28.25 20.75 24.75 23.75 23.5 24 23 Cumulative TOS, h 19.75 48 68.75 93.5 117.25 140.75 164.75 187.75          CO conv 11.35 14.63 17.22 19.18 20.57 21.51 22.35 22.98          Products distribution wt%         CH4 20.92 18.68 18.05 17.22 17.46 16.58 17.30 16.98 C2-C4 9.69 8.92 8.68 8.31 8.58 7.82 8.51 8.38 C5-C8 17.96 6.79 9.30 7.99 8.33 10.20 7.77 7.95 C9-C12 20.21 20.59 19.39 20.53 18.66 19.01 17.45 17.94 C12+ 31.21 45.02 44.53 45.95 46.56 44.81 47.98 47.81 CH4, mol% 16.61 15.08 14.38 13.96 13.93 13.92 13.78 13.68 CO2, mol% 7.02 5.45 4.06 3.30 2.84 2.54 2.30 2.13 CH4, C atom% 18.88 16.80 16.22 15.46 15.68 14.87 15.53 15.23 C5+ Selectivity 69.4 72.4 73.2 74.5 73.6 74.0 73.2 73.7          Alpha 0.82 0.81 0.81 0.80 0.84 0.87 0.86 0.86          CO, mol/sec.g 7.5E-08 9.7E-08 1.1E-07 1.3E-07 1.4E-07 1.4E-07 1.5E-07 1.5E-07 CH4  1.2E-08 1.5E-08 1.6E-08 1.8E-08 1.9E-08 2.0E-08 2.0E-08 2.1E-08 CO2  5.3E-09 5.3E-09 4.6E-09 4.2E-09 3.9E-09 3.6E-09 3.4E-09 3.2E-09 C2-C4  2.1E-09 2.5E-09 2.8E-09 3.1E-09 3.3E-09 3.3E-09 3.6E-09 3.7E-09 C4-C8  1.8E-09 9.2E-10 1.5E-09 1.4E-09 1.6E-09 2.1E-09 1.6E-09 1.7E-09 C9-C12  1.35E-09 1.7E-09 1.9E-09 2.3E-09 2.2E-09 2.5E-09 2.2E-09 2.4E-09 C12+  1.1E-09 2.5E-09 2.8E-09 3.3E-09 3.5E-09 3.6E-09 3.8E-09 4.0E-09          yCO 0.217 0.211 0.206 0.202 0.199 0.198 0.196 0.195 yCO2 0.002 0.002 0.002 0.002 0.001 0.001 0.001 0.001 yH2 0.434 0.422 0.411 0.404 0.398 0.394 0.391 0.388 yH2O 0.026 0.034 0.041 0.046 0.050 0.053 0.055 0.057 YCH2 0.028 0.036 0.043 0.048 0.052 0.054 0.056 0.058          PH2 130.33 126.51 123.42 121.05 119.36 118.21 117.17 116.39    259 Day 1 2 3 4 5 6 7 8 TOS, h 19.75 28.25 20.75 24.75 23.75 23.5 24 23 Cumulative TOS, h 19.75 48 68.75 93.5 117.25 140.75 164.75 187.75 PCO 65.24 63.33 61.83 60.67 59.84 59.28 58.77 58.39 PCO2 0.59 0.59 0.52 0.47 0.44 0.41 0.39 0.37 PH2O 7.77 10.26 12.34 13.92 15.06 15.83 16.53 17.05 PCH2 8.4 10.9 12.9 14.4 15.5 16.2 16.9 17.4 Overall mass balance, % -3.0 3.0 2.2 1.8 0.6 -1.5 1.3 0.7 overall carbon balance,% 0.6 0.7 1.3 1.2 1.7 0.8 2.0 1.9          PH2O/PH2 0.06 0.08 0.10 0.11 0.13 0.13 0.14 0.15          CO, mol/sec.g 1.5E-06 1.9E-06 2.3E-06 2.5E-06 2.7E-06 2.8E-06 3.0E-06 3.0E-06 CH4  2.5E-07 2.9E-07 3.3E-07 3.5E-07 3.8E-07 4.0E-07 4.1E-07 4.2E-07 CO2  1.0E-07 1.0E-07 9.3E-08 8.4E-08 7.7E-08 7.2E-08 6.8E-08 6.5E-08 C2-C4  4.2E-08 5.0E-08 5.6E-08 6.1E-08 6.6E-08 6.7E-08 7.1E-08 7.3E-08 C4-C8  3.7E-08 1.8E-08 3.0E-08 2.9E-08 3.2E-08 4.3E-08 3.2E-08 3.4E-08 C9-C12  2.7E-08 3.4E-08 4.0E-08 4.5E-08 4.3E-08 4.9E-08 4.4E-08 4.7E-08 C12+  2.2E-08 5.0E-08 5.7E-08 6.7E-08 7.0E-08 7.1E-08 7.7E-08 8.0E-08          CO,TOF (S-1) 7.2E-04 9.2E-04 1.1E-03 1.2E-03 1.3E-03 1.4E-03 1.4E-03 1.4E-03 CH4  1.2E-04 1.4E-04 1.6E-04 1.7E-04 1.8E-04 1.9E-04 1.9E-04 2.0E-04 CO2  5.0E-05 5.0E-05 4.4E-05 4.0E-05 3.7E-05 3.4E-05 3.2E-05 3.1E-05 C2-C4 2.0E-05 2.4E-05 2.7E-05 2.9E-05 3.2E-05 3.2E-05 3.4E-05 3.5E-05 C4-C8  1.7E-05 8.7E-06 1.4E-05 1.4E-05 1.5E-05 2.0E-05 1.5E-05 1.6E-05 C9-C12 1.3E-05 1.6E-05 1.8E-05 2.2E-05 2.1E-05 2.3E-05 2.1E-05 2.2E-05 C12+ 1.1E-05 2.4E-05 2.7E-05 3.2E-05 3.3E-05 3.4E-05 3.7E-05 3.8E-05 C5+ 4.1E-05 4.9E-05 5.9E-05 6.7E-05 6.9E-05 7.8E-05 7.3E-05 7.7E-05            260 Table K.12. Experimental condition and summary of results for RUN27EXP1, with 5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=230 °C, P=20 bar and H2/CO=2, GHSV=0.02 mol/ h.g  Day 1 2 3 4 5 6 7 8 TOS, h 24 23.75 24 24 24 24.25 24.5 23.15 Cumulative TOS, h 24 47.75 71.75 95.75 119.75 144 168.5 191.65           CO conv 6.65 9.32 11.37 13.66 14.81 15.72 16.48 16.85           Products distribution wt%          CH4 18.71 24.65 23.66 20.87 14.60 19.40 19.13 20.05 C2-C4 43.07 13.64 8.18 7.87 7.10 11.13 9.86 9.26 C5-C8 4.48 8.27 8.05 7.90 6.56 7.94 7.83 8.04 C9-C12 9.52 21.10 20.62 20.35 19.73 18.55 17.99 17.47 C12+ 24.22 32.35 39.50 43.01 52.01 42.98 45.19 45.19 CH4, mol% 21.16 19.08 17.55 15.81 13.93 15.41 15.29 15.47 CO2, mol% 17.14 12.33 8.91 6.47 2.84 4.57 4.03 3.72 CH4, C atom% 17.25 22.42 21.42 18.82 13.07 17.50 17.24 18.08 C5+ Selectivity 38.2 61.7 68.2 71.3 78.3 69.5 71.0 70.7    64.9       Alpha 0.74 0.76 0.75 0.77 0.74 0.73 0.74 0.75           CO, mol/sec.g 4.4E-08 6.2E-08 7.6E-08 9.1E-08 9.9E-08 1.0E-07 1.1E-07 1.1E-07 CH4  9.4E-09 1.2E-08 1.3E-08 1.4E-08 1.5E-08 1.6E-08 1.7E-08 1.7E-08 CO2  7.6E-09 7.7E-09 6.7E-09 5.9E-09 5.3E-09 4.8E-09 4.4E-09 4.2E-09 C2-C4  1.1E-08 2.8E-09 1.6E-09 2.0E-09 3.3E-09 3.8E-09 3.5E-09 3.1E-09 C4-C8  4.0E-10 7.0E-10 8.0E-10 9.6E-10 1.2E-09 1.2E-09 1.2E-09 1.2E-09 C9-C12  5.1E-10 1.1E-09 1.2E-09 1.5E-09 2.2E-09 1.6E-09 1.7E-09 1.6E-09 C12+  8.5E-10 1.1E-09 1.6E-09 2.1E-09 3.9E-09 2.5E-09 2.8E-09 2.8E-09           yCO 2.2E-01 2.1E-01 2.1E-01 2.0E-01 2.0E-01 2.0E-01 2.0E-01 2.0E-01 yCO2 2.7E-03 2.7E-03 2.4E-03 2.1E-03 1.9E-03 1.7E-03 1.6E-03 1.5E-03 yH2 4.5E-01 4.5E-01 4.4E-01 4.3E-01 4.2E-01 4.2E-01 4.2E-01 4.2E-01 yH2O 1.3E-02 1.9E-02 2.4E-02 3.0E-02 3.3E-02 3.6E-02 3.8E-02 3.E-02 YCH2 1.5E-02 2.2E-02 2.7E-02 3.2E-02 3.5E-02 3.7E-02 3.9E-02 4.0E-02           PH2 136.62 133.72 131.41 128.81 127.48 126.43 125.54 125.11 PCO 65.32 63.85 62.73 61.46 60.82 60.31 59.88 59.67    261 Day 1 2 3 4 5 6 7 8 TOS, h 24 23.75 24 24 24 24.25 24.5 23.15 Cumulative TOS, h 24 47.75 71.75 95.75 119.75 144 168.5 191.65 PCO2 0.80 0.81 0.72 0.63 0.56 0.51 0.48 0.45 PH2O 3.86 5.75 7.33 9.10 10.01 10.74 11.34 11.65 PCH2 4.7 6.6 8.1 9.7 10.6 11.3 11.8 12.1 Overall mass balance, % -1.1 2.6 1.2 1.1 -0.3 1.9 1.2 0.8 overall carbon balance,% -2.6 0.2 1.0 1.3 -3.6 1.2 1.2 1.8           PH2O/PH2 0.03 0.04 0.06 0.07 0.08 0.08 0.09 0.09           CO, mol/sec.g 8.9E-07 1.2E-06 1.5E-06 1.8E-06 2.0E-06 2.1E-06 2.2E-06 2.2E-06 CH4  1.9E-07 2.4E-07 2.7E-07 2.9E-07 3.1E-07 3.2E-07 3.4E-07 3.5E-07 CO2  1.5E-07 1.5E-07 1.3E-07 1.2E-07 1.0E-07 9.6E-08 8.8E-08 8.3E-08 C2-C4  2.2E-07 5.7E-08 3.3E-08 3.9E-08 6.5E-08 7.7E-08 7.0E-08 6.1E-08 C4-C8  8.1E-09 1.4E-08 1.6E-08 1.9E-08 2.3E-08 2.3E-08 2.4E-08 2.5E-08 C9-C12  1.0E-08 2.2E-08 2.5E-08 3.E-08 4.4E-08 3.3E-08 3.4E-08 3.2E-08 C12+  1.7E-08 2.2E-08 3.2E-08 4.2E-08 7.7E-08 5.1E-08 5.6E-08 5.5E-08           CO,TOF (S-1) 7.2E-04 9.2E-04 1.1E-03 1.2E-03 1.3E-03 1.4E-03 1.4E-03 1.4E-03 CH4  1.2E-04 1.4E-04 1.6E-04 1.7E-04 1.8E-04 1.9E-04 1.9E-04 2.0E-04 CO2  5.0E-05 5.0E-05 4.4E-05 4.0E-05 3.7E-05 3.4E-05 3.2E-05 3.1E-05 C2-C4 2.0E-05 2.4E-05 2.7E-05 2.9E-05 3.2E-05 3.2E-05 3.4E-05 3.5E-05 C4-C8  1.7E-05 8.7E-06 1.4E-05 1.4E-05 1.5E-05 2.0E-05 1.5E-05 1.6E-05    C9-C12 1.3E-05 1.6E-05 1.8E-05 2.2E-05 2.1E-05 2.3E-05 2.1E-05 2.2E-05 C12+ 1.1E-05 2.4E-05 2.7E-05 3.2E-05 3.3E-05 3.4E-05 3.7E-05 3.8E-05 C5+ 4.1E-05 4.9E-05 5.9E-05 6.7E-05 6.9E-05 7.8E-05 7.3E-05 7.7E-05            262 Table K.13. Experimental condition and summary of results for RUN30EXP1, with 15Co/Al2O3(0.1) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.07 mol/ h.g  Day 1 2 3 4 5 6 7 TOS, h 24 23.25 23.75 24.75 21 26 22 Cumulative TOS, h 24 47.25 71 95.75 116.75 142.75 164.75         CO conv 15.0 20.6 27.9 39.7 35.4 32.8 30.9         Products distribution wt%        CH4 11.33 11.04 10.12 8.29 8.52 9.59 9.79 C2-C4 9.04 8.14 6.92 5.54 5.38 5.70 5.60 C5-C8 13.78 10.41 12.48 12.66 9.66 8.83 6.35 C9-C12 35.76 28.66 28.19 25.90 23.40 21.11 19.85 C12+ 30.09 41.75 41.54 43.58 48.94 51.24 54.68 CH4, mol% 9.53 9.10 8.33 6.90 7.04 7.87 8.00 CO2, mol% 1.29 0.92 0.80 0.87 0.65 0.48 0.46 CH4, C atom% 10.11 9.84 9.00 7.35 7.55 8.52 8.69 C5+ Selectivity 79.6 80.8 82.2 82.1 82.0 81.2 80.9         Alpha 0.83 0.87 0.89 0.90 0.91 0.90 0.91         CO, mol/sec.g 7.35E-07 1.01E-06 1.36E-06 1.94E-06 1.73E-06 1.60E-06 1.51E-06 CH4  7.00E-08 9.16E-08 1.14E-07 1.34E-07 1.22E-07 1.26E-07 1.21E-07 CO2  9.50E-09 9.29E-09 1.10E-08 1.69E-08 1.13E-08 7.72E-09 7.02E-09 C2-C4  2.39E-08 2.82E-08 3.17E-08 3.53E-08 3.02E-08 2.97E-08 2.72E-08 C4-C8  1.37E-08 1.47E-08 2.38E-08 3.46E-08 2.37E-08 1.99E-08 1.33E-08 C9-C12  2.44E-08 2.56E-08 3.43E-08 4.56E-08 3.60E-08 2.98E-08 2.62E-08 C12+  1.19E-08 2.44E-08 3.25E-08 4.74E-08 4.81E-08 4.61E-08 4.64E-08         yCO 0.208 0.197 0.182 0.157 0.166 0.172 0.176 yCO2 0.000 0.000 0.001 0.001 0.001 0.000 0.000 yH2 0.423 0.401 0.372 0.322 0.340 0.351 0.359 yH2O 0.036 0.051 0.070 0.102 0.091 0.083 0.078 YCH2 0.037 0.051 0.070 0.103 0.091 0.084 0.079         PH2 126.83 120.32 111.47 96.58 102.00 105.36 107.68 PCO 62.32 59.05 54.59 47.07 49.84 51.55 52.72 PCO2 0.14 0.14 0.17 0.27 0.18 0.12 0.11 PH2O 10.88 15.16 20.96 30.68 27.18 25.01 23.49    263 Day 1 2 3 4 5 6 7 TOS, h 24 23.25 23.75 24.75 21 26 22 Cumulative TOS, h 24 47.25 71 95.75 116.75 142.75 164.75 PCH2 11.02 15.31 21.13 30.95 27.35 25.13 23.60 Overall mass balance, % 1.41 3.17 1.82 2.41 1.89 0.93 2.83 overall carbon balance,% 0.66 1.35 1.83 2.08 2.19 2.34 2.32         PH2O/PH2 0.09 0.13 0.19 0.32 0.27 0.24 0.22         CO, mol/sec.g 4.90E-06 6.71E-06 9.10E-06 1.29E-05 1.16E-05 1.07E-05 1.01E-05 CH4  4.67E-07 6.11E-07 7.58E-07 8.92E-07 8.13E-07 8.41E-07 8.07E-07 CO2  6.33E-08 6.19E-08 7.31E-08 1.13E-07 7.54E-08 5.15E-08 4.68E-08 C2-C4  1.59E-07 1.88E-07 2.11E-07 2.35E-07 2.01E-07 1.98E-07 1.81E-07 C4-C8  9.13E-08 9.83E-08 1.59E-07 2.31E-07 1.58E-07 1.33E-07 8.88E-08 C9-C12  1.62E-07 1.70E-07 2.28E-07 3.04E-07 2.40E-07 1.98E-07 1.75E-07 C12+  7.96E-08 1.63E-07 2.17E-07 3.16E-07 3.21E-07 3.08E-07 3.09E-07         CO,TOF(S-1) 5.2E-03 7.2E-03 9.7E-03 1.4E-02 1.2E-02 1.1E-02 1.1E-02 CH4  5.0E-04 6.5E-04 8.1E-04 9.5E-04 8.7E-04 9.0E-04 8.6E-04 CO2  6.8E-05 6.6E-05 7.8E-05 1.2E-04 8.0E-05 5.5E-05 5.0E-05 C2-C4 1.7E-04 2.0E-04 2.3E-04 2.5E-04 2.1E-04 2.1E-04 1.9E-04 C4-C8  9.7E-05 1.0E-04 1.7E-04 2.5E-04 1.7E-04 1.4E-04 9.5E-05    C9-C12 1.7E-04 1.8E-04 2.4E-04 3.2E-04 2.6E-04 2.1E-04 1.9E-04 C12+ 8.5E-05 1.7E-04 2.3E-04 3.4E-04 3.4E-04 3.3E-04 3.3E-04 C5+ 3.6E-04 4.6E-04 6.4E-04 9.1E-04 7.7E-04 6.8E-04 6.1E-04                  264 Table K.14. Experimental condition and summary of results for RUN32EXP1, with 5Co/Al2O3(0.9) catalyst,  tested in CSTR reactor at T=245 °C, P=20 bar and H2/CO=2, GHSV=0.04 mol/ h.g  Day 2 3 4 5 6 7 8 9 TOS, h 23.75 23 24 25 23.25 22.75 29 24 Cumulative TOS, h 44 67 91 116 139.25 162 191 215          CO conv 15.97 18.94 19.36 19.90 20.24 20.59 21.05 22.52          Products distribution wt%         CH4 19.7 18.7 19.1 18.9 18.7 18.8 19.1 19.3 C2-C4 7.4 7.8 8.4 8.3 8.8 8.7 10.0 10.4 C5-C8 12.9 11.6 11.0 11.5 10.6 10.0 10.8 11.2 C9-C12 26.2 24.2 23.6 22.6 20.1 19.3 17.9 17.6 C12+ 33.8 37.6 37.9 38.7 41.9 43.2 42.2 41.6 CH4, mol% 14.9 14.3 14.5 14.3 14.3 14.3 14.7 14.9 CO2, mol% 1.7 1.3 1.2 1.1 1.0 1.0 1.1 1.1 CH4, C atom% 17.8 16.9 17.2 17.0 16.8 17.0 17.2 17.4 C5+ Selectivity 72.8 73.5 72.5 72.8 72.5 72.5 70.9 70.3          Alpha 0.81 0.82 0.81 0.80 0.79 0.82 0.82 0.81          CO, mol/sec.g 4.35E-07 5.2E-07 5.3E-07 5.4E-07 5.5E-07 5.6E-07 5.7E-07 6.1E-07 CH4  6.50E-08 7.4E-08 7.7E-08 7.8E-08 7.9E-08 8.0E-08 8.4E-08 9.1E-08 CO2  7.37E-09 6.7E-09 6.2E-09 5.9E-09 5.8E-09 5.8E-09 6.1E-09 6.7E-09 C2-C4  8.84E-09 1.1E-08 1.2E-08 1.2E-08 1.4E-08 1.4E-08 1.7E-08 1.9E-08 C4-C8  7.30E-09 7.9E-09 7.7E-09 8.0E-09 7.8E-09 7.5E-09 8.4E-09 9.3E-09 C9-C12  9.36E-09 1.0E-08 1.0E-08 1.0E-08 9.2E-09 8.9E-09 8.6E-09 9.1E-09 C12+  7.67E-09 1.0E-08 1.1E-08 1.1E-08 1.2E-08 1.2E-08 1.2E-08 1.3E-08          yCO 0.211 0.205 0.204 0.203 0.202 0.201 0.201 0.198 yCO2 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 yH2 0.420 0.409 0.407 0.405 0.403 0.402 0.400 0.394 yH2O 0.039 0.047 0.048 0.050 0.051 0.052 0.053 0.057 YCH2 0.040 0.048 0.049 0.050 0.051 0.052 0.053 0.057           PH2 126.14 122.57 122.06 121.40 120.99 120.57 120.01 118.22 PCO 63.21 61.44 61.19 60.87 60.66 60.45 60.17 59.27 PCO2 0.20 0.19 0.17 0.16 0.16 0.16 0.17 0.19 PH2O 11.81 14.17 14.52 14.96 15.23 15.51 15.87 17.03 PCH2 12.0 14.4 14.7 15.1 15.4 15.7 16.0 17.2    265 Day  2 3 4 5 6 7 8 9 TOS, h 23.75 23 24 25 23.25 22.75 29 24 Cumulative TOS, h 44 67 91 116 139.25 162 191 215 Overall mass balance, % 0.6 0.5 -1.0 -0.8 0.4 -1.6 -1.1 -1.8 overall carbon balance,% 2.3 2.7 2.7 2.9 2.8 3.0 2.9 3.0          PH2O/PH2 0.09 0.12 0.12 0.12 0.13 0.13 0.13 0.14                            CO, mol/sec.g 8.7E-06 1.0E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.1E-05 1.2E-05 CH4  1.3E-06 1.5E-06 1.5E-06 1.5E-06 1.6E-06 1.6E-06 1.7E-06 1.8E-06 CO2  1.5E-07 1.3E-07 1.2E-07 1.2E-07 1.2E-07 1.2E-07 1.2E-07 1.3E-07 C2-C4  1.8E-07 2.2E-07 2.4E-07 2.5E-07 2.8E-07 2.7E-07 3.5E-07 3.9E-07 C4-C8  1.5E-07 1.6E-07 1.5E-07 1.7E-07 1.6E-07 1.5E-07 1.7E-07 1.9E-07 C9-C12  1.9E-07 2.1E-07 2.1E-07 2.0E-07 1.8E-07 1.8E-07 1.7E-07 1.8E-07 C12+  1.5E-07 2.1E-07 2.1E-07 2.2E-07 2.4E-07 2.5E-07 2.5E-07 2.6E-07          CO, TOF ( S-1) 2.1E-03 4.1E-03 4.9E-03 5.0E-03 5.2E-03 5.3E-03 5.4E-03 5.5E-03 CH4  3.8E-04 6.2E-04 7.0E-04 7.3E-04 7.4E-04 7.5E-04 7.6E-04 8.0E-04 CO2  6.3E-05 7.0E-05 6.4E-05 5.9E-05 5.6E-05 5.5E-05 5.6E-05 5.8E-05 C2-C4 1.3E-04 8.4E-05 1.1E-04 1.2E-04 1.2E-04 1.3E-04 1.3E-04 1.7E-04 C4-C8  6.2E-05 7.0E-05 7.5E-05 7.4E-05 7.9E-05 7.5E-05 7.1E-05 8.0E-05 C9-C12 5.5E-05 8.9E-05 9.8E-05 9.9E-05 9.7E-05 8.7E-05 8.5E-05 8.2E-05 C12+ 5.5E-05 7.3E-05 9.9E-05 1.0E-04 1.0E-04 1.2E-04 1.2E-04 1.2E-04 C5+ 1.7E-04 2.3E-04 2.7E-04 2.7E-04 2.8E-04 2.8E-04 2.8E-04 2.8E-04            266 Appendix L: Experimental results for the Re-Co/Al2O3 catalysts Summary of conditions and experimental results for promoted catalysts.  Table L.1. Experimental condition and summary of results for RUN33EXP1, with 0.5Re-5Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.05 mol/ h.g  Day 2 3 4 5 6 7 8 TOS, h 23.5 24 24.5 24 21.5 26.75 22 Cumulative TOS, h 47.25 71.25 95.75 119.75 141.25 168 190         Products distribution wt%        CH4 13.7 15.1 15.6 16.1 15.9 16.9 17.6 C2-C4 9.9 11.1 11.5 11.6 11.4 12.1 12.3 C5-C8 16.1 49.2 14.1 37.8 13.2 13.0 11.9 C9-C12 27.6 11.5 22.4 13.9 19.8 19.5 20.0 C12+ 32.6 13.0 36.2 20.3 38.7 38.5 38.3 CH4, mol% 11.3 11.9 12.2 12.6 12.3 13.1 13.5 CO2, mol% 1.9 1.6 1.4 1.3 1.3 1.3 1.3 CH4, C atom% 12.2 13.5 14.0 14.5 14.3 15.2 15.8 C5+ Selectivity 76.3 73.7 72.7 71.9 71.7 71.0 70.1         Alpha 0.82 0.81 0.82 0.84 0.84 0.79 0.79         CO, mol/sec.g 9.7E-07 9.2E-07 8.8E-07 8.5E-07 8.6E-07 8.1E-07 7.8E-07 CH4  1.1E-07 1.1E-07 1.1E-07 1.1E-07 1.1E-07 1.1E-07 1.1E-07 CO2  1.9E-08 1.4E-08 1.2E-08 1.1E-08 1.1E-08 1.0E-08 9.8E-09 C2-C4  2.9E-08 2.8E-08 2.8E-08 2.7E-08 2.7E-08 2.7E-08 2.6E-08 C4-C8  2.2E-08 6.8E-08 1.7E-08 4.7E-08 1.6E-08 1.5E-08 1.3E-08 C9-C12  2.4E-08 9.2E-09 1.7E-08 1.0E-08 1.4E-08 1.3E-08 1.3E-08 C12+  1.9E-08 6.8E-09 1.7E-08 9.4E-09 1.8E-08 1.7E-08 1.6E-08         yCO 1.7E-01 1.7E-01 1.7E-01 1.7E-01 1.7E-01 1.8E-01 1.8E-01 yCO2 1.58E-03 1.2E-03 1.0E-03 9.7E-04 9.4E-04 8.7E-04 8.2E-04 yH2 3.7E-01 3.74E-01 3.8E-01 3.8E-01 3.8E-01 3.9E-01 3.9E-01 yH2O 8.1E-02 7.71E-02 7.3E-02 7.1E-02 7.2E-02 6.7E-02 6.5E-02 YCH2 8.2E-02 7.8E-02 7.4E-02 7.2E-02 7.3E-02 6.8E-02 6.6E-02         PH2 110.46 112.27 114.13 115.08 114.63 116.79 117.92 PCO 49.69 50.67 51.64 52.14 51.92 53.03 53.61 PCO2 0.47 0.37 0.32 0.29 0.28 0.26 0.25 PH2O 24.27 23.14 21.94 21.33 21.63 20.21 19.47 PCH2 24.7 23.5 22.3 21.6 21.9 20.5 19.7 Overall mass balance, % 2.1 0.6 0.9 0.2 1.0 0.9 -0.1 overall carbon balance,% 1.8 3.4 3.4 3.5 3.7 3.5 3.5    267 Day 2 3 4 5 6 7 8 TOS, h 23.5 24 24.5 24 21.5 26.75 22 Cumulative TOS, h 47.25 71.25 95.75 119.75 141.25 168 190 PH2O/PH2 0.22 0.21 0.19 0.19 0.19 0.17 0.17         CO, mol/sec.g 1.9E-05 1.8E-05 1.7E-05 1.7E-05 1.7E-05 1.6E-05 1.6E-05 CH4  2.2E-06 2.2E-06 2.1E-06 2.1E-06 2.1E-06 2.1E-06 2.1E-06 CO2  3.7E-07 2.9E-07 2.5E-07 2.3E-07 2.2E-07 2.1E-07 2.0E-07 C2-C4  5.8E-07 5.7E-07 5.6E-07 5.5E-07 5.4E-07 5.4E-07 5.3E-07 C4-C8  4.5E-07 1.3E-06 3.5E-07 9.4E-07 3.2E-07 3.0E-07 2.6E-07 C9-C12  4.8E-07 1.8E-07 3.3E-07 2.0E-07 2.9E-07 2.7E-07 2.6E-07 C12+  3.7E-07 1.3E-07 3.5E-07 1.9E-07 3.7E-07 3.4E-07 3.2E-07                 CO,TOF(S-1) 1.3E-02 8.6E-03 8.2E-03 7.8E-03 7.6E-03 7.7E-03 7.2E-03 CH4  1.0E-03 9.7E-04 9.7E-04 9.5E-04 9.5E-04 9.4E-04 9.4E-04 CO2  5.8E-04 1.6E-04 1.3E-04 1.1E-04 1.0E-04 9.9E-05 9.2E-05 C2-C4 3.7E-04 2.6E-04 2.5E-04 2.5E-04 2.4E-04 2.4E-04 2.4E-04 C4-C8  4.4E-04 2.0E-04 6.0E-04 1.5E-04 4.2E-04 1.4E-04 1.3E-04    C9-C12 3.9E-04 2.1E-04 8.1E-05 1.5E-04 9.0E-05 1.3E-04 1.2E-04 C12+ 1.6E-04 1.7E-04 6.0E-05 1.6E-04 8.3E-05 1.6E-04 1.5E-04 C5+ 9.9E-04 5.8E-04 7.4E-04 4.6E-04 5.9E-04 4.3E-04 4.0E-04               268 Table L.2. Experimental condition and summary of results for RUN34EXP1, with 0.3Re-3Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.05 mol/ h.g  Day 1 2 3 4 5 6 7 8 TOS, h 23.75 23.5 24 24.5 24 21.5 26.75 22 Cumulative TOS, h 23.75 47.25 71.25 95.75 119.75 141.25 168 190                       CO conv 31.77 29.39 26.70 24.78 23.38 22.55 21.57 20.38            Products distribution wt%           CH4 12.0 13.4 15.2 16.5 17.2 17.5 18.9 19.9 C2-C4 16.2 13.2 14.2 15.5 15.8 16.1 17.1 17.8 C5-C8 27.7 15.7 15.3 14.0 13.6 14.0 13.8 13.7 C9-C12 25.4 25.7 25.1 24.6 15.8 23.3 21.0 18.7 C12+ 18.7 31.9 30.2 29.4 21.0 29.1 29.2 29.9 CH4, mol% 9.7 10.4 11.7 12.6 13.1 13.4 14.2 14.8 CO2, mol% 1.9 1.6 1.4 1.3 1.3 1.2 1.3 1.3 CH4, Catom% 10.7 12.0 13.6 14.9 15.5 15.8 17.0 18.0 C5+ Selectivity 71.8 73.4 70.6 68.0 50.5 66.4 64.0 62.3            Alpha 0.77 0.78 0.78 0.78 0.76 0.75 0.74 0.75            CO, mol/sec.g 9.3E-07 8.6E-07 7.8E-07 7.3E-07 6.9E-07 6.6E-07 6.3E-07 6.0E-07 CH4  9.0E-08 9.0E-08 9.1E-08 9.1E-08 9.0E-08 8.8E-08 8.9E-08 8.E-08 CO2  1.7E-08 1.4E-08 1.1E-08 9.8E-09 8.8E-09 8.3E-09 7.9E-09 7.6E-09 C2-C4  4.8E-08 3.2E-08 3.0E-08 3.0E-08 2.9E-08 2.9E-08 2.9E-08 2.8E-08 C4-C8  3.6E-08 1.9E-08 1.7E-08 1.4E-08 1.3E-08 1.3E-08 1.2E-08 1.1E-08 C9-C12 2.1E-08 1.9E-08 1.6E-08 1.5E-08 9.0E-09 1.3E-08 1.1E-08 9.2E-09 C12+  9.1E-09 1.6E-08 1.3E-08 1.2E-08 9.9E-09 1.2E-08 9.9E-09 9.4E-09            yCO 1.7E-01 1.7E-01 1.8E-01 1.8E-01 1.9E-01 2.0E-01 1.9E-01 1.9E-01 yCO2 1.5E-03 1.2E-03 9.4E-04 8.1E-04 7.3E-04 6.8E-04 6.6E-04 6.3E-04 yH2 3.7E-01 3.8E-01 3.9E-01 4.0E-01 4.0E-01 4.1E-01 4.1E-01 4.1E-01 yH2O 7.8E-02 7.2E-02 6.5E-02 6.0E-02 5.6E-02 5.4E-02 5.2E-02 4.9E02 YCH2 7.9E-02 7.3E-02 6.6E-02 6.1E-02 5.7E-02 5.5E-02 5.2E-02 4.9E-02            PH2 110.97 113.79 116.97 119.22 120.84 121.80 122.94 124.30 PCO 50.92 52.40 54.05 55.22 56.06 56.55 57.14 57.83 PCO2 0.45 0.35 0.28 0.24 0.22 0.21 0.20 0.19 PH2O 23.27 21.47 19.41 17.94 16.89 16.26 15.51 14.62 PCH2 23.7 21.8 19.7 18.2 17.1 16.5 15.7 14.8 Overall mass balance, % 1.8 3.0 1.7 1.2 0.9 0.4 0.4 -0.2    269 Day 1 2 3 4 5 6 7 8 TOS, h 23.75 23.5 24 24.5 24 21.5 26.75 22 Cumulative TOS, h 23.75 47.25 71.25 95.75 119.75 141.25 168 190 overall carbon balance,% 2.5 3.3 3.4 3.5 3.3 3.2 3.4 3.3            PH2O/PH2 0.21 0.19 0.17 0.15 0.14 0.13 0.13 0.12                                CO, mol/sec.g 3.1E-05 2.9E-05 2.6E-05 2.4E-05 2.3E-05 2.2E-05 2.1E-05 2.0E-05 CH4  3.0E-06 3.0E-06 3.0E-06 3.0E-06 3.0E-06 2.9E-06 3.0E-06 2.9E-06 CO2  5.8E-07 4.6E-07 3.7E-07 3.3E-07 2.9E-07 2.8E-07 2.6E-07 2.5E-07 C2-C4  1.6E-06 1.1E-06 1.0E-06 1.0E-06 9.8E-07 9.6E-07 9.6E-07 9.4E-07 C4-C8  1.2E-06 6.3E-07 5.5E-07 4.6E-07 4.4E-07 4.3E-07 4.0E-07 3.7E-07 C9-C12  7.2E-07 6.2E-07 5.5E-07 4.9E-07 3.0E-07 4.3E-07 3.7E-07 3.1E-07 C12+  3.0E-07 5.2E-07 4.4E-07 4.0E-07 3.3E-07 3.5E-07 3.3E-07 3.1E-07            CO,TOF(S-1) 7.6E-03 7.0E-03 6.4E-03 5.9E-03 5.6E-03 5.4E-03 5.1E-03 4.9E-03 CH4  7.3E-04 7.3E-04 7.4E-04 7.4E-04 7.3E-04 7.2E-04 7.3E-04 7.2E-04 CO2  1.4E-04 1.1E-04 9.1E-05 7.9E-05 7.2E-05 6.7E-05 6.4E-05 6.2E-05 C2-C4 3.9E-04 2.6E-04 2.5E-04 2.5E-04 2.4E-04 2.3E-04 2.3E-04 2.3E-04 C4-C8  2.9E-04 1.5E-04 1.3E-04 1.1E-04 1.1E-04 1.1E-04 9.7E-05 9.1E-05    C9-C12 1.7E-04 1.5E-04 1.3E-04 1.2E-04 7.3E-05 1.0E-04 8.9E-05 7.5E-05 C12+ 7.4E-05 1.3E-04 1.1E-04 9.6E-05 8.0E-05 8.6E-05 8.1E-05 7.7E-05 C5+ 5.4E-04 4.3E-04 3.8E-04 3.3E-04 2.6E-04 3.0E-04 2.7E-04 2.4E-04             270 Table L.3. Experimental condition and summary of results for RUN35EXP1, with 1.2Re-12Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.05 mol/ h.g  Day 1 2 3 4 5 6 7 8 TOS, h 17 24 24 24 33.25 17.5 23.5 22 Cumulative TOS, h 17 41 65 89 122.25 139.75 163.25 185.25          CO conv 85.59 92.82 91.43 88.75 85.25 80.11 75.26 75.26          Products distribution wt%         CH4 27.0 25.0 21.2 18.0 15.8 13.7 13.6 12.7 C2-C4 11.2 11.0 11.0 9.8 9.2 8.3 8.3 8.1 C5-C8 21.9 16.8 10.5 12.2 10.9 10.4 10.5 9.8 C9-C12 20.1 31.3 32.4 31.2 29.5 29.3 26.7 26.5 C12+ 19.7 15.9 24.8 28.8 34.6 38.3 40.9 43.0 CH4, mol% 26.2 24.9 20.2 16.5 13.9 12.2 12.0 10.8 CO2, mol% 19.8 22.5 22.2 21.3 19.7 18.1 17.3 15.2 CH4, C atom% 24.6 22.7 19.2 16.2 14.1 12.2 12.1 11.3 C5+ Selectivity 61.8 64.0 67.7 72.2 75.1 78.0 78.1 79.2          Alpha 0.80 0.74 0.73 0.74 0.74 0.75 0.77 0.78          CO, mol/sec.g 2.8E-06 3.0E-06 3.0E-06 2.9E-06 2.8E-06 2.7E-06 2.6E-06 2.4E-06 CH4  7.3E-07 7.5E-07 6.0E-07 4.8E-07 3.8E-07 3.2E-07 3.1E-07 2.6E-07 CO2  5.5E-07 6.8E-07 6.6E-07 6.1E-07 5.4E-07 4.8E-07 4.5E-07 3.7E-07 C2-C4  1.2E-07 1.3E-07 1.2E-07 1.0E-07 7.3E-08 7.5E-08 7.3E-08 6.4E-08 C4-C8  9.9E-08 8.4E-08 4.9E-08 5.4E-08 4.5E-08 4.1E-08 4.1E-08 3.5E-08 C9-C12 6.1E-08 1.0E-07 1.0E-07 9.0E-08 6.7E-08 7.5E-08 6.7E-08 5.9E-08 C12+  3.2E-08 3.5E-08 5.1E-08 5.7E-08 6.9E-08 6.7E-08 6.9E-08 6.5E-08          yCO 4.2E-02 2.1E-02 2.5E-02 3.3E-02 4.3E-02 5.3E-02 5.8E-02 7.2E-02 yCO2 5.0E-02 6.2E-02 6.0E-02 5.6E-02 4.9E-02 4.3E-02 4.0E-02 3.3E-02 yH2 1.1E-01 8.3E-02 8.9E-02 1.0E-01 1.1E-01 1.3E-01 1.3E-01 1.5E-01 yH2O 2.0E-01 2.1E-01 2.1E-01 2.1E-01 2.0E-01 2.0E-01 1.9E-01 1.8E-01 YCH2 2.5E-01 2.7E-01 2.7E-01 2.6E-01 2.5E-01 2.4E-01 2.3E-01 2.2E-01          PH2 33.81 24.80 26.63 30.07 34.28 38.23 40.49 46.53 PCO 12.70 6.39 7.61 9.95 13.00 15.85 17.41 21.51    271 Day 1 2 3 4 5 6 7 8 TOS, h 17 24 24 24 33.25 17.5 23.5 22 Cumulative TOS, h 17 41 65 89 122.25 139.75 163.25 185.25 PCO2 14.94 18.62 17.99 16.72 14.82 13.04 12.15 9.97 PH2O 60.53 64.01 63.23 61.81 60.29 58.87 57.98 55.46 PCH2 75.5 82.6 81.2 78.5 75.1 71.9 70.1 65.4 Overall mass balance, % 0.0 6.6 4.0 5.2 6.4 5.8 5.6 7.7          PH2O/PH2 1.79 2.58 2.37 2.06 1.76 1.54 1.43 1.19          CO, mol/sec.g 2.3E-05 2.5E-05 2.5E-05 2.4E-05 2.3E-05 2.2E-05 2.2E-05 2.0E-05 CH4  6.1E-06 6.2E-06 5.0E-06 4.0E-06 3.2E-06 2.7E-06 2.6E-06 2.2E-06 CO2  4.6E-06 5.6E-06 5.5E-06 5.1E-06 4.5E-06 4.0E-06 3.7E-06 3.1E-06 C2-C4  1.0E-06 1.1E-06 1.0E-06 8.3E-07 6.1E-07 6.3E-07 6.1E-07 5.3E-07 C4-C8  8.3E-07 7.0E-07 4.1E-07 4.5E-07 3.7E-07 3.5E-07 3.4E-07 2.9E-07 C9-C12  5.1E-07 8.7E-07 8.4E-07 7.5E-07 5.6E-07 6.3E-07 5.6E-07 4.9E-07 C12+ 2.6E-07 2.9E-07 4.3E-07 4.7E-07 5.7E-07 5.6E-07 5.7E-07 5.4E-07                   CO,TOF (S-1) 1.9E-02 2.0E-02 2.0E-02 1.9E-02 1.9E-02 1.8E-02 1.7E-02 1.6E-02 CH4  4.9E-03 5.0E-03 4.0E-03 3.2E-03 2.6E-03 2.2E-03 2.1E-03 1.8E-03 CO2  3.7E-03 4.5E-03 4.4E-03 4.1E-03 3.7E-03 3.2E-03 3.0E-03 2.5E-03 C2-C4 8.1E-04 8.8E-04 8.2E-04 6.7E-04 4.9E-04 5.0E-04 4.9E-04 4.3E-04 C4-C8  6.7E-04 5.6E-04 3.3E-04 3.6E-04 3.0E-04 2.8E-04 2.7E-04 2.3E-04    C9-C12 4.1E-04 7.0E-04 6.7E-04 6.0E-04 4.5E-04 5.0E-04 4.5E-04 4.0E-04 C12+ 2.1E-04 2.3E-04 3.4E-04 3.8E-04 4.6E-04 4.5E-04 4.6E-04 4.3E-04 C5+ 1.3E-03 1.5E-03 1.3E-03 1.3E-03 1.2E-03 1.2E-03 1.2E-03 1.1E-03          272 Table L.4. Experimental condition and summary of results for RUN36EXP1, , with 1.2Re-12Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.08 mol/ h.g Day 1 2 3 4 5 6 TOS, h 20 24.5 25 21.5 24 24 EXP Cumulative TOS, h 20 44.5 69.5 91 115 139         CO conv 66.67 64.75 60.38 59.26 58.58 57.75         Products distribution wt%        CH4 5.3 5.2 6.1 6.8 6.9 7.1 C2-C4 3.5 3.1 3.3 3.7 3.4 3.4 C5-C8 7.6 6.7 11.5 8.3 5.7 6.2 C9-C12 30.0 36.7 18.5 22.7 19.1 20.4 C12+ 45.7 47.3 55.4 56.9 61.9 60.7 CH4, mol% 4.5 4.4 5.1 5.5 5.8 5.9 CO2, mol% 4.0 3.8 1.9 1.3 1.1 1.0 CH4, Catom% 4.7 4.6 5.4 6.0 6.1 6.3 C5+ Selectivity 83.2 90.7 85.4 87.9 86.7 87.3         Alpha 0.88 0.86 0.89 0.88 0.89 0.88         CO, mol/sec.g 3.87E-06 3.76E-06 3.51E-06 3.44E-06 3.40E-06 3.35E-06 CH4  1.73E-07 1.67E-07 1.79E-07 1.90E-07 1.96E-07 1.99E-07 CO2  1.56E-07 1.43E-07 6.52E-08 4.58E-08 3.88E-08 3.47E-08 C2-C4  4.11E-08 3.53E-08 3.42E-08 3.65E-08 3.46E-08 3.45E-08 C4-C8  4.04E-08 3.52E-08 5.57E-08 3.98E-08 2.77E-08 2.94E-08 C9-C12 1.07E-07 1.26E-07 5.99E-08 6.89E-08 5.83E-08 6.21E-08 C12+  1.03E-07 1.12E-07 1.03E-07 1.06E-07 1.15E-07 1.14E-07         yCO 9.773E-02 1.028E-01 1.146E-01 1.175E-01 1.193E-01 1.215E-01 yCO2 7.884E-03 7.201E-03 3.245E-03 2.278E-03 1.926E-03 1.718E-03 yH2 1.719E-01 1.816E-01 2.014E-01 2.064E-01 2.096E-01 2.138E-01 yH2O 1.876E-01 1.817E-01 1.714E-01 1.687E-01 1.669E-01 1.643E-01 YCH2 1.955E-01 1.889E-01 1.746E-01 1.710E-01 1.688E-01 1.660E-01         PH2 51.56 54.48 60.42 61.92 62.89 64.13 PCO 29.32 30.85 34.38 35.26 35.80 36.44 PCO2 2.37 2.16 0.97 0.68 0.58 0.52 PH2O 56.29 54.52 51.42 50.62 50.06 49.29 PCH2 58.7 56.7 52.4 51.3 50.6 49.8 Overall mass balance, % 0.1 -0.2 1.9 3.7 2.4 2.4     273 Day 1 2 3 4 5 6 TOS, h 20 24.5 25 21.5 24 24 EXP Cumulative TOS, h 20 44.5 69.5 91 115 139 PH2O/PH2 1.09 1.00 0.85 0.82 0.80 0.77        CO, mol/sec.g 3.226E-05 3.133E-05 2.922E-05 2.868E-05 2.835E-05 2.795E-05 CH4 1.438E-06 1.392E-06 1.490E-06 1.582E-06 1.634E-06 1.662E-06 CO2 1.301E-06 1.194E-06 5.430E-07 3.820E-07 3.236E-07 2.892E-07 C2-C4 3.423E-07 2.944E-07 2.853E-07 3.044E-07 2.881E-07 2.872E-07 C4-C8 3.368E-07 2.937E-07 4.640E-07 3.313E-07 2.312E-07 2.447E-07 C9-C12 8.912E-07 1.046E-06 4.990E-07 5.742E-07 4.861E-07 5.173E-07 C12+ 8.602E-07 9.320E-07 8.574E-07 8.829E-07 9.574E-07 9.482E-07               CO,TOF (S-1) 2.59E-02 2.52E-02 2.35E-02 2.31E-02 2.28E-02 2.25E-02 CH4 1.16E-03 1.12E-03 1.20E-03 1.27E-03 1.31E-03 1.34E-03 CO2 1.05E-03 9.60E-04 4.37E-04 3.07E-04 2.60E-04 2.33E-04 C2-C4 2.75E-04 2.37E-04 2.29E-04 2.45E-04 2.32E-04 2.31E-04 C4-C8 2.71E-04 2.36E-04 3.73E-04 2.66E-04 1.86E-04 1.97E-04 C9-C12 7.16E-04 8.41E-04 4.01E-04 4.62E-04 3.91E-04 4.16E-04 C12+ 6.92E-04 7.49E-04 6.89E-04 7.10E-04 7.70E-04 7.62E-04 C5+ 1.68E-03 1.83E-03 1.46E-03 1.44E-03 1.35E-03 1.37E-03              274 Table L.5. Experimental condition and summary of results for RUN37EXP1, with 1.2Re-12Co/Al2O3(0.7) catalyst,  tested in CSTR reactor at T=220 °C, P=20 bar and H2/CO=2, GHSV=0.12 mol/ h.g  Day 1 2 3 4 5 6 7 TOS, h 22.25 24.75 23 26.5 20.5 25.5 24 Cumulative TOS, h 22.25 47 70 96.5 117 142.5 166.5         CO conv 54.56 48.11 45.23 43.47 40.86 35.08 35.08         Products distribution wt%        CH4 6.6 8.1 9.0 9.5 10.1 11.4 12.2 C2-C4 5.4 6.2 6.8 7.0 7.4 7.9 8.2 C5-C8 7.0 5.5 7.1 7.3 6.9 7.3 10.5 C9-C12 25.9 25.8 24.9 24.8 23.4 22.6 21.9 C12+ 54.5 54.1 51.8 51.1 51.9 49.8 49.7 CH4, mol% 5.6 6.8 7.6 8.0 8.5 9.5 10.2 CO2, mol% 5.5 4.7 3.6 3.1 2.5 1.7 1.4 CH4, Catom% 5.9 7.1 8.0 8.4 9.0 10.1 10.9 C5+ Selectivity 87.4 85.4 83.9 83.1 82.3 79.7 82.1         Alpha 0.87 0.84 0.83 0.84 0.82 0.86 0.86         CO, mol/sec.g 4.46E-06 3.93E-06 3.70E-06 3.55E-06 3.34E-06 3.04E-06 2.87E-06 CH4  2.50E-07 2.68E-07 2.81E-07 2.85E-07 2.83E-07 2.89E-07 2.93E-07 CO2  2.44E-07 1.86E-07 1.33E-07 1.08E-07 8.40E-08 5.24E-08 4.02E-08 C2-C4  7.59E-08 7.76E-08 7.94E-08 7.92E-08 7.44E-08 7.53E-08 7.44E-08 C4-C8  4.38E-08 3.23E-08 3.87E-08 3.82E-08 3.42E-08 3.28E-08 3.11E-08 C9-C12 1.04E-07 9.07E-08 8.26E-08 7.90E-08 5.64E-08 6.16E-08 5.64E-08 C12+  1.35E-07 1.31E-07 1.16E-07 1.11E-07 8.47E-08 8.84E-08 8.47E-08         yCO 1.2E-01 1.4E-01 1.5E-01 1.5E-01 1.6E-01 1.6E-01 1.7E-01 yCO2 8.2E-03 6.1E-03 4.4E-03 3.5E-03 2.7E-03 1.7E-03 1.3E-03 yH2 2.5E-01 2.8E-01 2.9E-01  3.0E-01 3.1E-01 3.2E-01 3.3E-01 yH2O 1.4E-01 1.2E-01 1.2E-01 1.1E-01 1.0E-01 9.6E-02 9.1E-02 YCH2 1.5E-01 1.3E-01 1.2E-01 1.2E-01 1.1E-01 9.8E-02 9.2E-02         PH2 74.22 82.94 86.56 88.80 92.18 96.90 99.57    275 Day 1 2 3 4 5 6 7 TOS, h 22.25 24.75 23 26.5 20.5 25.5 24 Cumulative TOS, h 22.25 47 70 96.5 117 142.5 166.5 PCO 37.37 42.02 44.08 45.32 47.12 49.63 51.01 PCO2 2.46 1.84 1.31 1.06 0.82 0.51 0.39 PH2O 42.41 37.12 35.09 33.79 31.73 28.85 27.18 PCH2 44.9 39.0 36.4 34.9 32.6 29.4 27.6 Overall mass balance, % 14.6 8.3 5.3 5.9 5.5 2.5 2.6 Carbon balance, % -0.6 -0.1 0.8 1.0 1.3 1.6 1.7         PH2O/PH2 0.57 0.45 0.41 0.38 0.34 0.30 0.27         CO, mol/sec.g 3.7E-05 3.3E-05 3.1E-05 3.0E-05 2.8E-05 2.5E-05 2.4E-05 CH4  2.1E-06 2.2E-06 2.3E-06 2.4E-06 2.4E-06 2.4E-06 2.4E-06 CO2  2.0E-06 1.5E-06 1.1E-06 9.0E-07 7.0E-07 4.4E-07 3.3E-07 C2-C4  6.3E-07 6.5E-07 6.6E-07 6.6E-07 6.2E-07 6.3E-07 6.2E-07 C4-C8  3.6E-07 2.7E-07 3.2E-07 3.2E-07 2.8E-07 2.7E-07 2.6E-07 C9-C12  8.6E-07 7.6E-07 6.9E-07 6.6E-07 4.7E-07 5.1E-07 4.7E-07 C12+ 1.1E-06 1.1E-06 9.7E-07 9.2E-07 7.1E-07 7.4E-07 7.0E-07                 CO,TOF  (S-1) 2.99E-02 2.64E-02 2.48E-02 2.38E-02 2.24E-02 2.04E-02 1.92E-02 CH4  1.68E-03 1.80E-03 1.88E-03 1.91E-03 1.90E-03 1.94E-03 1.96E-03 CO2  1.64E-03 1.24E-03 8.92E-04 7.26E-04 5.63E-04 3.51E-04 2.69E-04 C2-C4 5.08E-04 5.20E-04 5.32E-04 5.30E-04 4.99E-04 5.04E-04 4.99E-04 C4-C8  2.93E-04 2.17E-04 2.59E-04 2.56E-04 2.29E-04 2.19E-04 2.09E-04    C9-C12 6.94E-04 6.08E-04 5.53E-04 5.29E-04 3.78E-04 4.13E-04 3.78E-04 C12+ 9.07E-04 8.76E-04 7.78E-04 7.43E-04 5.68E-04 5.92E-04 5.68E-04 C5+ 1.89E-03 1.70E-03 1.59E-03 1.53E-03 1.17E-03 1.22E-03 1.15E-03         276 Appendix M: Residence time of the entire reactor system  The residence time of the entire reactor system was calculated as follows: Residence time of the entire reactor system = Gas residence time in Hot condenser+ Gas residence time in cold condenser + Gas residence time in the reactor +Gas residence time in pipelines Inlet flow rate is 70 ml (STP)/min for all the experiments.  Inlet flow rate to the reactor at operating condition (20 bar, 220 oC) 70𝑚𝑙(𝑆𝑇𝑃)𝑚𝑖𝑛×(220 + 273)(273)×120= 6.3 𝑚𝑙/𝑚𝑖𝑛 Inlet flow rate to the reactor at operating condition (20 bar, 220 oC) 70𝑚𝑙(𝑆𝑇𝑃)𝑚𝑖𝑛×(120 + 273)(273)×120= 5 𝑚𝑙/𝑚𝑖𝑛 Inlet flow rate to the reactor at operating condition (1 bar, 2 oC) 70𝑚𝑙(𝑆𝑇𝑃)𝑚𝑖𝑛×(2 + 273)(273)×11= 70.5𝑚𝑙/𝑚𝑖𝑛 Gas residence time in the reactor=Reactor volume/Inlet flowrate=300/6.3=47.6 min Gas residence time in the Hot condenser=Hot condenser volume/Inlet flowrate=150/5=30 min Gas residence time in the Cold condenser=Cold condenser volume/Inlet flowrate=300/70.5=4.2 min Residence time of the pipelines is negligible, since the total volume of pipelines is less than 50 ml. Therefore, the total residence time is ~ 81.8 min~ 1.5 h     277 Maximum average conversion achieved throughout the experiments is 85%, in which the outlet flowrate is about 37 ml (STP)/min. In case of replacing the inlet flowrate (70 ml(STP)/min) by the minimum flowrate in the system (37 ml(STP)/min), the total residence time increases to about 2.5 h.   The hydrodynamic response time of a CSTR reactor is approximately 4 times of the residence time inside the reactor. Therefore, the average hydrodynamic response time of the system is approximately 8 h.            278 Appendix N: Effect of Co particle size on TOFCO at t=48 h Table N.1. Effect of Co particle size on activity of the Re-Co/Al2O3 and Co/Al2O3 catalysts at time t*=48 h  Catalyst dCo (nm) CO conv at t=48 h (%) NCO (µmol/g) TOFCO  (s-1) 𝑇𝑂𝐹𝐶𝑂2   (s-1) TOFFT (s-1) Co/Al 2O3 5Co/Al2O3(0) 22 14 14 1.4E-02 1.0E-04 1.4E-02 20Co/Al2O3(0.6) 13 39 51 1.1E-02 6.1E-05 1.1E-02 15Co/Al2O3(0.1) 10 43 70 9.2E-03 7.7E-05 9.1E-03 15Co/Al2O3(0.1) 10 34 70 1.3E-02 8.1E-05 1.3E-02 15Co/Al2O3(0.1) 10 27 70 1.2E-02 1.3E-04 1.2E-02 15Co/Al2O3(0.1) 10 41 70 1.5E-02 1.5E-04 1.5E-02 5Co/Al2O3(0.7) 2 14 7 1.4E-03 1.2E-04 1.3E-03 5Co/Al2O3(0.7) 2 3 7 7.1E-04 9.5E-05 6.2E-04 5Co/Al2O3 (0.9) 1 17 10 1.3E-03 3.7E-05 1.3E-03 5Co/Al2O3 (0.9) 1 3 10 9.1E-04 7.5E-05 8.4E-04  1.2Re-12Co/Al2O3(0) 11 92 75 2.0E-02 4.4E-03 1.6E-02 Re-Co/Al 2O3 1.2Re-12Co/Al2O3(0) 11 62 75 2.4E-02 1.1E-03 2.3E-02 1.2Re-12Co/Al2O3(0) 11 46 75 2.5E-02 9.9E-04 2.4E-02 0.5Re-5Co/Al2O3(0.7) 5 33 56 8.4E-03 1.4E-04 8.3E-03 0.3Re-3Co/Al2O3(0.9) 2 28 62 6.6E-03 9.8E-5 6.5E-03    279 0 5 10 15 20 250.0000.0050.0100.0150.0200.0250.030   5Co/Al2O3(0) 20Co/Al2O3(0.6)15Co/Al2O3(0.1)5Co/Al2O3(0.7) 5Co/Al2O3(0.9) 0.5Re-5Co/Al2O3(0.7) 0.3Re-3Co/Al2O3(0.9) 1.2Re-12Co/Al2O3(0)TOFFT, S-1dCo, nm Figure N.1. TOFFT  (at t=48 h) versus Co particle size. For the Re-Co/Al2O3 catalysts the CO conversion is between 32 to 61% and for the Co/Al2O3 catalysts the CO conversion is between 3 to 43%. Error bars represent four data points for 15Co/Al2O3(0.1) catalyst and two data points for 1.2Re-12Co/Al2O3(0) and 5Co/Al2O3(0.9) catalyst at varied CO conversions as reported in Table N.1          280 Appendix O: MS analysis and relative intensity of the peaks   Table O.1. The expected relative intensity of the peaks for different compounds in MS   To calculate the amount of carbon exiting the fixed bed reactor in the form of CO2 and CO the following calculation was done. Total amount of carbon on 20Co/Al2O3(0.6) measured by CH analysis was 6.5 wt%.The used catalyst was hydrogenated in the stainless steel fixed bed reactor. The mass of the catalyst used in the reactor before hydrogenation was 0.38 g. Therefore, the amount of C on the catalyst before hydrogenation is equals to: 𝑚𝑐 = 6.5 ×0.38100= 0.0247 𝑔 𝑛𝑐 =0.02512= 2.1 × 10−3 𝑚𝑜𝑙 𝑛𝑐/𝑔𝑐𝑎𝑡 =0.00120.38= 5.4 × 10−3𝑚𝑜𝑙𝑔 Where mc is the mass of carbon on the catalyst before hydrogenation and nc is the moles of carbon on the catalyst before hydrogenation. mass 15 (amu) 16 (amu) 26 (amu) 27 (amu) 28 (amu) 29 (amu) 44 (amu) CO … … … … 100 … … CO2 … …  … … … … 100 CH4 79 100 … … … … … C2H4 … …  62 64 100 … … C2H6 … … 23 33 100 … … C3H8 … … … 33 59 100 100    281 The amount of CO2 and CO in the outlet gas was measured by plotting the flowrate of CO2 and CO versus time .To obtain the aforementioned plot, the MS was calibrated for relative intensity (Ire) of CO2 to He  and CO to He as follows: 𝐼𝑟𝑒 =𝐼𝐶𝑂2(𝑚𝑎𝑠𝑠44)𝐼𝐻𝑒(𝑚𝑎𝑠𝑠4)                                                                                                                                          O.1 𝑌𝐶𝑂2 =𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑜𝑓 𝐶𝑂2𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑜𝑓 𝐻𝑒= 𝐼𝑟𝑒 × 0.1354 (𝑐𝑎𝑙𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟)                                                      O.2 𝑌𝐶𝑂 , was calculated with the same procedure for mass 28.  To calculate the maximum amount of CO2 and CO, it was assumed that mass 44 and mass 28 are just detected because of formation of CO2 and CO at the outlet gas. However, actually the formation of hydrocarbons such as C2H4, C2H6 and C3H8 could also affect these peaks.  The total flow of He in the reactor was set to 30 sccm. Therefore, the flowrate of CO2 and CO was calculated in sccm and plotted versus TOS using Equation O.2.The area under the curve in Figure O.1 shows the total amount of CO2 exiting the reactor in sccm (0.2029 sccm). Also, the area under the curve in Figure O.2 shows the total amount of CO exiting the reactor in sccm (3.1918 sccm).    282 -20 0 20 40 60 80 100 120 140 1600.0000.0050.0100.0150.0200.0250.0300.035  CO2 (sccm)Time (min) Figure O.1. CO2 outlet flow rate versus TOS for 20Co/Al2O3(0.6) -20 0 20 40 60 80 100 120 140 1600.000.020.040.060.080.100.120.140.16  CO (sccm)Time (min) Figure O.2. CO outlet flow rate versus TOS for 20Co/Al2O3(0.6)  0.2029 𝑠𝑐𝑐𝑚 =0.202922414= 5.3 × 10−5 𝐶𝑂2 𝑚𝑜𝑙    283 5.3 × 10−5 𝐶𝑂2 𝑚𝑜𝑙0.38 𝑔𝑐𝑎𝑡= 1.4 × 10−4 𝐶𝑂2  𝑚𝑜𝑙𝑔𝑐𝑎𝑡   3.1918 𝑐𝑐𝑚 =3.191822414= 1.4 × 10−4 𝐶𝑂 𝑚𝑜𝑙 1.4 × 10−4 𝐶𝑂  𝑚𝑜𝑙0.38 𝑔𝑐𝑎𝑡= 3.7 × 10−4 𝐶𝑂 𝑚𝑜𝑙𝑔𝑐𝑎𝑡  The maximum percentage of carbon exited in the form of CO2 can be calculated as follows: 𝐶𝑂2(𝑚𝑜𝑙𝑔𝑐𝑎𝑡)𝑛𝑐(𝑚𝑜𝑙𝑔𝑐𝑎𝑡)=1.4 × 10−45.4 × 10−3× 100~3% The maximum percentage of carbon exited in the form of CO can be calculated as follows: 𝐶𝑂 (𝑚𝑜𝑙𝑔𝑐𝑎𝑡)𝑛𝑐(𝑚𝑜𝑙𝑔𝑐𝑎𝑡)==3.7 × 10−45.4 × 10−3× 100~7% The maximum percentage of C exited in the form of CO and CO2 is (7+3=10%) for 20Co/Al2O3(0.6).  The same procedure was applied for 5Co/Al2O3(0.7). The maximum percentage of carbon exited the reactor in the form of (CO+ CO2) was ~ 7 mol% for this catalyst.          284 Appendix P: Estimated parameters for the empirical models Table P.1. Estimated parameters for the empirical models (Co/Al2O3 catalysts with deactivation), Co particle size is measured with CO chemisorption  Catalyst, Co dp (nm) Average CO Conversion (%) Model kd  R2 5Co/Al2O3(0), 22 nm 14 Linear -1.4E-03±7.7E-5 0.72   Exponential 2.2E-03±1.5E-04 0.68   Hyperbolic 2.6E-03±1.8E-04 0.71   Reciprocal  1.4E-02±1.9E-04 0.82 20 Co/Al2O3(0.6), 13 nm 35 Exponential 5.8E-03±3.5E-04 0.83   Hyperbolic 9.0E-03±5.4E-04 0.89   Reciprocal  8.6E-02±5.5E-04 0.97 15Co/Al2O3(0.1), 10 nm 37 Exponential 3.8E-03±1.9E-04 0.86   Hyperbolic 5.1E-03±2.6E-05 0.91   Reciprocal  5.7E-02±2.8E-04 0.98 15Co/Al2O3(0.1), 10 nm 33 Exponential 2.9E-03±2.2E-04 0.89   Hyperbolic 3.8E-03±2.6E-04 0.92   Reciprocal  3.5E-02±2.6E-04 0.96 15Co/Al2O3(0.1), 10 nm 30 Exponential 2.8E-03±1.1E-04 0.95   Hyperbolic 3.5E-03±1.3E-04 0.95   Reciprocal  3.2E-02±2.6E-04 0.96 15Co/Al2O3(0.1), 10 nm 25 Linear 9.6E-04±3.1E-5 0.94   Exponential 7.0E-04±1.3E-5 0.93   Hyperbolic 1.8E-04±2.6E-5 0.93   Reciprocal  8.9E-03±1.3E-04 0.96    285 Table P.2. Estimated parameters for the empirical models (Re-Co/Al2O3 catalysts), Co particle size is measured with CO chemisorption    Catalyst, dCo(nm) Average CO Conversion (%) Model kd  R2 0.5Re-5Co/Al2O3(0.7), 5 nm 30 Exponential 9.0E-03±8.3E-04 0.46   Hyperbolic 1.5E-02±1.9E-03 0.56   Reciprocal 3.5 E-02±3.1E-04 0.94 0.3Re-3Co/Al2O3 (0.9), 2 nm 24 Exponential 3.5E-03±1.1E-04 0.94   Hyperbolic 4.5E-03±2.7E-04 0.97   Reciprocal 4.0E-02± 3.9E-04 0.98 1.2Re-12Co/Al2O3(0), 11nm 82 linear 8.2E-04±3.0E-05 0.98   Exponential 9.0E-04±2.1E-5 0.97   Hyperbolic 9.6E-04±2.8E-5 0.97   Reciprocal 1.2E-02±3.6E-04 0.87 1.2Re-12Co/Al2O3(0), 11 nm 60 Exponential 2.1E-3±1.1E-4 0.81   Hyperbolic 2.5E-3±1.3E-4 0.84   Reciprocal 2.2E-02±1.7E-04 0.94 1.2Re-12Co/Al2O3(0), 11 nm 40 Exponential 4.5E-03±2.3E-04 0.91   Hyperbolic 6.1E-03±3.2E-4 0.92   Reciprocal 3.6E-02±4.8E-03 0.94    286 -20 0 20 40 60 80 100 120 140 160 1800.820.840.860.880.900.920.940.960.981.001.02   Measured Modeled5Co/Al2O3(0), GHSV=0.04 mol/g.h 0 50 100 150 2000.40.50.60.70.80.91.0   Measured Modeled20Co/Al2O3(0.6), GHSV=0.04 mol/g.h Figure P.1. Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS     287 0 50 100 150 200 2500.50.60.70.80.91.0   Measured Modeled15Co/Al2O3(0.1), GHSV=0.04 mol/g.h0 20 40 60 80 100 1200.900.920.940.960.981.001.02   Measured Modeled15Co/Al2O3(0.1), GHSV=0.16 mol/g.h Figure P.2. Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS     288 -20 0 20 40 60 80 100 120 140 160 1800.650.700.750.800.850.900.951.001.05   Measured Modeled15Co/Al2O3(0.1), GHSV=0.07 mol/g.h0 50 100 150 200 2500.600.650.700.750.800.850.900.951.001.05   Measured Modeled0.5Re-5Co/Al2O3(0.7), GHSV=0.05 mol/g.h Figure P.3. Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS    289 0 50 100 150 200 2500.50.60.70.80.91.0   Measured Modeled0.3Re-3Co/Al2O3(0.9), GHSV=0.05 mol/g.h-20 0 20 40 60 80 100 120 140 160 1800.750.800.850.900.951.00   Measured Modeled1.2Re-12Co/Al2O3(0), GHSV=0.08 mol/g.h Figure P.4. Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS    290 0 50 100 150 200 250 3000.750.800.850.900.951.001.05   Measured Modeled, Reciprical Modeled, Linear1.2Re-12Co/Al2O3(0), GHSV=0.05 mol/g.h0 50 100 150 2000.60.70.80.91.0   Measured Modeled1.2Re-12Co/Al2O3(0), GHSV=0.12 mol/g.h Figure P.5. Comparison between experimental data and reciprocal power law fit of CO consumption rate as a function of TOS       291 Appendix Q: Kinetic models  Kinetics of CO consumption   The rate of CO consumption was calculated for each of the sets of operating conditions shown in Table ‎7.5 and these data were applied to the 3 most commonly used models presented previously by van Steen and Schulz [182], Yates and Satterfield [183], and Iglesia et al. [184]. In addition, an empirical power law was applied to these data. Table Q.1 summarizes the various models, the estimated parameters, their standard errors and the regression coefficient (R2) for each model.  Subsequently, the models were modified to allow for variation in the exponents used to describe the CO and H2 pressure dependence of the rate of CO consumption.  Generally, these modified models gave a better fit to the experimental data than the original models by these authors.  The best fit to the experimental CO consumption data of the present study was obtained with the empirical power law model in which all the estimated parameters were statistically significant. Also, the regression coefficient is 0.99 for the modified Schulz model, but several of the model parameters were statistically insignificant. The high standard deviation of the estimated parameters in this model is likely because there are too many parameters in the model and they are not independent.  Therefore the best fitted model is the power law and the parity plot of the power law model is shown in Figure Q.1.     292 Table Q.1. Estimated kinetic parameters for CO consumption rate by fitting the measured data to different kinetic models.  Kinetic expression1  Kinetic parameters Ref. 𝑘0× 10−9∗ Ea (kJ/mol) k0΄× 10−2 −∆𝐻 (kJ/mol) c d e R2  𝑟 =𝑎𝑃𝐻21.5𝑃𝐶𝑂 𝑃𝐻2𝑂⁄(1 +𝑏𝑃𝐶𝑂𝑃𝐻2𝑃𝐻2𝑂)2 13.6±1.3 137±25 1.27±0.09 75.6±21.3 --- --- --- 0.75 Schulz [182] 𝑟 =𝑎𝑃𝐻2𝑃𝐶𝑂(1 + 𝑏𝑃𝐶𝑂)2 2.43±0.37 86.0±39.0 2.60±0.35 -9.6±37.0 --- --- --- 0.48 Satterfield [183] 𝑟 =𝑎𝑃𝐶𝑂0.547𝑃𝐻20.95(1 + 𝑏𝑃𝐶𝑂) 9.05±1.56 73.4±41.4 3.37±0.92 -26.4±69.0 --- --- --- 0.46 Iglesia [184] 𝑟 = 𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒  1680±169 6.43±1.92 --- --- -0.13±0.01 -0.23±0.01 0.54±0.01 0.98 Power law 𝑟 =𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒⁄(1 +𝑏𝑃𝐶𝑂𝑃𝐻2𝑃𝐻2𝑂)2 1340±9.08 17.5±165 0.08±0.93 70.9±45.8 0.03±0.85 -0.14±0.84 -0.4±0.8 0.99 Modified Schulz 𝑟 =𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑(1 + 𝑏𝑃𝐶𝑂) 419±1320 59.7±40.7 2.2±15.5 13.8±44.6 0.38±1.7 0.23±0.08 --- 0.65 Modified Iglesia 𝑟 =𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑(1 + 𝑏𝑃𝐶𝑂)2 139±414 79.5±57.9 2.24±7.97 24.5±22.8 0.88±0.17 0.21±0.07 --- 0.69 Modified Satterfield 1  In the kinetic expressions: 𝑎 = 𝑘0 exp (−𝐸𝑎𝑅(1𝑇−1?̅?)), 𝑏 = 𝑘0′  exp (∆𝐻𝑅(1𝑇−1?̅?)), where ?̅? = 493   Dimensions of k0 and 𝑘0′  depend on the model, rate of reaction is in (mol g-1 s-1), pressures are in (psi)   293  Figure Q.1. Parity plot for rate of CO consumption applied to the power law model. Parameter values as reported in Table Q.1. Rate equation: 𝒓 = 𝒂𝑷𝑪𝑶𝒄 𝑷𝑯𝟐𝒅 𝑷𝑯𝟐𝑶𝒆 with R2=0.981  Kinetics of CH4 formation  The inclusion of the activity parameter for the CH4 formation rate in Run 2 and Run 3 improved the fit of the experimental data to the kinetic models. Figure Q.2 shows the parity plot for the modified Schulz model using the activity factor and the case where the activity factor was not included.  Clearly the activity factor improves the model fit. Therefore, the complete set of CH4 formation rate data were corrected for deactivation in the case of Run 2 and Run 3 data. The corrected data were applied to several models of FT kinetics reported in the literature for CO consumption rate and their modified forms. The reason for using the same models as CO consumption rate models is that the same parameters that affect the CO consumption rate can also affect the formation rate of the products especially CH4, which is one of the main products 1 1.5 2 2.5 3 3.5 4 4.5 5x 10-611.522.533.544.555.5x 10-6EXPERIMENTAL, mol/(sec.gcat)PREDICTED, mol/(sec.gcat)   294 of the FT synthesis. Table Q.2 summarizes the kinetic expressions, together with the estimated parameter values for CH4 formation rate. As can be seen in Table Q.2, the modified version of the kinetic equation proposed by Schulz [182], the  equation proposed by Satterfield [183] and the modified version of the Satterfield model as well as the power law kinetics were best fitted to the measured CH4 formation rates. However the standard deviation of the parameters for the modified Schulz model and the modified Satterfield model was large. The large standard deviation in these models is likely because there are several parameters in the models and some of them are not independent.  Therefore, the best fitted models are the Satterfield and the power law model.   0.0 5.0x10-71.0x10-61.5x10-62.0x10-60.05.0x10-71.0x10-61.5x10-62.0x10-6   without activity factor with activity factorPredicted (mol/(sec.gcat))Experimental (mol/(sec.gcat)) Figure Q.2. Parity plot comparison of the fitted modified Schulz model to the measured CH4 formation rate: with and without the activity factor for Run2 and Run3     295 Table Q.2. Estimated kinetic parameters for activity-corrected CH4 formation rate by fitting the measured data to different kinetic models.  Kinetic expression1  Kinetic parameters Ref. k0× 10−9∗ Ea (kJ/mol) k0΄× 10−2 −∆𝐻 (kJ/mol) c d e R2 𝑟=𝑎𝑃𝐻21.5𝑃𝐶𝑂 𝑃𝐻2𝑂⁄(1 +𝑏𝑃𝐶𝑂𝑃𝐻2𝑃𝐻2𝑂)2 2.76±0.94  363±82  2.18±0.53  188±60  --- --- --- 0.78  Schulz [182] 𝑟 =𝑎𝑃𝐻2𝑃𝐶𝑂(1 + 𝑏𝑃𝐶𝑂)2 0.82±0.20 337±60  6.58±1.14  124±43  --- --- --- 0.89  Satterfield [183] 𝑟 =𝑎𝑃𝐶𝑂0.547𝑃𝐻20.95(1 + 𝑏𝑃𝐶𝑂) (20.70± 6410)×E2  (2.89±758)×E2  (1.29±397)×E4  133± 75800  --- --- --- 0.87  Iglesia [184] 𝑟 = 𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒  31.4±21.8 128±14 --- --- -0.57±0.06 0.80±0.11 0.14± 0.08 0.88 Power law 𝑟=𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒⁄(1 +𝑏𝑃𝐶𝑂𝑃𝐻2𝑃𝐻2𝑂)2 3.40±2.75 27.3±392.9 0.5±3.0 201±78 0.17±1.7 0.15±0.19 0.61± 1.98 0.9 Modified Schulz 𝑟 =𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑(1 + 𝑏𝑃𝐶𝑂) 40.2±36.8  148±14  -0.08±0.28  -312±624  -0.58±0.11  0.84±0.13  --- 0.88  Modified Iglesia 𝑟 =𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑(1 + 𝑏𝑃𝐶𝑂)2 4.9±16.2  268±210  1.63±5.63  146±50  0.33±1.61  0.82±0.12  --- 0.9  Modified Satterfield 1  In the kinetic expressions:𝑎 = 𝑘0 exp (−𝐸𝑎𝑅(1𝑇−1?̅?)), 𝑏 = 𝑘0′  exp (∆𝐻𝑅(1𝑇−1?̅?)), where ?̅? = 493. Dimensions of k0 and 𝑘0′  depend on the model, rate of reaction is in (mol g-1 s-1), pressures are in (psi)   296 Kinetics of C2+ formation rate  There are several approaches to modeling the higher hydrocarbon formation rates.  In many studies the chain propagation is described by the FTS α-value and the dependence of the α-value on process conditions is described empirically [2].    In the present work, the empirical power law kinetics to various C2+ fractions was applied.  In addition, the FTS α-value was correlated to a power law. The results from the fit to these data are summarized in Table Q.3.  The results show that the fit to these data was relatively low (R2<0.65), partly due to the error associated with the measurement of the relatively low rates of reaction for the higher hydrocarbons. Clearly with more data sets and larger variation in experimental parameters the fits would be better.  Also the negative value for activation energy (Ea) of C9+ compounds is likely occurred because “𝑎” in the power law kinetic model is the combination of several parameters such as reaction rate constant, adsorption and desorption equilibrium constants.  Therefore, a negative value for Ea in C9+ products shows that the adsorption of these molecules on the active sites, which is an exothermic reaction, has a significant impact on the reaction rate.  Figure Q.3 illustrates the ASF plots for two sets of experimental data from the present study.  These data show the hydrocarbon product distribution up to carbon number 60 as determined from the FID hot gas analysis and the FID liquid analysis. As shown in Figure Q.3, the ASF plots showed significant deviation at low carbon number as reported elsewhere [24, 25], and this deviation was observed over all of the operating conditions.    297 Consequently, although we have calculated the α-values for all conditions, the values reflect the probability of chain growth at high carbon numbers (n ≥ 10). Therefore, they do not properly describe the product distribution measured at low carbon number.  The measured ASF α-values have been correlated to the operating conditions using an empirical power law correlation.  The estimated power law parameter values and the goodness-of-fit are summarized in Table Q.4.  The results show that the correlation is not strong and this is in part due to the fact that over the chosen operating conditions, the calculated α-values did not vary over a wide range.  Much of the change in product distribution was in the CH4 and light hydrocarbon products (C2-C8) and this variation was not captured by the estimated α-values.      298 Table Q.3. Best fitted kinetic parameters for the formation rate of various C2+ components  Kinetic expression* Kinetic parameters k0×10-8 Ea (kJ/mol) c×10-1 d×10-1 e×10-1 R2 Power law  𝑟 = 𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒   C2-C4 1.62±1.61 92.9±17.9 -2.41±0.79 2.55±1.39 3.62±1.09 0.63 C5-C8 4.85±4.48 98.3±15.8 -1.15±0.72 1.78±1.59 -3.59±0.9 0.41 C9-C12 8.64±9.35 -49.3±17.5 -1.24±0.85 -9.13±1.35 1.09±0.15 0.65 C12+ 3.97±2.20 -42.5±98.8 0.27±0.48 -5.04±0.84 7.69±0.74 0.64 * 𝑎 = 𝑘0 exp (−𝐸𝑎𝑅(1𝑇−1?̅?))  Table Q.4. Estimated power law parameters for ASF α-values  Kinetic expression* Kinetic parameters k0 Ea (kJ/mol) c×10-2 d×10-2 e×10-2 R2 𝛼 = 𝑎𝑃𝐶𝑂𝑐 𝑃𝐻2𝑑 𝑃𝐻2𝑂𝑒   0.77±0.05 -9.22±1.26 2.41±0.65 -6.69±1.0  9.44±0.87   0.58     299  Figure Q.3. Illustrative ASF plots to determine the α-value as a function of operating conditions.  The estimation of the parameters of the all the kinetic models reported here, was achieved through a non-linear regression analysis using a Marquardt method. The fit was achieved in MATLAB routines provided below. The data were treated as independent, single response data for each of the component rates. Estimation of kinetic parameters in MRTLAB clear all clc global  x0 y0 a global verbose verbose(1:2) = 1; % Activity term parameter estimation % input number of responses % format short e 0 10 20 30 40 50 601E-41E-30.010.1110100  Wn/n)Carbon number, nR10E14:230C; H2/CO=3/1;P= 14.6 bar = 0.763R10E7:230C; H2/CO =1/1; 21.4 bar= 0.901   300 nvar=1; x0=0.; y0=0.;   %T,K  t,h     x=[ % T,K  t,h      CO,psi      H2,psi   H2O,psi  knt  %RUN 1  483 72  90.96737715 73.72027633 17.24710082 1 483 96  91.5336152  75.46058406 16.07303114 2 483 121 87.25326015 62.60062046 24.65263968 3 483 143 87.35758279 62.92254078 24.43504201 4 493 167 43.93001742 89.00075898 33.09386925 5 493 193 44.94194757 90.56477454 31.7975571  6 493 213 45.61888886 91.59670249 31.2645441  7 493 237 86.29876203 59.43845685 26.97396264 8 493 264 86.45412047 59.59472024 26.81400111 9 493 288 68.02129025 136.0985538 47.64154909 10 493 312 67.10258754 134.3199003 48.93057595 11 493 337 67.46081051 135.2439461 48.08243346 12 493 357 64.35170222 129.1801956 52.51130665 13 493 384 66.32845768 133.5137086 48.97863521 14 493 411 66.58678537 133.9315093 48.7395924  15 493 430 66.32518938 133.355831  49.21038748 16 493 453 65.55449092 131.7039224 50.53128099 17 493 477 41.32134973 169.9416617 43.10213551 18 493 501 40.72886707 168.5773676 44.30299903 19 493 527 24.57444862 130.2675616 56.22929286 20 493 551 25.13707374 131.095886  55.47312434 21 493 575 25.39550224 131.6478966 55.15019662 22 493 596 25.71064975 132.0824997 54.79691151 23 493 620 26.88664268 134.2121553 53.21518036 24  %RUN 2  503 24  31.52017694 65.08054647 38.85379306 32 503 48  30.49976222 63.33088617 40.46160985 33 503 71  28.46815553 58.19214449 44.39118942 34 503 92  30.52820162 62.30245728 41.4485135  35 483 115 30.83594489 111.4239036 18.75650157 36 483 142 30.34223514 110.5813199 19.39562013 37 483 166 29.58993137 109.2989472 20.36667809 38    301 483 186 29.60495744 109.3258192 20.34497695 39 493 210 59.20548637 119.0533683 44.6151543  40 493 231 59.14032545 119.0282861 44.55764185 41 493 258 56.14793406 113.4866676 48.21574948 42 503 282 15.91468648 119.5335719 60.03204334 43 503 309 17.26498822 121.9080493 58.15438806 44 503 328 16.80625011 120.8398589 59.27171727 45 483 351 125.0583624 105.2417619 19.9619968  46 483 375 125.6764426 106.8164654 19.0049386  47 483 399 126.7882502 109.8593767 17.07295705 48 503 424 108.3361729 60.27491769 47.43013775 49 503 448 111.3505713 68.21057476 42.51780249 50 503 471 112.2978185 70.1103345  41.56701713 51 493 495 50.48819172 104.2315994 53.45744533 52 493 522 48.39436872 100.1666356 56.28666675 53 493 544 49.35701476 101.9859917 55.05701209 54 503 566 41.481713   88.9611491  62.48122192 55 503 593 41.59359151 89.03413124 62.5370558  56 503 614 42.21839075 89.96070449 62.10387363 57 483 638 63.70005789 128.2427358 37.68325205 58 483 665 64.20429471 129.2984664 36.89232221 59 483 687 64.50258058 129.8055406 36.59288651 60 493 711 54.59762337 111.9837537 48.23306173 61 493 735 55.24731513 113.1710223 47.46145702 62 493 755 56.00719569 114.5341522 46.59558986 63 483 780 49.35472579 98.82934387 15.87734042 64 483 804 48.97968059 98.0736385  16.42326766 65 483 827 49.26717284 98.64668906 16.01373162 66 493 855 25.23830685 102.2251094 25.55830884 67 493 879 25.06805795 102.0310704 25.6019305  68 493 898 25.23830685 102.2251094 25.55830884 69 503 921 20.60260886 95.00287689 30.47550815 70 503 947 20.36136755 94.58376186 30.80190645 71 503 972 20.16934953 94.1750994  31.19944899 72 503 996 79.78113864 60.54306902 19.0389433  73 503 1021  79.9800917  61.0313055  18.74992263 74 503 1043    80.37211089 62.10127759 18.0725855  75 493 1065    57.18530217 115.8699903 46.08454118 76 493 1089    57.4034842  116.5995149 45.35119462 77 493 1114    58.40729203 118.3996445 44.2091425  78  % RUN 7  493 41.25   63.43735106 129.2136741 52.39375488 79 493 64.5    66.28649856 134.4039448 48.87149281 80 493 89.75   66.95730225 135.6942324 47.93946804 81    302 493 112.75  66.8378607  135.4311698 48.15554856 82 493 137.75  66.94210307 135.6536698 47.9776277 83 493 162.75  67.01529159 135.7830466 47.9776277 84 493 186.25  66.62785673 135.0160893 48.46408991 85  493 210.5   66.40820072 134.5591957 48.82101808 86 493 234.75  66.67861037 135.0875529 48.43293141 87 493 258.75  66.39070005 134.5181403 48.85645662 88  % RUN 3  483  22  63.53   127.96  37.92   89 483  46  64.90   130.60  36.09   90 483  68  63.48   127.88  37.95   91 %503    90  22.67   55.73   82.91   92 %503    115 21.41   53.71   84.00   93 503 139 24.41   58.09   82.02   94 503 163 25.94   61.16   79.81   95 503 187 27.89   64.40   77.95   96 503 211 27.55   63.27   79.09   97 503 233 30.94   69.38   75.20   98 503 279 31.61   69.50   75.98   99 %503    304 33.87   73.77   73.11   100 503 327 32.70   71.45   74.76   101 493 350 51.75   105.43  53.65   102 493 373 51.87   105.55  53.66   103 493 395 51.99   105.72  53.57   104 493 432 52.48   106.63  52.99   105 493 449 56.31   114.25  47.54   106 503 473 15.99   120.10  59.66   107 503 496 14.55   118.39  60.17   108 503 519 14.48   118.40  60.01   109 503 543 14.49   118.35  60.11   110 %493    642 39.41   84.51   65.99   111 493 664 44.40   93.66   60.00   112 493 688 45.03   94.71   59.40   113 493 711 46.11   96.59   58.24   114 503 733 38.04   82.42   67.01   115 503 762 37.55   81.36   67.83   116 503 783 37.95   82.48   66.79   117 503 805 38.10   81.96   67.76   118];  oldx=x; [nx,mx] = size(x);     %---------------------------------------------------------------------    303 %C1 production rate   % C1 formation rate % T=220C (493K) yT2_C1=[ % RUN 1  9.1692E-08 9.41309E-08 8.01687E-08 9.17786E-08 2.68757E-07 2.80049E-07 4.54806E-07 1.25203E-07 1.25203E-07 2.82709E-07 2.68184E-07 2.70934E-07 2.63287E-07 2.69559E-07 2.46652E-07 2.41278E-07 2.29322E-07 3.31401E-07 3.69056E-07 3.08312E-07 2.84981E-07 2.85959E-07 3.80066E-07 3.02436E-07 1.68063E-07 1.77866E-07 1.76114E-07 1.75321E-07 2.09447E-07 2.11173E-07 2.22713E-07  % RUN 2  4.57E-07 3.93E-07 2.94E-07 2.93E-07 1.92E-07    304 1.95E-07 1.93E-07 1.95E-07 2.01E-07 1.94E-07 1.97E-07 1.16E-06 1.10E-06 1.05E-06 6.37E-08 6.17E-08 5.91E-08 9.38E-08 9.65E-08 8.46E-08 2.65E-07 2.54E-07 2.60E-07 4.46E-07 3.65E-07 4.27E-07 1.75E-07 1.74E-07 1.93E-07 3.29E-07 3.09E-07 3.12E-07 1.56E-07 1.76E-07 1.67E-07 1.39E-07 1.56E-07 1.15E-07 7.30E-07 6.99E-07 6.44E-07 8.08E-08 7.37E-08 6.83E-08 2.00E-07 2.48E-07 2.43E-07  % RUN 7  2.20806E-07    305 2.12597E-07 2.16413E-07 2.15999E-07 2.20706E-07 2.21967E-07 2.22705E-07 2.23125E-07 2.23883E-07 2.26093E-07  % RUN 3  1.7972E-07 1.7462E-07 1.7307E-07 4.3723E-07 4.3980E-07 5.2600E-07 4.2255E-07 4.5453E-07 3.6911E-07 4.0175E-07 2.3725E-07 1.9142E-07 2.2620E-07 2.0589E-07 2.3450E-07 8.2709E-07 8.2818E-07 8.9530E-07 9.1890E-07 3.0681E-07 3.2079E-07 3.2598E-07 4.7680E-07 3.8432E-07 4.1286E-07 4.7432E-07]; %--------------------------------------------------------------------- y = yT2_C1;   oldy=y;     %      kd0      Ed   %theta=[.01 10 .01 10 ];  % for shultz model    306 %theta=[.01 10 .001 10 ];  % for satterfield model %theta=[.01 10 .01 10 ];  % for Iglesia model %theta=[.001 10  .010   0.01 0.01];  % for power law %theta=[.001 10  -.010   0.01 0.1 0.1 0.01];  % for Schulz modified-run %7,9,10 theta=[.001 10  .0001   .1 0.1 0.1 10];  % for Schulz modified-including Run 3   %theta=[.1 10  .010   0.01 0.1 10 ];  % for iglesia modified for %RUN 1-R10 %theta=[.01 10  .010 0.1 0.001 10 ];  % for iglesia modified-including %R12 %theta=[.01 10  .010   0.01 0.1 10 ];  % for Satterfield modified for %RUN 1-R10 %theta=[.001 100  .010   0.01 0.01 10 ];  % for Satterfield modified-Including RUN 3 %theta=[.1 10 .01 .01 .01 10 ]; % Ataallah Sari et al   np=length(theta); pin=theta;     % Begin calculation by calling L-M leat squares routine % [a,p,kvg,iter,corp,covp,covr,stdresid,Z,r2]=leasqr(x,y,pin,'rC1_a_1_modelmulti',0.00001,10000);   disp('RESPONSE:') if kvg ==1     disp ('PROBELM CONVERGED')     elseif kvg == 0     disp('PROBLEM DID NOT CONVERGE') end     r=y-a; disp ('X-values:')     disp (oldx')      disp ('Y-values')     disp(oldy)      disp('actvity values for all of run')     disp(a')     disp('a-values - i.e. model calculated responses')     disp(a)     disp('Residuals:')     disp (r)     disp ('Standardized residuals')     disp (stdresid)     disp ('Estimated parameter values are;')    307     disp (p)     disp ('Covariance of estimated parameters')     disp (covp)     disp('R2 values is:')     disp (r2)     disp (iter)     plot (oldy,a,'o'), hold, plot(oldy,oldy)     xlabel('EXPERIMENTAL, mol/(sec.gcat)')    ylabel('CALCULATED, mol/(sec.gcat)') ----------------------------------------------------------------------------- % FT activity model. % Modified by Farnaz Sotoodeh, April 2012.   function a = rC1_a_1_modelmulti (x,pin)     global x0 y0     [nxx,mxx]=size(x);       for i = 1:nxx           %Schulz         %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)^1.5*x(i,3)/x(i,5)/(1+pin(3)*exp(pin(4)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)*x(i,3)/x(i,5))^2;                  %Iglesia        %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)^0.95*x(i,3)^0.547/(1+pin(3)*exp(-pin(4)*1000/8.314*(1/x(i,1)-1/493))*x(i,3));  % Iglesia             %Iglesia modified         %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)^pin(4)*x(i,3)^pin(3)/(1+pin(5)*exp(-pin(6)*1000/8.314*(1/x(i,1)-1/493))*x(i,3));  % Iglesia           %Power law         a(i) =pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,3)^pin(3)*x(i,4)^pin(4)*x(i,5)^pin(5);                  %Satterfield         %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)*x(i,3)/(1+pin(3)*exp(-pin(4)*1000/8.314*(1/x(i,1)-1/493))*x(i,3))^2;             308         %Satterfield modified         %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)^pin(4)*x(i,3)^pin(3)/(1+pin(5)*exp(-pin(6)*1000/8.314*(1/x(i,1)-1/493))*x(i,3))^2;                          % modified version of Schulz       % a(i) = pin(1)*(exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493)))*x(i,3)^pin(3)*x(i,4)^pin(4)/x(i,5)^pin(5)/(1+pin(6)*exp(-pin(7)*1000/8.314*(1/x(i,1)-1/493))*x(i,3)*x(i,4)/x(i,5))^2;                 %Rautavuoma and Van der Baan         %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)*x(i,3)^0.5/(1+pin(3)*exp(-pin(4)*1000/8.314*(1/x(i,1)-1/493))*x(i,3)^0.5)^3;              % Ataallah Sari et al.         %a(i) = pin(1)*exp(-pin(2)*1000/8.314*(1/x(i,1)-1/493))*x(i,4)^pin(4)*x(i,3)^pin(3)/(1+pin(5)*exp(-pin(6)*1000/8.314*(1/x(i,1)-1/493))*x(i,3)^pin(3))^2;      end      a = a'; --------------------------------------------------------------------------    function [f,p,kvg,iter,corp,covp,covr,stdresid,Z,r2]= ...       leasqr(x,y,pin,F,stol,niter,wt,dp,dFdp,options) %function[f,p,kvg,iter,corp,covp,covr,stdresid,Z,r2]= %                   leasqr(x,y,pin,F,{stol,niter,wt,dp,dFdp,options}) % % Version 3.beta %  {}= optional parameters % Levenberg-Marquardt nonlinear regression of f(x,p) to y(x), where: % x=vec or mat of indep variables, 1 row/observation: x=[x0 x1....xm] % y=vec of obs values, same no. of rows as x. % wt=vec(dim=length(x)) of statistical weights.  These should be set %   to be proportional to (sqrt of var(y))^-1; (That is, the covariance %   matrix of the data is assumed to be proportional to diagonal with diagonal %   equal to (wt.^2)^-1.  The constant of proportionality will be estimated.), %   default=ones(length(y),1). % pin=vector of initial parameters to be adjusted by leasqr. % dp=fractional incr of p for numerical partials,default= .001*ones(size(pin)) %   dp(j)>0 means central differences. %   dp(j)<0 means one-sided differences. % Note: dp(j)=0 holds p(j) fixed i.e. leasqr wont change initial guess: pin(j) % F=name of function in quotes,of the form y=f(x,p)    309 % dFdp=name of partials M-file in quotes default is prt=dfdp(x,f,p,dp,F) % stol=scalar tolerances on fractional improvement in ss,default stol=.0001 % niter=scalar max no. of iterations, default = 20 % options=matrix of n rows (same number of rows as pin) containing %   column 1: desired fractional precision in parameter estimates. %     Iterations are terminated if change in parameter vector (chg) on two %     consecutive iterations is less than their corresponding elements %     in options(:,1).  [ie. all(abs(chg*current parm est) < options(:,1)) %      on two consecutive iterations.], default = zeros(). %   column 2: maximum fractional step change in parameter vector. %     Fractional change in elements of parameter vector is constrained to be %     at most options(:,2) between sucessive iterations. %     [ie. abs(chg(i))=abs(min([chg(i) options(i,2)*current param estimate])).], %     default = Inf*ones(). % %          OUTPUT VARIABLES % f=vec function values computed in function func. % p=vec trial or final parameters. i.e, the solution. % kvg=scalar: =1 if convergence, =0 otherwise. % iter=scalar no. of interations used. % corp= correlation matrix for parameters % covp= covariance matrix of the parameters % covr = diag(covariance matrix of the residuals) % stdresid= standardized residuals % Z= matrix that defines confidence region % r2= coefficient of multiple determination   % All Zero guesses not acceptable % Richard I. Shrager (301)-496-1122 % Modified by A.Jutan (519)-679-2111 % Modified by Ray Muzic 14-Jul-1992 %       1) add maxstep feature for limiting changes in parameter estimates %          at each step. %       2) remove forced columnization of x (x=x(:)) at beginning. x could be %          a matrix with the ith row of containing values of the %          independant variables at the ith observation. %       3) add verbose option %       4) add optional return arguments covp, stdresid, chi2 %       5) revise estimates of corp, stdev % Modified by Ray Muzic 11-Oct-1992 %   1) revise estimate of Vy.  remove chi2, add Z as return values % Modified by Ray Muzic 7-Jan-1994 %       1) Replace ones(x) with a construct that is compatible with versions %          newer and older than v 4.1. %       2) Added global declaration of verbose (needed for newer than v4.x) %       3) Replace return value var, the variance of the residuals with covr,    310 %          the covariance matrix of the residuals. %       4) Introduce options as 10th input argument.  Include %          convergence criteria and maxstep in it. %       5) Correct calculation of xtx which affects coveraince estimate. %       6) Eliminate stdev (estimate of standard deviation of parameter %          estimates) from the return values.  The covp is a much more %          meaningful expression of precision because it specifies a confidence %          region in contrast to a confidence interval..  If needed, however, %          stdev may be calculated as stdev=sqrt(diag(covp)). %       7) Change the order of the return values to a more logical order. %       8) Change to more efficent algorithm of Bard for selecting epsL. %       9) Tighten up memory usage by making use of sparse matrices (if %          MATLAB version >= 4.0) in computation of covp, corp, stdresid. % Modified by Sean Brennan 17-May-1994 %          verbose is now a vector: %          verbose(1) controls output of results %          verbose(2) controls plotting intermediate results % % References: % Bard, Nonlinear Parameter Estimation, Academic Press, 1974. % Draper and Smith, Applied Regression Analysis, John Wiley and Sons, 1981. % %set default args   % argument processing %   plotcmd='plot(x(:,1),y,''+'',x(:,1),f); shg'; %if (sscanf(version,'%f') >= 4), vernum= sscanf(version,'%f'); if vernum(1) >= 4,   global verbose   plotcmd='plot(x(:,1),y,''+'',x(:,1),f); figure(gcf)'; end; if (exist('OCTAVE_VERSION'))   global verbose end;   if(exist('verbose')~=1), %If verbose undefined, print nothing     verbose(1)=0    %This will not tell them the results     verbose(2)=0    %This will not replot each loop end; if (nargin <= 8), dFdp='dfdp'; end; if (nargin <= 7), dp=.001*(pin*0+1); end; %DT if (nargin <= 6), wt=ones(length(y),1); end;    % SMB modification if (nargin <= 5), niter=20; end;    311 if (nargin == 4), stol=.0001; end; %   y=y(:); wt=wt(:); pin=pin(:); dp=dp(:); %change all vectors to columns % check data vectors- same length? m=length(y); n=length(pin); p=pin;[m1,m2]=size(x); if m1~=m ,error('input(x)/output(y) data must have same number of rows ') ,end;   if (nargin <= 9),   options=[zeros(n,1) Inf*ones(n,1)];   nor = n; noc = 2; else   [nor noc]=size(options);   if (nor ~= n),     error('options and parameter matrices must have same number of rows'),   end;   if (noc ~= 2),     options=[options(noc,1) Inf*ones(noc,1)];   end; end; pprec=options(:,1); maxstep=options(:,2); %   % set up for iterations % f=feval(F,x,p); fbest=f; pbest=p; r=wt.*(y-f); sbest=r'*r; nrm=zeros(n,1); chgprev=Inf*ones(n,1); kvg=0; epsLlast=1; epstab=[.1 1 1e2 1e4 1e6];   % do iterations % for iter=1:niter,   pprev=pbest;   prt=feval(dFdp,x,fbest,pprev,dp,F);   r=wt.*(y-fbest);   sprev=sbest;   sgoal=(1-stol)*sprev;   for j=1:n,     if dp(j)==0,       nrm(j)=0;    312     else       prt(:,j)=wt.*prt(:,j);       nrm(j)=prt(:,j)'*prt(:,j);       if nrm(j)>0,         nrm(j)=1/sqrt(nrm(j));       end;     end     prt(:,j)=nrm(j)*prt(:,j);   end; % above loop could ? be replaced by: % prt=prt.*wt(:,ones(1,n)); % nrm=dp./sqrt(diag(prt'*prt)); % prt=prt.*nrm(:,ones(1,m))';   [prt,s,v]=svd(prt,0);   s=diag(s);   g=prt'*r;   for jjj=1:length(epstab),     epsL = max(epsLlast*epstab(jjj),1e-7);     se=sqrt((s.*s)+epsL);     gse=g./se;     chg=((v*gse).*nrm); %   check the change constraints and apply as necessary     ochg=chg;     for iii=1:n,       if (maxstep(iii)==Inf), break; end;       chg(iii)=max(chg(iii),-abs(maxstep(iii)*pprev(iii)));       chg(iii)=min(chg(iii),abs(maxstep(iii)*pprev(iii)));     end;      if (verbose(1) & any(ochg ~= chg)),        disp(['Change in parameter(s): ' ...           sprintf('%d ',find(ochg ~= chg)) 'were constrained']);      end;     aprec=abs(pprec.*pbest);       %--- % ss=scalar sum of squares=sum((wt.*(y-f))^2).     if (any(abs(chg) > 0.1*aprec)),%---  % only worth evaluating function if       p=chg+pprev;                       % there is some non-miniscule change       f=feval(F,x,p);       r=wt.*(y-f);       ss=r'*r;       if ss<sbest,         pbest=p;         fbest=f;         sbest=ss;       end;       if ss<=sgoal,         break;    313       end;     end;                          %---   end;   epsLlast = epsL; %   if (verbose(2)), %     eval(plotcmd); %   end;   if ss<eps,     break;   end   aprec=abs(pprec.*pbest); %  [aprec chg chgprev]   if (all(abs(chg) < aprec) & all(abs(chgprev) < aprec)),     kvg=1;     if (verbose(1)),       fprintf('Parameter changes converged to specified precision\n');     end;     break;   else     chgprev=chg;   end;   if ss>sgoal,     break;   end; end;   % set return values % p=pbest; f=fbest; ss=sbest; kvg=((sbest>sgoal)|(sbest<=eps)|kvg); if kvg ~= 1 , disp(' CONVERGENCE NOT ACHIEVED! '), end;   % CALC VARIANCE COV MATRIX AND CORRELATION MATRIX OF PARAMETERS % re-evaluate the Jacobian at optimal values jac=feval(dFdp,x,f,p,dp,F); msk = dp ~= 0; n = sum(msk);           % reduce n to equal number of estimated parameters jac = jac(:, msk);  % use only fitted parameters   %% following section is Ray Muzic's estimate for covariance and correlation %% assuming covariance of data is a diagonal matrix proportional to %% diag(1/wt.^2). %% cov matrix of data est. from Bard Eq. 7-5-13, and Row 1 Table 5.1      314 if vernum(1) >= 4,   Q=sparse(1:m,1:m,(0*wt+1)./(wt.^2));  % save memory   Qinv=inv(Q); else   Qinv=diag(wt.*wt);   Q=diag((0*wt+1)./(wt.^2)); end; resid=y-f;                                    %un-weighted residuals covr=resid'*Qinv*resid*Q/(m-n);                 %covariance of residuals Vy=1/(1-n/m)*covr;  % Eq. 7-13-22, Bard         %covariance of the data   jtgjinv=inv(jac'*Qinv*jac);         %argument of inv may be singular covp=jtgjinv*jac'*Qinv*Vy*Qinv*jac*jtgjinv; % Eq. 7-5-13, Bard %cov of parm est d=sqrt(abs(diag(covp))); corp=covp./(d*d');   covr=diag(covr);                 % convert returned values to compact storage stdresid=resid./sqrt(diag(Vy));  % compute then convert for compact storage Z=((m-n)*jac'*Qinv*jac)/(n*resid'*Qinv*resid);   %%% alt. est. of cov. mat. of parm.:(Delforge, Circulation, 82:1494-1504, 1990 %%disp('Alternate estimate of cov. of param. est.') %%acovp=resid'*Qinv*resid/(m-n)*jtgjinv   %Calculate R^2 (Ref Draper & Smith p.46) % r=corrcoef(y,f); if (exist('OCTAVE_VERSION'))   r2=r^2; else   r2=r(1,2).^2; end   % if someone has asked for it, let them have it %  if (verbose(2)), eval(plotcmd); end,  if (verbose(1)),    disp(' Least Squares Estimates of Parameters')    disp(p')    disp(' Correlation matrix of parameters estimated')    disp(corp)    disp(' Covariance matrix of Residuals' )    disp(covr)    disp(' Correlation Coefficient R^2')    disp(r2)    sprintf(' 95%% conf region: F(0.05)(%.0f,%.0f)>= delta_pvec''*Z*delta_pvec',n,m-n)    315     %   runs test according to Bard. p 201.   n1 = sum((f-y) < 0);   n2 = sum((f-y) > 0);   nrun=sum(abs(diff((f-y)<0)))+1;   if ((n1>10)&(n2>10)), % sufficent data for test?     zed=(nrun-(2*n1*n2/(n1+n2)+1)+0.5)/(2*n1*n2*(2*n1*n2-n1-n2)...       /((n1+n2)^2*(n1+n2-1)));     if (zed < 0),       prob = erfc(-zed/sqrt(2))/2*100;       disp([num2str(prob) '% chance of fewer than ' num2str(nrun) ' runs.']);     else,       prob = erfc(zed/sqrt(2))/2*100;       disp([num2str(prob) '% chance of greater than ' num2str(nrun) ' runs.']);     end;   end; end   % A modified version of Levenberg-Marquardt % Non-Linear Regression program previously submitted by R.Schrager. % This version corrects an error in that version and also provides % an easier to use version with automatic numerical calculation of % the Jacobian Matrix. In addition, this version calculates statistics % such as correlation, etc.... % % Version 3 Notes % Errors in the original version submitted by Shrager (now called version 1) % and the improved version of Jutan (now called version 2) have been corrected. % Additional features, statistical tests, and documentation have also been % included along with an example of usage.  BEWARE: Some the the input and % output arguments were changed from the previous version. % %     Ray Muzic     <rfm2@ds2.uh.cwru.edu> %     Arthur Jutan  <jutan@charon.engga.uwo.ca>   ---------------------------------------------------------------- function prt=dfdp(x,f,p,dp,func) % numerical partial derivatives (Jacobian) df/dp for use with leasqr % --------INPUT VARIABLES--------- % x=vec or matrix of indep var(used as arg to func) x=[x0 x1 ....] % f=func(x,p) vector initialsed by user before each call to dfdp % p= vec of current parameter values % dp= fractional increment of p for numerical derivatives %      dp(j)>0 central differences calculated %      dp(j)<0 one sided differences calculated %      dp(j)=0 sets corresponding partials to zero; i.e. holds p(j) fixed    316 % func=string naming the function (.m) file %      e.g. to calc Jacobian for function expsum prt=dfdp(x,f,p,dp,'expsum') %----------OUTPUT VARIABLES------- % prt= Jacobian Matrix prt(i,j)=df(i)/dp(j) %================================ m=length(x);n=length(p);      %dimensions ps=p; prt=zeros(m,n);del=zeros(n,1);       % initialise Jacobian to Zero for j=1:n       del(j)=dp(j) .*p(j);    %cal delx=fract(dp)*param value(p)            if p(j)==0            del(j)=dp(j);     %if param=0 delx=fraction            end       p(j)=ps(j) + del(j);       if del(j)~=0, f1=feval(func,x,p);            if dp(j) < 0, prt(:,j)=(f1-f)./del(j);            else            p(j)=ps(j)- del(j);            prt(:,j)=(f1-feval(func,x,p))./(2 .*del(j));            end       end       p(j)=ps(j);     %restore p(j) 

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