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CH₄ decompostion kinetics on supported Co and Ni catalysts Zhang, Yi 2004

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CH 4 Decomposition Kinetics on Supported Co and Ni Catalysts by Y I Z H A N G B.Sc., Dalian University of Technology, 1993 M . S c , Beijing University of Chemical Technology, 1999 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE D E G R E E OF DOCTOR OF PHILOSOPHY in THE F A C U L T Y OF G R A D U A T E STUDIES (DEPARTMENT OF C H E M I C A L A N D BIOLOGICAL ENGINEERING) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A February, 2004 © YI Z H A N G , 2004 11 Abstract Methane activation is important in a number of reactions that aim to convert natural gas to more valuable products using supported metal catalysts. As a potential alternative to steam reforming and partial oxidation, catalytic decomposition of CH4 may provide H2 without CO contamination for use with P E M fuel cells. However, the mechanism of carbon deposition and catalyst deactivation during CH4 decomposition is complex and not fully understood. The present work is aimed at clarifying some aspects of catalyst deactivation during the decomposition of C H 4 at moderate temperatures on low loading Co and N i catalysts. The experimental observations presented in the present work suggest that catalyst deactivation was a consequence of the competition between the rate of encapsulating carbon formation and the rate of carbon diffusion. Stable activity or catalyst deactivation during C H 4 decomposition was observed, depending on which of these two rates was greater. The experimental observations also show that the gas phase composition KM , and catalyst properties such as metal particle size and metal-support interaction have a critical effect on catalyst deactivation: catalyst deactivation was reduced with increasing KM and with increasing metal particle size; catalyst deactivation was increased by a strong metal-support interaction. A general kinetic model of C H 4 decomposition on supported metal catalysts has been developed based on experimental observations and the deactivation mechanism described above. The initial rate increase was described by including the rate of carbon nucleation at the tailing face of the metal particle using two methods: Cluster nucleation (Kinetic Model I) and Boltzmann nucleation (Kinetic Model U). The fit of literature data to Kinetic Model I and Kinetic Model II confirmed the presence of carbon nucleation at the tailing face. The observed CH4 decomposition activity profiles on supported Co catalysts with either stable activity or m declining activity were well described by the kinetic model. The site density profde along the metal particle was obtained and the effect of metal particle size on the CH4 decomposition activity has been quantified by fitting the observed CH4 decomposition activity profiles to the developed kinetic model. Keywords: CH4 decomposition; hydrogen production; filamentous carbon; deactivation; metal particle size; catalyst metal loading; coke formation threshold; carbon nucleation; kinetics. iv Table of Contents Abstract i i Table of Contents iv List of Tables ix List of Figures xi Nomenclature xviii Preface xxvi Chapter 1 Introduction 1 1.1 CH4 Decomposition 1 1.2 Motivation 2 1.3 Objectives of the Research 3 Chapter 2 Literature Review 5 2.1 Applications of C H 4 Decomposition 6 2.2 Carbon Formation during CH4 Decomposition.... 7 2.2.1 C arbon Morphologies 7 2.2.2 Mechanism of CFC Formation 9 2.2.3 Thermodynamic Properties of CFC 12 2.3 Kinetic Studies of C H 4 Decomposition 13 2.3.1 General Activity Profile 13 2.3.2 Kinetic Model of Steady CFC Growth 14 2.3.3 Empirical Deactivation Model 17 2.3.4 Previous Kinetic Studies of C H 4 Activation 20 2.3.5 Induction Period of CFC 21 2.4 Influence of Metal Catalyst Properties on Catalyst Deactivation 23 2.4.1 Influence of Metal Type and Metal Particle Size on Catalyst Deactivation 24 2.4.2 Metal-Support Interaction Effect on Catalyst Deactivation 26 V 2.5 Effect of Operating Conditions on Catalyst Deactivation 27 2.6 Summary of Literature Review 29 Chapter 3 Experimental 30 3.1 Introduction 30 3.2 Catalyst Preparation 30 3.3 Catalyst Characterization 32 3.3.1 BET Surface Area and Pore Volume 32 3.3.2 CO Chemisorption 32 3.3.3 Transmission Electron Microscopy (TEM) 33 3.3.4 Temperature Programmed Reduction (TPR) 33 3.3.5 X-ray Photoelectron Spectroscopy (XPS) 34 3.3.6 X-Ray Diffraction (XRD) 34 3.4 Catalyst Activity for Methane Decomposition 35 3.4.1 Activity Measurement 35 3.4.2 Description of the Measured Catalyst Activity Profile 37 3.5 Characterization Data 39 Chapter 4 Catalyst Deactivation Kinetics and Mechanism 42 4.1 Introduction 42 4.2 Activity Observations 42 4.2.1 Evidence and Significance of C H X Migration and Filamentous Carbon Formation 42 4.2.2 Effect of Temperature on Activity 45 4.2.3 Effect of H 2 and CO on the Catalyst Activity 48 4.3 Prediction of Stable Activity 52 4.3.1 Influence of KM on Catalyst Activity and Deactivation 52 4.3.2 Coking Threshold and Filamentous Carbon Formation Threshold 52 _ _ • • vi 4.3.3 Stable Catalyst Activity Prediction during CH4 Decomposition... 55 4.4 Catalyst Deactivation Mechanism 59 4.4.1 Catalyst Deactivation 59 4.4.2 Explanation of Temperature Effects on Catalyst Deactivation 62 4.4.3 Effect of CO and KM on Catalyst Deactivation 64 4.5 Summary 66 Chapter 5 Effect of Catalyst Properties on Catalyst Activity 69 5.1 Introduction 69 5.2 Dependency of the Catalyst Activity on Metal Particle Size 69 5.2.1 Dependency of the Catalyst Activity on Co Particle Size 69 5.2.2 Dependency of the Catalyst Activity on N i Particle Size 72 5.2.3 Stable Catalyst Activity on Supported Co and N i Catalysts 72 5.3 Effect of Metal Particle Size on Thresholds 77 5.3.1 Dependency of K*M on the Metal Particle Size 77 5.3.2 Effect of Metal Particle Size on (K*M-KfM) 80 5.4 Effect of MSI on Catalyst Activity 83 5.4.1 Effect of Additives on MSI 83 5.4.2 MSI Order among the Modified Catalysts 95 5.4.3 Catalyst Activity over Modified Co Catalysts 98 5.4.4 Effect of MSI on Catalyst Deactivation 101 5.4.5 Carbon Species on the Used Catalyst 103 5.5 Summary 106 Chapter 6 Kinetic Model 109 6.1 Introduction 109 6.2 Description of the Kinetic Model 110 6.2.1 Terminology and Assumptions 110 V l l 6.2.2 General Description of the Kinetic Model 113 6.2.3 Description of the Boundary Conditions at the Leading Face 115 6.2.4 Description of the Boundary Conditions at the Tailing Face 118 6.3 Kinetic Model I and Kinetic Model II Fit to Literature Data 122 6.4 Kinetic Model I Fit to Co/Si0 2 Catalyst Activity Data 133 6.4.1 Typical Examples of Kinetic Model I Fit on Co/Si0 2 Catalysts.. 133 6.4.2 Effect of Metal Particle Size 140 6.5 Summary 146 Chapter 7 Conclusions and Recommendations 148 7.1 Conclusions 148 7.2 Recommendations 150 References 152 Appendices 158 Appendix A Differential Reactor 158 A . 1 Introduction 158 A.2 Catalyst Testing Parameters 158 A.3 Reactor Flow Pattern: Plug Flow Operation 159 A.4 Reactor Isothermal Operation 160 A.5 Diagnostic Tests for Interphase (External) Transport Effects 161 A.6 Diagnostic Tests for Internal Transport Effect 162 A . 7 Reactor Differential Operation 163 Appendix B Example of Activity Calculation and Curve Fitting 165 B. 1 Example of Activity Calculation 165 B.2 Examples of Curve Fitting Results 167 B.3 Calculation of K*u and KfM 169 B.4 Carbon Diffusivity Data 172 viii Appendix C XPS Spectra ; 173 C. 1 XPS Survey Scan Spectra 173 C.2 XPS Narrow Scan Co 2p Spectra 176 C.3 XPS Narrow Scan C Is Spectra 178 C. 4 XPS Narrow Scan O Is Spectra 180 Appendix D Gas Flow and GC Calibration 182 D. 1 Gas Flow Calibration 182 D.2 GC Calibration 186 Appendix E X R D Results , 189 Appendix F Program of General Kinetic Model 194 F. 1 Simple Model I without Surface Reaction 194 F.2 Simple Model II without Surface Reaction 203 F.3 Model I with Surface Reaction 210 F.4 Common Matlab Function Files 219 Appendix G Effect of t' on the Estimate of r and \Q0kd 223 Appendix H Conversion of KM to Carbon Activity 226 ix List of Tables Table 2.1 Different morphologies of carbon deposit (Nolan et al., 1998) 8 Table 2.2 Comparison of activation energies for diffusion of carbon through metal, ED, and that for carbon filament growth, E 12 Table 2.3 Kinetic models of CFC steady growth during CHU cracking 18 Table 2.4 Empirical models of deactivation during CH4 cracking 19 Table 3.1 Properties of Co/SiC>2 catalysts of the present study 40 Table 3.2 Properties of N i / S i 0 2 catalysts of the present study 40 Table 3.3 Properties of Ni/ZrCh catalysts of the present study 41 Table 3.4 Properties of modified 12wt% Co/SiC»2 catalysts in the present study 41 Table 5.1 Summarized data of catalyst TPR profiles of modified Co catalysts 86 Table 5.2 Summarized data from XPS characterization of modified Co catalysts 94 Table 5.3 Carbon species on the used catalysts surface from XPS measurement 106 Table 6.1 Activation energy of carbon nucleation steps 121 Table 6.2 Parameters from the kinetic models fit to the data for the initial stage of carbon deposition 125 Table 6.3 Effect of metal particle size on kinetic parameters estimated at 773K over Co/Si0 2 catalysts (923K reduction, 773K reaction with KM = 0.06 arm). .141 Table A. 1 Parameters of catalyst and reactor 158 Table A.2 Steps for ensuring plug flow operation in laboratory reactors 159 Table A.3 Criteria for Isothermal Operation 161 Table B . l Example of activity calculation spreadsheet 165 Table B.2 Carbon diffusivity data (Yokoyama et al., 1998) 172 Table D. 1 Description of Mass flow controller 182 Table D.2 Sensor conversion factors for specified gases 182 Table D.3 Calibration of gas flow for each flow controller 183 X Table D.4 Response factor and retention time of GC 188 Table E. 1 Calculation of C03O4 particle size for different catalysts 193 Table G . l Effect of t on the Estimation of r and 100A:rf 223 Table H . 1 Conversion table of KM = P*t I PCH) to ac = KePCHt / p£ 226 xi List of Figures Figure 2.1 Simplified representation of the structure of parallel (left) and fishbone type (right) carbon nanofibres. The cross sections shown relate to the projections observed by T E M 9 Figure 2.2 Typical rate versus time curve for CH4 decomposition (Snoeck et al., 1997a) 10 Figure 2.3 Schematic of CFC formation mechanism 11 Figure 2.4 Change in H2 production as a function of time-on-stream at 923K with 0.5%Mo-4.5%Fe/Al2O3 catalyst. The decrease in hydrogen production for a catalyst bed of 1 g is about 6%/hr while for a catalyst bed of 3 g is less than 1%/hr (Shah et a l , 2001) ( • lg ; • 3g) 28 Figure 3.1 Block diagram of the experimental set-up used for CH4 decomposition catalyst tests 36 Figure 3.2 Activity of 12wt% Co/Si0 2 catalysts, with different KM =P1HJPCHi r a t i o s (Reduced at 923K, reacted at 773K, total gas flow 185 mL/min, weight of catalyst=0.2g; lines are the fit of Equation (3.2) to the experimental data points; • KM = 0.01 atm; • KM = 0.03 atm; • KM = 0.05 atm) 38 Figure 4.1 T E M image of 12wt% Co/Si0 2 catalyst (reduced at 723K) after 120 min reaction in 5%CH 4 /Ar at 723K, showing the presence of filamentous carbon, diameter « 10 nm 43 Figure 4.2 CO production rate over S i 0 2 and 12wt% Co/Si0 2 (reduced at 723K) exposed to 140 mL/min of 5%CH 4 /Ar at 723K (A CO production rate on S i0 2 ; — CO production rate on Co/Si0 2 ; • CH4 decomposition rate on Co/Si0 2 ) 45 Figure 4.3 Effect of temperature on the activity of 12wt% Co/Si0 2 catalysts, reduced at 923K and reacted with 5%CH 4 /Ar at 140 mL/min. (Lines are 1 s t order decay model fit to the experimental data points) 47 Figure 4.4 Arrhenius plots of maximum CH4 decomposition rate (TOF, min"1) (0), and decay constant (100kd) (A) versus 1000/T 48 Figure 4.5 Effect of the presence of H 2 or CO on (a) the maximum activity (TOF) and (b) the decay constant (100kd) on the 12wt% Co/Si0 2 catalyst (reduced at 923K), exposed to 5%CH 4 /Ar at the reaction temperature indicated 49 X l l Figure 4.6 TEM micrograph of 12wt% Co/Si02 catalyst (reduced at 923K) after reaction in 5%CH4/1.4%H2/Ar at 773K for 60 min showing the presence of filamentous carbon with diameter « 25nm 50 Figure 4.7 TEM micrograph of 12wt% Co/Si02 (reduced at 923K) after reaction in 5%CH4/0.4%CO/Ar at 773K for 60 min showing presence of filamentous carbon with diameter « 25nm 51 Figure 4.8 Comparison of CH4 decomposition TOFs in the presence of CO or H 2 at 773K on 12wt% Co/Si02 (reduced at 923K) (The total gas flow 140 mL/min. • lOOfc^^emin"1 with 5%CH4; A 100^ =0.46 mm 1 with 1.4%H2/4%CH4; *> loo*, =0.4 min"1 with 0.4%CO/ 5%CH4) 51 Figure 4.9a Dependence of maximum rate r'on KM with 12wt% Co/Si02 (reduced at 923K) at 773K (K'M =0.082 + 0.003 atm) 53 Figure 4.9b Dependence of decay constant 100 kd on KM with 12wt% Co/Si02 (reduced at923K)at773K(^ = 0.061 ± 0.004 afm) 55 Figure 4.10 Stable activity on 12wf% Co/Si02 (reduced at 923K) with KM = 0.074 atm at 773K 56 Figure 4.11a Dependence of maximum rate r*on KM with 5wt% Ni/Si02 (reduced at 923K)at773K(AT^ =0.110 ±0.009 atm) 57 Figure 4.1 lb Dependence of decay constant 100 kd on KM with 5wt% Ni/Si02 (reduced at 923K) at 773K (KfM =0.032±0.003 atm) 58 Figure 4.12 Stable activity on 5wt% Ni/Si02 (reduced at 923K) with KM =0.09 atm at 773K 59 Figure 4.13 Schematic representation of catalyst deactivation mechanism during CH 4 decomposition 62 Figure 5.1a Dependence of the maximum catalyst activity (Max TOF) on Co particle size (• 723K Reduction, 723K Reaction; • 923K Reduction, 773K Reaction with KM = 0 . 0 6 atm) 71 Figure 5.1b Dependence of the catalyst decay constant (I00kd) on Co particle size (• 723K Reduction, 723K Reaction; • 923K Reduction, 773K Reaction KM = 0 . 0 6 atm) 71 Figure 5.2a Dependence of the catalyst maximum activity (Max TOF) on metal particle size at 773K with KM = 0 . 0 6 atm (• Co/Si02; ANi/Si0 2; X Ni/Zr02 ; catalysts were reduced at 923K) 73 X l l l Figure 5.2b Dependence of the catalyst decay constant (I00kd) on metal particle size at 773K with KM = 0.06 atm (• Co/Si0 2 ; A N i / S i 0 2 ; x Ni /Zr0 2 ; catalysts were reduced at 923K) 73 Figure 5.3a Stable catalyst activity on 30wt% Co/Si0 2 (reduced at 923K with Co particle size 26 nm) at 773K with KM = 0.06 atm 74 Figure 5.3b T E M micrograph of 30wt% Co/Si0 2 (reduced at 923K) after reaction at 773K with KM = 0.06 atm showing the presence of filamentous carbon 74 Figure 5.4a Stable catalyst activity on N i / S i 0 2 catalysts at 773K with KM =0.06 atm (•12wt% N i / S i 0 2 with N i particle size 43.3 nm; • 15wt% Ni /S i0 2 with N i particle size 49.5 nm; catalysts were reduced at 923K) 75 Figure 5.4b T E M micrograph of 15wt% N i / S i 0 2 (reduced at 923K) after reacted at 773K with KM — 0.06 atm showing the presence of filamentous carbon 76 Figure 5.5 Stable catalyst activity on Ni /Zr0 2 catalysts at 773K with KM - 0.06 atm (• 8wt% Ni /Z r0 2 with N i particle size 20 nm; • 12wt% Ni /Zr0 2 with N i particle size 32 nm; catalysts were reduced at 923K) 76 Figure 5.6 Deviation of the coking threshold from graphite equilibrium and the effect of metal crytallite size during CH4 decomposition on N i and Co catalysts at 773K. ( • Co/Si0 2 ; A Ni /S i0 2 ; AG C = 0.101(104/dp) + 6.68; catalysts were reduced at 923K) 79 Figure 5.7 The fdamentous carbon formation threshold, KfM , versus metal particle size on Co catalysts at 773K 82 Figure 5.8 The difference between the coking threshold and the fdamentous carbon formation threshold, (K*M -KfM), increases with the increasing particle size of Coat773K 82 Figure 5.9 TPR profdes of modified Co catalysts, a: 12wt% Co/Si0 2 ; b: Co/BaO/Si0 2; c: Co/Zr0 2 /S i0 2 ; d: Co/La 2 0 3 /S i0 2 88 Figure 5.10 Surface Co 2p Spectra on modified catalysts, a: unreduced 12wt% Co/Si0 2 ; b: reduced 12wt% Co/Si0 2 ; c: reduced Co/BaO/Si0 2 ; d: reduced Co/Zr0 2 /S i0 2 ; e: reduced Co/La 2 0 3 /S i0 2 . (Note that the raw data of XPS measurement is shown in Appendix C.) 93 Figure 5.1 l a Dependence of maximum catalyst activity (TOF, r ) on Co particle size over modified Co catalysts. (Unfilled symbol: Reduction 723K, 140 mL/min 5%CH 4 /Ar at 723K; filled symbol: Reduction 923K, 185 mL/min 23%CH 4/12%H 2/Ar at 773K; • and • Co/Si0 2 ; O and • Co/J3aO/Si02; O and • Co/Zr0 2 /Si0 2 ; A and • Co/La 2 0 3 /S i0 2 ) 99 xiv Figure 5.11b Dependence of catalyst decay constant (\00kd) on Co particle size over modified Co catalysts. (Unfilled symbol: Reduction 723K, 140 mL/min 5%CH 4 /Ar at 723K; filled symbol: Reduction 923K, 185 mL/min 23%CH 4/12%H 2/Ar at 773K; • and • Co/Si0 2 ; O and • Co/BaO/Si0 2; O and • Co/Zr0 2 /S i0 2 ; A and • Co/La 2 0 3 /S i0 2 ) 100 Figure. 5.12 Stable catalyst activity on modified Co catalysts. (•Co/Si0 2 ; •Co/BaO/Si0 2 ; •Co/Zr0 2 /S i0 2 ; A C o / L a 2 0 3 / S i 0 2 , Reduction 923K, Reaction 773K with KM =0.06 atm) 101 Figure 5.13 XPS spectra of C Is on used catalysts surface, a: Co/BaO/Si0 2; b: Co/Zr0 2 /S i0 2 ; c: Co/La 2 0 3 /S i0 2 106 Figure 6.1 Schematic drawing of general kinetic model 112 Figure 6.2 Initial weight gain versus time for various H 2 , CO, C 0 2 , C H 4 and H 2 0 at 900K and lOlkPa on Fe foil( A 7^7^ =0.13bar 2, JPmP c 2 o =0.21 bar 3 ;*P C 0 P^ = 0.12bar2,PC0Pl0 = 2.0bar3; • PC0PH^ =0.06bar2, PCOtP£0 = 2.\ bar3) 123 Figure 6.3 Carbon deposition rate versus time for various H 2 CO, C 0 2 , C H 4 and H 2 0 at 900K and lOlkPa. (Filled symbol is for the initial period measured at small time interval; unfilled symbol is measured at the larger time interval; A and ^PCOPH2 =0.13 bar2, PC0P*0 =0.21 bar3; O and* PC0PH^ = 0.12 bar2, PcaPc0 =2.0 bar3; O and • PC0PH^ =0.06 bdx2,PcoPc0 = 2.1 bar3) 124 Figure 6.4a Single carbon atom profile along the depth of Fe foil obtained by fitting literature data to the Kinetic Model 1 126 Figure 6.4b Carbon deposition rate obtained by fitting literature data to the Kinetic Model I 127 Figure 6.4c Site density changes as a function of time-on-stream obtained by fitting literature data to the Kinetic Model 1 128 Figure 6.5a Single carbon atom profile along the Fe foil obtained by fitting literature data to the Kinetic Model II 130 Figure 6.5b Carbon deposition rate obtained by fitting literature data to the Kinetic Model II 131 Figure 6.5c Detailed information obtained by fitting literature data to the Kinetic Model II 132 Figure 6.6a Single carbon atom profile along diffusion path with steady carbon growth on 30wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I 134 XV Figure 6.6b Carbon deposition with steady carbon growth on 30wt% Co/Si0 2 (923K reduction, 773K reaction with KM =0.06 atm) fitted to the Kinetic Model I 135 Figure 6.6c Detail information obtained from experimental data with steady carbon growth on 30wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I 136 Figure 6.7a Single carbon atom profile along diffusion path with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model 1 137 Figure 6.7b Carbon deposition with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model 1 138 Figure 6.7c Detailed information obtained from experimental data with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model 1 139 Figure 6.7d Detailed information obtained from experimental data with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model 1 140 Figure 6.8a Effect of metal particle size on Ds, the carbon diffusivity through Co 141 Figure 6.8b Effect of metal particle size on Z),, the carbon surface diffusivity at the tailing face 142 Figure 6.8c Effect of metal particle size on kfSvlPCH/j • Surface/Active Site, the initial TOF for C H 4 decomposition 142 Figure 6.8d Effect of metal particle size on kflkg, equilibrium constant for carbon CFL; decomposition 143 Figure 6.8e Effect of metal particle size on kencap, rate constant for encapsulating carbon formation 143 Figure A. 1 Diagnostic tests for interphase (external) transport effect (A140mL(STP)/min; 4210 mL(STP)/min, SV=19,000hr" \ T=673K, 5%CH 4 /Ar, 12wt%Co/Si0 2) 162 Figure A.2 Diagnostic tests for intraparticle transport effects (AParticle size= 170pm, •Particle size=90um, T=673K, 140mL/min, 5%CH 4 /Ar, SV=19,000hr"1, 12wt% Co/Si0 2 ) 163 Figure A.3 Diagnostic tests for differential operation 164 XVI Figure B . l Maximum C H 4 decomposition rate versus KM at 773K on 5wt% Co/Si02 (reduced at 923K) with K*M = 0.033 ± 0.001 atm 169 Figure B.2 Decay constant versus KM at 773K on 5wt% Co/SiC»2 (reduced at 923K) with Kf = 0.027 ± 0.006 atm 169 Figure B.3 Maximum C H 4 decomposition rate versus KM at 773K on 10wt% Co/SiC>2 (reduced at 923K) with K[ = 0.030 ± 0.003 atm 170 Figure B.4 Decay constant versus KM at 773K on 10wt% Co/Si0 2 (reduced at 923K) with Kf = 0.027 + 0.003 atm 170 M Figure B.5 Maximum C H 4 decomposition rate versus KM at 773K on 30wt% Co/Si0 2 (reduced at 923K) with K[ =0.071±0.002 atm 171 Figure B.6 Maximum C H 4 decomposition rate versus KM at 773K on 15wt% Ni/SiC>2 (reduced at 923K) with K[ =0.135 ±0.010 atm 171 Figure B.7 Maximum C H 4 decomposition rate versus KM at 773K on 30wt% Ni/Si02 (reduced at 923K) with AT* = 0.092 ± 0.004 atm 172 Figure C. 1 Survey scan spectrum on Co/BaO/SiCh after reduction 173 Figure C.2 Survey scan spectrum on Co/BaO/Si02 after reaction 173 Figure C.3 Survey scan spectrum on Co/ZrCVSiC^ after reduction 174 Figure C.4 Survey scan spectrum on Co/ZrCVSiCh after reaction 174 Figure C.5 Survey scan spectrum on Co/La20 3 /Si0 2 after reduction 175 Figure C.6 Survey scan spectrum on Co/La203/Si02 after reaction 175 Figure C.7 Comparison of raw data and fit data of surface Co 2p Spectra on modified catalysts, a: unreduced 12wt% Co/Si0 2 ; b: reduced 12wt% Co/SiCh; c: reduced Co/BaO/SiCh; d: reduced Co/ZrCVSiCh; e: reduced Co /La 2 0 3 /S i0 2 178 Figure C.8 Comparison of raw data and fit data of C Is spectra on used catalysts surface. a: Co/BaO/Si0 2 ; b: Co/Zr0 2 /Si0 2 ; c: Co /La 2 0 3 /S i0 2 179 Figure C.9 XPS O Is spectra on used catalysts surface, a: Co/BaO/SiC»2; b: Co/Zr0 2 /S i0 2 ; c: Co/La 2 0 3 /S i0 2 181 Figure D . l Measured flow versus calibrated reading. (5.16%CH 4/Ar in Ch 2) 183 Figure D.2 Measured flow versus calibrated reading. (5.2%CH 4/Ar in Ch 2) 184 XVII Figure D.3 Measured flow versus calibrated reading. (4.82%H 2/10.4%CH 4/Ar in Ch 2). 184 Figure D.4 Measured flow versus calibrated reading. (Pure H 2 in Ch 3) 185 Figure D.5 Measured flow versus calibrated reading. (Ar in Ch 4) 185 Figure E. 1 X R D Pattern of 12wt% Co/Si0 2 after calcinations (TC03O4) 189 Figure E.2 X R D Pattern of 12wt% Co/BaO/Si0 2 after calcinations ( • C o 3 0 4 ) 190 Figure E.3 X R D Pattern of 12wt% Co/Zr0 2 /S i0 2 after calcinations (TC03O4) 191 Figure E.4 X R D Pattern of 12wt% Co/La 2 0 3 /S i0 2 after calcinations ( • C o 3 0 4 ) 192 Figure E.5 Standard X R D pattern for C o 3 0 4 193 F i g u r e d Effect of t on the estimation of r (Activity profile with KM =0.02atfmof Figure 3.2) 224 Figure G.2 Effect of /* on the estimation of \§0kd (Activity profile with KM = O.Olatm of Figure 3.2) 224 Figure G.3 Effect of t* on the estimation of r (Activity profile with KM = Q.05atm of Figure 3.2) 225 Figure G.4 Effect of t' on the estimation of \00kd (Activity profile with KM = 0.05atm of Figure 3.2) 225 XVU1 Nomenclature * Active site of catalyst metal surface; [CHxS] Site density of active site occupied by adsorbed carbon species on the catalyst surface, where x = 0 ~ 3 ; [CPS] Site density of active site occupied by encapsulated site occupied by encapsulating carbon; [HS] Site density of active site occupied by adsorbed hydrogen atom on the catalyst surface; [Sv], [S] Site density of available active site on the leading face; [SV0] Site density of the total active site on the leading face; a Activity factor; ac Activity of carbon ac =KePCH / P^ ; aNi Surface area of Nickel; C Amount of carbon deposited by the time; C M Carbon atom in the bulk phase of the metal crystal at site ssl; Cb2 Carbon atom at site ssl segregating out of the metal particle; cC(M. fj Concentration of carbon dissolved in nickel at the front of the particle (gas side); cc{m,r) Concentration of carbon dissolved in nickel at the rear of the particle (support side); cc(Nt sm) Saturation concentration of carbon in nickel; CHX Carbon species, x = 0 ~ 3 ; CHXS, CHX * Adsorbed carbon species on the catalyst surface, x = 0 ~ 3 ; CHXS] Chemisorbed species on the metal active site Sl, x = 0~3; CHxS2 Chemisorbed species on the support S2, x = 0~3; C m a x Maximum amount of carbon deposited by the time; Cm f Carbon dissolved in nickel at the front of the particle (gas side); CNir Carbon dissolved in nickel at the rear of the particle (support side); C Encapsulating carbon on the leading face of metal particle; cp Heat capacity; XIX CPS Active site occupied by encapsulating carbon; CS Adsorbed single carbon atom on the active site; Cw Carbon atom at a site in the final carbon phase, most likely to be a carbon fdament (whisker); D Diameter of reactor; d Reaction order with respect to the activity factor; da Average diffusion path length, da = (2/3)dp ; d[CpS] Changing rate of site density of active site occupied by the encapsulating carbon; Dl Surface diffusivity of carbon at the interface of metal and support; dp Average metal particle diameter; d'p Average catalyst particle size; Ds Diffusivity of carbon in the metal particle; DsNj Diffusivity of carbon in nickel; dSv Changing rate of site density of active site of catalysts; dx Finite distance of the finite layer of metal slab; E Activation energy of reaction; ED Activation energy of carbon diffusion through metal; G Mass velocity; hs Heat transfer coefficient between catalyst exterior surface and bulk fluid; HS, H* Chemisorbed H species; i Size of critical cluster, 10; (z +1) Nr Carbon nucleation rate on the tailing face of the metal particle; K Symbol used for equilibrium coefficients; k Empirical rate constant for the carbon deposition reaction; kx Defined as kx = k[PCH ; k[ Rate constant for reaction CH4 + 25, —C// 3S, + HS,; k2 Defined as k2 = k'20s ; k'2 Rate constant for reaction CH^ + s2  k* > CH^S1 + 51,; &3 Rate constant for reaction 2HSt —K->—> H2 + 25,; X X " - A K. K, CH KCH2 KCHS KCH, CHt KCH, K K CH, K K graphite growth KM K M Rate constant for reaction CH.S.^-^CH^+^H,; 3 — x Rate constant for reaction CH3S2 —^•CHXS2 + —^—H2; Effective thermal conductivity of catalyst bed, assuming 26.5 W/mK; Equilibrium constant for reaction CNi f + * <=> C * ; Equilibrium constant for reaction CH * +* <=> C * +H * ; Equilibrium constant for reaction CH2 * +* <^> CH * +H * ; Forwarding reaction rate constant for CH3S + 3S <=> CS + 3HS ; Equilibrium constant for reaction CH3S + 35 <=> CS + 3HS ; Forwarding reaction rate constant for CH4 + 2* <=> CH3 * +H *; Equilibrium constant for reaction CH4 + 2* <=> CH3 * +H *; Equilibrium constant for reaction CH4 + * <=> CH4 * ; Constant in the Scherrer equation, 0.89; Rate constant for the deactivation; Equilibrium constant for reaction CH4 = C(graphite) + 2H2; Rate constant for encapsulating carbon formation; Rate constant for the forwarding reaction of C H 4 dissociation CH4+2S-*CH3S + HS; Combined rate constant for the gasification k = kr KCH,KH Equilibrium constant for the reaction with graphite carbon formation; Rate constant for the carbon growth step; Equilibrium constant for reaction 2HS < K" > 2S + H2; Defined as P„JPCHt\ Defined as k~M = k~M • KU1; Experimentally determined threshold constant for the C H 4 cracking; Rate coefficients of the forward and the reverse reaction of the rate-determining step CH4 * +* CH3 * +H *; xxi KfM Filamentous carbon formation threshold; knucl Rate constant for the carbon nucleation step; Kobserved Observed equilibrium constant for the reaction with fdamentous carbon formation; k Thermal conductivity of catalyst particle, assuming 1.7x 10" W/mK; kr Reverse reaction constant C7f4 + 2S • » CH3S + HS; Kr Defined as K, = K3K,K5; Kj Defined as K'r=Kr/ K%2 = K,K4K51K^1; K' Defined as term K'r = K'r/(Ke-cC(Ni,sal)); Kw Equilibrium constant for reaction C N i r ts> Cw; L Catalyst bed length; L M Length of diffusion path of carbon in the metal; L R Reactor length; M Molecular weight of graphitic carbon; mc0 Total number of moles of surface metal sites; n Reaction order; «,(/) Site density of single carbon atom on the tailing face of metal slab; nc (t,x) Site density of single carbon atom in the metal particle; nCH Cumulative CH4 consumption as a function of time-on-stream; ncr Site density of carbon in the carbon tubes on the tailing face, for Kinetic Model I; nj (t) Site density of critical cluster on the tailing face; tijit) Site density of small clusters containing j atoms; nM Mass flux of carbon in the diffusion direction; np (t) Site density of encapsulating carbon on the leading face of metal slab; NPe Peclet number (Dimensionless); N P e Minimum Peclet number (Dimensionless); dn Nr Defined as Nr = — - = D.n,nr; dt 1 1 x NRC/t Reynolds number based on particle diameter (Dimensionless); X X I I ns (t) Site density of single carbon atom on the leading face; nx (r) Site density of stable carbon cluster on the tailing face of metal slab; PCH, > PH, Partial pressure of C H 4 and H 2 in the gas phase; PCO Partial pressure of CO; P C O i Partial pressure of C 0 2 ; R Gas constant; r Measured methane decomposition rate; r* Maximum rate of carbon deposition; R Rate of reaction per unit mass of catalyst; rc Carbon deposition rate; rd Carbon diffusion rate leaving the leading face of the metal particle; rd Average carbon diffusion rate through the metal particle; rj Impinging carbon diffusion rate on the tailing face of the metal particle; re Encapsulating carbon formation rate; (rf -rg) Net rate of carbon formation; rf Carbon deposition rate; rf „ Net rate of carbon formation; rg Carbon gasification rate; rgrowth Carbon growth rate on the tailing face of the metal particle; rM Radius of metal particle size; rm a x Maximum rate of carbon deposition rate; rnucl Carbon nucleation rate on the tailing face of the metal particle; rp Radius of catalyst particle; rr n Net rate of carbon removal; rt Radius of rector; Rv Rate of reaction per unit volume of catalyst; S, S{ Metal Active site; S2 Support site; ssl A subsurface site just below the surface on which the surface reactions take place; XX111 ssl A subsurface site just below the interface between the nickel particle and the support; Sv Available active site on the leading face; SV Space velocity; 5 v 0 Total active site on the leading face of catalyst; T Temperature; t Time-on-stream; t Time at which the rate of carbon deposition reaches its maximum value; Tb Temperature of bulk fluid; Ts Temperature of catalyst surface; Tw Temperature of reactor wall; u Superficial velocity; V Volume of reactor; w Instrumental peak broadening, w = 0.004 radians; W Full width at half maximum of the diffraction peak (FWHM); X Length in the carbon diffusion direction of metal slab; X Conversion of the reaction; xstable Defined as xstable = aiDi £ «, (t) dt; z Direction of carbon diffusion in the metal; 8 Defined as B = ^ W2-w2 ; y Surface tension of carbon fibres; ACC Free energy deviation between the reaction for filamentous carbon formation and graphite carbon formation; AG°mphite Free energy observed for the reaction with graphite carbon formation; AG°bserval Free energy observed for the reaction with filamentous carbon formation; AH Heat of reaction; A#2°98 Standard heat of reaction at 298 K ; 0 Diffraction angle in the X-ray diffraction measurement, radians; 6*, 0S) Surface coverage of the available surface active site; 6CH s Fractional surface coverage by species CHxSi, where x = 0 ~ 3; xxiv 6CH Active site occupied by the species indicated by the subscription, where x = 0~3; OCH s2 Fractional surface coverage by species CHXS2, where x = 0 ~ 3; 6HS Fractional surface coverage by species HS ; 0 Orientation angle between the graphite basal planes and the tube axis; X Wavelength of radiation Cu Kct, 1.54 A; p Gibbs free energy for the graphite with radius r ; p Contribution of free energy from structural defects compared to graphite; p0 Gibbs free energy for the graphite without curvature; /i Viscosity of the fluid, gas phase; p Density of gas phase; pc Density of graphitic carbon; pu Density of the metal; pp Density of catalyst particle; a, and <JX Capture number that describes the diffusion flows of single atoms to critical cluster or stable clusters; axD^nlnx Single carbon nucleation rate due to the growth of stable cluster; O Metal dispersion defined as the metal atoms on the surface relative to the reduced metal; co Mass fraction of carbon in the metal; og Mass fraction of carbon in the metal at the interface between the gas phase and metal phase; coL Mass fraction of carbon in the metal in the metal at the interface of metal and support; . X X V Acronyms: B.E. Binding energy; C A E M Controlled atmosphere electron microscopy; CFC Catalytic fdamentous carbon; C N Carbon nanofibres; C V D Chemical vapour deposition; FDD Flame ionization detector; FT Fischer-Tropsch; F W H M Full width at half maximum of the diffraction peak; GC Gas chromatograph; M F C Mass flow controller; MS Mass spectroscopy; MSI Metal-support interaction; P E M Proton exchange membrane; PV Pore volume; RDS Rate determining step; SA Surface area; SV Space velocity; TCD Thermal conductivity detector; T E M Transmission electron microscopy; TOF Turnover frequency; TPR Temperature programmed reduction; XPS X-ray photoelectron spectroscopy; X R D X-ray diffraction; xxvi Preface Methane activation is important in a number of reactions that aim to convert natural gas to more valuable products using supported metal catalysts. These reactions include C H 4 steam reforming and dry reforming for synthesis gas production, and C H 4 homologation for higher hydrocarbon synthesis. As a potential alternative to steam reforming and partial oxidation, catalytic decomposition of C H 4 may provide H2 without CO contamination for use with P E M fuel cells. However, the mechanism of carbon deposition and catalyst deactivation during C H 4 decomposition is complex and not fully understood. The present work is aimed at clarifying some aspects of the catalyst deactivation during the decomposition of C H 4 at moderate temperatures on low loading Co and Ni catalysts. Effects of gas composition and supported metal catalyst properties, such as metal particle size and metal-support interaction, in particular, were examined. Furthermore, based on the experimental observations, a kinetic model was developed to describe the deactivation and steady growth of fdamentous carbon after an initial rate increase that is ascribed to carbon nucleation. The organization of the present thesis is briefly outlined in the following section. The present thesis includes 7 Chapters, References and Appendices. In Chapter 1, the interest in the application of C H 4 decomposition, the motivation and the objectives of the present study are presented. The detailed literature review of previous contributions and existing questions are discussed in Chapter 2. Then, the experimental set-up, catalyst characterization and activity measurement methods are presented in Chapter 3, including an explanation of how measured activity profiles were analyzed and presented in the present work. In Chapter 4, the deactivation mechanism is discussed based on the experimental observations of effect of gas phase compositions. Furthermore, the coking threshold and fdamentous carbon formation XXV11 threshold, related the onset of carbon formation and the fdamentous carbon formation, respectively, are presented. In Chapter 5, the effect of metal properties, such as the metal type and metal-support interaction, on the deactivation are presented. The correlation of the coking threshold and the difference between two thresholds with the metal particle size is also discussed. In Chapter 6, a kinetic model that includes carbon nucleation and encapsulating carbon formation is developed to describe the catalyst deactivation or steady growth of carbon filaments after the initial rate increase. In Chapter 7, the conclusions of the present study are summarized. Recommendations for future work are also presented. The important calculations and experimental details are shown in Appendix A to confirm that the operation conditions in the present study are in the differential reactor mode. The GC operating conditions, Calibration of GC and mass flow controller, XPS Spectra and X R D diffraction profdes of catalysts and the script fde of kinetic model in Matlab are also provided in Appendices. I wish to express appreciation to my supervisor, Dr. Kevin J. Smith, for the guidance and many valuable comments made throughout my study. I wish to thank my research committee members: Dr. X . Tony B i , Dr. Keith A.R. Mitchell, and Dr. Paul A . Watkinson and colleagues for their help. I also wish to thank Dr. Xiaonial L i for the TPR measurement. I gratefully acknowledge Dr. K . C . Wong for XPS measurements and Dr. ChangChun Y u for helpful discussions of the XPS results. Finally, I wish to acknowledge the support of my husband, Weiguo Ma, who has shown a great deal of patience during my Ph. D studies. Chapter 1 Introduction 1 Chapter! Introduction 1.1 CH 4 Decomposition Hydrogen, being a clean source of energy, is predicted to be the fuel of the future. Currently, the production of hydrogen from hydrocarbons, particularly C H 4 , has attracted a lot of attention for fuel cell applications. Among the fossil fuels, C H 4 has the highest H/C ratio and thus is the most obvious source for hydrogen. Steam reforming of C H 4 represents the current technology for hydrogen production. Other common methods of hydrogen production include auto-thermal reforming and partial oxidation. However, all these processes involve the formation of a large amount of CO2 as a by-product and this is of concern since CO2 is a major greenhouse gas. C02-ffee hydrogen production via C H 4 decomposition has been suggested as a possible route to circumvent CO2 formation during H2 production. Since only hydrogen and carbon are formed in the decomposition process, separation of hydrogen is not an issue. The other main advantage of this approach is the simplicity of the C H 4 decomposition process as compared to conventional H 2 production methods. For example, the high- and low- temperature water-gas shift reactions and C 0 2 removal step (involved in the conventional methods) are completely eliminated (Choudhary et al., 2003a). Furthermore, as a potential alternative to steam reforming and partial oxidation, non-oxidative cracking or decomposition of C H 4 may provide hydrogen without carbon monoxide contamination. Proton exchange membrane (PEM) fuel cells have a requirement for CO<10 ppm in the hydrogen fuel. Currently, the water-gas shift reaction and the methanation reaction are used to reduce the CO concentration in hydrogen produced by steam reforming, dry reforming and partial oxidation of C H 4 . But these purification steps add substantial cost to the operation of Chapter 1 Introduction 2 a fuel cell. In view of the stringent CO intolerance of the state-of-the-art P E M fuel cells, it is desirable to explore CO-free fuel processing alternatives. Another research interest in C H 4 decomposition stems from the interest of new materials synthesis. Filamentous carbon, formed during C H 4 decomposition, possesses a variety of properties with prospective applications as catalyst supports, reinforcement material, selective adsorbents, and as energy storage devices. Based on the above three research interests, C H 4 decomposition has drawn a lot of attention recently. Although CH4 decomposition has been investigated for the above purposes in the past, little attention has been paid to catalyst deactivation. In particular, the kinetics of C H 4 decomposition, that include the initial nucleation and deactivation, have not been incorporated in published kinetic or mechanistic models of the C H 4 decomposition process on supported metal catalysts. 1.2 Motivation The motivation for the current study of CH4 decomposition is associated with the deactivation phenomena from previous studies of CH4 homologation. In previous work (Zadeh and Smith, 1998), the initial high rate of CH4 decomposition on supported Co catalysts at 723K and 101 kPa, decreased rapidly but continued despite the nominal coverage of surface Co by C H X being greater than 1. A semi-empirical model that was developed to describe this observation assumed that the decomposition of CH4 on a Co site was followed by the migration of the resulting CH3 surface species from the metal to the support. The migration step was essential to explain the decreased but sustained catalyst activity observed during CH4 decomposition. However, an alternative mechanism for C H 4 decomposition is that fdamentous carbon was formed during the reaction, which is common especially on N i catalysts at high Chapter 1 Introduction 3 temperature (> 773K). The generally accepted mechanism of fdamentous carbon growth (Baker et al., 1972) implies that fdamentous carbon forms without encapsulation of the catalyst metal surface that is responsible for the decomposition of the C H 4 gas. In neither of the above two mechanisms will the metal active site be occupied by the carbon species. Hence, the present work is aimed at clarifying the deactivation mechanism during the decomposition of C H 4 at moderate temperatures on low loading Co and N i catalysts. One objective of the present study is to determine whether the carbon fdament formation mechanism occurs during C H 4 decomposition under mild conditions (temperature 723K ~ 773K) on Co catalyst. The conditions at which the on-set of fdamentous carbon formation occurs will be elucidated so that the kinetic model of Zadeh and Smith (1998) can be extended to account for fdamentous carbon formation. 1.3 Objectives of the Research The goal of the present work is aimed at clarifying the mechanism of catalyst deactivation during C H 4 decomposition at moderate temperatures on low loading Co and N i catalysts. Effects of supported metal catalyst properties, such as particle size, metal-support interaction, and gas composition, in particular, were examined. Furthermore, based on the experimental observations, a kinetic model was developed to describe the experimentally observed deactivation or steady growth of filamentous carbon after an initial rate increase that was ascribed to carbon nucleation. The main objectives of the present study are: A. To clarify the significance of carbon species migration and carbon bulk diffusion; B. To illuminate the effect of operating parameters, temperature and gas phase composition, on the catalyst deactivation during C H 4 decomposition; C. To determine the operating conditions for the on-set of filamentous carbon formation; Chapter 1 Introduction 4 D. To elucidate the mechanism of catalyst deactivation; E. To clarify the effect of catalyst properties, metal particle size and metal-support interaction, on the deactivation during C H 4 decomposition; F. To develop a kinetic model that includes carbon nucleation and encapsulating carbon formation, to describe the observed C H 4 decomposition rate as either stable activity or decreasing activity after the initial rate increase. Chapter 2 Literature Review 5 Chapter 2 Literature Review Effective utilization of methane remains one of the long-standing problems in catalysis (Choudhary et al., 2003a). Over the past several years, C H 4 conversion to more valuable products has attracted significant attention either through direct conversion, such as by C H 4 oxidative coupling, C H 4 aromatisation or the cyclic C H 4 homologation reaction; or by indirect conversion to syngas (CO+H2) produced by conventional steam reforming, dry reforming, partial oxidation or the more recently proposed cyclic process with C H 4 cracking at high temperature or moderate temperature followed by gasification of carbon with steam or oxygen, in order to produce high purity H2 and syngas separately (Choudhary et al.,1999, 2001a, 2001b, 2002a, 2002b, 2003a, 2003b). In all of the above processes, the activity of the catalyst in the C H 4 activation step and the carbon species formed in this step, are important and influence the selectivity, yield to the desired products and the life time of the catalyst. Previously, C H 4 decomposition was studied as an important side reaction in a number of reactions that aim to convert natural gas to more valuable products using supported metal catalysts. Accordingly, extensive attention has been paid to the mechanism of carbon deposition and subsequently the prevention of catalyst deactivation by carbon deposition. Currently, because of the increased interest in H 2 production free of C 0 2 and CO, and the synthesis of new materials as discussed in Chapter 1, C H 4 decomposition has been investigated as a primary reaction of interest. In the following sections, contributions by researchers and unresolved questions relevant to C H 4 decomposition kinetics are discussed in detail. Chapter 2 Literature Review 6 2.1 Appl icat ions o f C H 4 Decomposi t ion A number of new processes have been proposed for high purity H2 production. Sternberg (1995, 1998, 1999a, 1999b) described a non-catalytic fossil fuel decarbonization process at temperatures above 1073K, to produce particulate carbon and H 2 for use as an energy source and thereby reduce greenhouse gas emissions. Muradov (1998 and 2001a, b) proposed catalytic pyrolysis of C H 4 to produce H 2 and elemental carbon using alumina-supported 10wt% Fe203 and NiO operated at 1123K. Poirier and Sapundzhiev (1997) proposed a concept for a fuel processor based on the catalytic decomposition of natural gas to H 2 for fuel cell applications: natural gas is decomposed over a catalyst, carbon is deposited on the catalyst and H 2 is produced. Once the catalytic bed is fdled with carbon, catalyst is regenerated by burning carbon in air. This processor produced a H 2 gas stream with purity greater than 95% (compared to 75% with conventional steam reforming.). Meanwhile, Amiridis and coworkers (Zhang et al., 1996a; Zhang and Amiridis, 1998; Aiello et al., 2000) also proposed the combination of C H 4 cracking-steam regeneration in two distinct steps as an alternative to conventional steam reforming. The two-step process allowed for a partial separation of the products, since only H 2 was produced during the cracking step, and probably, a better control of the selectivity during the steam gasification step. Such a separation was made practically possible because of the ability of nickel particles to form carbon nanofibres (Section 2.2.1), and thus accumulate significant amounts of carbon on the catalyst before deactivation occurred. Direct cracking of a diluted 20%CFL; over 16.4wt% N i / S i 0 2 catalyst and regeneration was mainly studied by Amiridis and coworkers (Zhang et al., 1996a; Zhang and Amiridis, 1998; Aiello et al., 2000). Choudhary and coworkers (2002b) also examined the feasibility of cyclic production of H 2 mainly on N i catalysts supported on S i0 2 , Al 2 03, H Y and Z r 0 2 and Ni /Zr0 2 were identified as promising catalysts for the cyclic stepwise steam reforming of CH4 to H 2 and C 0 2 at 773K. From the point view of CO Chapter 2 Literature Review 7 impurity for P E M fuel cell application, Choudhary et al. (2001a) reported that there were still low levels of CO formed, due to the interaction of surface carbon (formed from C H 4 decomposition) with the support. The amount of CO has been quantitatively analyzed (part per million levels) by methanation of the CO and subsequent analysis by flame ionization detection (FID). The CO content in the H2 stream was dependent on the support used. The low levels of CO coupled with the stability of the catalysts for C H 4 decomposition made this an interesting conceptual process for H2 production for fuel cell applications. From the point view of new materials research, Kuvshinov and coworkers (Kuvshinov et al., 1998; Ermakova et al., 1999 and Ermakova et al., 2000) used high loading N i catalysts with different preparation methods as a novel way to produce fdamentous carbon and H 2 by catalytic C H 4 decomposition. Avdeeva et al. (1999) studied C H 4 decomposition on coprecipitated 60-75wt% Co-alumina catalyst at 748K to 773K. Otsuka and co-workers (1999, 2001 and 2003) reported C H 4 decomposition over N i on different supports. Their main focus in this area was to understand what factors controlled the carbon nanofibre morphology. 2.2 Carbon Formation during C H 4 Decomposition C H 4 decomposition is described by Equation (2.1). C H 4 decomposition is an endothermic reaction. H2 is the only gas phase product and carbon is produced as a solid deposit during C H 4 decomposition. CH, > C + 2H2 AH°29S = 75.6M I mol (z. l) 2.2.1 Carbon Morphologies Catalyzed deposition of carbon from the gas phase results in a number of different carbon morphologies, among which filaments, nanotubes and encapsulated carbon are the most Chapter 2 Literature Review 8 important. Carbon nanotubes and filaments are referred to as catalytic filamentous carbon (CFC) or carbon nanofibers (CN) (Shaikhutdinov et al., 1997) in the present study, which are cylindrical or tubular carbon with radii in the nanometer scale and lengths up to several micrometers. The primary differences among these three carbon deposits are shown in Table 2.1 and a schematic of parallel type and fishbone type carbon nanofibres is provided in Figure 2.1. Table 2.1 Different morphologies of carbon deposit (Nolan et al., 1998). Type Shape Orientation of graphite layer Position of catalyst particle H 2 effect Filaments Carbon cones are "stacked" 0<9O (Filaments with large orientation are often not hollow) At their tip H 2 is believed to satisfy the valences at cone edges (the orientation angle 0 increases) Nanotubes Low H 2 end member of cylindrical carbon deposit 0=0 At their tip Essentially a filament without graphite edges, requiring no valence-satisfying species such as H 2 Encapsulated carbon Multilayer "shells" encapsulating catalyst particles N/A Surrounded by graphite carbon N/A Note: Orientation of graphite layer is the orientation angle 0 between the graphite basal planes and the tube axis. Note that carbon deposition has been studied for two different reasons in the past. Conventionally, carbon formation had been studied to eliminate or reduce the formation of catalytic filamentous carbon (CFC) on catalysts in steam reforming of CH4. Recently, a great deal of effort has been directed towards optimization of process conditions for CFC formation for H2 production, and to tuning the properties of the CFC for desired new materials production. Chapter 2 Literature Review 9 axis Parallel type Fishbone type I I axis I Figure 2.1 Simplified representation of the structure of parallel (left) and fishbone type (right) carbon nanofibres. The cross sections shown relate to the projections observed by T E M . 2.2.2 Mechanism of CFC Formation The mechanism of CFC formation has attracted a lot of attention because of the unique activity behaviour observed during CFC formation. A typical CFC growth activity profile is presented in Figure 2.2. A steady-state activity can be obtained, contrary to an expected activity drop as carbon deposition on the metal catalyst surface removes catalyst sites for CH4 decomposition. Chapter 2 Literature Review 10 Figure 2.2 Typical rate versus time curve for CFL; decomposition (Snoeck et al., 1997a). Based on the qualitative and quantitative data obtained from experiments using the technique of controlled atmosphere electron microscopy (CAEM), a mechanistic interpretation on the growth of CFC was first proposed by Baker et al. (1972). They proposed that the adsorption and decomposition of the carbon-containing gas on one side of a metal particle, led to the formation of carbon atoms which then dissolved into the metal particle, diffused through the metal particle, and precipitated on the opposite side of the particle in the form of filamentous carbon. Snoeck et al. (1997a) included a carbon segregation step into the above mechanism. Figure 2.3 shows a schematic description of the CFC formation mechanism. Chapter 2 Literature Review 11 Selvedge due to segregation behaviour Diffusion of carbon through metal Adsorbed carbon Metal particle Carbon filament Support Figure 2.3 Schematic of CFC formation mechanism. Regarding the rate determining step (RDS) in CFC formation, there is a debate in literature. The diffusion of carbon through the catalyst metal particle is generally considered to be RDS in the growth of CFC. The strongest quantitative evidence for the carbon diffusion as the RDS was the observation from several in situ electron microscopy studies that demonstrated that the activation energy E for fdament growth from acetylene was in excellent agreement with the activation energy for diffusion of carbon through the bulk metal E D (Holstein et al. 1995). The data given in Table 2.2 demonstrate the agreement. However, kinetic studies (Alstrup et al., 1993) have also shown that the first CH4 dehydrogenation step is RDS. The driving force for carbon diffusion from the metal-gas interface (where adsorption and decomposition of feed gas molecules takes place) to the metal-nanofiber interface (where carbon precipitates to form carbon nanofibers) has been proposed to be either an isothermal carbon concentration gradient or a temperature gradient. According to the study of Holstein et al. Chapter 2 Literature Review 12 (1995), however, bulk metal carbides can be ruled out as intermediates and Soret diffusion can be ruled out as a positive driving force for carbon diffusion. Table 2.2 Comparison of activation energies for diffusion of carbon through metal, ED, and that for carbon filament growth, E . Metal ED, kJ/mol E , kJ/mol a-Fe 78-80 67±5 76±8 y-Fe 148-154 142+12 Ni 139-145 145 Co 145-162 139±7 Cr 110-117 113+15 V 116 115+12 Mo 139-172 145±17 2.2.3 Thermodynamic Properties of CFC In earlier studies of CFC formation from CO and C H 4 , attempts were made to characterize the thermodynamic properties for carbon formed by measuring equilibria of reaction. These studies observed that the equilibrium constants of reactants were smaller than the equilibrium constants corresponding to the formation of graphite. In addition, Rostrup-Nielsen (1972) observed that the deviations depended on the nickel particle size. The equilibrium constant obtained varied from catalyst to catalyst and the equilibrium correlated with the maximum nickel particle size of the catalyst. Thus the greatest deviations from graphite data were observed on catalysts with small nickel particles. The deviation from graphite data was explained by a more disordered structure of carbon formed during CFC formation and by a contribution from the surface energy of the carbon nanofibers. Chapter 2 Literature Review 13 2.3 Kinetic Studies of C H 4 Decomposition For the last two decades, much attention has been paid to CFC deposited on 3d-metal catalysts (Ni, Fe, Co and their alloys) as exemplified by the studies of Baker (1989), Rostrup-Nielsen (1972) and Geus (1985). However, the factors controlling the formation of CFC are still not well understood. 2.3.1 General Activity Profile During CFC production, the measured catalyst activity generally undergoes the following changes as the reaction proceeds: (1) an initial increase in activity; (2) a stable activity (the time for CFC formation); and (3) a decrease in activity (time of catalyst deactivation). Based on these observations, the general carbon decomposition process is assumed to involve three stages: (1) an induction period; (2) a steady-state growth and gasification of filamentous carbon; (3) catalyst encapsulation (Baker et al., 1972; Kuvshinov et al., 1998). However, these three stages are not always observed. On the one hand, some researchers reported stable activity without deactivation. For example, Snoeck and co-workers (1997a) reported that the weight versus time curve for the C H 4 cracking has only two zones: one with an increasing rate of carbon formation and one with a constant rate. The zone with decreasing rate, due to gradual deactivation of catalyst observed by Baker et al. (1972), was not been observed by Snoeck and co-workers (1997a). Accordingly, the kinetics describing stable activity was developed based on the experimental observations of steady growth of CFC. Typically, Safvi et al. (1991), Alstrup and Tavares (1993) and Snoeck et al. (1997a and 1997b) investigated the kinetics of C H 4 decomposition over supported metal catalysts without considering catalyst deactivation. These kinetic models of steady CFC growth will be discussed in Section 2.3.2 in detail. On the other Chapter 2 Literature Review 14 hand, some researchers observed only deactivation instead of steady growth of CFC. Accordingly, deactivation models were developed by these investigations. Typically, Demicheli et al. (1991) and Kuvshinov et al. (1998) investigated deactivation during CH4 decomposition using empirical models, which will be discussed in Section 2.3.3. However, although the mechanism for CFC formation, as discussed in Section 2.2.2, has been generally accepted and kinetic models have been developed, neither the kinetic models for steady growth nor the empirical models for deactivation can describe the general activity profde. In particular, the initial rate increase observed in the beginning of the reaction has not been considered. (Studies related to the induction period will be discussed in Section 2.3.5.) Hence, a general kinetic model, especially one that includes carbon nucleation and encapsulating carbon formation, is needed. 2.3.2 Kinetic Model of Steady CFC Growth Various kinetic models have been suggested for steady CFC growth during CH4 decomposition. Table 2.3 gives the detailed mechanisms, rate equations and reaction conditions examined. In the simplest model it was assumed that the rate of CFC formation was proportional to the carbon activity in the gas phase, independent of the nature of the carbon containing gas and applicable to endothermic as well as to exothermic reactions (Audier and Coulon, 1985). (Note that the diffusion process was only considered as a true rate-determining step (in the sense that other steps could be considered equilibrated) at low ac (gas), where ac is the activity of carbon {ac=K.ePCHJ and Ke is the equilibrium constant for the reaction:CH4 -C(graphite) + 2H2)) Lund and co-workers (Lund and Yang, 1989; Safvi et al., 1991; Chitrapu and Lund, 1992) further examined this dependence using ct-Fe, y-Fe and N i catalysts. At low ac, the dependence was strong, but as ac increased it became weaker. Chapter 2 Literature Review 15 Accordingly, a one-dimensional model of the fdament growth process, considering a disk shape metal particle, was proposed to qualitatively explain this dependency (Safvi et al., 1991). However, quantitatively the model predicted a much higher carbon growth rate than was observed. Furthermore, a two-dimensional model (Chitrapu et al., 1992) was proposed to refine this one-dimensional model by accounting for the variation in diffusion path length with filament radius using a pear shape particle. However, the results were not significantly better than those obtained via the one-dimensional approximations, and the two-dimensional model required significantly more computational effort. Hence only one-dimensional model equations are listed in Table 2.3. Note that the effort of Lund and co-workers (Safvi et al., 1991; Chitrapu and Lund, 1992) was focused on the steady-state carbon growth. The driving force for carbon diffusion was shown to be through the gradient in chemical potential (one-dimensional model, with activity of carbon equal to 1 at interface of metal and support) or concentration (two-dimensional model) of the dissolved carbon between the top and bottom surface of the particle. Based on studies of carbon deposition on Fe films, Grabke and co-workers (1980) suggested a kinetic model for the dissociative adsorption of CH4. In this model it was assumed that adsorbed CH4 was stepwise dehydrogenated. Furthermore, Alstrup et al. (1993) showed that the linearized versions of the Grabke-type kinetic models could be fitted accurately to experimental results for the steady-state carbon deposition on silica-supported nickel catalyst, but only below a critical carbon activity, which depended weakly on the temperature. This linearized version of Grabke-type kinetic models is useful to determine whether the chemisorption of the C H 4 molecule or the dehydrogenation of methyl is the rate-limiting step. More recently, Snoeck and coworkers (1997a and 1997b) proposed a rigorous CFC formation model. The coupling of the surface reaction, the segregation process, and the diffusion of carbon through the nickel particle led to a detailed model of the process of carbon filament Chapter 2 Literature Review 16 formation, which formed the basis for the kinetic modeling of the carbon formation and carbon gasification reaction. In this model, it was assumed that the diffusion of carbon through Ni originated from a concentration gradient, which implied a different solubility at the nickel-gas and the nickel-carbon interface. A thermodynamic basis for the different solubilities was provided. The segregation of carbon, taking place at the gas side of the N i particle, was added as one of the steps in the global mechanism of carbon filament formation and gasification. The segregation process was described in a way similar to that of gas adsorption. Based on the Hougen-Watson approach, the following rate equation was derived for the above mechanism (Snoeck and coworkers, 1997a and 1997b): k+ . K • P M K -r • p2 ftM rCHi . cC(Ni,f) rH2 K, (\ + K r +—^-r .pi/2 + K ' P ">2 *-2'2^ ^ 1 + A C CC(Ni,f) + £ CC(Ni,f) rH2 +J^CH4 rCHj Since cC(Nif), the carbon concentration at the catalyst support side could not be measured or calculated, it was eliminated by coupling the diffusion step with the rate equation for the surface reaction during steady-state growth, i.e., c C ( M / ) = cC(Nisal) +———rc. For the case with low carbon affinity, it was assumed that the concentration of carbon dissolved in Ni was almost uniform over the whole nickel particle for all experimental conditions and equal to the concentration of carbon at the support side of the particle: c c ( M 7 ) « c c ( M . r ) « c c ( M m ( ) since da l(DSM • am)< cC(Nisat). (Note: symbols see nomenclature.) For the cases that the concentration gradients through the N i particle were non-negligible, the concentration of carbon in the N i particle could not be assumed to be uniform and was not equal to the saturation concentration at the support side. Chapter 2 Literature Review 17 Also of note is the fact that the abstraction of the first H atom from molecularly adsorbed CH4, with the formation of an adsorbed methyl group, was treated as the rate-determining step. This was contrary to theoretical studies that showed that the activation energy for the activation of gas phase C H 4 (CH4 + 2* <=> CHi * +H *, where * represents an active catalyst site) was less than that of adsorbed C H 4 (CH 4 * +*« C7/ 3 * +H *) over group VIII metal catalysts (Shustorovich and Bell, 1991). It is more reasonable to assume that the first step of the activation reaction can be written as CH4 +2* <=> CH3 *+H*, but Snoeck et al. (1997b) explained that the difference in RDS could arise from the fact that the theoretical studies and their kinetic studies (Snoeck et al., 1997 a and b) were performed in a completely different pressure range. 2.3.3 Empirical Deactivation Model Since most kinetic studies have focused on the steady-state CFC growth, there is no kinetic model that describes the deactivation of the catalyst. Only empirical models, proposed by Demicheli et al. (1991) and Kuvshinov et al. (1998), are available to describe the deactivation of the catalyst during CH4 cracking. Table 2.4 gives the detailed rate equations and reaction conditions examined. Demicheli et al. (1991) considered the activity factor, a , dependent on the time, temperature and CH4 and H2 partial pressures. Kuvshinov et al. (1998) investigated the deactivation of the catalyst proposing a carbon blocking of the surface active sites. Then, the rate of deposit was found to be proportional to the amount of CFC on the catalyst, the rate of CFC formation was in inverse proportion to the exponent of the product of the CH4 to H2 concentration ratio and time. Chapter 2 Literature Review 18 Table 2.3 Kinetic models of CFC steady growth during CH4 cracking. Reference Rate equation Mechanism Catalysts, operation range Safvi and co-workers (1991) • . - • " ' [ ' W o - i l (2-4) r lr J , . - 1 9 9 0 0 , a = 1.43 exp( ) Where T (2.5) p = 2 3.2 (2.6) y = 2 .42 x 10"' e x p ( - ^ P - ) ( 2 - 7 ) «„=-p.D,!£- (2-8) az where D^ = a(\- pa )e"° (2.9) Boundary conditions: ac (z = 0) = ac (gasphase) (2.10) a c ( z = Z.) = 1.0 a-Fe, 7-Fe and Ni Alstrup and Tavares (1993) Assume CH 4 dissociative chemisorption is RDS: rCIP2H2=kCHf2^T- (211) Assume the dehydrogenation of methyl is RDS: r /pi =KCHIKCH3 E*PCH< rClrHl „ i / 2 U D2 \L-VA> KH ^H2 General micro kinetic model: rC~^CH. ^Crlfi „ @Crlfirl ~ I KCH) 1 (2.i3) rc — kCH^ 6CH^ 9 0CH^ 6H \ KCH, ) Based on stepwise dehydrogenation of surface species after chemisorption of the CH 4 molecule. H +2* <=> 2H* K CH4 +2*o CH, *+H* kCHi 1 KCHt CH, * +* o CH2 * +H * kCH; IKCHi CH 2 * +* o CH * + H * CH *+*<=> C*+H* C * +ss \ » Chl + * Cbi + ss2 <=> Cb2 + ss\ Ch2 + ws <=> Cy, + ss2 Ni/Si02 Nio.99Cuo.01/ Si0 2 Ni0.9Cuo.i/ Si0 2 Temperature range 723-863K PCH. • 20-80kPa PHl--5-15kPa Snoeck et al. (1997b) Non-reversible model: the rate-determining step contains forward and reverse ku-Kau -Po.-Jir-Pl (2.14) Reversible model: The approximate reversible version K •«<»,'-Pc.-jfi-PS, (2.15) rc = -CH4+*oCH4* KCH>' CH4 *+*->0/3 *+H* k*M CH, *+*<=> CH, *+H* K CH2*+*<^>CH*+H* KCHi CH *+*<=> C * +H * K 2//*c>// , + 2 * \IKH c => c Ni catalyst promoted with low level of K 773K-823K P rCH, • 1.5~10bar PHI : 0-1.5 bar Chapter 2 Literature Review 19 Table 2.4 Empirical models o f deactivation during CH4 cracking. Reference Rate equation Mechanism Catalysts and operation range Demicheli et al. (1991) rc=r*a (2.16) r" = k(PCHt -P„2/Ke)l(\ + KHP^)"{2.\1) Where a = exV(-kilPCHtT/P„i) (2.18) r = t-t (2.19) where n = 7 The activity factor a was dependent on the time, temperature and CH 4 and H 2 pressure. da d r (2.20) where d=l rd = kdPCH, I ^ H, (2 21) Ni/Al 20 3-CaO CH 4 /H 2 /N 2 mixture 838K-938K Atmospheric pressure Kuvshino v et al. (1998) The dependence for the CFC rate formation: rfc/rfr=,c=[-^l^r2(^-cL)+c"]"<"+,, <2-22) rtm=k(PCH,-P^/Kjl + KHP^)' (2.23) where n = 1 CH 4 adsorption on an ensemble of nickel atoms High loading >30wt% Ni Zadeh and Smith (1998) The rate of change of coverage of different surface species follows directly from equations: cieSi 2 2 - 2kx9s^ + k20CH^ + k30HSi a t (2.24) d t (2.25) — k\Q1 c 2ki0 uc j 1 i , 5 H i , (2.26) LHX\ _ 1 n - / C 4 f 7 c / / j S i (2.27) deCHxSl _ k f ) d t (2.28) The cumulative CH 4 consumption as a function of exposure time are given by: ncHA=-l(.mc0)k,eldt CH4 + 25, — C H , S X + HS, CH,S, + S2 —£-> CH3S2 + 5, 2HSl^-+H2+2St CH,S2-^CHxS2+^H2 (2.30) k2 = k29s^ Co/Si02 Loading < 12wt% 723 K Chapter 2 Literature Review 20 2.3.4 Previous Kinetic Studies of CH4 Activation As mentioned in Chapter 1, the motivation of the present research work stems in part from previous CH4 non-oxidative homologation work (Zadeh and Smith, 1998). Non-oxidative homologation is a route to higher hydrocarbons via a two-step process, which involves high temperature decomposition (CH4+2S->CHXS + HS) followed by low temperature hydrogenation (CHxS + H2->S + CH4,C2H6,C3Hg). In previous work (Zadeh and Smith, 1998), the initial high rate of C H 4 decomposition on supported Co catalysts at 623K and lOlkPa, decreased rapidly but continued despite the nominal coverage of surface Co being greater than 1. To quantify these observations, a kinetic model of CH4 activation was developed assuming decomposition of gas phase C H 4 on a Co site, followed by migration of the resulting C H 3 surface species from the Co to the support, and then followed by stepwise dehydrogenation of CH3S1 and CH3S2. In this model, the migration of carbon species from the metal site to the support site was considered essential for the active site regeneration. The simplified reaction mechanism is shown as in Table 2.4. The model was based only on data obtained from the decomposition of CH4 in the first 2 min of reaction, and consequently pertains only to the very early stage of the reaction. Migration of carbon species from the metal to the support as proposed by Zadeh and Smith (1998) was based on a number of observations from the literature. For example, Ferreira-Aparicio et al. (1997) proposed carbon species diffusion from active metal sites, where CH4 was dehydrogenated, to silica and alumina supports during C H 4 decomposition over Co, Ni , Ru, Rh, Pt, Ir catalysts. Carbon species diffusion was invoked based on the observation that CFf4 was consumed in quantities greater than expected i f one assumed a 1:1 C H X : metal adsorption stoichiometry. In addition, during the decomposition reaction, a simultaneous release of CO and Chapter 2 Literature Review 21 H 2 occurred in the temperature range 550K - 873K as a result of the consumption of the hydroxyl groups of the support by C H X . An alternative explanation for active site regeneration during CH4 decomposition is through the formation of CFC. However, the formation of CFC or the diffusion of carbon through the metal particle was not considered in the model by Zadeh and Smith (1998). Although the mechanism of CFC formation from CO, C H 4 and other hydrocarbons has been studied extensively on N i catalysts, carbon deposition studies on supported Co catalysts are far fewer (Koerts and Santen, 1991; Guczi et al., 1997; Zadeh and Smith, 1998; Boskovic and Smith, 1996) due to the lower activity and lower capacity for carbon deposition of Co compared to N i (Ermakova et al., 2000). However, data presented recently by Avdeeva et al. (1999) demonstrated that co-precipitated 60-75 wt% Co-alumina catalysts showed a high capacity for CFC formation during C H 4 decomposition at 773K. However it is unclear i f CFC could form on the low loading Co catalysts at moderate temperature. Hence, one of the objectives of the present study is to clarify whether CFC formation can account for sustained C H 4 decomposition activity over extended time periods. 2.3.5 Induction Period of CFC The initial rate increase observed during CFC formation is generally referred to as an induction period. Under some reaction conditions, no induction period is observed. Furthermore, under many conditions, graphitic carbon fibres do not grow, although the gas-phase composition is such that fibre growth was expected according to thermodynamics. Consequently, the cause of the initial rate increase and how the induction period affects the CFC formation is a critical question that needs to be addressed. In existing C V D processes, carbon nucleation is considered the most important step for carbon nanotube or diamond formation on the metal surface (Liu and Dandy, 1996; Grujici et al., Chapter 2 Literature Review 22 2002). However carbon nucleation has not been examined in detail for the CFC formation process over metal catalysts. Note that although the accepted mechanism for CFC, discussed in Section 2.2.2, rationalizes the steady-state growth of CFC, the important nucleation step, manifested in an initial rate increase during CFC formation, is not explained by this mechanism (De Jone and Geus, 2000). Snoeck et al. (1997a,b) mentioned that carbon nucleation is important and that the nucleation of CFC was caused by the formation of a solution of carbon in N i that was supersaturated with respect to CFC. The degree of supersaturation was determined by the affinity for carbon formation of the gas phase. It was experimentally observed that the nucleation of CFC was much more difficult under conditions with a low affinity for carbon formation, leading to a slow nucleation and very long periods of increasing rate of carbon formation, but also to a small number of carbon filaments that was finally able to nucleate under these conditions. However, although Snoeck et al. (1997a,b) considered the nucleation of carbon, it was not included in the kinetic steps. Instead, more attention was paid to the experimental procedure. A series of experiments were sequentially performed on "used" catalyst samples, on which carbon was first deposited under standard conditions with a high affinity for carbon formation, so that the experimentally observed rates of carbon formation were all based on the same number of growing carbon filaments. Again, this model only described the steady state of carbon growth and did not describe the initial nucleation. A kinetic model that includes carbon nucleation is worthy of development. Note that, besides carbon nucleation, two possible explanations exist for the observed initial rate increase during C H 4 decomposition. The first is related to the formation of metal carbide. Hoogenraad (1995) has studied the nucleation phase of carbon fibres by using magnetic measurements. In this study, it was assumed that metal carbide was the active site for C H 4 decomposition and metal carbide formation was considered crucial for the start of carbon fibre Chapter 2 Literature Review 23 growth. The study suggested that the formation of carbide causes the initial rate increase. The second opinion is that the faceting of metal particles caused the initial rate increase. It has been stressed by a number of workers that the surface structure of the metal may play a role in the growth process. Alstrup (1988) related the fact that the N i (110) and N i (100) surface were much more active for C H 4 dissociation than the N i (111) surface. The above faceting of the metal particles was in line with electron microscopy observations. Faceting of the metal particle to allow for both hydrocarbon dissociation and graphite precipitation constituted a reasonable alternative for the nucleation phase. It should be noted, however, that all of these observations on the structure metal-particle faceting, inevitably have to be carried out after cooling of the sample and this could invoke crystal shape changes. To date, it remains unclear which of the explanations correctly account for the observed induction period. 2.4 Influence of Metal Catalyst Properties on Catalyst Deactivation The mechanism of catalyst deactivation during C H 4 decomposition is complex. E X A F S and Mossbauer spectroscopies have shown that the form of catalyst remains metallic even after being encapsulated by graphite layers and detached from the alumina support with carbon fibres (Shah et al., 2001). Hence, it was postulated that the catalyst was actually not deactivated by poisoning or change in surface structure, but was isolated from methane by encapsulation and could not participate in C H 4 hydrogenation (Shah et al., 2001). Consequently, the decay constant depends on the rate of carbon build up on the surface of the catalyst, which in turn is a consequence of a number of interacting effects, including the metal type, metal particle size, metal-support interaction and the rate of carbon removal from the metal surface due to carbon bulk diffusion through metal particle, the rate of gasification due to the presence of H 2 , C H X migration rate from the metal to the support, and subsequently the formation of carbon with different morphologies. Nevertheless few studies have focused on the deactivation during CH4 Chapter 2 Literature Review 24 decomposition. Consequently, the mechanism and factors affecting the deactivation are not fully understood. 2.4.1 Influence of Metal Type and Metal Particle Size on Catalyst Deactivation It is generally accepted that the active catalytic site for C H 4 decomposition and CFC growth is a metallic species. The ferrous metals of Group VIII are particularly active as catalysts for the growth of carbon fdaments, the most important being (alloys of) Fe, Co and Ni . A l l of these metals can dissolve carbon and/or form metal carbides. N i is the most common and active catalyst for CH4 decomposition. Shah et al. (2001) also reported H2 productivity results with undiluted C H 4 decomposition on 0.5%M-4.5%Fe/Al 2O3, where M=Mo, N i , or Pd at reaction temperature 973-1073K. Investigations of Co catalysts for C H 4 catalytic cracking are few. Only Avdeeva et al. (1999) reported fdament carbon formation on a 60-75wt% C0/AI2O3 catalyst from CH4 decomposition at 773K. On all metal catalysts T E M measurements generally showed that the diameter of the CFC was closely related to the diameter of the metal particle. Also, it has been reported that the thermodynamic properties of CFC could be correlated to the metal particle size (Rostrup-Nielsen, 1972). Accordingly, coking threshold, corresponding to the operating conditions at which carbon deposition and carbon gasification rates are equal, was dependent on the metal particle size. This suggested that the metal particle size is critical to the carbon growth process. The metal particle size effect for C H 4 decomposition kinetics has been discussed in a number of studies. Firstly, it was reported in literature that the particle diameter was critical for CFC formation (Baker, 1989). Nickel was the most active catalyst for decomposition of hydrocarbons including C H 4 . The catalytic activity for the methane decomposition depended on the size of N i metal particles; i.e., the particle size from 60 to 100 nm was most effective. However, nickel particles larger than 200 nm were incapable of producing filaments and were Chapter 2 Literature Review 25 covered by a carbonaceous crust that isolated them from the reaction medium (Takenaka et al., 2003). For this reason, unsupported nickel powder, liable to strong sintering in hydrocarbon medium, could not produce carbon filaments. Very small particles also appeared to inhibit graphite nucleation. N i particles with diameters of 10-50 nm were known to initiate the growth of CFC, but the formation of CFC did not occur i f the metal particle size was less than 7 nm (Kim et al., 2000). However, the carbon diffusion rate is faster on smaller particles due to the short diffusion path. For a given temperature, the rate of filament growth had an inverse square root dependence with metal particle size (Baker, 1989). Secondly, Bartholomew (2001) reported that carbon formation and carbon gasification rates were influenced differently by modifications in metal crystallite surface chemistry, which were in turn a function of catalyst size. Also, the formation of coke and CFC involves the formation of C-C bonds on multi-atom sites, and hence, one might expect coke or carbon formation on metals to be structure sensitive. Alstrup and Travares (1993) also reported that one way to reduce the risk of carbon encapsulation and still be able to operate close to the carbon formation limit was to dilute the N i surface of the catalyst with atoms which were much less reactive toward CH4 than nickel, e.g., by alloying with copper, taking advantage of the different ensemble requirements for the steam reforming and the carbon formation process. The carbon formation activity and the rate of deactivation were shown to be strongly dependent on metal particle size during the reforming of CH4 with CO2 (Bitter et al., 1998 and Zhang et al., 1996b). Solymosi et al. (1994) reported that the turnover frequency (TOF) for CH4 decomposition over Pd catalysts decreased with the type of support in the order Ti02>Al203>Si02>MgO and this trend was interpreted as being due either to differences in Pd particle size (dispersion decreased in the same order), or the ease with which carbon migration occurred from the metal to the support. However, in this study, the effects of metal particle size Chapter 2 Literature Review 26 on C H 4 decomposition activity were not distinguished from support effects. However, the particle size effect on the catalyst deactivation during C H 4 decomposition was not reported. The effect of metal loading, which is related to metal particle size, is quite unclear in the literature. Hence, a large range of metal loadings was used in literature: low loading catalysts (5wt% to 20wt% metal) were often used in studies reported in literature; catalysts with 0.1 wt% loading were used by Poirier and Sapundzhiev (1997) in their fuel processor application; meanwhile, Shaikhutdinov et al. (1995) used very high loading nickel catalysts, from 30 to 95wt%, to maximize the catalyst carbon capacity. So, it is necessary to clarify the metal particle size effect on the catalyst activity and deactivation during C H 4 decomposition measured on catalysts with different metal loadings. Also of note is the fact that the effect of Co metal particle size on CFC formation has not been reported in the literature. Hence it remains unclear as to whether CFC formation during C H 4 decomposition under the mild reaction conditions employed during C H 4 homologation, can indeed explain the observed kinetics (Zadeh and Smith, 1998) on supported Co catalysts with low metal loading. 2.4.2 Metal-Support Interaction Effect on Catalyst Deactivation Due to recent research interests, some attention also has been paid to enhancing CFC formation. Demicheli et al. (1994) reported that at low content of K , the K facilitated the formation of carbon filaments due to a reduced adhesion strength between the N i particles and the alumina, i.e. the interaction between metal and support. This statement was based on the experimental detection of the location of potassium, at the interface between nickel and carbon, using STEM-EDX. This particular localization of the alkali could lower the adhesion strength of the graphite to the metal particle. Snoeck et al. (1997a) also suggested that the MSI was important in explaining why full or hollow fibres were formed from supported metal particles. Briefly, at low temperature, Chapter 2 Literature Review 27 nucleation was slow and carbon atoms reached the entire metal-support interface via diffusion, and nucleation of a full fibre was observed. At higher temperatures, the nucleation started before the entire metal-support interface had been saturated with carbon atoms. Consequently, the metal/support interaction must be overcome to lift the particle at places where there was no excretion of carbon. They proposed this mechanism based on the observation that pear-shaped, conical or drop-wise particles accompanied the formation of hollow filaments. Similarly, Tavares et al. (1986) suggested that very small particles appeared to inhibit graphite nucleation because the enhanced MSI prevented the particle from being lifted from the surface, again preventing graphite nucleation. Furthermore, on high loaded Ni/SiC»2 and Fe/SiC»2 (80-90wt% of metal), the carbon yield was demonstrated to depend on the interaction between metal and silica. The presence of silicate in amount of ~2wt% in the 90%Ni-10%SiO2 catalyst gave rise to rapid catalyst deactivation. However, for Fe catalysts, silicate can both inhibit and promote the process of carbon formation (Ermakova and Ermakov, 2002). 2.5 Effect of Operating Conditions on Catalyst Deactivation H2 evolution parallels CH4 decomposition and adsorption of H2 onto the metal catalyst can promote gasification of deposited carbon species. The presence of H2 can also affect the carbon morphology (Nolan et al., 1995). But the importance of operating conditions, especially the ratio of P„ I PCHi, on the CFC formation and deactivation has not been fully recognized. Different researchers used different mixtures of C H 4 and H2 to study CH4 decomposition. Consequently, some researchers observed a steady CFC growth whereas activity profiles with deactivation under certain operating conditions, as shown in Figure 2.4 (Shah et al., 2001), have also been reported. Figure 2.4 shows that on the same catalyst, the decay constant is different for Chapter 2 Literature Review 28 two cases and the H 2 concentration or P* IPCHi was quite different in these two cases. Hence, the effect of the ratio of P* I PCHt on the catalyst activity and deactivation needs be addressed. 3 4 Time-on-stream, hr Figure 2.4 Change in H 2 production as a function of time-on-stream at 923K with 0.5%Mo-4.5%Fe/Al2O3 catalyst. The decrease in hydrogen production for a catalyst bed of 1 g is about 6%/hr while for a catalyst bed of 3 g is less than 1%/hr (Shah et al., 2001) (• lg ; • 3g). . Furthermore, a promotional effect of CO on the decomposition of ethylene over Fe to form CFC has been reported (Rodriguez et al., 1993), pointing to a strong influence of gas phase components on CFC formation. Chapter 2 Literature Review 29 2.6 Summary of Literature Review Based on the literature described in this chapter, although CH4 decomposition has been studied extensively, there remain many unresolved issues with respect to the decomposition kinetics, such as the nucleation manifested in the initial rate increase and the formation of encapsulating carbon corresponding to catalyst deactivation. Also, the effect of factors such as metal particle size and gas phase composition on the activity and deactivation of the catalyst during CH4 decomposition remains unclear. The present work is aimed at addressing some of the above issues of deactivation during the decomposition of CH4 at moderate temperature on low loading Co and N i catalysts and developing a general kinetic model, which can describe the general activity profde of either steady growth or deactivation after the initial rate increase, that is ascribed to carbon nucleation. Chapter 3 Experimental 30 Chapter 3 Experimental 3.1 Introduction In this chapter the details of the experimental methods used in the present study for catalyst preparation, catalyst characterization and catalyst activity measurement during C H 4 decomposition, are presented. In Section 3.2, the preparation methods for N i , Co catalysts supported on S i 0 2 and ZrC>2, and the modified Co catalysts, are presented. In Section 3.3 the details of the catalyst characterization methods are given. The number of catalyst active sites was measured by CO chemisorption and the metal particle size was estimated from the CO uptake. Filamentous carbon formation was detected by transmission electron microscopy (TEM). Temperature programmed reduction (TPR) and X-ray photoelectron spectroscopy (XPS) were performed on modified Co catalysts. The experimental set-up for the C H 4 decomposition activity measurements is presented in Section 3.4. In Section 3.4.1, the details of the apparatus are presented. The method used to analyze the measured activity profile is described in Section 3.4.2. Finally, catalyst characterization data are presented in Section 3.5. 3.2 Catalyst Preparation Co catalysts were prepared by incipient wetness impregnation of the silica support using an aqueous solution of Co(N0 3 ) 2 '6Ff 2 0 (+98%, Aldrich). Precalcined (25 hr at 773K) silica gel (grade 62, 60-200 mesh, 15A, Aldrich 24398-1) with a BET surface area of 300 m 2/g and pore volume of 1.15 mL/g was used as the support. After impregnation, the catalysts were vacuum-dried at 383K for 37 hr and then calcined for 10 min at 723K. Note that using extended drying Chapter 3 Experimental 31 times and short calcinations times have been shown to provide improved Co dispersion on SiC>2 support (Coulter and Sault, 1995). N i catalysts were prepared by incipient wetness impregnation of the support using an aqueous solution of Ni(N0 3 ) 2 # 6H20 (+98%, Aldrich). After impregnation, the catalysts were dried at 383K for 37 hr and then calcined for 10 min at 723K. Besides SiC»2, ZrC>2 (Saint-Gobain Norpro Corp.) with a BET surface area of 52.9 m 2/g and pore volume of 0.3 mL/g was used as the support. Modified Co/Si0 2 catalysts were prepared by step-wise incipient wetness impregnation. The pre-calcined (773K for 25 hr in air) silica support (Grade 62, 60-200 mesh, 15A, Aldrich 24398-1) was impregnated with an aqueous solution (de-ionized water) of Ba(N0 3 ) 2 (99.1+% Assay), or La(N0 3) 3*6H20 (99.9%, REO) or Z r O C l 2 ' 8 H 2 0 (99.9%, metals basis). The impregnation was followed by drying in vacuum or in air at 373K for 37 hr, and then calcining in air at 723K for 10 min. The modified S i 0 2 supports contained BaO, La20 3 or Zr0 2 , which were formed during calcination. A further impregnation was then carried out on the modified silica with an aqueous solution of Co(N0 3 )2*6H 2 0 (98+%, Aldrich 23926-7), followed by the same drying and calcination procedure. The modified catalyst will be designated as Co/Me xO y/Si02, where Me stands for Ba, Zr or La. The nominal Co loading for all modified catalysts Co/Me xO y/Si02 was 12 wt%. For Co/Me xO y/Si02 catalysts, the atomic ratio of Co to added metal (Co: Me where Me is Ba, Zr or La) was kept constant at Co: Me = 14:1 by setting the nominal metal loading for Ba, Zr and La to 2.0 wt%, 1.34 wt% and 2.02 wt%, respectively. Analysis of the calcined catalysts by X-ray diffraction (XRD) confirmed the presence of Co 304 in each case and this was the only phase detected by X R D . The C 0 3 O 4 particle size, estimated from X R D line broadening, was 9.9 nm on SiC>2, 11.8 nm on BaO/Si02, 6.5 nm on the Zr02/Si02 support, and 11.7 nm on La20 3/Si02 (Appendix E). Chapter 3 Experimental 32 Before being exposed to reactant, all catalysts were reduced by temperature-programmed reduction (TPR) in a lOOmL/min 40%H2/Ar to the desired temperature in one hour. 3.3 Catalyst Characterization 3.3.1 BET Surface Area and Pore Volume Catalyst surface areas and pore volumes were measured by N 2 adsorption-desorption at 77K using a FlowSorb II 2300 Micromeritics analyzer. A 30%N2/He mixture, fed at 15 mL/min was used for surface area measurement and a 95%N2/He mixture fed at 20 mL/min was used for pore volume measurement. Samples were degassed at 398K for approximately 3 hours prior to measurement. 3.3.2 CO Chemisorption The catalyst metal dispersion was determined by CO chemisorption. The CO uptake was measured gravimetrically (Perkin-Elmer TGS-2 thermogravimetric analyzer with a sensitivity of ±1 ug). About 10 mg of sample was dried at 523K for 8 hr in He. The drying temperature was chosen to avoid the transformation of C03O4 to CoO, which was shown by in situ X R D and EXAFS measurements to occur in the temperature range 623-673K, under inert atmospheres (Khodakov et al., 1997). After drying, the catalyst was cooled to 323K and then reduced in a 40%H2/He gas mixture flowing at 400 mL/min while heating from 323K to the desired temperature (Table 3.1) in 1 hour, followed by cooling to 323K. The degree of reduction was calculated from the catalyst weight change during TPR knowing the Co loading and assuming that C03O4 was the only reducible species. Following a 5 min He purge after cooling, CO adsorption was initiated using a 12%CO/He gas mixture flowing at 400 mL/min and lOlkPa total pressure. After the sample weight stabilized, the sample was flushed in pure He. No CO desorption was detected during this purge and hence the measured weight gain was attributed to Chapter 3 Experimental 33 CO chemisorption at 323K. The catalyst dispersion, reported as a mole percent of reduced Co, was calculated from the CO uptake, assuming a 1:1 adsorption stoichiometry. The Co particle size was estimated from the equation dp (nm)=0.962/O, where O is the metal dispersion (Juszczyk et al., 1993). The N i particle size was estimated from the equation dp (nm)=0.971AD, where O is the metal dispersion (Lesage et al., 1995). 3.3.3 Transmission Electron Microscopy (TEM) The formation of fdamentous carbon was detected by T E M (Hitachi H-800 electron microscope) examination of the used catalysts. T E M specimens were prepared by dispersing the used catalysts in ethanol and applying a drop of this dispersion onto a carbon coated copper grid, followed by drying. The microscope was operated at an acceleration voltage of 100 to 150 kV, with magnification in the range of 10,000-100,000x's. The average metal particle size was estimated directly from the number average diameter of the filaments observed by T E M , assuming that the metal particle size equals the filament diameter (Baker, 1989). 3.3.4 Temperature Programmed Reduction (TPR) TPR was performed in a stainless steel micro-reactor. About 80mg of catalyst sample was loaded in the isothermal zone of the reactor and heated at a rate of 10 K/min to 623K in 60mL/min Ar, to desorb physically adsorbed water. After the sample was cooled to room temperature, the Ar stream was switched to 60 mL/min reducing gas 5%H2 (99.999%, Praxair)/95%Ar (99.999%), Praxair), and the temperature was increased at a rate of 10 K/min to 1007K. The gas flow was controlled with a calibrated Brooks mass flow controller. The reactor effluent gas passed through a 4A molecular sieve trap to remove the produced water, and was then analyzed by gas chromatography using a TCD (thermal conductivity detector). Chapter 3 Experimental 34 3.3.5 X-ray Photoelectron Spectroscopy (XPS) XPS measurements were performed in a Leybold M A X 200 instrument with hemispherical energy analyzer equipped with an achromatic A l K a source (1486.6eV) (operated at 15 kV, 20mA emission current). The spectra are collected with a pass energy of 192eV for survey scan and a pass energy of 48eV for narrow scan. For all samples, Si 2p with binding energy (B.E.) 103.5eV was taken as an internal reference. Co 2p, O 2p and C Is spectra were obtained by narrow scan (Appendix C). The Co 2p3/2 and 2pi/ 2 was fitted assuming a theoretical ratio of 2:1 and the spin-orbit coupling of Co 2p is fixed at either 15.0eV (for C03O4 and metallic Co) or 15.7eV (for CoO). The 2p3/2 shake up line was fitted with one peak. Catalysts examined by XPS were reduced to a maximum temperature of 723K, following TPR procedures described in Section 3.3.4. To minimize the exposure of the reduced or used catalysts to air, the catalyst samples were transferred from the reactor to the XPS chamber using a glove box filled with inert N 2 . 3.3.6 X-Ray Diffraction (XRD) Catalyst samples were firstly ground into powder and then coated on a glass slide. X R D patterns of catalysts were recorded with a Siemens D5000 powder diffractometer using monochromatized Cu K a radiation (A=1.54A), operated at 40 kV and 30 mA. The step-scans were taken over the range of 26 from 25 to 75° in steps of 0.04°. Diffraction patterns derived from the diffractograms were compared with standard data files. The particle size of C03O4 was determined using the diffraction peak of 28=36.8° according to the Scherrer equation (3.1): Bcosd const (3.1) Chapter 3 Experimental 35 where dp is the metal particle size, A; X is the wavelength (Cu Koc), 1.54 A; Kconsr is a constant at 0.89; 6 = Jw2 - w2 , W is the full width at half maximum of the diffraction peak (FWHM), which was obtained by fitting the diffraction peak profile; w is instrumental peak broadening = 0.004 radians; 6 is the diffraction angle, radians. The raw data of X R D is shown in Appendix E. 3.4 Catalyst Activity for Methane Decomposition 3.4.1 Activity Measurement The methane decomposition rate on the catalysts of interest was measured in a fixed-bed reactor operated isothermally in differential mode. A flow diagram of the reactor and the on-line analytical equipment are shown in Figure 3.1. Gas flow rates were controlled by calibrated Brooks 5878 mass flow controllers. The stainless steel reactor (/ = 60 cm, o.d. = 0.95 cm) was loaded with 0.2 g catalyst (average particle size 0.17 mm) that was supported on a quartz wool plug. A thermocouple was placed close to the top of the catalyst bed to control the reaction temperature. A Varian Star 3400CX gas chromatograph, fitted with flame ionization and thermal conductivity detectors connected in series, and equipped with a 60/80 Carbosieve G column, was used for the product and feed gas analyses. UHP grade H 2 , CH4, He, Ar (99.999%, Praxair), 5%CH 4/Ar calibrated gas (Praxair), 4.82%H2/10.4CH4/2.01%C2H4/3.75%C2H6/Ar calibrated gas (Praxair) and CP grade CO (Purity 99.5%>, Praxair) were used in the experiments. The methane decomposition rate was measured by the change in CH4 flow rate (Appendix B . l ) . The ratio of H2production rate to the CH4 decomposition rate was assumed 2:1, based on previous studies from this laboratory (Zadeh and Smith, 1998) and literature reports (Avdeeva et al., 1999). Furthermore, no higher hydrocarbons were produced under the experimental conditions of the present study. Chapter 3 Experimental 36 Tests to determine the significance of external and internal diffusional effects were done following the guidelines given by Froment and Bischoff (1990). For the range of experimental conditions used in the present study, internal and external gradients in concentration and temperature were insignificant, as shown in Appendix A. VENT t MFC1 GC: gas chromatograph; TCD: thermal conductivity detector; FID: flame ionization detector; MS: mass spectroscopy; MFC: mass flow controller. Figure 3.1 Block diagram of the experimental set-up used for C H 4 decomposition catalyst tests. Chapter 3 Experimental 37 3.4.2 Description of the Measured Catalyst Activity Profile Figure 3.2 shows typical curves of the measured CH4 decomposition rate versus time for Co catalyst in the presence of a H2/CH4 feed. The activity profdes for C H 4 decomposition were of similar form for many of the catalysts investigated herein. The C H 4 decomposition rate first increases to a maximum, then decreases. The activity profiles are conveniently described by a kinetic equation of the type r = r*a , where r* is the maximum decomposition rate and a is the catalyst activity factor (Demicheli et al., 1991). If the time corresponding to the maximum is designated t , and i f the rate is 1 s t order with respect to the activity factor, i.e. da I' dt- -kdad , where d = 1 and kd is the decay constant, the methane decomposition kinetics after the maximum can be described by Equation (3.2): r _ r*P-K,{'-'') (3-2) The maximum rate was identified directly from the activity profile. Curve fitting the decomposition rate data (after the maximum rate) versus (t — t*) using Table 2D curve software (SPSS Inc.), as shown in Figure 3.2, provided estimates of r* and kd. These two parameters were conveniently used to discuss the catalyst maximum activity (r*) and decay constant, kd, throughout the present study. For all of the data reported herein, the fits to the 1s t order decay model had regression coefficients R 2 > 0.90. The sensitivity of r* and kd to the value of t' chosen directly from the activity profile, was insignificant, as shown in Appendix G. For the case of a measured activity profile without the maximum that occurred in the absence of H2, the activity profile can simply be described by Equation (3.3) (Equation (3.2) with t =0): Chapter 3 Experimental 38 r = r e (3-3) Similarly, curve fitting of the measured C H 4 decomposition rate versus time data using Table 2D Curve software (SPSS Inc.), provided estimates of r* and kd . In the present study, the decay constant kdof a 1 s t order decay model was used to quantify the catalyst deactivation. In the following sections, the effect of process variables on deactivation will be discussed in terms of kd. 0 10 20 30 Time, min 40 50 60 Figure 3.2 Activity of 12wt% Co/Si0 2 catalysts, with different KM = P„ IPCH ratios (Reduced at 923K, reacted at 773K, total gas flow 185 mL/min, weight of catalyst=0.2g; lines are the fit of Equation (3.2) to the experimental data points; • KM = 0.01 atm; • KM = 0.03 atm; A KM - 0.05 atm). Chapter 3 Experimental 39 In the present study, both decreasing activity and stable activity were observed on supported Co and N i catalysts. The maximum activity in the case of declining activity was determined by the method described above. The maximum activity in the case of stable activity, r*, was estimated directly from the measured stable activity. 3.5 Characterization Data Properties of the Co/SiC>2 catalysts are listed in Table 3.1. A series of catalysts with estimated metal dispersion in the range 3.4 - 12.6% were obtained by reducing 5-30wt% Co/SiC>2 at 723K and 923K. The data of Table 3.1 show that reduction of the C03O4 precursor was almost complete for all catalysts except the 30wt%> Co/Si0 2 catalyst. The average Co particle size, estimated from the metal dispersion assuming pure Co particles, increased with increased Co loading (Table 3.1). The metal particle size of 11.4 nm, estimated by CO chemisorption on the 12 wt% Co/Si02 reduced at 723K, was in good agreement with the metal particle size (9.6 nm) estimated previously by X R D line-broadening (Zadeh and Smith, 1998), and with the 10 nm estimated from the T E M micrograph of the same catalyst after reaction. Similarly, properties of Ni/Si02, Ni/Zr02 and modified Co catalysts 12wt%Co/MexOy/Si02 are listed in Table 3.2, Table 3.3 and Table 3.4, respectively. These data will be referred to in the following chapters. Chapter 3 Experimental 40 Table 3.1 Properties of Co/SiCh catalysts of the present study. Co Loading BET SA PV Reduction Temperature Reduction Degree0 CO Uptake Metal Dispersion dP (CO uptake) d, (TEM) wt% m2/g cc/g K mol% mmol/g % nm nm 5 Co 239 0.971 923 100 0.084 9.2 10.4 -8 Co 230 1.080 923 100 0.103 7.1 13.5 -10 Co 217 0.989 723 96.9 0.208 12.6 7.6 -923 100 0.094 5.4 17.8 -12 Co 210 0.889 723 96.5 0.166 8.4 11.4 10a 923 100 0.102 5.0 19.4 25" 30 Co - -723 76.5 0.240 6.2 15.6 -923 89.4 0.155 3.4 28.3 26" Estimated metal particle size; BET SA - surface area; PV - pore volume Estimated from TEM image of catalyst after reaction at 723K Measured from TEM image of catalyst after reaction at 773K. Catalyst was reduced in 40%H2/He from 323K to the desired temperature in one hour. Table 3.2 Properties of Ni/SiCh catalysts of the present study, Metal Loading BET SA PV CO Uptake" Metal Dispersion" d, (CO uptake)a d, (TEM)b wt% m2/g cc/g mmol/g % nm nm 2Ni 277.6 0.690 • 0.012 3.6 27.2 31.7 5Ni 250.5 0.618 0.027 3.1 30.9 33.2 8Ni 218.5 0.566 0.036 2.6 36.8 32.5 12 Ni 234.5 0.566 0.041 2.0 43.3 50.0 15 Ni 201.5 0.485 0.050 2.0 49.5 62.5 30 Ni 163.3 0.390 0.107 2.1 47.2 50.0 BET SA - surface area; PV - pore volume; d - estimated metal particle size. ": Catalyst was reduced in 40%H2/He from 323K to 923K in an hour. Reduction degree was 100 mol% for all catalysts. b: Measured from TEM image of catalyst after reaction at 773K. Chapter 3 Experimental 41 Table 3.3 Properties o f Ni/ZrC"2 catalysts of the present stuc iy-Metal Loading BET SA PV CO Uptake3 Metal Dispersion3 (CO uptake)3 wt% m2/g cc/g mmol/g % nm 2Ni 45.36 0.205 0.031 9.2 10.5 5Ni 42.38 0.187 0.061 7.2 13.5 8Ni 40.42 0.178 0.065 4.8 20.2 12 Ni 39.51 0.166 0.061 3.0 32.3 BET SA - surface area; PV - pore volume; dp - estimated metal particle size. Catalyst was reduced in 40%H2/He from 323K to 923K in one hour. Reduction degree was 100 mol% for all catalysts. Table 3.4 Properties o f modified 12wt% Co/SiC^ catalysts in the present study. Catalyst BET SA PV Reduction Temperature Reduction Degree" CO Uptake Metal Dispersion d, (CO uptake) m2/g cc/g K mol% mmol/g % nm Co/Si02 210 0.889 723 96.5 0.166 8.4 11.4 923 100 0.102 5.0 19.4 Co/BaO/Si02 211.1 0.468 723 88.2 0.094 5.2 18.4 923 100 0.064 3.1 30.8 Co/Zr02/Si02 223.1 0.487 723 80.0 0.113 6.9 13.9 923 100 0.105 4.5 21.4 Co/La203/ Si0 2 197.0 0.472 723 99.9 0.120 5.9 16.3 923 100 0.082 3.5 27.7 BET SA - surface area; PV - pore volume; dp - estimated metal particle size. Catalyst was reduced in 40%H2/He from 323K to the desired temperature in one hour. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 42 Chapter 4 Catalyst Deactivation Kinetics and Mechanism 4 .1 I n t r o d u c t i o n In this chapter, a mechanism of catalyst deactivation during CH4 decomposition is discussed based on experimental observations. Firstly, the significance of filamentous carbon formation versus the migration of CFfx species from the metal to the support is discussed in terms of carbon removal and active site regeneration. Secondly, effects of temperature, H2 and CO partial pressures, on the catalyst activity are presented. Based on the observations of the effect of gas phase composition on catalyst deactivation, a catalyst deactivation mechanism was developed and used to explain the experimental observations. Most importantly, the carbon formation threshold was coupled with the proposed filamentous carbon formation threshold to predict stable activity corresponding to the steady growth of filamentous carbon during catalytic CH4 decomposition. 4 . 2 A c t i v i t y O b s e r v a t i o n s 4.2.1 Evidence and Significance of C H X Migration and Filamentous Carbon Formation The first question addressed in the present study arose from a previous homologation study on 12wt% Co/Si02. As described in Section 2.3.4, it was unclear whether filamentous carbon formed during CH4 decomposition at low temperature, 723K. In order to detect filamentous carbon by T E M on the 12wt% Co/Si0 2 after reaction with 5%CH 4 /Ar at 723K, the reaction time was extended to 120 min. Evidence of filamentous carbon growing from metal particles, corresponding to a low but stable CH4 decomposition activity, is shown in Figure 4.1. The micrograph shows that the diameter of the filamentous carbon was about 10 nm, close to the initial metal particle size of 11.4 nm measured by CO chemisorption on the unused Co catalyst. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 43 Figure 4.1 T E M image of 12wt% Co/Si0 2 catalyst (reduced at 723K) after 120 min reaction in 5%CH4/Ar at 723K, showing the presence of fdamentous carbon, diameter « 10 nm. Additional experiments were performed to detect the migration of carbon species (CHX), formed during C H 4 decomposition, from the Co to the S i 0 2 support. The migration of these species from the Co to the S i 0 2 support, where interaction with hydroxyl groups produces CO (Ferreira-Aparicio et al., 1997), was detected using mass spectroscopy by measuring the production of CO during CH4 decomposition. Data of Figure 4.2 show that minimal amounts of CO were detected when S i 0 2 alone was exposed to 5%CH 4 /Ar at 723K. However, CO production during CH4 decomposition on the 12wt% Co/Si0 2 was significant, especially within the first few minutes of reaction. In accordance with the arguments presented by Ferreira-Aparicio et al. (1997) we assume that the source of CO is C H X species that migrate from the metal onto the support where they react with hydroxyl groups to produce CO. The possibility of CO production due to C H X and OH interaction localized near the metal particle perimeter cannot be ruled out, but the continued CO production after the initial rapid decline suggests that CHX Chapter 4 Catalyst Deactivation Kinetics and Mechanism 44 migration to the support occurs, albeit to a small extent. Also note that the possibility of CO being produced from CH4 interacting with unreduced metal oxide is small, since it is highly unlikely that the unreduced cobalt would react with methane following a one-hour reduction in 40% hydrogen at the same temperature. Furthermore, for the 12wt% Co/Si02 catalyst of Figure 4.2, the degree of reduction was 96.5 mol%>, so that approximately 12 micromoles of oxygen would be available for reaction with C H 4 to produce an equivalent number of moles of CO. This is much less than the 77 micromoles of CO produced during the reaction period shown in Figure 4.2. Filamentous carbon was observed under the reaction conditions shown in Figure 4.1. According to the fdamentous carbon formation mechanism, carbon is removed from the metal surface by bulk diffusion through the metal particle. In addition, evidence for the migration of carbon species from the Co metal site to the support was provided by the production of CO during the CH4 decomposition and the previously reported kinetic model that, of necessity, included a CHx migration step from the metal to the support (Zadeh and Smith, 1998). These observations suggest that both carbon diffusion through the metal to form fdamentous carbon, and the migration of C H X from the metal to the support occur, and both contribute to the regeneration of active metal sites during CH4 decomposition. However, the rapid decline in CO production (Figure 4.2) suggests that migration of CHX from the metal to the support is only significant in the first 2 to 3 min of reaction. The regeneration of active metal sites for CH4 decomposition over extended periods is mainly due to bulk diffusion of carbon through the metal particle to form filamentous carbon between the metal and support. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 45 0 5 10 15 20 25 30 Time, min Figure 4.2 CO production rate over Si02 and 12wt% Co/Si02 (reduced at 723K) exposed to 140 mL/min of 5%CH 4 /Ar at 723K (A CO production rate on S i0 2 ; — CO production rate on Co/Si02; • CH4 decomposition rate on Co/Si02). 4.2.2 Effect of Temperature on Activity The effect of decomposition temperature on the catalyst activity for CH4 decomposition was determined on 12wt% Co/Si0 2 catalysts, operated in the temperature range 723-873K. Figure 4.3 shows the catalytic activity versus time-on-stream of the 12wt% Co/Si02 catalyst, at different decomposition temperatures. Generally, the initial C H 4 decomposition rate was high but the catalyst deactivated rapidly. At 823K, for example, the CH4 decomposition rate decreased to only 2.3% of its initial value after 30 minutes reaction. As discussed in Section 3.4.2, curve fitting of the measured C H 4 decomposition rate versus time data to Equation (3.3) using Table Chapter 4 Catalyst Deactivation Kinetics and Mechanism 46 2D Curve software, provided estimates of r* and kd. The influence of decomposition temperature on r* and kd is shown in Figure 4.4. The maximum CH4 decomposition turn over frequency, (Max TOF, where TOF = r /active site, 1/min) increased from 1.4 to 9.4 1/min over the temperature range 723-873K with an apparent activation energy of 66.3 kJ/mol. The catalyst decay constant also increased with increasing temperature with apparent activation energy of 122.7 kJ/mol. Note that the data at 873K in Figure 4.3 show a single data point with high activity followed by a series of points at low activity. The data were not well described by the 1s t order decay model. The fast decay is largely complete somewhere between point 1 and 2. However to be consistent with the other temperature data, and to capture this very rapid initial activity decay, the 1s t order decay model was still used to fit the experimental data at 873K. Consequently, the estimated value of kd reported in figure 4.4 had a large error, as shown by the error bar for that data point. The apparent activation energy of 66.3 kJ/mol estimated for the maximum C H 4 decomposition rate on the 12 wt% Co/Si02 catalyst with average Co particle size of 9.5 nm, was in reasonable agreement with the 56 kJ/mol reported for C H 4 decomposition on Co/Si02 with metal particle size 10.3 nm (Zadeh and Smith, 1998). These values were somewhat higher than the value of 42 kJ/mol reported for the decomposition of C H 4 on Co/Si02 catalysts at less than a monolayer coverage (Koerts et al., 1992). Note also that these values are significantly lower than the activation energies reported for Fe and N i catalysts when carbon diffusion through the metal is the RDS (Galuszka and Back, 1984; Holstein et al. 1995). Chapter 4 Catalyst Deactivation Kinetics and Mechanism 47 c I u. O 10 9 8 7 6 5 4 3 2 1, 0 0 0 .0 .0 .0 .0 .0 .0 .0 .0 .0 I \ A 4 1 o 723 K Exp o 773 K Exp A 823 K Exp x 873 K Exp 20 40 T i m e , m i n 60 Figure 4.3 Effect of temperature on the activity of 12wt% Co/Si0 2 catalysts, reduced at 923K and reacted with 5%CH 4 /Ar at 140 mL/min. (Lines are 1s t order decay model fit to the experimental data points). Figure 4.4 Arrhenius plots of maximum CH4 decomposition rate (TOF, min"1) (0), and decay constant (100 kd) (A) versus 1000/T. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 48 4.2.3 Effect of H 2 and CO on the Catalyst Activity To determine the effect of adding small quantities of H 2 or CO to the C H 4 feed, a series of experiments were done to compare changes in the CH4 decomposition activity due to the presence of 1.2%H2 or 0.4%CO added to the 5%CH 4 /Ar on 12wt% Co/Si0 2 . By fitting the experimental data to the 1 s t order decay model, Equation (3.3), the maximum TOF and &d were obtained and these values were plotted in Figure 4.5. Data of Figure 4.5 show that H 2 not only decreased the decay constant of the catalyst but also reduced the maximum decomposition TOF. T E M of the used catalyst after one hour reaction (Figure 4.6) showed filamentous carbon formation during CH4 decomposition in the presence of 1.4%H2 in the feed at 773K. The data of Figure 4.5 also show that CO addition decreased the rate of catalyst deactivation, similar to the effect of adding H 2 . However, an important difference between the effects of H 2 and CO is that the high maximum C H 4 decomposition TOF was maintained upon the introduction of CO, whereas H 2 addition reduced the maximum TOF. No higher hydrocarbons were detected upon CO addition, suggesting that no Fischer-Tropsch (FT) type reaction (from H 2+CO to higher hydrocarbons) occurred at the reaction conditions. Hence, the CO promotional effect could not be explained by assuming that FT type reactions removed H and thereby enhanced C H 4 decomposition. Furthermore, no CO decomposition was detected, based on the measured CO flow rate change through the reactor. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 49 c £ x n S 2 1 0 I 1 1 1 1 1 1 I I i I I , I I • I I T=773K T=773K T=773K T=823K T=823K T=823K H2=1.2% CO=0.4% H2=1.5% CO=0.4% Experimental conditions T=773K T=773K H2=1.2% T=773K 0 0 = 0 . 4 % T=823K T=823K H2=1.5% T=823K CO=0.4% Experimental conditions Figure 4.5 Effect of the presence of H 2 or CO on (a) the maximum activity (TOF) and (b) the decay constant (100 kd) on the 12wt% Co/Si0 2 catalyst (reduced at 923K), exposed to 5%CH 4 /Ar at the reaction temperature indicated. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 50 Figure 4.6 T E M micrograph of 12wt% Co/SiC»2 catalyst (reduced at 923K) after reaction in 5%CH 4/1.4%H 2/Ar at 773K for 60 min showing the presence of fdamentous carbon with diameter « 25nm. Figure 4.7 presents a T E M micrograph that showed fdamentous carbon formation after the catalyst was exposed to 5%CH 4 /Ar at 773K with 0.4%CO in the feed, corresponding to the steady C H 4 decomposition shown in Figure 4.8. Although CO is known to form fdamentous carbon at higher temperature on supported metal catalysts, no fdamentous carbon was detected by T E M when the Co catalyst was exposed to a 2vol.%CO in Ar. Consequently, we conclude that C H 4 decomposition was the main source of the fdamentous carbon shown in Figure 4.7, corresponding to the steady C H 4 decomposition activity shown in Figure 4.8. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 51 Figure 4.7 T E M micrograph of 12wt% Co/Si0 2 (reduced at 923K) after reaction in 5%CH 4/0.4%CO/Ar at 773K for 60 min showing presence of filamentous carbon with diameter « 25nm. 0 20 40 T i m e , m i n 60 Figure 4.8 Comparison of C H 4 decomposition TOFs in the presence of CO or H 2 at 773K on 12wt% Co/Si0 2 (reduced at 923K) (The total gas flow 140 mL/min. • 100/:, =4.6 min"1 with 5%CH 4 ; A100*, =0.46 min"1 with 1.4%H 2/4%CH 4; • 100*,, =0.4 min"1 with 0.4%CO/ 5%CH 4). Chapter 4 Catalyst Deactivation Kinetics and Mechanism 52 In order to show the difference between activity profdes manifested by different decay constants, 100 kd, the complete activity profdes are presented in Figure 4.8. These plots confirm that the magnitude of the decay constant reflected the slope of the activity versus time-on-stream profiles. 4.3 Prediction of Stable Activity 4.3.1 Influence of KM on Catalyst Activity and Deactivation In the present study, the effect of H 2 was discussed in Section 4.2.3. Additional experiments were performed, in which the P„21 PCHt ratio was varied and the CH4 decomposition activity profile determined at the same temperature, 773K, on certain Co or N i supported catalysts. The term KM = PHi I PCH) is in the same form as the equilibrium constant for the methane decomposition reaction. In order to discuss the measured activity simply, the two parameters, r* and kd were obtained from curve fitting the activity profiles at different KM. The data in Figure 4.9 and Figure 4.11 show that the ratio KM=PH~ IPCHt had a significant effect on the catalyst activity and deactivation: both catalyst activity, r* and decay constant, kd decreased with increasing KM at 773K on the 12wt% Co/SiC>2 catalyst and on 5wt% N i / S i 0 2 catalyst, respectively. 4.3.2 Coking Threshold and Filamentous Carbon Formation Threshold The point at which the C H 4 decomposition activity is zero, estimated by drawing a trendline through the data of Figure 4.9a, corresponds to the coking threshold, K*M = ' PL ^ V CH* J According to Snoeck et al. (1997b), the coking threshold defines those conditions at which there is no carbon deposition and no carbon gasification on the catalyst surface, i.e., the coking Chapter 4 Catalyst Deactivation Kinetics and Mechanism 53 threshold corresponds to the conditions for which the rates of all consecutive steps of carbon . When KM<K*M, C H 4 decomposition with fdament formation are zero, K*M = carbon deposition will occur, whereas when KM > K*M, carbon gasification occurs 0.8 0.7 0.6 8 0.5 O) I 0.4 o E E 0.3 0.2 0.1 0.0 K M = (0.082±0.003)-(0.084±0.006)r* R 2 = 0.9886 0.00 0.02 0.04 0.06 0.08 K M = P H 2 2 / P C H 4 , atm 0.10 Figure 4.9a Dependence of maximum rate r* on KM with 12wt% Co/Si0 2 (reduced at 923K) at 773K (K*M = 0.082 ± 0.003 atm). Chapter 4 Catalyst Deactivation Kinetics and Mechanism 54 Similarly, Figure 4.9b shows that 100 kd approaches zero with increasing KM. The point at which lOOA^ is zero, obtained by drawing a trendline through the data of Figure 4.9b, is defined herein as the filamentous carbon formation threshold, KfM = \PCHAJ . Filamentous carbon formation threshold, KfM, is proposed by analogy to the coking threshold K*M , and also because it is generally accepted that stable activity during C H 4 decomposition corresponds to filamentous carbon formation. Figure 4.9b shows that 100A:d decreases with increasing KM and the point where 100 kd reaches zero is defined as KfM, corresponding to filamentous carbon formation and stable activity (i.e. kd =0). When the value of KM>KfM, stable activity will be observed whereas when KM < KfM, deactivation occurs (kd > 0). Chapter 4 Catalyst Deactivation Kinetics and Mechanism 55 2.5 2.0 c 1.5 1 o o 1.0 0.5 0.0 0.00 K M =(0.061 ±0.004)-(0.014±0.003)100kd R2 = 0.9665 0.02 0.04 KM=PH22/PCH4> atm 0.06 0.08 Figure 4.9b Dependence of decay constant 100 kd on KM with 12wt% C o / S i 0 2 (reduced at 923K) at 773K (KfM = 0.061 ± 0.004 atm). 4.3.3 Stable Catalyst Activity Prediction during C H 4 Decomposition As discussed in Chapter 2, stable catalyst activity during C H 4 decomposition is critical for practical processes aimed at producing pure H 2 and nanofibre carbon. The two thresholds K*M and KfM can be used to predict the operating conditions (i.e. the value of KM) needed for stable activity during C H 4 decomposition on certain catalysts at fixed temperature. Stable activity with carbon deposition would occur during C H 4 decomposition when KM satisfies the condition: KfM < KM < K*M . Figure 4.9 shows that on 12wt% Co/S i0 2 catalyst at 773K A^=0.082±0.003atm and AT^=0.061±0.004atm. Hence, KM must satisfy the condition: Chapter 4 Catalyst Deactivation Kinetics and Mechanism 56 0.061 ± 0.004 = < KM <K'M =0.082+ 0.003 atm, for stable activity during C H 4 decomposition to be obtained. Figure 4.10 shows that stable activity was indeed obtained when ATM=0.074atm on the same catalyst at 773K. 0.3 r - . 0.0 1 1 ' ' L ' 1 0 10 20 30 40 50 60 Time, min Figure 4.10 Stable activity on 12wt% Co/Si0 2 (reduced at 923K) with KM = 0.074 atm at 773K. Stable activity during C H 4 decomposition is often reported on high loading N i catalysts (Shaikhutdinov et al., 1995), but deactivation has been observed on low loading N i catalyst, for example 5wt% N i / S i 0 2 (the effect of metal loading on the activity wil l be discussed in detail in Chapter 5) in the present study. The dependence of r* and kd on KM is presented in Figure 4.11a and Figure 4.11b as determined over 5wt% N i / S i 0 2 catalyst at 773K. K*M and KfM were Chapter 4 Catalyst Deactivation Kinetics and Mechanism 57 obtained from Figure 4.11a and Figure 4.11b, respectively. Hence, iC* /=0.110±0.009atm and A^=0.032±0.003atm. Consequently, KM must satisfy the condition: 0.03210.003 = ^  < KM < K*M =0.110 ±0.009 atm for stable activity to be observed during C H 4 decomposition on 5wt% Ni/SiCh at 773K. Figure 4.12 shows that indeed stable activity was obtained when KM = 0.09atm. The results presented in Figure 4.10 and Figure 4.12 show that stable activity can obtained provided KM is chosen such that KfM < KM < K'M . 1.4 1.2 1.0 n u o > 0.8 c o I 0.6 0.4 0.2 0.0 0.00 KM=(0.110±0.009)-(0.080±0.010)r* R 2 = 0.9456 0.02 0.04 0.06 0.08 0.10 KM, atm Figure 4.11a Dependence of maximum rate / o n KM with 5wt% N i / S i 0 2 (reduced at 9 2 3 K ) a t 7 7 3 K ( r ; =0.110 ±0.009 atm). Chapter 4 Catalyst Deactivation Kinetics and Mechanism 58 0.0 1 ' 1 1 i I 0.010 0.015 0.020 0.025 0.030 0.035 KM, atm Figure 4.1 lb Dependence o f decay constant 100 kd on KM wi th 5wt% N i / S i 0 2 (reduced at 923K) at 773K (KfM = 0.032 ± 0.003 atm). Chapter 4 Catalyst Deactivation Kinetics and Mechanism 59 0.5 0.1 l 1 i i t i I 0 20 40 60 80 100 120 Time, min Figure 4.12 Stable activity on 5wt% Ni /S i0 2 (reduced at 923K) with KM =0.09 atm at 773K. 4 . 4 Catalyst Deactivation Mechanism 4.4.1 Catalyst Deactivation The decomposition of C H 4 on supported Co catalysts reported herein showed that under some conditions, the catalyst deactivated. The mechanism of the deactivation is thought to be due to encapsulation of the metallic particle by graphite carbon layers (Shah et al., 2001). EXAFS and Mossbauer spectroscopies have shown that the form of catalyst remains metallic even after encapsulation (Shah et al., 2001). Hence, it was postulated that the metallic catalyst was not deactivated by poisoning or by changes in surface structure, but rather was isolated from C H 4 by encapsulation and hence could not catalyze C H 4 decomposition. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 60 However, as already reported, stable catalyst activity was observed under certain conditions on both Co and N i catalyst. According to the mechanism of fdamentous carbon formation, as discussed in Section 2.2.2, stable activity corresponds to steady growth of fdamentous carbon and T E M micrographs of used catalysts confirmed that filamentous carbon were indeed formed under these conditions (Figure 4.6 and Figure 4.7). Based on these observations, it is necessary to account for both the encapsulating carbon formation and filamentous carbon formation during C H 4 decomposition. A mechanism that accounts for both effects is schematically represented in Figure 4.13 and is described as: 1) the single atomic carbon, resulting from reversible reaction CH4 <z> C + 2H2, deposits on the surface of the metal catalyst; 2) the single atomic carbon reacts through two parallel paths: 2a) encapsulating carbon formation: assuming that the encapsulating carbon can not be gasified by H2, the number of active metal sites on the surface will decrease due to the formation of encapsulating carbon and consequently, the catalyst deactivates; 2b) the atomic carbon diffuses through the metal particle and deposits at the back of the metal particle, the catalyst active site being regenerated by the carbon bulk diffusion and hence stable catalyst activity is observed. The competition between the rate of encapsulating carbon formation and the bulk diffusion rate determines the observed rate of deactivation The decay constant of the catalyst (kd) is a consequence of a number of interacting rates, including the net C H 4 decomposition rate, the carbon removal rate by bulk diffusion through metal particle and the encapsulating carbon formation rate. (drfJdt) kd = ~r K rc 1 rf,n = r,l 1 rf,n = ('/." ~ rr,n ) 1 T'/> (4. 1) Equation (4.1) shows fhat£(, is dependent on the relative encapsulating carbon formation rate ( r e / r f n , the ratio of encapsulating carbon formation rate to net rate of carbon formation Chapter 4 Catalyst Deactivation Kinetics and Mechanism 61 rate), in which encapsulating carbon formation rate ( r , ) is equal to the difference ( r ( / ) between the net rate of carbon formation (r f n, the net rate of formation and gasification of carbon or coke precursor) and the rate of carbon removal from the active metal site (r r n, the net rate of removal by migration from metal to support or diffusion with filamentous carbon formation), i.e. relrf,n = rJrf,n -(r/,n ~rr,n)lrf,n- m other words, the relative magnitude of the formation rates of atomic carbon, encapsulating carbon and filamentous carbon, determine the observed activity profile and consequently, carbon with different morphologies, either encapsulating or filamentous carbon, dominates on the catalyst surface. Since the ensemble size of the encapsulating carbon formation is 6, nC-S^^-nCp S with n=6 (Chen et al., 2001) (4.2), the encapsulating carbon formation rate (Chen et al., 2001) can be written as r -k n" e encap s The bulk diffusion of atomic carbon can be described as (4.3). (ns Idx-nj dx) (2/3)dp (4.4) Equation (4.4) is modified from Snoeck et al. (1997b). where rc, the encapsulating carbon formation rate, l/cm2/s; ns, the site density of atomic carbon on the surface of metal surface, 1/cm2; kencap, rate constant of encapsulating carbon formation, cm Is; rd is the carbon bulk diffusion rate, 1/cm /s; Ds, carbon bulk diffusivity, cm Is; dp, metal particle size; «,, the site density of atomic carbon on the interface between the 2 , , metal and support, 1/cm ; dx, the finite divided thickness along the carbon diffusion path. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 62 Gas phase C H 4 T T f n (Single carbon atom) and C " T T T T T T T h Support Figure 4.13 Schematic representation of catalyst deactivation mechanism during C H 4 decomposition. 4.4.2 Explanation of Temperature Effects on Catalyst Deactivation The decay constant kd was observed to increase with increasing decomposition temperature, and the increase followed an Arrhenius dependence on temperature with apparent activation energy of 122.7 kJ/mol (Figure 4.4). On Ni-Al 2 03 catalysts, the apparent activation energy associated with kd for carbon formation from CH4-H2 mixtures has been reported as 229 kJ/mol (Demicheli et a l , 1991). The leading face The tailing face Chapter 4 Catalyst Deactivation Kinetics and Mechanism 63 As already discussed, the rate of catalyst deactivation is a consequence of a number of interacting processes: the net rate of the C H 4 decomposition rate, the carbon removal rate by bulk diffusion through the metal particle and the encapsulating carbon formation rate. Although the net rate of C H 4 decomposition, formation of encapsulating carbon and carbon removal by diffusion all increase with temperature, the difference among them varies with temperature because of differences in their respective activation energies. According to Holstein (1994), the activation energy for fdamentous carbon diffusion through Co is in the range of 145-162 kJ/mol and this activation energy is independent of reactant (either hydrocarbons or CO). The apparent activation energy for the migration of C H X species from Co to Si02 support has been estimated at 48 kJ/mol (Zadeh and Smith, 1998). The present study has reported an activation energy for CH4 decomposition of 66 kJ/mol. The activation energy for atomic carbon hydrogenation is 70 kJ/mol and the activation energy for the encapsulating carbon is 32 kJ/mol during CO methanation (Bartholomew, 2001). Consequently, an increase in reaction temperature would impact the carbon diffusivity through Co most significantly, which in turn would be expected to reduce the observed rate of catalyst deactivation. However, this is contrary to the observed effect of temperature on kd. Note that the competition between filamentous carbon and encapsulating carbon formation also depends on the concentration of atomic carbon at the surface, ns. The rate of encapsulating carbon formation can be written as rc=kma,pn" (Chen et al., 2001) whereas for bulk (n Idx-njdx) diffusion rd = A . As the temperature increases the atomic carbon concentration (2/3)rf, increases, manifested by the increase in the maximum decomposition rate, r* (Figure 4.4). Consequently, at higher temperature, the increased atomic carbon concentration increases the encapsulating carbon formation rate much more significantly than the bulk diffusion. We Chapter 4 Catalyst Deactivation Kinetics and Mechanism 64 conclude, therefore, that the increased decay constant with temperature is associated with the resulting relative increase in the encapsulating carbon formation rate with increased temperature. This result is also in agreement with the observation that the more reactive, amorphous forms of carbon, identified at low reaction temperatures, are converted to less reactive graphitic forms at higher temperatures over a period of time (Bartholomew, 2001). Note that as the C H 4 decomposition temperature increases, the reactivity in H2 of the carbonaceous deposit decreases (Koerts, 1991), a consequence of increased formation of un-reactive encapsulating carbon. 4.4.3 Effect of CO and KM on Catalyst Deactivation The data of Figure 4.5 show that the presence of either H 2 or CO in the feed reduces the decay constant. At 773K, addition of small amounts of H 2 or CO decreased the decay constant and stable activity was retained for a significant period of time during which filamentous carbon formation was detected (Figure 4.6 and Figure 4.8). However, addition of H 2 reduced the maximum TOF compared to the case without H 2 in the feed, whereas addition of CO had no significant effect on the maximum TOF. Furthermore, the data in Figure 4.9 - Figure 4.11 show that the ratio KM -( T>2 \ had a significant effect on the deactivation of catalysts. Stable P2 \PCHtJ activity and catalyst deactivation were observed at different ratios even on the same catalyst. When the value of KfM <KM <K'M , stable activity will be observed whereas when KM< Kfu, deactivation occurs. A similar effect of H 2 during the catalytic disproportionation of CO has been reported (Nolan, 1995) and two functions of H 2 are possible: (1) to "clean" the catalytic surface by the reaction C+2H2=>CH4 or (2) to modify the carbon/metal interaction. As discussed for the deactivation mechanism, the relative magnitude of the rate of carbon deposition, rate of the Chapter 4 Catalyst Deactivation Kinetics and Mechanism 65 carbon gasification, the rate of carbon removal by the bulk diffusion through the metal particle, and encapsulating carbon formation are critical for catalyst deactivation. As the ratio of KM increases, the H 2 partial pressure increases, which enhances the gasification of carbon. Consequently, the net rate of carbon deposition decreased, manifested by a decreasing maximum r* and a decrease in the surface concentration of atomic carbon. The decrease in atomic carbon will cause a significant decrease in the encapsulating carbon formation rate (Equation (4.2)), compared to the small change in carbon diffusion rate (Equation (4.3)). Consequently, catalyst stability is enhanced because the formation of encapsulating carbon is less favoured. With CO added to the C H 4 feed, two explanations for the reduction in kd can be postulated: CO decreases the C H 4 decomposition rate (rf „ decreases) or CO adsorption changes the carbon-metal interface such that carbon diffusivity through the metal is increased (rrri increases). The high maximum TOF upon CO addition, shown in Figure 4.5, rules out the first possibility. Hence we conclude that the reconstruction of the Co surface following CO adsorption enhances carbon diffusivity and this is consistent with the stable, high C H 4 decomposition activity reported in Figure 4.8. A similar promotional effect of CO on the decomposition of ethylene over Fe to form filamentous carbon has been reported (Rodriguez et al., 1993). The behaviour was rationalized in terms of a reconstruction of the Fe surface in the presence of co-adsorbed CO, which resulted in the formation of surfaces with differing activities. Although the catalyst stability was improved by addition of either CO or H 2 (Figure 4.8), the mechanism of each gas is postulated to be different: CO adsorption enhances the carbon diffusion rate by surface modification, promoting filamentous carbon formation without reducing C H 4 decomposition activity whereas the presence of H 2 enhances the carbon gasification rate and thereby reduces the concentration of atomic carbon on the surface. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 66 Consequently, catalyst stability is enhanced due to the stronger reduction in the rate of formation of encapsulating carbon relative to the carbon removal rate. Catalyst deactivation observed during C H 4 decomposition on the Co/SiC»2 catalysts has been discussed in terms of the competition between encapsulating carbon formation and carbon diffusion from the Co surface. Another common deactivation mechanism for supported metal catalysts is by sintering of the metal particles. However, for the present reaction, this mechanism is not relevant. The initial Co particle size measured by CO chemisorption (11.4 nm, Table 3.1) is close to the size of the Co particle on the filamentous carbon tip, observed by T E M (~10nm, Figure 4.1) after 120 min reaction in C H 4 at 723K. The Co particle size measured by T E M at 773K after reaction in the presence of H 2 or CO in the feed was ~25 nm (Figure 4.6 and Figure 4.7), somewhat larger than the 19.4 nm measured by CO chemisorption of the unused catalysts. The apparent increase in particle size in this case could be due to the fact that fdamentous carbon formation favoured larger metal particles and the T E M image consequently reports the larger particle size selectively, whereas CO chemisorption provides an estimate of the average metal particle size. We conclude that no significant sintering in the temperature range of 723~773K during C H 4 decomposition occurred, in agreement with the results of Avdeeva et al. (1999), who reported that the Co particle size (approx. 25 nm) did not increase at 773-823K on 60-75wt% Co-alumina catalysts exposed to C H 4 for 50 min. 4.5 Summary The experimental observations reported herein, suggest that the migration of C H X from the metal to the support makes a contribution to the regeneration of active metal sites in the first 2 to 3 min of reaction. The regeneration of active metal sites for CH4 decomposition over Chapter 4 Catalyst Deactivation Kinetics and Mechanism 67 extended periods is mainly due to bulk diffusion of carbon through the metal particle to form fdamentous carbon between the metal and support. The effect of operating conditions such as temperature and gas phase composition, expressed as KM= P^ /PCH), on CH4 decomposition activity for supported Co catalysts was investigated in terms of r* and kd estimated by 1 s t order decay model fitting. The apparent activation energy for the maximum C H 4 decomposition rate was 66.3 kJ/mol and for the decay constant 122.7 kJ/mol on 12wt% Co/SiC>2 catalysts. The KM= P„ IPCHt ratio had a critical effect on the CH4 decomposition profile: both r* and kd decreased with decreasing KM = P% I PCHt. Stable catalyst activity was observed under some conditions and the conditions for stable activity can be predicted from the relative magnitudes of the coking threshold, K*M, and the filamentous carbon formation threshold, KfM . Stability corresponds to the condition: KfM<KM<K'M. Based on these experimental observations, the catalyst deactivation mechanism for CH4 decomposition incorporating competition between encapsulating carbon formation and filamentous carbon formation due to bulk carbon diffusion was proposed. The decay constant during C H 4 decomposition depends on the build up of encapsulating carbon on the surface of the catalyst, which in turn is a consequence of a number of interacting processes: carbon deposition rate, carbon removal rate by bulk diffusion through metal particle and encapsulating carbon formation rate. Accordingly, the relative magnitude of formation rates of important types of carbon including atomic carbon and encapsulating or filamentous carbon on the catalyst surface, determine whether stable activity or catalyst deactivation is observed. Consequently, either encapsulating or filamentous carbon dominates on the catalyst. Chapter 4 Catalyst Deactivation Kinetics and Mechanism 68 The effect of temperature and gas phase composition, KM , on the activity profde can be explained well by the competition between the rate of encapsulating carbon formation and the rate of carbon diffusion. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 69 Chapter 5 Effect of Catalyst Properties on Catalyst Activity 5.1 Introduction As discussed in Section 2.4, supported metal catalyst properties such as metal particle size and metal-support interaction (MSI) have a significant effect on the catalyst activity during C H 4 decomposition. In this chapter, the observations of the dependency of the catalyst activity on the metal particle size, and stable catalyst activities over large particles of both Ni and Co are presented in Section 5.2. In Section 5.3, the dependency of coking threshold on the metal particle size (Rostrup-Nielsen, 1972) is described by the developed relationship using the experimental data of the present study. Furthermore, the effect of the metal particle size on the difference between the coking threshold and the filamentous carbon formation threshold is presented. Hence, the ease of observation of steady growth of filamentous carbon on high loading catalysts is rationalized. Finally, the effect of MSI on catalyst deactivation is discussed based on the study of modified Co catalysts. 5.2 Dependency of the Catalyst Activity on Metal Particle Size 5.2.1 Dependency of the Catalyst Activity on Co Particle Size The influence of metal particle size (or dispersion) on C H 4 decomposition activity was measured at two different operating conditions using Co/SiC>2 catalysts with varying metal particle size (or metal dispersion) as given in Table 3.1. At each operating condition, the maximum TOF (Max TOF=r* /the number of active site) and the decay constant (100^) were estimated by fitting the experimental data to the 1 s t order decay model, and the values obtained are plotted in Figure 5.1a and Figure 5.1b, respectively. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 70 The data of Figure 5.1a show a general trend of increasing maximum TOF with increased metal particle size (or decreased Co dispersion), indicative of the structure sensitivity of the CH4 decomposition reaction on supported metal catalysts (Boskovic and Smith, 1996). Note that the effect of metal particle size on TOF was small under the low temperature, low C H 4 partial pressure conditions of Figure 5.1a (5%CH 4/Ar at lOlkPa and 723K); however at higher temperature and C H 4 partial pressure (23%CH 4/12%H 2/Ar with KM =0.06 at lOlkPa and 773K), the Co particle size effect is much more significant. The data of the present study clearly show the structure sensitivity of the maximum C H 4 decomposition rate on Co/Si02 catalysts, since the maximum C H 4 decomposition TOF increased with increased metal particle size in the range of 7.6-28.3 nm (or decreased Co dispersion in the range of 12.6-3.4%). The two sets of data in Figure 5.1b show a general trend of decreasing &rfwifh increased metal particle size (or decreased Co dispersion). Since reduced kd implies a decrease in rjrfn (rjrf n=rdlrf n=(rfn-rrn)lrLn), and since the maximum rate of carbon formation increased with increasing metal particle size (Figure 5.1a), we can conclude that the filamentous carbon formation is favoured (rr„ increases) with increasing metal particle size. Previous studies on N i and Fe catalysts have also shown an increase in carbon filament growth rate with particle size or decreased dispersion (Baker 1989; Galuszka and Back, 1984). Note that, unlike in previous studies, the present data were obtained on the same S i 0 2 support so that support effects did not influence the effect of metal particle size (or metal dispersion). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 71 7 6 = 5 E i 4h-i s E ">< CO £ 2 1 0 10 15 20 M e t a l P a r t i c l e S i z e , n m 25 30 Figure 5.1a Dependence of the maximum catalyst activity (Max TOF) on Co particle size (• 723K Reduction, 723K Reaction; A 923K Reduction, 773K Reaction with KM = 0 . 0 6 atm). c £ o o 2 r A • A A 10 15 Metal Particle Size, nm 20 25 Figure 5.1b Dependence of the catalyst decay constant (\00kd) on Co particle size (• 723K Reduction, 723K Reaction; A 923K Reduction, 773K Reaction KM = 0 . 0 6 atm). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 72 5.2.2 Dependency of the Catalyst Activity on Ni Particle Size Furthermore, the influence of metal particle size (or metal dispersion) on C H 4 decomposition activity was measured at one set of operating conditions using two sets of N i catalysts, supported on S i 0 2 and Z r 0 2 as given in Table 3.2 and Table 3.3, respectively. The maximum TOF (Max TOF) and the decay constant (I00kd) were estimated by fitting the experimental data to the 1 s t order decay model and the values obtained are plotted in Figure 5.2a and Figure 5.2b, respectively. The data of Figure 5.2a show a general trend of increasing maximum TOF with increasing N i particle size (or decreasing N i dispersion), similar to Co/Si02. The data of the present study clearly show the structure sensitivity of the maximum C H 4 decomposition on Ni /S i0 2 and Ni /Zr0 2 catalysts. Note that on N i catalysts, catalyst deactivation was only observed on two catalysts with quite low loading. Data in Figure 5.2b show a similar trend of decreased 100^ with increased Ni particle size (or decreased N i dispersion). 5.2.3 Stable Catalyst Activity on Supported Co and N i Catalysts In the present study, stable catalyst activities were obtained on catalysts with high loading. Figure 5.3a shows that stable activity was obtained on 30wt% Co/Si0 2 with average Co particle size 26 nm. Also T E M analysis of the used 30wt% Co/Si0 2 catalyst, reacted under the conditions indicated in Figure 5.3b, confirmed that filamentous carbon was formed. Hence, stable activity corresponded to the steady growth of filamentous carbon. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 73 20 r-18 -16 -0 10 20 30 40 50 60 Meta l Par t ic le s i ze , nm Figure 5.2a Dependence of the catalyst maximum activity (Max TOF) on metal particle size at 773K with KM = 0.06 atm (• Co/Si0 2 ; A N i / S i 0 2 ; x Ni /Zr0 2 ; catalysts were reduced at 923K). 10 15 20 25 Metal Particle size, nm 30 35 Figure 5.2b Dependence of the catalyst decay constant (\00kd) on metal particle size at 773K with KM = 0.06 atm (• Co/Si0 2 ; A N i / S i 0 2 ; x Ni /Zr0 2 ; catalysts were reduced at 923K). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 74 Figure 5.3a Stable catalyst activity on 30wf% Co/Si0 2 (reduced at 923K with Co particle size 26 nm) at 773K with KM = 0 . 0 6 atm. Figure 5.3b T E M micrograph of 30wt% Co/Si0 2 (reduced at 923K) after reaction at 773K with KM - 0 . 0 6 atm showing the presence of fdamentous carbon. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 75_ Similarly, Figure 5.4a shows that stable activity was obtained on 12wt% Ni/SiC»2 and 15wt% Ni/Si02 with large metal particle size, namely 43.3 nm and 49.5 nm (from CO uptake), respectively. T E M micrographs of Figure 5.4b and Figure5.4c again confirm that filamentous carbon was formed on 12wt% and 15wt% N1/S1O2, respectively. Similarly, Figure 5.5 shows that stable activity was obtained on the 8wt% Ni/Zr02 and the 12wt% Ni/Zr02 with large metal particle size and it can be deduced that filamentous carbon formed on 8wt% Ni/Zr02 and 12wt% Ni/Zr02. These observations suggest that stable catalyst activity corresponding to the steady growth of filamentous carbon occurs on the high loading catalyst with large metal particle size. «- 0.8 re u O 0.3 I ' ' ' 1 ' ' 0 10 20 30 40 50 60 70 Time, min Figure 5.4a Stable catalyst activity on Ni/Si02 catalysts at 773K with KM =0.06 atm (•12wt% N i / S i 0 2 with N i particle size 43.3 nm; • 15wt% N i / S i 0 2 with N i particle size 49.5 nm; catalysts were reduced at 923K). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 76 Figure 5.4b T E M micrograph of 15wt% Ni /S i0 2 (reduced at 923K) after reacted at 773K with KM - 0 . 0 6 atm showing the presence of fdamentous carbon. x o 0.0 1 ' ' — . L _ _ — 1 0 10 20 30 40 T i m e , m in Figure 5.5 Stable catalyst activity on Ni /Zr0 2 catalysts at 773K with KM = 0 . 0 6 atm (• 8wt% Ni /Zr0 2 with N i particle size 20 nm; A 12wt% Ni /Zr0 2 with N i particle size 32 nm; catalysts were reduced at 923K). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 77 Based on the above results, it can be concluded that on both N i and Co catalysts, the maximum rate increased with increasing metal particle size and the decay constant decreased with increasing metal particle size. Furthermore, when the catalyst metal particle size is such that kd —» 0, then stable catalyst activity, corresponding to the steady growth of filament carbon, is obtained during C H 4 decomposition. 5.3 Effect of Metal Particle Size on Thresholds The two critical thresholds, coking threshold, K*M and the fdamentous carbon threshold, KfM, were discussed in Section 4.3.2. According to the definition of coking threshold, K*M corresponds to the equilibrium constant, KM, where the carbon deposition rate is equal to the carbon gasification rate. It has been reported (Rostrup-Nielsen, 1972) that compared to the equilibrium constants based on graphite, the K*M values obtained with filamentous carbon were lower and varied from catalyst to catalyst and the variations were correlated with maximum metal particle size. In the present study, the effect of metal particle size on the coking threshold is further discussed based on the data obtained in the present study. Furthermore, the effect of metal particle size on the difference between the two thresholds is discussed. 5.3.1 Dependency of K*M on the Metal Particle Size As mentioned in Section 4.3.2, coking threshold K*M was estimated by extrapolating the plot of maximum CH4 decomposition rate versus KM to zero. Coking threshold is expressed as were obtained (Appendix B.3). It was reported that the difference in the Gibbs free energy change between filamentous carbon and graphitic carbon formation from C H 4 or CO 4 /rate=0 . In the present study, different K*M on Co/Si02 catalysts with different loading Chapter 5 Effect of Catalyst Properties on Catalyst Activity 78 decomposition can be expressed by Equation (5.1) and Equation (5.2) in terms of the equilibrium constant (Rostrup-Nielsen, 1972 and Alstrup, 1988). A G C = AG°A J M,E R F - A G g m p h j l e (5 1) AGC = -RT ln\ '' K A observed is y graphite j (5.2) On the basis of electron microscope observations that the diameter of the carbon fdament was close to and not greater than that of the metal particle, Rostrup-Nielsen reported that deviations from graphite equilibrium for CO and C H 4 decomposition, on a large number of N i catalysts could be explained by the extra energy required by the surface and defect structure of the fdaments, as expressed by Equation (5.3) (Rostrup-Nielsen, 1972). AGc=p-p0+p ( 5 3 ) The term M~Mo corresponds to the extra surface energy due to the cylindrical form of the fdament. The term p corresponds to the extra energy from surface defects. A simple Kelvin equation model can be used to determine AG C , as shown in Equation (5.4) or Equation (5.5): AGc={y*M/pc)*(\/rM) + p ( 5 4 ) AGc=2(y*M/pc)*(l/dp) + M ( 5 5 ) Equation (5.4) shows that the surface energy increases with decreasing filament diameter or metal particle size. According to Equation (5.5), by linear regression of AGC versus lid , y, the surface tension of the carbon fibres, and p*, the defect contribution, can be estimated from the obtained slope and intercept. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 79 In the present study, AG C on different Co and N i catalysts was calculated from the value of K*M (as reported in Section 4.3.2 and Appendix B.3) and K hlle = 0.462 atm at 773K (Rostrup-Nielsen, 1972) using Equation (5.2). The obtained values of AGC are plotted versus the reciprocals of average metal particle size, in Figure 5.6. The data of Figure 5.6 show a linear relationship as described by Equation (5.5). Note that the difference between the present study and Rostrup-Nielsen's study is that the average metal particle size was used in Equation (5.4) to (5.5) not the maximum metal particle size. 20 r 16 -o E 12 -—) XL O 8 < 4 -0 -0 20 40 60 80 100 120 10 4 /dp,Ang' 1 Figure 5.6 Deviation of the coking threshold from graphite equilibrium and the effect of metal crytallite size during CH4 decomposition on N i and Co catalysts at 773K. ( • C0/S1O2; A Ni /S i0 2 ; AGC =0.101(104ldp) + 6.68; catalysts were reduced at 923K). According to the intercept and slope of the data of Figure 5.6, the surface tension was estimated as 8.42 J/m 2 and the defect contribution to AGC was approximately 6.68 kJ/mol at 773K, assuming the density of filamentous carbon was equal to 2.0 g/mL. The value of the surface tension is comparable to the surface tensions of about 7.9 and 7.4 J/m at 773K for the CO-CO2 and CH4-H2 equilibria, respectively (Rostrup-Nielsen, 1972); the defect contribution of Chapter 5 Effect of Catalyst Properties on Catalyst Activity 80 6.68 kJ/mol is comparable to values of 8.4 and 2.9 kJ/mol at 773K for the C O - C 0 2 and C H 4 - H 2 equilibria, respectively (Rostrup-Nielsen, 1972). The result from the present study confirmed that the deviation from graphite could be explained by a more disordered structure of the carbon formed, and by a contribution from the surface energy of the carbon filament. The metal (Ni or Co catalyst) appeared to have no influence on the observed equilibrium. 5.3.2 Effect of Metal Particle Size on (K*M-KfM) As mentioned above, by analogy to the coking threshold, we have defined a filamentous carbon formation threshold: KfM, which corresponds to the term KM where the net carbon deposition rate is equal to the carbon bulk diffusion rate. The difference between the definitions of the two thresholds is that at the coking threshold, the net carbon formation rate is equal to zero, whereas at the filamentous carbon formation threshold, the net rate is constant but not zero. As mentioned in Section 4.3.2, filamentous carbon formation threshold, KfM, was obtained by extrapolating the decay constant ku at different KM to zero. On Co/Si0 2 catalysts with different loading, different KfM were further obtained by extrapolation (as reported in Section 4.3.2 and Appendix B.3) and these values are plotted versus metal particle size in Figure 5.7. Furthermore, the difference between the coking threshold and filamentous carbon threshold, (K*M -KfM), is plotted versus metal particle size in Figure 5.8. At the filamentous carbon formation threshold, catalyst stable activity was obtained with carbon formation rate equal to carbon diffusion rate, with the encapsulating carbon formation p rate neglected. The carbon formation rate can be simplified into k —°2"' when KM approaches K*M (Figure 4.9a and Figure 4.1 la). The diffusion rate of carbon can be described as Chapter 5 Effect of Catalyst Properties on Catalyst Activity 81 Equation (4.3) rd=Ds (ns I dx-nxl dx) (2/3)d„ . The filamentous carbon formation threshold can be simplified into Equation (5.6) noting that the carbon formation rate is equal to the carbon diffusion rate: Note that Equation (5.6) shows that the influence of metal type on the filamentous carbon formation threshold occurs through the Ds. The data in Figure 5.7 show that the dependence of KfM on metal particle size is not a simple linear relationship. This can be explained by noting that ns and ns - « , are also dependent on metal particle size, dp, since the activity of carbon formation is dependent on metal particle size as described in Section 5.2. However, the data in Figure 5.8 show a clear trend that the difference between the coking threshold and filamentous carbon threshold increases with increasing metal particle size on Co catalysts with different loadings. According to the discussion in Section 4.4.3, stable catalyst activity with carbon deposition during C H 4 decomposition occurs when KM satisfies KfM <KM <K*M. The increasing difference between the coking threshold and filamentous carbon formation threshold, with increased metal particle size shown in Figure 5.8, indicates that the window of suitable operating conditions for stable catalyst activity with filamentous carbon formation is wider with increasing metal particle size. This is consistent with the observation in Section 5.2 that under the same KM , stable catalyst activity with filamentous carbon formation was obtained on larger metal particles because the condition KfM <KM < K*M can be satisfied when the difference in thresholds increases (i.e. (K*M -KfM) increases). Dstis (ns I dx - nj dx) k(2/3)dP (5.6) Chapter 5 Effect of Catalyst Properties on Catalyst Activity 82 0.07 | , 0.06 - " 0.05 -E 0.04 -ro x f 0.03 - • • 0.02 -0.01 -0.00 ' 1 1 1 '• 1 1 0 5 10 15 20 25 30 dp, nm Figure 5.7 The filamentous carbon formation threshold, KfM , versus metal particle size on Co catalysts at 773K. 0.08 r 0.07 -0.06 -E 0.05 -rs 0.04 -s 0.03 -0.02 -0.01 -0.00 -10 15 dp, nm 20 25 30 Figure 5.8 The difference between the coking threshold and the filamentous carbon formation threshold, (K*M -KfM), increases with the increasing particle size of Co at 773K. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 83 5.4 Effect of MSI on Catalyst Activity In this section, the influence of BaO, La2C>3 and Z r 0 2 added to the S i 0 2 support of the Co/Si0 2 catalyst, is reported. The catalysts with S i 0 2 modified by additives BaO, La203, and Zr0 2 were designated as Co/BaO/Si0 2 , Co/La 203/Si0 2 and Co/Zr0 2 /S i0 2 , respectively. The Co/BaO/Si0 2 , Co/La 203/Si0 2 and Co/Zr0 2 /S i0 2 catalysts were prepared by step-wise incipient wetness impregnation. Section 3.2 and Table 3.4 summarize the preparation details and characterization data of these modified catalysts. On the basis of a detailed characterization study of the modified catalysts, using TPR, XPS and CO chemisorption, the influence of the addition of BaO, La203 and Z r 0 2 on the activity and deactivation of the 12wt% Co/Si0 2 catalyst during C H 4 decomposition was investigated. 5.4.1 Effect of Additives on MSI 5.4.1.1 Effect of Additives on Reduction Behavior of Co Species and MSI In order to clarify the effect of additives, BaO, La203 and Zr0 2 , on the reduction behaviour of C03O4 species, the catalysts were characterized by TPR. The TPR profiles of the 12wt% Co/Si0 2 catalyst and modified catalysts Co/BaO/Si0 2 , Co/Zr0 2 /S i0 2 and Co/La 2 0 3 /S i0 2 , are shown in Figure 5.9. Generally, the TPR profiles could be resolved into three peaks. The peak position and relative intensity of each peak, representing the relative H 2 consumption, is summarized in Table 5.1. The TPR profile for the base 12wt% Co/Si0 2 catalyst of Figure 5.9a shows two major reduction peaks with maxima at 536K and 663K. A broad shoulder extending to 837K was also observed. The first two reduction peaks are usually identified as the two-step reduction of C03O4—»CoO—»Co. The stoichiometric H 2 consumption ratio associated with the two reduction steps is 1:3. However, for the Co/Si0 2 catalyst the ratio calculated from the data of Table 5.1 is Chapter 5 Effect of Catalyst Properties on Catalyst Activity 84 1:2.2, suggesting that not all the CoO species are reduced to Co. Rather, less reducible or irreducible species are formed during the C03O4 reduction, most likely through interaction with the support, to yield, for example, Co2SiC<4 (Riva et al., 2000; Ming et al., 1995). The broad shoulder that exists in the TPR profile at high temperature (around 837K) is assigned to the reduction of Co species that interact with the S1O2 support (Riva et al., 2000). The H 2 consumption of this broad shoulder was 8.2% of the total H2 consumption during TPR of the Co/Si0 2 catalyst. For the Co/BaO/Si02 catalyst, the TPR profde of Figure 5.9b was very similar to that of the Co/SiC>2 catalyst. The low temperature reduction peaks shifted slightly to higher temperature (the first from 536K to 543K; the second from 663K to 670K). The relative H 2 consumption of the broad high temperature shoulder (around 843K) was 8.4% for the Co/BaO/SiC»2, essentially the same as the 8.2% obtained with Co/SiC>2. In addition, the consumption ratio of the first two peaks was 1:2.4, similar to the 1:2.2 obtained with Co/SiC^. The result suggests that BaO changed the interaction between Co and the BaO/SiC>2 support slightly and that the reducibility of the Co species was slightly changed by the addition of the BaO to the support. For the Co/Zr02/Si02 catalyst, the TPR profile of Figure 5.9c shows that the second low temperature reduction peak shifted slightly to higher temperature (the second peak from 663K to 683K), indicative of a small increase in resistance to reduction. Also, in the high temperature region, a sharp peak replaced the broad shoulder at 852K. It is further observed that the relative Ff2 consumption at high temperature increased from 8.2% for the Co/Si02 catalyst, to 41.4% for the Co/Zr02/Si02 catalyst. In addition, the H2 consumption ratio of the first two peaks was 1:3. Hence the high temperature H2 consumption must be associated with a Co-Zr interaction that prevents the reduction of Co species generated during the calcination step. This observation confirms that a strong interaction between cobalt and zirconium replaced the cobalt-silica Chapter 5 Effect of Catalyst Properties on Catalyst Activity 85 interaction (Feller et al., 1999). Feller et al. claimed that the Co-Zr interaction was formed due to an interaction between the zirconium salt and cobalt ions. In the present case, the interaction probably results from residual zirconium salt not converted to Z r 0 2 during the short-term calcination. For the Co/La203/SiC»2 catalyst, the TPR profile of Figure 5.9d shows that the first reduction peak moved to higher temperature (from 536K to 588K) and increased in intensity relative to the first reduction peak of the Co/SiO*2 catalyst. The second reduction peak was replaced by a sharp peak at higher temperature 703K (663K for Co/SiC>2 catalyst) and the H2 consumption ratio of the two peaks was 1:0.6. These observations are indicative of increased resistance to reduction of the oxides, especially CoO, on the La2CVSiC)2 support. The relative intensity of the broad peak at high temperature decreased from 8.2% for Co/SiC»2 to 4.1% for the Co/La2C>3/SiC>2 catalyst. Apparently, the addition of La2C>3 increased the reduction temperature of both C03O4 and CoO, but also resulted in Co-support species, produced during reduction, that were not subsequently reduced to Co metal. Note that the TPR of the Co/La203/Si02 catalyst also shows that i f the catalyst is reduced at 723K, the degree of reduction of the Co oxide will be lower than that obtained on the Co/Si02. From the TPR results, it can be concluded that the addition of BaO, La203 and Zr02 to the Si02 support, all influenced the MSI and hence the reduction behaviour of the Co species. The addition of BaO increased the interaction marginally; the addition of Zr02 resulted in a very strong Co-Zr02/Si02 interaction and Co species that could only be reduced above 850K; the addition of La203 resulted in an interaction between Co and the modified La203/Si02 support that increased the reduction temperature of C03O4 and CoO and produced species that were not reducible during TPR. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 86 Table 5.1 Summarized data of catalyst TPR profiles of modified Co catalysts. Catalyst 1st Peak 2nd Peak 3m Peak Temp, K Relative Intensity Temp, K Relative Intensity Temp, K Relative intensity 12wt% Co/Si02 536 28.8% 663 63.0% 837 8.2% Co/BaO/Si02 543 27.0% 670 64.5% 843 8.4% Co/Zr02/Si02 533 14.5% 683 44.1% 852 41.4% Co/La 20 3/Si0 2 588 61.7% 703 34.2% 843 4.1% Note: In TPR, catalysts were reduced from 323K to 950K in 5%H2/He in an hour. Catalyst reduction degrees reported in Table 3.1 and 3.4 were calculated based on the catalysts were reduced from 323K to the desired reduction temperature in 40% H2/He in an hour. 1. I U i 1 1.05 " a ! | Co/SiCb 1.00 0.95 a O 0.90 1- \ | 0.85 0.80 JA 0.75 1 ! L 250 450 650 850 1050 Temp, K Chapter 5 Effect of Catalyst Properties on Catalyst Activity 87 0.50 r 0.45 -0.40 -0.35 -0.30 -CO c f 0.25 -O 1— 0.20 -0.15 -0.10 -0.05 -ono -! ! b BaO/Co/Si02 250 350 450 550 650 750 850 950 1050 Temp, K 1.85 1.80 ro Q O  1.65 1.55 1.50 . Zr02/Co/Si02 ! M i \ i i i i i 250 350 450 550 650 750 Temp,K 850 950 1050 Chapter 5 Effect of Catalyst Properties on Catalyst Activity 88 250 350 450 550 650 750 850 950 1050 Temp, K Figure 5.9 TPR profiles of modified Co catalysts, a: 12wt% Co/Si0 2 ; b: Co/BaO/Si0 2; c: Co/Zr0 2 /S i0 2 ; d: Co/La 2 0 3 /S i0 2 . 5.4.1.2 Effect of Additives on Surface Species To clarify the effect of additives BaO, L a 2 0 3 and Z r 0 2 on the distribution of surface Co species, reduced catalysts were characterized by XPS, as described in Section 3.3.5. The base Co/Si0 2 catalyst was characterized before and after reduction at 723K. Other catalysts modified by BaO, L a 2 0 3 and Z r 0 2 were characterized by XPS after reduction at 723K. The reduction temperature of 723K was chosen because at this reduction temperature it was easier to detect different MSI effects from the TPR results compared to reduction at 923K. The effect of additives on catalyst deactivation was also significant when the catalysts were reduced at 723K as discussed in Section 5.4.3. In general, Co 2p, O Is and Si 2p spectra were obtained from each XPS measurement. Detailed results from the XPS analysis are summarized in Table 5.2, including Co 2p3/2 binding energy (B.E.), the intensity of the shake-up shoulder relative to the Co 2p intensity, and the calculated Co: Si ratio. Among the modified catalysts, BaO was detected Chapter 5 Effect of Catalyst Properties on Catalyst Activity 89 by the presence of the M5N45N45 Auger peak with kinetic energy 597.7eV; Zr02 was detected at a 3d5/2 B.E. of 182.6eV with energy difference 2.4eV between 3ds/2 and 3d3/2; La203 was detected at a 3d 5 / 2 B.E. of 836.3eV. The fitted Co 2p spectra of the various catalysts are presented in Fig. 5.10 and Table 5.2 (Comparisons between the fitted and measured spectra given in Appendix C). For the calcined Co/Si0 2 catalyst, the Co 2p3/2 B.E. was 780.3eV; The Co 2p 3 / 2 B.E. of the reduced catalysts was in the range 780.7eV to 782.3eV (with Si 2p at 103.5 eV). Riva et al. (2000) reported the Co 2p 3 / 2 B.E. of C03O4 as 780.1eV; Co 2p 3 / 2 B.E. of CoO as 780.5 eV; Co 2p 3 / 2 B.E . of metallic Co as 777.8 eV with Si 2p reference at 103.3 eV (Riva et al., 2000). Meanwhile, Ming and Baker (1995) reported the Co 2p 3 / 2 B.E. of C o 2 S i 0 4 as 781.3 eV with Si 2p at 103.5 eV as reference. Accordingly, for the calcined Co/Si0 2 catalyst of the present study, the Co 2p3/2 B.E. of 780.3eV is assigned to C03O4 (Riva et al., 2000) and this observation is in agreement with X R D data showing the presence of C03O4 after calcination. The Co 2p3/2 B.E. of the reduced catalysts was in the range 780.7eV to 782.3eV, indicative of the presence of surface C o 2 + probably as Co2SiC>4 (B.E. 781.3eV) (Ming and Baker, 1995) or CoO (B.E. 780.5eV) (Riva et al., 2000). The shake-up shoulder at higher B.E. for the reduced catalysts is ascribed to unreduced C o 2 + interacting with the support. The assignment is supported by the fact that the TPR data show that CoO is reduced at low temperature (<723K). Also, steps were taken to minimize the exposure of the reduced catalysts to air (to avoid re-oxidation of Co) prior to the XPS measurement (Catalysts were sealed in inert gas after cooling be fore being loaded and transferred to the XPS using a glove box. Hence it was assumed that there was no oxidation of the reduced catalyst during the sample transfer.). To quantify the MSI, the relative intensity of the shake-up shoulder was calculated as the ratio of the fitted peak area of the shake-up shoulder to the Co 2p3/2 fitted peak area (Bianchi, 2001). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 90 Compared to the reduced Co/SiC»2 catalyst, the spectra of the other reduced catalysts show that the relative intensity of the Co species interacting with silica was dependent upon which of BaO, Zr02, and La 203 were present. The relative intensity of the shake-up shoulder was 12% for the reduced Co/Si02 catalyst. The relative intensity of the shake-up shoulder was mot available for the reduced Co/BaO/Si02 catalyst because the Co 2p and Ba 3d peaks could not be resolved. However, the conclusion that the addition of BaO had little effect on the interaction of Co species with silica could be drawn from the TPR data of Figure 5.9. Conversely, a much stronger Co-Zr02/Si02 interaction is apparent for the reduced Co/Zr02/Si02 catalyst, the relative intensity of the shake-up shoulder increasing from 12% to 28%. This result is also consistent with the increased relative H2 consumption at high temperature (850K) that was observed during TPR. For the reduced Co/La203/Si02 catalyst, the relative intensity of the shake-up increased to 18%, again consistent with the stronger MSI identified from TPR data and ascribed to the higher resistance of the cobalt oxides to reduction at low temperature (<723K) on this catalyst. The energy difference (AE) between Co 2p3/2 and 2p./2 (AE=15eV for C03O4 and metallic Co, AE=15.7eV for CoO) also make it possible to distinguish the different phases of Co present on the catalyst surface (Riva et al., 2000). A AE=15.7eV applies to C o 2 + in general, even when cobalt forms silicate through reaction with the Si02 support (Riva et al., 2000). In the present study, AE = 15.7eV and the presence of a shake-up shoulder at higher B.E. was observed for all reduced catalysts. The AE=15eV listed in Table 5.2 for the unreduced Co/Si02 catalyst confirms that Co species were in the form of C03O4 after calcination, consistent with X R D data already noted. The XPS spectrum of the un-reduced Co/Si02 catalyst (Figure 5.10a) also shows a very small shake-up shoulder at higher B.E., suggesting that there is very little interaction between Co species and the silica support. However, AE=15.7eV for the reduced Co/Si02 catalyst. Figure Chapter 5 Effect of Catalyst Properties on Catalyst Activity 91 5.10b also shows that the shake-up shoulder at higher B.E. for the reduced Co/Si0 2 catalyst was more intense than for the unreduced catalyst. The interaction between Co and S i 0 2 to yield cobalt silicate must therefore occur during the catalyst reduction step. T— 55 c c 810 805 800 795 790 785 780 775 770 765 Binding energy, eV Figure 5.10 Surface Co 2p Spectra on modified catalysts, a: unreduced 12wt% Co/Si0 2 ; b: reduced 12wt% Co/Si0 2 ; c: reduced Co/BaO/Si0 2 ; d: reduced Co/Zr0 2 /S i0 2 ; e: reduced Co/La 2 0 3 /S i0 2 . (Note that the raw data of XPS measurement is shown in Appendix C.) Chapter 5 Effect of Catalyst Properties on Catalyst Activity 92 7.5 5.7 - ! ! | 5.5 1 1 1 — 1 1 1—i i—i i i 810 805 800 795 790 785 780 775 770 765 Binding energy, eV Figure 5.10 Surface Co 2p Spectra on modified catalysts, a: unreduced 12wt% Co/Si0 2 ; b: reduced 12wt% Co/Si0 2 ; c: reduced Co/BaO/Si0 2 ; d: reduced Co/Zr0 2 /S i0 2 ; e: reduced Co/La 2 0 3 /S i0 2 . (Note that the raw data of XPS measurement is shown in Appendix C.) Chapter 5 Effect o f Catalyst Properties on Catalyst Activi ty 93 820 810 800 790 780 Binding energy, eV 770 760 810 805 800 795 790 785 780 Binding energy, eV 775 770 765 Figure 5.10 Surface Co 2p Spectra on modified catalysts, a: unreduced 12wt% Co/Si0 2 ; b: reduced 12wt% Co/Si0 2 ; c: reduced Co/BaO/Si0 2 ; d: reduced Co /Z r0 2 /S i0 2 ; e: reduced Co /La 2 0 3 /S i0 2 . (Note that the raw data of XPS measurement is shown in Appendix C.) Chapter 5 Effect of Catalyst Properties on Catalyst Activity 94 Table 5.2 Summarized data from XPS characterization of modified Co catalysts. Catalysts Co (eV) Med (AE) 0 Is Relative intensity 100Co:Si Co 2p3 /2 AEC eV eV Shoulder/2p3/2 % Atomic Co/Si02 without Reduction b 780.3 15 ~ 533.0 1.9 Co/SiC-2 after Reductionb 780.7 15.7 533.0 12 1.9 Co/BaO/Si02 after Reduction b 781.2 15.7 597.7 (M 5 N 4 5 N45) 533.0 -Co/Zr02/SiOz after Reductionb 781.6 15.7 182.6 (3d5/2AE=2.4) 533.0 28 2.6 Co/La 20 3/Si0 2 after Reductionb 782.3 15.7 836.3 (3d5/2) 533.0 18 1.1 a The shake-up shows the interaction of Co with silica. b Catalysts were reduced from 323K to 723K in 1 hour. ° AE =(Co 2pI /2- Co 2p3/2). dMe: Ba, LaorZr. e Si 2p with binding energy 103.5eV was taken as an internal reference. 5.4.1.3 Effect of Additives on Co Dispersion The 100Co:Si ratio calculated from the XPS analysis and listed in Table 5.2 is indicative of the Co dispersion of the catalyst: a higher dispersion corresponds to higher 100Co:Si ratio. The data of Table 5.2 show that the 100Co:Si ratio was 1.9 for the Co/SiO"2 catalyst, both before and after reduction. Note that for the reduced Co/BaO/SiCh catalyst, the 100Co:Si ratio is not reported because the Co 2p and Ba 3d peaks could not be resolved (B.E. of Ba 3d5/2=779.7eV, Co 2p 3 / 2 B.E.=778.0eV for Co 0 and 780.5eV for Co 2 + ) . For the reduced Co/La 20 3/Si02 catalyst, the 100Co:Si ratio decreased to 1.1, compared to the Co/SiC>2 catalyst, whereas for the reduced Co/ZrCVSiCh catalysts, the 100Co:Si ratio increased to 2.6, suggesting.that ZrC*2 assisted the dispersion of Co species over the support due to the strong interaction between Co and ZrC>2. Note that although the 100Co:Si ratio determined from the XPS peak intensity data is indicative of the dispersion of the Co species on the surface, this ratio included unresolved Co 0 (B.E. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 95 778.OeV) and C o 2 + species. Hence the dispersion of active Co 0 as determined by CO chemisorption is considered the more accurate measure of active Co sites. Table 3.4 summarized the active cobalt dispersion, particle size and the number of active sites as determined by CO chemisorption on the Co/Si02 and modified Co/Si02 catalysts reduced at 723K and 923K. Note that the dispersion is calculated relative to the total amount of reduced Co on the catalyst. Also note that at a reduction temperature of 723K, the TPR results show that the different MSI effects among the catalysts, as reflected in the relative intensities of the high temperature reduction peak (850K), will be important. Conversely, the TPR data show that reduction at 923K will result in complete reduction of the Co. On Co/BaO/Si02, Co/La203/Si02 and Co/Zr02/Si02, the CO uptake decreased compared to the Co/Si02 catalyst. After accounting for the degree of reduction of the Co species, the results show that the Co dispersion decreased on all the modified catalysts. Among the modified catalysts, Co/Zr02/Si02 had the highest dispersion. When the catalysts were reduced at 973K, however, the differences in dispersion were not as pronounced, compared to the catalysts reduced at 723K. In particular, the Co dispersion obtained on the Co/Si02 and the Co/Zr02/Si02 were approximately equal when catalysts were reduced at 973K. 5.4.2 MSI Order among the Modified Catalysts MSI effects are known to influence the reduction of metal oxides and metal dispersion on supported metal catalysts (Haddad et al., 1996; Riva et al., 2000; Ming and Baker, 1995; Van Steen et al., 1996; Khodakov et al., 1997; Rodrigues and Bueno, 2002). A strong MSI increases the difficulty of the reduction of the precursor oxide, either by increasing the reduction temperature of existing oxides or by the production of metal-support species (such as Co2Si04) that are difficult to reduce or are irreducible. Furthermore, a strong MSI decreases the mobility of the metal surface species such that the metal dispersion is enhanced. In the present study, the Chapter 5 Effect of Catalyst Properties on Catalyst Activity 96 strength of the MSI is of interest, and a number of techniques have been used to determine the relative strength of the MSI between Co and a S i 0 2 support, modified by the addition of BaO, La203 and Zr0 2 . The interaction between Co and S i 0 2 was not significantly affected by the addition of BaO to the S i 0 2 . The small increase in H 2 consumption during the extended high temperature TPR and the small increase in reduction peak temperatures suggest a small increase in the MSI. However, the lower relative intensity of the Co 2p3/2 shake-up shoulder as measured by XPS, suggests a small reduction in the Co-silica interaction. The behaviour of trie Co/Zr0 2 /S i0 2 catalyst deviated significantly from the Co/Si0 2 catalyst. The addition of Z r 0 2 resulted in a very strong MSI, evidenced by the increased H 2 consumption in the high temperature region (850K) of the TPR experiment. The TPR experiment also showed that the C03O4 reduced to CoO was subsequently all reduced to Co. However, a significant fraction of the Co present on the catalyst after calcination could only be reduced at high temperature. Hence by reducing the catalyst at 723K, a significant portion of the cobalt remains unreduced because of the strong MSI. The strong MSI yields increased dispersion of Co surface species, as evidenced by the increased 100Co:Si ratio determined by XPS. The high shake-up peak intensity also points to a strong MSI on this catalyst. The strong MSI is also consistent with the small particle size of the C03O4 precursor determined by X R D and noted previously. For the Co/La 203/Si0 2 catalyst, the increase in temperature associated with the reduction of both Co304 (at 588K) and CoO (at 703K) suggest a stronger interaction between these species and La, compared to Si. Although there was little decrease in the high temperature H 2 consumption, compared to Co/Si0 2 , the TPR peak intensities point to a significant portion of C03O4 that was reduced at low temperature, but formed species that did not reduce at high Chapter 5 Effect of Catalyst Properties on Catalyst Activity 97 temperature. Hence a strong MSI occurs during the reduction of this catalyst. The intensity of the Co 2p3/2 shake-up shoulder also suggests a strong MSI. However, the strong MSI did not improve Co dispersion, as indicated by the Co/Si ratio estimated by XPS. These data suggest that La2C>3 located on top of the Co and are consistent with XPS data that confirmed the presence of La (Table 5.2) on the catalyst surface. The results obtained here do not agree with those of Haddad et al. (1996), who reported that L a 3 + moderates a strong Co-silica interaction and enhances the reducibility of the Co oxide. However, in the present work, La was added to the support prior to Co and the resulting MSI on the modified support yields a stronger MSI. The effects of aqueous impregnation of Co/SiC>2 catalysts has already been described in literature (Haddad et al., 1996), and the different sequence of impregnating steps used in the present study are the most likely source of the observed effects of La. Although the La results in a stronger MSI between Co and the modified silica support, the result is a reduced dispersion because La locates on top of the Co. The Co dispersion, as determined from CO uptake measurements on catalysts reduced at 723K was higher on the Co/Si0 2 catalyst than either of Co/BaO/Si0 2 , C o / L a 2 0 3 / S i 0 2 or Co/Zr02/Si02. However, based on the different MSI strengths noted in the previous paragraph, much higher dispersion would have been expected for the Co/Zr02/Si02 catalyst, in particular. The CO uptake measurement is assumed to titrate active sites available on the Co surface. However, it is possible that the CO uptake on Co is reduced by the presence of the modified supports. Previous studies have suggested that the perimeter of the Co particles may be decorated by the support (Zadeh and Smith, 1998), reducing CO uptake. This effect would be particularly pronounced for the Co/Zr02/Si02 catalyst with more highly dispersed Co. Furthermore, there might be an electronic effect associated with the modified catalysts that reduces CO uptake. The latter observation is consistent with the lower CH4 decomposition TOF Chapter 5 Effect of Catalyst Properties on Catalyst Activity 98_ data reported on the modified catalysts (Section 5.4.3) and shown in Figure 5.11a. The strong interaction of the Co species with Zr ensures good dispersion, but decreases reducibility. By increasing reduction temperature, more Co is reduced and the benefit of the strong interaction in aiding the dispersion of Co over the modified support is evident. The data of Table 3.4 show similar dispersion (as determined from CO uptake) for both the Co/Zr02/Si02 and the Co/Si02 catalysts when reduced at 923K. The catalyst characterization results point to a change in the strength of the Co-support interaction when the S i 0 2 support was modified by the addition of BaO, La203 or Zr02. The data suggest that the strength of the MSI between Co and the support can be ranked in increasing order as Co/Si0 2 * Co/BaO/Si0 2 < Co/La 2 0 3 /S i0 2 < Co/Zr0 2 /S i0 2 . 5.4.3 Catalyst Activity over Modified Co Catalysts The effect of BaO, Z r 0 2 and L a 2 0 3 on the C H 4 decomposition activity of the Co/Si0 2 was determined at two sets of reaction conditions, as indicated in Figure 5.11. Based on the observations in Section 5.2, that C H 4 decomposition is very dependent on the structure (Boskovic and Smith, 1996; Solymosi et al., 1994), the effect on catalyst activities must be compared based on TOFs. Following the procedures described in Chapter 3, TOF and decay constant 100*,, indicating the activity and stability of catalyst respectively, were obtained from the measured activity profiles and are plotted in Figure 5.11a and Figure 5.11b, respectively. In order to compare to the Co/Si02 catalyst, the dependency of TOFs and decay constant 100*, on metal particle size measured on Co/Si02 catalysts are also plotted in Figure 5.11a and Figure 5.11b. Chapter 5 Effect of Catalyst Properties on Catalyst Activity 99 10 15 20 Metal Particle size, nm 25 30 35 Figure 5.11a Dependence of maximum catalyst activity (TOF, r*) on Co particle size over modified Co catalysts. (Unfilled symbol: Reduction 723K, 140 mL/min 5%CH 4 /Ar at 723K; filled symbol: Reduction 923K, 185 mL/min 23%CH 4/12%H 2/Ar at 773K; • and • Co/Si0 2 ; O and • Co/BaO/Si0 2; O and • Co/Zr0 2 /S i0 2 ; A and • Co/La 2 0 3 /Si0 2 ) . Figure 5.11a shows that the correlation of the C H 4 decomposition TOF with Co dispersion (or equivalent Co metal particle size) obtained on Co/Si0 2 catalysts, is also valid for the catalysts reduced at 723K in which the MSI had been modified by the addition of BaO, Zr0 2 , and L a 2 0 3 to the S i 0 2 support. The effect of using the modified support is adequately accounted for by the Co dispersion and on the promoted catalysts the same dependency on metal particle size was observed as with the Co/Si0 2 catalysts reduced at 723K. However, the modified support apparently has some impact on Co catalyst activity for the catalysts reduced at 923 K, which results in a decrease in C H 4 activity (maximum TOF) by approximately a factor of two. The Chapter 5 Effect of Catalyst Properties on Catalyst Activity 100 lower TOFs of the modified catalysts can be explained by the electronic effect of metallic Co and S i 0 2 modified with BaO, Z r0 2 , and L a 2 0 3 . The ability of Co to dissociate CFf4 was reduced because the B.E. of Co shifted to higher B.E. for the modified catalysts. 18 16 14 12 | 10 •D XL O o ° 8 10 15 20 Metal Particle Size, nm 25 30 Figure 5.11b Dependence of catalyst decay constant ( 1 0 0 * r f ) on Co particle size over modified Co catalysts. (Unfilled symbol: Reduction 723K, 140 mL/min 5%CH 4 /Ar at 723K; filled symbol: Reduction 923K, 185 mL/min 23%CH 4/12%H 2/Ar at 773K; • and • Co/Si0 2 ; O and • Co/BaO/Si0 2; O and • Co/Zr0 2 /Si0 2 ; A and • Co/La 2 0 3 /Si0 2 ) . Data in Figure 5.11b shows that the decay constant (ktl) decreased with increasing metal particle size on Co/Si0 2 catalysts. For the case of catalysts reduced at 723K, the decay constant determined for Co/BaO/Si0 2 was close to the correlation of the dependency of decay constant Chapter 5 Effect of Catalyst Properties on Catalyst Activity 101 obtained for the Co/SiC»2 catalyst. However, the decay constants determined for Co/La2C>3/Si02 and Co/ZrOySiCh were dramatically higher than that obtained on the Co/SiC»2 catalyst. For the case of catalysts reduced at 923K, deactivation was observed only on Co/ZrCVSiCh catalyst, similar to the Co/SiO"2 catalysts as shown in Figure 5.11b. Also, the decay constant determined for Co/ZrCVSiCh catalyst was close to the correlation obtained on the Co/SiC»2 catalysts. For Co/BaG7SiC»2 and Co/I^OySiC^ catalyst reduced at 923K (with metal particle size 30.8 and 27.7 nm respectively), stable catalyst activities were obtained at 773K during CH4 decomposition, as shown in Figure 5.12. ~ 0.40 o E 0.10 I o •g 0.05 -rt I O 0.00 1 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Time, min Figure. 5.12 Stable catalyst activity on modified Co catalysts. ("Co/SiCb; •Co/BaO/Si02; •Co/Zr02/Si02; ACo/La203/Si02, Reduction 923K, Reaction 773K with KM = 0.06 atm) 5.4.4 Effect of MSI on Catalyst Deactivation The effect of a strong MSI on filamentous carbon formation has been reported to affect the deformation of the metal particle at the tip of the filament and also to influence the formation Chapter 5 Effect of Catalyst Properties on Catalyst Activity 102 of hollow or solid fdaments (Snoeck et al., 1997a). In both cases, the effect is related to the strength by which the particle is held to the support. The present study suggests a third effect of the metal support interaction that leads to increased catalyst deactivation. According to the mechanism of carbon fdament formation described in Chapter 4, the formation of encapsulating carbon can be ascribed to the imbalance between the rate of carbon formation and the rate of carbon removal from the metal surface. If carbon is not removed from the surface, then the active surface carbon transforms into inert, encapsulating graphitic carbon that causes deactivation. Carbon removal from the surface is a consequence of diffusion through the metal particle and excretion at the back of the particle to build graphitic layers and fdaments. During this process, the metal particle is detached from the support surface. However, i f the MSI is strong such that the excretion process is decreased, then the carbon removal rate will decrease significantly, resulting in a build up of encapsulating carbon and deactivation. For the case of catalysts reduced at 723K, the data of the present study have shown that BaO had only a minor effect on the Co-support interaction, whereas the presence of La203 and Zr0 2 enhanced the MSI. Consequently, the expectation would be that the Co particle would be more difficult to detach from the La203 and Z r 0 2 modified support surface and hence the carbon removal rate by filament formation would be decreased. As evidenced by the XPS data, described in Section 5.4.5, more graphitic carbon would therefore cover the surface of the catalyst and this would lead to increased deactivation. Conversely, it is easier to detach the metal particle from the support and balance the carbon formation and removal rates such that filament formation continues, in the case when the MSI is weaker, as was the case with the Co/Si0 2 and Co/BaO/Si0 2 catalysts. This expectation was indeed observed on the decay constant of catalyst reduced at 723K (Figure 5.1 lb). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 103 Note that the catalysts used for activity measurements were reduced at 723K or 923K. The catalysts reduced at 723K yielded Co species that were not completely reduced and interacted with the support, whereas, for the catalysts reduced at 923K, more Co species interacting with the support could be reduced. Consequently, in the latter case, the correlation between decay constant and metal particle size, obtained with the Co/Si0 2 catalysts, was also followed by the Co/Zr0 2/SiC>2 catalyst, suggesting that the higher reduction temperature reduced the MSI and hence allowed carbon removal by fdament formation. Stable catalyst activities were also obtained on Co/BaO/SiCh and Co/L^CVSiCh reduced at 923K, a consequence of the large metal particle size of these catalysts (Figure 5.12). 5.4.5 Carbon Species on the Used Catalyst Additional information about the carbon species on the catalyst surface was obtained by XPS analysis of the used catalysts. C Is spectra on used, modified catalysts are shown in Figure 5.13. The spectra show that the shape and peak position of C Is on Co/BaO/SiCh and Co/La 203/Si02 catalysts are similar. The data also show that the line positions are shifted to low B.E. with a shoulder at low B.E. The data were fitted by two peaks at B.E. 283.4eV (carbidic carbon) and at 285eV (graphitic carbon). The relative concentration of carbon species with lower B.E. on the surface was estimated from the fitted peak area and is listed in Table 5.3. The decay constant determined for each catalyst is also listed in Table 5.3. Data in Table 5.3 show that the magnitude of kd correlates inversely with the relative concentration of carbidic carbon observed on the used catalyst surface. For the Co/ZrCVSiC^ catalyst, only graphitic carbon was detected corresponding to a high decay constant, \00kd =15.3 min"1, as indicated in Table 5.3. For Co/La203/Si02 catalyst, 34% of the carbon was carbidic and the decay constant decreased, \§0kd = 7.7 min"1. For the Co/BaO/SiC»2 catalyst, 66% of the carbon was carbidic and the decay Chapter 5 Effect of Catalyst Properties on Catalyst Activity 104 constant decreased further to \00kd - 2.2 min"1. Hence the more carbidic carbon on the catalyst surface, the lower the rate of catalyst deactivation. According to the catalyst deactivation mechanism discussed in Chapter 4, there are two kinds of carbon on the catalyst surface: single carbon atoms which can diffuse through metal particle and encapsulating carbon which encapsulates the catalyst surface and deactivates the catalyst. Consequently, the carbidic carbon detected by XPS at low B.E. can be ascribed to the single carbon atoms that can diffuse through the metal particle. The graphitic carbon with higher B.E. can be ascribed to the encapsulating carbon that deactivates the catalyst. The competition between the fdamentous carbon that is formed from the single C atoms that have diffused through the metal particle and the encapsulating carbon determine whether catalyst deactivation or stable catalyst activity is observed. Accordingly, the deactivation mechanism can explain the correlation of the magnitude of I00kt/ with the relative concentration of carbidic carbon observed on the used catalyst surface: the more inert carbon that exists on the catalyst surface, the higher the decay constant. The distribution of carbon species confirmed that the competition between the encapsulating carbon and the filamentous carbon determines the rate of catalyst deactivation. Consequently, different carbon species, carbidic carbon or graphitic carbon dominates on the catalyst surface. For example, on Co/ZrCVSiC^ reduced at 723K, the resistance to carbon diffusion is high because of the strong MSI. Consequently a very high decay constant results with more graphitic carbon residing on the catalyst surface. Chapter 5 Effect o f Catalyst Properties on Catalyst Act ivi ty 105 4.0 3.5 2 3.0 § 2.5 2.0 1.5 300 295 290 285 280 Binding energy, eV 275 270 300 295 290 285 280 275 270 B i n d i n g e n e r g y , eV Chapter 5 Effect of Catalyst Properties on Catalyst Activity 106 4.0 3.5 & ZZ 3.0 >> '35 I 2.5 2.0 1 .5 295 290 285 280 275 Binding energy, eV Figure 5.13 XPS spectra of C Is on used catalysts surface, a: Co/BaO/Si0 2; b: Co/Zr0 2 /S i0 2 ; c: Co/La 2 0 3 /S i0 2 . Table 5.3 Carbon species on the used catalysts surface from XPS measurement. Used catalysts C Is 283.4eV/(285eV+283.4eV) . % Decay constant, 100 kd 1/min Co/BaO/Si0 2 after Reaction 66 2.2 Co/Zr0 2 /S i0 2 after Reaction 0(284.7eV) 15.3 Co /La 2 0 3 /S i0 2 after Reaction 34 7.7 5.5 Summary The structure sensitivity of activity has been observed on the low loading Co and N i catalysts during C H 4 decomposition: the maximum decomposition activity increased with increasing metal particle size (decreasing metal dispersion) and the decay constant decreased with increasing metal particle size (decreasing metal dispersion). Chapter 5 Effect of Catalyst Properties on Catalyst Activity 107 The coking threshold K*M obtained on Co/SiC»2 with different loading in the present study followed the linear relationship of K*M versus the reciprocal of the average metal particle size. A fdamentous carbon formation threshold, KfM, has also been defined as the value of KM =P^ I PCHf corresponding to the formation of filamentous carbon at a particular temperature. The difference between the coking threshold, K*M, and the filamentous carbon formation threshold, KfM , increased with the increasing metal particle size, consistent with the observation that it was easier to obtain stable activity with filamentous carbon formation on the catalyst with larger metal particle size under the same gas phase composition, KM , and temperature. The effect of BaO, La203 and Zr02, added to the Si02 support of Co catalysts, has also been investigated. The effect of the modified support on the catalyst reduction behaviour, dispersion and MSI was studied by TPR, XPS and CO chemisorption. The results suggest an increasing MSI among the catalysts in the order Co/Si02 » Co/BaO/Si02 < Co/La 203/Si0 2 < Co/Zr02/Si02. The rate of catalyst deactivation was affected by the modified support: increased deactivation corresponded to an increased MSI. It is suggested that the latter observation is a consequence of the Co particle being held more strongly to the support, such that filament formation is reduced, which in turn results in an increase in the formation of encapsulating carbon and hence deactivation. XPS analysis of carbon species on the used catalyst identified the presence of carbidic carbon, ascribed to single carbon atoms that diffuse through the metal particle and form filamentous carbon, and graphitic carbon, ascribed to encapsulating carbon that deactivated the catalyst. The competition between filamentous carbon formation and encapsulating carbon formation determined the rate of deactivation. Data presented herein demonstrate a correlation Chapter 5 Effect of Catalyst Properties on Catalyst Activity 108 between the magnitude of the catalyst decay constant and the relative concentration of carbidic carbon on the catalyst surface. Chapter 6 Kinetic Model 109 Chapter 6 Kinetic Model 6.1 Introduction In the present study, catalyst activity-versus-time profdes have been measured on different catalysts for C H 4 decomposition. In general, the profiles have a period of initial increasing activity followed by a period of either stable activity or decreasing activity, and the profiles depend on the catalyst and process conditions. From the point of view of the catalyst, as described in Section 5.2, stable catalyst activity was obtained on Co catalysts with a large metal particle size (>26 nm). Catalyst deactivation after an initial rate increase was observed on catalysts with a small metal particle size (<26 nm). From the point view of process conditions, as described in Section 4.2, stable catalyst activity was observed when the condition KfM <KM < K*M was satisfied. On the other hand deactivation after an initial rate increase was observed when the condition KM <KfM < K'M was satisfied. In Chapter 2, the generally accepted mechanistic steps of carbon nanofibre growth were described as: carbon atom deposition on the exposed surface of the metal catalyst; dissolution of the carbon atom and diffusion through the metal particle and finally precipitation at the back of the metal particle. However, the initial growth mechanism, corresponding to the observed zone of increasing activity, was ignored. Recently, in a review of carbon nanofibres by De Jone and co-workers (2000), it was pointed out that this generally accepted mechanism rationalized the steady-state growth of carbon nanofibres but it did not touch upon the important question of nucleation. Some speculation about carbon nucleation has been made by Snoeck and co-workers (1997a). They proposed that the dependence of the number of growing filaments on the affinity of carbon formation must be taken into account when modeling the kinetics of filamentous carbon formation. Hence, in their study the mode of experimentation, performed with used Chapter 6 Kinetic Model 110 catalysts on which carbon was previously deposited under standard conditions, ensured that the rate of growth of the carbon filaments was always based on the same number of fdaments. However, to date no kinetic model has been reported for fdamentous carbon formation during catalytic hydrocarbon decomposition that includes the nucleation step. On the other hand, models have been developed for carbon nanotube and diamond production during the C V D process that addressed the issue of carbon nucleation. In the present study, an initial rate increase period was observed during the initial 2-5 min of the start of the CH4 decomposition reaction. Hence, it is necessary to include carbon nucleation and growth into the existing mechanism for carbon filament formation. Furthermore, as described in Chapter 2, the kinetic model developed for catalytic filament formation describes only the steady growth of filamentous carbon. For the case of decreasing activity, only an empirical model exists. Based on the experimental observations of the present study, a more general kinetic model of C H 4 decomposition has to be developed, in which two important features are incorporated. The first is that carbon nucleation at the interface of the metal and support be considered in order to describe the initial rate increase observed during CH4 decomposition; the second is that the competition between encapsulating carbon formation and carbon dissolution/diffusion on the surface of catalyst be considered to account for catalyst deactivation. 6.2 Description of the Kinetic Model 6.2.1 Terminology and Assumptions 6.2.1.1 Terminology Some terminology needs to be defined before describing the kinetic model. Site density, is defined as the number of atomic sites per unit surface area, with units 1/cm2; the leading face Chapter 6 Kinetic Model 1U_ refers to the interface between the metal and gas phase, where single carbon atoms are formed by the reversible reaction CH4 <-> C + 2H2; the tailing face refers to the interface between the metal and support, where the single carbon atom is excreted from the metal particle and nucleates with other carbon atoms. On the leading face, two kinds of carbon species exist: atomic carbon and encapsulating carbon: ns, site density of single carbon atom on the leading face;' n , site density of encapsulating carbon on the leading face. On the tailing face, three kinds of carbon species exist each with different site density as follows: n,, site density of single carbon atom on the tailing face; nt, site density of critical cluster on the tailing face; nx, site density of stable cluster on the tailing face. Assuming that small clusters containing j atoms with surface concentration rij(t) may grow or decay, the growth becomes more probable than decay when the cluster size exceeds the critical number / . A critical cluster is a cluster of carbon atoms with a certain critical number / . Stable clusters are all larger clusters than the critical cluster and are considered to be stable. They may form nuclei even i f some atoms leave during the subsequent growth. Note that nCT of Figure 6.1 is the site density of carbon in the carbon tubes of the metal particle on the tailing face. nCT is used for Model II, which will be described in Section 6.2.4.2. Chapter 6 Kinetic Model 112 Gas phase C H 4 T T f n (Single carbon atom) and n s p and cluster n ^ (or nCT) The leading face The tailing face Support Figure 6.1 Schematic drawing of general kinetic model. 6.2.2.2 Model Assumptions A one dimensional diffusion model was used to describe the diffusion of carbon through the metal particle. The choice was based on the results from a study of a two-dimensional model (Chitrapu et al., 1992) showing that the 2-D model was not significantly better than that obtained from a one-dimensional approximation of carbon filament formation, and that the two-dimensional model required significantly more computational effort. In the present study, the Co metal particle supported on SiC»2 was approximated as a metal slab as shown in Figure 6.1. The sides of the catalyst slab were assumed not to participate in the excretion of carbon, and hence, it was assumed that the flux of carbon in the radial direction was zero. The driving force for carbon diffusion was through the concentration gradient of single carbon atoms through the particle. Chapter 6 Kinetic Model 113 There was a uniform diffusion path length, (2/3) dp. It was also assumed that all single carbon atoms had the same opportunity to nucleate. The structure of the nanofibres produced was not considered. 6.2.2 General Description of the Kinetic Model The model is shown schematically in Figure 6.1. The model assumed that single carbon atoms were formed by C H 4 stepwise dehydrogenation at the leading face. When a single carbon atom was formed on the leading face of the metal catalyst particle, it reacted through two parallel paths: a) it diffused through the metal particle and subsequently nucleated and grew at the tailing face of the metal particle; or b) it formed encapsulating carbon and it was assumed that the encapsulating carbon could not be gasified in H 2 ; the number of active metal sites on the surface decreased due to the formation of encapsulating carbon and consequently, the catalyst deactivated. Hence single carbon atom diffusion through the metal slab was described using a one-dimensional model. At the leading face, stepwise dehydrogenation and encapsulating carbon formation were considered. At the tailing face, carbon nucleation and growth were considered. The interstitial diffusion of carbon through the metal particle was described by the unsteady state diffusion equation, which was the main equation of the kinetic model: dn, c = D. (6.1) dt s dx2 Initial condition: 'C li=0~(2 / 3)rJ,, = 0 att=0 for all x; (6.2) Boundary conditions: dnc ( r / - r » ) - r i at x = 0 (the leading face), t>0; (6.3) dt Chapter 6 Kinetic Model 114 = rd - rnucl - rwowlli at x = (2 / 3)dp (the tailing face), t>0; (6.4) x = ( 2 / 3 ) r f „ where nc (t, x) Site density of single carbon atom in the metal particle, 1/cm2; t Time-on-stream, s; x Length in the carbon diffusion direction, cm; Ds Diffusivity of carbon in the metal particle, cm2/s; dp Average metal particle diameter, cm; rf Carbon deposition rate, l/cm2/s; rg Carbon gasification rate, l/cm2/s; {rf —r) Measured methane decomposition rate, l/cm2/s; re Encapsulating carbon formation rate, l/cm2/s; rlt Carbon diffusion rate leaving the leading face of the metal particle, l/cm2/s; rtl The incoming carbon diffusion rate to the tailing face of the metal particle, l/cm2/s; rgrowth Carbon growth rate on the tailing face, l/cm2/s; rnucl Carbon nucleation rate on the tailing face, l/cm2/s; The initial condition is described by Equation (6.2) and the two boundary conditions are described by Equation (6.3) and (6.4). Equation (6.2) describes the initial condition that the site density of single carbon atoms is zero along the metal slab at time zero. Boundary condition (6.3) describes the site balance at the leading face at any reaction time. The site balance requires that the site density change of single carbon atoms is equal to the net carbon formation rate from C H 4 stepwise dehydrogenation and gasification (CHA <-> C + 2H2), minus the net carbon consumption rate determined by the encapsulating carbon formation rate and the carbon diffusion rate. It was critical to include an encapsulating carbon formation step in the boundary condition at the leading face to account for the catalyst deactivation because encapsulating Chapter 6 Kinetic Model 115 carbon cannot be gasified by H 2 . The other boundary condition Equation (6.4), describes the site density balance at the tailing face. This site balance required that the site density change of single carbon atoms is equal to the incoming diffusion rate from the leading face minus the single carbon consumption rate by carbon nucleation and carbon growth. In the present study, two methods used for carbon nucleation and growth on the surface of metal substrates in C V D processes were modified to describe the carbon nucleation and excretion rate at the tailing face. The detailed description is presented in Section 6.2.4. The above system of 2 n d order partial differential equations combined with algebraic equations, consisting of the site balance equations at the leading face and tailing face have been resolved without assuming any RDS. The unsteady state diffusion equation was solved using the finite volume method. By fitting experimental C H 4 decomposition rate data to the model, parameters such as bulk carbon diffusivity Ds, surface carbon diffusivity Z),, and reaction rate constant for carbon formation kf, gasification kg and encapsulating carbon formation kencap, were estimated. The Marquardt's compromise methodology was used for the parameter estimation. The kinetic model allowed the carbon concentration profile in the metal to be developed as a function of time, to show the changes of the driving force for carbon diffusion. 6.2.3 Description of the Boundary Conditions at the Leading Face Equation (6.3) shows the general description of the balance of single carbon atoms on the leading face. According to the overall mechanism, reactions including C H 4 dehydrogenation, carbon gasification, and formation of encapsulating carbon were considered at the leading face. In order to describe the net rate of carbon deposition, [rf -rg), the following elementary steps in Equation (6.5) to (6.9) were used to describe the stepwise dehydrogenation of C H 4 . Since the activation energy for the activation of gas phase C H 4 (CH4 + 2S -» CH3S + HS, where S Chapter 6 Kinetic Model 116 represents an active catalyst site) is less than that of adsorbed CH4 (CH4S + S -» CH3S + HS) over Group VIII metal catalysts (Shustorovich and Bell, 1991), it is reasonable to assume that the first step of the CH4 decomposition can be written according to Equation (6.5). CH4 + 2 S <-> CH3S + HS (6.5) CH3S + S+± CH2S + HS (6.6) CH2S + S<r> CHS + HS (6.7) CHS + S <-> CS + HS (6.8) 2HS ( K" >2S + H2 (6.9) Assuming that the rate of Equation (6.5) was slow, the reaction of Equation (6.9) was assumed at equilibrium with equilibrium constant KH. Hence the concentration of HS can be expressed by Equation (6.11) obtained from Equation (6.10). KH~~[Hsf (6.10) H ' (6.11) Since Equation (6.5) is slow, the reaction steps of Equation (6.6) to (6.8) were lumped together into the reaction of Equation (6.12), which was also assumed to be at equilibrium with equilibrium constant KCH . Hence, the concentration of CH3S was expressed by Equation (6.15), obtained from Equation (6.12) by substitution of Equation (6.11) into Equation (6.14). CH3S + 3S < Kcfh > CS + 3HS (6.12) K = [HSf[CS] c">-[CH3S)[Sf ( 6 1 3 ) Chapter 6 Kinetic Model 117 [CH3S]-. 1 [HSf[CS] [SY (6.14) 1 [CH3S] = —^—P^[CS] KCH%KH (6.15) According to the reaction of Equation (6.5), the net rate of carbon deposition, (rf -r), is described by Equation (6.16). Hence, the net rate of carbon deposition Equation (6.17) was obtained by substitution of Equation (6.11) and (6.15) into Equation (6.16). rf -rg=kfPCHt[Sf -kr[CH3S][HS] (6.16) rf-rg=kfPCHi[Sf-kr K C H , K l Pi [S][cs] = kfpCHt [ST -kgPl [S][cs] (6.17) The ensemble size associated with the formation of encapsulating carbon was assumed to be 6 carbon atoms, as described in Chapter 4. The encapsulating carbon formation rate was described by Equation (4.2) and Equation (4.3). The carbon diffusion rate at the leading face was described by Equation (6.18): D. d(nc I dx) dx (6.18) Finally the boundary condition at the leading face at t>0 was expressed by Equation (6.19): dric dt dt x=0 = (Tf -rg)~rd -re =kfPCHi[Sf -kg^S][CS\-Ds^^ k n6 encap s x=0 (6.19) The site conservation described by Equation (6.20) was used to calculate the site density of [CS]. Assuming the concentration of HS and CH 3 S is small, the site conservation Equation (6.20) was simplified into Equation (6.21). Chapter 6 Kinetic Model U 8 [Sv] + [CS] + [CH3S] + [HS] + [CPS] = [Sv0 ] ( 6 2 0 ) [Sv] + [CS] + [CPS] = [Sv0] (6.21) Assuming that the encapsulating carbon occupied the same site as the single carbon atom, the change in number of active sites was described as: i f - - < r ' - , ' ) + r ' (6.22) and change in sites occupied by encapsulating carbon was described as: dt encap s (6.23) 6.2.4 Description of the Boundary Conditions at the Tailing Face Two models were used to describe the boundary conditions at the tailing face and they are described in detail in the following Section. 6.2.4.1 Description of Kinetic Model I (Cluster Nucleation Model) The Model I (Cluster nucleation model) describing the boundary conditions at the tailing face is derived from the nucleation model for C V D processes (Liu and Dandy, 1996). The basic idea of the nucleation model is that small clusters containing j atoms with surface concentration rtj(t) may grow or decay, the growth becomes more probable than decay when the cluster size exceeds the critical number / . A l l larger clusters were therefore considered to be stable and hence may form nuclei, even i f some atoms leave during the subsequent growth. Based on the model for C V D processes (Liu and Dandy, 1996), the induction period of carbon growth was described as: initially, atomic carbon with site density ns (1/cm2) deposited on the metal surface from stepwise C H 4 dehydrogenation, then diffused through the metal particle with diffusivity Ds and at the tailing face of the metal particle, the single carbon atom nx (t) diffused over the tailing Chapter 6 Kinetic Model 119 face with diffusivity D{. This surface diffusion led to the formation and growth of clusters. Assuming small clusters containing j atoms with surface concentration « • (/) may grow or decay, growth becomes more probable than decay when the cluster size exceeds a certain critical size / . A l l larger clusters were therefore considered to be stable and hence may form nuclei. The rate of critical cluster growth depended on the rate at which single carbon atoms attached to them. The concentration of stable clusters, nx(t) increased with time. The capture number terms, cr, and ax , describe the diffusion flows of single atoms to critical clusters or stable clusters, and have been described in the relevant literature (Liu and Dandy, 1996). The capture numbers were assumed to be slowly varying quantities, with cr, and crx in the range from 2 to 4 and 5 to 10, respectively (Liu and Dandy, 1996). Herein, cr, and cr^ . were assumed to be 4 and 5, respectively. The critical size / of the critical cluster was taken as 10. The surface diffusion coefficient of single atoms was expressed as £>,. The surface concentration of single carbon atoms, nx, was expressed by the following mass balance equation at the tailing face: dnc dt dn, , = ~j7 ~  rd ~  rnuc, ~  rgroWth =  rd " °", " (»  + l ) N r " 0 A , Jt=(2/3)rf t ° - Z ^ l The term, axDln]nx, describes the rate of single carbon atom addition to the stable cluster nx. The term, (i + l)Nr, describes the nucleation rate of single carbon atoms into critical clusters that then grow into stable clusters. The term, rd, describes the rate of impingement of single carbon atoms from the leading face of metal particle via the bulk diffusion of interstitially dissolved carbon in metal particle as given by Equation (6.25) Chapter 6 Kinetic Model 120 • d(ncldx) d i dx Equation (6.26) and (6.27) describe the probability of single carbon atom growth and the calculation of critical cluster site density on the tailing face. Equation (6.28) describes the growth rate of critical clusters into stable clusters. n: 1 / 2n, {xstable - i) xstable > A 0 xstable < ij (6-26) where xstable = aA^dt (6 2 ? ) Nr=^ = Din]ni ( 6 2 g ) 6.2.4.2 Description of Kinetic Model II (Boltzmann Nucleation Model) The second method used in the present study to describe the boundary conditions at the tailing face is referred to as the Boltzmann nucleation model, which is modified from the atomic-scale analysis of C V D of carbon nanotubes (Grujicic et al., 2002). In the atomic-scale analysis of C V D of Carbon nanotubes (Grujicic et al., 2002), the carbon nucleation and carbon growth was described using elementary reaction steps, listed in Table 6.1. Similar to the Cluster Nucleation Model, C atoms with site density ns (1/cm2) deposit on the metal surface from the gas phase, diffuse through the metal particle with diffusivity Ds, and subsequently nucleate and grow at the tailing face. Chapter 6 Kinetic Model 121 Table 6.1 Activation energy of carbon nucleation steps. Reaction I: Nucleation of the outer carbon tube wall n C(s)-»n C(CT) n>10 E =149.4 kJ/mol Reaction II: Growth of the outer carbon tube wall C(s)+n(CT)-> (n+l)C(CT) E =128.7 kJ/mol Reaction I states that when the number of nearest-neighbour carbon atoms reaches (or exceeds) a critical value, carbon atoms arrange themselves into a graphite-like structure to nucleate the outer wall of the carbon tube. The critical number of carbon atoms required for nucleation was assumed to be 10 and was assumed to be independent of processing conditions. The activation energy term, E, for nucleation, was taken from the work of Lee et al. (1999). The activation energy was estimated by subtracting an average energy of the ten adjacent single atoms from that for the ten corresponding atoms in the newly nucleated wall of the carbon tube. The nucleation reaction is assumed to be irreversible. Equation (6.29) describes the nucleation rate of a single carbon atom at the tailing face. Reaction II describes the case when a single carbon atom is adjacent to a nucleus of a (non-innermost) wall of a carbon tube, it can attach to the nucleus giving rise to growth. An average value of the activation energy used herein was obtained from the work of Lee et al. (1999). The activation energy was estimated by subtracting the average energy of a single carbon atom from that for a carbon atom at the edge of a nucleus of the newly nucleated wall of a carbon tube. The growth process is also considered to be irreversible. Equation (6.30) describes the carbon growth rate and Equation (6.31) describes the changing rate of carbon nuclei. f. = 10k 10 nucl nuclei (6.29) Chapter 6 Kinetic Model 122 rgrowth kgrowth nCT n\ dn C T (I ! (6.30) (6.31) Finally, the boundary condition at the tailing face was expressed as Equation (6.32), by substitution of Equation (6.25), Equation (6.29) and (6.30) into Equation (6.4) dnr dt j r = ( 2 / 3 ) d . dnx dt rd  rnucl growth _ n d(nc/dx) dx 10knuci ni ~  kgrowlh nCT ni (6.32) 6.3 Kinetic Model I and Kinetic Model II Fit to Literature Data Very few literature studies have reported the rate of reaction during the initial stage of carbon deposition during C H 4 decomposition or related reaction. Figure 6.2 shows experimental data during the initial stage of reaction and carbon deposition, reproduced from the literature (Sacco et al., 1984) for various reactants. A l l the experiments were performed with 6x6x0.25 mm polycrystalline Fe foil. Data in Figure 6.2 show the weight gain of a Fe foil versus time-on-stream for small time intervals during the initial 5 min of reaction. A set of carbon deposition rates was then estimated by differentiating the data of Figure 6.2. These rates are plotted in Figure 6.3, showing that the carbon deposition rate first decreased then increased to high carbon deposition rates for two of the three cases. In only one case was the initial rate decrease not obtained and those data are similar to the observations of the present study. Chapter 6 Kinetic Model 123 2 0 0 T i m e , m i n Figure 6.2 Initial weight gain versus time for various H 2 , CO, CO2, CH4 and H2O at 900K and lOlkPa on Fe M\(A PC0PH^ = 0.13 bar2, ^ P c 2 0 =0.21 b a r 3 ; * / ' ^ =0.12bar 2,P c oP c 2 o=2.0bar 3; • PC0PH^ = 0.06bar2, PC0P20=2.\ bar3). The initial rate decrease followed by a rate increase shown in Figure 6.3 can be well explained by the proposed general kinetic model. The initial rate decrease corresponds to the initial unsteady state carbon diffusion stage of the reaction during which critical clusters have not yet formed. The diffusion rate decreases with time-on-stream because the single carbon atom accumulating at the tailing face has not yet been excreted and the driving force for diffusion, the difference in single carbon atom concentration between the leading and tailing face of the particle, decreases with time. As diffusion proceeds, the single carbon at the tailing face starts to nucleate, excrete and grow at the tailing face. During this period, the site density of single carbon atoms at the tailing face decreases and the driving force for the carbon diffusion increases. The Chapter 6 Kinetic Model 124 increased carbon deposition rate corresponds to the period of carbon nucleation. The reason that for one set of data in Figure 6.3 the initial rate decrease was absent might be because the carbon nucleation rate was high due to the high initial carbon deposition rate. Consequently, the carbon nucleation started earlier and was not detected. The observations made in the present study also correspond to this scenario. 0.12 0.00 ' 1 . . I 0 5 10 15 20 Time, min Figure 6.3 Carbon deposition rate versus time for various H2 CO, CO2, C H 4 and H2O at 900K and lOlkPa. (Filled symbol is for the initial period measured at small time interval; unfdled symbol is measured at the larger time interval; A and A PC0PH^ =0.13 bar2, Pca Plo=0.2\ bar3; O and* PC0PHi =0.12 bar2, PcoPco = 2.0 bar3; O and • PC0PHi =0.06 bar 2 ,P C 0 7P c 2 0 = 2.1 bar3). Chapter 6 Kinetic Model 125 In order to further check the proposed kinetic models, one set of data of Figure 6.3 with stable activity (PC0PH, =0.13bar2, PC0Pl0 =0.21 bar3) was selected and fitted to the two kinetic models Kinetic Model I and Kinetic Model II, described in Section 6.2. Note that because of the complexity of the gas phase composition, the kinetics of the carbon deposition and gasification surface reactions are not included in these models. Rather, it is assumed that there is no change in ns during the reaction. To simplify, encapsulating carbon formation is assumed neglected on the leading face. (Also note that x refers to the direction of the depth of the Fe foil.) Model parameters were estimated using Marquart's Compromise with an initial guess of parameters. The computer code used to perform the numerical calculations is listed in Appendix F. The fitted parameters are listed in Table 6.2. From the model fitting, the site density profiles along the depth of Fe foil were obtained and the changes in site density for different carbon clusters were also obtained. The fitting results of Kinetic Model I and Kinetic Model II are presented in Figure 6.4 and Figure 6.5. Table 6.2 Parameters from the kinetic models fit to the data for the initial stage of carbon deposition. ns xlO - 1 7 Ds xlO6 Z^xlO 2 0 R 2 F-value 1/cm2 cmV1 cmV1 Model I 6.635±0.04 2.660±0.02 7.69910.02 0.69 14.6 Model II 7.812+0.020 3.86110.010 ^ x l O ^ c m V ^ x l O - ' V m V 1 0.37 2.3 3.48610.014 4.78610.020 Chapter 6 Kinetic Model 126 Figure 6.4a Single carbon atom profde along the depth of Fe foil obtained by fitting literature data to the Kinetic Model I. Chapter 6 Kinetic M o d e l 127 0.08 ro u O) 0.07 c o E 0.06 E o> .*-» ro L . c 0.05 o '55 O a. E o u CD T3 CD | 0.03 CD 0.04 l 0.02 o o O Experimental data Fitted data O O 10 15 T ime , m in 20 O 25 Figure 6.4b Carbon deposition rate obtained by fitting literature data to the Kinetic Model I. Chapter 6 Kinetic Model 128 Figure 6.4c Site density changes as a function of time-on-stream obtained by fitting literature data to the Kinetic Model I. Figures 6.4a, b and c show the literature results fitted to the Kinetic Model I. Figure 6.4a shows the change in single carbon atom site density along the depth of Fe foil with time-on-stream. The profile of single carbon atom site density was very steep at the very beginning of the reaction. The profile then levelled off since the diffusion driving force decreased when single carbon atoms accumulated at the tailing face. The profile then became steep again due to an increased driving force for diffusion since the single carbon atom site density decreased as the carbon nucleation and growth at the tailing face occured. Finally, the profile stabilized corresponding to stable carbon growth at the tailing face. Figure 6.4b shows the fitted carbon deposition rate on the Fe foil had three stages with respect to time-on-stream: an initial rate Chapter 6 Kinetic Model 129 decrease, a rate increase and a stable rate consistent with the profde changes described in Figure 6.4a. The period corresponding to an initial rate decrease is associated with the unsteady state carbon diffusion, with single carbon atoms accumulating at the tailing face of the particle. The period of rate increase corresponds to carbon nucleation. The final, stable carbon deposition rate corresponds to the steady growth of carbon. Data in Figure 6.4c shows the changes in «,, , and nx with time-on-stream and the carbon diffusion rate at the tailing face. The profile of «, also shows three stages: an initially increase, a decrease and a constant value. The profile of also shows three stages: an initial stage when ni is equal to zero, a sharp increase and then a steady increase. The profile of nx shows two stages: initial equal to zero, then steady increases. The profile of carbon diffusion rate at the tailing face shows an initial low rate followed by a rapid increase and then a decrease to a stable value. The three stages were therefore assigned as: Stage (i): corresponding to the unsteady state diffusion, «, increases and nt, and nx are equal to zero since single carbon atoms are accumulating on the tailing face and have not yet nucleated into carbon clusters. Consequently, the carbon diffusion rate at the tailing face is low; Stage (ii): carbon nucleation and growth have begun. Then «, decreases, while ni, and nx increase. Consequently, the carbon diffusion rate increases since the driving force for diffusion increased. Stage (iii): Carbon nucleation and growth at the tailing face reach a steady value and the carbon diffusion rate at the tailing face decreases to a stable level. Chapter 6 Kinetic Model 130 Figure 6.5a Single carbon atom profde along the Fe foil obtained by fitting literature data to the Kinetic Model TJ. Chapter 6 Kinetic Model 131 g 0 . 0 3 1 ' • ' . I 2 0 5 1 0 1 5 2 0 2 5 Time, min Figure 6.5b Carbon deposition rate obtained by fitting literature data to the Kinetic Model II. Chapter 6 Kinetic Model 132 x 10 17 x 10" t^T x i g 1 8 Time, min i 1 2 ' ; 10 ou O) c re a> re 4 ? o C N ~ X 10 E 8 10 20 Time, min 30 a: 10 20 Time, min or 10 20 Time, min 30 Figure 6.5c Detailed information obtained by fitting literature data to the Kinetic Model H. Similarly, Figure 6.5a, b and c show the results obtained from literature data fitted to the Kinetic Model II. Again, the site density profiles along the Fe foil with time-on-stream were obtained and are plotted in Figure 6.5a. Figure 6.5b shows the fitted carbon deposition rate on Fe foil with time-on-stream. Detailed information about changes in «,, and nCT with time, and the carbon diffusion rate at the tailing face, are presented in Figure 6.5c. Similarly, three stages during the initial reaction are apparent. However, as described in Section 6.2, there is a difference between Model I and Model II. In Model II, there is continuous nucleation and growth of carbon nanofibres at the tailing face. The nucleation and growth of carbon start from time zero, although the initial diffusion rate is low. Chapter 6 Kinetic Model 133 The model parameter values listed in Table 6.2 show that the fitting of Kinetic Model I is better than Kinetic Model II based on a comparison of the F-statistics. Also, only one parameter, surface diffusivity D{, was used to describe the carbon nucleation and carbon growth in Kinetic Model I. Consequently, in the following Section, only Kinetic Model I was used to describe the experimental data obtained in the present study. 6 . 4 K i n e t i c M o d e l I F i t t o C o / S i 0 2 C a t a l y s t A c t i v i t y D a t a 6.4.1 Typical Examples of Kinetic Model I Fit on Co/SiC»2 Catalysts As mentioned in the model description, the proposed kinetic model can describe the steady growth of filamentous carbon and deactivation, after the initial rate increase that is a consequence of the nucleation. In this section, two typical profiles obtained during CFL; decomposition, which show deactivation and steady carbon growth, are fitted by Kinetic Model I. Figure 6.6a, b and c show the fit of Kinetic Model I to the experimental data on 30wt% Co/SiC»2 with steady carbon growth. Similar to Figure 6.4a and Figure 6.5a, the carbon site density profiles in Figure 6.6a show three stages: steep profiles level off, corresponding to the initial unsteady state diffusion; the profile then becomes steep with the start of carbon nucleation and growth; finally, a stable profile, corresponding to the steady growth of carbon nanofibers, is apparent. Figure 6.5b shows that the steady growth of carbon nanofibres after the initial rate increase, was well described by the Kinetic Model I. Figure 6.5c shows similar information as described in Figure 6.3c. However, the difference between Figure 6.5c and Figure 6.3c is that the profile for ns, the site density of single carbon atoms at the leading face, changes with time-on-steam in Figure 6.5c because the surface reaction was included in the former calculation. Chapter 6 Kinetic Model 134 Figure 6.6a Single carbon atom profde along diffusion path with steady carbon growth on 30wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I. Chapter 6 Kinetic Model 135 Figure 6.6b Carbon deposition with steady carbon growth on 30wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I. Chapter 6 Kinetic Model 136 "0 10 20 30 "0 10 20 30 Time, min Time, min Figure 6.6c Detail information obtained from experimental data with steady carbon growth on 30wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I. Figure 6.7a, b and c show the fit of the Kinetic Model I to the experimental data on 10wt% Co/SiC>2, with deactivation after the initial rate increase. The site density profiles along the diffusion path at different reaction times. Figure 6.7a also shows the presence of three stages of reaction during CH4 decomposition. Figure 6.7b shows that the catalyst deactivation after the initial rate increase was well described by the kinetic model I. The information described in Figure 6.7c is similar to Figure 6.6c except that in this instance n5 decreases with increasing reaction time. The density of active sites and sites occupied by the encapsulating carbon are described in Figure 6.7d. The available active sites decrease with time-on-stream. Meanwhile, the active sites occupied by encapsulating carbon increase with time-on-stream and this increase is that causes the catalyst to deactivate in this example. Chapter 6 Kinetic Model 137 Figure 6.7a Single carbon atom profde along diffusion path with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I. Chapter 6 Kinetic Model 138 ure6.7b Carbon deposition with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM - 0.06 atm) fitted to the Kinetic Model I. Chapter 6 Kinetic Model 139 Figure 6.7c Detailed information obtained from experimental data with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I. Chapter 6 Kinetic Model 140 0 20 40 60 0 20 40 60 Time, min Time, min Figure 6.7d Detailed information obtained from experimental data with deactivation on 10wt% Co/Si0 2 (923K reduction, 773K reaction with KM = 0.06 atm) fitted to the Kinetic Model I. 6.4.2 Effect of Metal Particle Size To better understand the effect of metal particle size on filamentous carbon formation kinetics, experimental data on Co/SiC^ catalysts with different Co loadings under the same C H 4 decomposition condit ions,^ =0.06atm and T=773K, were fitted to the proposed Kinetic Model I. The estimated parameter values obtained in each case are listed in Table 6.3. Also, typical parameters are plotted versus metal particle size in Figure 6.8a, b, c, d and e. Chapter 6 Kinetic Model 141 Table 6.3 Effect of metal particle size on kinetic parameters estimated at 773K over Co/Si0 2 catalysts (923K reduction, 773K reaction with KM = 0.06 atm). "\Catalyst Parameters wt% Co 8 10 12 30 d, nm 13.5 17.8 19.4 28.0 £ > s x l 0 1 4 cm2/s 4.05±0.20 6.0810.001 5.9010.23 13.610.23 D, xlO 1 6 cm2/s 4.54±0.38 6.1610.02 0.9610.04 0.51710.01 A^xlO 1 9 Pa'cmV 14.2±0.42 8.8010.04 7.0210.004 4.1010.16 kgx\022 Pa"2s"'cm2 2.8210.24 2.11+0.04 0.7710.0004 0.2410.001 ^ x l O 7 5 cm'V 17.710.64 2.9510.01 0.5510.00003 1.13xl0-4il.01xl0"7 R 2 % 0.68 0.84 0.78 0.92 CM E u o * in Q 0 10 15 20 dp, nm 25 30 Figure 6.8a Effect of metal particle size on Ds, the carbon diffusivity through Co. Chapter 6 Kinetic Model 142 0 10 15 dp, nm 20 25 30 Figure 6.8b Effect o f metal particle size on Dl, the carbon surface diffusivity at the tailing face. 2 (O a> > X o a. * u •E * CM 1.0 a) 0.1 0 10 15 20 dp, nm 25 30 Figure 6.8c Effect o f metal particle size on kfSvlPCHt • Surface /Active Site, the initial TOF for CH4 decomposition. Chapter 6 Kinetic Model 143 0 10 15 20 25 30 dp, nm Figure 6.8d Effect of metal particle size on kf lkg, equilibrium constant for carbon CH. decomposition. 1.E+02 1.E+01 o 1.E+00 o 1.E-01 in " * Q. 1.E-02 1.E-03 1.E-04 Figure 6.8e Effect of metal particle size on kencttp, rate constant for encapsulating carbon formation. Chapter 6 Kinetic Model 144 The modeling results of Table 6.3 and of Figure 6.8a show that the carbon diffusivity through Co was in the range of 4.05xl0" 1 4 to 1.36xl0"13 cm2/s. The range of values was two order of magnitude lower than that reported with Co foil at 773K, Ds =6.94x10"12 cm2/s (Yokoyama et al., 1998). However, the carbon diffusion coefficient is dependent upon the carbon activity. Safvi et al. (1991) reported values from lxlO" 9 to lx lO" 6 cm2/s as carbon activity ranged from 0 to 35 on y-Fe at 1033K. In the present study, the carbon activity of the gas phase was approximately 7.0. However, the carbon activity for the data reported by Yokoyama et al. (1998) was unclear. Furthermore, modeling results of Figure 6.8a show that the diffusivity, Ds, increased with increasing metal particle size. One possible explanation of this observation is that carbon diffusion is structure sensitive and that the (100) and (110) surfaces are more suitable for carbon diffusion (Yang and Chen, 1989). The (100) and (110) faces are apparently favoured at the gas/metal interface whereas the (111) face is favoured at the graphite/ metal interface, based on a study of carbon filament growth on fine particles of a-Fe, Co and N i catalyst from CH4 at 700°C (Yang and Chen, 1989). In the present study, the decreased carbon diffusivity, Ds, with decreasing metal particle size might be explained by the fact that the formation of (100) and (110) faces was less favourable on the small metal particles due to the presence of defect sites that result in high coordination sites on small metallic particle. Modeling results of Figure 6.8b show that the carbon surface diffusivity, 7J>,, decreased with increasing metal particle size, resulting in a weaker ability for carbon nucleation. This observation may be explained by noting that (111) face was favourable on the small metal particles due to the presence of defect sites that result in high coordination sites on small metallic particle. Chapter 6 Kinetic Model 145 Modeling results of Figure 6.8c show the initial TOF for methane dissociation, kfSvlPCHi • Surface/Active Site (1/s/site, where the units of kfSvlPCHi are l/cm2/s; Surface is the surface area of metallic particle calculated from CO uptake, cm2/gcat; Active Site is the active metallic site obtained from CO uptake during CO chemisorption, mmol/gcat.) increased with increasing metal particle size. This observation is indicative of a structure sensitive C H 4 decomposition on supported Co catalysts. The result obtained here agrees with that of Wei and Iglesia (2003), who reported that on all noble metals, turnover rate increased with increasing metal dispersion obtained for CH4-CO2 and C H 4 - H 2 0 reactions, suggesting that the coordinatively unsaturated surface atoms prevalent in small crystallites are significantly more active than those in the low-index planes predominately exposed on large crystallites. Wei and Iglesia (2003) also pointed out that similar effects have been predicted theoretically for model metal surfaces by Szuromi et al. (1985). Szuromi et al. (1985) have suggested that it was the presence of high coordination sites that was crucial for the lowering of activation barriers for the carbon-hydrogen bond cleavage process, and theoretical calculations show that the activation barrier is lower on a step on N i (211) than N i (111), and certain defect sites on small metallic particles might have lower activation energies for CH4 dissociative adsorption (Beebe et al., 1987). Hence, the initial TOF for methane dissociation, k jSv\PCHi-Surface I Active Site, decreased with the increasing metal particle size and this observation can be explained by the fact that, analogous to the activity for CH4 decomposition on N i , the initial TOF is high on the coordinatively unsaturated surface atoms prevalent in small Co crystallites; the initial TOF is low on the low-index planes that predominate on large Co crystallites. Note that in Section 5.2 it was observed that the maximum TOF increased with increasing metal particle size. There is a difference between the initial TOF reported in Figure 6.8c obtained by modelling and maximum TOF obtained from experimental observations. The initial TOF, determined by the number of Chapter 6 Kinetic Model 146 metallic sites on catalyst initially, whereas the maximum TOF, obtained after the initial rate increase, reflects the carbon formation rate determined by a number of complex reaction steps such as the carbon deposition, the carbon diffusion, encapsulating carbon formation and carbon nucleation. Modeling results of Figure 6.8d show that the equilibrium constant, expressed as kflkg (atm), increased with metal particle size. This is consistent with the discussion in Section 5.3 that demonstrated that the equilibrium constant increases with increasing metal particle size, or the diameter of the carbon nanofibre. Finally, the results of Figure 6.8e show that the encapsulating carbon formation rate constant, kcncap, decreased with increasing metal particle size. It is suggested that encapsulating carbon formation was not favoured on the surfaces of large metal particles. Yang and Chen (1989) reported results that encapsulating carbon formation was dependent on the exposed face of the metal: the encapsulating carbon formation favoured binding on Ni (111) followed in the order (111) > (311) > (100) > (110). Hence, the encapsulating carbon formation rate constant, kencap, decreased with increasing metal particle size is likely a result of the low-index planes (100) and (110) being predominate on large crystallites. 6.5 Surnmary A general kinetic model of CH4 decomposition on supported metal catalysts has been developed based on experimental observations and a deactivation mechanism. The initial increase in activity was described by carbon nucleation. In addition, the developed model described not only the catalyst deactivation but also the steady activity observed in some cases after the initial rate increase. The carbon nucleation at the tailing face was described using two methods: Cluster nucleation (Model I) and Boltzmann nucleation (Model II). The fit of literature Chapter 6 Kinetic Model 147 data to Kinetic Model I and Model II confirm the presence of carbon nucleation at the tailing face. The experimental kinetic data on supported Co catalysts were well described by the kinetic model. The site density profile along the metal particle was also obtained in the present study. Furthermore, the effect of metal particle size on the activity of CH4 decomposition has been quantified by fitting the experimental data to the proposed kinetic model. Chapter 7 Conclusions and Recommendations 148 Chapter 7 Conclusions and Recommendations 7.1 Conclusions The kinetics of CH4 decomposition on supported Co and N i catalysts has been investigated. The catalyst activity and deactivation were discussed in terms of the maximum rate and decay constant of a 1 s t order decay model. The experimental observations presented herein suggest that the migration of C H X from the metal to the support made a small contribution to the regeneration of active metal sites only in the first 2 to 3 min of reaction. In agreement with previous studies on Fe and N i , filamentous carbon formation reduced the rate of catalyst deactivation during C H 4 decomposition by removing carbon from the metal surface. The presence of H 2 or CO reduced the net rate of carbon deposition and increased the net rate of carbon removal by diffusion through the Co, respectively. Hence, stable CH4 decomposition activity and filamentous carbon formation were observed on supported Co catalysts with low metal loading in the presence of H 2 or CO. The increased decay constant with temperature was ascribed to rapid ageing of the carbon species deposited on the catalyst surface as reaction temperature increased. Based on the above observations, it was concluded that catalyst deactivation was a consequence of the competition between the rate of encapsulating carbon formation and the rate of carbon diffusion. Stable activity or catalyst deactivation during C H 4 decomposition was observed, depending on which of these two rates was greater. The structure sensitivity of the CH4 decomposition reaction has been observed on low loading Co and N i catalysts: the maximum decomposition activity increased with increasing metal particle size (decreasing metal dispersion) and the decay constant decreased with increasing metal particle size (decreasing metal dispersion). Chapter 7 Conclusions and Recommendations 149 The coking threshold K'M obtained on Co/SiC»2 with different loading in the present study followed the linear relationship of K*M versus the reciprocal of the average metal particle size. A fdamentous carbon formation threshold, KfM, has also been defined as the value of KM =P^ IPCH corresponding to the formation of filamentous carbon at a particular temperature. The difference between the coking threshold, K*M, and the filamentous carbon formation threshold, KfM , increased with the increasing metal particle size, consistent with the observation that it was easier to obtain stable activity with filamentous carbon formation on the catalyst with larger metal particle size under the same gas phase composition, KM , and temperature. The effect of BaO, L a 2 0 3 and Zr02, added to the Si02 support of Co catalysts, has also been investigated. The effect of the modified support on the catalyst reduction behaviour, dispersion and MSI was studied by TPR, XPS and CO chemisorption. The results suggest an increasing MSI among the catalysts in the order Co/Si02 « Co/BaO/Si02 < Co/La203/Si02 < Co/Zr0 2/Si02- The rate of catalyst deactivation was affected by the modified support: increased deactivation corresponded to an increased MSI. It is suggested that the latter observation is a consequence of the Co particle being held more strongly to the support, such that filament formation is reduced, which in turn results in an increase in the formation of encapsulating carbon and hence deactivation. XPS analysis of carbon species on used catalysts identified the presence of carbidic carbon, ascribed to single carbon atoms that diffuse through the metal particle and form filamentous carbon, and graphitic carbon, ascribed to encapsulating carbon that deactivated the catalyst. The competition between filamentous carbon formation and encapsulating carbon formation determined the rate of deactivation. Data presented herein demonstrate a correlation Chapter 7 Conclusions and Recommendations 150 between the magnitude of the catalyst decay constant and the relative concentration of carbidic carbon on the catalyst surface. A general kinetic model of C H 4 decomposition on supported metal catalysts has been developed based on experimental observations and the deactivation mechanism described above. The model described not only the catalyst deactivation but also the steady activity observed in some cases after the initial rate increase. The initial rate increase was described by including the rate of carbon nucleation at the tailing face of the metal particle in model using two methods: Cluster nucleation (Model I) and Boltzmann nucleation (Model II). The fit of literature data to Model I and Model II confirmed the presence of carbon nucleation at the tailing face. The experimental kinetic data on supported Co catalysts were well described by the kinetic model. The site density profile along the metal particle was also obtained and the effect of metal particle size on the CH4 decomposition activity has been quantified by fitting the experimental data to the proposed kinetic model. 7.2 Recommendations In the present study, the carbon deposition rate was obtained from the gas phase analysis and consequently, the initial carbon deposition rate was not measured for small time intervals. It is suggested that in the future, the carbon deposition rate be measured from the weight change of catalyst at small time intervals in order to develop more reliable parameter estimates for the nucleation steps of the model. It should be noted that this study has addressed the transient nucleation and growth stage in filamentous carbon on the tailing face of the metal particle. However, some limitations remain: One assumption made in present model is that there was no steric limitation during Chapter 7 Conclusions and Recommendations 151 nucleation. 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In order to make sure the activity measured is the intrinsic activity, the effect of external mass transfer and internal diffusion must be minimized. The guidelines for catalyst testing described by Dautzenberg (1988), by Rase (1990) and by Froment and Bischoff (1990) were followed in the present study and are described in the following sections. A.2 Catalyst Testing Parameters The available catalyst and reactor parameters are presented in Table A . 1. Table A . 1 Parameters of catalyst and reactor. Symbol & value Diameter of reactor D=7.5xlCr3m Diameter of catalyst particle ^=1.7xl0"4m Length of reactor Z,„=6xl0"' m Length of catalyst bed Z=lxl0" 2m Appendices 159 A.3 Reactor Flow Pattern: Plug Flow Operation Even when plug flow is believed to prevail, great care must be exercised to ensure that the flow pattern is ideal. The diameter of the PFR (D) must be at least 10 times the catalyst particle diameter (d'p)(D/d'p >10). This eliminates the influence of the reactor walls on the flow pattern. In the present study, D/d'p =44, which satisfied the condition D/d'p >10. Furthermore, axial gradients may exist by virtue of conversion. These effects are minimized by selecting the correct ratio of bed length to particle diameter (L/d'p). For gas-solid systems the catalyst bed length (L) should be at least 50 times greater than the particle diameter (L/d'p>50). For the experimental set-up of the present study L/d'p=59, which satisfied the criteria L/d'p=50. Furthermore, Table A.2 gives the alternative steps to calculate the required Lld'p for laboratory fixed-bed reactors: Table A.2 Steps for ensuring plug flow operation in laboratory reactors. 1. Determine the viscosity of the fluid medium at reactor conditions: Assuming viscosity of fluid medium equal to pure Ar, JU = 2.1 x 10 5 Ns I m1 2. Calculate the superficial fluid velocity (u): u = V _180cc/ minx 10"6 / 60 * (673 / 273) = 0A7m/s (A.l) KD2 I 3.14x(7.5xl0 - 3 ) 2 V 3. Calculate the particle Reynolds number: (A.2) Herein, p = l.7S4kg/m3; Accordingly, NRtp = ud'pp _ 0 .17m/sx0.17xlQ- 3 mxl .784£g/m 3 p ~ 2.1xl0" 5 Ns I m2 = 2.46 4. Calculate the Peclet number: Appendices 160 Np = (0.087)7V°e23 (-^-) (for gas-phase operation) (A.3) d P Herein, " ^ = 59 then NPg = (0 .087)7^(-^) = 0.087 x (2.46)° 2 3 (59) = 6.31 5. Calculate Np •. ' c m in Af . =8«ln—-— (-A41 Hereinn=l, then Np =8«ln—-— = 8 x l n — - — = 0.84 1-X 1-0.1 6. Acceptable deviation from plug flow can be assumed if: N P e > NPenyin (A.5) Herein, NPe = 6.31 > NPemin = 0.84, which is acceptable deviation from plug flow. 7. The minimum LId'p follows from: — > 92.0A^ 2 3tt In (for gas-phase operation) (A.6) dp p 1-X Herein, = 59 > 92.0/VR°2 3n In—— = 92.0x (2.46)"° 2 3 x l x I n — — = 7.88 d'p R e" 1-X 1-0.1 The above calculations show that Lld'p of the present study satisfied the required Lid' for laboratory plug flow operation of fixed-bed reactors. A.4 Reactor Isothermal Operation The extent to which catalyst activity measurements are disturbed by intrareactor, interphase, and intraparticle effects of heat transport was assessed by evaluating the experimental catalyst performance using the mathematical criteria in Table A.3. In all cases, the criteria for isothermal operation were met. Appendices 161 Table A. 3 Criteria for Isothermal Operation. Intrareactor (A.7) |AH|R v r, 2 _ 75600x0.03x455x(3.75x 10°f , „ _ „„RT„, „ „ 8.314x773 khT„ 1.2x773 =1.56xl0"2 < 0.2—^=0.2x-E 42000 =3.06xl0"2 Interphase 0.357 < 0.3--c„G (A.8) \&H\Rpd 75600 x 0.03 x 455x1.7x10 R7" 8.314x773 (A.9) d'pG A.r , 0.357 «. =- n==c„G = 22.5 x 773 = 0.01 < 0 . 3 — - = 0.3x-£ 42000 = 4.59x10 0.357 ( UxlO^xO.n -x520x0.12 = 22.5J/m2/5/A: 2.1xl0~: Intraparticle kpTs P < 0 .75^ (A. 10) =75600x0.03x455x(8.5xl0-)- l f f 4 < q A q ^8.314x773 = 1 ^ 1.7xl0"2*773 £ 42000 Where p p = 455kg/m3; CP = 520J / kg / K • E =42kmol/mol; | A / / | = 15.6101 mol; kb =\.2W I ml K ; k=\.lx\Q-2W ImlK; T =773K; G = uxp = 0.07x1.784 = 0.12 kg/m2/s. = 1.Smmollmin/gear = 0.03molIsIkgcat; Rv -R xp = 0.03* 455mol I s I m3. A. 5 Diagnostic Tests for Interphase (External) Transport Effects A check for external transport limitations was performed using guidelines described by Froment and Bischoff (1990). In a flow system, the flow rate can be varied while the space velocity is kept constant. If the conversion remains constant, the influence of interphase and intrareactor effects may be assumed to be negligible. Figure A . l shows the conversion hardly changed with varied flow rates while space velocity was kept constant. The diagnostic test confirms that there was no external transport limitation at the conditions of the present study. Appendices 162 14 12 g 10 re a> E c o CD > C o o 8 10 15 Time, m in Figure A. 1 Diagnostic tests for interphase (external) transport effect (A140mL(STP)/min; *210 mL(STP)/min, SV=19,000hr"!, T=673K, 5%CH 4 /Ar, 12wt% Co/Si0 2). A.6 Diagnostic Tests for Internal Transport Effect Changing the catalyst particle.size can be used to test intraparticle effects. If there is no change in catalyst activity with change in particle size (assuming the exposed surface area of active catalyst is constant), the catalyst is considered to be free of intraparticle gradients. Figure A.2 shows that the conversion does not change with the change of catalyst particle size during CH4 decomposition over Co catalyst. This result confirmed that there was no intraparticle effect in the present study. Appendices 163 Figure A.2 Diagnostic tests for intraparticle transport effects (AParticle size=T70um, •Particle size=90um, T=673K, 140mL/min, 5%CH 4 /Ar, SV=19,000hr \ 12wt% Co/Si0 2 ). Based on the above observations, it can be concluded that for the range of experimental conditions of present study, there were no internal or external gradients of concentration or temperature. A. 7 Reactor Differential Operation Differential operation is reached when the conversion over the catalyst bed is so small that the change in composition over the catalyst bed does not influence the rate of carbon formation. It is the limited to the linear part of the conversion versus space-time curve. Also, the flow of fluid through a packed bed generally results in a decreasing gradient of total pressure. This can produce an axial change of reactant partial pressure. In order to ensure isobaric operation, the particle diameter should be selected carefully. This differential operation allows one to assume that temperature, pressure and concentration are constant through the thin catalyst bed layer. In this sense the differential reactor is the simplest gradientless reactor. Appendices 164 30 25 20 c o 2 15 > C o ° 10 • 2 min • 10 min • 30 min • 40 min • • • • A 0.1 0.12 0.14 0.16 0.18 0.2 Contact time, sec • 0.22 0.24 0.26 Figure A.3 Diagnostic tests for differential operation. Differential operation was checked by a number of experimental tests. The results of CH4 conversion versus contact time at different time-on-stream, shown in Figure A.3, confirmed that operating conditions of the current study was limited to the linear part of the conversion versus space-time curve. For the most severe conditions, the conversion of methane, based on the feed flow rate through the catalyst bed, was below 15%. Appendices 165 Appendix B Example of Activity Calculation and Curve Fitting B.l Example of Activity Calculation Table B. 1 Example of activity calculation spreadsheet. Run Y144 650 Rdn 500Rxn 5wt%Co Si0 2 CH4=182 H2=10 Ar=48 varain GC Rxn at 500 and Rdn from 50 TO 650°C in an hour Catalyst 0.05 5wt% Co/Si02 Reduction 650 °C Feed Flow Meter (set point) 182 cc/min Cat wt 0.25g CH 4 in CH4/Ar feed content 0.57 (FID) Rxn Temp 500 °C CH 4/Ar Ar H 2 Total Meter Feed Flow 182 48.00 10.00 Corrected Meter Flow, seem 127.61 80.53 15.33 223.47 cc/min Measured Total Flow CH 4 Ar H 2 Feed mol frac 0.57 0.36 0.07 Feed mmol/min 5.69 3.59 0.68 9.97 mmol/min Experiment H 2TCD CH 4 FID" Calibration Factors 2.62E-13 2.27E-12 CH 4 from FID H 2 CH 4 from FID C Sampling No. Time min moles/area moles/area fraction of moles fraction of moles CH 4 X b mmol/ min/g SI 0.5 2729588 2023387 0.56 0.09 1.38 0.31 S2 3.8 2976535 2017234 0.56 0.10 1.68 0.38 S3 7.1 3126477 2007769 0.56 0.10 2.14 0.49 S4 10.4 3168554 2005892 0.56 0.10 2.23 0.51 S5 13.7 3117019 2005129 0.56 0.10 2.27 0.52 S6 17.0 3045161 2009570 0.56 0.10 2.05 0.47 S7 20.3 2953359 2014678 0.56 0.09 1.80 0.41 S8 23.6 2855800 2019168 0.56 0.09 1.58 0.36 S9 26.9 2775058 2024542 0.56 0.09 1.32 0.30 Appendices 166 SIO 30.2 2674955 2028177 0.56 0.09 1.14 0.26 Sl l 33.5 2619172 2032761 0.57 0.08 0.92 0.21 S12 36.8 2564711 2030958 0.57 0.08 1.01 0.23 S13 40.1 2490466 2034264 0.57 0.08 0.85 0.19 S14 43.4 2451519 2037638 0.57 0.08 0.68 0.16 S15 46.7 2420696 2039165 0.57 0.08 0.61 0.14 S16 50.0 2389595 2039240 0.57 0.08 0.60 0.14 S17 53.3 2362315 2040876 0.57 0.08 0.52 0.12 S18 56.6 2410885 2039089 0.57 0.08 0.61 0.14 S19 59.9 2329779 2042022 0.57 0.07 0.47 0.11 S20 63.2 2311303 2041744 0.57 0.07 0.48 0.11 S21 66.5 2306260 2041338 0.57 0.07 0.50 0.11 Note: a: CH 4 FID calibration factors=Moles of CH 4 in the sampling valve/area in FID (calibrated gas); Conversion of CH4= 100*(molar fraction of CH 4 in inlet-molar fraction of C H 4 in outlet)/molar fraction of CH 4 in inlet; c: Decomposition rate of CH4=Conversion of CH4*total molar flow rate/weight of catalyst. Appendices 167 B.2 Examples o f Curve Fitting Results 0.55 D:\YI new\thesis draft\ information\Y144 5wt% Co/Si02.x ls Rank 20 Eqn 8098 Decay1_(a,b) rA2=0.98158513 DF Adj rA2=0.97851598 FitStdErr=0.01939872 Fstat=692.95114 a=0.51466899 b=0.037004129 10 20 30 (t-t*), min 40 50 Appendices 168 Rank 20 Eqn8098 Decayl_(a,b) r2CoefDet D F A d j r 2 FitStdErr F-value 0.9815851279 0.9785159825 0.0193987197 692.95114099 Parm Value Std Error t-value 95% Confidence Limits P>|t| a 0.514668986 0.012766141 40.31515693 0.487089414 0.542248557 0.00000 b 0.037004129 0.001649077 22.43930035 0.033441515 0.040566743 0.00000 Area Xmin-Xmax 11.681120496 Function min 0.0824192932 1st Deriv min -0.019044878 2nd Deriv min 0.0001128572 Area Precision 1.485066e-19 X-Value 49.500000000 X-Value 1.302334e-10 X-Value 49.500000000 Function max 0.5146689856 1st Deriv max -0.003049854 X-Value 1.302334e-10 X-Value 49.500000000 2nd Deriv max X-Value 0.0007047391 1.302334e-10 Procedure Minimization Iterations LevMarqdt Least Squares 8 r 2 Coef Det DF Adj r 2 Fit Std Err Max Abs Err 0.9815851279 0.9785159825 0.0193987197 0.0371376971 Source Sum of Squares DF Mean Square F Statistic P>F Regr 0.26076467 1 0.26076467 692.951 0.00000 Error 0.0048920342 13 0.00037631033 Total 0.2656567 14 Description: Y144 5wt% Co/Si02 X Variable: time Xmin: 0.0000000000 Xmax: 49.500000000 Xrange: 49.500000000 Xmean: 24.640000000 Xstd: 16.256198818 Xmedian: 23.100000000 X@Ymin: 46.200000000 X@Ymax: 0.0000000000 X@Yrange: 46.200000000 Y Variable: rate, mmol/min/g Ymin: 0.1070120911 Ymax: 0.5181675635 Yrange: 0.4111554724 Ymean: 0.2448871252 Ystd: 0.1377515113 Ymedian: 0.2102216655 Y@Xmin: 0.5181675635 Y@Xmax: 0.1101102729 Y@Xrange: 0.4080572906 Appendices 169 B.3 Calculation of K*M and K.L 0 I i i i i i 1 0 0.005 0.01 0.015 0.02 0.025 0.03 K M , atm Figure B . l Maximum C H 4 decomposition rate versus KM at 773K on 5wt% Co/Si02 (reduced at 923K) with K\ = 0.033 ± 0.001 atm. O.o 1 1 1 1 ' 1 1 0 0.005 0.01 0.015 0.02 0.025 0.03 K M , atm Figure B.2 Decay constant versus KM at 773K on 5wt% Co/Si02 (reduced at 923K) with Kf =0.027 ±0.006 atm. Appendices 170 Figure B.3 Maximum C H 4 decomposition rate versus KM at 773K on 10wt% Co/Si0 2 (reduced at 923K) with K\ = 0.030 ± 0.003 atm. 0.000 0.005 0.010 0.015 0.020 0.025 0.030 KM, atm Figure B.4 Decay constant versus KM at 773K on 10wt% Co/Si0 2 (reduced at 923K) with Kf = 0.027 ± 0.003 atm. Appendices 171 2.0 0.2 h 0.0 1 1 1 1 1 1 0.04 0.045 0.05 0.055 0.06 0.065 KM, atm Figure B.5 Maximum CH4 decomposition rate versus KM at 773K on 30wt% Co/SiCh (reduced at 923K) with K[ = 0.071 ± 0.002 atm. Figure B.6 Maximum C H 4 decomposition rate versus KM at 773K on 15wt% Ni/SiC>2 (reduced at 923K) with K[ =0.135 + 0.010atm. Appendices 172 0.90 0.80 S 0.70 a c 0.60 E =5 0.50 E E 0.40 of 2 0.30 | 0.20 0.10 0.00 K M =(0.092±0.004)-(0.081±0.006)r R 2 = 0.995 0.00 0.01 0.02 0.03 0.04 0.05 K M atm 0.06 0.07 0.08 Figure B.7 Maximum C H 4 decomposition rate versus KM at 773K on 30wt% Ni/SiC»2 (reduced at 923K) with AT* = 0.092 + 0.004 atm. Note that the simple linear correlation described the data of Figure B . l , Figure B.5 to Figure B.7 quite well. To be consistent, the linear correlation was also used to describe the data of Figure B.2, Figure B.3 and Figure B.4 although the middle point was below the line in each case. This approach provided reasonable estimates of the x-axis intercept, as shown by the deviation errors of estimation of K*u and Kf, listed in the caption of each figure. B.4 Carbon Diffusivity Data TableB.2 Carbon diffusivity data(Yokoyama et al., 1998). Host Z)0(m2/s) ED (kJ/mol) Temperature range, K Ref Pd 1.99526xl0"5 132 1223 1378 Present work r-Fe 6.60693 xlO"5 157 1198 1371 Smith 2.34423xl0"5 148 1123 1578 Agren Co 1.77828xl0"4 174 1125 1370 Smith 8.12831xl0"6 149 723 1073 Cernak et. al. Ni 3.38844xl0"5 149 1125 1372 Smith 3.01995xl0'5 149 843 1123 Cermak and Mehrer Appendices 173 A p p e n d i x C X P S S p e c t r a C. 1 XPS Survey Scan Spectra 5 OE + 05 4 5E + 05 4 OE + 05 3 5E + 05 > 3 OE + 05 c 2 5E + 05 >4-» 2 OE + 05 1 5E + 05 1 OE + 05 5 OE + 04 0 OE + 00 200 400 600 800 B.E., eV 1000 1200 Figure C. 1 Survey scan spectrum on Co/BaO/Si02 after reduction. 6.0E+05 5.0E+05 4.0E+05 c 3.0E+05 CD 2.0E+05 1.OE+05 0.0E+00 200 400 600 800 B.E., eV 1000 1200 Figure C.2 Survey scan spectrum on Co/BaO/Si02 after reaction. Appendices 174 6.0E+05 5.0E+05 h 4.0E+05 h c 3.0E+05 a> 200 400 600 800 B.E., eV 1000 1200 Figure C.3 Survey scan spectrum on Co/Zr0 2/Si02 after reduction. 5.0E + 05 4.5E + 05 4.0E + 05 3.5E + 05 3.0E + 05 c 2.5E + 05 •*-» - 2.0E + 05 1.5E + 05 1.0E + 05 5.0E + 04 0.0E + 00 • 11. . - J 1 1 I I I 200 400 600 B.E., eV 800 1000 1200 Figure C.4 Survey scan spectrum on Co/ZrOySiO^ after reaction. Appendices 175 6.0E+05 5.0E+05 4.OE+05 | 3.0E+05 2.OE+05 1.OE+05 h 0.0E+00 200 400 600 800 B.E., eV 1000 1200 Figure C.5 Survey scan spectrum on Co/La 2 0 3 /S i0 2 after reduction. 6.0E+05 5.0E+05 4.0E+05 1 3.0E+05 CD 2.0E+05 h 1.OE+05 0.0E+00 200 400 600 B.E., eV 800 1000 1200 Figure C.6 Survey scan spectrum on Co/La 203/Si0 2 after reaction. Appendices 176 C.2 XPS Narrow Scan Co 2p Spectra V OS c c 810 805 800 795 790 785 Binding energy.eV 780 775 770 805 800 795 790 785 780 775 Binding Energy, eV 770 Appendices 820 810 800 790 780 770 760 Binding energy, eV Appendices 178 810 805 800 795 790 785 780 775 770 765 Binding energy, eV Figure C.l Comparison of raw data and fit data of surface Co 2p Spectra on modified catalysts, a: unreduced 12wt% Co/Si0 2 ; b: reduced 12wt% Co/Si0 2 ; c: reduced Co/BaO/Si0 2 ; d: reduced Co/Zr0 2 /S i0 2 ; e: reduced Co/La 2 0 3 /S i0 2 . C.3 XPS Narrow Scan C Is Spectra 0> (/) C <D 4.0 3.5 3.0 2.5 2.0 1.5 300 295 290 285 280 275 270 Binding energy, eV Appendices 179 4.0 3.5 >> 3.0 "<75 | 2.5 2.0 1.5 300 295 290 285 280 275 270 Binding energy, eV CD 4.0 3.5 3.0 § 2.5 2.0 1.5 295 290 285 280 Binding energy, eV 275 Figure C.8 Comparison of raw data and fit data of C Is spectra on used catalysts surface, a: Co/BaO/Si0 2 ; b: Co/Zr0 2 /Si0 2 ; c: Co/La 2 0 3 /S i0 2 . Appendices C.4 XPS Narrow Scan O Is Spectra Binding Energy, eV Appendices 181 Binding Energy, eV Figure C . 9 X P S O Is spectra on used catalysts surface, a: Co/BaO /Si0 2 ; b-Co /Zr0 2 /Si0 2 ; c: Co/La 2 0 3 /Si0 2 . Appendices 182 Appendix D Gas Flow and GC Calibration D . l Gas Flow Calibration In the present study, four mass flow controllers were used in the activity test. The calibrated gas, full range and the sensor conversion factor of the calibrated gas were listed in Table D . l . Sensor conversion factors for specified gases were listed in Table D.2. Table D . l Description of Mass flow controller Channel Calibration gases Full Range, Sensor conversion factor of Number SCCM calibrated gas 1 o 2 20 0.99 2 CH 4 200 0.81 3 10%H 2S/90%H 2 60 0.99 4 He 300 1.39 Table D.2 Sensor conversion factors for specified gases Gases Sensor conversion factor Ar 1.40 He 1.39 H 2 1.01 H2S 0.85 10%H 2S/90%H 2 0.99* CH 4 0.81 CO 0.99 N 2 1.005 o 2 0.99 *Sensor conversion factor for gas mixture=100/(10/0.85+90/1.01)=0.99 Appendices 183 Table D.3 Calibration of gas flow for each flow controller Gas (Channel) Calibration equation 5.16%CH4/Ar (Ch2) Flow=1.7295xReading 5.2%CH4/Ar (Ch2) Flow=l .6507xReading-7.2505 4.82% H 2 ) 10.4% CH 4 , 2.01% C 2 H 4 , 3.75% C 2 H 6 /Ar (Ch2) Flow=1.4935xReading Pure CH 4(Ch 2) Flow=l .OxReading H 2 (Ch 3) Flow= 1.0677xReading Ar (Ch 4) Flow=0.7759xReading+32.029 Figure D. 1 Measured flow versus calibrated reading. (5.16%CH 4/Ar in Ch 2). Appendices 184 350 300 h 0 I 1 1 . I 0 50 100 150 200 Reading from the flow controller, SCCM Figure D . 2 Measured flow versus calibrated reading. (5.2%CH 4/Ar in Ch 2). 180 160 c 140 E | 120 s 100 re o re 0C 80 60 40 20 0 y = 1.4935x R 2 = 0.9998 20 40 60 80 100 Reading from the flow controller, seem 120 Figure D . 3 Measured flow versus calibrated reading. (4.82%H 2/10.4%CH 4/Ar in Ch 2). Appendices 185 0 l 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 Reading from the flow controller, SCCM Figure D.4 Measured f low versus calibrated reading. (Pure H2 in Ch 3). 158 , 162 Reading of mass flow controller, SCCM Figure D.5 Measured flow versus calibrated reading. (Ar in Ch 4). Appendices D.2 GC Calibration D.2.1 GCSetup THE SAMPLING LOOP VOLUME IS 250 uL. GC SET UP INFORMATION: GC COLUMN: 60/80 CARBOSIEVE G 5' R59225 SUPELCO INITIAL COLUMN TEMP 100°C INITIAL COL HOLD TIME 3.00 MIN INJECTOR TEMP 100°C AUXILIARY TEMP 200°C INITIAL AUX HOLD TIME 0.00 Detector temp 150°C TCD A ATTEN RANGE A/Z SIG 32 0.5 yes pos FILAMENT TEMP 175°C FID B ATTEN RANGE A/Z 16 8 yes PLOT SPEED 1.0 CM/MIN ZERO OFFSET 15% PLOT SIGNAL A TIME TICKS YES INSTR EVEN CODES YES USER NUMBER 0-0 PRINT USER NUMBER NO PRINT REPORT YES PRINT RUN LOG NO PLOT PRGM TIME SPEED SIG 1 1.5 1.0 B INITIAL RELAYS -1-2-3-4 RELAYS PRGM TIME STATE Appendices 1 0.50 2 2 0.70 -2 3 3.00 -2 RUN MODE 1-ANALYSIS PEAK MEASUREMENT PARAMETER 1-AREA LONG REPORT FORMAT NO RESULT CALCULATION TYPE 1 -AREA% DIVISOR 1.000 AMOUNT STANDARD 1.0 MULTIPLIER 1.0 RESULT UNITS REPORT UNIDENTIFIED PEAKS YES UNINDENTIFIED PEAK FACTOR 0.0 SAMPLE ID SUBSTRACT BLANK BASELINE YES PEAK REJECT VALUE 10000 SIGNAL TO NOISE RATIO 5 TANGENT PEAK HEIGHT 10 INITIAL PEAK WIDTH 2 SEQUENCE AUTOMATION RUNS OF TABLE SINGLE STOP AUTOMATION AFTER ERROR 0 PRGM METHOD RUNS 1 1 5 Appendices 188 D.2.2 GC Calibration A calibrated gas chromatograph (GC) with a thermal conductivity detector (TCD) and a flame ionization detector (FED) were used for the sampling and analysis of CH4 decomposition activity. For calibration, an analyzed gas mixture (Praxair) of 4.82% H 2 , 10.4 % C H 4 , 2.01% C2H4, 3.75%i C2H6 balanced with Ar was used. By repeat analyses, calibration factors (Moles of component in the sampling loop/Peak area) were obtained. Retention time and response factor were listed in Table D.4. Table D.4 Response factor and retention time of GC. Component Retention time, min Response factors, moles/area H 2 1.04 2.62xl0"13 CH 4 2.09 2.27xl0"12 Appendices 189 Appendix E X R D Results Source File: Datal ChiA2=84.95131805 SS=4I711.09716 Data Set: D a t a l _ B COD=0.94856 CorrCoef=0.97394 Date: 10/09/2003 # of Data Points=501 Degree of Freedom=491 3.0x10' -5.0x101 Fitting Resul ts 40 42 2-Theta, degree Ea2kM. Peak Type 1 Gaussian 2 Gaussian 3 Gaussian AreaFHT 53.56061 157.58963 32.60607 FWHM 0.84521 0.8379 0.84831 MaxHulciht 70.69724 221.05878 45.26889 CenmrGrvtv 31.26113 36.82697 44.8355 AreaFltTP 21.97301 64.65048 13.3765 243.75631 BaseL ine: C O N S T A N T Figure E. 1 X R D Pattern of 12wt% Co/Si0 2 after calcinations ( T C o 3 0 4 ) . Appendices 190 Source File: Datal ChiA2=183.8792100 SS=89916.93368 Data Set: D a t a l _ B COD=0.94416 CorrCoef=0.97168 Date: 10/09/2003 # of Data Points=501 Degree of Freedom=489 4.0x10 3 .5x10' -3 .0x10 2 -2.5x10 2 e/3 £> 2.0x10 2 >. 1 1.5x102H c 1.0x10 2 -5.0x10' 0.0 - | -5.0x10' Fitting Results T T T * f 4 f • i 1 t f t ->—i—1—r— 28 30 32 34 36 38 40 42 —r-44 46 48 2-Theta,degree 50 52 Peak 8 Paak Tvpft 1 Gaussian 2 Gaussian 3 Gaussian 4 Gaussian AreaFitT 84.45406 204.43427 28.44771 40.83239 FWHM 0.80458 0.70305 0.48024 0.68246 MaxHalnht 116.08286 331.23504 61.96795 67.76251 CnnmrGrvly 31.23026 36.61559 38.5 44.79096 ArsaFltTP 23.57943 57.07769 7.94255 11.40033 356.16844 BaseLine: C O N S T A N T Figure E.2 X R D Pattern of 12wt% Co/BaO/Si0 2 after calcinations ( T C o 3 0 4 ) . Appendices 191 Source File: Datal Chi*2=289.6895592 SS=142237.5736 Data Set: D a t a l _ B COD=0.95675 Corr Coef=0.978I4 Date: 10/09/2003 # of Data Points=50! Degree of Freedom=491 5x10' 4x10 3x10 2 H O £ 2x10'- I 1x10 04 -1x10 28 Fitting Resul ts 30 32 34 - r -36 ^ 1 1 ' 1— 38 40 42 2-Theta, degree ~ r — 44 46 48 50 52 E M K 1 Peak Type 1 Gaussian 2 Gaussian 3 Gaussian ftrcaFHT 114.14262 385.50376 88.64124 FWHM 1.21306 1.26717 1.23919 MaxHeiaht 110.90764 378.86898 88.849 CenterGryty 31.27909 36.83028 44.8596 AreaFIITP 19.40252 65.52981 15.06767 588.28763 BaseL ine: C O N S T A N T Figure E.3 X R D Pattern of 12wt% Co/Zr0 2 /S i0 2 after calcinations ( T C o 3 0 4 ) . Appendices 192 Source File: Datal ChiA2=123.5918852 SS=60683.61563 Data Set: D a t a l _ B COD=0.94636 CorrCoef=0.97281 Date: 10/09/2003 # of Data Points=501 Degree of Freedom=491 3.5x10 3.0x10 H 2.5x10 H co 2.0x10 H O f 1.5x10H 1.0x10 5.0x10 0.0 -j -5.0x10' -i 1 1 1 1 r— 28 30 32 34 36 — I 1 1 1 1 — 38 40 42 2-Theta, degree 44 46 ~48~ 50 52 Fitting Results Peak* Peak Type 1 Gaussian 2 Gaussian 3 Gaussian AreaFitT 46.97437 174.78516 41.42623 FWHM 0.57013 0.71022 0.71731 MaxHalaht 87.33545 280.87968 66.03809 CenmrGrvIv 31.32547 36.88327 44.8636 AreaFHTP 17.84B37 66.41133 15.7403 263.18576 BaseLine: CONSTANT Figure E.4 X R D Pattern of 12wt% Co/La 2 0 3 /S i0 2 after calcinations ( T C o 3 0 4 ) . Appendices 193 43-1003 Quality/: C C A S N u m b e r : M o l e c u l a r W e i g h t : 240.80 V o l u m e [ C D ] : 528.30 Dx: 6.055 D m : S . G . : F d 3 m ( 2 2 7 ) Cel l P a r a m e t e r s : a 8.084 b c « P r S S / F O M : F 3 0 = 3 1 7 ( . 0 0 3 2 . 3 0 ) l / lcor: 4.30 R a d : C u K a l L a m b d a : 1.54056 Filter: d -sp: c a l c u l a t e d Co3 0 4 C o b a l t Ox ide Ref: Grier. D , McCar thy . G., Nor th D a k o t a State Un ivers i ty . F a r g o . Nor th D a k o t a U S A ICDD Grant - in -A id , (1991) 0 25 50 75 100 125 2 6 " 29 int-f h k I 29 int-f h k I 29 int-f h k I 19.000 16 1 1 1 69.741 <1 4 4 2 103.58 <1 6 4 4 31.271 33 2 2 0 74.117 3 6 2 0 107.90 2 8 2 2 36.845 100 3 1 1 77.338 8 5 3 3 111.20 7 7 5 1 38.546 9 2 2 2 78.403 4 6 2 2 112.33 2 6 6 2 44.808 20 4 0 0 82.625 2 4 4 4 116.91 3 8 4 0 49.081 <1 3 3 1 85.759 1 5 5 1 120.48 <1 9 1 1 55.655 9 4 2 2 90.963 4 6 4 2 121.69 <1 8 4 2 59.353 32 5 1 1 94.096 11 7 3 1 126.71 1 6 6 4 65.231 38 4 4 0 99.331 4 8 0 0 130.73 6 9 3 1 68.628 1 5 3 1 102.51 <1 7 3 3 137.99 10 8 4 4 Figure E.5 Standard X R D pattern for C o 3 0 4 . Table E. 1 Calculation o f C03O4 particle size for different catalysts. Catalyst 26 FWHM dp,rm? 12wt% Co/Si02 36.82 0.84 9.9 Co/BaO/Si02 36.82 0.70 11.8 Co/Zr02/Si02 36.83 1.27 6.5 Co/La 20 3/Si0 2 36.88 0.71 11.7 d p=0.89*A/(B*cose). Appendices 194 Appendix F Program of General Kinetic Model F. 1 Simple Model I without Surface Reaction clear all global PCH4 PH2 x y global Ds criticalsigmai stablesigmax criticall ns D l weight global time dp tsetfmal nyfmaln Cayfinal dx xdirection ac kp % "empirical.m" is matlab routine that uses Marquardt method % to estimate parameters in the non linear regression. % Finite differences are used to estimate the differential needed; % ODE is solved by matlab builtin function ODE45; % Dependent variable is a set of methane decomposition rate, mmol/min/g % Independent variables is a set of time,unit is min % It includes 4 subroutines as follows: % 'sumf.m' evaluate the sum of squares for specified a; % 'nucleation' evaluate the rate of methane decomposition using given parameeter a % 'coeff.m' evaluate augmented matrix; % 'molfun.m' gives the r.h.s. functions of ODEs; % 'gaussj.m' is a function m-file that uses Gauss elimination with % scaled partial selection to solve linear equation. critically 10; % Assuming crtitical cluster size=10 criticalsigmai= 10 ;stablesigmax= 1; dp=0.25/10; % depth of Fe foil ,in cm weight=6e-3*6e-3*0.25e-3*7874*1000; % Weight of foil,g % Independent and dependent variables x=[l.l 1.6 2.0 2.6 3.0 3.5 3.9 4.8 6.0 7.4 9.3 11.9 14.7 17.4 21.8 24.1]; y=[0.058 0.053 0.047 0.040 0.037 0.038 0.041 0.050 0.059 0.065 0.068 0.069 0.067 0.066 0.067 0.069]; n=length(x); % a=[ns,Ds,Di] a0=[6.428 2.64 7.699] % Initial guess tol=le-6;maxit=100; relax=1.0; iter=0; maxda= 1 e 10; a=a0 ;m=length(a); I=eye(m,m);relax=l .0; % Step 2 and 3:Set initial lamda=le-3 and calculate the sum of squares lamda=le-3; S=feval('sumf,a); while iter<maxit & maxda>tol % Step 4th : evaluate the augmented coefiient matrix Appendices 195 alpha=coeff('nucleation',x,y,a); da=gaussj (alpha); acoeffold=alpha(l :m,l :m); b=alpha(:,m+l); % Step 5th: evaluate the new augmented coeffient matrix acoeff=acoeffold+I*lamda; alpha=[acoeff b]; % Step 6th: calculate new da da=gaussj(alpha); % Step 7 th and 8th: calculate new a and Snew anew=a+relax * da; Snew=feval('sumf,anew); % Set suitable lambda to satisfy Snew > S while Snew > S lamda=10*lamda; acoeff=acoeffold+I*lamda; alpha=[acoeff b]; da=gaussj (alpha); % Step 6th: calculate new da anew=a+rel ax * da; % Step 7 th and 8th: calculate new a and Snew Snew=feval('sum f,anew); end % Set and begin next newton's regression a=anew;lamda=0.1 *lamda;S=Snew; iter=iter+l; maxda=max(abs(da./a)) da end if maxda <= tol fprintf('\n Sucessful solution in %2.0f iterations!\n',iter) i=[ 1 :length(a)] ;result=[i;a]; for j=l:n fO' )=nucleation(x(j), a); end % Statistical calculations: % rA2 Coeef Det % Sum of squares due to error SSE=sum((y-f).A2); % Sum of squares about mean yavg=sum(y)/n; SSM=sum((y-yavg).A2); % Degree of freedom: DOF=n-m; Appendices 196 % Coefficient of determination r2=l-SSE/SSM; % DF Adj r2m degree of freedom adjusted r2 DOFr2=l-(SSE*(n-l))/(SSM*(DOF-l)); % Fit Standard Error StdErr=(SSE/DOF)A0.5; % F statistic value F_stat=((SSM-SSE)/(m-l))/(SSE/DOF); % Standard error alpha=coeff('nucleation',x,f,a); alpha 1 =alpha( 1 :m, 1: m); Coviance=inv(alphal'*alphal); for i=l :m Cii(i)=Coviance(i,i); end % Based on DOF 14 , confidence level=0.05 tvalpha=2; coefficientSE=tvalpha*(Cii.*SSE/DOF).A0.5 % Final standard error % Calculation for plotting newn=100; dxf=(x(length(x))-x( 1 ))/5 0; xfine=[x(l):dxf:x(length(x))]; for j=1: length(xfme) finalratem(j)=nucleation(xfineO'),a); i f xfme(j)=l.l timeflnal=time; fmalresult=Cayfmal; else timefmal=[timefmal;time]; fmalresult=[finalresult;Cayfinal]; end end Num=size(fmalresult,2); nlfmal=fmalresult(:,Num-2); % nc at the tailing face corresponding to xfine xfinal=criticalsigmai*Di.*fmalresult(:,Num-l); % Calculation of xstable nxfmal=fmalresult(:,Num); % nx at the tailing face corresponding to xfine % Caculation of diffusion rate at the tailing face Rdjtailfinal:=Ds.*(finalresult(:,Num-3)-finalresult(:,Num-2))./dx./dx; % Calculation of diffusion rate profile for j=2:Num-3 Rdj final(: ,j )=Ds/dx/dx. * (finalresult(: j -1 )-finalresult(: ,j)); end % No surface reaction, assuming the surface carbon concentration is constant Rdjfmal(:,l)=0; % Calculation of ni Appendices 197 for j=1: length(timefmal) if xfmal(j) > criticall ni(j)=0.5*nlfmal(j)*(xfmal(j)-criticall); else ni(j)=0; end end dn3=Di.*nlfinal.*ni'; % Calculation of nucleation rate % Changing rate of nl at the tailing face dn2=Rdjtailfmal-stablesigmax*Di.*nlfmal.*nxflnal-(criticalI+l)*criticalsigrnai*dn3; Rdj final(: ,Num-2)=dn2; % Plot resit figure(l) colormap('default') surf(xdirection,timefmal( 1:100:1000), fmalresult( 1:100:1000,1 :Num-2)) xlabel('x direction, cm') ylabel('Time, min') zlabel('Site density, l/cmA2') figure(2) plot(x,y,'ko') xlabel('Time, min') ylabel('Mefhane decomposition rate, mmol/min/g cat') Legend('Experimental data','Fitted data') hold on plot(xfine,finalratem,'k-') hold off figure(3) subplot(2,2,l),plot(timefmal,nlfmal,'k-') xlabel('Time, mm') ylabel('n_l, l/cmA2') subplot(2,2,3),plot(timefinal,nxfmal,'k-') xlabel('Time, min') ylabel('n„x, l/cmA2') subplot(2,2,2),plot(timefinal,ni','k-') xlabel('Time, min') ylabel('nj, l/cmA2') subplot(2,2,4),plot(timefinal,Rdjfmal(:,Num-3),'k-') xlabel('Time, min') ylabel('Tailing face R _ d J , l/cmA2/s') figure(4) subplot(2,2,1 ),plot(timefmal,xfmal,'k-') xlabel('Time, min') ylabel('xstable, l/cmA2') subplot(2,2,2),plot(timefmal,dn2,'k-') Appendices xlabel(Time, min') ylabel('dn2, l/cmA2/s') subplot(2,2,3),plot(timefmal,dn3;k-') xlabel('Time, min') ylabel('dn3, l/cmA2/s') Surface=6*6/10/10/weight; subplot(2,2,4),plot(xfine,finalratem/Surface/le3*6.02e23,'k-') xlabel('Time, min') ylabel('diffusion rate at leading face, l/cmA2/s') figure(5) colormap('coor) surf(xdirection,timefmal(l :500:20000),finalresult(l :500:20000,1 :Num-2)) xlabel('x direction, cm') ylabel('Time, min') zlabel('Site density, l/cmA2') else error('Marquardts method did not converge') end % Print and plot results: fprintf('\n Sucessful solution in %2.()f iterations!\n',iter) i=[l :length(a)];result=[i;a]; fprintf('\n Parameter:\n') fprintf(' a(%l .Of) = %8.3e\n*,result) fprintf('\n\n Numeric summary:\n') fprintfC SSE=%8.6f SSM=%8.6f\n',SSE,SSM) fprintfC r*2 Coef Det=%8.6f DF Ajsr2=%8.6f\n*,r2,DOFr2) fprintfC At Std Err=%8.6f F-value=%8.6f\n*,StdErr,F_stat) fprintf('\n\n\n Result of constants :\n') fprintfC ns - %8.3e Std= %8.3e\n\n*,ns,coefficientSE(l)*ns/a(l)) fprintfC Ds = %8.3e cmA2/s Std= %8.3e\n',Ds/60,coefficientSE(2)*Ds/a(2)/60) fprintfC D l = %8.3e cmA2/s Std= %8.3e\n',Di/60,coefficientSE(3)*Di/a(3)/60) fprintf('\n\n\n Result of constants An') fprintfC ns = %8.3e Std= %8.3e\n\n',ns,coefficientSE(l)) fprintfC Ds = %8.3e cmA2/s Std= %8.3e\n',Ds/60,coefficientSE(2)/60) fprintfC D l = %8.3e cmA2/s Std= %8.3e\n',Di/60,coefficientSE(3)/60) Appendices function rate^nucleationttse^a) % m file for nucleation global Ds ns Di global dx global time tsetfmal Cayfinal dx xdirection ac weight global criticalsigmai stablesigmax D l nx ni criticall ns Ds dp Rdj ac tsetold Cayold % Initial condition of nucleation rate, nx, ni Nr=0;nx=0;ni=0; % Calculation of surface diffusion coefficient % Base on iron case ns=a(l)*lel7; Di=a(3)*le-16*60*le0*le-4; % cmA2/s Ds=a(2)*le-14*le4*60*le4; % cmA2/s Surface=6*6/10/10/weight; % cmA2/g catalyst % y is a vector, y(l) is the x/sigmai/D; y(2)is n l ;y(3)is the nx; m=50+l; % Finite grid of depth of Fe foil; xmax=dp; % Assuming 6m is the maximum distance i.e. infinite mm=m-l; % n is the number of x points dx=xmax/mm ;xdirection=0: dx: xmax; % Calculate a vector of Caj at time 0 % Initial condition at t=0 with all x>0, Ca=CaO i f t se t=l . l y0=[0 0]; % Initial condition for xstable/Di/criticalsigmai,nx Ca0=0; % Concentration of carbon site density at the leading face; Cal=ns; % Concentration of carbon site density at the tailing face; % Set initial conditions of nc along the Fe foil for j =2: length(xdirection) Caj(j)=Ca0; end Caj(l)=Cal; % boundary condition at surface at t=0, Ca=Cal Cay=[Caj y0]; % Using ode23 solve the odes [time,Ca]=ode23('mollun',[0 tset],Cay); % Initial conditions for next time frame; Cayold=Ca(size(Ca,l),:); % Initial time for next time frame tsetold=tset; else [time,Ca]=ode23('molfun',[tsetold tset],Cayold); end if tset~=tsetold Cayold=Ca(size(Ca, 1),:); tsetold=tset; end Cayfinal=Ca; % Caculate the methane decomposition rate at the leading face rate=Rdj/6.02e23*le3*Surface; % mmol/min/cmA2 into mmol/min/g catalyst Appendices 200 rate=rate; [tset rate] Appendices 201 function Caprime==molfun(t,Cay) global criticalsigmai stablesigmax D l nx ni criticall ns Ds dp Rdj ac weight global dx % molfun.m is a function fde which can calculate the rhs of pde, at any time t, % the pde can be discretized at position i by using a central difference in space % Input arguments: % t- time,vector % Cay- a vector of concentration at different x space direction at % same time direction t,and with xstable/Di/criticalsigmai,nx at the tailing face % Output arguments: % Caprime- a vector of first directive of Ca at different x space direction % at the same time direction t % Length of vector Cay m=lengfh(Cay); mra=m-3; Ca=Cay(l :mm+l); % nc along the length of Fe foil n=Cay(m-2:m); % n l ,n l integral,n3 at the tailing face Caprime(l)=0; % Assuming the concentration of ns is constant; % Calculate the rhs of unsteady state of carbon diffusion; for i=2:mm Caprime(i)=Ds*(Ca(i-l)-2*Ca(i)+Ca(i+l))/dxA2; end % Carbon diffusion rate at the tailing face; Rdjtail=Ds*(Ca(mm)-Ca(mm+l))/dx/dx; % Directives of xstable/Di/criticalsigmai dnl=n(l); % Calculation of xstable xstable=criticalsigmai*Di*n(2); % Calculation of ni i f xstable > criticall ni=0.5*n(l)*(xstable-criticall); else ni=0; end % Nucleation rate dn3=Di*n(l)*ni; % Site balance of n l on the tailing face dn2=Rdjtail-stablesigmax*Di*n(l)*n(3)-(criticalI+l)*criticalsigmai*dn3;% rate of nl % First derivatives of nc at the tailing face; Caprime(mm+1 )=dn2; % Vector of rhs of ODE Caprime=[Caprime';dnl ;dn3]; % Calculation of methane decomposition rate, mmol/min/g Rdj=Ds*(Ca(l)-Ca(2))/dx/dx; Surface=6*6/10/10/weight;% cmA2/g catalyst Appendices 202 rate=Rdj/6.02e23*le3*Surface; % [t xstable n(l) n(3) rate Ca(l)-Ca(2) dn2 Rdj Rdjtail ni ns-n(l)] _____ Appendices F.2 Simple Model TJ without Surface Reaction 203 clear all global PCH4 PH2 x y knucleation kgrowth global dx weight global Ds criticalsigmai stablesigmax critical! ns D l kgowth knucleation global time dp tsetfinal nyfinaln Cayfinal dx xdirection ac % "empirical.m" is matlab routine that uses Marquardt method % to estimate parameters in the non linear regression. % Finite differences are used to estimate the differential needed; % ODE is solved by matlab builtin function ODE; % Dependent variable is a set of methane decomposition rate, mmol/min/g % Independent variables is a set of time,unit is min % It includes 4 subroutines as follows: % 'sumf.m' evaluate the sum of squares for specified a; % 'nucleation' evaluate the rate of methane decomposition using given parameeter a % 'coeff.m' evaluate augmented matrix; % 'molfun.m' gives the r.h.s. functions of ODEs; % 'gaussj.m' is a function m-file that uses Gauss elimination with % scaled partial selection to solve linear equation. criticall=10; % Assuming crtitical cluster size= 18 criticalsigmai=10;stablesigmax=l; dp=0.25/10; % Depth ofFe foil ,in cm weight=6e-3*6e-3*0.25e-3*7874*1000; % Weight of foil,g % Given independent and dependent variable values for the regression: x=[l.l 1.6 2.0 2.6 3.0 3.5 3.9 4.8 6.0 7.4 9.3 11.9 14.7 17.4 21.8 24.1]; y=[0.058 0.053 0.047 0.040 0.037 0.038 0.041 0.050 0.059 0.065 0.068 0.069 0.067 0.066 0.067 0.069]; % y is in micromol/min n=length(x); % User defined the number of parameters going to be fitted: % Step 1st: set initial of parameter % a0=[sv0 Ds knucl kgrowth] a0=[8.616 3.734 3.803 4.916] tol=le-6;maxit=100; relax=1.0; iter=0; maxda=lel0; a=a0 ;m=length(a); I=eye(m,m);relax=l .0; % Step 2 and 3:Set initial lamda==le-3 and calculate the sum of squares lamda=le-3; S=feval('sumf,a); Appendices 204 while iter<maxit & maxda>tol % Step 4th : evaluate the augmented coeffient matrix alpha=coeff('nucleation',x,y,a); da=gaussj(alpha); acoeffold=alpha(l :m,l :m); b=alpha(:,m+l); % Step 5th: evaluate the new augmented coeffient matrix acoeff=acoeffold+I*lamda; alpha=[acoeff b]; % Step 6th: calculate new da da=gaussj (alpha); % Step 7 th and 8th: calculate new a and Snew anew=a+relax * da; Snew=feval('sum f, anew); % Set suitable lambda to satisfy Snew > S while Snew > S lamda=10*lamda; acoeff=acoeffold+I*lamda; alpha=[acoeff b]; da=gaussj (alpha); % Step 6th:calculate new da anew=a+relax * da; % Step 7 th and 8th: calculate new a and Snew Snew=feval('sumf,anew); end % Set and begin next newton's regression a=anew;lamda=0.1 *lamda;S=Snew; iter=iter+l; maxda:=max(abs(da./a)) end if maxda <= tol i=[ 1 :length(a)] ;result=[i;a]; for j=l:n f(j )=nucleation(x(j ),a); end % Statistical calculations: %r A2CoeefDet % Sum of squares due to error SSE=sum((y-f).A2); % Sum of squares about mean yavg=sum(y)/n; S SM=sum((y-yavg). A2); % Degree of freedom: DOF=n-m; Appendices 205 % Coefficient of determination r2=l-SSE/SSM; % DF Adj r2m degree of freedom adjusted r2 DOFr2=l-(SSE*(n-l))/(SSM*(DOF-l)); % Fit Standard Error StdErr=(SSE/DOF)A0.5; % F statistic value F_stat=((SSM-SSE)/(m-l))/(SSE/DOF); % Standard error alpha=coeff('nucleation',x,f,a); alpha l=alpha(l :m,l :m); Coviance=inv(alphal '*alphal); for i=l:m Cii(i)=Coviance(i,i); end % Based on DOF=14 , confidence level=0.05 tvalpha=2; coefficientSE=tvalpha*(Cii.*SSE/DOF).A0.5 % Final standard error % Calculation of variables for plotting newn=100; dxf=(x(length(x))-x( 1 ))/50; xfine=[x(l):dxf:x(length(x))]; for j=l dength(xfine) finalratem(j)=nucleation(xfine(j),a); if xfinefj)—1.1 timefinal^time; fmalresult=Cayfmal; else timefinal=[timefmal;time]; finalresult=[finalresult;Cayfmal]; end end Num=size(fmalresult,2); % Calculation of n l at the tailing face corresponding the xfine n 1 final_finalresult(: ,Num-1); % Calculation of net at the tailing face corresponding the xfine nctfinal=finalresult(:,Num); % Carbon diffusion rate profile calculation Rdj tailfinal=Ds. * (finalresult(: ,Num-2)-finalresult(: ,Num-1)) ./dx/dx; forj=2:Num-l Rdjfmal(:,j)=::Ds.*(finalresult(:,j-l)-finalresult(:,j))./dx./dx; end Rdjfinal(:,l)=0; % Growth and nucleation rate dgrowth=kgrowth*nlfinal.Astablesigmax.*nctfmal; dnucleation=knucleation.*nl final.Acriticalsigmai; dnct=dnucleation; Appendices 206 dn 1 =Rdj final(: ,Num-1 )-criticalsigmai. *dnucleation-stablesigmax. *dgrowth; Caprime(:,Num)=dnl; figure(l) surf(xdirection,timefmal(1:500:20000),finalresult( 1:500:20000,1 :Num-1)) colormap('coor) xlabel('x direction, cm') ylabel('Time, min') zlabel('Site density, l/cmA2') figure(2) plot(x,y,'ko') xlabel('Time, min') ylabel('Methane decomposition rate, mmol/min/g cat') Legend('Experimental data','Fitted data') hold on plot(xfine,finalratem,'k-') hold off figure(3) subplot(2,2,l),plot(timefmal,nlfmal,'k-') xlabel('Time, min') ylabel('n_], l/cmA2') subplot(2,2,2),plot(timefmal,nctfmal,'k-') xlabel('Time, min') ylabel(*n_c_t, l/cmA2') Surface=6*6/10/10/weight; % cmA2/g catalyst subplot(2,2,3),plot(xfme,fmalratem./le3./Surface.*6.02e23,'k-') xlabel('Time, min') ylabel('R_dj at leading face, l/cmA2/s') subplot(2,2,4), plot(timefinal,Rdjtailfinal,'k-') xlabel('Time, min') ylabel('R_dJ at tailing face, l/cmA2/s') figure(4) surf(xdirection,timefinal(l :500:20000),fmalresult(l :500:20000,1 :Num-l)) colormap('cool') xlabel('x direction, cm') ylabel('Time, min') zlabel('Site density, 1 /cmA2') else error('Marquardts method did not converge') end fprintf('\n literature with boltzman method\n') % Print and plot results: fprintf('\n Sucessful solution in %2.Of iterations!\n',iter) fprintf('\n ParameterAn') fprintfC a(%1.0f) = %8.6e\n',result) Appendices 207 fprintf('\n\n Numeric summary:\n') fprintfC SSE=%8.6f SSM=%8.6:f\n',SSE,SSM) fprintfC rA2 Coef Det=%8.6f DF Ajsr2=%8.6f\n',r2,DOFr2) fprintfC fit Std Err=%8.6f F-value-%8.6f\n',StdErr,F_stat) fprintf('\n\n\n Result of constants :\n') fprintfC ns = %8.3e Std= %8.3e\n\n',ns,coefficientSE(l)*ns/a(l)) fprintfC Ds = %8.3e cmA2/s Std- %8.3e\n',Ds/60,coefficientSE(2)*Ds/a(2)/60) fprintfC knucleation = %8.3e cmA2/s Std= %8.3e\n',knucleation/60/exp(-35743*4.18/900/8.314),coefficientSE(3)*knucleation/60/a(3 )/exp(-35743*4.18/900/8.314)) fprintfC kgrowth = %8.3e cmA2/s Std= %8.3e\n',kgrowth/60/exp(-30785*4.18/8.314/900),coefficientSE(3)*kgrowth/60/a(3)/exp(-30785*4.18/8.314/900)) Appendices 208 function rate=nucleation(tset,a) % m file for caculation o f methane decomposition rate using parameter a at given time tset global Ds ns D i global dx weight global time tsetfmal Cayfinal dx xdirection ac weight global criticalsigmai stablesigmax D l nx ni criticall ns Ds dp Rdj ac tsetold Cayold knucleation kgrowth % Calculation o f surface diffusion coefficient ns=a( l ) * le l7 ; Ds=a(2)* 1 e-14* 1 e4*60* 1 e4; knucleation=a(3)*le-175*60*exp(-35743*4.18/900/8.314); kgrowth=a(4)* 1 el 0*60*exp(-30785*4.18/8.314/900); Surface=6*6/10/10/weight; % cm A 2/g catalyst % Divide depth o f Fe foi l into 50 section m=50+l ; xmax=dp; % Assuming 6m is the maximum distance i.e. infinite mm=m-1; % n is the number o f t points dx=xmax/mm;xdirection=0: dx: xmax; % Calculate a vector o f Caj at time 0 % Initial condition at t=0 wi th all x>0, Ca=Ca0 i f tset==l. l y0=[0]; %nct Ca0=0; % Site density of carbon at the tailing face Cal=ns; % Site density of carbon at the leading face % Initial condition o f carbon site density for j =2: length(xdirection) Caj(j)=Ca0; end Caj ( l )=Cal ; % Boundary condition at surface at t=0, Ca=Cal Cay=[Caj y0]; [time,Ca]=ode23('molfun',[0 tset],Cay); Cayold=Ca(size(Ca, 1),:); tsetold=tset; else [time,Ca] :=ode23( ,molfun',[tsetold tset],Cayold); end i f tset~=tsetold Cayold=Ca(size(Ca, 1),:); tsetold=tset; end Cayfmal=Ca; rate=Rdj/6.02e23* 1 e3*Surface; % mmol/min/cm A 2 into mmol/min/g catalyst rate=rate; [tset rate] Appendices 209 function Caprime=molfun(t,Cay) global criticalsigmai stablesigmax D l nx ni criticall ns Ds dp Rdj ac knucleation kgrowth global dx weight % molfun.m is a function fde which can calculate rhs of pde, at any time t, % the pde can be discretized at position i by using a central difference in space % Input arguments: % t- time,vector % Cay- a vector of concentration at different x space direction at % same time direction t,and with xstable/Di/criticalsigmai,nx at the tailing face % Output arguments: % Caprime- a vector of first directive of Ca at different x space direction % at the same time direction t m=length(Cay);mm=m-2; Ca=Cay(l:mm+l); % n=[nl,n(ct)] the site density at the tailing face n=Cay(m-l:m); % Calculation of rhs of unsteady state diffusion equation Caprime(l)=0; for i=2:mm Caprime(i)=Ds*(Ca(i-l)-2*Ca(i)+Ca(i+l))/dxA2; end % Carbon diffusion rate at the tailing face Rdjtail=Ds*(Ca(mm)-Ca(mm+l))/dx/dx; nl=n(l); nct=n(2); % Calculation of impinging rate, diffusion rate dgrowth=kgrowth*nlAstablesigmax*nct; dnucleation=knucleation*nlAcriticalsigmai; dnct=dnucleation; % Carbon site density change rate dnl=Rdjtail-criticalsigmai*dnucleation-stablesigmax*dgrowth; C aprime(mm+1 )=dn 1; Caprime=[Caprime';dnct]; % Carbon diffusion rate at the leading face Rdj=Ds*(Ca(l)-Ca(2))/dx/dx; Surface=6*6/10/10/weight; % cmA2/g catalyst rate=Rdj/6.02e23 * 1 e3 * Surface; Appendices 210 F.3 Model I with Surface Reaction clear all global PCH4 PH2 x y Ds criticalsigmai stablesigmax criticall ns D l global time dp tsetfinal nyfmaln Cayfinal dx xdirection global k l k2 PCH4 PH2 SvO ratej kp Surface % "empirical.m" is matlab routine that uses Marquardt method % to estimate parameters in the non-linear regression. % Finite differences are used to estimate the differential needed; % ODE is solved by matlab builtin function ODE45; % Dependent variable is a set of methane decomposition rate, mmol/min/g % Independent variables is a set of time, min % It includes 4 subroutines as follows: % 'sumf.m' evaluate the sum of squares for specified a; % 'nucleation' evaluate the rate of methane decomposition using given parameeter a % 'coeff.m' evaluate augmented matrix; % 'molfun.m' gives the r.h.s. functions of ODEs; % 'gaussj.m' is a function m-file that uses Gauss elimination with % scaled partial selection to solve linear equation. criticall=10; criticalsigmai=4;stablesigmax=5; dpl=18.1 % Diameter of particle size, nm site=0.105 % CO adsorption data mmol/g cat Surface=site*le-3*6.02e23*6.79e-20*le4; dp=2/3*dpl*le-7; % Length of diffusion path, cm % Given independent and dependent variable values for the regression (Y64): x=[0.5:3.3:56.6]; y=[0.326 0.368 0.356 0.343 0.332 0.321 0.309 0.309 0.309 0.306 0.312 0.300 0.306 0.299 0.291 0.293 0.272 0.279] PCH4=0.23*101325; PH2=0.12*101325; n=length(x); %a=[Ds, Di , kf, kg, kp] a0=[6 6.0 9.0 2 3.1] tol=le-3;maxit=100; relax=1.0; iter=0; maxda=lel0; a=a0;m=lengfh(a); I=eye(m,m);relax-1.0; % Step 2 and 3:Set initial lamda==le-3 and calculate the sum of squares lamda=le-3; Appendices 211 S=feval('sumf,a); while iter<maxit & maxda>tol % Step 4th : evaluate the augmented coeffient matrix alpha=coeff('nucleation',x,y,a); da=gaussj (alpha); acoeffold=alpha(l :m,l :m); b=alpha(:,m+l); % Step 5th: evaluate the new augmented coeffient matrix acoeff=acoeffold+I*lamda; alpha=[acoeff b]; % Step 6th: calculate new da da=gaussj (alpha); % Step 7 th and 8th: calculate new a and Snew anew=a+relax*da; Snew=feval('sumf,anew); % Set suitable lambda to satisfy Snew > S while Snew > S lamda=l 0*lamda; acoeff=acoeffold+I*lamda; alpha=[acoeff b]; da=gaussj(alpha); % Step 6th:calculate new da anew=a+relax*da; % Step 7 th and 8th: calculate new a and Snew Snew=feval('sum f ,anew); end % Set and begin next newton's regression a=anew;lamda=0.1 *lamda;S=Snew; iter=iter+l; maxda=max(abs(da./a)) da end if maxda <= tol for j=l:n f(j)=nucleation(x(j),a); end % Statistical calculations: % r A 2 Coeef Det % Sum of squares due to error SSE=sum((y-f).A2); % Sum of squares about mean yavg=sum(y)/n; SSM=sum((y-yavg) A 2 ) ; % Degree of freedom: DOF=n-m; Appendices 212 % Coefficient of determination r2=l-SSE/SSM; % DF Adj r2m degree o f freedom adjusted r2 DOFr2=l-(SSE*(n-l))/(SSM*(DOF-l)); % Fit Standard Error StdErr=(SSE/DOF)A0.5; % F statistic value F_stat=((SSM-SSE)/(m-l))/(SSE/DOF); % Standard error alpha=coeff('nucleation',x,f,a); alpha 1 =alpha( 1: m, 1: m) Co viance=inv(alpha 1' * alpha 1); for i=l:m Cii(i)=Coviance(i,i) end % Based on DOF ! 4, confidence level=().()5 tvalpha=2.0; coefficientSE=tvalpha* (Cii. * SSE/DOF). A0.5; % Calculation o f plooting results newn=100; dxf=(x(length(x))-0.5)/100; xfme=[0.5 :dxf:x(length(x))]; for j=l :length(xfme) finalratem(j)=nucleation(xfme(j),a); ifxfme(j)=-0.5 timefinal=time; fmalresult=Cayfmal; else timefmal=[timefmal;time]; finalresult=[finalresult;Cayfinal]; end end Num=size(finalresult,2); nlfinal=fmalresult(:,Num-4); % Calculation of nl at the tainlign face corresponding to xfiue; xfinal=criticalsigmai*Di.*fmalresult(:,Num-3);% Calculation of xstable coiTesponding to xfme nxfinal=fmalresult(:,Num-2); % Calcualtion of nx corresponding to xfine; Svfinal=fmalresult(:,Num-l); % Calculation of Sv on the leading face corresponding to xfine; Spfinal=fmalresult(:,Num); % Calculation of Sv on the leading face corresponding to xfine; nsfinal=finalresult(:,l); % Calculation of Sv on the leading face corresponding to xfme; % Calculation of diffusion at the tailing face Rdj tailfmal=Ds/dx/dx. * (finalresult(: ,Num- 5 )-finalresult(: ,Num-4)); Ratej=kl*PCH4.*Svfmal A2-k2*PH2A2.*(SvO-Svfmal-Spfmal).*Svfmal; % Rate of reaction % Rate of ns is equal to reaction rate minus diffusion rate minus the changing rate to encapsulating rate .. % Rate of site encapsulated by the encapsulated carbon Appendices 213 dSp=kp.*nsfinal.A6; Rdj final=zeros(size(finalresult, 1) ,Num-4); Rdjfinal(:, 1 )=Ratej-dSp; % Calculation of diffusion profile for j=2:Num-4 Rdj fmal(: j )=-Ds/dx/dx. * (fmalresult(: ,j )-fmalresult(: j -1)); end dn4=ratej -Rdj final(: ,2)-dSp; % Rate of ns dn5=-dn4-dSp; %RateofSv % Calculation of ni corresponding to xfine for j=1 dength(timefinal) i f xfmalfj) > criticall ni(j)=0.5*nlfmal(j)*(xfmal(j)-criticall); else niG)=0; end end % Calculation of growth rate and changing rate of nl dn3=Di.*nl final. *ni'; dn2=Rdjtailfmal-stablesigmax*Di.*nlfmal.*nxfmal-(criticalI+l)*criticalsigmai*dn3;% rate of nl % Plot results figure(l) surf(xdirection,timefinal(50:50:1000),finalresult(50:50:1000,l:Num-4),-finalresult(50:50:1000,l:Num-4)) colormap('default') xlabel('x direction, cm') ylabel(Time, min') zlabel('Site density, l/cmA2') figure(6) surf(xdirection,timefmal(50:50:1000),finalresult(50:50:1000,l:Num-4)) colormap('coor) xlabel('x direction, cm') ylabel(Time, min') zlabel('Site density, l/cmA2') figure(2) plot(x,y,'ko') xlabel('Time, min') ylabel('Methane decomposition rate, mmol/min/g cat') Legend('Experimental data','Fitted data') hold on plot(xfine,finalratem,'k-') hold off figure(3) Appendices 214 subplot(2,2,l),plot(timeflnal,nsflnal,'k-,) xlabel(Time, rain') ylabel('n_s, l/craA2') subplot(2,2,2),plot(timefinal,nlfinal,'k-') xlabel('Tirae, min') ylabel('n_l, l/cmA2') subplot(2,2,3),plot(timefmal,ni','k-') xlabel('Time, min') ylabel('n_i, l/cmA2*) subplot(2,2,4),plot(timefmal,nxfmal,'k-') xlabel('Time, min') ylabel('n_x, l/cmA2') figure(4) subplot(2,2,3),plot(dmefmal,Rdjfinal(:,l),'k-') xlabel('Time, min') ylabel('Leading face R _ d J , l/cmA2/s') subplot(2,2,4),plot(timefinal,Rdjfmal(:,Num-4),'k-') xlabel('Time, min') ylabel('Tailing face R _ d J , l/cmA2/s') subplot(2,2,l),plot(timefinal,Svfinal,'k-') xlabel('Time, min') ylabel('S_v, l/cmA2') subplot(2,2,2),plot(timefinal,Spfmai;k-') xlabel('Time, min') ylabel('S_p, l/cmA2') figure(5) subplot(2,2,1 ),plot(timefmal,xfinal,'k-') xlabel('Time, min') ylabel('xstable, l/cmA2') subplot(2,2,2),plot(timefinal,dn2,'k-') xlabel(Time, min') ylabel('dn2, l/cmA2/s') subplot(2,2,3),plot(timefinal,dSp,'k-') xlabel(Time, min') ylabel(*rate, l/cmA2/s') hold on subplot(2,2,3),plot(timefinal,Ratej,'k-') xlabel('Time, min') ylabel('rate, l/cmA2/s') hold on subplot(2,2,3),plot(timefinal,Rdjfmal(:,l);k-') xlabel('Time, min') ylabel('rate, l/cmA2/s') hold off subplot(2,2,4),plot(timefinal,dSp./Rdjfinal(:,l),'k-') xlabel('Time, min') Appendices 215 ylabel('ratio') else error('Marquardts method did not converge') end % Print and plot results: fprintf('\n Sucessful solution in %2.Of iterations!\n',iter) i = [ l :length(a)];result=[i;a]; fprintf('\n 10wtCo/SiO2\n') fprintf('\n ParameterAn') fprintfC a(%1.0f) = %8.3e\n',result) fprintf('\n\n Numeric summaryAn') fprintfC SSE=%8.6f SSM=%8.6f\n',SSE,SSM) fprintfC r A 2 Coef Det=%8.6f DF Ajsr2=%8.61V,r2,DOFr2) fprintfC fit Std Err=%8.6f F-value=%8.6:f\n*,StdErr,F_stat) fprintf('\n\n\n Result o f constants :\n') fprintfC Ds = %8.3e cm A2/s Std= %8.3e\n',Ds/60,coefficientSE(l)*Ds/a(l)/60) fprintfC D l = %8.3e cm A2/s Std= %8.3e\n',Di/60,coefficientSE(2)*Di/a(2)/60) fprintfC k l =%8.3e Std= %8.3e\n',kl,coefficientSE(3)*kl/a(3)) fprintfC k2 = %8.3e Std= %8.3e\n',k2,coefficientSE(4)*k2/a(4)) fprintfC kp = %8.3e Std= %8.3e\n',kp,coefficientSE(5)*kp/a(5)) fprintf('\n\n\n Result o f constants An') fprintfC Ds = %8.3e cm A2/s Std= %8.3e\n',Ds/60,coefficientSE(l)) fprintfC D l = %8.3e cm A2/s Std= %8.3e\n',Di/60,coefficientSE(2)) fprintfC k l = %8.3e Std= %8.3e\n',kl,coefficientSE(3)) fprintfC k2 = %8.3e Std= %8.3e\n*,k2,coefficientSE(4)) fprintfC kp = %8.3e Std= %8.3e\n',kp,coefficientSE(5)) Appendices 216 function rate=nucleation(tset,a) % function fde for calculation of rate global Ds ns D l dx global time dp tsetfmal nyfinaln Cayfmal dx xdirection ac global k l k2 PCH4 PH2 SvO ratej kp Surface global criticalsigmai stablesigmax D l Nr nx ni criticall ns Ds dp Rdj ac global criticalsigmai stablesigmax D l Nr nx ni criticall ns Ds dp Rdj ac tsetold Cayold % Initial condition of Nr, nx,ni Nr=0;nx=0;ni=0; % Calculation of surface diffusion coefficient % Base on iron case Sv0=l/6.79e-20/le4; % l/cmA2 Ds=a(l)*le-14*60; Di=a(2)* 1 e-19*60* 1 e3; %cmA2/s kl=a(3)*le-19; k2=a(4)*le-22; kp=a(5)*le-74; % y is a vector, y(l) is the x/sigmai/D;y(2)is n l ; % y(3)is active site on the leading face;encapsulating carbon site density; % Divide the diffusion direction into finte grid m=5+l; xmax=dp; % Assuming 6m is the maximum distance i.e. infinite mm=m-1; % n is the number of t points dx=xmax/ mm ;xdirection=0: dx: xmax; % Calculate a vector of Caj at time 0 % Initial condition at t=0 with all x>0, Ca=CaO iftset=0.5 y0=[0 0 SvO 0]; % Integral of n l and nx ,active site,encapsulating carbon site density; Ca0=0; % Concentration of oxygen at the leading face; Cal=0; % Concentation of carbon at the tailing face; for j=2:length(xdirection) Caj(j)=CaO; end Caj(l)=Cal; % Boundary condition at surface at t=0, Ca=Cal Cay=[Caj y0]; [time,Ca]=ode23('molfun',[0 tset],Cay); % Set initial condition for the next time frame Cayold=Ca(size(Ca,l),:); tsetold=tset; else [time,Ca]=ode23('moliun',[tsetold tset],Cayold); end if tset~=tsetold Cayold=Ca(size(Ca, 1),:); tsetold=tset; end Cayfinal^Ca; Appendices 217 % Call ode45 to solve a series of ODEs: D rate=ratej/6.02e23*le3*Surface; % mmol/min/cmA2 into mmol/min/g catalyst rate=rate; [tsetrate] function Caprime=molfun(t,Cay) global criticalsigmai stablesigmax D l Nr nx ni criticall ns Ds dp Rdj ac global Ds ns Rdj Surface dx global k l k2 PCH4 PH2 SvO ratej kp % molfun.m is a function file which can calculate rhs of pde, at any time t, % the pde can be discretized at position i by using a central difference in space % Input arguments: % t- time,vector % Cay- a vector of concentration at different x space direction at % same time direction t,and with xstable/Di/criticalsigmai,nx at the tailing face % Output arguments: % Caprime- a vector of first directive of Ca at different x space direction % at the same time direction t % Length of vector Cay m=length(Cay);mm=m-3-2; Ca=Cay(l:mm+l); % n=[nl, n l integral, n3, n(l), ns, sv, sp]; n=[Cay(m-2-2 :m-2);Cay( 1) ;Cay(m-1 :m)]; ns=n(4); % Carbon site density on the leading face; Sp=n(6); % Site density of encapsulating carbon on the leading face; Sv=n(5); % Surface active site on the leading face; ratej=kl*PCH4*SvA2-k2*PH2A2*(SvO-Sv-Sp)*Sv; % Rate of reaction on the leading face; % Rate of ns is equal to reaction rate minus diffusion rate minus the changing rate to encapsulating rate; % Rate of site encapsulated by the encapsulated carbon; dSp=kp*nsA6; % Changing rate of encapsulating carbon site density; Rdj=Ds*(Ca(l)-Ca(2))/dx/dx;% Carbon diffusion rate at the leading face; dn4=ratej-Rdj-dSp; % Rate of ns single atom on the surface dn5=-ratej+Rdj; % Rate of sv % [t ns xstable n(2) n(3) Rdj dn4] % Calulation of rhs of unsteady state diffusion equation ^ Caprime(l)=dn4; fori=2:mm Caprime(i)=Ds*(Ca(i-l)-2*Ca(i)+Ca(i+l))/dxA2; end % Carbon diffusion rate at the tailing face Rdjtail=Ds*(Ca(mm)-Ca(mm+l))/dx/dx; % Changing rate of xstable/Di/criticalsigmai=dnl; dnl=n(l); xstable=criticalsigmai*Di*n(2); % Calculation of xstable Appendices 218 % Calculation of ni i f xstable > criticall ni=0.5*n(l)*(xstable-criticali); else ni=0; end % Calculation of growth rate dn3=Di*n(l)*ni; dn2=Rdjtail-stablesigmax*Di*n(l)*n(3)-(criticalI+l)*criticalsigmai*dn3; % Rate of nl Caprime(mm+1 )=dn2; Caprime=[Caprime';dnl ;dn3;dn5;dSp]; % Calculation of methane decomposition rate, mmol/min/g rate=ratej/6.02e23*le3*Surface; % [t xstable n(l) n(3) rate dn2 Sv SvO-Sv-Sp dn5 ns Sp] Appendices 219 F.4 Common Matlab Function Files %gaussj.m function x=gaussj(A) % gaussj.m is a function m-fde that uses Gauss elimination with % scaled partial selection to solve linear equation of the form: % [A]*{X}={C} % Input argument: % A=argumented coefficient matrix with the column vector of the rhs % constants, c, included as its n+lst column % Output argument: % X=vector of solution values n=size(A,l); nm=n-l; np=n+l; % Carry out elimination process n-1 times for k=l:nm kp=k+l; % Search for largest coefficient of x(k) for rows k through % n. pivot is the row index of the largest scaled coefficient, for i=k:n maxAij(i)=abs(A(i,k)); for j=k:n if abs(A(ij))>maxAij(i); max Aij (i)=abs( A(i ,j)); end end S(i)=A(i,k)/maxAij(i); end absSpivot=abs(A(k,k))/maxAij(i); pivot=k; for i=kp:n ifabs(S(i))>absSpivot absSpivot=abs(S(i)); pivot=i; end end % Exchange rows k and pivot i f pivot~=k i f pivot~=k for j=k:np temp=A(pivot,j); A(pivot,j)=A(k,j); A(k,j)=temp; end end % Eliminate coefficient of x(k) from rows k+1 through n Appendices 220 for i=kp:n quot=A(i,k)/A(k,k); A(i ,k)=0; for j=kp:np A ( i j ) = A ( i j ) - q u o t * A ( k j ) ; end end end % Carry additional elimination process n-1 times to get the final matrix % has non-zero elements only on the main diagonal, for k= l :nm kn=np-k; i f A ( k , k ) = 0 error('Zero pivot coefficient encountered!') end % Eliminate coefficient o f x(k) from rows n-k through 1 for i=(n -k ) : - l : l quot=A(i,kn)/A(kn,kn); A(i,np)=A(i,np)-quot*A(kn,np); end end % Result f o r i = l : n x(i)=A(i,np)/A(i, i); end Appendices function alpha=coeff(f,x,y,a) % 'coeff.m' is a function m-fde that calculates the % augmented Jacobian matrix required by Marquardt's % method for nonlinear curve fitting. % % Input arguments: % f = dummy name of curve fitting function % df = dummy name of partial derivative function % x = vector of x values % y = vector of y values % a = vector of parameter estimates % Output argument: % alpha - augmented Jacobian matrix % Evaluate lengths of x and a vectors n=length(x);m=length(a);mp=m+l; % Determine vector of differences and matrix of partial differentials for k=d:n ftemp(k)=feval(f,x(k), a); diff(k)=y(k)-ftemp(k); end for i=l:m dela=l e-4*a(i);a(i)=a(i)+dela; for k=l:n ftempnew(k)=feval(f,x(k), a); dfda(i,k)=(-ftemp(k)+ftempnew(k))/dela; end end % Calculate elements of the augmented Jacobian matrix alpha=zeros(m,mp); for i=l:m for j=i:m for k=l:n alpha(i,j )=alpha(i ,j )+dfda(i,k) * dfdafj ,k); end if j — i alphafj ,i)=alpha(i,j); end end fork=l:n alpha(i,mp)=alpha(i,mp)+diff(k)*dfda(i,k); end end Appendices 222 function f=sumf(a) global PCH4 PH2 x y tsetold % Input argument: % a=given parameters % Output argument: % f=sum of difference square n=length(y); f=0; for i=l:n fxik=nucleation(x(i),a); f=f+(y(i)-fxik)A2; end Appendices 223 Appendix G Effect of t" on the Estimate of r and 100A:rf As described in the Section 3.4.2, the activity profde was described by the modified first order decay model Equation (3.2). Equation (3.2) required t , the reaction time corresponding to the maximum reaction rate to be determined, hi order to estimate the error in r and 100&rf, caused by the value of t determined from experimental data, value of t was shifted to one time interval before and after the chosen, t . Then, r* and 1 Q0kd with standard errors were estimated corresponding to these different t* values, as listed in Table G. 1 and Figure G. 1 to Figure G.4. Data of Table G. 1 and Figure G. 1 to Figure G.4 include the parameters with standard errors, estimated at different t values for two different activity profiles with different gas phase composition KM . Data of Table G . l and Figure G . l to Figure G.4 show that for both cases, the estimated errors in r and 100&rf resulting from possible errors in identifying t , are small since the estimations corresponding to the shifted t are located within the standard errors of the optimal r and 100&rf estimates. Table G . l Effect of t on the Estimation of r and \00kd . * Identified t , min * r , mmol/min/g cat 100&d, 1/min KM=0.02 10.4 1.42±0.09 3.30±0.31 13.7 (Optimal) 1.42±0.07 3.82±0.31 17.0 1.41±0.06 3.71±0.30 KM=0.05 7.1 0.39±0.01 0.69±0.06 10.4 (Optimal) 0.39±0.01 0.75±0.06 13.7 0.39±0.01 0.78±0.07 Appendices 224 1.55 | 1.50 - T ra _ u f 1.45 -1 o <> | 1.40 -1.35 - 1 1.30 I 1 1 1 1 1 1 1 10 11 12 13 14 15 16 17 18 Indentif ied t*, min F i g u r e d Effect of t on the estimation of r (Activity profile with KM =0.02atmof Figure 3.2). 4.5 4.0 f c E o o 3.0 I- I 2.5 I 1 1 1 1 1 1 1 10 11 12 13 14 15 16 17 18 Indentified t*, min Figure G.2 Effect of /* on the estimation of \00kd (Activity profile with Ku = Omatm of Figure 3.2). Appendices 225 0.40 ro u - ? ]c | 0.39 o E E 0.38 9 11 Indentified t*, min 13 15 Figure G.3 Effect of t* on the estimation of r (Activity profde with KM = 0.05atm of Figure 3.2). 0.9 c E o o 0.8 0.7 0.6 0.5 I 1 1 1 1 1 5 7 9 11 13 15 Indentified t*, min Figure G.4 Effect of t on the estimation of \00kd (Activity profde with KM = 0.05atm of Figure 3.2). Appendices 226 A p p e n d i x H C o n v e r s i o n o f KM t o C a r b o n A c t i v i t y In the present study, KM = I PCHi was used to describe the gas phase composition. The gas phase composition can also be expressed as carbon activity ac ~KePCH IP^ . The conversion of KM = P„21 PCHi to ac =KePCHt /P^ can be expressed as ac= KJ KM . Herein, the equilibrium constant Ke =0A62atm (Rostrup-Nielson, 1972). Table H. 1 Conversion table of KM = P^ I Pc„4 to ac = KePCHt //% . ac=KePCHJP2Hi 0.01 46.2 0.02 23.1 0.03 15.4 0.04 11.6 0.05 9.2 0.06 7.7 0.07 6.6 0.08 5.8 0.09 5.1 0.1 4.6 0.11 4.2 

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