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A kinetic study of decalin selective ring opening reactions over Iridium supported on H-Beta zeolite… Alzaid, Ali H. 2011

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A KINETIC STUDY OF DECALIN SELECTIVE RING OPENING REACTIONS OVER IRIDIUM SUPPORTED ON H-BETA ZEOLITE CATALYST  by  Ali H. Alzaid  B.Sc., The University of Alberta, 2007  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE STUDIES  (CHEMICAL AND BIOLOGICAL ENGINEERING)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) June 2011 © Ali H. Alzaid, 2011  Abstract Selective ring opening of naphthenic rings is the optimum process for reducing the cyclo-paraffin and aromatic content of gas oils in order to improve its quality and consequently its value. The aim of this study was to examine the reaction rates of ring opening of a model multi-ring compound, namely decalin, using a bifunctional catalyst. Three catalysts, Pd/H-Y-30, Ir/H-Beta-300 and Ir/H-Beta-25, were tested to examine the activity and yield of ring opened products at the same reaction conditions. The reaction was performed in a continuously-stirred, batch reactor at 350°C and 3 MPa H2 pressure. The results showed that Ir/H-Beta-25 had the highest activity and yield of ring opened products. By comparing the Ir/H-Beta-25 catalyst and the Ir/H-Beta-350 catalyst, it was concluded that higher activity was achieved with higher acidity, confirming the important role of catalyst acidity in selective ring opening. The effect of reaction conditions, namely temperature (275-350°C) and pressure (3-6 MPa), on the activity and product selectivity was also investigated. Results showed that as the temperature increased, the initial catalyst activity increased. Although the effect of pressure was minimal at 275°C, as the temperature increased, the effect of pressure became more significant and higher conversions were achieved at higher pressures. The concentration of ring opened products increased as the conversion increased for all temperatures and pressures. The ring opened product concentrations increased with increased temperature at 3 MPa. At 275°C, higher ring opened product concentrations were obtained at higher conversions as the pressure increased. Based on the experimental results, a Langmuir-Hinshelwood (L-H) kinetic model for the ring opening of decalin was developed. The kinetic model assumed a bifunctional catalytic process in which hydrogenation/dehydrogenation reactions occurred on metal sites, whereas isomerization, ring-opening and cracking occurred on acid sites. The model parameters were estimated by minimizing the difference between measured ii  experimental data and model predictions by the sum of least-squares method. The model was able to estimate the experimental results well, with a R2 of 0.8. Activation energies estimated from the model parameters showed that ring opening had the lowest activation energy (135.4 kJ/mol), whereas cracking had the highest (229.7 kJ/mol).  iii  Table of Contents Abstract ...................................................................................................................... ii Table of Contents ....................................................................................................... iv List of Tables .............................................................................................................. vi List of Figures ........................................................................................................... viii Acknowledgements .................................................................................................. xv Dedication ............................................................................................................... xvi Chapter 1.  Introduction ........................................................................................... 1  1.1  Background .......................................................................................................................1  1.2  Literature review ..............................................................................................................5  1.3  Summary of literature review and study objectives ..................................................... 31  Chapter 2.  Experimental ........................................................................................ 34  2.1  Catalyst preparation ...................................................................................................... 34  2.2  Catalyst characterization ............................................................................................... 36  2.3  Catalytic activity measurements ................................................................................... 37  Chapter 3.  Results and discussion .......................................................................... 40  3.1  Catalyst characterization ............................................................................................... 40  3.2  Catalytic activity ............................................................................................................ 41  3.2.1  Preliminary studies to test the activity of different catalysts.................................. 41  3.2.2  Effect of temperature .............................................................................................. 44  3.2.3  Effect of pressure..................................................................................................... 46  3.3  Product distribution ...................................................................................................... 48  3.4  Summary of findings ...................................................................................................... 61  Chapter 4.  Reaction mechanism and kinetic study ................................................. 62  4.1  Reaction mechanism ..................................................................................................... 62  4.2  Kinetic development...................................................................................................... 63  iv  4.3  Mole balance ................................................................................................................. 68  4.4  Parameter estimation.................................................................................................... 70  Chapter 5.  Conclusion and recommendations ........................................................ 77  5.1  Conclusion ..................................................................................................................... 77  5.2  Recommendations......................................................................................................... 78  References ................................................................................................................ 79 Appendices ............................................................................................................... 83 Appendix A Catalyst characterization ....................................................................................... 84 A.1  BET surface area, pore volume and average pore size full analysis results ............ 85  A.2  Temperature-programmed reduction and CO chemisorption analysis .................. 86  A.3  Sample reports......................................................................................................... 89  Appendix B Matlab code for kinetic model parameter estimation ........................................ 124 Appendix C Arrhenius equation calculations .......................................................................... 178 Appendix D Experimental error analysis ................................................................................. 181 Appendix E GC-MS scan sample .............................................................................................. 186  v  List of Tables Table 1. A comparison of the weight compositions of different heavy gas oil fuels [4]. ... 3 Table 2. Description of reaction steps [29]. ..................................................................... 22 Table 3. Estimated kinetic parameters for the RO Langmuir-Hinshelwood kinetic model [29]. ................................................................................................................................... 23 Table 4. Comparison of RO yields and selectivity on Pt-Ir and Ni-Mo carbide supported on H-Y [42]. ....................................................................................................................... 27 Table 5. SiO2/Al2O3 molar ratio, BET surface area, pore volume and average pore diameter of all catalysts .................................................................................................... 40 Table 6. Metal dispersion, reduction temperature and degree of reduction for all metal catalysts. ........................................................................................................................... 41 Table 7. Estimated reaction kinetic parameters for all reaction temperature tested. .... 75 Table 8. The pre-exponential factors AJ and activation energies Eaj for all kj .................. 76 Table 9. Isotherm tabular report………………………..………………………………………………………..91 Table 10. BET surface area report…………………………………………………………………………………95 Table 11. Langmuir surface area report…………………………………………….…………………………97 Table 12. t-plot report…………………………………………….…………………………………………….......99 Table 13. BJH adsorption pore distribution report….………………………………………………....101 Table 14. BJH desorption pore distribution report….………………………………………………....108 Table 15. CO pulse chemisorption peak table….…………………………………………..…………….118  vi  Table 16. Error analysis for two experiment runs performed at T=350°C and P=6 MPa. ......................................................................................................................................... 183 Table 17. Error analysis for two experiment runs performed at T=275°C and P=3 MPa 184 Table 18. Error analysis for two GC-MS injections of the same sample for decalin (D), ring opened products (R), cracked products (C), and isomers (I) concentrations. ......... 185  vii  List of Figures Figure 1. World’s largest oil reserves in 2009 (in billion barrels) *2+.................................. 2 Figure 2. Synthetic sweet crude production from Canadian oil sands upgrading system and an overview of U.S. refinery system [4]. ...................................................................... 4 Figure 3. Typical cetane numbers for saturated and ring opened products formed from naphthalene [5, 6]. .............................................................................................................. 5 Figure 4. Mechanism of decalin reactions over acid catalysts. PC: protolatic cracking, I: isomerization, β: β-scission, DS: desorption, HT: hydrogen transfer, HeT: hydride transfer, TA: transalkylation [20]. ....................................................................................... 6 Figure 5. Key reaction for the conversion of multi-ring aromatics [35]. ............................ 7 Figure 6. Typical ROP groups and structures [25]. ........................................................... 10 Figure 7. Decalin conversion over H-Beta-25 (■), H-Beta-75 (○), H-Y-12 (  ), H-  Mordenite-20 ( ), and H-MCM-41 ( ) at (a) 250°C, [b] 270°C and 2 MPa. Data in (b) for H-MCM-41 are at 300°C [25]. ........................................................................................... 11 Figure 8. Concentration of reactants and main reaction product groups as a function of conversion for H-Beta-25 and H-Beta-75(filled), H-Y-12(open), and H-Mordenite-20 (halffilled). Reactants and product groups: [a]trans-decalin (■, □, ), cis-decalin (●,○, ), and isomers ( ,  ,  ), [b]ROP ( ,  ,  ), C ( , ◊,  ), and HP (  ,  ,  ) [25]. ............ 12  Figure 9. Proposed reaction mechanism for the hydroconversion of tetralin on bifunctional catalyst [17]. ................................................................................................. 14 Figure 10. Comparison of the activity of platinum-modified (open) and proton-form (filled) zeolites. Pt- and H-Beta (□, ■), Pt- and H-Y (○, ●), Pt- and H-Mordenite ( ,  )  [36]. ................................................................................................................................... 15 Figure 11. Product distribution over Pt/H-Beta at 2 MPa, H2, and 270°C. Trans-decalin (■), cis-decalin (○), isomers (  ), ring opened products ( ), cracking products (♦), and  heavy products ( ) [36]. .................................................................................................. 16 Figure 12. Typical isomer products as reported by Kubicka et al. [36]. ........................... 16 viii  Figure 13. Typical ring opened products as reported by Kubicka et al. [36]. ................... 17 Figure 14. Reaction scheme of decalin transformations on Pt-modified zeolite Beta. D, I, R and C stand for decalin, skeletal isomers of decalin, ring opened products (C 10alkylnaphthenes) and cracking products (products with less than 10 carbon atoms in the molecule), respectively. Indices O and OO denote an olefin and diene, respectively [29]. 20 Figure 15. Kinetic model prediction (solid line) and experimental data (open symbols) at different reaction conditions [29]. .................................................................................... 24 Figure 16. Reaction mechanism of decalin ring opening reaction [42]. ........................... 26 Figure 17. Effect of temperature and pressure on decalin conversion for Ir/H-Beta-ALD [30]. ................................................................................................................................... 28 Figure 18. Selectivity of reaction products versus decalin conversion at 250°C and 2 MPa [30]. ................................................................................................................................... 29 Figure 19. The effect of reaction temperature (A) and pressure (B) on selectivity to isomers in decalin ring opening over Ir/H-Beta-ALD [30]. ................................................ 30 Figure 20. The effect of reaction temperature (A) and pressure (B) on selectivity to ring opened products (ROP) in decalin ring opening over Ir/H-Beta-ALD [30]........................ 31 Figure 21. Catalysts preparation steps flow diagram. ...................................................... 35 Figure 22. Schematic diagram of reactor and data collection system. ............................ 39 Figure 23. Activity of Ir(2)/H-Beta-25, Ir(2)/H-Beta-350 and Pd(2)/H-Y-30 catalysts at T=350°C and P=3 MPa. ...................................................................................................... 42 Figure 24. Decalin conversion as a function of time for fresh and used catalysts at 325°C and 3 MPa, ........................................................................................................................ 43 Figure 25. Ring opened products content for Ir(2)/H-Beta-25, Ir(2)/H-Beta-350 and Pd(2)/H-Y-30 catalysts at T=350°C and P=3 MPa.............................................................. 44 Figure 26. Activity of Ir(2)/H-Beta-25 catalyst at P=3 MPa and T=275-350°C.................. 45 Figure 27. Activity of Ir(2)/H-Beta-25 catalyst at P=5 MPa and T=275-350°C.................. 45 Figure 28. Activity of Ir(2)/H-Beta-25 catalyst at P=6 MPa and T=275-350°C.................. 46 Figure 29. Activity of Ir(2)/H-Beta-25 catalyst at T=275°C and P=3-6 MPa. ..................... 47 Figure 30. Activity of Ir(2)/H-Beta-25 catalyst at T=300°C and P=3-6 MPa. ..................... 47  ix  Figure 31. Activity of Ir(2)/H-Beta-25 catalyst at T=350°C and P=3-6 MPa. ..................... 48 Figure 32. Product concentrations versus total decalin conversions at T=275-350°C and P=3-6 MPa (fitted lines are trend lines). ........................................................................... 51 Figure 33. Ring opened product concentration as a function of conversion at T=275350°C and P=3 MPa. .......................................................................................................... 52 Figure 34. Ring opened product concentration as a function of conversion at T=275350°C and P=5 MPa........................................................................................................... 52 Figure 35. Ring opened product concentration as a function of conversion at T=275350°C and P=6 MPa. .......................................................................................................... 53 Figure 36. Ring opened product concentration as a function of conversion at P=3-6 MPa and T=275°C. ..................................................................................................................... 53 Figure 37. Ring opened product concentration as a function of conversion at P=3-6 MPa and T=300°C. ..................................................................................................................... 55 Figure 38. Ring opened product concentration as a function of conversion at P=5-6 MPa and T=325°C. ..................................................................................................................... 55 Figure 39. Ring opened product concentration as a function of conversion at P=3-6 MPa and T=350°C. ..................................................................................................................... 56 Figure 40. Skeletal isomers of decalin product concentration as a function of conversion at T=275-350°C and P=3 MPa. .......................................................................................... 57 Figure 41. Concentration of Skeletal isomers of as a function of conversion at T=275350°C and P=5 MPa. .......................................................................................................... 57 Figure 42. Skeletal isomers of decalin product concentration as a function of conversion at T=275-350°C and P=6 MPa. .......................................................................................... 58 Figure 43. Skeletal isomers product concentration as a function of conversion at P=3-6 MPa and T=275°C. ............................................................................................................. 59 Figure 44. Skeletal isomers product concentration as a function of conversion at P=3-6 MPa and T=300°C. ............................................................................................................. 59 Figure 45. Skeletal isomers product concentration as a function of conversion at P=5-6 MPa and T=325°C. ............................................................................................................. 60  x  Figure 46. Skeletal isomers product concentration as a function of conversion at P=3-6 MPa and T=350°C. ............................................................................................................. 60 Figure 47. Proposed reaction mechanism for decalin conversion over Ir/H-Beta-25 catalyst. Indices o and oo stand for olefin and diene, respectively. ................................ 63 Figure 48. Mole Balance for Lumped Systems [45]. ......................................................... 69 Figure 49. Measured (points) and model predicted (line) concentrations as a function of time. .................................................................................................................................. 74     1 Figure 50. Arrhenius plot of ln k j versus   for all reaction temperatures tested. ... 75 T  Figure 51. Simplified temperature-programmed reduction mechanism [47]..……………...86 Figure 52. Isotherm linear plot……………………………………………………………………………………..93 Figure 53. Isotherm log plot………………………………………………………………………………………….94 Figure 54. BET surface area plot……………………………………………………………………………………96 Figure 55. Langmuir surface area plot…………………………….…………………………………………….98 Figure 56. t-plot Harkins and Jura…………………………….…………………………………..………......100 Figure 57. BJH adsorption cumulative pore volume….…………………………………..…………...102 Figure 58. BJH adsorption dV/dw pore volume…….….…………………………………..…………...103 Figure 59. BJH adsorption dV/dlog(w) pore volume…….….…………………………………….....104 Figure 60. BJH adsorption pore area…….….…………………………………………………………….....105 Figure 61. BJH adsorption dA/dw pore area…….….…………………………………………………....106 Figure 62. BJH adsorption dA/dlog(w) pore area…….….………………………………………….....107 Figure 63. BJH desorption cumulative pore volume.….……………………………………………....109 Figure 64. BJH desorption dV/dw pore volume.….…………………………………….…………......110 Figure 65. BJH desorption dV/dlog(w) pore volume.….….………………………….…………......111 Figure 66. BJH desorption cumulative pore area.….….………………………….…………………….112 Figure 67. BJH desorption dA/dw pore area.….….………………………….…………….…………….113 xi  Figure 68. BJH desorption dA/dlog(w) pore area.….….………………………….……………………114 Figure 69. TCD signal versus time for TPR and CO chemisorption experiments….……….119 Figure 70. Temperature versus time for TPR and CO chemisorption experiments….....120 Figure 71. TCD signal versus temperature for TPR and CO chemisorption experiments…………………………………………………………….….….………………………….………………121 Figure 72. TCD concentration versus time for TPR and experiment.…….……………….......122 Figure 73. TCD concentration versus temperature for TPR and experiment.……..……....123     1 Figure 74. Arrhenius plot of ln k j versus   for all k j at all temperatures tested....180 T  Figure 75. Average decalin conversions at T=350°C and P=6 MPa. …………………………..183 Figure 76. Average decalin conversions at T=275°C and P=3 MPa. ............................... 184 Figure 77. MS scan for a liquid sample collected at 120 min for the reaction performed at T=350°C and P=6MPa……………………………………………………………………………………………..187  xii  List of Abbreviations Aj  Pre-exponential factor of reaction j  aj  Catalyst deactivation factor of reaction j  BET  Brunauer-Emmett-Teller  C  Cracked products  Ci  Concentration of species i, mol/l  D  Decalin  DBT  Dibenzothiophene  DH  Dehydrogenated products  DHN  Decalin  Eaj  Activation energy of reaction j  FID  Flame Ionization detector  GC  Gas chromatograph  HGO  Heavy gas oil  HP  Heavy products  R  Ring opened products  RC  Ring contraction/isomer products  RO  Ring opened products  ROP  Ring opened products  I  Skeletal isomer products  k  Rate constant, 1/(min g)  K  Reaction equilibrium constant  LCO  Light cycle oil  L-H  Langmuir-Hinshelwood  LP  Light products  mcat  Catalyst mass, kg/m3  MS  Mass spectroscopy xiii  R2  Degree of explanation  SCO  Synthetic crude oil  STP  Standard temperature and pressure  THN  Tetralin  TPR  Temperature-programmed reduction  v  Volumetric flow rate, m3/min  V  Volume, m3  ZH  Acidic catalyst site  ZIr  Iridium metallic catalyst site  Greek Ωj  Catalyst effectiveness factor of reaction j  ρ  Density, kg/m3  Ѳ  Fraction coverage of metallic catalyst site  Ѳ*  Fraction coverage of metallic catalyst site  Subscripts exp  Experimental  pred  Model predicted  j  Reaction j  i  Chemical species i  o  Olefin  oo  Dien  cat  Catalyst  xiv  Acknowledgements I offer my deepest appreciation and gratitude to my supervisor, Professor Kevin Smith, for his continuous guidance and support throughout my study. My thanks go to Professor Mark Martinez and Professor Xiaotao Bi for being part of my examination committee. I also extend my sincere gratefulness to the Research and Development Center of Saudi Aramco for their sponsorship. I thank my friends and colleagues in the Catalysis Group: Farnaz Sotoodeh, Hooman Rezaei, Shahrzad Jooya, Vickie Whiffen, Shahin Goodarznia, Ross Kukard, Pooneh Ghasvareh, Zhuangzhi Wu, for their help when I needed it. My appreciation also goes to the staff in the administration, store and workshop of Chemical & Biological Engineering for their cooperation. Finally, special thanks go to my parents, my sister, my brother and my wife for their love and care throughout my journey.  xv  Dedication To my father my mother my sister my brother  To my lovely wife  xvi  Chapter 1.  Introduction  1.1 Background Health and environmental concerns associated with societies use of fossil fuels have prompted regulatory actions to limit the emissions of contaminants such as hydrocarbons, carbon monoxide, nitrogen oxides and aromatic-produced particulate matter. In addition, aromatics reduce the quality of middle-distillate fuels because of poor ignition properties, i.e. low cetane number in diesel fuel and high smoke point in jet fuel. This calls for new technologies to improve the quality of fuels [1]. In Canada, the oil sands resource is a strategic source of energy supply for North America with established reserves of 169.9 billion barrels and potential reserves of 300 billion barrels, upon improving extraction technologies. As shown in Figure 1, Canada ranks second in terms of proven reserves of crude oil [2]. In terms of daily production, 1.5 million barrels/day were produced in 2009 and the production is estimated to increase to 3 million barrels/day in 2014 and up to 5 million barrels/day in 2030. Annual revenues from oil sands reached $12.5 billion in 2003 and it is estimated to reach $43 billion in 2014 based on projected production. In 2009, over 136,000 people were directly employed in the oil sands industry [3]. Figure 2 shows an overview of a Canadian oil sands upgrading system and a generic U.S. refinery system [4]. Canadian oil sands upgrading consists of three main stages: extraction and washing to recover the oil, C/H ratio improvement by carbon rejection (using fluid coker technology), or H2 addition, (by, for example, LC-Fining), and finally hydrotreating to remove metal, sulfur and other contaminants to produce a synthetic sweet crude oil. Although bitumen-derived synthetic crude oil (SCO) has low sulfur content and zero residues, the high cyclo-paraffinic and aromatic content causes  1  processing difficulties that lead to decreased attractiveness of SCO [1]. In fact, a generic U.S. refinery cannot process SCO without further treatment.  259.9  Saudi Arabia 169.9  Alberta*  137.6  Iran  Iraq  115  Kuwait  101.5  Venezuela  99.4  United Arab Emirates  97.8 60  Russia  44.3  Libya  37.2  Nigeria 0  50  100  150  200  250  300  Oil reserves, billion barrels *Total reserves in Alberta were 171.3 billion barrels: 169.9 billion barrels of oil sands and 1.4 billion barrels of conventional oil  Figure 1. World’s largest oil reserves in 2009 (in billion barrels) [2].  Table 1 shows the composition of different heavy gas oil fuels. As seen in the table, heavy gas oil (HGO) derived from bitumen has a cycloparaffin and aromatic content of more than 90% compared to 60% in conventional paraffinic HGO [4]. Figure 3 shows the typical cetane numbers for saturated and ring opened products formed from naphthalene. The cetane number is a measure of the fuel’s injection delay and is directly related to combustion quality of diesel fuel during ignition [5, 6]. The aromatic and cycloparaffinic content of HGO can be reduced using 2  commercially proven hydrogenation technologies. However, the cetane number improvement by aromatic saturation is insufficient to enhance the quality of HGO significantly as the cetane number of HGO remains relatively low [1, 7, 8]. Other commercially proven technologies such as hydrocracking can be used to saturate the aromatics and reduce the number of ring structures. However, hydrocracking produces lower carbon number paraffins which have low cetane number [9]. Therefore, the optimum process would be selective ring opening of cycloparaffins without reducing the carbon number of the paraffins produced.  Table 1. A comparison of the weight compositions of different heavy gas oil fuels [4]. Composition  “Paraffinic” HGO  HGO  Bitumen-derived HGO  wt%  wt%  wt%  Paraffins  37.9  13.6  1.8  Cyclo-paraffins  44.4  45.7  35.4  Aromatics  14.5  36.1  55.4  Polars  3.1  4.6  7.4  Cyclo-paraffins + Aromatics  58.9  81.8  90.8  3  Figure 2. Synthetic sweet crude production from Canadian oil sands upgrading system and an overview of U.S. refinery system [4].  4  Figure 3. Typical cetane numbers for saturated and ring opened products formed from naphthalene [5, 6].  1.2 Literature review Many studies have reported on the subject of selective ring opening reactions, using different feeds, catalysts, reaction systems, and reaction conditions [1, 6, 10-30]. In addition, many patents discuss the process and catalysts for selective ring opening of naphthenes [18, 31-34]. This reflects the academic and industrial importance of the reaction. In this section, the most relevant studies to the present research are reviewed. Corma et al. [20] has studied the cracking of tetralin and decalin over a series of zeolites. Medium pore zeolites (ZSM-5, MCM-22, ITQ-2), large pore zeolites (USY, Beta), ultra-large pore zeolites (UTD-1) and mesoporous zeolites (MCM-41) were tested. The reaction was performed in a fixed-bed reactor at 500°C and atmospheric pressure, with 0.005-0.100 g/g catalyst to reactant by changing catalyst weight. A gas chromatograph, connected to a thermal conductivity detector and flame ionization detector, was used to analyze the reaction products. The study found that pore size has a strong effect on  5  activity and selectivity of ring opening reactions. The highest activity was obtained for the UTD-1, due to higher diffusion rates into the catalyst pores compared to the other catalysts tested. However, this catalyst, along with USY, produced high amounts of naphthalene and coke. On the other hand, Beta zeolites produced lower naphthalene and coke yields compared to the other large pore zeolites considered, with high selectivity to ring opened products. The study concluded that in order to improve light cycle oil (LCO) by decreasing the number of aromatics and increasing the cetane index, the LCO should be reacted over a bifunctional catalyst supported on large pore zeolite USY or even better Beta zeolite. These catalysts result in the opening of naphthenic rings while minimizing the cracking of alkyl chains. Based on experimental results, Corma et al. [20] proposed a reaction mechanism for the ring opening of decalin as shown in Figure 4. The study assumed that decalin undergoes direct ring opening on acid sites to form ring opened products which is then isomerized and cracked.  Figure 4. Mechanism of decalin reactions over acid catalysts. PC: protolatic cracking, I: isomerization, β: β-scission, DS: desorption, HT: hydrogen transfer, HeT: hydride transfer, TA: transalkylation (reprinted with permission from Academic Press) [20]. 6  McVicker et al. [35] studied the selective ring opening of naphthenic molecules over several Pt, Ir, Ru, Ni metal based catalysts and metal supported catalysts. Different model  compounds  were  used  as  a  feed  including  methylcyclopentane,  methylcyclohexane (MCH), n-pentylcyclopentane (PCP), n-butylcyclohexane, decalin, perhydroindan,  bicycle[3.3.0]octane,  ethylcyclopentane,  1,1-,  1,2-,  and  1,3-  dimethylcyclopentane, and 1,2,4-trimethylcyclohexance. The reactions took place in a fixed-bed downflow reactor at different conditions. Decalin and perhydroindan reactions were carried out at 275°C, 3540 kPa, LHSV of 1.6 and 6649 std m3/m3 (2000 std ft3/barrel) H2/feed ratio. Bicyclo[3.3.0]octane reaction was carried out at 225°C, and LHSV of 1.6 and 0.8 hr-1 with the other conditions unchanged. Figure 5 shows the proposed mechanism for the conversion of multi-ring aromatics. According to the study, hydrogenation/dehydrogenation occurs on metal sites and isomerization occurs on acid sites. However, it is argued that ring opening occurs on metal sites and hydrocracking/dealkylation occurs on metal and acid sites. The figure also shows that naphthalene is hydrogenated to tetralin and decalin which are isomerized before being ring opened.  Figure 5. Key reaction for the conversion of multi-ring aromatics (reprinted with permission from Academic Press) [35]. 7  These authors reported that Ir was the most active and selective metal for cleaving unsubstituted C-C bonds in five-membered ring naphthenes (MCH and PCP) among a series of metals examined. The rates of ring opening over Ir decreased with increasing alkyl group substitution. Pt was less active than Ir but showed better performance in breaking substituted C-C bonds. Ring-opening on the Ir follows a dicarbene mechanism in which cyclopentyl rings bond perpendicularly to the Ir surface leading to a nonstatistical product distribution. Pt follows a multiplet mechanism where the cyclopentyl ring adsorbs parallel (flat) to the metal surface allowing simultaneous interaction of all C-C bonds in the ring, leading to a statistical product distribution. The parallel adsorption of trans-substituted cyclopentyl rings is inhibited on the Pt surface which explains the sensitivity of ring opening rates to cis/trans ratio (increasing with increasing cis- concentration). Ir is also the most active and selective metal for direct ring opening of sixmembered ring naphthenes. However, ring opening of six-membered ring naphthenes is much slower and less selective than cyclopentyl ring opening. In order to improve sixmembered ring opening, these rings must be isomerized to five-membered rings with minimal branching. This can be achieved by optimizing the acidity and metal/acid properties of the catalyst. Kubicka et al. [25] studied the activity, selectivity and the effect of acidity and pore structure of five zeolites for decalin ring opening reactions. Zeolites H-Beta-25, HBeta-75, H-Y-12, H-Mordenite-41, and H-MCM-20 (the number associated with the catalyst name represents the SiO2/Al2O3 molar ratio) were examined. A mixture of decalin isomers with cis:trans ratio of 2:3 was used as a starting material. The reaction took place in a 300 ml stainless steel electrically heated autoclave reactor operated at 200-300°C and a total pressure of 2 MPa, with a H2 partial pressure of 1.7 MPa (H2:decalin molar ratio of 1:13). Internal and external diffusion was suppressed by using a catalyst size below 63 µm and a stirrer speed of 1500 rpm, respectively.  8  The liquid product was analyzed using a gas chromatograph and for selected experiments the gas product was also analyzed separately. The resulting liquid product was found to contain more than 200 components. The products were grouped as follows: decalin (mixture of cis- and trans-decalin), decalin isomers (I) containing any other bicyclic structures, ring opened products (ROP) containing C10 monocyclic products, cracking products (C) containing all products with molecular weight lower than decalin, and heavy products (HP) containing all products with more than 10 carbon atoms. According to the study, decalin needs to undergo skeletal isomerization prior to ring opening in agreement with McVicker et al.’s [35] findings. The most abundant skeletal  isomers  identified  in  this  study  were  methylbicyclo[4.3.0]nonanes,  dimethylbicyclo[3.2.1]octanes, and dimethylbicyclo[3.3.0]octanes. Typical ROP groups obtained are shown in Figure 6. Propyl-ROPs, as defined in Figure 6, were the main ring opened products, and the main cracked products were C6-saturated naphthenes and isobutene, which proceeds with ring opening and isomerization simultaneously. Due to H-Y zeolites shape-selective properties, more dimethylbicyclooctane isomers were formed over H-Y zeolite, whereas methylbicyclononane isomers were more abundant over H-Beta zeolites. This led to higher formation of ethyl-ROP, as defined in Figure 6, and lower formation of propyl-ROP for the H-Y zeolite compared to H-Beta zeolite [25]. Based on the experimental results reported by Kubicka et al. [25] it was concluded that the Bronsted acid sites play an essential role in both isomerization and ring opening, in agreement with McVicker et al. [35]. It was also found that catalyst initial activity, defined as the activity after 1 h reaction time, increased with increasing Bronsted acidity (H-Beta-25 > H-Y-12 > H-Beta-75 >> H-Mordenite-20 > H-MCM-41), except for H-Mordenite-20, as shown in Figure 7. The initial activity also increased with increasing temperature as shown in Figure 7. In addition, both catalyst acidity and pore structure influenced catalyst deactivation. For the highly Bronsted acidic H-Mordenite, rapid deactivation was noticed. Despite the equal acidity of H-Y-12 and H-Beta-25, more  9  deactivation was noticed for the H-Y-12 due to the presence of large cavities enabling coke formation. Although higher initial activity was observed for H-Y-12 and H-Beta-75 resulted in higher conversion after 180 min of reaction, the conversion obtained after 9 h of reaction decreased as follows: H-Beta-25 > H-Beta-75 > H-Y-12 >> H-Mordenite-20 > H-MCM-41. As seen in Figure 8, the maximum yield of ROP over proton-form zeolites was found to be 10 mol% which is lower than the values reported for metal-modified zeolites. Figure 8 also confirms the remark made earlier that decalin needs to undergo skeletal isomerization prior to ring opening.  Figure 6. Typical ROP groups and structures (reprinted with permission from Academic Press) [25].  10  Figure 7. Decalin conversion over H-Beta-25 (■), H-Beta-75 (○), H-Y-12 (  ), H-  Mordenite-20 ( ), and H-MCM-41 ( ) at (a) 250°C, [b] 270°C and 2 MPa. Data in (b) for H-MCM-41 are at 300°C (reprinted with permission from Academic Press) [25].  11  Figure 8. Concentration of reactants and main reaction product groups as a function of conversion for H-Beta-25 and H-Beta-75(filled), H-Y-12(open), and H-Mordenite-20 (halffilled). Reactants and product groups: [a]trans-decalin (■, □, isomers ( ,  ,  ), [b]ROP ( ,  ,  ), C ( , ◊,  ), and HP (  ), cis-decalin (●,○, ), and ,  ,  ) (reprinted with  permission from Academic Press) [25]. 12  Arribas et al. [17] studied the hydrogenation and ring opening of tetralin over several catalysts, namely USY zeolite, Pt(0.25-4)/USY catalysts, Pt(1)/γ-Al2O3, Ir(1)/USY, Ir(1)/γ-Al2O3, and bimetallic Pt(1)Ir(1)/USY. Tetralin (THN)/cyclohexane weight ratio of 50/50 was used as a feed and the reaction took place in fixed-bed reactor at 275°C, total pressure of 3.0 MPa, H2/THN molar ratio of 10 and WHSV of 2.5h-1. Based on the experimental results, a reaction mechanism was proposed as shown in Figure 9. The study suggested that the isomerization (ring contraction) of the C6 naphthenic ring of decalin was the key step leading to ring opened products (ROP), in agreement with the results of McVicker et al. [35] and Kubicka et al. [25]. The presence of Pt on USY zeolite increased the rate of isomerization and consequently ring opening compared to the parent zeolite, in agreement with McVicker et al. [35]. Although this study is in agreement with McVicker et al. [35] in that it concludes that hydrogenation/dehydrogenation occur on a metal site, the authors argue that ring opening and cracking occur exclusively on acid sites, and isomerization of decalin is activated by a bifunctional route involving both metal and acid sites. In terms of ROP yield, it was noticed that the yield increased with increasing Pt and acid site proximity and increasing metal content in the range of 0.25-4 wt%. However, the ROP yield seemed to level off above 2 wt% Pt metal content. Optimum ROP yield and selectivity was obtained with Pt(2)/USY with 20 wt% yield and a 1.5 ratio of ring opening/cracking.  13  Figure 9. Proposed reaction mechanism for the hydroconversion of tetralin on bifunctional catalyst (reprinted with permission from Elsevier Science) [17].  In the second part of the study, Kubicka et al. [36] investigated the activity and selectivity of Pt supported on zeolites (Beta, Y, Mordenite) for decalin ring opening reactions. The reaction was performed at 200-250°C and 2 MPa total pressure. In order to study the effect of H2, the H2 partial pressure was varied from 0.7-3.7 MPa at 250°C reaction temperature. Other experimental procedures are as mentioned above in Kubicka et. al. [25]. Based on the experimental results, it was found that compared to parent zeolites, Pt-modified zeolites increased the initial reaction rates of isomerization and ring opening by 3 and 5 times, respectively, as shown in Figure 10. These results are in agreement with McVicker et al. [35] and Arribas et al. [17]. Figure 11 shows that ROP yields of 30 mol% were achieved. This is due to the bifunctional reaction initiation routes: protolytic cracking of decalin over Bronsted acid sites as in parent zeolites, and decalin dehydrogenation followed by protonation by Bronsted acid sites, isomerization  14  and ring opening. In addition, lower yields of cracking and heavy products were obtained for Pt/zeolites due to lower acidity resulting from an interaction between Pt metal sites and Bronsted acid sites inside zeolite channels. Furthermore, the effect of the presence of H2 was studied. It was noticed that higher H2 pressure resulted in lower heavy products and consequently lower deactivation. The conversion was 3 times higher for Pt/H-Y catalyst in the presence of H2, whereas for the Pt/H-Beta, a decrease of 10% in activity was achieved when H2 was not present. No H2 pressure effect was noticed on the rates of isomerization and ring opening as they remained unchanged.  Figure 10. Comparison of the activity of platinum-modified (open) and proton-form (filled) zeolites. Pt- and H-Beta (□, ■), Pt- and H-Y (○, ●), Pt- and H-Mordenite ( ,  )  (reprinted with permission from Academic Press) [36].  15  Figure 11. Product distribution over Pt/H-Beta at 2 MPa, H2, and 270°C. Trans-decalin (■), cis-decalin (○), isomers (  ), ring opened products ( ), cracking products (♦), and  heavy products ( ) (reprinted with permission from Academic Press) [36]. In terms of product distribution, typical isomer products and ring opened products obtained are shown in Figures 12 and 13. Similar isomers were obtained for the Pt-modified zeolites and the parent zeolites. However for the ROP products, more methyl-cC6, as defined in Figure 13, was obtained for the Pt-modified zeolites which was explained by Pt-promoting isomerization of ring opened products.  Figure 12. Typical isomer products as reported by Kubicka et al. (reprinted with permission from Academic Press) [36]. 16  Figure 13. Typical ring opened products as reported by Kubicka et al. (reprinted with permission from Academic Press) [36]. Santikunaporn et al. [5] studied the ring opening of decalin (63:37 trans:cis, pure trans, and pure cis) and tetralin on H-Y and Pt/H-Y catalysts in a fixed bed reactor. The reaction of decalin was performed at 260°C and 2 MPa total pressure with a H2:decalin molar ratio of 65. The pulse experiments were performed at 260-327°C at 0.2 MPa total pressure. The tetralin reaction was performed at 327°C and 2 MPa total pressure with a H2:tetralin molar ratio of 60. Additional experiments were conducted with physical mixtures of zeolites and metal catalysts: Pt>>H-Y where Pt/SiO2 was placed in front of HY zeolite, H-Y>>Pt where H-Y zeolite was placed in front, and two systems where Pt/SiO2 and H-Y were mixed in ratios (1:1) and (1:2). The reaction products were classified as: cracked products, ring contraction (RC) C10 products, ring opening C10 products, and dehydrogenation products. For the conversion of decalin, the highest acidity H-Y zeolite resulted in the highest initial conversion of decalin. However, it was noticed that the deactivation rate increased with increasing acidity of the zeolite. Supporting Pt on H-Y zeolite resulted in lower cracking and lower initial activity. However, the stability of the catalyst was enhanced significantly. Low cis-to-trans ratios were obtained in the product which was explained by cis-to-trans isomerization and more significantly due to higher selectivity of 17  cis-decalin conversion to ROP. It was also concluded that Pt/H-Y catalyst is more effective for the ring opening of tetralin than H-Y zeolite as the metal enhances the hydrogenation to decalin. The study also noted that ROP is a secondary product formed from ring contraction/isomer products in agreement with the studies discussed earlier [17, 25, 35, 36]. Mouli et al. [37] investigated decalin ring opening reactions with Pt-Ir supported on mesoporous Zr-MCM-41. The study was performed in a trickle bed reactor at 300400°C in H2 at a total pressure of 5.0 MPa with a liquid hourly space velocity of 1.5 h -1 and a H2 flow of 50 ml(STP)/min. The feed consisted of 80-10-10 wt% heptane, dodecane and decalin. The liquid product was analyzed using a gas chromatograph (GCMS). The products were grouped as: cracked products (C), ring opened products (RO), and heavy and dehydrogenation products. The study found that an increase in Ir led to an increase in ring opened product yield and selectivity. However, the maximum conversion achieved was 55 wt% at 400°C. The study suggested that 1.5 wt% Ir and 0.75 wt% Pt on Zr-MCM-41 was the optimum loading for high ring opening yield (15 wt%). Ardakani et al. [15] studied the gas-phase hydrogenation of naphthalene using a series of H-Y zeolites, bulk Mo2C and Mo2C/H-Y catalysts. A 10 wt% naphthalene in nheptane solution was used as feed. The reaction was carried out in a fixed bed reactor at 280-340°C in the presence of H2 (H2/naphthalene 30 mol/mol) with a total pressure of 3.0 MPa for at least 5 hr with space velocity (SV) of 7.27 h-1. The liquid product was analyzed periodically using a gas chromatograph (GC) equipped with a flame ionization detector (FID). The products were lumped into five groups as follows: light hydrocarbons (LP), mainly alkylbutane and alkylpentane, tetralin (THN),  cis-  and  trans-decalin  (DHN),  ring  opened  products  (ROP)  mainly  alkylcyclohexanes, alkylbenzenes and alkylindenes, and heavy products (HP) consisting of aromatics and naphthenes with more than 10 carbon atoms, mainly alkyltetralins. The study reported that Mo2C/H-Y increased hydrogenation and subsequently increased formation of ROP compared to H-Y zeolites or bulk Mo2C. It was also noticed 18  that the yield of ROP was dependent on the SiO2:Al2O3 ratio and the Mo2C loading. A maximum ROP yield of 33 wt% was obtained with 7.4 wt% Mo 2C loading on moderate acidity H-Y zeolite (SiO2:Al2O3 molar ratio of 12:1). The authors also reported that addition of dibenzothiophene (1000 ppmw DBT) to the feed decreased the conversion of naphthalene while the tetralin and ROP selectivity remained almost unchanged. In a study of hydrogenation and ring opening of tetralin (THN), Ma et al. [38] used USY zeolite and Pt/USY catalysts to test the activity and ring opened products (ROP) yield. The reaction was performed in a fixed bed reactor at 100-300°C, a total pressure of 4.0 MPa with H2/THN ratio of 12:16. The study confirmed that cracking is a sequential reaction that follows ring opening and increases significantly with an increase in catalyst acidity. By impregnating the USY zeolite with Pt, the yield of ROP increased significantly. This was explained by lower cracking due to less catalyst acidity and the introduction of metal sites which facilitates hydrogenation/dehydrogenation reactions that also enhances ring opening reactions. Liu and Smith [39] investigated naphthalene selective ring opening reaction over Mo2C/H-Y catalysts with a range of 7-27 wt% Mo2C loading. The reaction was carried out in a fixed bed reactor at 300°C in the presence of H2 (H2/naphthalene 20-30 mol/mol) with a total pressure of 3.0 MPa for at least 5 hr with space velocity (SV) of 1 h-1. The liquid product was analyzed periodically using a gas chromatograph (GC) equipped with a flame ionization detector (FID). The products were lumped into three groups as follows: tetralin and decalin (Hydro), ring opened products (ROP) mainly alkylcyclohexanes, alkylbenzenes and alkylindenes, and aromatics and naphthenes with more than 10 carbons (Poly), mainly alkyltetralins. The study showed that the amount and strength of acid sites, including Bronsted acid sites, decreased with increasing Mo2C loading. The performance of the Mo2C/H-Y catalyst could not be obtained by mixing Mo2C and H-Y mechanically. Compared to Mo2C catalyst, higher deactivation rate was obtained for Mo2C/H-Y due to carbon deposition on acidic sites. Higher selectivity of Hydro products (98.9 wt%) were obtained 19  using Mo2C catalyst with only 0.8 wt % ROP selectivity compared to 62.4-66.3 wt% Hydro products and 19.3-22.1 wt% ROP selectivities for the Mo2C/HY. Kubicka et al. [29] also studied the kinetics of ring opening of decalin over Pt/HBeta zeolite for the reaction conditions 200-290°C, 1-6 MPa (0.7-5.6 MPa H2 partial pressure) and catalyst concentration of 10-40 g/l. Other experimental conditions were as described above [36]. Based on the experimental results, a reaction mechanism was proposed as shown in Figure 14. The reaction mechanism consists of the following steps: skeletal isomerization of decalin, ring opening or isomerization and, cracking of ROP alkyl branches.  Figure 14. Reaction scheme of decalin transformations on Pt-modified zeolite Beta. D, I, R and C stand for decalin, skeletal isomers of decalin, ring opened products (C10alkylnaphthenes) and cracking products (products with less than 10 carbon atoms in the molecule), respectively. Indices  O  and  OO  denote an olefin and diene, respectively  (reprinted with permission from Elsevier Science) [29]. As the catalyst used is bifunctional, the hydrogenation/dehydrogenation was assumed to occur on the metallic Pt sites in agreement with previous studies [17, 35, 36], isomerization occurred exclusively on acid sites in agreement with McVicker et al. [35], and ring opening and cracking only occurred on the acid sites, in agreement with Arribas et al. [17]. Also, it was assumed that the adsorption/desorption on both Pt and  20  acid sites were in quasi-equilibrium. Since the hydrogenation/dehydrogenation reactions are much faster than the reactions occurring on acid sites, they were also assumed to be at quasi-equilibrium. In addition, it was assumed that the hydrocarbons adsorb non-dissociatively on a single site whereas H2 adsorbs dissociatively on two sites. The reactions occurring on the acid sites were assumed to be rate determining. Based on the proposed elementary reaction steps of the mechanism shown in Table 2, a kinetic model was derived using the Langmuir-Hinshelwood approach and the mass balance equations of a batch reactor. Using the results obtained experimentally, model parameters were estimated by solving the differential equations for all chemical species using the software package Modest [40]. The minimization of the objective function, defined as the sum of squares of residuals, was achieved using the SimplexLevenberg-Marquardt method. The temperature dependence of the rate, adsorption and equilibrium constants was described by the Arrhenius and van’t Hoff equations, respectively. The H2 concentration in the liquid phase was calculated using Henry’s constant for the H2-n-decane system [41]. The estimated parameters are shown in Table 3. Figure 15 shows the experimental data and model predictions. Most of the parameters as reported were estimated with less than 10% standard error.  21  Table 2. Description of reaction steps (reprinted with permission from Elsevier Science) [29].  22  Table 3. Estimated kinetic parameters for the RO Langmuir-Hinshelwood kinetic model (reprinted with permission from Elsevier Science) [29].  Ai: pre-exponential factor of reaction step i Eai: activation energy of reaction step i H: reaction enthalpy Subscripts: ads-HC: hydrocarbon adsorption reaction step ads-H2: H2 adsorption reaction step eq1: equilibrium of reaction step 1  23  Figure 15. Kinetic model prediction (solid line) and experimental data (open symbols) at different reaction conditions (reprinted with permission from Elsevier Science) [29]. 24  Mouli et al. [42] studied decalin ring opening reactions over Pt-Ir and Ni-Mo carbide supported on H-Y and H-Beta catalysts. The study was performed in a trickle bed reactor at 200-260°C in H2 at a total pressure of 5.0 MPa with a liquid hourly space velocity of 1.5 h-1 and a H2 flow of 50 ml (STP)/min. The feed consisted of decalin:nheptane in a  1:9 volumetric ratio. The liquid product was analyzed using a gas  chromatograph (GC-MS). The proposed reaction mechanism is shown in Figure 16. As shown in the figure, the products were grouped as: cracked products (C), ringcontraction products (RC), ring opened products (RO), dehydrogenation products (DH) and cracking and dealkylated products. From the figure, the study confirmed the finding first reported by McVicker et al. [35] that the route toward ring opened products is through  ring  contraction  or  isomerization.  The  study  also  stated  that  hydrogenation/dehydrogenation occurred on metal sites whereas the ring contraction, ring opening and cracking occurred on the acid sites. However, the role of metal in ring opening was not clearly defined. The proposed mechanism suggested that possible dealkylation/cracking of decalin and ring contraction/isomer products could occur directly. Higher conversion of decalin was obtained on Pt-Ir/H-Y compared to Pt-Ir/H-Beta for all temperatures tested, with a conversion of 99% at 260°C. The RO selectivity, defined as RO wt% divided by (RC+C+DH), reached 63% at a maximum yield of 35% at 220°C on Pt-Ir/H-Y compared to 12% selectivity at a maximum yield of 15% on Pt-Ir/HBeta at 260°C. The Ni-Mo carbide supported on H-Y and H-Beta resulted in higher conversions (>80%) compared to the other supports tested (SBA-15, silica-alumina, and γ-alumina which had negligible conversion). It was also found that high conversions were obtained on Ni-Mo carbide/H-Y catalysts at relatively low temperatures (240-260°C) whereas high conversions were obtained for Ni-Mo carbide/H-Beta catalysts at relatively high temperatures (280-300°C). In terms of RO yield, Ni-Mo carbide/H-Y catalysts had a maximum yield of 33.7% at 240°C compared to a maximum yield of 21.8% at 300°C for  25  Ni-Mo carbide/H-Beta. The Ni-Mo carbide/H-Y catalysts had a maximum 40% RO selectivity at 240°C compared to a maximum of 26% at 280°C for the Ni-Mo carbide/HBeta. Based on these results, the study suggested that the H-Y catalyst had higher yield and selectivity than H-Beta catalyst for both Pt-Ir and Ni-Mo carbide catalysts. A comparison of RO yield and selectivity on Pt-Ir and Ni-Mo carbide supported on H-Y are shown in Table 4. As shown, the Ni-Mo carbide/H-Y gave a maximum RO yield of 33.7% at 240°C which is comparable to the yield of 31.7% at 220°C over Pt-Ir/HY. However, the Pt-Ir/H-Y gave a higher selectivity of 65.1% at 220°C compared to Ni-Mo carbide /H-Y selectivity of 39.8% at 240°C.  Figure 16. Reaction mechanism of decalin ring opening reaction (reprinted with permission from Elsevier Science) [42].  26  Table 4. Comparison of RO yields and selectivity on Pt-Ir and Ni-Mo carbide supported on H-Y (reprinted with permission from Elsevier Science) [42].  In one of their more recent publications, Kubicka et al. [30] studied the ring opening of decalin over Ir supported on zeolite catalysts. The study focused on the ring opened products using 1 wt% Ir or 2 wt% Pt impregnated on H-Y-12, H-Beta-300, HBeta-25. Also 2.3 wt% Ir was impregnated on H-Beta-25 using the atomic layer deposition (ALD) technique [43]. The same experimental setup was used as in their previous studies [25, 29, 36] with operating temperature in the range of 250-310°C and pressure of 2-6 MPa. The study found that identical decalin conversion versus time data was obtained for different catalysts with high acidity. The study therefore suggested that for the high acidity catalysts, decalin conversion is neither affected by different zeolite support structures (H-Y or H-Beta) nor metal type (1 wt% Ir versus 2 wt% Pt). For less acidic catalysts using H-Beta-300 as the support, higher decalin conversion was found for the 2 wt% Pt/H-Beta-300 catalyst versus the 1 wt% Ir/H-Beta-300. This however would not give a direct comparison of the effect of metal as the metal percentage in each catalyst was different. Figure 17 shows the effect of temperature and pressure on the conversion, which increased with increasing temperature. However, the study reported unexpectedly that the conversion decreased as the H2 pressure increased. The pressure effect was significant at 250°C but the effect of pressure decreased as the reaction temperature increased. This was explained by the reaction equilibrium between decalin and isomers and that temperature increase favored decalin conversion.  27  In terms of the product selectivity, as shown in Figure 18, the study confirmed that isomers are the primary product of decalin ring opening, followed by ring opened products then cracked products. From Figure 18, the study concluded that higher ring opened products and cracking products were obtained for the Ir catalysts versus Pt. Also H-Y catalysts yielded higher ring opened and cracked products selectivity compared to H-Beta. The study also suggested that mild catalyst acidity favors high ring opened selectivity based on Ir/H-Beta-ALD results in Figure 18.  Figure 17. Effect of temperature and pressure on decalin conversion for Ir/H-Beta-ALD (reprinted with permission from Kluwer Academic Publishers) [30]. The study also investigated the effect of temperature and pressure on the selectivity of isomers and ring opened products for the Ir/H-Beta-ALD catalyst, as shown in Figures 19 and 20. The selectivity to isomers increased with increasing temperature; on the other hand the selectivity of ring opened products decreased due to cracking of ring opened products. Figures 19 and 20 also show that the selectivity to isomers decreased as the pressure increased, leading to increased ring opened products.  28  Figure 18. Selectivity of reaction products versus decalin conversion at 250°C and 2 MPa (reprinted with permission from Kluwer Academic Publishers) [30]. 29  Figure 19. The effect of reaction temperature (A) and pressure (B) on selectivity to isomers in decalin ring opening over Ir/H-Beta-ALD (reprinted with permission from Kluwer Academic Publishers) [30].  30  Figure 20. The effect of reaction temperature (A) and pressure (B) on selectivity to ring opened products (ROP) in decalin ring opening over Ir/H-Beta-ALD (reprinted with permission from Kluwer Academic Publishers) [30].  1.3 Summary of literature review and study objectives  As shown in the literature review, many studies have explored the reaction of selective ring opening using different supported and unsupported catalysts. For multiring naphthenes, typical model compounds used as a feed include decalin [5, 20, 25, 29, 30, 36, 37, 42], tetralin [17, 38] and naphthalene [15, 39]. Reactor types used were either packed-bed continuous flow reactors or continuously-stirred batch reactors. 31  In terms of the reaction mechanism of the selective ring opening, many studies [6, 25, 29, 30, 35-37, 42] agreed that the reaction starts with naphthenic ring saturation, followed by isomerization then ring opening and eventually cracking. However, there is still some debate on the catalyst sites used (metal versus acid sites) for each reaction step. In terms of catalyst, McVicker et al. [35] examined different metal (Pt, Ir, Ru, Ni) and metal supported catalysts, and concluded that Ir was the most active and selective metal for the ring opening of both five-membered ring naphthenes and six-membered ring naphthenes. However, ring opening of six-membered ring naphthenes is much slower and less selective than five-membered ring naphthenes. In order to improve sixmembered ring opening, these rings must be isomerized to five-membered rings with minimal branching, by optimizing the acidity and metal/acid properties. This can be achieved by supporting Ir on an acidic support, i.e. a zeolite, to facilitate the isomerization reactions. The study by Corma et al. investigated several zeolites with variable pore sizes, medium-sized pore zeolites (ZSM-5, MCM-22, ITQ-2), large pore zeolites (USY, Beta), ultra-large pore zeolites (UTD-1) and mesoporous zeolites (MCM-41). Among all the zeolites tested, Beta zeolites produced lower cracking, naphthalene and coke yields with high selectivity of ring opened products. The superiority of Beta zeolites for selective ring opening reactions was also confirmed by Kubicka et al [25]. Based on these studies, supporting Ir on H-Beta should give an efficient catalyst for selective ring opening, a catalyst formulation which has not been explored until very recently by Kubicka et al. [30]. However, no kinetic model was developed for this catalyst. Therefore, the aim of this study was to examine the reaction rates for the selective ring opening of a multi-ring model compound over Ir/H-Beta-25 catalyst. Specifically, the effect of reaction conditions, namely temperature and pressure, on the ring opened product yield was investigated. Decalin was used in this study to eliminate the ring saturation step and focus on the ring opening reactions. The reaction was 32  performed in a continuously-stirred batch reactor system as it is most efficient for studying reaction kinetics. Based on the experimental results, a kinetic model for the ring opening of decalin, namely the molecular Langmuir-Hinshelwood (L-H) model, was developed and validated. The model parameters were estimated by minimizing the difference between measured experimental data and model predictions by the sum of least-squares method.  33  Chapter 2.  Experimental  2.1 Catalyst preparation Three catalysts were synthesized for this study: Ir(2)/H-Beta-25, Ir(2)/H-Beta350, and Pd(2)/H-Y-30. The number in parentheses next to the metal name represents the metal weight percent, whereas the numbers next to the zeolites, 25, 350 and 30 represent the SiO2/Al2O3 molar ratio of the zeolite. Figure 21 shows a flow diagram that summarizes the catalysts preparation steps. In order to prepare these catalysts, NH4-Beta-25 (CP814E), H-Beta-350 (CP811C-300) and H-Y-25 (CBV720) zeolites were obtained from Zeolyst International. The ammonium form zeolite was transformed to a proton form using a step calcination process, where the zeolite was ramped to 120°C at a rate of 10°C/min step, calcined at 120°C for 2 hours, ramped to 500°C at the same rate of 10°C/min and finally calcined at 500°C for 5 hours. The calcination was performed in stagnant air environment. IrCl3.xH2O (52 wt% Ir) and PdCl2 (≥ 99.9%) precursors were obtained from Pressure Chemical Company and Sigma-Aldrich, respectively. Supports H-Beta-300 (5.79 g), H-Beta-25 (6.18 g) and H-Y-25 (4.16 g) were impregnated with 0.31 M Ir3+, 0.13 M Ir3+ and 0.40 M Pd2+ aqueous solutions prepared from the corresponding precursors to get the desired Ir and Pd loading of 2 wt% by the incipient wetness method. The incipient wetness method requires the volume of the metal solution to be the same as the total pore volume of the zeolites. This was achieved by measuring the total pore volume of the zeolite analytically, as explained later in the catalyst characterization section. After impregnation, the catalysts were aged for 24 hours and then calcined in a muffle oven in air at 500°C for 3 h [44]. No catalyst reduction was performed as the catalysts were reduced in the reactor (in-situ) during the reactor heat up and stabilization period.  34  Figure 21. Catalysts preparation steps flow diagram.  35  2.2 Catalyst characterization Temperature-programmed reduction (TPR) of the calcined catalysts was performed using a Micromeritics Autochem II 2920. A catalyst sample (0.1 g) was loaded into the reactor, pre-treated with 50 ml (STP)/min He while heating to 300°C at a rate of 20°C/min and holding the final temperature for 2 h. After cooling to ambient temperature in He flow of 50 ml (STP)/min, the reactor was heated at a rate of 10°C/min to a final temperature of 500°C in 30 ml (STP)/min flow of 10% H 2 in Ar for the TPR analysis, holding the final temperature for 1 h. The hydrogen consumption was determined by monitoring the change in the gas mixture concentration using a thermal conductivity detector (TCD) (refer to Appendix A for more details). Using the Micromeritics Autochem II 2920, the CO uptake of the reduced catalyst was determined by pulsed chemisorption in order to calculate metal dispersion. After cooling to ambient temperature in a He flow of 50 ml (STP)/min at the end of the TPR analysis, the catalyst sample was repeatedly injected with CO pulses from a 20 ml (STP)/min 10% CO in He flow, until there was no further CO uptake by the sample as indicated by the TCD. The CO uptake by the sample is determined by finding the difference between total amount of CO injected and the amount eluted from the sample (refer to Appendix A for more details). The total BET surface area, pore volume, and average pore width of the reduced catalysts was measured by the Micromeritics ASAP 2020 Accelerated Surface Area and Porosimetry analyzer. The catalyst sample was placed in the catalyst tube, degassed at 1.33 kPa/s and a temperature rate of 10°C/min until 0.04 kPa and 300°C. The temperature was then held at 300°C for 240 min. After that, the sample was transferred to the analysis section to analyze BET surface area using N 2 (refer to Appendix A for more details).  36  2.3 Catalytic activity measurements The desired reaction was performed in a continuously stirred 300 ml autoclave batch reactor. The reaction was performed at temperatures of 275, 300, 325 and 350°C and pressures of 3, 5 and 6 MPa for each temperature tested. The internal and external diffusion effects were suppressed by using a catalyst particle size below 63 µm and stirring at 1500 rpm, respectively as reported by Kubicka et al. [25]. Figure 22 shows a schematic diagram of the reactor and data collection system used in the study. At the start of each reaction experiment, the reactor was initially charged with 100 ml of decalin (mixture of cis + trans - anhydrous, ≥99%, Sigma-Aldrich) and 0.5 g of catalyst. The reactor was then sealed and purged with N2 for 15 minutes to remove air from the system followed by purging with H2 for 15 minutes. Subsequently the reactor was pressurized with H2 up to the corresponding desired pressure at ambient temperature. The reactor was then ramped to the desired temperature. During the course of the reaction, liquid samples (0.1 ml) were collected periodically. The first sample was collected 45 minutes after the start of the ramping to allow the temperature to stabilize. In the first hour of sample collection, a sample was collected every 15 minutes. After that, a liquid sample was collected every hour up to 5 hours of reaction time after the first sample collection. The controller shown in Figure 22 controlled the reactor temperature and mixing speed. A thermocouple placed inside the reactor measured the reaction temperature and a signal is sent to the controller. The controller in turn sent a signal to the heater jacket around the reactor to adjust the heater output based on the desired temperature set in the controller. A magnetic sensor monitored the mixing speed of the mixer and transmitted a signal to the controller. Based on the signal received, the controller sent another signal to the mixer motor in order to adjust the mixing speed. The pressure was monitored by the controller using a pressure transducer connected to the reactor. The temperature,  37  pressure and mixing speed received by the controller were sent to a PC through a RS232 connection where it was recorded every second. The liquid samples collected were analyzed by gas chromatograph using 14-A Shimadzu gas chromatograph equipped with flame ionization detector (FID) and AT™-5 25 M x 0.53 mm capillary column. To confirm product identities, a Shimadzu QP-2010S GC/MS equipped with Restek RTX5 30 M x 0.25 mm capillary column was used. In addition, gas samples were collected occasionally and analyzed using a gas chromatograph. The results indicated low amounts of cracked products in the gas phase compared to the liquid phase. Therefore, the products present in the gas phase were ignored in the following discussion. The reproducibility of the system was confirmed by repeating selected experiments and the results obtained were in agreement with less than ±11 % error in decalin conversion. The details of the error analysis are shown in Appendix D.  38  Figure 22. Schematic diagram of reactor and data collection system.  39  Chapter 3.  Results and discussion  3.1 Catalyst characterization Table 5 shows the SiO2/Al2O3 molar ratio, the BET surface area, pore volume and average pore diameter of all catalysts used in the present study. Detailed analysis results are shown in Appendix A.1. The SiO2/Al2O3 molar ratios are as reported by the manufacturer. The SiO2/Al2O3 molar ratios are related to the acidity of the catalysts; as the SiO2/Al2O3 molar ratio increases, lower acidities are expected for the corresponding catalysts. Therefore, the catalyst acidity is expected to decrease in the order: Ir(2)/HBeta-25 > Pd(2)/H-Y-30 >> Ir(2)/H-Beta-350. From Table 5, it can also be noticed that the specific surface area decreased after impregnating the catalysts with the Ir or Pt except for Ir/H-Beta-350.  Table 5. SiO2/Al2O3 molar ratio, BET surface area, pore volume and average pore diameter of all catalysts Catalyst  SiO2/Al2O3  Specific surface area  Pore volume  Pore size  Metal  molar ratio a  (m2/g)  (cm3/g)  (nm)  content  Measured Reported a  (wt%)  H-Beta-25  25  587±62  680  0.73±0.09  4.95±.30  -  H-Beta-350  350  505±87  620  0.37±0.07  2.89±.09  -  H-Y-30  30  782  780  0.48  2.46  -  Ir(2)/H-Beta-25  25  573±11  -  0.72±0.05  5.01±0.42  2  Ir(2)/H-Beta-350  350  521  -  0.37  2.85  2  Pd(2)/H-Y-30  30  755  -  0.47  2.49  2  a  Reported values by manufacturer, Zeolyst International  40  Table 6 shows the metal dispersion, reduction temperature and degree of reduction for the metal-containing catalysts. Detailed analysis results are shown in Appendix A.2. The metal dispersions of Table 6 range between 12-23 mol%. The reduction temperatures were relatively low compared to the reaction temperatures, which ensures complete reduction of the catalyst in-situ, prior to reaching the desired reaction temperature. Although the degree of reduction of Ir(2)/H-Beta-25 and Pd(2)/HY-30 catalysts were relatively high with values >75 mol%, a lower degree of reduction was obtained for the Ir(2)/H-Beta-350 catalyst with only 58.9 mol%. This could be due to the lower acidity of the Ir(2)/H-Beta-350 compared to the other catalysts considered.  Table 6. Metal dispersion, reduction temperature and degree of reduction for all metal catalysts. Catalyst  Metal  Metal  Reduction  Degree of  content  dispersion  Temperature  reduction  (wt%)  (mol%)  (°C)  (mol%)  Ir(2)/H-Beta-25  2  22.9  153.6  97.9  Ir(2)/H-Beta-350  2  17.4  173.7  58.9  Pd(2)/H-Y-30  2  12.1  78.8  79.5  3.2 Catalytic activity 3.2.1 Preliminary studies to test the activity of different catalysts  Figure 23 shows the activity of the Ir(2)/H-Beta-25, Ir(2)/H-Beta-350 and Pd(2)/HY-30 catalysts as reflected in the decalin conversion, measured at the same operating conditions of 3 MPa H2 and 350C. A higher activity was obtained for the Ir(2)/H-Beta-25 41  catalyst compared to the Ir(2)/H-Beta-350 and Pd(2)/H-Y-30 catalysts, both of which had very similar conversions.  60  Conversion, wt%  50 40 30 20  Ir(2)/H-Beta-25 Ir(2)-H-Beta-350 Pd(2)/H-Y-30  10 0 0  50  100 150 Time, min  200  250  Figure 23. Activity of Ir(2)/H-Beta-25, Ir(2)/H-Beta-350 and Pd(2)/H-Y-30 catalysts at T=350°C and P=3 MPa. The Ir(2)/H-Beta-25 and the Ir(2)/H-Beta-350 had the same metal content and zeolite support, although the H-Beta-25 would have higher acidity than the H-Beta-350. A direct comparison between these catalysts leads to the conclusion that higher activity is achieved with higher acidity, confirming that catalyst acidity plays an important role in reaction activity. However, as the reaction proceeded, a lower increase in the conversion was noticed for the Ir(2)/H-Beta-25 due to catalyst deactivation. The deactivation effect was confirmed by recovering the Ir(2)/H-Beta-25 catalyst and repeating the experiment with the used catalyst. The results showed lower catalyst activity than the fresh catalyst at the same experimental conditions. Figure 24 shows the results of the two experiments using the fresh and used Ir(2)/H-Beta-25 catalyst. Note that the x-axis is a normalized time variable which is independent of catalyst mass. The normalized time variable was used to take into account the different catalyst weights in the fresh catalyst versus recovered catalyst experiments. Clearly, catalyst 42  deactivation occurred as lower conversions were obtained with the used catalyst compared to the fresh catalyst. However, the deactivation effect on the conversion was relatively small with the difference in conversion at the end of the run less than 5 wt%. Hence, over a run period of 5 hours, the extent of catalyst deactivation was ignored when developing the reaction kinetics in the following sections. 70  Conversion, wt%  60 50 40  Fresh Used  30 20 10 0 0  0.25  0.5 0.75 1 1.25 1.5 Time, min*g catalyst/g decalin  1.75  2  Figure 24. Decalin conversion as a function of time for fresh and used catalysts at 325°C and 3 MPa, Although the Ir(2)/H-Beta-350 and the Pd(2)/H-Y-30 have different acidities, the similar catalyst activity indicate that the metal and the zeolite play a role in the reaction. Further experiments with Pd(2)/H-Beta-25 and Ir(2)/H-Y would shed some light on the relative roles of the metal and zeolite. Such experiments were not part of the present study since the focus here was to investigate the kinetics of the most active catalyst, namely the Ir(2)/H-Beta-25. In terms of the selectivity of the 3 catalysts for ring opened products, defined as products with ten carbons and one or no cyclic rings, Figure 25 shows that a higher content of ring opened products was obtained for the Ir(2)/H-Beta-25 when compared to the other catalysts at the same conversion. This indicates that Ir(2)/H-Beta-25 catalyst is not only the most active catalyst, it is also the most selective toward the 43  desired ring opened products. Hence, Ir(2)/H-Beta-25 was chosen as the focus of further study.  Ring opened products, wt%  50 40 30 20  Ir(2)/H-Beta-25  10  Ir(2)/H-Beta-350 Pd(2)/HY-30  0 0  20  40 60 Conversion, wt%  80  100  Figure 25. Ring opened products content for Ir(2)/H-Beta-25, Ir(2)/H-Beta-350 and Pd(2)/H-Y-30 catalysts at T=350°C and P=3 MPa.  3.2.2 Effect of temperature  The effect of temperature on the conversion of decalin over the Ir(2)/H-Beta-25 for the temperature range of 275-350°C is shown in Figures 26-28. The figures show that as the temperature increased, the initial catalyst activity increased. This agrees with the results obtained by Kubicka et al. for Pt/H-Beta and Pt/H-Y for the temperature range of 200-270°C [36] and for Ir/H-Beta-ALD [30] for the temperature range of 250-290°C. However, at higher temperatures (> 325 C), the end of run conversions were lower than that obtained at 300°C. This can be explained by the catalyst deactivation already described, the rate of which also increases with increased temperature. Figure 27 shows that although higher conversion was achieved initially at 325°C compared to 300°C, lower conversion was obtained at the end of run. However, Figure 28 shows that at the  44  higher pressure of 6 MPa the activities at 300°C and 325°C were similar at the end of run. Keeping in mind that the H2 is in excess in both cases, this observation supports the role of deactivation which is slower at higher pressures due to higher H2 partial pressure.  Conversion, wt%  80 60 40 T=275°C T=300°C T=350°C  20 0 0  50  100  150 Time, min  200  250  300  Figure 26. Activity of Ir(2)/H-Beta-25 catalyst at P=3 MPa and T=275-350°C.  Conversion, wt%  80 60 40 T=275°C T=300°C T=325°C T=350°C  20 0 0  50  100  150 200 Time, min  250  300  Figure 27. Activity of Ir(2)/H-Beta-25 catalyst at P=5 MPa and T=275-350°C.  45  100  Conversion, wt%  80 60 40  T=275°C T=300°C T=325°C T=350°C  20 0 0  50  100  150 Time, min  200  250  300  Figure 28. Activity of Ir(2)/H-Beta-25 catalyst at P=6 MPa and T=275-350°C.  3.2.3 Effect of pressure  The effect of pressure on the decalin conversion is shown in Figures 29-31 for pressures from 3 to 6 MPa at 275, 300 and 350°C, respectively. Figure 29 indicates that the effect of pressure was minimal at 275°C. However, as the temperature increased, the effect of pressure became more significant and higher conversions were achieved at higher pressures even though H2 was in excess at all the pressures tested. This can be explained by the formation of lower heavy products at higher H2 partial pressure, leading to a reduced deactivation rate. The same results with respect to the effect of pressure were obtained by Kubicka et al. [36] for Pt/H-Y. Different results were obtained by Kubicka et al. [30] for Ir/H-Beta-ALD catalyst in which the decalin conversion increased with decreasing pressure in the temperature range 250-290°C. Different reaction temperatures would result in different equilibrium between decalin and isomer products, leading to a different pressure effect on the reaction. In addition to the different temperature range used, the difference in results between Kubicka et al. [30]  46  and the present work could be due to different catalyst preparation methods (incipient wetness in this study versus atomic layer deposition).  Conversion, wt%  80 60 40 P=3 MPa P=5 MPa P=6 MPa  20 0 0  50  100  150 Time, min  200  250  300  Figure 29. Activity of Ir(2)/H-Beta-25 catalyst at T=275°C and P=3-6 MPa.  100  Conversion, wt%  80 60 P=3 MPa P=5 MPa P=6 MPa  40 20 0 0  50  100  150 Time, min  200  250  300  Figure 30. Activity of Ir(2)/H-Beta-25 catalyst at T=300°C and P=3-6 MPa.  47  Conversion, wt%  80 60 40 P=3 MPa P=5 MPa P=6 MPa  20 0 0  50  100  150 Time, min  200  250  300  Figure 31. Activity of Ir(2)/H-Beta-25 catalyst at T=350°C and P=3-6 MPa.  3.3 Product distribution Although the feed consisted of cis- and trans-decalin only, the reaction resulted in more than 200 products (refer to Appendix E for a GC-MS scan sample). A similar number of products has been reported in previous studies [29, 36]. To simplify the discussion and development of the reaction kinetics, the products were grouped according to structural similarities. Five major groups were identified: decalin (D) which consisted of both cis- and trans-decalin; skeletal isomers of decalin (I) consisting of all products with ten carbon atoms and two cyclic rings; ring-opened products (R) consisting of all products with ten carbon atoms and one or no cyclic rings; cracked products (C) consisting of all products with less than ten carbon atoms; and finally heavy products (HP) consisting of all products with more than ten carbon atoms [29]. The reproducibility of the product distribution was confirmed by repeated injection of the same sample and the error was found to be less than 4% for all product concentrations except for cracked products which had an error of 17.25%. The relatively high error is  48  due to the relatively low concentrations of cracked products obtained. The details of the error analysis are shown in Appendix D. Based on this grouping, Figure 32 shows the product concentrations as a function of decalin conversion for all temperatures and pressures tested. The concentration of HP was less than 4 wt% for all conditions tested and was therefore ignored in further discussions and the kinetic analysis. Figure 32 shows that the major products of the studied reaction were ring opened products and decalin isomers. The cracked product concentrations were significantly lower at all temperatures and pressures. A more detailed discussion of the effect of temperature and pressure on major product concentration follows. Figures 33-35 compares the concentration of ring opened products versus total decalin conversion for the temperature range of 275-350°C at 3, 5, and 6 MPa, respectively. The concentration of ring opened products increased as the conversion increased for all temperatures and pressures. The conversion of ring opened products was slower than the production of ring-opened products, leading to increased concentration of ring opened products and relatively low production of cracked products. These results agree with previous results reported for Pt/H-Y and Pt/H-Beta in Figure 11 [36] and also agrees with the results reported for Ir/H-Beta-ALD in Figure 18 [30]. Although the ring opened product concentrations tend to increase with increased temperature at 3 MPa, no clear trend was noticed for the effect of reaction temperature on the concentration of ring opened products at higher pressures, unlike the trends for Ir/H-Beta-ALD shown in Figure 20 [30]. Figures 36-39 show the concentration of ring opened products versus total decalin conversion for the pressure range of 3-6 MPa at 275°C, 300°C, 325°C, and 350°C, respectively. The figures confirm the conclusion obtained earlier that the concentration of ring opened products increased as the decalin conversion increased for all temperatures and pressures.  49  Looking more closely at the figures, it can be seen in Figure 36 that although the concentration of ring opened product was similar for all pressures at lower conversion at 275°C, higher ring opened product concentrations were obtained at higher conversions as the pressure increased, in agreement with the results obtained for Ir/HBeta/ALD reported in Figure 20 [30].  50  Figure 32. Product concentrations versus total decalin conversions at T=275-350°C and P=3-6 MPa (fitted lines are trend lines). 51  7E-03 Concentration, mol/l  6E-03 5E-03 4E-03 3E-03 2E-03  T=275°C T=300°C  1E-03  T=350°C  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 33. Ring opened product concentration as a function of conversion at T=275350°C and P=3 MPa.  8E-03 Concentration, mol/l  7E-03 6E-03 5E-03 4E-03 T=275°C  3E-03  T=300°C  2E-03  T=325°C  1E-03  T=350°C  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 34. Ring opened product concentration as a function of conversion at T=275350°C and P=5 MPa.  52  8E-03 Concentration, mol/l  7E-03 6E-03 5E-03 4E-03 T=275°C  3E-03  T=300°C  2E-03  T=325°C  1E-03  T=350°C  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 35. Ring opened product concentration as a function of conversion at T=275350°C and P=6 MPa.  6E-03 Concentration, mol/l  5E-03 4E-03 3E-03 2E-03  P=3 MPa  1E-03  P=5 MPa P=6 MPa  0E+00 0  20  40 Conversion, mol%  60  80  Figure 36. Ring opened product concentration as a function of conversion at P=3-6 MPa and T=275°C.  53  On the other hand, Figure 37 shows that at 300°C, the highest ring opened product concentrations were obtained at the lowest pressure (3 MPa), at similar conversions. Figure 38 shows that at 325°C, higher concentrations of ring opened products were obtained at 6 MPa in the conversion range of 70-85 mol%. At higher and lower conversions, the concentrations were similar. The differences observed in Figures 36-38 are significant since the error in ring opened product concentration was relatively low at 2% as shown in Appendix D. At 350°C, Figure 39 shows that the concentration of ring opened products was similar as the pressure varied from 3 to 6 MPa showing that at this temperature the effect of pressure was not significant. Figures 40-42 show the concentration of skeletal isomers of decalin versus total decalin conversion for the temperature range of 275-350°C at 3, 5, and 6 MPa, respectively. A general trend can be noticed from all the figures that the concentration of isomers increased to some maximum and then decreased at higher conversions. This indicates that the isomers were a primary product where they are produced initially and subsequently are consumed to produce other secondary products, in agreement with previous studies [5, 17, 20, 29, 30, 36, 42].  54  7E-03 Concentration, mol/l  6E-03 5E-03 4E-03 3E-03 P=3 MPa  2E-03  P=5 MPa  1E-03  P=6 MPa  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 37. Ring opened product concentration as a function of conversion at P=3-6 MPa and T=300°C. 8E-03 Concentration, mol/l  7E-03 6E-03 5E-03 4E-03 3E-03 2E-03  P=5 MPa P=6 MPa  1E-03 0E+00 40  60 80 Conversion, mol%  100  Figure 38. Ring opened product concentration as a function of conversion at P=5-6 MPa and T=325°C.  55  8E-03 Concentration, mol/l  7E-03 6E-03 5E-03 4E-03 3E-03  P=3 MPa  2E-03  P=5 MPa  1E-03  P=6 MPa  0E+00  40  60 80 Conversion, mol%  100  Figure 39. Ring opened product concentration as a function of conversion at P=3-6 MPa and T=350°C. Figure 40 shows that at 3 MPa, the isomer concentration decreased as the reaction temperature increased from 275 to 350°C. Clearly higher temperature favored the conversion of isomers to ring opened products leading the concentration of isomers to decrease as the concentration of ring opened products increased, as shown in Figure 33. At 5 MPa, Figure 41 shows a similar trend with temperature with the exception of the reaction temperature 325°C where the highest concentration of isomers was obtained. Note also that the difference in isomer concentrations at different temperatures is smaller compared to the results at 3 MPa shown in Figure 40. The difference in isomer concentration as a function of temperature was also smaller at 6 MPa, as shown in Figure 42, compared to lower pressures. Figure 42 also shows that at 6 MPa, although similar isomer concentrations were obtained for all temperatures at lower conversion, the concentrations of isomers decreased as the temperature increased at higher conversions, similar to the lower pressure previously. These results contradict the results obtained for Ir/H-Beta-ALD reported in Figure 19  56  which showed an increase in isomer product concentration as the temperature increased at 6 MPa [30].  Concentration, mol/l  6E-03 5E-03 4E-03 3E-03 2E-03 T=275°C T=300°C T=350°C  1E-03  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 40. Skeletal isomers of decalin product concentration as a function of conversion at T=275-350°C and P=3 MPa.  6E-03 Concentration, mol/l  5E-03 4E-03 3E-03 T=275°C T=300°C T=325°C T=350°C  2E-03 1E-03  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 41. Concentration of Skeletal isomers of as a function of conversion at T=275350°C and P=5 MPa.  57  Concentration, mol/l  6E-03 5E-03 4E-03 3E-03 2E-03  T=275°C T=300°C T=325°C T=350°C  1E-03  0E+00 0  20  40 60 Conversion, mol%  80  100  Figure 42. Skeletal isomers of decalin product concentration as a function of conversion at T=275-350°C and P=6 MPa. Figures 43-46 show the concentration of skeletal isomer products versus total decalin conversion for the temperature range of 3-6 MPa at 275°C, 300°C, 325°C, and 350°C, respectively. The figures confirm the conclusion obtained earlier that the concentration of isomer products follow a parabolic trend where it increases initially, reaches a maximum and then decreases at higher conversions for all temperatures and pressures studied. By examining Figure 43, it can be seen that although the isomer concentrations were similar at lower conversions, lower isomer concentrations were obtained at higher pressures as the conversion increased at 275°C. This is in agreement with the results obtained for Ir/H-Beta-ALD at similar conditions, as shown in Figure 19 [30]. The same trend is noticed in Figure 45 at 325°C. However, a different conclusion can be made from Figure 44 as more isomers were formed at higher pressure at the reaction temperature of 300°C. Figure 46 shows no clear trend of pressure effect on the concentration of isomers at 350°C.  58  6E-03 Concentration, mol/l  5E-03 4E-03  3E-03 2E-03  P=3 MPa P=5 MPa P=6 MPa  1E-03 0E+00 0  20  40 Conversion, mol%  60  80  Figure 43. Skeletal isomers product concentration as a function of conversion at P=3-6 MPa and T=275°C.  Concentration, mol/l  6E-03 5E-03 4E-03 3E-03 2E-03  P=3 MPa P=5 MPa P=6 MPa  1E-03  0E+00 20  40  60 Conversion, mol%  80  100  Figure 44. Skeletal isomers product concentration as a function of conversion at P=3-6 MPa and T=300°C.  59  Concentration, mol/l  6E-03 5E-03 4E-03 3E-03 2E-03 P=5 MPa  1E-03  P=6 MPa 0E+00 40  60 80 Conversion, mol%  100  Figure 45. Skeletal isomers product concentration as a function of conversion at P=5-6 MPa and T=325°C.  Concentration, mol/l  5E-03 4E-03 4E-03 3E-03 3E-03 2E-03 2E-03 1E-03 5E-04 0E+00  P=3 MPa P=5 MPa P=6 MPa 40  60 80 Conversion, mol%  100  Figure 46. Skeletal isomers product concentration as a function of conversion at P=3-6 MPa and T=350°C.  60  3.4 Summary of findings Among the three catalysts tested, Ir/H-Beta-25 showed the highest activity and yield of ring opened products. In addition, the role of catalyst acidity was confirmed, with higher activity resulting from higher catalyst acidity. In terms of the effect of operating conditions, results showed that the initial catalyst activity increased as the temperature increased. At 275°C, the effect of pressure was minimal. However, as the temperature increased, the effect of pressure became more significant and higher conversions were achieved at higher pressures. The concentration of ring opened products increased as the conversion increased for all temperatures and pressures examined. At 3 MPa, the concentration of ring opened products increased with increased temperature. At 275°C, higher ring opened products concentrations were obtained at higher conversions as the pressure increased. No clear effect of reaction temperature and pressure was noticed at other reaction conditions. The highest ring-opened product yield was 52.63 mol%, obtained at a total decalin conversion of 90.31 mol% at T=325°C and P= 6 MPa.  61  Chapter 4. Reaction mechanism and kinetic study 4.1 Reaction mechanism The catalyst used for the reaction of decalin is a bifunctional catalyst containing metallic sites created by Ir and acidic sites created by H-Beta zeolite. In the present study, it was assumed that hydrogenation/dehydrogenation reactions occur on metal sites, whereas ring opening and cracking reactions occur on acid sites, in agreement with previous studies [5, 6, 29, 36, 42]. From Figure 32-46 and the detailed discussion of results above, it can be concluded that the reaction of decalin proceeds with skeletal isomerization as a primary product, followed by ring opening as a secondary product and finally cracking of ring opened products. All of these steps occur on the acid sites. The metal sites facilitate the reaction by hydrogenating and dehydrogenating reaction intermediates to improve the selectivity and eliminate H2 transfer and protolytic cracking, as reported in the literature [29, 36]. Based on these steps, a reaction mechanism for the reaction of decalin can be proposed, as shown in Figure 47 [29]. Note that the adsorption and desorption steps on both metallic and acidic sites are not shown in this simplified mechanism. In the reaction mechanism presented by Kubicka et al. [29], decalin (D) adsorbs on a metallic site and dehydrogenates to form an olefin (Do). The olefin desorbs from the metallic site and adsorbs on an acidic site to react and form a skeletal isomer intermediate (Io). Two routes for the skeletal isomer intermediate (Io) are possible: it either desorbs from the acidic site and adsorbs on a metallic site to hydrogenate and form a skeletal isomer (I), or it remains bound on the acidic site and undergoes further  62  reaction to form a ring opened product intermediate (Roo). Again, the ring opened product intermediate (Roo) either desorbs from the acidic site and adsorbs to a metallic site to hydrogenate and form ring opened product intermediates (R o and Roo), or it reacts on the acidic site to form cracked product intermediates (Co and Coo). The ring opened product intermediate (Ro) also desorbs from the metallic site and adsorbs on an acidic site to react to a cracked product intermediate (Co). Finally, the cracked product intermediates (Co and Coo) desorb from the acidic sites and adsorb on metallic sites to hydrogenate and eventually form a cracked product (C).  Figure 47. Proposed reaction mechanism for decalin conversion over Ir/H-Beta-25 catalyst. Indices o and oo stand for olefin and diene, respectively.  4.2 Kinetic development In order to develop the Langmuir-Hinshelwood kinetics for the mechanism described above, the reaction mechanism shown in Figure 47 can be written as a series of 27 elementary steps as shown in Equations 1 to 27 below. Z H and ZIr refer to acidic and Ir metal sites, respectively. Equations 1 to 4 describe the rate limiting surface reaction steps occurring on the acidic sites. Equations 11 to 16 describe the hydrogenation and dehydrogenation reaction steps occurring on the Ir metallic sites. 63  Equations 5 to 10 and 17 to 27 describe the adsorption/desorption steps occurring on the acidic and metallic sites, respectively. k1 ;K1 ZH Do ← → ZH Io  ZH Io  k2 → ZH R oo  (1) (2)  k3 ZH R oo → ZH Coo + Co  (3)  k4 ZH R o → ZH Co + Co  (4)  K5 Do + ZH ←→ ZH Do  (5)  K6 Io + ZH ←→ ZH I o  (6)  K7 R o + ZH ← → ZH R o  (7)  K8 Co + ZH ←→ Z H Co  (8)  K9 R oo + ZH ←→ ZH R oo  (9)  K10 Coo + ZH ←→  ZH Coo  (10)  K11 ZIr Do + 2ZIr H ←→  ZIr D + 2ZIr  (11)  K12 ZIr Io + 2ZIr H ←→  ZIr I + 2ZIr  (12)  K13 ZIr R o + 2ZIr H ←→  ZIr R + 2ZIr  (13)  K14 ZIr Co + 2ZIr H ←→  ZIr C + 2ZIr  (14)  K15 ZIr R oo + 2ZIr H ←→  ZIr R o + 2ZIr  (15)  K16 ZIr Coo + 2ZIr H ←→  ZIr Co + 2ZIr  (16) 64  K  17 ⎯ → 2Z Ir H 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (17)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   H 2 + 2Z Ir ←⎯  K  18 ⎯ → Z Ir D 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (18)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   D + Z Ir ←⎯  € 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    €  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (19)	
   K  20 ⎯ → Z Ir R 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (20)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   R + Z Ir ←⎯  K  21 ⎯ → Z Ir C 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (21)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   C + Z Ir ←⎯  €  K  22 ⎯ → Z Ir Do 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (22)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   Do + Z Ir ←⎯  €  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (23)	
    € K 24 ⎯→ Z Ir R o 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (24)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   R o + Z Ir ←⎯ K  25 ⎯ → Z Ir C o 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (25)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   C o + Z Ir ←⎯  € K 26 ⎯→ Z Ir R oo 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (26)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   R oo + Z Ir ←⎯ € K 27 ⎯→ Z Ir C oo 	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (27)	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   C oo + Z Ir ←⎯ 	
    € € From	
  Equations	
  1	
  to	
  4,	
  the	
  reaction	
  rates	
  can	
  be	
  written	
  as	
  follows:	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (28)	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (29)	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (30)	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  (31)	
    65  * where k, K and θi are the reaction constants, equilibrium constant, and fractional  coverage of species i on the acid sites, respectively. The adsorption/desorption steps shown in Equations 5 to 10 and 17 to 27, are assumed to be fast enough for the quasi-equilibrium hypothesis to be applied. It is also assumed that each chemical species adsorbs to a single site and H2 adsorbs dissociatively. Therefore, the equilibrium constants can be written as follows:  K 5−10 =  K17 =  θ i* θ v* ⋅ Ci θ H2  θ v2 ⋅ C H  K 18− 27 =  θi θ v ⋅ Ci  (32)  (33)  (34)  where K, ߠ,	ߠ௜∗ , C are the equilibrium constant, fractional coverage on metal sites, fractional coverage on acid sites, and the concentration, respectively. Subscripts v, i and H refer to acid vacant sites, species i, and hydrogen, respectively. In addition, the hydrogenation/dehydrogenation reaction steps shown in Equations 11 to 16 occurring on the metallic sites are much faster than the reactions occurring on the acid sites. Therefore, they are assumed to be in quasi-equilibrium and their equilibrium constants can be expressed as follows:  K 11−16  θ j ⋅ θ v2 = θ i ⋅ θ H2  (35)  where K and ߠ, are the equilibrium constant, and fractional coverage on metal sites, respectively. Subscripts v, i, j and H denote acid vacant sites, reactant species i, product species j, and hydrogen, respectively. The fractional coverage of vacant sites for both the acid and metal sites are calculated from the following site balance equations: 66  €  	
    θ v + θ D + θ I + θ C + θ R + θ Do + θ I o + θ C o + θ R o + θ C oo + θ R oo + θ H = 1	
    	
  	
  	
  	
  	
  	
  (36)	
    	
    	
    	
  	
  	
  	
  	
  	
  (37)	
    	
    θ v* + θ D* o + θ I*o + θ C* o + θ R* o + θ C* oo + θ R* oo = 1	
    	
    The	
   fractional	
   coverage	
   terms	
   in	
   Equations	
   28	
   to	
   31	
   can	
   be	
   eliminated	
   using	
    €so	
  that	
  the	
  rate	
  expressions	
  can	
  be	
  written	
  as	
  follows:	
   Equations	
  32	
  and	
  37	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (38)	
    	
    	
    r2 =  k2 K 6CIo 	
   	
   1+ K 5CDo + K 6CI o + K 7CR o + K 8CC o + K 9CR oo + K10CC oo  	
  	
  	
  	
  	
  	
  (39)	
    	
    	
    r3 =  k 3 K 9CRoo 	
   	
   1+ K 5CDo + K 6CI o + K 7CR o + K 8CC o + K 9CR oo + K10CC oo  	
  	
  	
  	
  	
  	
  (40)	
    	
    r4 =  k 4 K 7CRo 	
   	
   1+ K 5CDo + K 6CI o + K 7CR o + K 8CC o + K 9CR oo + K10CC oo  	
  	
  	
  	
  	
  	
  (41)	
    € 	
    € 	
    €  Using	
  equations	
  33-­‐36,	
  the	
  concentration	
  of	
  intermediates	
  can	
  be	
  expressed	
  as:	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (42)	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (43)	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (44)	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (45)	
    67  	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (46)	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (47)	
    	
   4.1  Mole	
  balance	
    	
   The	
   number	
   of	
   mole	
   balance	
   equations	
   is	
   NC	
   ,	
   where	
   NC	
   is	
   the	
   number	
   of	
   chemical	
  species.	
  Referring	
  to	
  Figure	
  48,	
  the	
  general	
  mole	
  balance	
  for	
  lumped	
  systems	
   assuming	
  no	
  exchange	
  with	
  pseudo	
  phases	
  can	
  be	
  written	
  as:	
  	
   	
   	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  [Input	
  -­‐	
  Output]	
  	
  	
  +	
  	
  	
  [Reaction	
  gen/con]	
  	
  	
  	
  	
  	
  	
  	
  	
  =[Molar	
  accumulation	
  rate]	
   	
    NR ⎡ ⎤ ⎡ dC dV ⎤ i 	
  	
  	
   v f ⋅ Cif − v⋅ Ci + ⎢ mcat ⋅ ∑ v ji ⋅ Ω j ⋅ a j ⋅ rj ⎥ = ⎢V ⋅ 	
  	
   	
   + Ci ⋅ ⎣ dt dt ⎥⎦ ⎢ ⎥ ⎣ ⎦ j =1 	
    [  ]  	
  	
  	
  	
  	
  	
  (48)	
    where	
   v	
   is	
   the	
   volumetric	
   flow	
   rate,	
   Ci	
   is	
   the	
   concentration	
   of	
   species	
   i,	
   V	
   is	
   the	
   total	
   € volume,	
   mcat	
   is	
   the	
   catalyst	
   mass,	
   υji	
   is	
   the	
   stoichiometric	
   coefficient	
   of	
   species	
   i	
   in	
    reaction	
  j,	
  Ωj	
  is	
  the	
  overall	
  effectiveness	
  factor,	
  aj	
  is	
  the	
  catalyst	
  activity,	
  rj	
  is	
  the	
  rate	
  of	
   reaction	
  j.	
  In	
  addition,	
  NR	
  is	
  the	
  number	
  of	
  reactions.	
    68  	
   Figure	
  1.	
  Mole	
  Balance	
  for	
  Lumped	
  Systems	
  [45].	
   The	
   general	
   mole	
   balance	
   described	
   earlier	
   can	
   be	
   simplified	
   for	
   the	
   specific	
   system	
  being	
  studied.	
  For	
  this	
  study,	
  the	
  following	
  assumptions	
  can	
  be	
  made:	
   •  No	
  input/output:	
    •  100%	
  catalyst	
  effectiveness	
  (very	
  small	
  particles):	
    •  No	
  catalyst	
  deactivation:	
  	
    •  Negligible	
  change	
  in	
  liquid	
  density:	
  	
   Applying	
   these	
   assumptions	
   to	
   the	
   general	
   mole	
   balance	
   equation	
   for	
   lumped	
    systems	
  described	
  in	
  Equation	
  48	
  will	
  lead	
  to	
  the	
  following	
  simplified	
  equation:	
   (49)	
   where	
   ρcat	
   is	
   the	
   catalyst	
   density	
   calculated	
   taking	
   into	
   account	
   the	
   liquid	
   withdrawn	
   during	
  sample	
  collection.	
   Therefore,	
   the	
   mole	
   balance	
   equation	
   for	
   decalin	
   (D),	
   decalin	
   isomers	
   (I),	
   ring	
   opened	
  products	
  (R),	
  and	
  cracked	
  products	
  (C)	
  can	
  be	
  written	
  as	
  following:	
   	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (50)	
    69  	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
   	
    	
    	
   	
    	
    	
    	
  	
  	
  	
  	
  	
  (51)	
    	
    	
    	
  	
  	
  	
  	
  	
  (52)	
    	
    	
    	
  	
  	
  	
  	
  	
  (53)	
    	
   4.2  Parameter	
  estimation	
    	
   Given	
   the	
   limited	
   number	
   of	
   data	
   points	
   obtained	
   due	
   to	
   the	
   nature	
   of	
   experimental	
   setup	
   used,	
   the	
   number	
   of	
   parameters	
   present	
   in	
   the	
   rate	
   expressions	
   given	
   in	
   Equations	
   38	
   to	
   41	
   needs	
   to	
   be	
   reduced.	
   Therefore,	
   similar	
   equilibrium	
   constants	
  were	
  assumed	
  to	
  be	
  equal	
  in	
  agreement	
  with	
  Kubicka	
  et	
  al.	
  [29]	
  as	
  follows:	
   	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (54)	
    	
   	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (55)	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
   	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (56)	
    	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
    	
   	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (57)	
    	
  	
  	
    where	
  KA	
  and	
  KM,	
  refer	
  to	
  the	
  equilibrium	
  constants	
  of	
  adsorption	
  on	
  acid	
  sites	
   and	
   metal	
   sites,	
   respectively,	
   KH	
   refers	
   to	
   the	
   equilibrium	
   constant	
   for	
   H2	
   adsorption,	
   and	
  KHD	
  refers	
  to	
  the	
  equilibrium	
  constants	
  for	
  hydrogenation/dehydrogenation	
  steps.	
   In	
  addition,	
  KH	
  and	
  KHD	
  are	
  always	
  present	
  as	
  a	
  product	
  and	
  therefore	
  cannot	
  be	
   estimated	
   independently.	
   Therefore	
   they	
   were	
   lumped	
   into	
   one	
   term,	
   KHHD.	
   This	
   resulted	
  in	
  the	
  following	
  rate	
  expressions	
  which	
  were	
  used	
  for	
  parameter	
  estimation:	
    70  	
    	
    	
    	
    	
    	
    r2 =  	
    	
    r3 =  	
    r4 =  	
    	
    	
    	
    € 	
    	
    € 	
    	
    	
    k 2 K A CIo  (  1+ K A CDo + CI o + CR o + CC o + CR oo + CC oo  )  k 3 K A CRoo  (  1+ K A CDo + CI o + CR o + CC o + CR oo + CC oo  )  k 4 K A CRo  (  1+ K A CDo + CI o + CR o + CC o + CR oo + CC oo 	
    )  	
    	
  	
  	
  	
  	
  	
  (58)	
    	
    	
    	
  	
  	
  	
  	
  	
  (59)	
    	
    	
    	
  	
  	
  	
  	
  	
  (60)	
    	
    	
    	
  	
  	
  	
  	
  	
  (61)	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (62)	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (63)	
    € 	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (64)	
    	
    	
    	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (65)	
    	
    	
    	
    	
    	
    	
   	
    	
    	
    	
  	
  	
  	
  	
  	
  (66)	
    	
    	
    	
    	
    	
    	
   	
    	
    	
    	
  	
  	
  	
  	
  	
  (67)	
    	
   Note	
   that	
   in	
   the	
   above	
   equations	
   KM	
   was	
   eliminated	
   by	
   division	
   resulting	
   in	
   7	
   parameters	
  to	
  be	
  estimated	
  for	
  each	
  reaction	
  temperature:	
  k1-­‐k4,	
  K1,	
  KA,	
  and	
  KHHD.	
   The	
  concentration	
  of	
  H2	
  in	
  the	
  liquid	
  was	
  estimated	
  using	
  Henry’s	
  constant	
  for	
  a	
   similar	
   system	
   (H2	
   in	
   n-­‐decane)	
   [41]	
   and	
   experimentally	
   measured	
   reactor	
   pressures.	
   The	
  parameters	
  were	
  estimated	
  by	
  minimizing	
  the	
  objective	
  function	
  using	
  the	
  sum	
  of	
   least-­‐squares	
  method.	
  The	
  objective	
  function	
  was	
  defined	
  as	
  the	
  sum	
  of	
  squares	
  of	
  the	
    71  difference	
   between	
   experimental	
   concentrations	
   and	
   model	
   calculated	
   concentrations	
   for	
  all	
  chemical	
  species	
  i	
  at	
  all	
  reaction	
  times	
  t	
  as	
  shown	
  in	
  Equation	
  68:	
   	
   	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (68)	
    The	
   minimization	
   of	
   the	
   objective	
   function	
   was	
   achieved	
   using	
   a	
   Nelder-­‐Mead	
   simplex	
   (direct	
   search)	
   method	
   implemented	
   in	
   MATLAB	
   R2007b	
   version	
   7.5.0.342.	
   At	
   each	
  iteration	
  in	
  parameter	
  estimation,	
  the	
  four	
  ordinary	
  differential	
  equations	
  (ODEs)	
   given	
   in	
   Equations	
   (50)	
   to	
   (53)	
   were	
   solved	
   simultaneously	
   in	
   order	
   to	
   calculate	
   the	
   model	
  predicted	
  concentrations	
  CD,	
  CI,	
  CR	
  and	
  CC.	
  MATLAB	
  R2007b	
  version	
  7.5.0.342	
  was	
   used	
  to	
  conduct	
  the	
  required	
  calculations	
  in	
  order	
  to	
  estimate	
  the	
  parameters	
  (refer	
  to	
   Appendix	
  B	
  for	
  MATLAB	
  code).	
   The	
  estimated	
  parameters	
  are	
  shown	
  in	
  Table	
  7.	
  As	
  expected,	
  all	
  rate	
  constants	
   in	
   Table	
   7	
   increased	
   as	
   the	
   temperature	
   increased,	
   except	
   for	
   k2	
   between	
   325	
   and	
   350°C.	
   As	
   shown	
   by	
   the	
   rate	
   constants	
   in	
   Table	
   7,	
   the	
   highest	
   initial	
   reaction	
   rates	
   were	
   obtained	
  for	
  the	
  isomerization	
  of	
  decalin	
  followed	
  by	
  ring	
  opening	
  of	
  isomers	
  and	
  then	
   cracking	
  or	
  ring	
  opened	
  products,	
  at	
  all	
  temperatures	
  examined.	
   The	
  measured	
  and	
  predicted	
  concentrations	
  as	
  a	
  function	
  of	
  time	
  are	
  plotted	
  in	
   Figure	
   49.	
   The	
   degree	
   of	
   explanation	
   (R2)	
   was	
   calculated	
   using	
   Equation	
   69	
   and	
   was	
   found	
  to	
  be	
  relatively	
  high	
  at	
  0.8.	
  This	
  value	
  is	
  acceptable	
  due	
  to	
  the	
  complexity	
  of	
  the	
   reaction	
  mechanism	
  and	
  rate	
  expressions.	
   	
    	
    	
    	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (69)	
    The	
   reaction	
   constants	
   can	
   be	
   expressed	
   using	
   the	
   Arrhenius	
   equations	
   as	
   follows:	
   	
    	
    	
    	
    	
   	
    	
    	
    	
    	
  	
  	
  	
  	
  	
  (70)	
    	
    72  The pre-exponential factors AJ and activation energies Eaj can be obtained from     1 the intercept and slope of a plot of ln k j versus   respectively, as shown in Figure T  50. The results are displayed in Table 8. Detailed calculations are shown in Appendix C. The activation energies can be related to the production and consumption of chemical species. From Table 8, it can be seen that reaction step 2 in Figure 47, ring opening of isomers, has the lowest activation energy which means the lowest reaction barrier. This agrees with the observed results of highest production of ring opened products compared to all other products. Compared to reaction step 2, reaction step 1, the isomerization of decalin, has a higher activation energy leading to slower isomerization of decalin compared to ring opening of isomers. This confirms the observed results of increased production of isomers initially to a peak followed by a decrease in isomers concentration as reaction proceeds. As for reaction steps 3 and 4, cracking of ring opened products, Table 8 shows activation energies higher than that of reaction step 2. This also agrees with the results that the production of cracked products was slower than the production of ring opened products leading the ring opened products concentration to continue to increase, even with the formation of cracked products. Kubicka et al. [29] reported activation energy values for the same reaction mechanism considered in this study, using a Pt/H-Beta-25 catalyst with 2 wt% Pt as shown in Table 3 in the literature review section. By comparing the values, it can be concluded that the isomerization of decalin has a lower reaction barrier for the Pt/HBeta-25 catalyst than the Ir/H-Beta-25 catalyst. However, the ring opening of isomers has a lower reaction barrier for the Ir/H-Beta-25 catalyst. In addition, a higher reaction barrier for cracking is obtained for the Ir/H-Beta-25 catalyst compared to Pt/H-Beta-25.  73  Figure 49. Measured (points) and model predicted (line) concentrations as a function of time.  74  Table 7. Estimated reaction kinetic parameters for all reaction temperature tested. Parameter  Reaction temperature, °C 275° value  300 Std.  error  value  325 Std. error  value  350 Std. error  value  Std. error  k1, 1/(min g)  1.030  0.162  12.438  0.063  58.037  0.575 62.914  0.139  k2, 1/(min g)  0.437  0.069  3.408  0.017  14.436  0.143 13.600  0.203  k3, 1/(min g)  0.117  0.0187  1.860  0.009  2.912  0.029  6.542  0.087  k4, 1/(min g)  0.005  0.001  0.149  0.001  1.504  0.015  1.924  0.155  K1  0.796  0.000  1.535  0.000  2.592  0.000  2.055  0.093  KA  0.006  0.001  0.012  0.000  0.005  0.000  0.011  0.414  KHHD  115.5  0.3  936.8  0.3  1221.4  0.5 5578.9  0.5  6  k1 k2 k3 k4  4  ln(k)  2 0  -2 -4 -6 1.60E-03 1.65E-03 1.70E-03 1.75E-03 1.80E-03 1.85E-03 1/T, 1/K     1 Figure 50. Arrhenius plot of ln k j versus   for all reaction temperatures tested. T   75  Table 8. The pre-exponential factors AJ and activation energies Eaj for all kj Parameter  ln(Aj), 1/(min g)  Eaj, kJ/mol  Value  Std. error  Value  Std. error  k1  35.6  8.1  159.8  39.2  k2  29.3  7.2  135.4  35.1  k3  30.0  7.8  144.0  37.9  k4  45.8  10.3  229.7  50.0  76  Chapter 5. Conclusion and recommendations 5.1 Conclusion Three catalysts, Pd/H-Y-30, Ir/H-Beta-300 and Ir/H-Beta-25, were tested to examine the activity and yield of ring opened products at the same reaction conditions. The results showed that the Ir/H-Beta-25 had the highest activity and yield of ring opened products among all the catalysts tested. By comparing Ir/H-Beta-25 and Ir/HBeta-350, it was concluded that higher activity was achieved with higher acidity, confirming that catalyst acidity plays an important role in reaction activity. In terms of the effect of operating conditions, results showed that the initial catalyst activity increased as the temperature increased. Although the effect of pressure was minimal at 275°C, as the temperature increased, the effect of pressure became more significant and higher conversions were achieved at higher pressures. In terms of ring opened products, the concentration increased as the conversion increased for all temperatures and pressures. The ring opened product concentrations increased with increased temperature at 3 MPa. At 275°C, higher ring opened product concentrations were obtained at higher conversions, as the pressure increased. No clear effect of reaction temperature and pressure was noticed at other reaction conditions. The highest ring-opened product yield was 52.63 mol%, obtained at a total decalin conversion of 90.31 mol% at T=325°C and P= 6 MPa. Based on the experimental results, a kinetic model for the ring opening of decalin, namely the molecular Langmuir-Hinshelwood (L-H) model, was developed. The model parameters were estimated by minimizing the difference between measured experimental data and model predictions by sum of least-squares method. The model  77  was able to estimate the experimental results well with a degree of explanation (R 2) of 0.8. From the estimated activation energies of the reaction steps, ring opening of isomers had the lowest activation energy, i.e. the lowest reaction barrier. This agrees with the observed results of highest production of ring opened products compared to all other products. The isomerization of decalin had a higher activation energy leading to slower isomerization of decalin compared to ring opening of isomers. This confirms the observed results of increased production of isomers initially to a peak followed by a decrease in isomers concentration as reaction proceeds. Cracking of ring opened products had lower activation energies than ring opening of isomers leading the ring opened products concentration to continue to increase, even with the formation of cracked products.  5.2 Recommendations Additional tests using Pd(2)/H-Beta-25 and Ir(2)/H-Y-30 would shed some light on the relative roles of the metal type and zeolite structure on reaction activity and ring opening selectivity. In addition, further investigation of catalyst deactivation is recommended. In particular, the effect of operating conditions, namely temperature and pressure on catalyst deactivation rate need to be examined. Based on this recommended study, a deactivation rate term can be developed and included in the kinetic expressions in order to improve the model predictions. Finally, reaction runs can be performed using the same operating conditions and different catalysts in order to develop kinetic models and estimate the kinetic parameters. The kinetic parameters can then be compared with the parameters obtained in this study to evaluate the performance of each catalyst. 78  References [1] H. Du, C. Fairbridge, H. Yang, Z. Ring, Applied Catalysis A, General 294 (2005) 1. [2] A. Burrowes, R. Marsh, M. Teare, C. Evans, S. Ramos, D. Rokosh, ST98 (2010) . [3] Alberta Energy, 2011 (2011) 7. [4] S. Cairney, Natural Resources Canada's CanmetENERGY PCC V2 Proposal (2010) . [5] M. Santikunaporn, J.E. Herrera, S. Jongpatiwut, D.E. Resasco, W.E. Alvarez, E.L. Sughrue, Journal of Catalysis 228 (2004) 100. [6] M.A. Arribas, A. Corma, M. Diaz-Cabanas, A. Martnez, Applied Catalysis A: General 273 (2004) 277. [7] A. Stanislaus, B.H. Cooper, Catal. Rev. - Sci. Eng. 36 (1994) 75. [8] J. Barbier, E. Lamy-Pitara, P. Marecot, J.P. Boitiaux, J. Cosyns, F. Verna, in: D.D. Eley,Herman Pines and Paul B.Weisz (Ed.), Advances in Catalysis, Academic Press, 1990, p. 279. [9] J.W. Ward, Fuel Process Technol 35 (1993) 55. [10] S. Albertazzi, E. Rodriguez-Castellon, M. Livi, A. Jimenez-Lopez, A. Vaccari, Journal of Catalysis 228 (2004) 218. [11] S. Albertazzi, N. Donzel, M. Jacquin, D.J. Jones, M. Morisi, J. Roziere, A. Vaccari, Catalysis Letters 96 (2004) 157. [12] S. Albonetti, G. Baldi, A. Barzanti, E.R. Castellon, A.J. Lopez, D.E. Quesada, A. Vaccari, Catalysis Letters 108 (2006) 197.  79  [13] M. Al-Sabawi, H. de Lasa, AICHE J. 55 (2009) 1538. [14] M. Al-Sabawi, H. de Lasa, Chem. Eng. Sci. 65 (2009) 626. [15] S.J. Ardakani, X. Liu, K.J. Smith, Applied Catalysis A: General 324 (2007) 9. [16] M.A. Arribas, A. Martínez, Applied Catalysis A: General 230 (2002) 203. [17] M.A. Arribas, P. Concepcion, A. Martinez, Applied Catalysis A: General 267 (2004) 111. [18] W.C. Baird Jr., J.G. Chen, G.B. McVicker, Patent WO; 2002008158 (2002) . [19] Z. Cao, X. Xu, Y. Qi, S. Lu, B. Qi, Petrol Sci Technol 22 (2004) 617. [20] A. Corma, V. Gonzalez-Alfaro, A.V. Orchilles, Journal of Catalysis 200 (2001) 34. [21] P.T. Do, W.E. Alvarez, D.E. 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[47] Micromeritics Instrument Corporation, AutoChem II 2920 Automated Catalyst Characterization System Operators Manual V3.05 (2006).  82  Appendices  Appendices  83  Appendix A Catalyst characterization  84  A.1 BET surface area, pore volume and average pore size full analysis results  A.1.1 BET surface area calculation:  The BET surface area can be determined from the following equation [46]: 𝑃/𝑃0 𝐶−1 𝑃 1 = + 𝑃 𝑉𝑚 𝐶 𝑃0 𝑉𝑚 𝐶 𝑉 1−𝑃 0 P = equilibrium pressure P0 = saturation pressure of the adsorbate gas V = volume adsorbed Vm = volume adsorbed at monolayer coverage C = constant  85  A.2 Temperature-programmed  reduction  and  CO  chemisorption analysis A.2.1 Temperature –programmed reduction:  As shown in the Figure 51, Autochem II 2920 performs TPR measurement using the following simplified steps [47]: 1. Gas flows into analyzer. 2. As the temperature changes, gas interacts with the sample. 3. Gas flows past the detector. 4. The detector collects the data. 5. Software performs calculations and plots results.  Figure 51. Simplified temperature-programmed reduction mechanism [47].  86  A.2.2 Injection loop calibration:  The injection loop is calibrated using the following steps [47]: 1.  Injecting a known gas volume thorough the analyzer septum using a glass syringe  and determining the average peak area. 2.  Injections the same gas using the analyzers internal loop and determining the  average peak area. 3.  Determining the volume of the loop by comparing the two average peak areas. These equations are used in dose loop calibration [47]:  𝑉𝑆𝑆𝑇𝑃 = 𝑉𝑆  273.15 𝑃𝑎 × 273.15 + 𝑇𝑎 760 𝑚𝑚𝐻𝑔 𝑉𝑙 = 𝑉𝑆  𝐴𝑙 × 𝑉𝑆𝑆𝑇𝑃 𝐴𝑆  𝑉𝑆𝑆𝑇𝑃 = Volume of syringe at STP, cm3 𝑉𝑆 = Physical volume of syringe, cm3 𝑇𝑎 = Ambient temperature, °C 𝑃𝑎 = Ambient pressure, 𝑚𝑚𝐻𝑔 𝑉𝑙 = Effective loop volume, cm3 𝐴𝑙 = Average peak area of loop injections 𝐴𝑆 = Average peak area of loop injections  87  A.2.3 Percent dispersion:  The percent dispersion is calculated using the following equation [47]: 𝑃𝐷 =  𝑉𝑠 × 𝑆𝐹𝑐𝑎𝑙𝑐 𝑀𝑊 × 100 𝑚𝑠𝑎𝑚𝑝𝑙𝑒 × 22414  𝑃𝐷 = Percent dispersion 𝑉𝑆 = Volume sorbed, cm3 at STP 𝑆𝐹 = Calculated stoichiometry factor 𝑚𝑠𝑎𝑚𝑝𝑙𝑒 = sample mass, g 𝑀𝑊 = molecular weight, g/mol  88  A.3 Sample reports Samples of the reports obtained from Micromeritics ASAP 2020 and Micromeritics Autochem II 2920 are shown in the following pages. The reports are for Ir(2)/H-Beta-25 catalyst.  89  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 1  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Summary Report Surface Area Single point surface area at p/p° = 0.201129019: 594.8372 m²/g BET Surface Area: 584.3339 m²/g Langmuir Surface Area: 778.4202 m²/g t-Plot Micropore Area: 368.1393 m²/g t-Plot External Surface Area: 216.1946 m²/g BJH Adsorption cumulative surface area of pores between 17.000 Å and 3000.000 Å width: 207.036 m²/g BJH Desorption cumulative surface area of pores between 17.000 Å and 3000.000 Å width: 225.3666 m²/g Pore Volume Single point adsorption total pore volume of pores less than 630.782 Å width at p/p° = 0.968357495: 0.669561 cm³/g t-Plot micropore volume: 0.169903 cm³/g BJH Adsorption cumulative volume of pores between 17.000 Å and 3000.000 Å width: 0.699773 cm³/g BJH Desorption cumulative volume of pores between 17.000 Å and 3000.000 Å width: 0.708940 cm³/g Pore Size Adsorption average pore width (4V/A by BET): 45.8342 Å BJH Adsorption average pore width (4V/A): 135.199 Å BJH Desorption average pore width (4V/A): 125.829 Å  90  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 2  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Table 9. Isotherm tabular report. Isotherm Tabular Report Absolute Quantity Elapsed Time Relative Adsorbed (h:min) Pressure (p/p°) Pressure (kPa) (mmol/g) 0.010598366 0.029296641 0.059748142 0.080552876 0.100860000 0.121258082 0.141598452 0.161770312 0.181264612 0.201129019 0.247467603 0.300539444  1.0494171 2.9027168 5.9229523 7.9886124 10.0059991 12.0345132 14.0573107 16.0654763 18.0066797 19.9846241 24.5974742 29.8830210  6.20774 6.61249 6.93008 7.07736 7.19632 7.30131 7.39389 7.47940 7.55603 7.63118 7.79695 7.97868  0.350820857 0.400180256 0.450080368 0.499918966 0.550057272 0.599803765 0.649534127 0.699100325 0.748420679 0.797264122 0.820410861 0.848986061 0.872835710 0.897602884 0.921507913  34.8901564 39.8039542 44.7718289 49.7356064 54.7304157 59.6886680 64.6467249 69.5926816 74.5159676 79.3951736 81.7151819 84.5819797 86.9810262 89.4746042 91.8873539  8.14895 8.32129 8.50322 8.70131 8.92223 9.17493 9.47486 9.84270 10.31299 10.96419 11.38499 12.02500 12.70947 13.60899 14.74674  0.944637248 0.968357495 0.973448599 0.982645102 0.988923163 0.978045433 0.971792683  94.2263955 96.6405937 97.1765930 98.1416181 98.8215753 97.7439293 97.1339045  16.34332 19.31234 20.52648 22.95118 24.98553 24.67579 24.24055  0.953230476 0.921529894 0.900354929 0.874743288  95.2995497 92.1517691 90.0460824 87.4960637  21.38721 17.01944 15.39709 14.13289  00:56 01:47 01:58 02:07 02:14 02:20 02:27 02:32 02:38 02:43 02:47 02:53 02:59 03:01 03:06 03:12 03:17 03:23 03:29 03:36 03:43 03:52 04:01 04:11 04:20 04:32 04:45 04:59 05:15 05:17 05:33 05:59 06:14 06:39 07:07 07:12 07:20 07:22 07:54 08:35 08:58 09:21 09:23  Saturation Pressure (kPa) 98.7233493  99.4427890  99.7181734  99.9571430  100.0259850  91  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 3  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Isotherm Tabular Report Absolute Quantity Elapsed Time Relative Adsorbed (h:min) Pressure (p/p°) Pressure (kPa) (mmol/g) 0.854718848 0.827575602 0.799845162 0.746908850 0.700171223 0.652907450 0.601225454 0.550055813 0.499982447 0.450030676 0.399426490 0.349560448  85.5230809 82.8372009 80.0905512 74.8170416 70.1557376 65.4342376 60.2677871 55.1477887 50.1359845 45.1335872 40.0652650 35.0684336  13.39272 12.53617 11.79065 10.73870 10.12626 9.67845 9.30486 9.01199 8.77101 8.55455 8.35320 8.17471  0.299917841 0.250886945 0.200845190 0.143165955  30.0896650 25.1705738 20.1500667 14.3633190  8.00128 7.82998 7.64695 7.41171  09:37 09:52 10:07 10:22 10:34 10:43 10:52 10:59 11:06 11:12 11:19 11:25 11:27 11:33 11:39 11:45 11:52  Saturation Pressure (kPa)  100.3263592  92  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 4  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Isotherm Linear Plot Ir(2)/H-Beta-25 - Adsorption Ir(2)/H-Beta-25 - Desorption  25  Quantity Adsorbed (mmol/g)  20  15  10  5  0 0.0  0.1  0.2  0.3  0.4  0.5  0.6  Relative Pressure (p/p°)  0.7  0.8  0.9  1.0  Figure 52. Isotherm linear plot.  93  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 5  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Isotherm Log Plot 25  Ir(2)/H-Beta-25 - Adsorption Ir(2)/H-Beta-25 - Desorption  Quantity Adsorbed (mmol/g)  20  15  10  5  0 0.01  0.05  0.1  Relative Pressure (p/p°)  0.5  1  Figure 53. Isotherm log plot.  94  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 6  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Table 10. BET surface area report. BET Surface Area Report BET Surface Area: 584.3339 ± 7.6492 m²/g Slope: 0.168217 ± 0.002165 g/mmol Y-Intercept: -0.001235 ± 0.000301 g/mmol C: -135.190701 Qm: 5.98868 mmol/g Correlation Coefficient: 0.9995034 Molecular Cross-Sectional Area: 0.1620 nm² Relative Pressure (p/p°) 0.059748142 0.080552876 0.100860000 0.121258082 0.141598452 0.161770312 0.181264612 0.201129019  Quantity Adsorbed (mmol/g) 6.93008 7.07736 7.19632 7.30131 7.39389 7.47940 7.55603 7.63118  1/[Q(p°/p - 1)]  0.00917 0.01238 0.01559 0.01890 0.02231 0.02580 0.02930 0.03299  95  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 7  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BET Surface Area Plot Ir(2)/H-Beta-25  0.030  0.025  1/[Q(p°/p - 1)]  0.020  0.015  0.010  0.005  0.000 0.00  0.02  0.04  0.06  Figure 54. BET surface area plot.  0.08  0.10  0.12  Relative Pressure (p/p°)  0.14  0.16  0.18  0.20  96  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 8  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Table 11. Langmuir surface area report. Langmuir Surface Area Report Langmuir Surface Area: 778.4202 ± 5.5783 m²/g Slope: 0.125348 ± 0.000898 g/mmol Y-Intercept: 0.128595 ± 0.012395 kPa·g/mmol b: 0.974746 1/kPa Qm: 7.97782 mmol/g Correlation Coefficient: 0.999846 Molecular Cross-Sectional Area: 0.1620 nm² Pressure (kPa)  5.9229523 7.9886124 10.0059991 12.0345132 14.0573107 16.0654763 18.0066797 19.9846241  Quantity Adsorbed (mmol/g) 6.93008 7.07736 7.19632 7.30131 7.39389 7.47940 7.55603 7.63118  p/Q (kPa·g/mmol) 0.855 1.129 1.390 1.648 1.901 2.148 2.383 2.619  97  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 9  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Langmuir Surface Area Plot Ir(2)/H-Beta-25  2.5  p/Q (kPa·g/mmol)  2.0  1.5  1.0  0.5  0.0 0  1  2  3  4  5  6  7  8  9  10  11  Pressure (kPa)  12  13  14  15  16  17  18  19  20  Figure 55. Langmuir surface area plot.  98  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 10  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Table 12. t-plot report. t-Plot Report Micropore Volume: 0.169903 cm³/g Micropore Area: 368.1393 m²/g External Surface Area: 216.1946 m²/g Slope: 0.623576 ± 0.013363 mmol/g·Å Y-Intercept: 4.900567 ± 0.054390 mmol/g Correlation Coefficient: 0.998625 Surface Area Correction Factor: 1.000 Density Conversion Factor: 0.0015468 Total Surface Area (BET): 584.3339 m²/g Thickness Range: 3.5000 Å to 5.0000 Å Thickness Equation: Harkins and Jura t = [ 13.99 / ( 0.034 - log(p/p°) ) ] ^ 0.5 Relative Pressure (p/p°) 0.010598366 0.029296641 0.059748142 0.080552876 0.100860000 0.121258082 0.141598452 0.161770312 0.181264612 0.201129019 0.247467603 0.300539444 0.350820857 0.400180256 0.450080368 0.499918966 0.550057272 0.599803765 0.649534127  Statistical Thickness (Å) 2.6390 2.9878 3.3352 3.5218 3.6849 3.8369 3.9805 4.1177 4.2468 4.3761 4.6736 5.0157 5.3492 5.6924 6.0619 6.4613 6.9030 7.3926 7.9492  Quantity Adsorbed (mmol/g) 6.20774 6.61249 6.93008 7.07736 7.19632 7.30131 7.39389 7.47940 7.55603 7.63118 7.79695 7.97868 8.14895 8.32129 8.50322 8.70131 8.92223 9.17493 9.47486  99  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 11  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  t-Plot Ir(2)/H-Beta-25  Not Fitted Points  0.5  2.0  Harkins and Jura  9  8  Quantity Adsorbed (mmol/g)  7  6  5  4  3  2  1  0 0.0  1.0  1.5  2.5  Figure 56. t-plot Harkins and Jura.  3.0  3.5  4.0  4.5  Thickness (Å)  5.0  5.5  6.0  6.5  7.0  7.5  8.0  100  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 12  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Table 13. BJH adsorption pore distribution report. BJH Adsorption Pore Distribution Report Faas Correction Halsey t = 3.54 [ -5 / ln(p/p°) ] ^ 0.333 Width Range: Adsorbate Property Factor: Density Conversion Factor: Fraction of Pores Open at Both Ends: Pore Width Range (Å) 1765.3 - 1135.2 1135.2 - 748.6 748.6 - 630.8 630.8 - 366.1 366.1 - 261.0 261.0 - 201.8 201.8 - 163.7 163.7 - 138.5 138.5 - 117.0 117.0 - 104.0 104.0 - 84.0 84.0 - 70.3 70.3 - 60.2 60.2 - 52.4 52.4 - 46.2 46.2 - 41.2 41.2 - 36.9 36.9 - 33.3 33.3 - 30.1 30.1 - 27.2 27.2 - 24.5 24.5 - 22.2 22.2 - 21.3 21.3 - 20.4 20.4 - 19.4  Average Width (Å) 1317.0 863.8 679.4 430.3 295.5 223.4 178.5 148.8 125.8 109.6 91.6 75.8 64.3 55.7 48.9 43.3 38.7 34.9 31.5 28.5 25.7 23.2 21.7 20.8 19.9  Incremental Pore Volume (cm³/g) 0.075793 0.091740 0.046413 0.116374 0.063345 0.045971 0.037091 0.028671 0.027098 0.017933 0.027699 0.019693 0.015256 0.012286 0.010211 0.008797 0.007872 0.007178 0.006937 0.006937 0.007717 0.007377 0.003478 0.003610 0.004296  17.000 Å to 3000.000 Å 9.53000 Å 0.0015468 0.00 Cumulative Pore Volume (cm³/g) 0.075793 0.167533 0.213946 0.330320 0.393666 0.439637 0.476728 0.505399 0.532497 0.550430 0.578129 0.597822 0.613077 0.625364 0.635574 0.644371 0.652244 0.659421 0.666358 0.673296 0.681012 0.688389 0.691867 0.695477 0.699773  Incremental Pore Area (m²/g) 2.302 4.248 2.733 10.818 8.576 8.230 8.314 7.707 8.617 6.543 12.091 10.399 9.488 8.830 8.358 8.119 8.127 8.238 8.813 9.742 12.031 12.719 6.403 6.942 8.649  Cumulative Pore Area (m²/g) 2.302 6.550 9.283 20.101 28.677 36.907 45.221 52.928 61.545 68.088 80.179 90.577 100.066 108.895 117.253 125.372 133.499 141.737 150.550 160.292 172.323 185.042 191.445 198.387 207.036  101  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 13  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Adsorption Cumulative Pore Volume Halsey : Faas Correction  Ir(2)/H-Beta-25  0.7  0.6  Pore Volume (cm³/g)  0.5  0.4  0.3  0.2  0.1  0.0 10  50  100  Pore Width (Å)  500  1,000  Figure 57. BJH adsoption cumulative pore volume.  102  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 14  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Adsorption dV/dw Pore Volume Halsey : Faas Correction  Ir(2)/H-Beta-25 0.0045  0.0040  0.0035  Pore Volume (cm³/g·Å)  0.0030  0.0025  0.0020  0.0015  0.0010  0.0005  0.0000 10  50  100  Pore Width (Å)  500  1,000  Figure 58. BJH adsoption dV/dw pore volume.  103  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 15  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Adsorption dV/dlog(w) Pore Volume Halsey : Faas Correction  Ir(2)/H-Beta-25 0.6  dV/dlog(w) Pore Volume (cm³/g·Å)  0.5  0.4  0.3  0.2  0.1  0.0 10  50  100  Pore Width (Å)  500  1,000  Figure 59. BJH adsorption dV/dlog(w) pore volume.  104  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 16  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Adsorption Cumulative Pore Area Halsey : Faas Correction  Ir(2)/H-Beta-25 200  180  160  Pore Area (m²/g)  140  120  100  80  60  40  20  0 10  50  100  Pore Width (Å)  500  1,000  Figure 60. BJH adsorption cumulative pore area.  105  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 17  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Adsorption dA/dw Pore Area Halsey : Faas Correction  Ir(2)/H-Beta-25 9  8  7  Pore Area (m²/g·Å)  6  5  4  3  2  1  0 10  50  100  Pore Width (Å)  500  1,000  Figure 61. BJH adsorption dA/dw pore area.  106  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 18  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Adsorption dA/dlog(w) Pore Area Halsey : Faas Correction  Ir(2)/H-Beta-25 400  350  dA/dlog(w) Pore Area (m²/g·Å)  300  250  200  150  100  50  0 10  50  100  Pore Width (Å)  500  1,000  Figure 62. BJH adsorption dA/dlog(w) pore area.  107  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 19  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Table 14. BJH desorption pore distribution report. BJH Desorption Pore Distribution Report Faas Correction Halsey t = 3.54 [ -5 / ln(p/p°) ] ^ 0.333 Width Range: Adsorbate Property Factor: Density Conversion Factor: Fraction of Pores Open at Both Ends: Pore Width Range (Å) 1765.3 - 901.6 901.6 - 705.7 705.7 - 431.2 431.2 - 261.1 261.1 - 207.2 207.2 - 166.1 166.1 - 143.8 143.8 - 121.8 121.8 - 105.3 105.3 - 83.6 83.6 - 70.5 70.5 - 60.8 60.8 - 52.6 52.6 - 46.2 46.2 - 41.2 41.2 - 36.9 36.9 - 33.2 33.2 - 30.0 30.0 - 27.2 27.2 - 24.6 24.6 - 22.2 22.2 - 19.5  Average Width (Å) 1075.8 779.3 503.6 304.8 227.6 181.8 153.2 130.8 112.2 91.6 75.8 64.8 56.0 48.9 43.3 38.7 34.8 31.4 28.4 25.8 23.3 20.6  Incremental Pore Volume (cm³/g) 0.011652 0.016664 0.112982 0.180256 0.066998 0.052384 0.030818 0.036473 0.032437 0.046348 0.025938 0.018046 0.014237 0.010399 0.008065 0.007166 0.006583 0.005328 0.005315 0.005424 0.006278 0.009148  17.000 Å to 3000.000 Å 9.53000 Å 0.0015468 0.00 Cumulative Pore Volume (cm³/g) 0.011652 0.028316 0.141298 0.321553 0.388552 0.440935 0.471754 0.508227 0.540664 0.587012 0.612950 0.630997 0.645233 0.655633 0.663697 0.670864 0.677446 0.682775 0.688090 0.693514 0.699792 0.708940  Incremental Pore Area (m²/g) 0.433 0.855 8.974 23.656 11.775 11.527 8.046 11.155 11.566 20.237 13.692 11.138 10.170 8.501 7.443 7.398 7.563 6.784 7.477 8.424 10.799 17.755  Cumulative Pore Area (m²/g) 0.433 1.289 10.262 33.919 45.694 57.221 65.267 76.422 87.988 108.225 121.916 133.055 143.224 151.725 159.168 166.565 174.128 180.912 188.389 196.813 207.612 225.367  108  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 20  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Desorption Cumulative Pore Volume Halsey : Faas Correction  Ir(2)/H-Beta-25 0.7  0.6  Pore Volume (cm³/g)  0.5  0.4  0.3  0.2  0.1  0.0 10  50  100  Pore Width (Å)  500  1,000  Figure 63. BJH desorption cumulative pore volume.  109  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 21  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Desorption dV/dw Pore Volume Halsey : Faas Correction  Ir(2)/H-Beta-25  0.0030  Pore Volume (cm³/g·Å)  0.0025  0.0020  0.0015  0.0010  0.0005  0.0000 50  100  Pore Width (Å)  500  1,000  Figure 64. BJH desorption dV/dw pore volume.  110  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 22  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Desorption dV/dlog(w) Pore Volume Halsey : Faas Correction  Ir(2)/H-Beta-25 0.8  0.7  dV/dlog(w) Pore Volume (cm³/g·Å)  0.6  0.5  0.4  0.3  0.2  0.1  0.0 50  100  Pore Width (Å)  500  1,000  Figure 65. BJH desorption dV/dlog(w) pore volume.  111  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 23  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:08AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Desorption Cumulative Pore Area Halsey : Faas Correction  Ir(2)/H-Beta-25 220  200  180  160  Pore Area (m²/g)  140  120  100  80  60  40  20  0 10  50  100  Pore Width (Å)  500  1,000  Figure 66. BJH desorption cumulative pore area.  112  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 24  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:09AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Desorption dA/dw Pore Area Halsey : Faas Correction  Ir(2)/H-Beta-25  6  Pore Area (m²/g·Å)  5  4  3  2  1  0 50  100  Pore Width (Å)  500  1,000  Figure 67. BJH desorption dA/dw pore area.  113  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 25  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:09AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  BJH Desorption dA/dlog(w) Pore Area Halsey : Faas Correction  Ir(2)/H-Beta-25 300  dA/dlog(w) Pore Area (m²/g·Å)  250  200  150  100  50  0 50  100  Pore Width (Å)  500  1,000  Figure 68. BJH desorption dA/dlog(w) pore area.  114  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 26  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:09AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Options Report Sample Tube Warm freespace: 1.0000 cm³ Cold freespace: 1.0000 cm³ Non-ideality factor: 0.0000620 Use Isothermal Jacket: No Use Filler Rod: No Vacuum seal type: None Analysis Conditions Preparation Fast evacuation: No Unrestricted evacuation from: 0.67 kPa Vacuum setpoint: 1.3 Pa Evacuation time: 0.10 h Leak test: No Use TransSeal: No Free Space Free-space type: Measured Lower dewar for evacuation: Yes Evacuation time: 0.10 h Outgas test: No p° and Temperature p° and T type: Measure p° at intervals during analysis. Calculate the Analysis Bath Temperature from these values. Measurement interval: 120 min Dosing Use first pressure fixed dose: No Use maximum volume increment: No Target tolerance: 5.0% or 0.6666 kPa Low pressure dosing: No Equilibration Equilibration time (p/p° = 1.000000000): 10 s Minimum equilibration delay at p/p° >= 0.995: 600 s Sample Backfill Backfill at start of analysis: Yes Backfill at end of analysis: Yes Backfill gas: N2 Adsorptive Properties Adsorptive: Nitrogen Maximum manifold pressure: 123.323 kPa Non-ideality factor: 0.0000620  115  Full Report Set ASAP 2020 V3.01 H  Unit 1  Serial #: 336  Page 27  Sample: Ir(2)/H-Beta-25 Operator: Ali 01-MAR-11 Submitter: File: C:\...\ASAP20~1\000-738.SMP Started: Completed: Report Time: Sample Mass: Cold Free Space: Low Pressure Dose:  02/03/2011 8:02:37AM 03/03/2011 3:56:03PM 25/05/2011 11:34:09AM 0.1707 g 86.1367 cm³ None  Analysis Adsorptive: Analysis Bath Temp.: Thermal Correction: Warm Free Space: Equilibration Interval: Automatic Degas:  N2 77.215 K No 27.8151 cm³ Measured 10 s Yes  Comments: ALI-005 Ir(2)/H-Beta-25 (CP814E) (from Desicator)  Adsorptive Properties Density conversion factor: 0.0015468 Therm. tran. hard-sphere diameter: 3.860 Å Molecular cross-sectional area: 0.162 nm² Inside diameter of sample tube: 9.53 mm  116  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 1  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:38AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  Summary Report Experiment 1: Degassing and TPR Analysis Type: Temperature Programmed Reduction Calibration: (292_0077) 002-009 ALI H2 TCD Calibration 15-JUN-10 Measured Flow Rate: 30.06 cm³ STP/min Signal Offset: -0.43871 Signal Inverted: Yes Temperature at Maximum (°C)  Peak Number 1  153.6  Quantity (µmol/g)  Peak Concentration (%)  152.74307  0.48  Experiment 2: CO Pulse Chemi on Ir/CP814E Analysis Type: Pulse Chemisorption Calibration: None Measured Flow Rate: 30.05 cm³ STP/min Signal Offset: -1.11243 Signal Inverted: Yes Temperature at Maximum (°C)  Peak Number 1 2 3 4 5 6 7  34.5 34.4 34.4 34.4 34.2 34.2 34.2  Area 0.00136 0.00220 0.01373 0.01410 0.01422 0.01505 0.01519  Peak Height 0.00202 0.00382 0.01849 0.02153 0.02177 0.02222 0.02206  117  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 2  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:38AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  Pulse Chemisorption Report Experiment 2: CO Pulse Chemi on Ir/CP814E Analysis Type: Pulse Chemisorption Calibration: None Measured Flow Rate: 30.05 cm³ STP/min Signal Offset: -1.11243 Signal Inverted: Yes  Table 15.  CO pulse chemisorption  Peak Table Temperature at Quantity Maximum (°C) Adsorbed (µmol/g)  Peak Number 1 2 3 4 5 6 7 Element  iridium  34.5 34.4 34.4 34.4 34.2 34.2 34.2  Cumulative Quantity (µmol/g)  10.81165 10.15250 1.13746 0.85200 0.75924 0.10570 0.00000  10.81165 20.96414 22.10160 22.95360 23.71284 23.81854 23.81854  Pulse Chemisorption Analysis Summary Percent of Atomic Stoichiometry Atomic Sample Weight Factor CrossMass (%) Sectional Area (nm²) 2.0000  192.217  Active Loop Volume at 107.7 °C: Cumulative Quantity: Metal Dispersion: Metallic Surface Area: Metallic Surface Area: Active Particle Diameter:  1.000  0.0620  Density (g/cm³)  22.560  0.04075 cm³ STP 23.81854 µmol/g 22.8917% 0.8895 m²/g sample 44.4725 m²/g metal 5.9803 nm  118  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 3  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:38AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  TCD Signal (a.u.) vs. Time TCD Signal (a.u.) - Degassing and TPR TCD Signal (a.u.) - CO Pulse Chemi on Ir/CP814E  0.04  TCD Signal (a.u.)  0.03  0.02  0.01  0.00  -0.01  0  10  20  30  40  50  60  Time (minutes)  70  80  90  100  110  Figure 69. TCD signal versus time for TPR and CO chemisorption experiments.  119  120  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 4  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:39AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  Temperature vs. Time Temperature - Degassing and TPR  Temperature - CO Pulse Chemi on Ir/CP814E  500  450  400  Temperature (°C)  350  300  250  200  150  100  50 0  10  20  30  40  50  60  Time (minutes)  70  80  90  100  110  Figure 70. Temperature versus time for TPR and CO chemisorption experiments.  120  120  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 5  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:39AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  TCD Signal (a.u.) vs. Temperature TCD Signal (a.u.) - Degassing and TPR TCD Signal (a.u.) - CO Pulse Chemi on Ir/CP814E  0.04  TCD Signal (a.u.)  0.03  0.02  0.01  0.00  -0.01  50  100  150  200  250  300  Temperature (°C)  350  400  450  Figure 71. TCD signal versus temperature for TPR and CO chemisorption experiments.  121  500  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 6  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:39AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  TCD Concentration vs. Time TCD Concentration - Degassing and TPR 10.25  10.20  10.15  TCD Concentration  10.10  10.05  10.00  9.95  9.90  9.85  9.80  9.75 0  10  20  30  40  50  60  Time (minutes)  70  80  90  100  110  4226- No experiments were selected for inclusion in this report.  Figure 72. TCD concentration versus time for TPR experiment.  122  120  Micromeritics Instrument Corporation -- AutoChem II 2910 AutoChem II 2920 V3.05  Unit 1  Serial # 350  Page 7  Sample: Ir(2)/H-Beta-25 (ALI-002) TPR & CO Chem Operator: Ali 15-JUN-10 Submitter: File: E:\RESEARCH\2920\002-010.SMP Started: 15/06/2010 2:33:31PM Completed: 15/06/2010 11:36:02PM  Sample Mass: 0.1531 g Report Time: 25/05/2011 11:46:39AM  Comments: 2 wt% Cacined Ir/CP814E (ALI-002) TPR and CO pulse chemisorption  TCD Concentration vs. Temperature TCD Concentration - Degassing and TPR 10.25  10.20  10.15  TCD Concentration  10.10  10.05  10.00  9.95  9.90  9.85  9.80  9.75 50  100  150  200  250  300  Temperature (°C)  350  400  450  500  4226- No experiments were selected for inclusion in this report.  Figure 73. TCD concentration versus temperature for TPR experiment.  123  Appendix B Matlab code for kinetic model parameter estimation  124  %This is the main code %Run this code clear all %List experimental data %t:time (min); m: mass (g); V: volume (ml); %D: decalin; R: ring opened products; C: cracked products; I: isomers; %HP: heavy products; CH_ideal: ideal hydrogen concentration (mol/l) %CH_henry: Henry's law concentration (mol/l); T:temperature (C); %P:pressure (MPa); mw: waste mass (g); Vw: waste volume (ml)  % t m(g) V(ml) D R C I HP CH_ideal (t) CH_ideal(avg) CH_henry(t) CH_henry(avg) T(t) P(t) Tavg P(avg) mw(g) Vw(ml) DATA_005=[0 0.2132 0.1 1.28E-02 8.76E-04 4.90E-05 6.79E-04 1.42E-04 5.95E-01 5.95E-01 2.66E-02 2.66E-02 275.80 2.71653 275.80 2.71653 2.07320 2.30000; 15 0.199 0.1 1.17E-02 1.26E-03 6.60E-05 1.53E-03 7.61E-06 5.90E-01 5.94E-01 2.61E-02 2.64E-02 275.20 2.68896 274.92 2.70540 1.51900 1.60000; 30 0.1763 0.1 1.07E-02 1.49E-03 8.08E-05 2.32E-03 6.54E-06 5.85E-01 5.89E-01 2.56E-02 2.60E-02 275.40 2.66827 275.02 2.68416 1.32630 1.50000; 45 0.2041 0.1 1.04E-02 1.60E-03 9.38E-05 2.55E-03 1.04E-05 5.76E-01 5.81E-01 2.49E-02 2.53E-02 275.10 2.62690 274.99 2.64708 1.65410 1.80000; 60 0.2123 0.1 9.81E-03 1.37E-03 1.23E-04 3.29E-03 3.35E-06 5.67E-01 5.72E-01 2.41E-02 2.45E-02 275.30 2.58553 274.91 2.60580 1.72230 1.90000; 120 0.201 0.1 8.25E-03 2.15E-03 3.16E-04 3.38E-03 4.66E-04 5.42E-01 5.52E-01 2.20E-02 2.28E-02 275.00 2.46832 274.97 2.51422 1.57100 1.70000; 180 0.2114 0.1 6.85E-03 2.95E-03 4.44E-04 4.39E-03 2.95E-05 5.07E-01 5.22E-01 1.92E-02 2.04E-02 275.00 2.30974 274.97 2.37725 1.60140 1.70000; 240 0.1869 0.1 5.91E-03 4.02E-03 2.60E-04 4.49E-03 1.33E-05 4.72E-01 5.05E-01 1.67E-02 1.91E-02 274.90 2.15116 274.96 2.30041 1.42690 1.50000; 300 0.2161 0.1 5.10E-03 4.27E-03 2.97E-04 5.01E-03 1.54E-05 4.37E-01 4.53E-01 1.43E-02 1.53E-02 274.80 1.99258 274.95 2.06325 1.44610 1.60000]; DATA_004=[0 0.2044 0.1 8.74E-03 1.76E-03 1.45E-04 1.96E-03 3.99E-04 5.64E-01 5.64E-01 3.22E-02 3.22E-02 299.90 2.68896 299.90 2.68896 1.49440 1.70000 15 0.1731 0.1 7.55E-03 3.16E-03 2.10E-04 2.17E-03 1.20E-05 5.47E-01 5.54E-01 3.04E-02 3.11E-02 303.30 2.62001 299.97 2.64128 1.96310 2.20000  125  30 0.1758 0.1 6.75E-03 3.16E-03 2.70E-04 2.92E-03 1.00E-05 5.19E-01 5.31E-01 2.73E-02 2.85E-02 300.50 2.47522 300.35 2.53198 1.73580 1.90000 45 0.1802 0.1 6.03E-03 3.33E-03 3.17E-04 3.43E-03 1.14E-05 4.93E-01 5.06E-01 2.46E-02 2.58E-02 299.90 2.35111 300.03 2.40907 1.25020 1.30000 60 0.0336 0.02 5.49E-03 4.38E-03 3.22E-04 2.91E-03 1.66E-05 4.67E-01 4.80E-01 2.21E-02 2.33E-02 300.10 2.22701 300.01 2.28514 1.32360 1.57000 120 0.0999 0.06 4.06E-03 4.87E-03 3.57E-04 3.78E-03 4.32E-05 4.01E-01 4.29E-01 1.62E-02 1.87E-02 299.90 1.90985 299.96 2.04655 1.38990 1.61000 180 0.1692 0.1 3.35E-03 5.44E-03 4.62E-04 3.81E-03 7.18E-05 3.72E-01 3.83E-01 1.40E-02 1.48E-02 299.90 1.77195 299.94 1.82549 1.44920 1.60000 240 0.1756 0.1 3.02E-03 6.36E-03 5.23E-04 3.18E-03 7.32E-05 3.63E-01 3.75E-01 1.33E-02 1.42E-02 300.00 1.73058 299.95 1.78504 1.41560 1.70000 300 0.1841 0.1 2.80E-03 6.56E-03 5.38E-04 3.18E-03 8.56E-05 3.66E-01 3.64E-01 1.35E-02 1.34E-02 300.00 1.74437 299.96 1.73307 1.34410 1.50000];  DATA_013=[0 0.182 0.1 1.26E-02 6.28E-04 2.97E-04 5.01E-04 1.31E-05 9.49E-01 9.49E-01 6.75E-02 6.75E-02 275.50 4.32991 275.50 4.32991 2.32200 2.60000 15 0.182 0.1 1.20E-02 9.16E-04 3.80E-04 6.82E-04 9.88E-06 9.39E-01 9.41E-01 6.61E-02 6.63E-02 275.30 4.28164 274.99 4.28784 1.50200 1.60000 30 0.196 0.1 1.10E-02 1.20E-03 5.19E-04 1.30E-03 1.13E-05 9.30E-01 9.32E-01 6.48E-02 6.50E-02 275.20 4.24028 274.92 4.24590 1.48600 1.50000 45 0.194 0.1 1.09E-02 1.17E-03 5.48E-04 1.44E-03 1.24E-05 9.18E-01 9.22E-01 6.32E-02 6.37E-02 274.90 4.18512 274.98 4.20281 1.46400 1.50000 60 0.195 0.1 1.03E-02 1.42E-03 1.22E-04 2.10E-03 8.82E-06 9.08E-01 9.11E-01 6.17E-02 6.21E-02 274.80 4.13685 274.99 4.15104 1.47500 1.60000 120 0.196 0.1 8.44E-03 2.30E-03 2.01E-04 3.01E-03 0.00E+00 8.76E-01 8.89E-01 5.75E-02 5.92E-02 275.00 3.99206 274.97 4.05186 1.63600 1.70000 180 0.199 0.1 6.98E-03 3.40E-03 2.55E-04 3.32E-03 7.85E-06 8.35E-01 8.52E-01 5.22E-02 5.43E-02 274.90 3.80591 274.95 3.88239 1.76900 1.90000 240 0.209 0.1 5.99E-03 3.34E-03 2.86E-04 4.02E-03 8.16E-06 7.88E-01 8.30E-01 4.65E-02 5.15E-02 275.00 3.59217 274.95 3.78117 1.77900 1.90000 300 0.182 0.1 5.02E-03 4.63E-03 2.95E-04 4.07E-03 8.64E-06 7.38E-01 7.60E-01 4.08E-02 4.32E-02 274.90 3.36464 274.96 3.46138 1.80200 2.10000];  126  DATA_009=[0 0.1907 0.1 9.12E-03 1.93E-03 1.20E-04 1.74E-03 1.99E-05 8.99E-01 8.99E-01 8.18E-02 8.18E-02 300.60 4.28854 300.60 4.28854 1.82070 2.10000 15 0.1926 0.1 7.86E-03 2.51E-03 1.72E-04 2.38E-03 1.91E-05 8.68E-01 8.81E-01 7.62E-02 7.86E-02 300.30 4.13685 299.98 4.20019 1.47260 1.70000 30 0.1917 0.1 6.67E-03 3.20E-03 2.37E-04 2.83E-03 8.15E-06 8.33E-01 8.48E-01 7.02E-02 7.27E-02 300.50 3.97138 299.96 4.04001 1.61170 1.80000 45 0.172 0.1 5.91E-03 3.43E-03 2.92E-04 3.30E-03 1.98E-05 7.94E-01 8.11E-01 6.38E-02 6.65E-02 300.10 3.78522 299.96 3.86506 1.80200 2.10000 60 0.1684 0.1 5.11E-03 3.90E-03 3.40E-04 3.58E-03 3.57E-05 7.52E-01 7.71E-01 5.72E-02 6.01E-02 300.10 3.58527 300.01 3.67459 1.52840 1.70000 120 0.1715 0.1 3.42E-03 4.18E-03 3.52E-04 4.95E-03 5.97E-05 6.15E-01 6.80E-01 3.82E-02 4.67E-02 300.00 2.93027 299.97 3.24009 1.70150 1.90000 180 0.1715 0.1 2.92E-03 5.03E-03 4.65E-04 4.53E-03 4.49E-05 5.12E-01 5.58E-01 2.65E-02 3.15E-02 299.90 2.44074 299.96 2.65831 1.23150 1.40000 240 0.1813 0.1 2.29E-03 5.16E-03 6.04E-04 4.86E-03 9.42E-05 4.54E-01 5.18E-01 2.09E-02 2.71E-02 299.90 2.16495 299.96 2.46816 1.74130 1.90000 300 0.1636 0.1 2.06E-03 5.49E-03 7.92E-04 4.58E-03 1.20E-04 4.30E-01 4.38E-01 1.87E-02 1.94E-02 300.00 2.04774 299.96 2.08792 1.51360 1.70000]; DATA_012=[0 0.211 0.1 6.68E-03 2.85E-03 2.16E-04 3.77E-03 1.32E-05 8.14E-01 8.14E-01 7.00E-02 7.00E-02 326.00 4.05412 326.00 4.05412 2.29100 2.50000 15 0.204 0.1 5.20E-03 3.39E-03 3.05E-04 4.62E-03 2.10E-05 7.23E-01 7.62E-01 5.52E-02 6.13E-02 325.30 3.59906 324.83 3.79035 1.75400 1.90000 30 0.191 0.1 4.64E-03 3.85E-03 3.70E-04 4.66E-03 3.39E-05 6.53E-01 6.84E-01 4.50E-02 4.94E-02 324.80 3.24743 325.08 3.40242 1.38100 1.50000 45 0.169 0.1 3.57E-03 4.11E-03 4.35E-04 5.46E-03 5.48E-05 6.08E-01 6.29E-01 3.89E-02 4.17E-02 324.60 3.01990 325.01 3.12612 1.52900 1.70000 60 0.182 0.1 3.24E-03 4.33E-03 5.04E-04 5.52E-03 5.04E-05 5.81E-01 5.94E-01 3.56E-02 3.72E-02 324.50 2.88890 324.97 2.95157 1.61200 1.75000 120 0.179 0.1 2.51E-03 4.75E-03 7.34E-04 5.66E-03 7.29E-05 5.48E-01 5.58E-01 3.16E-02 3.28E-02 325.00 2.72343 324.94 2.77400 1.65900 1.90000 180 0.186 0.1 2.14E-03 5.28E-03 8.40E-04 5.34E-03 1.01E-04 5.45E-01 5.44E-01 3.13E-02 3.12E-02 325.00  127  2.70964 324.99 2.70324 1.65600 1.90000 240 0.196 0.1 1.92E-03 6.65E-03 1.13E-03 4.01E-03 7.15E-05 5.48E-01 5.44E-01 3.17E-02 3.12E-02 324.90 2.72343 324.97 2.70571 1.75600 1.90000 300 0.167 0.1 1.80E-03 6.73E-03 1.14E-03 4.03E-03 7.44E-05 5.52E-01 5.49E-01 3.21E-02 3.17E-02 324.80 2.74411 324.93 2.72756 0.00000 0.00000];  DATA_008=[0 0.1755 0.1 9.41E-03 1.76E-03 1.44E-04 2.49E-03 0.00E+00 1.06E+00 1.06E+00 1.14E-01 1.14E-01 299.90 5.05386 299.90 5.05386 2.05550 2.30000 15 0.1919 0.1 8.05E-03 2.48E-03 3.13E-04 3.16E-03 9.07E-06 1.03E+00 1.04E+00 1.06E-01 1.10E-01 300.40 4.88838 299.91 4.95958 2.00190 2.20000 30 0.1967 0.1 6.98E-03 2.87E-03 4.21E-04 3.62E-03 8.92E-06 9.81E-01 1.00E+00 9.73E-02 1.01E-01 299.90 4.67465 299.88 4.76957 2.14670 2.30000 45 0.175 0.1 6.23E-03 3.47E-03 5.45E-04 3.77E-03 8.96E-06 9.33E-01 9.56E-01 8.81E-02 9.23E-02 299.90 4.44712 299.97 4.55391 1.85500 2.10000 60 0.174 0.1 5.16E-03 3.48E-03 6.47E-04 4.68E-03 9.11E-06 8.82E-01 9.07E-01 7.87E-02 8.32E-02 300.10 4.20580 300.08 4.32225 1.83400 2.10000 120 0.1909 0.1 3.34E-03 4.55E-03 7.91E-04 4.28E-03 1.68E-05 7.22E-01 7.98E-01 5.27E-02 6.44E-02 299.80 3.44048 299.96 3.80164 1.43090 1.60000 180 0.2441 0.1 2.47E-03 5.76E-03 1.26E-03 4.45E-03 4.34E-05 5.95E-01 6.52E-01 3.58E-02 4.30E-02 299.90 2.83375 299.93 3.10760 1.53410 1.70000 240 0.186 0.1 2.18E-03 5.56E-03 1.45E-03 4.78E-03 6.75E-05 5.15E-01 6.00E-01 2.68E-02 3.64E-02 299.90 2.45453 299.95 2.85998 1.33600 1.40000 300 0.1837 0.1 1.86E-03 5.84E-03 1.65E-03 4.67E-03 5.32E-05 4.79E-01 4.92E-01 2.32E-02 2.45E-02 300.00 2.28216 299.96 2.34671 1.55370 1.80000]; DATA_016=[0 0.1931 0.1 6.57E-03 3.79E-03 4.45E-04 1.91E-03 3.59E-05 5.84E-01 5.84E-01 3.75E-02 3.75E-02 350.40 3.02680 350.40 3.02680 1.64310 1.80000 15 0.1715 0.1 5.41E-03 4.46E-03 6.12E-04 2.70E-03 7.60E-05 6.00E-01 5.92E-01 3.96E-02 3.85E-02 349.90 3.10954 350.18 3.06562 1.80150 2.10000 30 0.1724 0.1 4.58E-03 4.94E-03 7.62E-04 2.73E-03 8.53E-05 6.09E-01 6.03E-01 4.08E-02 4.00E-02 350.00 3.15780 350.09 3.12652 1.99240 2.30000 45 0.1729 0.1 4.22E-03 5.09E-03 8.30E-04 2.88E-03 8.88E-05 6.13E-01 6.09E-01 4.12E-02 4.08E-02 349.60 3.17159 349.97 3.15626 1.55290 1.70000  128  60 0.176 0.1 3.89E-03 5.01E-03 8.78E-04 3.18E-03 1.16E-04 6.18E-01 6.15E-01 4.19E-02 4.15E-02 349.80 3.19917 350.04 3.18481 1.70600 1.90000 120 0.1906 0.1 3.38E-03 5.27E-03 9.71E-04 3.26E-03 1.79E-04 6.45E-01 6.29E-01 4.58E-02 4.35E-02 350.20 3.34396 349.94 3.25922 1.82060 2.10000 180 0.1802 0.1 3.04E-03 5.36E-03 1.05E-03 3.43E-03 2.23E-04 6.63E-01 6.51E-01 4.83E-02 4.66E-02 350.00 3.43359 349.97 3.37338 2.10020 2.50000 240 0.1784 0.1 2.77E-03 5.69E-03 1.15E-03 3.22E-03 2.65E-04 6.77E-01 6.60E-01 5.04E-02 4.78E-02 350.00 3.50943 349.97 3.41700 1.62840 1.90000 300 0.1849 0.1 2.52E-03 5.76E-03 9.59E-04 3.57E-03 2.64E-04 6.92E-01 6.83E-01 5.26E-02 5.13E-02 350.00 3.58527 349.93 3.53736 1.85490 2.10000];  DATA_014=[0 0.1947 0.1 5.32E-03 4.36E-03 5.52E-04 3.65E-03 0.00E+00 7.78E-01 7.78E-01 6.66E-02 6.66E-02 350.20 4.03343 350.20 4.03343 2.32470 2.70000 15 0.1978 0.1 4.05E-03 4.71E-03 8.98E-04 4.19E-03 6.66E-05 7.37E-01 7.50E-01 5.98E-02 6.19E-02 349.80 3.81970 350.08 3.88682 1.88780 2.10000 30 0.1881 0.1 3.12E-03 5.66E-03 9.42E-04 4.10E-03 7.31E-05 7.28E-01 7.31E-01 5.83E-02 5.87E-02 349.50 3.77143 350.03 3.78675 2.21810 2.50000 45 0.1957 0.1 2.73E-03 5.72E-03 1.11E-03 4.26E-03 1.02E-04 7.16E-01 7.24E-01 5.63E-02 5.76E-02 350.30 3.70938 350.21 3.75014 1.69570 1.90000 60 0.1714 0.1 2.54E-03 5.94E-03 1.11E-03 4.21E-03 1.08E-04 7.12E-01 7.10E-01 5.57E-02 5.54E-02 350.00 3.68870 349.87 3.67926 1.71140 1.90000 120 0.1966 0.1 2.34E-03 5.70E-03 1.48E-03 4.25E-03 1.89E-04 7.31E-01 7.19E-01 5.87E-02 5.68E-02 349.90 3.78522 349.96 3.72470 1.84660 2.10000 180 0.1866 0.1 2.01E-03 6.19E-03 1.47E-03 4.20E-03 1.46E-04 7.45E-01 7.36E-01 6.11E-02 5.96E-02 350.00 3.86106 349.96 3.81335 1.72660 1.90000 240 0.1944 0.1 1.97E-03 5.98E-03 1.66E-03 4.23E-03 1.92E-04 7.59E-01 7.43E-01 6.33E-02 6.07E-02 349.90 3.93001 349.95 3.84952 1.86440 2.10000 300 0.1945 0.1 1.53E-03 6.48E-03 1.63E-03 4.09E-03 2.81E-04 7.69E-01 7.62E-01 6.51E-02 6.38E-02 349.90 3.98517 349.98 3.94806 1.73450 1.90000]; DATA_010=[0 0.1823 0.1 1.25E-02 7.67E-04 6.55E-05 4.41E-04 8.63E-06 1.11E+00 1.11E+00 9.30E-02 9.30E-02 275.50 5.08144 275.50 5.08144 2.23230 2.50000 15 0.2076 0.1 1.18E-02 1.02E-03 6.05E-05 8.56E-04 3.89E-05 1.09E+00 1.11E+00 8.96E-02 9.14E-02 274.90  129  4.98491 274.90 5.03587 2.00140 2.20000 30 0.1714 0.1 1.13E-02 1.44E-03 4.55E-05 8.92E-04 2.07E-05 1.08E+00 1.09E+00 8.77E-02 8.92E-02 274.60 4.92975 275.03 4.97310 2.10970 2.30000 45 0.1897 0.1 1.06E-02 1.19E-03 9.86E-05 1.84E-03 3.95E-06 1.07E+00 1.08E+00 8.52E-02 8.69E-02 274.60 4.86080 274.93 4.90995 2.01400 2.20000 60 0.184 0.1 1.00E-02 1.44E-03 1.09E-04 2.15E-03 7.54E-06 1.33E-06 0.00E+00 8.26E-02 2.70E-01 274.40 4.78496 275.00 4.83791 2.16440 2.30000 120 0.2044 0.1 8.24E-03 2.73E-03 1.78E-04 2.59E-03 3.43E-05 0.00E+00 0.00E+00 7.70E-02 4.01E-01 274.80 4.61949 274.93 4.71886 1.92400 2.10000 180 0.174 0.1 6.81E-03 3.31E-03 1.39E-04 3.50E-03 7.02E-06 9.72E-01 9.95E-01 7.07E-02 7.42E-02 274.70 4.42643 274.95 4.53646 2.03870 2.20000 240 0.1987 0.1 5.72E-03 3.32E-03 2.00E-04 4.52E-03 7.21E-06 9.22E-01 9.72E-01 6.36E-02 7.07E-02 274.60 4.19891 274.96 4.42813 1.48620 1.60000 300 0.1962 0.1 4.78E-03 5.22E-03 2.47E-04 3.48E-03 3.75E-05 8.67E-01 8.97E-01 5.63E-02 6.02E-02 274.70 3.95070 274.94 4.08770 1.65981 1.90000];  DATA_011=[0 0.1875 0.1 6.50E-03 2.58E-03 3.44E-04 3.78E-03 1.03E-05 9.80E-01 9.80E-01 1.02E-01 1.02E-01 325.90 4.88149 325.90 4.88149 2.51750 2.80000 15 0.1862 0.1 4.77E-03 3.72E-03 4.43E-04 4.05E-03 1.70E-05 8.61E-01 9.15E-01 7.82E-02 8.83E-02 324.90 4.28164 325.19 4.54974 2.07620 2.30000 30 0.1748 0.1 3.75E-03 4.48E-03 5.82E-04 3.52E-03 2.33E-05 7.64E-01 8.07E-01 6.16E-02 6.88E-02 324.90 3.79901 325.02 4.01532 2.01480 2.30000 45 0.1706 0.1 3.14E-03 5.20E-03 7.16E-04 4.78E-03 5.00E-05 6.95E-01 7.25E-01 5.09E-02 5.55E-02 324.70 3.45427 325.10 3.60593 1.84060 2.10000 60 0.1777 0.1 2.74E-03 5.71E-03 7.54E-04 4.08E-03 4.57E-05 6.53E-01 6.71E-01 4.50E-02 4.75E-02 324.80 3.24743 324.93 3.33604 1.69770 2.00000 120 0.1962 0.1 2.01E-03 6.18E-03 1.12E-03 4.01E-03 6.82E-05 5.99E-01 6.16E-01 3.79E-02 4.00E-02 324.90 2.97854 324.92 3.06323 1.67620 1.90000 180 0.1822 0.1 1.57E-03 6.86E-03 1.49E-03 3.46E-03 5.94E-05 5.89E-01 5.91E-01 3.66E-02 3.69E-02 325.00 2.93027 324.95 2.93947 1.60220 1.80000 240 0.1813 0.1 1.41E-03 7.04E-03 1.54E-03 3.40E-03 6.32E-05 5.92E-01 5.90E-01 3.70E-02 3.67E-02 325.00 2.94406 324.96 2.93371 1.70130 2.00000 300 0.1887 0.1 1.30E-03 7.07E-03 1.52E-03 3.42E-03 1.24E-04 5.98E-01 5.92E-01 3.77E-02 3.70E-02 325.00  130  2.97164 324.93  2.94511 1.59870 1.90000];  DATA_015=[0 0.171 0.1 4.52E-03 4.80E-03 5.65E-04 3.20E-03 3.75E-05 8.59E-01 8.59E-01 8.12E-02 8.12E-02 350.20 4.45401 350.20 4.45401 2.00100 2.30000 15 0.167 0.1 3.39E-03 5.20E-03 8.99E-04 3.64E-03 6.23E-05 7.95E-01 8.18E-01 6.94E-02 7.36E-02 349.90 4.11617 349.97 4.24011 1.62700 1.90000 30 0.1647 0.1 2.75E-03 5.67E-03 1.15E-03 3.60E-03 7.16E-05 7.81E-01 7.85E-01 6.71E-02 6.77E-02 350.00 4.04722 350.09 4.06644 1.72470 2.10000 45 0.1699 0.1 2.20E-03 5.93E-03 1.62E-03 3.59E-03 0.00E+00 7.82E-01 7.79E-01 6.71E-02 6.66E-02 349.40 4.04722 349.81 4.03313 1.59990 1.90000 60 0.1665 0.1 2.01E-03 6.09E-03 1.75E-03 3.39E-03 1.34E-04 7.66E-01 7.77E-01 6.44E-02 6.65E-02 349.30 3.96449 350.62 4.03233 1.34650 1.70000 120 0.1932 0.1 1.67E-03 5.98E-03 1.80E-03 3.86E-03 7.99E-05 7.90E-01 7.76E-01 6.87E-02 6.63E-02 350.00 4.09549 349.89 4.02222 1.59320 1.90000 180 0.1899 0.1 1.38E-03 6.83E-03 2.07E-03 3.04E-03 8.92E-05 8.05E-01 7.95E-01 7.13E-02 6.95E-02 349.90 4.17133 349.97 4.11927 1.59990 1.90000 240 0.1942 0.1 1.28E-03 6.86E-03 2.18E-03 3.02E-03 9.15E-05 8.18E-01 8.03E-01 7.36E-02 7.08E-02 350.00 4.24028 349.97 4.15836 1.79420 2.10000 300 0.1971 0.1 1.16E-03 6.57E-03 1.85E-03 3.61E-03 2.16E-04 8.28E-01 8.19E-01 7.53E-02 7.37E-02 349.90 4.28854 349.95 4.24243 2.28710 2.70000]; T=DATA_005(:,1)'; %Extracting experimental data %RO-Ir(2)HBeta-005 Results CDX_005=DATA_005(:,4)'; CRX_005=DATA_005(:,5)'; CCX_005=DATA_005(:,6)'; CIX_005=DATA_005(:,7)'; CHX_ideal_t_005=DATA_005(:,9)'; CHX_ideal_avg_005=DATA_005(:,10)'; CHX_hen_t_005=DATA_005(:,11)'; CHX_hen_avg_005=DATA_005(:,12)'; CHX_005=CHX_hen_t_005; T_t_005=DATA_005(:,13)'; P_t_005=DATA_005(:,14)'; T_avg_005=DATA_005(:,15)'; P_avg_005=DATA_005(:,16)';  131  m_0=100*0.896; m_005(1)=m_0; V_005(1)=100; m_w=0; V_w=0; %mass and volume correction calculations for i=2:9 m_w=m_w+DATA_005(i-1,17)'; V_w=V_w+DATA_005(i-1,18)'; m_005(i)=m_005(1)-m_w; V_005(i)=V_005(1)-V_w; end %RO-Ir(2)HBeta-004 Results CDX_004=DATA_004(:,4)'; CRX_004=DATA_004(:,5)'; CCX_004=DATA_004(:,6)'; CIX_004=DATA_004(:,7)'; CHX_ideal_t_004=DATA_004(:,9)'; CHX_ideal_avg_004=DATA_004(:,10)'; CHX_hen_t_004=DATA_004(:,11)'; CHX_hen_avg_004=DATA_004(:,12)'; CHX_004=CHX_hen_t_004; T_t_004=DATA_004(:,13)'; P_t_004=DATA_004(:,14)'; T_avg_004=DATA_004(:,15)'; P_avg_004=DATA_004(:,16)'; m_0=100*0.896; m_004(1)=m_0; V_004(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_004(i-1,17)'; V_w=V_w+DATA_004(i-1,18)'; m_004(i)=m_004(1)-m_w; V_004(i)=V_004(1)-V_w; end %RO-Ir(2)HBeta-013 Results CDX_013=DATA_013(:,4)'; CRX_013=DATA_013(:,5)'; CCX_013=DATA_013(:,6)'; CIX_013=DATA_013(:,7)'; CHX_ideal_t_013=DATA_013(:,9)';  132  CHX_ideal_avg_013=DATA_013(:,10)'; CHX_hen_t_013=DATA_013(:,11)'; CHX_hen_avg_013=DATA_013(:,12)'; CHX_013=CHX_hen_t_013; T_t_013=DATA_013(:,13)'; P_t_013=DATA_013(:,14)'; T_avg_013=DATA_013(:,15)'; P_avg_013=DATA_013(:,16)'; m_0=100*0.896; m_013(1)=m_0; V_013(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_013(i-1,17)'; V_w=V_w+DATA_013(i-1,18)'; m_013(i)=m_013(1)-m_w; V_013(i)=V_013(1)-V_w; end %RO-Ir(2)HBeta-009 Results CDX_009=DATA_009(:,4)'; CRX_009=DATA_009(:,5)'; CCX_009=DATA_009(:,6)'; CIX_009=DATA_009(:,7)'; CHX_ideal_t_009=DATA_009(:,9)'; CHX_ideal_avg_009=DATA_009(:,10)'; CHX_hen_t_009=DATA_009(:,11)'; CHX_hen_avg_009=DATA_009(:,12)'; CHX_009=CHX_hen_t_009; T_t_009=DATA_009(:,13)'; P_t_009=DATA_009(:,14)'; T_avg_009=DATA_009(:,15)'; P_avg_009=DATA_009(:,16)'; m_0=100*0.896; m_009(1)=m_0; V_009(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_009(i-1,17)'; V_w=V_w+DATA_009(i-1,18)'; m_009(i)=m_009(1)-m_w; V_009(i)=V_009(1)-V_w; end  133  %RO-Ir(2)HBeta-012 Results CDX_012=DATA_012(:,4)'; CRX_012=DATA_012(:,5)'; CCX_012=DATA_012(:,6)'; CIX_012=DATA_012(:,7)'; CHX_ideal_t_012=DATA_012(:,9)'; CHX_ideal_avg_012=DATA_012(:,10)'; CHX_hen_t_012=DATA_012(:,11)'; CHX_hen_avg_012=DATA_012(:,12)'; CHX_012=CHX_hen_t_012; T_t_012=DATA_012(:,13)'; P_t_012=DATA_012(:,14)'; T_avg_012=DATA_012(:,15)'; P_avg_012=DATA_012(:,16)'; m_0=100*0.896; m_012(1)=m_0; V_012(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_012(i-1,17)'; V_w=V_w+DATA_012(i-1,18)'; m_012(i)=m_012(1)-m_w; V_012(i)=V_012(1)-V_w; end %RO-Ir(2)HBeta-008 Results CDX_008=DATA_008(:,4)'; CRX_008=DATA_008(:,5)'; CCX_008=DATA_008(:,6)'; CIX_008=DATA_008(:,7)'; CHX_ideal_t_008=DATA_008(:,9)'; CHX_ideal_avg_008=DATA_008(:,10)'; CHX_hen_t_008=DATA_008(:,11)'; CHX_hen_avg_008=DATA_008(:,12)'; CHX_008=CHX_hen_t_008; T_t_008=DATA_008(:,13)'; P_t_008=DATA_008(:,14)'; T_avg_008=DATA_008(:,15)'; P_avg_008=DATA_008(:,16)'; m_0=100*0.896; m_008(1)=m_0; V_008(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_008(i-1,17)';  134  V_w=V_w+DATA_008(i-1,18)'; m_008(i)=m_008(1)-m_w; V_008(i)=V_008(1)-V_w; end %RO-Ir(2)HBeta-010 Results CDX_010=DATA_010(:,4)'; CRX_010=DATA_010(:,5)'; CCX_010=DATA_010(:,6)'; CIX_010=DATA_010(:,7)'; CHX_ideal_t_010=DATA_010(:,9)'; CHX_ideal_avg_010=DATA_010(:,10)'; CHX_hen_t_010=DATA_010(:,11)'; CHX_hen_avg_010=DATA_010(:,12)'; CHX_010=CHX_hen_t_010; T_t_010=DATA_010(:,13)'; P_t_010=DATA_010(:,14)'; T_avg_010=DATA_010(:,15)'; P_avg_010=DATA_010(:,16)'; m_0=100*0.896; m_010(1)=m_0; V_010(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_010(i-1,17)'; V_w=V_w+DATA_010(i-1,18)'; m_010(i)=m_010(1)-m_w; V_010(i)=V_010(1)-V_w; end %RO-Ir(2)HBeta-011 Results CDX_011=DATA_011(:,4)'; CRX_011=DATA_011(:,5)'; CCX_011=DATA_011(:,6)'; CIX_011=DATA_011(:,7)'; CHX_ideal_t_011=DATA_011(:,9)'; CHX_ideal_avg_011=DATA_011(:,10)'; CHX_hen_t_011=DATA_011(:,11)'; CHX_hen_avg_011=DATA_011(:,12)'; CHX_011=CHX_hen_t_011; T_t_011=DATA_011(:,13)'; P_t_011=DATA_011(:,14)'; T_avg_011=DATA_011(:,15)'; P_avg_011=DATA_011(:,16)'; m_0=100*0.896; m_011(1)=m_0;  135  V_011(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_011(i-1,17)'; V_w=V_w+DATA_011(i-1,18)'; m_011(i)=m_011(1)-m_w; V_011(i)=V_011(1)-V_w; end %RO-Ir(2)HBeta-014 Results CDX_014=DATA_014(:,4)'; CRX_014=DATA_014(:,5)'; CCX_014=DATA_014(:,6)'; CIX_014=DATA_014(:,7)'; CHX_ideal_t_014=DATA_014(:,9)'; CHX_ideal_avg_014=DATA_014(:,10)'; CHX_hen_t_014=DATA_014(:,11)'; CHX_hen_avg_014=DATA_014(:,12)'; CHX_014=CHX_hen_t_014; T_t_014=DATA_014(:,13)'; P_t_014=DATA_014(:,14)'; T_avg_014=DATA_014(:,15)'; P_avg_014=DATA_014(:,16)'; m_0=100*0.896; m_014(1)=m_0; V_014(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_014(i-1,17)'; V_w=V_w+DATA_014(i-1,18)'; m_014(i)=m_014(1)-m_w; V_014(i)=V_014(1)-V_w; end %RO-Ir(2)HBeta-015 Results CDX_015=DATA_015(:,4)'; CRX_015=DATA_015(:,5)'; CCX_015=DATA_015(:,6)'; CIX_015=DATA_015(:,7)'; CHX_ideal_t_015=DATA_015(:,9)'; CHX_ideal_avg_015=DATA_015(:,10)'; CHX_hen_t_015=DATA_015(:,11)'; CHX_hen_avg_015=DATA_015(:,12)';  136  CHX_015=CHX_hen_t_015; T_t_015=DATA_015(:,13)'; P_t_015=DATA_015(:,14)'; T_avg_015=DATA_015(:,15)'; P_avg_015=DATA_015(:,16)'; m_0=100*0.896; m_015(1)=m_0; V_015(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_015(i-1,17)'; V_w=V_w+DATA_015(i-1,18)'; m_015(i)=m_015(1)-m_w; V_015(i)=V_015(1)-V_w; end %RO-Ir(2)HBeta-016 Results CDX_016=DATA_016(:,4)'; CRX_016=DATA_016(:,5)'; CCX_016=DATA_016(:,6)'; CIX_016=DATA_016(:,7)'; CHX_ideal_t_016=DATA_016(:,9)'; CHX_ideal_avg_016=DATA_016(:,10)'; CHX_hen_t_016=DATA_016(:,11)'; CHX_hen_avg_016=DATA_016(:,12)'; CHX_016=CHX_hen_t_016; T_t_016=DATA_016(:,13)'; P_t_016=DATA_016(:,14)'; T_avg_016=DATA_016(:,15)'; P_avg_016=DATA_016(:,16)'; m_0=100*0.896; m_016(1)=m_0; V_016(1)=100; m_w=0; V_w=0; for i=2:9 m_w=m_w+DATA_016(i-1,17)'; V_w=V_w+DATA_016(i-1,18)'; m_016(i)=m_016(1)-m_w; V_016(i)=V_016(1)-V_w; end h=1e-15; t=T;  137  T_275=0; T_300=0; T_325=0; T_350=0; %averaging collected temperatures T_275=sum(T_avg_005+T_avg_013+T_avg_010)/(3*9); T_300=sum(T_avg_004+T_avg_009+T_avg_008)/(3*9); T_325=sum(T_avg_012+T_avg_011)/(2*9); T_350=sum(T_avg_016+T_avg_014+T_avg_015)/(3*9); T_005=mean(T_avg_005); T_013=mean(T_avg_013); T_004=mean(T_avg_004); T_009=mean(T_avg_009); T_008=mean(T_avg_008); T_012=mean(T_avg_012); T_016=mean(T_avg_016); T_014=mean(T_avg_014); T_010=mean(T_avg_010); T_011=mean(T_avg_011); T_015=mean(T_avg_015); Tref=mean(T_275+T_300+T_325+T_350); options=optimset('display', 'iter','LargeScale', 'off','MaxIter', 3000, ... 'MaxFunEvals', 6000, 'TolX', 1e-10, 'TolFUN', 1e-10); lb=[0 0 0 0 0 0 0]; % lower bound for parameters ub=[inf inf inf inf inf inf inf]; % Upper bound for parameters  % inital guess for parameters % k1 p0_275=[.8 p0_300=[2 p0_325=[5 p0_350=[100 % initial C_0_005 = C_0_004 = C_0_013 = C_0_009 = C_0_012 = C_0_008 =  k2 .5 1.5 4 10  k4 KE1 KHC .02 50 .01 50 .1]; .2 150 .1 150 .5]; 1 350 1.2 350 2]; 4 400 2 900 7];  KHHD  k3  concentration values [CDX_005(1);CRX_005(1);CCX_005(1);CIX_005(1)]; [CDX_004(1);CRX_004(1);CCX_004(1);CIX_004(1)]; [CDX_013(1);CRX_013(1);CCX_013(1);CIX_013(1)]; [CDX_009(1);CRX_009(1);CCX_009(1);CIX_009(1)]; [CDX_012(1);CRX_012(1);CCX_012(1);CIX_012(1)]; [CDX_008(1);CRX_008(1);CCX_008(1);CIX_008(1)];  138  C_0_016 C_0_014 C_0_010 C_0_011 C_0_015  = = = = =  [CDX_016(1);CRX_016(1);CCX_016(1);CIX_016(1)]; [CDX_014(1);CRX_014(1);CCX_014(1);CIX_014(1)]; [CDX_010(1);CRX_010(1);CCX_010(1);CIX_010(1)]; [CDX_011(1);CRX_011(1);CCX_011(1);CIX_011(1)]; [CDX_015(1);CRX_015(1);CCX_015(1);CIX_015(1)];  %Using fminsearchbnd, an optimization tool, to minimize the objective function and determine model parameters at each temperature [p_275,S_275]=fminsearchbnd(@OBJECTIVE_FUN_MLE_Thesis_all, p0_275,lb, ub, options,T,CDX_005,CRX_005,CCX_005,CIX_005,CHX_005,CDX_013,CRX_013, CCX_013,CIX_013,CHX_013,CDX_010,CRX_010,CCX_010,CIX_010,CHX_010, T_005, T_013, T_010, Tref, m_005, m_013, m_010, V_005, V_013, V_010); [p_300,S_300]=fminsearchbnd(@OBJECTIVE_FUN_MLE_Thesis_all, p0_300,lb, ub, options,T,CDX_004,CRX_004,CCX_004,CIX_004,CHX_004,CDX_009,CRX_009, CCX_009,CIX_009,CHX_009,CDX_008,CRX_008,CCX_008,CIX_008,CHX_008, T_004, T_009, T_008, Tref, m_004, m_009, m_008, V_004, V_009, V_008); [p_325,S_325]=fminsearchbnd(@OBJECTIVE_FUN_MLE_Thesis_325, p0_325,lb, ub, options,T,CDX_012,CRX_012,CCX_012,CIX_012,CHX_012,CDX_011,CRX_011, CCX_011,CIX_011,CHX_011,T_012,T_011, Tref, m_012, m_011,V_012,V_011); [p_350,S_350]=fminsearchbnd(@OBJECTIVE_FUN_MLE_Thesis_all, p0_350,lb, ub, options,T,CDX_016,CRX_016,CCX_016,CIX_016,CHX_016,CDX_014,CRX_014, CCX_014,CIX_014,CHX_014,CDX_015,CRX_015,CCX_015,CIX_015,CHX_015, T_016, T_014, T_015, Tref, m_016, m_014, m_015, V_016, V_014, V_015); % S is the min of objective function p_275' p_300' p_325' p_350'  %Extracting parameter values k1_275=p_275(1); k2_275=p_275(2); k4_275=p_275(3); k3_275=p_275(7); KE1_275=p_275(4); KHC_275=p_275(5); KHHD_275=p_275(6);  k1_300=p_300(1); k2_300=p_300(2); k4_300=p_300(3); k3_300=p_300(7); KE1_300=p_300(4);  139  KHC_300=p_300(5); KHHD_300=p_300(6);  k1_325=p_325(1); k2_325=p_325(2); k4_325=p_325(3); k3_325=p_325(7); KE1_325=p_325(4); KHC_325=p_325(5); KHHD_325=p_325(6);  k1_350=p_350(1); k2_350=p_350(2); k4_350=p_350(3); k3_350=p_350(7); KE1_350=p_350(4); KHC_350=p_350(5); KHHD_350=p_350(6);  %Error Calculation tspan=0:.01:300; %T=275 %Jacobian Matrix Calculation using finite difference %RO-Ir(2)HBeta-005 p=p_275; [t,yp1r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); % array of y1r to y6r [t,yp2r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp3r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp4r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp5r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp6r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp7r_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_005, T_005, Tref,m_005,V_005); [t,yp1l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1)-h p(2) p  140  (3) p(4) p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); % array of y1l to y6l [t,yp2l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp3l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp4l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp5l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp6l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_005, T_005, Tref,m_005,V_005); [t,yp7l_275_3]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_005, T_005, Tref,m_005,V_005); %RO-Ir(2)HBeta-013 p=p_275 [t,yp1r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); % array of y1r to y6r [t,yp2r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp3r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp4r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp5r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp6r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp7r_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_013, T_013, Tref,m_013,V_013); [t,yp1l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); % array of y1l to y6l [t,yp2l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp3l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp4l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp5l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp6l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_013, T_013, Tref,m_013,V_013); [t,yp7l_275_5]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_013, T_013, Tref,m_013,V_013);  141  %RO-Ir(2)HBeta-010 p=p_275 [t,yp1r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); % array of y1r to y6r [t,yp2r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp3r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp4r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp5r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp6r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp7r_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_010, T_010, Tref,m_010,V_010); [t,yp1l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); % array of y1l to y6l [t,yp2l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp3l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp4l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp5l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp6l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_010, T_010, Tref,m_010,V_010); [t,yp7l_275_6]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_010, T_010, Tref,m_010,V_010); df1dp1_275_3=(yp1r_275_3(:,1)-yp1l_275_3(:,1))/2/h; df1dp2_275_3=(yp2r_275_3(:,1)-yp2l_275_3(:,1))/2/h; df1dp3_275_3=(yp3r_275_3(:,1)-yp3l_275_3(:,1))/2/h; df1dp4_275_3=(yp4r_275_3(:,1)-yp4l_275_3(:,1))/2/h; df1dp5_275_3=(yp5r_275_3(:,1)-yp5l_275_3(:,1))/2/h; df1dp6_275_3=(yp6r_275_3(:,1)-yp6l_275_3(:,1))/2/h; df1dp7_275_3=(yp7r_275_3(:,1)-yp7l_275_3(:,1))/2/h; df2dp1_275_3=(yp1r_275_3(:,2)-yp1l_275_3(:,2))/2/h; df2dp2_275_3=(yp2r_275_3(:,2)-yp2l_275_3(:,2))/2/h; df2dp3_275_3=(yp3r_275_3(:,2)-yp3l_275_3(:,2))/2/h; df2dp4_275_3=(yp4r_275_3(:,2)-yp4l_275_3(:,2))/2/h; df2dp5_275_3=(yp5r_275_3(:,2)-yp5l_275_3(:,2))/2/h; df2dp6_275_3=(yp6r_275_3(:,2)-yp6l_275_3(:,2))/2/h; df2dp7_275_3=(yp7r_275_3(:,2)-yp7l_275_3(:,2))/2/h;  142  df3dp1_275_3=(yp1r_275_3(:,3)-yp1l_275_3(:,3))/2/h; df3dp2_275_3=(yp2r_275_3(:,3)-yp2l_275_3(:,3))/2/h; df3dp3_275_3=(yp3r_275_3(:,3)-yp3l_275_3(:,3))/2/h; df3dp4_275_3=(yp4r_275_3(:,3)-yp4l_275_3(:,3))/2/h; df3dp5_275_3=(yp5r_275_3(:,3)-yp5l_275_3(:,3))/2/h; df3dp6_275_3=(yp6r_275_3(:,3)-yp6l_275_3(:,3))/2/h; df3dp7_275_3=(yp7r_275_3(:,3)-yp7l_275_3(:,3))/2/h; df4dp1_275_3=(yp1r_275_3(:,4)-yp1l_275_3(:,4))/2/h; df4dp2_275_3=(yp2r_275_3(:,4)-yp2l_275_3(:,4))/2/h; df4dp3_275_3=(yp3r_275_3(:,4)-yp3l_275_3(:,4))/2/h; df4dp4_275_3=(yp4r_275_3(:,4)-yp4l_275_3(:,4))/2/h; df4dp5_275_3=(yp5r_275_3(:,4)-yp5l_275_3(:,4))/2/h; df4dp6_275_3=(yp6r_275_3(:,4)-yp6l_275_3(:,4))/2/h; df4dp7_275_3=(yp7r_275_3(:,4)-yp7l_275_3(:,4))/2/h; df1dp1_275_5=(yp1r_275_5(:,1)-yp1l_275_5(:,1))/2/h; df1dp2_275_5=(yp2r_275_5(:,1)-yp2l_275_5(:,1))/2/h; df1dp3_275_5=(yp3r_275_5(:,1)-yp3l_275_5(:,1))/2/h; df1dp4_275_5=(yp4r_275_5(:,1)-yp4l_275_5(:,1))/2/h; df1dp5_275_5=(yp5r_275_5(:,1)-yp5l_275_5(:,1))/2/h; df1dp6_275_5=(yp6r_275_5(:,1)-yp6l_275_5(:,1))/2/h; df1dp7_275_5=(yp7r_275_5(:,1)-yp7l_275_5(:,1))/2/h; df2dp1_275_5=(yp1r_275_5(:,2)-yp1l_275_5(:,2))/2/h; df2dp2_275_5=(yp2r_275_5(:,2)-yp2l_275_5(:,2))/2/h; df2dp3_275_5=(yp3r_275_5(:,2)-yp3l_275_5(:,2))/2/h; df2dp4_275_5=(yp4r_275_5(:,2)-yp4l_275_5(:,2))/2/h; df2dp5_275_5=(yp5r_275_5(:,2)-yp5l_275_5(:,2))/2/h; df2dp6_275_5=(yp6r_275_5(:,2)-yp6l_275_5(:,2))/2/h; df2dp7_275_5=(yp7r_275_5(:,2)-yp7l_275_5(:,2))/2/h; df3dp1_275_5=(yp1r_275_5(:,3)-yp1l_275_5(:,3))/2/h; df3dp2_275_5=(yp2r_275_5(:,3)-yp2l_275_5(:,3))/2/h; df3dp3_275_5=(yp3r_275_5(:,3)-yp3l_275_5(:,3))/2/h; df3dp4_275_5=(yp4r_275_5(:,3)-yp4l_275_5(:,3))/2/h; df3dp5_275_5=(yp5r_275_5(:,3)-yp5l_275_5(:,3))/2/h; df3dp6_275_5=(yp6r_275_5(:,3)-yp6l_275_5(:,3))/2/h; df3dp7_275_5=(yp7r_275_5(:,3)-yp7l_275_5(:,3))/2/h; df4dp1_275_5=(yp1r_275_5(:,4)-yp1l_275_5(:,4))/2/h; df4dp2_275_5=(yp2r_275_5(:,4)-yp2l_275_5(:,4))/2/h; df4dp3_275_5=(yp3r_275_5(:,4)-yp3l_275_5(:,4))/2/h; df4dp4_275_5=(yp4r_275_5(:,4)-yp4l_275_5(:,4))/2/h; df4dp5_275_5=(yp5r_275_5(:,4)-yp5l_275_5(:,4))/2/h; df4dp6_275_5=(yp6r_275_5(:,4)-yp6l_275_5(:,4))/2/h; df4dp7_275_5=(yp7r_275_5(:,4)-yp7l_275_5(:,4))/2/h;  143  df1dp1_275_6=(yp1r_275_6(:,1)-yp1l_275_6(:,1))/2/h; df1dp2_275_6=(yp2r_275_6(:,1)-yp2l_275_6(:,1))/2/h; df1dp3_275_6=(yp3r_275_6(:,1)-yp3l_275_6(:,1))/2/h; df1dp4_275_6=(yp4r_275_6(:,1)-yp4l_275_6(:,1))/2/h; df1dp5_275_6=(yp5r_275_6(:,1)-yp5l_275_6(:,1))/2/h; df1dp6_275_6=(yp6r_275_6(:,1)-yp6l_275_6(:,1))/2/h; df1dp7_275_6=(yp7r_275_6(:,1)-yp7l_275_6(:,1))/2/h; df2dp1_275_6=(yp1r_275_6(:,2)-yp1l_275_6(:,2))/2/h; df2dp2_275_6=(yp2r_275_6(:,2)-yp2l_275_6(:,2))/2/h; df2dp3_275_6=(yp3r_275_6(:,2)-yp3l_275_6(:,2))/2/h; df2dp4_275_6=(yp4r_275_6(:,2)-yp4l_275_6(:,2))/2/h; df2dp5_275_6=(yp5r_275_6(:,2)-yp5l_275_6(:,2))/2/h; df2dp6_275_6=(yp6r_275_6(:,2)-yp6l_275_6(:,2))/2/h; df2dp7_275_6=(yp7r_275_6(:,2)-yp7l_275_6(:,2))/2/h; df3dp1_275_6=(yp1r_275_6(:,3)-yp1l_275_6(:,3))/2/h; df3dp2_275_6=(yp2r_275_6(:,3)-yp2l_275_6(:,3))/2/h; df3dp3_275_6=(yp3r_275_6(:,3)-yp3l_275_6(:,3))/2/h; df3dp4_275_6=(yp4r_275_6(:,3)-yp4l_275_6(:,3))/2/h; df3dp5_275_6=(yp5r_275_6(:,3)-yp5l_275_6(:,3))/2/h; df3dp6_275_6=(yp6r_275_6(:,3)-yp6l_275_6(:,3))/2/h; df3dp7_275_6=(yp7r_275_6(:,3)-yp7l_275_6(:,3))/2/h; df4dp1_275_6=(yp1r_275_6(:,4)-yp1l_275_6(:,4))/2/h; df4dp2_275_6=(yp2r_275_6(:,4)-yp2l_275_6(:,4))/2/h; df4dp3_275_6=(yp3r_275_6(:,4)-yp3l_275_6(:,4))/2/h; df4dp4_275_6=(yp4r_275_6(:,4)-yp4l_275_6(:,4))/2/h; df4dp5_275_6=(yp5r_275_6(:,4)-yp5l_275_6(:,4))/2/h; df4dp6_275_6=(yp6r_275_6(:,4)-yp6l_275_6(:,4))/2/h; df4dp7_275_6=(yp7r_275_6(:,4)-yp7l_275_6(:,4))/2/h; %Jacobian Matrix Jac_275=[df1dp1_275_3 df1dp2_275_3 df1dp3_275_3 df1dp4_275_3 df1dp5_275_3 df1dp6_275_3 df1dp7_275_3 df2dp1_275_3 df2dp2_275_3 df2dp3_275_3 df2dp4_275_3 df2dp5_275_3 df2dp6_275_3 df2dp7_275_3 df3dp1_275_3 df3dp2_275_3 df3dp3_275_3 df3dp4_275_3 df3dp5_275_3 df3dp6_275_3 df3dp7_275_3 df4dp1_275_3 df4dp2_275_3 df4dp3_275_3 df4dp4_275_3 df4dp5_275_3 df4dp6_275_3 df4dp7_275_3 df1dp1_275_5 df1dp2_275_5 df1dp3_275_5 df1dp4_275_5 df1dp5_275_5 df1dp6_275_5 df1dp7_275_5 df2dp1_275_5 df2dp2_275_5 df2dp3_275_5 df2dp4_275_5 df2dp5_275_5 df2dp6_275_5 df2dp7_275_5 df3dp1_275_5 df3dp2_275_5 df3dp3_275_5 df3dp4_275_5 df3dp5_275_5 df3dp6_275_5 df3dp7_275_5 df4dp1_275_5 df4dp2_275_5 df4dp3_275_5 df4dp4_275_5 df4dp5_275_5 df4dp6_275_5 df4dp7_275_5  144  df1dp1_275_6 df1dp2_275_6 df1dp6_275_6 df1dp7_275_6 df2dp1_275_6 df2dp2_275_6 df2dp6_275_6 df2dp7_275_6 df3dp1_275_6 df3dp2_275_6 df3dp6_275_6 df3dp7_275_6 df4dp1_275_6 df4dp2_275_6 df4dp6_275_6 df4dp7_275_6];  df1dp3_275_6 df1dp4_275_6 df1dp5_275_6 df2dp3_275_6 df2dp4_275_6 df2dp5_275_6 df3dp3_275_6 df3dp4_275_6 df3dp5_275_6 df4dp3_275_6 df4dp4_275_6 df4dp5_275_6  %T=300 %Jacobian Matrix Calculation using finite difference %RO-Ir(2)HBeta-004 p=p_300; [t,yp1r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); % array of y1r to y6r [t,yp2r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp3r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp4r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp5r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp6r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp7r_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_004, T_004, Tref,m_004,V_004); [t,yp1l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); % array of y1l to y6l [t,yp2l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp3l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp4l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp5l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp6l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_004, T_004, Tref,m_004,V_004); [t,yp7l_300_3]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_004, T_004, Tref,m_004,V_004); %RO-Ir(2)HBeta-009 p=p_300  145  [t,yp1r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); % array of y1r to y6r [t,yp2r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp3r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp4r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp5r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp6r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp7r_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_009, T_009, Tref,m_009,V_009); [t,yp1l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); % array of y1l to y6l [t,yp2l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp3l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp4l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp5l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp6l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp7l_300_5]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_009, T_009, Tref,m_009,V_009); %RO-Ir(2)HBeta-008 p=p_300 [t,yp1r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); % array of y1r to y6r [t,yp2r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp3r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp4r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp5r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp6r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp7r_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_008, T_008, Tref,m_008,V_008);  146  [t,yp1l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); % array of y1l to y6l [t,yp2l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp3l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp4l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp5l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp6l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp7l_300_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_008, T_008, Tref,m_008,V_008); df1dp1_300_3=(yp1r_300_3(:,1)-yp1l_300_3(:,1))/2/h; df1dp2_300_3=(yp2r_300_3(:,1)-yp2l_300_3(:,1))/2/h; df1dp3_300_3=(yp3r_300_3(:,1)-yp3l_300_3(:,1))/2/h; df1dp4_300_3=(yp4r_300_3(:,1)-yp4l_300_3(:,1))/2/h; df1dp5_300_3=(yp5r_300_3(:,1)-yp5l_300_3(:,1))/2/h; df1dp6_300_3=(yp6r_300_3(:,1)-yp6l_300_3(:,1))/2/h; df1dp7_300_3=(yp7r_300_3(:,1)-yp7l_300_3(:,1))/2/h; df2dp1_300_3=(yp1r_300_3(:,2)-yp1l_300_3(:,2))/2/h; df2dp2_300_3=(yp2r_300_3(:,2)-yp2l_300_3(:,2))/2/h; df2dp3_300_3=(yp3r_300_3(:,2)-yp3l_300_3(:,2))/2/h; df2dp4_300_3=(yp4r_300_3(:,2)-yp4l_300_3(:,2))/2/h; df2dp5_300_3=(yp5r_300_3(:,2)-yp5l_300_3(:,2))/2/h; df2dp6_300_3=(yp6r_300_3(:,2)-yp6l_300_3(:,2))/2/h; df2dp7_300_3=(yp7r_300_3(:,2)-yp7l_300_3(:,2))/2/h; df3dp1_300_3=(yp1r_300_3(:,3)-yp1l_300_3(:,3))/2/h; df3dp2_300_3=(yp2r_300_3(:,3)-yp2l_300_3(:,3))/2/h; df3dp3_300_3=(yp3r_300_3(:,3)-yp3l_300_3(:,3))/2/h; df3dp4_300_3=(yp4r_300_3(:,3)-yp4l_300_3(:,3))/2/h; df3dp5_300_3=(yp5r_300_3(:,3)-yp5l_300_3(:,3))/2/h; df3dp6_300_3=(yp6r_300_3(:,3)-yp6l_300_3(:,3))/2/h; df3dp7_300_3=(yp7r_300_3(:,3)-yp7l_300_3(:,3))/2/h; df4dp1_300_3=(yp1r_300_3(:,4)-yp1l_300_3(:,4))/2/h; df4dp2_300_3=(yp2r_300_3(:,4)-yp2l_300_3(:,4))/2/h; df4dp3_300_3=(yp3r_300_3(:,4)-yp3l_300_3(:,4))/2/h; df4dp4_300_3=(yp4r_300_3(:,4)-yp4l_300_3(:,4))/2/h; df4dp5_300_3=(yp5r_300_3(:,4)-yp5l_300_3(:,4))/2/h; df4dp6_300_3=(yp6r_300_3(:,4)-yp6l_300_3(:,4))/2/h; df4dp7_300_3=(yp7r_300_3(:,4)-yp7l_300_3(:,4))/2/h;  147  df1dp1_300_5=(yp1r_300_5(:,1)-yp1l_300_5(:,1))/2/h; df1dp2_300_5=(yp2r_300_5(:,1)-yp2l_300_5(:,1))/2/h; df1dp3_300_5=(yp3r_300_5(:,1)-yp3l_300_5(:,1))/2/h; df1dp4_300_5=(yp4r_300_5(:,1)-yp4l_300_5(:,1))/2/h; df1dp5_300_5=(yp5r_300_5(:,1)-yp5l_300_5(:,1))/2/h; df1dp6_300_5=(yp6r_300_5(:,1)-yp6l_300_5(:,1))/2/h; df1dp7_300_5=(yp7r_300_5(:,1)-yp7l_300_5(:,1))/2/h; df2dp1_300_5=(yp1r_300_5(:,2)-yp1l_300_5(:,2))/2/h; df2dp2_300_5=(yp2r_300_5(:,2)-yp2l_300_5(:,2))/2/h; df2dp3_300_5=(yp3r_300_5(:,2)-yp3l_300_5(:,2))/2/h; df2dp4_300_5=(yp4r_300_5(:,2)-yp4l_300_5(:,2))/2/h; df2dp5_300_5=(yp5r_300_5(:,2)-yp5l_300_5(:,2))/2/h; df2dp6_300_5=(yp6r_300_5(:,2)-yp6l_300_5(:,2))/2/h; df2dp7_300_5=(yp7r_300_5(:,2)-yp7l_300_5(:,2))/2/h; df3dp1_300_5=(yp1r_300_5(:,3)-yp1l_300_5(:,3))/2/h; df3dp2_300_5=(yp2r_300_5(:,3)-yp2l_300_5(:,3))/2/h; df3dp3_300_5=(yp3r_300_5(:,3)-yp3l_300_5(:,3))/2/h; df3dp4_300_5=(yp4r_300_5(:,3)-yp4l_300_5(:,3))/2/h; df3dp5_300_5=(yp5r_300_5(:,3)-yp5l_300_5(:,3))/2/h; df3dp6_300_5=(yp6r_300_5(:,3)-yp6l_300_5(:,3))/2/h; df3dp7_300_5=(yp7r_300_5(:,3)-yp7l_300_5(:,3))/2/h; df4dp1_300_5=(yp1r_300_5(:,4)-yp1l_300_5(:,4))/2/h; df4dp2_300_5=(yp2r_300_5(:,4)-yp2l_300_5(:,4))/2/h; df4dp3_300_5=(yp3r_300_5(:,4)-yp3l_300_5(:,4))/2/h; df4dp4_300_5=(yp4r_300_5(:,4)-yp4l_300_5(:,4))/2/h; df4dp5_300_5=(yp5r_300_5(:,4)-yp5l_300_5(:,4))/2/h; df4dp6_300_5=(yp6r_300_5(:,4)-yp6l_300_5(:,4))/2/h; df4dp7_300_5=(yp7r_300_5(:,4)-yp7l_300_5(:,4))/2/h; df1dp1_300_6=(yp1r_300_6(:,1)-yp1l_300_6(:,1))/2/h; df1dp2_300_6=(yp2r_300_6(:,1)-yp2l_300_6(:,1))/2/h; df1dp3_300_6=(yp3r_300_6(:,1)-yp3l_300_6(:,1))/2/h; df1dp4_300_6=(yp4r_300_6(:,1)-yp4l_300_6(:,1))/2/h; df1dp5_300_6=(yp5r_300_6(:,1)-yp5l_300_6(:,1))/2/h; df1dp6_300_6=(yp6r_300_6(:,1)-yp6l_300_6(:,1))/2/h; df1dp7_300_6=(yp7r_300_6(:,1)-yp7l_300_6(:,1))/2/h; df2dp1_300_6=(yp1r_300_6(:,2)-yp1l_300_6(:,2))/2/h; df2dp2_300_6=(yp2r_300_6(:,2)-yp2l_300_6(:,2))/2/h; df2dp3_300_6=(yp3r_300_6(:,2)-yp3l_300_6(:,2))/2/h; df2dp4_300_6=(yp4r_300_6(:,2)-yp4l_300_6(:,2))/2/h; df2dp5_300_6=(yp5r_300_6(:,2)-yp5l_300_6(:,2))/2/h; df2dp6_300_6=(yp6r_300_6(:,2)-yp6l_300_6(:,2))/2/h; df2dp7_300_6=(yp7r_300_6(:,2)-yp7l_300_6(:,2))/2/h; df3dp1_300_6=(yp1r_300_6(:,3)-yp1l_300_6(:,3))/2/h;  148  df3dp2_300_6=(yp2r_300_6(:,3)-yp2l_300_6(:,3))/2/h; df3dp3_300_6=(yp3r_300_6(:,3)-yp3l_300_6(:,3))/2/h; df3dp4_300_6=(yp4r_300_6(:,3)-yp4l_300_6(:,3))/2/h; df3dp5_300_6=(yp5r_300_6(:,3)-yp5l_300_6(:,3))/2/h; df3dp6_300_6=(yp6r_300_6(:,3)-yp6l_300_6(:,3))/2/h; df3dp7_300_6=(yp7r_300_6(:,3)-yp7l_300_6(:,3))/2/h; df4dp1_300_6=(yp1r_300_6(:,4)-yp1l_300_6(:,4))/2/h; df4dp2_300_6=(yp2r_300_6(:,4)-yp2l_300_6(:,4))/2/h; df4dp3_300_6=(yp3r_300_6(:,4)-yp3l_300_6(:,4))/2/h; df4dp4_300_6=(yp4r_300_6(:,4)-yp4l_300_6(:,4))/2/h; df4dp5_300_6=(yp5r_300_6(:,4)-yp5l_300_6(:,4))/2/h; df4dp6_300_6=(yp6r_300_6(:,4)-yp6l_300_6(:,4))/2/h; df4dp7_300_6=(yp7r_300_6(:,4)-yp7l_300_6(:,4))/2/h; %Jacobian Matrix Jac_300=[df1dp1_300_3 df1dp2_300_3 df1dp3_300_3 df1dp4_300_3 df1dp5_300_3 df1dp6_300_3 df1dp7_300_3 df2dp1_300_3 df2dp2_300_3 df2dp3_300_3 df2dp4_300_3 df2dp5_300_3 df2dp6_300_3 df2dp7_300_3 df3dp1_300_3 df3dp2_300_3 df3dp3_300_3 df3dp4_300_3 df3dp5_300_3 df3dp6_300_3 df3dp7_300_3 df4dp1_300_3 df4dp2_300_3 df4dp3_300_3 df4dp4_300_3 df4dp5_300_3 df4dp6_300_3 df4dp7_300_3 df1dp1_300_5 df1dp2_300_5 df1dp3_300_5 df1dp4_300_5 df1dp5_300_5 df1dp6_300_5 df1dp7_300_5 df2dp1_300_5 df2dp2_300_5 df2dp3_300_5 df2dp4_300_5 df2dp5_300_5 df2dp6_300_5 df2dp7_300_5 df3dp1_300_5 df3dp2_300_5 df3dp3_300_5 df3dp4_300_5 df3dp5_300_5 df3dp6_300_5 df3dp7_300_5 df4dp1_300_5 df4dp2_300_5 df4dp3_300_5 df4dp4_300_5 df4dp5_300_5 df4dp6_300_5 df4dp7_300_5 df1dp1_300_6 df1dp2_300_6 df1dp3_300_6 df1dp4_300_6 df1dp5_300_6 df1dp6_300_6 df1dp7_300_6 df2dp1_300_6 df2dp2_300_6 df2dp3_300_6 df2dp4_300_6 df2dp5_300_6 df2dp6_300_6 df2dp7_300_6 df3dp1_300_6 df3dp2_300_6 df3dp3_300_6 df3dp4_300_6 df3dp5_300_6 df3dp6_300_6 df3dp7_300_6 df4dp1_300_6 df4dp2_300_6 df4dp3_300_6 df4dp4_300_6 df4dp5_300_6 df4dp6_300_6 df4dp7_300_6]; %T=325 %Jacobian Matrix Calculation using finite difference %RO-Ir(2)HBeta-012 p=p_325 [t,yp1r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); % array of  149  y1r to y6r [t,yp2r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) (3) p(4) p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp3r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) +h p(4) p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp4r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(4)+h p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp5r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(4) p(5)+h p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp6r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(4) p(5) p(6)+h p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp7r_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(4) p(5) p(6) p(7)+h],CHX_012, T_012, Tref,m_012,V_012);  p(2)+h p p(2) p(3) p(2) p(3) p(2) p(3) p(2) p(3) p(2) p(3)  [t,yp1l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); % array of y1l to y6l [t,yp2l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp3l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp4l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp5l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp6l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_012, T_012, Tref,m_012,V_012); [t,yp7l_325_5]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_012, T_012, Tref,m_012,V_012); %RO-Ir(2)HBeta-011 p=p_325 [t,yp1r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); % array of y1r to y6r [t,yp2r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp3r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp4r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp5r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp6r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp7r_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_008, T_008, Tref,m_008,V_008); [t,yp1l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1)-h p(2) p  150  (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); % array of y1l to y6l [t,yp2l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp3l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp4l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp5l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp6l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_008, T_008, Tref,m_008,V_008); [t,yp7l_325_6]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_008, T_008, Tref,m_008,V_008);  df1dp1_325_5=(yp1r_325_5(:,1)-yp1l_325_5(:,1))/2/h; df1dp2_325_5=(yp2r_325_5(:,1)-yp2l_325_5(:,1))/2/h; df1dp3_325_5=(yp3r_325_5(:,1)-yp3l_325_5(:,1))/2/h; df1dp4_325_5=(yp4r_325_5(:,1)-yp4l_325_5(:,1))/2/h; df1dp5_325_5=(yp5r_325_5(:,1)-yp5l_325_5(:,1))/2/h; df1dp6_325_5=(yp6r_325_5(:,1)-yp6l_325_5(:,1))/2/h; df1dp7_325_5=(yp7r_325_5(:,1)-yp7l_325_5(:,1))/2/h; df2dp1_325_5=(yp1r_325_5(:,2)-yp1l_325_5(:,2))/2/h; df2dp2_325_5=(yp2r_325_5(:,2)-yp2l_325_5(:,2))/2/h; df2dp3_325_5=(yp3r_325_5(:,2)-yp3l_325_5(:,2))/2/h; df2dp4_325_5=(yp4r_325_5(:,2)-yp4l_325_5(:,2))/2/h; df2dp5_325_5=(yp5r_325_5(:,2)-yp5l_325_5(:,2))/2/h; df2dp6_325_5=(yp6r_325_5(:,2)-yp6l_325_5(:,2))/2/h; df2dp7_325_5=(yp7r_325_5(:,2)-yp7l_325_5(:,2))/2/h; df3dp1_325_5=(yp1r_325_5(:,3)-yp1l_325_5(:,3))/2/h; df3dp2_325_5=(yp2r_325_5(:,3)-yp2l_325_5(:,3))/2/h; df3dp3_325_5=(yp3r_325_5(:,3)-yp3l_325_5(:,3))/2/h; df3dp4_325_5=(yp4r_325_5(:,3)-yp4l_325_5(:,3))/2/h; df3dp5_325_5=(yp5r_325_5(:,3)-yp5l_325_5(:,3))/2/h; df3dp6_325_5=(yp6r_325_5(:,3)-yp6l_325_5(:,3))/2/h; df3dp7_325_5=(yp7r_325_5(:,3)-yp7l_325_5(:,3))/2/h; df4dp1_325_5=(yp1r_325_5(:,4)-yp1l_325_5(:,4))/2/h; df4dp2_325_5=(yp2r_325_5(:,4)-yp2l_325_5(:,4))/2/h; df4dp3_325_5=(yp3r_325_5(:,4)-yp3l_325_5(:,4))/2/h; df4dp4_325_5=(yp4r_325_5(:,4)-yp4l_325_5(:,4))/2/h; df4dp5_325_5=(yp5r_325_5(:,4)-yp5l_325_5(:,4))/2/h; df4dp6_325_5=(yp6r_325_5(:,4)-yp6l_325_5(:,4))/2/h; df4dp7_325_5=(yp7r_325_5(:,4)-yp7l_325_5(:,4))/2/h; df1dp1_325_6=(yp1r_325_6(:,1)-yp1l_325_6(:,1))/2/h;  151  df1dp2_325_6=(yp2r_325_6(:,1)-yp2l_325_6(:,1))/2/h; df1dp3_325_6=(yp3r_325_6(:,1)-yp3l_325_6(:,1))/2/h; df1dp4_325_6=(yp4r_325_6(:,1)-yp4l_325_6(:,1))/2/h; df1dp5_325_6=(yp5r_325_6(:,1)-yp5l_325_6(:,1))/2/h; df1dp6_325_6=(yp6r_325_6(:,1)-yp6l_325_6(:,1))/2/h; df1dp7_325_6=(yp7r_325_6(:,1)-yp7l_325_6(:,1))/2/h; df2dp1_325_6=(yp1r_325_6(:,2)-yp1l_325_6(:,2))/2/h; df2dp2_325_6=(yp2r_325_6(:,2)-yp2l_325_6(:,2))/2/h; df2dp3_325_6=(yp3r_325_6(:,2)-yp3l_325_6(:,2))/2/h; df2dp4_325_6=(yp4r_325_6(:,2)-yp4l_325_6(:,2))/2/h; df2dp5_325_6=(yp5r_325_6(:,2)-yp5l_325_6(:,2))/2/h; df2dp6_325_6=(yp6r_325_6(:,2)-yp6l_325_6(:,2))/2/h; df2dp7_325_6=(yp7r_325_6(:,2)-yp7l_325_6(:,2))/2/h; df3dp1_325_6=(yp1r_325_6(:,3)-yp1l_325_6(:,3))/2/h; df3dp2_325_6=(yp2r_325_6(:,3)-yp2l_325_6(:,3))/2/h; df3dp3_325_6=(yp3r_325_6(:,3)-yp3l_325_6(:,3))/2/h; df3dp4_325_6=(yp4r_325_6(:,3)-yp4l_325_6(:,3))/2/h; df3dp5_325_6=(yp5r_325_6(:,3)-yp5l_325_6(:,3))/2/h; df3dp6_325_6=(yp6r_325_6(:,3)-yp6l_325_6(:,3))/2/h; df3dp7_325_6=(yp7r_325_6(:,3)-yp7l_325_6(:,3))/2/h; df4dp1_325_6=(yp1r_325_6(:,4)-yp1l_325_6(:,4))/2/h; df4dp2_325_6=(yp2r_325_6(:,4)-yp2l_325_6(:,4))/2/h; df4dp3_325_6=(yp3r_325_6(:,4)-yp3l_325_6(:,4))/2/h; df4dp4_325_6=(yp4r_325_6(:,4)-yp4l_325_6(:,4))/2/h; df4dp5_325_6=(yp5r_325_6(:,4)-yp5l_325_6(:,4))/2/h; df4dp6_325_6=(yp6r_325_6(:,4)-yp6l_325_6(:,4))/2/h; df4dp7_325_6=(yp7r_325_6(:,4)-yp7l_325_6(:,4))/2/h; %Jacobian Matrix Jac_325=[df1dp1_325_5 df1dp2_325_5 df1dp3_325_5 df1dp4_325_5 df1dp5_325_5 df1dp6_325_5 df1dp7_325_5 df2dp1_325_5 df2dp2_325_5 df2dp3_325_5 df2dp4_325_5 df2dp5_325_5 df2dp6_325_5 df2dp7_325_5 df3dp1_325_5 df3dp2_325_5 df3dp3_325_5 df3dp4_325_5 df3dp5_325_5 df3dp6_325_5 df3dp7_325_5 df4dp1_325_5 df4dp2_325_5 df4dp3_325_5 df4dp4_325_5 df4dp5_325_5 df4dp6_325_5 df4dp7_325_5 df1dp1_325_6 df1dp2_325_6 df1dp3_325_6 df1dp4_325_6 df1dp5_325_6 df1dp6_325_6 df1dp7_325_6 df2dp1_325_6 df2dp2_325_6 df2dp3_325_6 df2dp4_325_6 df2dp5_325_6 df2dp6_325_6 df2dp7_325_6 df3dp1_325_6 df3dp2_325_6 df3dp3_325_6 df3dp4_325_6 df3dp5_325_6 df3dp6_325_6 df3dp7_325_6 df4dp1_325_6 df4dp2_325_6 df4dp3_325_6 df4dp4_325_6 df4dp5_325_6 df4dp6_325_6 df4dp7_325_6];  152  %T=350 %Jacobian Matrix Calculation using finite difference %RO-Ir(2)HBeta-016 p=p_350; [t,yp1r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); % array of y1r to y6r [t,yp2r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp3r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp4r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp5r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp6r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp7r_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_016, T_016, Tref,m_016,V_016); [t,yp1l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); % array of y1l to y6l [t,yp2l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp3l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp4l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp5l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp6l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_016, T_016, Tref,m_016,V_016); [t,yp7l_350_3]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_016, T_016, Tref,m_016,V_016); %RO-Ir(2)HBeta-014 p=p_350 [t,yp1r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); % array of y1r to y6r [t,yp2r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp3r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp4r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3)  153  p(4)+h p(5) p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp5r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp6r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_009, T_009, Tref,m_009,V_009); [t,yp7r_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_009, T_009, Tref,m_009,V_009); [t,yp1l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_014, T_014, Tref,m_014,V_014); % array of y1l to y6l [t,yp2l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_014, T_014, Tref,m_014,V_014); [t,yp3l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_014, T_014, Tref,m_014,V_014); [t,yp4l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4)-h p(5) p(6) p(7)],CHX_014, T_014, Tref,m_014,V_014); [t,yp5l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4) p(5)-h p(6) p(7)],CHX_014, T_014, Tref,m_014,V_014); [t,yp6l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4) p(5) p(6)-h p(7)],CHX_014, T_014, Tref,m_014,V_014); [t,yp7l_350_5]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)-h],CHX_014, T_014, Tref,m_014,V_014); %RO-Ir(2)HBeta-015 p=p_350 [t,yp1r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1)+h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); % array of y1r to y6r [t,yp2r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2)+h p (3) p(4) p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp3r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2) p(3) +h p(4) p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp4r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2) p(3) p(4)+h p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp5r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2) p(3) p(4) p(5)+h p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp6r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2) p(3) p(4) p(5) p(6)+h p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp7r_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2) p(3) p(4) p(5) p(6) p(7)+h],CHX_015, T_015, Tref,m_015,V_015); [t,yp1l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1)-h p(2) p (3) p(4) p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); % array of y1l to y6l [t,yp2l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2)-h p (3) p(4) p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp3l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(2) p(3) -h p(4) p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015);  154  [t,yp4l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(4)-h p(5) p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp5l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(4) p(5)-h p(6) p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp6l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(4) p(5) p(6)-h p(7)],CHX_015, T_015, Tref,m_015,V_015); [t,yp7l_350_6]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],[p(1) p(4) p(5) p(6) p(7)-h],CHX_015, T_015, Tref,m_015,V_015);  p(2) p(3) p(2) p(3) p(2) p(3) p(2) p(3)  df1dp1_350_3=(yp1r_350_3(:,1)-yp1l_350_3(:,1))/2/h; df1dp2_350_3=(yp2r_350_3(:,1)-yp2l_350_3(:,1))/2/h; df1dp3_350_3=(yp3r_350_3(:,1)-yp3l_350_3(:,1))/2/h; df1dp4_350_3=(yp4r_350_3(:,1)-yp4l_350_3(:,1))/2/h; df1dp5_350_3=(yp5r_350_3(:,1)-yp5l_350_3(:,1))/2/h; df1dp6_350_3=(yp6r_350_3(:,1)-yp6l_350_3(:,1))/2/h; df1dp7_350_3=(yp7r_350_3(:,1)-yp7l_350_3(:,1))/2/h; df2dp1_350_3=(yp1r_350_3(:,2)-yp1l_350_3(:,2))/2/h; df2dp2_350_3=(yp2r_350_3(:,2)-yp2l_350_3(:,2))/2/h; df2dp3_350_3=(yp3r_350_3(:,2)-yp3l_350_3(:,2))/2/h; df2dp4_350_3=(yp4r_350_3(:,2)-yp4l_350_3(:,2))/2/h; df2dp5_350_3=(yp5r_350_3(:,2)-yp5l_350_3(:,2))/2/h; df2dp6_350_3=(yp6r_350_3(:,2)-yp6l_350_3(:,2))/2/h; df2dp7_350_3=(yp7r_350_3(:,2)-yp7l_350_3(:,2))/2/h; df3dp1_350_3=(yp1r_350_3(:,3)-yp1l_350_3(:,3))/2/h; df3dp2_350_3=(yp2r_350_3(:,3)-yp2l_350_3(:,3))/2/h; df3dp3_350_3=(yp3r_350_3(:,3)-yp3l_350_3(:,3))/2/h; df3dp4_350_3=(yp4r_350_3(:,3)-yp4l_350_3(:,3))/2/h; df3dp5_350_3=(yp5r_350_3(:,3)-yp5l_350_3(:,3))/2/h; df3dp6_350_3=(yp6r_350_3(:,3)-yp6l_350_3(:,3))/2/h; df3dp7_350_3=(yp7r_350_3(:,3)-yp7l_350_3(:,3))/2/h; df4dp1_350_3=(yp1r_350_3(:,4)-yp1l_350_3(:,4))/2/h; df4dp2_350_3=(yp2r_350_3(:,4)-yp2l_350_3(:,4))/2/h; df4dp3_350_3=(yp3r_350_3(:,4)-yp3l_350_3(:,4))/2/h; df4dp4_350_3=(yp4r_350_3(:,4)-yp4l_350_3(:,4))/2/h; df4dp5_350_3=(yp5r_350_3(:,4)-yp5l_350_3(:,4))/2/h; df4dp6_350_3=(yp6r_350_3(:,4)-yp6l_350_3(:,4))/2/h; df4dp7_350_3=(yp7r_350_3(:,4)-yp7l_350_3(:,4))/2/h; df1dp1_350_5=(yp1r_350_5(:,1)-yp1l_350_5(:,1))/2/h; df1dp2_350_5=(yp2r_350_5(:,1)-yp2l_350_5(:,1))/2/h; df1dp3_350_5=(yp3r_350_5(:,1)-yp3l_350_5(:,1))/2/h; df1dp4_350_5=(yp4r_350_5(:,1)-yp4l_350_5(:,1))/2/h; df1dp5_350_5=(yp5r_350_5(:,1)-yp5l_350_5(:,1))/2/h; df1dp6_350_5=(yp6r_350_5(:,1)-yp6l_350_5(:,1))/2/h; df1dp7_350_5=(yp7r_350_5(:,1)-yp7l_350_5(:,1))/2/h;  155  df2dp1_350_5=(yp1r_350_5(:,2)-yp1l_350_5(:,2))/2/h; df2dp2_350_5=(yp2r_350_5(:,2)-yp2l_350_5(:,2))/2/h; df2dp3_350_5=(yp3r_350_5(:,2)-yp3l_350_5(:,2))/2/h; df2dp4_350_5=(yp4r_350_5(:,2)-yp4l_350_5(:,2))/2/h; df2dp5_350_5=(yp5r_350_5(:,2)-yp5l_350_5(:,2))/2/h; df2dp6_350_5=(yp6r_350_5(:,2)-yp6l_350_5(:,2))/2/h; df2dp7_350_5=(yp7r_350_5(:,2)-yp7l_350_5(:,2))/2/h; df3dp1_350_5=(yp1r_350_5(:,3)-yp1l_350_5(:,3))/2/h; df3dp2_350_5=(yp2r_350_5(:,3)-yp2l_350_5(:,3))/2/h; df3dp3_350_5=(yp3r_350_5(:,3)-yp3l_350_5(:,3))/2/h; df3dp4_350_5=(yp4r_350_5(:,3)-yp4l_350_5(:,3))/2/h; df3dp5_350_5=(yp5r_350_5(:,3)-yp5l_350_5(:,3))/2/h; df3dp6_350_5=(yp6r_350_5(:,3)-yp6l_350_5(:,3))/2/h; df3dp7_350_5=(yp7r_350_5(:,3)-yp7l_350_5(:,3))/2/h; df4dp1_350_5=(yp1r_350_5(:,4)-yp1l_350_5(:,4))/2/h; df4dp2_350_5=(yp2r_350_5(:,4)-yp2l_350_5(:,4))/2/h; df4dp3_350_5=(yp3r_350_5(:,4)-yp3l_350_5(:,4))/2/h; df4dp4_350_5=(yp4r_350_5(:,4)-yp4l_350_5(:,4))/2/h; df4dp5_350_5=(yp5r_350_5(:,4)-yp5l_350_5(:,4))/2/h; df4dp6_350_5=(yp6r_350_5(:,4)-yp6l_350_5(:,4))/2/h; df4dp7_350_5=(yp7r_350_5(:,4)-yp7l_350_5(:,4))/2/h; df1dp1_350_6=(yp1r_350_6(:,1)-yp1l_350_6(:,1))/2/h; df1dp2_350_6=(yp2r_350_6(:,1)-yp2l_350_6(:,1))/2/h; df1dp3_350_6=(yp3r_350_6(:,1)-yp3l_350_6(:,1))/2/h; df1dp4_350_6=(yp4r_350_6(:,1)-yp4l_350_6(:,1))/2/h; df1dp5_350_6=(yp5r_350_6(:,1)-yp5l_350_6(:,1))/2/h; df1dp6_350_6=(yp6r_350_6(:,1)-yp6l_350_6(:,1))/2/h; df1dp7_350_6=(yp7r_350_6(:,1)-yp7l_350_6(:,1))/2/h; df2dp1_350_6=(yp1r_350_6(:,2)-yp1l_350_6(:,2))/2/h; df2dp2_350_6=(yp2r_350_6(:,2)-yp2l_350_6(:,2))/2/h; df2dp3_350_6=(yp3r_350_6(:,2)-yp3l_350_6(:,2))/2/h; df2dp4_350_6=(yp4r_350_6(:,2)-yp4l_350_6(:,2))/2/h; df2dp5_350_6=(yp5r_350_6(:,2)-yp5l_350_6(:,2))/2/h; df2dp6_350_6=(yp6r_350_6(:,2)-yp6l_350_6(:,2))/2/h; df2dp7_350_6=(yp7r_350_6(:,2)-yp7l_350_6(:,2))/2/h; df3dp1_350_6=(yp1r_350_6(:,3)-yp1l_350_6(:,3))/2/h; df3dp2_350_6=(yp2r_350_6(:,3)-yp2l_350_6(:,3))/2/h; df3dp3_350_6=(yp3r_350_6(:,3)-yp3l_350_6(:,3))/2/h; df3dp4_350_6=(yp4r_350_6(:,3)-yp4l_350_6(:,3))/2/h; df3dp5_350_6=(yp5r_350_6(:,3)-yp5l_350_6(:,3))/2/h; df3dp6_350_6=(yp6r_350_6(:,3)-yp6l_350_6(:,3))/2/h; df3dp7_350_6=(yp7r_350_6(:,3)-yp7l_350_6(:,3))/2/h; df4dp1_350_6=(yp1r_350_6(:,4)-yp1l_350_6(:,4))/2/h;  156  df4dp2_350_6=(yp2r_350_6(:,4)-yp2l_350_6(:,4))/2/h; df4dp3_350_6=(yp3r_350_6(:,4)-yp3l_350_6(:,4))/2/h; df4dp4_350_6=(yp4r_350_6(:,4)-yp4l_350_6(:,4))/2/h; df4dp5_350_6=(yp5r_350_6(:,4)-yp5l_350_6(:,4))/2/h; df4dp6_350_6=(yp6r_350_6(:,4)-yp6l_350_6(:,4))/2/h; df4dp7_350_6=(yp7r_350_6(:,4)-yp7l_350_6(:,4))/2/h; %Jacobian Matrix Jac_350=[df1dp1_350_3 df1dp2_350_3 df1dp3_350_3 df1dp4_350_3 df1dp5_350_3 df1dp6_350_3 df1dp7_350_3 df2dp1_350_3 df2dp2_350_3 df2dp3_350_3 df2dp4_350_3 df2dp5_350_3 df2dp6_350_3 df2dp7_350_3 df3dp1_350_3 df3dp2_350_3 df3dp3_350_3 df3dp4_350_3 df3dp5_350_3 df3dp6_350_3 df3dp7_350_3 df4dp1_350_3 df4dp2_350_3 df4dp3_350_3 df4dp4_350_3 df4dp5_350_3 df4dp6_350_3 df4dp7_350_3 df1dp1_350_5 df1dp2_350_5 df1dp3_350_5 df1dp4_350_5 df1dp5_350_5 df1dp6_350_5 df1dp7_350_5 df2dp1_350_5 df2dp2_350_5 df2dp3_350_5 df2dp4_350_5 df2dp5_350_5 df2dp6_350_5 df2dp7_350_5 df3dp1_350_5 df3dp2_350_5 df3dp3_350_5 df3dp4_350_5 df3dp5_350_5 df3dp6_350_5 df3dp7_350_5 df4dp1_350_5 df4dp2_350_5 df4dp3_350_5 df4dp4_350_5 df4dp5_350_5 df4dp6_350_5 df4dp7_350_5 df1dp1_350_6 df1dp2_350_6 df1dp3_350_6 df1dp4_350_6 df1dp5_350_6 df1dp6_350_6 df1dp7_350_6 df2dp1_350_6 df2dp2_350_6 df2dp3_350_6 df2dp4_350_6 df2dp5_350_6 df2dp6_350_6 df2dp7_350_6 df3dp1_350_6 df3dp2_350_6 df3dp3_350_6 df3dp4_350_6 df3dp5_350_6 df3dp6_350_6 df3dp7_350_6 df4dp1_350_6 df4dp2_350_6 df4dp3_350_6 df4dp4_350_6 df4dp5_350_6 df4dp6_350_6 df4dp7_350_6]; % degree of freedom = No of dependent variables * No of data points No of parameters DF=3*4*length(CDX_005)-length(p0_275); DF_325=2*4*length(CDX_005)-length(p0_275); SE_275=S_275/DF; SE_300=S_300/DF; SE_325=S_325/DF_325; SE_350=S_350/DF; Astar_275=Jac_275'*Jac_275; Astar_300=Jac_300'*Jac_300; Astar_325=Jac_325'*Jac_325; Astar_350=Jac_350'*Jac_350; Astarinv_275=inv(Astar_275);  157  Astarinv_300=inv(Astar_300); Astarinv_325=inv(Astar_325); Astarinv_350=inv(Astar_350); std_error_275=SE_275*sqrt(diag(Astarinv_275)) p_275' std_error_300=SE_300*sqrt(diag(Astarinv_300)) p_300' std_error_325=SE_325*sqrt(diag(Astarinv_325)) p_325' std_error_350=SE_350*sqrt(diag(Astarinv_350)) p_350'  %Model values calculation  [t,Y_005]=ode45('ODE_FUN_Thesis',tspan,C_0_005,[],p_275,CHX_005, T_005, Tref,m_005,V_005); [t,Y_004]=ode45('ODE_FUN_Thesis',tspan,C_0_004,[],p_300,CHX_004, T_004, Tref,m_004,V_004); [t,Y_013]=ode45('ODE_FUN_Thesis',tspan,C_0_013,[],p_275,CHX_013, T_013, Tref,m_013,V_013); [t,Y_009]=ode45('ODE_FUN_Thesis',tspan,C_0_009,[],p_300,CHX_009, T_009, Tref,m_009,V_009); [t,Y_012]=ode45('ODE_FUN_Thesis',tspan,C_0_012,[],p_325,CHX_012, T_012, Tref,m_012,V_012); [t,Y_008]=ode45('ODE_FUN_Thesis',tspan,C_0_008,[],p_300,CHX_008, T_008, Tref,m_008,V_008); [t,Y_014]=ode45('ODE_FUN_Thesis',tspan,C_0_014,[],p_350,CHX_014, T_014, Tref,m_014,V_014); [t,Y_010]=ode45('ODE_FUN_Thesis',tspan,C_0_010,[],p_275,CHX_010, T_010, Tref,m_010,V_010); [t,Y_011]=ode45('ODE_FUN_Thesis',tspan,C_0_011,[],p_325,CHX_011, T_011, Tref,m_011,V_011); [t,Y_015]=ode45('ODE_FUN_Thesis',tspan,C_0_015,[],p_350,CHX_015, T_015, Tref,m_015,V_015); [t,Y_016]=ode45('ODE_FUN_Thesis',tspan,C_0_016,[],p_350,CHX_016, T_016, Tref,m_016,V_016); %Exracting model predictions CD_005 CR_005 CC_005 CI_005  =real(abs(Y_005(:,1))); =real(abs(Y_005(:,2))); =real(abs(Y_005(:,3))); =real(abs(Y_005(:,4)));  CD_004 CR_004  =real(abs(Y_004(:,1))); =real(abs(Y_004(:,2)));  158  CC_004 CI_004  =real(abs(Y_004(:,3))); =real(abs(Y_004(:,4)));  CD_013 CR_013 CC_013 CI_013  =real(abs(Y_013(:,1))); =real(abs(Y_013(:,2))); =real(abs(Y_013(:,3))); =real(abs(Y_013(:,4)));  CD_009 CR_009 CC_009 CI_009  =real(abs(Y_009(:,1))); =real(abs(Y_009(:,2))); =real(abs(Y_009(:,3))); =real(abs(Y_009(:,4)));  CD_012 CR_012 CC_012 CI_012  =real(abs(Y_012(:,1))); =real(abs(Y_012(:,2))); =real(abs(Y_012(:,3))); =real(abs(Y_012(:,4)));  CD_008 CR_008 CC_008 CI_008  =real(abs(Y_008(:,1))); =real(abs(Y_008(:,2))); =real(abs(Y_008(:,3))); =real(abs(Y_008(:,4)));  CD_016 CR_016 CC_016 CI_016  =real(abs(Y_016(:,1))); =real(abs(Y_016(:,2))); =real(abs(Y_016(:,3))); =real(abs(Y_016(:,4)));  CD_014 CR_014 CC_014 CI_014  =real(abs(Y_014(:,1))); =real(abs(Y_014(:,2))); =real(abs(Y_014(:,3))); =real(abs(Y_014(:,4)));  CD_010 CR_010 CC_010 CI_010  =real(abs(Y_010(:,1))); =real(abs(Y_010(:,2))); =real(abs(Y_010(:,3))); =real(abs(Y_010(:,4)));  CD_011 CR_011 CC_011 CI_011  =real(abs(Y_011(:,1))); =real(abs(Y_011(:,2))); =real(abs(Y_011(:,3))); =real(abs(Y_011(:,4)));  CD_015 CR_015 CC_015 CI_015  =real(abs(Y_015(:,1))); =real(abs(Y_015(:,2))); =real(abs(Y_015(:,3))); =real(abs(Y_015(:,4)));  %Extracting model predictions at sample collection time  159  CD_005E =real(abs([CD_005(1) CD_005(1501) CD_005(3001) CD_005(4501) CD_005(6001) CD_005(12001) CD_005(18001) CD_005(24001) CD_005 (30001)])); CR_005E =real(abs([CR_005(1) CR_005(1501) CR_005(3001) CR_005(4501) CR_005(6001) CR_005(12001) CR_005(18001) CR_005(24001) CR_005 (30001)])); CC_005E =real(abs([CC_005(1) CC_005(1501) CC_005(3001) CC_005(4501) CC_005(6001) CC_005(12001) CC_005(18001) CC_005(24001) CC_005 (30001)])); CI_005E =real(abs([CI_005(1) CI_005(1501) CI_005(3001) CI_005(4501) CI_005(6001) CI_005(12001) CI_005(18001) CI_005(24001) CI_005 (30001)])); CD_004E =real(abs([CD_004(1) CD_004(1501) CD_004(3001) CD_004(4501) CD_004(6001) CD_004(12001) CD_004(18001) CD_004(24001) CD_004 (30001)])); CR_004E =real(abs([CR_004(1) CR_004(1501) CR_004(3001) CR_004(4501) CR_004(6001) CR_004(12001) CR_004(18001) CR_004(24001) CR_004 (30001)])); CC_004E =real(abs([CC_004(1) CC_004(1501) CC_004(3001) CC_004(4501) CC_004(6001) CC_004(12001) CC_004(18001) CC_004(24001) CC_004 (30001)])); CI_004E =real(abs([CI_004(1) CI_004(1501) CI_004(3001) CI_004(4501) CI_004(6001) CI_004(12001) CI_004(18001) CI_004(24001) CI_004 (30001)])); CD_013E =real(abs([CD_013(1) CD_013(1501) CD_013(3001) CD_013(4501) CD_013(6001) CD_013(12001) CD_013(18001) CD_013(24001) CD_013 (30001)])); CR_013E =real(abs([CR_013(1) CR_013(1501) CR_013(3001) CR_013(4501) CR_013(6001) CR_013(12001) CR_013(18001) CR_013(24001) CR_013 (30001)])); CC_013E =real(abs([CC_013(1) CC_013(1501) CC_013(3001) CC_013(4501) CC_013(6001) CC_013(12001) CC_013(18001) CC_013(24001) CC_013 (30001)])); CI_013E =real(abs([CI_013(1) CI_013(1501) CI_013(3001) CI_013(4501) CI_013(6001) CI_013(12001) CI_013(18001) CI_013(24001) CI_013 (30001)])); CD_009E =real(abs([CD_009(1) CD_009(1501) CD_009(3001) CD_009(4501) CD_009(6001) CD_009(12001) CD_009(18001) CD_009(24001) CD_009 (30001)])); CR_009E =real(abs([CR_009(1) CR_009(1501) CR_009(3001) CR_009(4501) CR_009(6001) CR_009(12001) CR_009(18001) CR_009(24001) CR_009 (30001)])); CC_009E =real(abs([CC_009(1) CC_009(1501) CC_009(3001) CC_009(4501) CC_009(6001) CC_009(12001) CC_009(18001) CC_009(24001) CC_009 (30001)]));  160  CI_009E =real(abs([CI_009(1) CI_009(1501) CI_009(3001) CI_009(4501) CI_009(6001) CI_009(12001) CI_009(18001) CI_009(24001) CI_009 (30001)])); CD_012E =real(abs([CD_012(1) CD_012(1501) CD_012(3001) CD_012(4501) CD_012(6001) CD_012(12001) CD_012(18001) CD_012(24001) CD_012 (30001)])); CR_012E =real(abs([CR_012(1) CR_012(1501) CR_012(3001) CR_012(4501) CR_012(6001) CR_012(12001) CR_012(18001) CR_012(24001) CR_012 (30001)])); CC_012E =real(abs([CC_012(1) CC_012(1501) CC_012(3001) CC_012(4501) CC_012(6001) CC_012(12001) CC_012(18001) CC_012(24001) CC_012 (30001)])); CI_012E =real(abs([CI_012(1) CI_012(1501) CI_012(3001) CI_012(4501) CI_012(6001) CI_012(12001) CI_012(18001) CI_012(24001) CI_012 (30001)])); CD_008E =real(abs([CD_008(1) CD_008(1501) CD_008(3001) CD_008(4501) CD_008(6001) CD_008(12001) CD_008(18001) CD_008(24001) CD_008 (30001)])); CR_008E =real(abs([CR_008(1) CR_008(1501) CR_008(3001) CR_008(4501) CR_008(6001) CR_008(12001) CR_008(18001) CR_008(24001) CR_008 (30001)])); CC_008E =real(abs([CC_008(1) CC_008(1501) CC_008(3001) CC_008(4501) CC_008(6001) CC_008(12001) CC_008(18001) CC_008(24001) CC_008 (30001)])); CI_008E =real(abs([CI_008(1) CI_008(1501) CI_008(3001) CI_008(4501) CI_008(6001) CI_008(12001) CI_008(18001) CI_008(24001) CI_008 (30001)])); CD_016E =real(abs([CD_016(1) CD_016(1501) CD_016(3001) CD_016(4501) CD_016(6001) CD_016(12001) CD_016(18001) CD_016(24001) CD_016 (30001)])); CR_016E =real(abs([CR_016(1) CR_016(1501) CR_016(3001) CR_016(4501) CR_016(6001) CR_016(12001) CR_016(18001) CR_016(24001) CR_016 (30001)])); CC_016E =real(abs([CC_016(1) CC_016(1501) CC_016(3001) CC_016(4501) CC_016(6001) CC_016(12001) CC_016(18001) CC_016(24001) CC_016 (30001)])); CI_016E =real(abs([CI_016(1) CI_016(1501) CI_016(3001) CI_016(4501) CI_016(6001) CI_016(12001) CI_016(18001) CI_016(24001) CI_016 (30001)])); CD_014E =real(abs([CD_014(1) CD_014(1501) CD_014(3001) CD_014(4501) CD_014(6001) CD_014(12001) CD_014(18001) CD_014(24001) CD_014 (30001)])); CR_014E =real(abs([CR_014(1) CR_014(1501) CR_014(3001) CR_014(4501) CR_014(6001) CR_014(12001) CR_014(18001) CR_014(24001) CR_014 (30001)]));  161  CC_014E =real(abs([CC_014(1) CC_014(1501) CC_014(3001) CC_014(4501) CC_014(6001) CC_014(12001) CC_014(18001) CC_014(24001) CC_014 (30001)])); CI_014E =real(abs([CI_014(1) CI_014(1501) CI_014(3001) CI_014(4501) CI_014(6001) CI_014(12001) CI_014(18001) CI_014(24001) CI_014 (30001)])); CD_010E =real(abs([CD_010(1) CD_010(1501) CD_010(3001) CD_010(4501) CD_010(6001) CD_010(12001) CD_010(18001) CD_010(24001) CD_010 (30001)])); CR_010E =real(abs([CR_010(1) CR_010(1501) CR_010(3001) CR_010(4501) CR_010(6001) CR_010(12001) CR_010(18001) CR_010(24001) CR_010 (30001)])); CC_010E =real(abs([CC_010(1) CC_010(1501) CC_010(3001) CC_010(4501) CC_010(6001) CC_010(12001) CC_010(18001) CC_010(24001) CC_010 (30001)])); CI_010E =real(abs([CI_010(1) CI_010(1501) CI_010(3001) CI_010(4501) CI_010(6001) CI_010(12001) CI_010(18001) CI_010(24001) CI_010 (30001)])); CD_011E =real(abs([CD_011(1) CD_011(1501) CD_011(3001) CD_011(4501) CD_011(6001) CD_011(12001) CD_011(18001) CD_011(24001) CD_011 (30001)])); CR_011E =real(abs([CR_011(1) CR_011(1501) CR_011(3001) CR_011(4501) CR_011(6001) CR_011(12001) CR_011(18001) CR_011(24001) CR_011 (30001)])); CC_011E =real(abs([CC_011(1) CC_011(1501) CC_011(3001) CC_011(4501) CC_011(6001) CC_011(12001) CC_011(18001) CC_011(24001) CC_011 (30001)])); CI_011E =real(abs([CI_011(1) CI_011(1501) CI_011(3001) CI_011(4501) CI_011(6001) CI_011(12001) CI_011(18001) CI_011(24001) CI_011 (30001)])); CD_015E =real(abs([CD_015(1) CD_015(1501) CD_015(3001) CD_015(4501) CD_015(6001) CD_015(12001) CD_015(18001) CD_015(24001) CD_015 (30001)])); CR_015E =real(abs([CR_015(1) CR_015(1501) CR_015(3001) CR_015(4501) CR_015(6001) CR_015(12001) CR_015(18001) CR_015(24001) CR_015 (30001)])); CC_015E =real(abs([CC_015(1) CC_015(1501) CC_015(3001) CC_015(4501) CC_015(6001) CC_015(12001) CC_015(18001) CC_015(24001) CC_015 (30001)])); CI_015E =real(abs([CI_015(1) CI_015(1501) CI_015(3001) CI_015(4501) CI_015(6001) CI_015(12001) CI_015(18001) CI_015(24001) CI_015 (30001)])); %Calculating degree of explanation R^2 and residuls R2_005_D = 1-sum((CDX_005-CD_005E).^2)/sum((CDX_005-mean(CDX_005)).  162  ^2); R2_005_R = 1-sum((CRX_005-CR_005E).^2)/sum((CRX_005-mean(CRX_005)). ^2); R2_005_C = 1-sum((CCX_005-CC_005E).^2)/sum((CCX_005-mean(CCX_005)). ^2); R2_005_I = 1-sum((CIX_005-CI_005E).^2)/sum((CIX_005-mean(CIX_005)). ^2); R2_005=1-(sum((CDX_005-CD_005E).^2)+sum((CRX_005-CR_005E).^2)+sum ((CCX_005-CC_005E).^2)+sum((CIX_005-CI_005E).^2))/(sum((CDX_005-mean (CDX_005)).^2)+sum((CRX_005-mean(CRX_005)).^2)+sum((CCX_005-mean (CCX_005)).^2)+sum((CIX_005-mean(CIX_005)).^2)); Residual_005_D=CDX_005-CD_005E; Residual_005_R=CRX_005-CR_005E; Residual_005_C=CCX_005-CC_005E; Residual_005_I=CIX_005-CI_005E; R2_013_D = 1-sum((CDX_013-CD_013E).^2)/sum((CDX_013-mean(CDX_013)). ^2); R2_013_R = 1-sum((CRX_013-CR_013E).^2)/sum((CRX_013-mean(CRX_013)). ^2); R2_013_C = 1-sum((CCX_013-CC_013E).^2)/sum((CCX_013-mean(CCX_013)). ^2); R2_013_I = 1-sum((CIX_013-CI_013E).^2)/sum((CIX_013-mean(CIX_013)). ^2); R2_013=1-sum((CDX_013-CD_013E).^2+(CRX_013-CR_013E).^2+(CCX_013CC_013E).^2+(CIX_013-CI_013E).^2)/sum((CDX_013-mean(CDX_013)).^2+ (CRX_013-mean(CRX_013)).^2+(CCX_013-mean(CCX_013)).^2+(CIX_013-mean (CIX_013)).^2); Residual_013_D=CDX_013-CD_013E; Residual_013_R=CRX_013-CR_013E; Residual_013_C=CCX_013-CC_013E; Residual_013_I=CIX_013-CI_013E; R2_004_D = 1-sum((CDX_004-CD_004E).^2)/sum((CDX_004-mean(CDX_004)). ^2); R2_004_R = 1-sum((CRX_004-CR_004E).^2)/sum((CRX_004-mean(CRX_004)). ^2); R2_004_C = 1-sum((CCX_004-CC_004E).^2)/sum((CCX_004-mean(CCX_004)). ^2); R2_004_I = 1-sum((CIX_004-CI_004E).^2)/sum((CIX_004-mean(CIX_004)). ^2); R2_004=1-sum((CDX_004-CD_004E).^2+(CRX_004-CR_004E).^2+(CCX_004CC_004E).^2+(CIX_004-CI_004E).^2)/sum((CDX_004-mean(CDX_004)).^2+ (CRX_004-mean(CRX_004)).^2+(CCX_004-mean(CCX_004)).^2+(CIX_004-mean (CIX_004)).^2); Residual_004_D=CDX_004-CD_004E; Residual_004_R=CRX_004-CR_004E; Residual_004_C=CCX_004-CC_004E; Residual_004_I=CIX_004-CI_004E;  163  R2_009_D = 1-sum((CDX_009-CD_009E).^2)/sum((CDX_009-mean(CDX_009)). ^2); R2_009_R = 1-sum((CRX_009-CR_009E).^2)/sum((CRX_009-mean(CRX_009)). ^2); R2_009_C = 1-sum((CCX_009-CC_009E).^2)/sum((CCX_009-mean(CCX_009)). ^2); R2_009_I = 1-sum((CIX_009-CI_009E).^2)/sum((CIX_009-mean(CIX_009)). ^2); R2_009=1-sum((CDX_009-CD_009E).^2+(CRX_009-CR_009E).^2+(CCX_009CC_009E).^2+(CIX_009-CI_009E).^2)/sum((CDX_009-mean(CDX_009)).^2+ (CRX_009-mean(CRX_009)).^2+(CCX_009-mean(CCX_009)).^2+(CIX_009-mean (CIX_009)).^2); Residual_009_D=CDX_009-CD_009E; Residual_009_R=CRX_009-CR_009E; Residual_009_C=CCX_009-CC_009E; Residual_009_I=CIX_009-CI_009E; R2_008_D = 1-sum((CDX_008-CD_008E).^2)/sum((CDX_008-mean(CDX_008)). ^2); R2_008_R = 1-sum((CRX_008-CR_008E).^2)/sum((CRX_008-mean(CRX_008)). ^2); R2_008_C = 1-sum((CCX_008-CC_008E).^2)/sum((CCX_008-mean(CCX_008)). ^2); R2_008_I = 1-sum((CIX_008-CI_008E).^2)/sum((CIX_008-mean(CIX_008)). ^2); R2_008=1-sum((CDX_008-CD_008E).^2+(CRX_008-CR_008E).^2+(CCX_008CC_008E).^2+(CIX_008-CI_008E).^2)/sum((CDX_008-mean(CDX_008)).^2+ (CRX_008-mean(CRX_008)).^2+(CCX_008-mean(CCX_008)).^2+(CIX_008-mean (CIX_008)).^2); Residual_008_D=CDX_008-CD_008E; Residual_008_R=CRX_008-CR_008E; Residual_008_C=CCX_008-CC_008E; Residual_008_I=CIX_008-CI_008E; R2_012_D = 1-sum((CDX_012-CD_012E).^2)/sum((CDX_012-mean(CDX_012)). ^2); R2_012_R = 1-sum((CRX_012-CR_012E).^2)/sum((CRX_012-mean(CRX_012)). ^2); R2_012_C = 1-sum((CCX_012-CC_012E).^2)/sum((CCX_012-mean(CCX_012)). ^2); R2_012_I = 1-sum((CIX_012-CI_012E).^2)/sum((CIX_012-mean(CIX_012)). ^2); R2_012=1-sum((CDX_012-CD_012E).^2+(CRX_012-CR_012E).^2+(CCX_012CC_012E).^2+(CIX_012-CI_012E).^2)/sum((CDX_012-mean(CDX_012)).^2+ (CRX_012-mean(CRX_012)).^2+(CCX_012-mean(CCX_012)).^2+(CIX_012-mean (CIX_012)).^2); Residual_012_D=CDX_012-CD_012E; Residual_012_R=CRX_012-CR_012E;  164  Residual_012_C=CCX_012-CC_012E; Residual_012_I=CIX_012-CI_012E; R2_016_D = 1-sum((CDX_016-CD_016E).^2)/sum((CDX_016-mean(CDX_016)). ^2); R2_016_R = 1-sum((CRX_016-CR_016E).^2)/sum((CRX_016-mean(CRX_016)). ^2); R2_016_C = 1-sum((CCX_016-CC_016E).^2)/sum((CCX_016-mean(CCX_016)). ^2); R2_016_I = 1-sum((CIX_016-CI_016E).^2)/sum((CIX_016-mean(CIX_016)). ^2); R2_016=1-sum((CDX_016-CD_016E).^2+(CRX_016-CR_016E).^2+(CCX_016CC_016E).^2+(CIX_016-CI_016E).^2)/sum((CDX_016-mean(CDX_016)).^2+ (CRX_016-mean(CRX_016)).^2+(CCX_016-mean(CCX_016)).^2+(CIX_016-mean (CIX_016)).^2); Residual_016_D=CDX_016-CD_016E; Residual_016_R=CRX_016-CR_016E; Residual_016_C=CCX_016-CC_016E; Residual_016_I=CIX_016-CI_016E; R2_014_D = 1-sum((CDX_014-CD_014E).^2)/sum((CDX_014-mean(CDX_014)). ^2); R2_014_R = 1-sum((CRX_014-CR_014E).^2)/sum((CRX_014-mean(CRX_014)). ^2); R2_014_C = 1-sum((CCX_014-CC_014E).^2)/sum((CCX_014-mean(CCX_014)). ^2); R2_014_I = 1-sum((CIX_014-CI_014E).^2)/sum((CIX_014-mean(CIX_014)). ^2); R2_014=1-sum((CDX_014-CD_014E).^2+(CRX_014-CR_014E).^2+(CCX_014CC_014E).^2+(CIX_014-CI_014E).^2)/sum((CDX_014-mean(CDX_014)).^2+ (CRX_014-mean(CRX_014)).^2+(CCX_014-mean(CCX_014)).^2+(CIX_014-mean (CIX_014)).^2); Residual_014_D=CDX_014-CD_014E; Residual_014_R=CRX_014-CR_014E; Residual_014_C=CCX_014-CC_014E; Residual_014_I=CIX_014-CI_014E; R2_010_D = 1-sum((CDX_010-CD_010E).^2)/sum((CDX_010-mean(CDX_010)). ^2); R2_010_R = 1-sum((CRX_010-CR_010E).^2)/sum((CRX_010-mean(CRX_010)). ^2); R2_010_C = 1-sum((CCX_010-CC_010E).^2)/sum((CCX_010-mean(CCX_010)). ^2); R2_010_I = 1-sum((CIX_010-CI_010E).^2)/sum((CIX_010-mean(CIX_010)). ^2); R2_010=1-sum((CDX_010-CD_010E).^2+(CRX_010-CR_010E).^2+(CCX_010CC_010E).^2+(CIX_010-CI_010E).^2)/sum((CDX_010-mean(CDX_010)).^2+ (CRX_010-mean(CRX_010)).^2+(CCX_010-mean(CCX_010)).^2+(CIX_010-mean (CIX_010)).^2);  165  Residual_010_D=CDX_010-CD_010E; Residual_010_R=CRX_010-CR_010E; Residual_010_C=CCX_010-CC_010E; Residual_010_I=CIX_010-CI_010E; R2_011_D = 1-sum((CDX_011-CD_011E).^2)/sum((CDX_011-mean(CDX_011)). ^2); R2_011_R = 1-sum((CRX_011-CR_011E).^2)/sum((CRX_011-mean(CRX_011)). ^2); R2_011_C = 1-sum((CCX_011-CC_011E).^2)/sum((CCX_011-mean(CCX_011)). ^2); R2_011_I = 1-sum((CIX_011-CI_011E).^2)/sum((CIX_011-mean(CIX_011)). ^2); R2_011=1-sum((CDX_011-CD_011E).^2+(CRX_011-CR_011E).^2+(CCX_011CC_011E).^2+(CIX_011-CI_011E).^2)/sum((CDX_011-mean(CDX_011)).^2+ (CRX_011-mean(CRX_011)).^2+(CCX_011-mean(CCX_011)).^2+(CIX_011-mean (CIX_011)).^2); Residual_011_D=CDX_011-CD_011E; Residual_011_R=CRX_011-CR_011E; Residual_011_C=CCX_011-CC_011E; Residual_011_I=CIX_011-CI_011E; R2_015_D = 1-sum((CDX_015-CD_015E).^2)/sum((CDX_015-mean(CDX_015)). ^2); R2_015_R = 1-sum((CRX_015-CR_015E).^2)/sum((CRX_015-mean(CRX_015)). ^2); R2_015_C = 1-sum((CCX_015-CC_015E).^2)/sum((CCX_015-mean(CCX_015)). ^2); R2_015_I = 1-sum((CIX_015-CI_015E).^2)/sum((CIX_015-mean(CIX_015)). ^2); R2_015=1-sum((CDX_015-CD_015E).^2+(CRX_015-CR_015E).^2+(CCX_015CC_015E).^2+(CIX_015-CI_015E).^2)/sum((CDX_015-mean(CDX_015)).^2+ (CRX_015-mean(CRX_015)).^2+(CCX_015-mean(CCX_015)).^2+(CIX_015-mean (CIX_015)).^2); Residual_015_D=CDX_015-CD_015E; Residual_015_R=CRX_015-CR_015E; Residual_015_C=CCX_015-CC_015E; Residual_015_I=CIX_015-CI_015E; R2_D_all=1-sum((CDX_015-CD_015E).^2+(CDX_011-CD_011E).^2+(CDX_010CD_010E).^2+(CDX_014-CD_014E).^2+(CDX_016-CD_016E).^2+(CDX_012CD_012E).^2+(CDX_008-CD_008E).^2+(CDX_009-CD_009E).^2+(CDX_004CD_004E).^2+(CDX_013-CD_013E).^2+(CDX_005-CD_005E).^2)/... sum((CDX_015-mean(CDX_015)).^2+(CDX_011-mean(CDX_011)).^2+ (CDX_010-mean(CDX_010)).^2+(CDX_014-mean(CDX_014)).^2+(CDX_016-mean (CDX_016)).^2+(CDX_012-mean(CDX_012)).^2+(CDX_008-mean(CDX_008)).^2+ (CDX_009-mean(CDX_009)).^2+(CDX_014-mean(CDX_004)).^2+(CDX_013-mean (CDX_013)).^2+(CDX_005-mean(CDX_005)).^2);  166  R2_all=1-sum((CDX_015-CD_015E).^2+(CRX_015-CR_015E).^2+(CIX_015CI_015E).^2+(CDX_011-CD_011E).^2+(CRX_011-CR_011E).^2+(CIX_011CI_011E).^2+(CDX_010-CD_010E).^2+(CRX_010-CR_010E).^2+(CIX_010CI_010E).^2+(CDX_014-CD_014E).^2+(CRX_014-CR_014E).^2+(CDX_016CD_016E).^2+(CRX_016-CR_016E).^2+(CIX_016-CI_016E).^2+(CDX_012CD_012E).^2+(CRX_012-CR_012E).^2+(CIX_012-CI_012E).^2+(CDX_008CD_008E).^2+(CRX_008-CR_008E).^2+(CIX_008-CI_008E).^2+(CDX_009CD_009E).^2+(CRX_009-CR_009E).^2+(CDX_004-CD_004E).^2+(CRX_004CR_004E).^2+(CIX_004-CI_004E).^2+(CDX_013-CD_013E).^2+(CRX_013CR_013E).^2+(CIX_013-CI_013E).^2+(CDX_005-CD_005E).^2+(CRX_005CR_005E).^2)/... sum((CDX_015-mean(CDX_015)).^2+(CRX_015-mean(CRX_015)).^2+ (CIX_015-mean(CIX_015)).^2+(CDX_011-mean(CDX_011)).^2+(CRX_011-mean (CRX_011)).^2+(CCX_011-mean(CCX_011)).^2+(CIX_011-mean(CIX_011)).^2+ (CDX_010-mean(CDX_010)).^2+(CRX_010-mean(CRX_010)).^2+(CCX_010-mean (CCX_010)).^2+(CIX_010-mean(CIX_010)).^2+(CDX_014-mean(CDX_014)).^2+ (CRX_014-mean(CRX_014)).^2+(CCX_014-mean(CCX_014)).^2+(CIX_014-mean (CIX_014)).^2+(CDX_016-mean(CDX_016)).^2+(CRX_016-mean(CRX_016)).^2+ (CCX_016-mean(CCX_016)).^2+(CIX_016-mean(CIX_016)).^2+(CDX_012-mean (CDX_012)).^2+(CRX_012-mean(CRX_012)).^2+(CCX_012-mean(CCX_012)).^2+ (CIX_012-mean(CIX_012)).^2+(CDX_008-mean(CDX_008)).^2+(CRX_008-mean (CRX_008)).^2+(CCX_008-mean(CCX_008)).^2+(CIX_008-mean(CIX_008)).^2+ (CDX_009-mean(CDX_009)).^2+(CRX_009-mean(CRX_009)).^2+(CCX_009-mean (CCX_009)).^2+(CIX_009-mean(CIX_009)).^2+(CDX_004-mean(CDX_004)).^2+ (CRX_004-mean(CRX_004)).^2+(CCX_004-mean(CCX_004)).^2+(CIX_004-mean (CIX_004)).^2+(CDX_013-mean(CDX_013)).^2+(CRX_013-mean(CRX_013)).^2+ (CCX_013-mean(CCX_013)).^2+(CIX_013-mean(CIX_013)).^2+(CDX_005-mean (CDX_005)).^2+(CRX_005-mean(CRX_005)).^2+(CCX_005-mean(CCX_005)).^2+ (CIX_005-mean(CIX_005)).^2); R2_all_2=1-sum((CDX_015-CD_015E).^2+(CRX_015-CR_015E).^2+(CIX_015CI_015E).^2+(CCX_015-CC_015E).^2+(CDX_011-CD_011E).^2+(CRX_011CR_011E).^2+(CCX_011-CC_011E).^2+(CIX_011-CI_011E).^2+(CDX_010CD_010E).^2+(CRX_010-CR_010E).^2+(CCX_010-CC_010E).^2+(CIX_010CI_010E).^2+(CDX_014-CD_014E).^2+(CRX_014-CR_014E).^2+(CCX_014CC_014E).^2+(CIX_014-CI_014E).^2+(CDX_016-CD_016E).^2+(CRX_016CR_016E).^2+(CCX_016-CC_016E).^2+(CIX_016-CI_016E).^2+(CDX_012CD_012E).^2+(CRX_012-CR_012E).^2+(CCX_012-CC_012E).^2+(CIX_012CI_012E).^2+(CDX_008-CD_008E).^2+(CRX_008-CR_008E).^2+(CCX_008CC_008E).^2+(CIX_008-CI_008E).^2+(CDX_009-CD_009E).^2+(CRX_009CR_009E).^2+(CCX_009-CC_009E).^2+(CIX_009-CI_009E).^2+(CDX_004CD_004E).^2+(CRX_004-CR_004E).^2+(CCX_004-CC_004E).^2+(CIX_004CI_004E).^2+(CDX_013-CD_013E).^2+(CRX_013-CR_013E).^2+(CCX_013CC_013E).^2+(CIX_013-CI_013E).^2+(CDX_005-CD_005E).^2+(CRX_005CR_005E).^2+(CCX_005-CC_005E).^2+(CIX_005-CI_005E).^2)/... sum((CDX_015-mean(CDX_015)).^2+(CRX_015-mean(CRX_015)).^2+ (CCX_015-mean(CCX_015)).^2+(CIX_015-mean(CIX_015)).^2+(CDX_011-mean (CDX_011)).^2+(CRX_011-mean(CRX_011)).^2+(CCX_011-mean(CCX_011)).^2+ (CIX_011-mean(CIX_011)).^2+(CDX_010-mean(CDX_010)).^2+(CRX_010-mean  167  (CRX_010)).^2+(CCX_010-mean(CCX_010)).^2+(CIX_010-mean(CIX_010)).^2+ (CDX_014-mean(CDX_014)).^2+(CRX_014-mean(CRX_014)).^2+(CCX_014-mean (CCX_014)).^2+(CIX_014-mean(CIX_014)).^2+(CDX_016-mean(CDX_016)).^2+ (CRX_016-mean(CRX_016)).^2+(CCX_016-mean(CCX_016)).^2+(CIX_016-mean (CIX_016)).^2+(CDX_012-mean(CDX_012)).^2+(CRX_012-mean(CRX_012)).^2+ (CCX_012-mean(CCX_012)).^2+(CIX_012-mean(CIX_012)).^2+(CDX_008-mean (CDX_008)).^2+(CRX_008-mean(CRX_008)).^2+(CCX_008-mean(CCX_008)).^2+ (CIX_008-mean(CIX_008)).^2+(CDX_009-mean(CDX_009)).^2+(CRX_009-mean (CRX_009)).^2+(CCX_009-mean(CCX_009)).^2+(CIX_009-mean(CIX_009)).^2+ (CDX_004-mean(CDX_004)).^2+(CRX_004-mean(CRX_004)).^2+(CCX_004-mean (CCX_004)).^2+(CIX_004-mean(CIX_004)).^2+(CDX_013-mean(CDX_013)).^2+ (CRX_013-mean(CRX_013)).^2+(CCX_013-mean(CCX_013)).^2+(CIX_013-mean (CIX_013)).^2+(CDX_005-mean(CDX_005)).^2+(CRX_005-mean(CRX_005)).^2+ (CCX_005-mean(CCX_005)).^2+(CIX_005-mean(CIX_005)).^2);  %Plotting experimental data versus model predictions figure; %RO-Ir(2)HBeta-005 subplot(4,3,1) plot(T,CDX_005,'bo',T,CIX_005,'md',T,CCX_005,'r+',T,CRX_005,'kx',t, CD_005,'b-',t,CI_005,'m-',t,CC_005,'r-',t,CR_005,'k-','MarkerSize', 7,'LineWidth',1.1) legend('Decalin (D)','Decalin Isomers (I)','Cracked products (C)','Ring opened products (R)',1) title('T=275C P=3MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-013 subplot(4,3,2) plot(T,CDX_013,'bo',T,CIX_013,'md',T,CCX_013,'r+',T,CRX_013,'kx',t, CD_013,'b-',t,CI_013,'m-',t,CC_013,'r-',t,CR_013,'k-','MarkerSize', 7,'LineWidth',1.1) %legend('Decalin (D)','Decalin Isomers (I)','Cracked products (C)','Ring opened products (RO)',1) title('T=275C P=5MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-010 subplot(4,3,3) plot(T,CDX_010,'bo',T,CIX_010,'md',T,CCX_010,'r+',T,CRX_010,'kx',t, CD_010,'b-',t,CI_010,'m-',t,CC_010,'r-',t,CR_010,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=275C P=6MPa') ylabel('Concentration, M')  168  xlabel('Time, min') %RO-Ir(2)HBeta-004 subplot(4,3,4) plot(T,CDX_004,'bo',T,CIX_004,'md',T,CCX_004,'r+',T,CRX_004,'kx',t, CD_004,'b-',t,CI_004,'m-',t,CC_004,'r-',t,CR_004,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=300C P=3MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-009 subplot(4,3,5) plot(T,CDX_009,'bo',T,CIX_009,'md',T,CCX_009,'r+',T,CRX_009,'kx',t, CD_009,'b-',t,CI_009,'m-',t,CC_009,'r-',t,CR_009,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=300C P=5MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-008 subplot(4,3,6) plot(T,CDX_008,'bo',T,CIX_008,'md',T,CCX_008,'r+',T,CRX_008,'kx',t, CD_008,'b-',t,CI_008,'m-',t,CC_008,'r-',t,CR_008,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=300C P=6MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-012 subplot(4,3,8) plot(T,CDX_012,'bo',T,CIX_012,'md',T,CCX_012,'r+',T,CRX_012,'kx',t, CD_012,'b-',t,CI_012,'m-',t,CC_012,'r-',t,CR_012,'k-','MarkerSize', 7,'LineWidth',1.1) %legend('Decalin (D)','Decalin Isomers (I)','Cracked products (C)','Ring opened products (RO)',1) title('T=325C P=5MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-011 subplot(4,3,9) plot(T,CDX_011,'bo',T,CIX_011,'md',T,CCX_011,'r+',T,CRX_011,'kx',t, CD_011,'b-',t,CI_011,'m-',t,CC_011,'r-',t,CR_011,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=325C P=6MPa') ylabel('Concentration, M') xlabel('Time, min')  169  %RO-Ir(2)HBeta-016 subplot(4,3,10) plot(T,CDX_016,'bo',T,CIX_016,'md',T,CCX_016,'r+',T,CRX_016,'kx',t, CD_016,'b-',t,CI_016,'m-',t,CC_016,'r-',t,CR_016,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=350C P=3MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-014 subplot(4,3,11) plot(T,CDX_014,'bo',T,CIX_014,'md',T,CCX_014,'r+',T,CRX_014,'kx',t, CD_014,'b-',t,CI_014,'m-',t,CC_014,'r-',t,CR_014,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=350C P=5MPa') ylabel('Concentration, M') xlabel('Time, min') %RO-Ir(2)HBeta-015 subplot(4,3,12) plot(T,CDX_015,'bo',T,CIX_015,'md',T,CCX_015,'r+',T,CRX_015,'kx',t, CD_015,'b-',t,CI_015,'m-',t,CC_015,'r-',t,CR_015,'k-','MarkerSize', 7,'LineWidth',1.1) title('T=350C P=6MPa') ylabel('Concentration, M') xlabel('Time, min') % Residual plot figure; subplot(4,3,1) plot(T,Residual_005_D,'bo',T,Residual_005_I,'md',T, Residual_005_C,'r+',T,Residual_005_R,'kx','MarkerSize',7,'LineWidth', 1.1) legend('Decalin (D)','Decalin Isomers (I)','Cracked products (C)','Ring opened products (RO)',1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,2) plot(T,Residual_013_D,'bo',T,Residual_013_I,'md',T, Residual_013_C,'r+',T,Residual_013_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,3) plot(T,Residual_010_D,'bo',T,Residual_010_I,'md',T,  170  Residual_010_C,'r+',T,Residual_010_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,4) plot(T,Residual_004_D,'bo',T,Residual_004_I,'md',T, Residual_004_C,'r+',T,Residual_004_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,5) plot(T,Residual_009_D,'bo',T,Residual_009_I,'md',T, Residual_009_C,'r+',T,Residual_009_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,6) plot(T,Residual_008_D,'bo',T,Residual_008_I,'md',T, Residual_008_C,'r+',T,Residual_008_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,8) plot(T,Residual_012_D,'bo',T,Residual_012_I,'md',T, Residual_012_C,'r+',T,Residual_012_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,9) plot(T,Residual_011_D,'bo',T,Residual_011_I,'md',T, Residual_011_C,'r+',T,Residual_011_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,10) plot(T,Residual_016_D,'bo',T,Residual_016_I,'md',T, Residual_016_C,'r+',T,Residual_016_R,'kx','MarkerSize',7,'LineWidth',  171  1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,11) plot(T,Residual_014_D,'bo',T,Residual_014_I,'md',T, Residual_014_C,'r+',T,Residual_014_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') subplot(4,3,12) plot(T,Residual_015_D,'bo',T,Residual_015_I,'md',T, Residual_015_C,'r+',T,Residual_015_R,'kx','MarkerSize',7,'LineWidth', 1.1) title('RO-Ir(2)HBeta-005 T=275C P=3MPa') ylabel('Residual C_X-C_Pred') xlabel('Time, min') % Displaying estimated paramter values fprintf('k1_275= fprintf('k1_300= fprintf('k1_325= fprintf('k1_350=  %.5f\n', %.5f\n', %.5f\n', %.5f\n',  k1_275); k1_300); k1_325); k1_350);  fprintf('k2_275= fprintf('k2_300= fprintf('k2_325= fprintf('k2_350=  %.5f\n', %.5f\n', %.5f\n', %.5f\n',  k2_275); k2_300); k2_325); k2_350);  fprintf('k3_275= fprintf('k3_300= fprintf('k3_325= fprintf('k3_350=  %.5f\n', %.5f\n', %.5f\n', %.5f\n',  k3_275); k3_300); k3_325); k3_350);  fprintf('k4_275= fprintf('k4_300= fprintf('k4_325= fprintf('k4_350=  %.5f\n', %.5f\n', %.5f\n', %.5f\n',  k4_275); k4_300); k4_325); k4_350);  fprintf('K1_275= fprintf('K1_300= fprintf('K1_325= fprintf('K1_350=  %.5f\n', %.5f\n', %.5f\n', %.5f\n',  KE1_275); KE1_300); KE1_325); KE1_350);  fprintf('KA_275= %.5f\n', KHC_275);  172  fprintf('KA_300= %.5f\n', KHC_300); fprintf('KA_325= %.5f\n', KHC_325); fprintf('KA_350= %.5f\n', KHC_350); fprintf('KHHD_275= fprintf('KHHD_300= fprintf('KHHD_325= fprintf('KHHD_350=  %.5f\n', %.5f\n', %.5f\n', %.5f\n',  KHHD_275); KHHD_300); KHHD_325); KHHD_350);  173  %This funciton is used to calculate the objective function function OBJ=OBJECTIVE_FUN_MLE_Thesis_all(p, T,CDX_3,CRX_3,CCX_3,... CIX_3,CHX_3,CDX_5,CRX_5,CCX_5,CIX_5,CHX_5, CDX_6,CRX_6,CCX_6,... CIX_6,CHX_6,T_3, T_5, T_6,Tref,m_3, m_5, m_6,V_3, V_5, V_6) C_0_3 = [CDX_3(1);CRX_3(1);CCX_3(1);CIX_3(1)]; C_0_5 = [CDX_5(1);CRX_5(1);CCX_5(1);CIX_5(1)]; C_0_6 = [CDX_6(1);CRX_6(1);CCX_6(1);CIX_6(1)]; %calculating model predictions using current parameters [Tm,Y_3]=ode45('ODE_FUN_Thesis',T,C_0_3,[],p,CHX_3, T_3, Tref,... m_3,V_3); [Tm,Y_5]=ode45('ODE_FUN_Thesis',T,C_0_5,[],p,CHX_5, T_5, Tref,... m_5,V_5); [Tm,Y_6]=ode45('ODE_FUN_Thesis',T,C_0_6,[],p,CHX_6, T_6, Tref,... m_6,V_6); %extracting model predictions CD_3 =real(abs(Y_3(:,1))); CR_3 =real(abs(Y_3(:,2))); CC_3 =real(abs(Y_3(:,3))); CI_3 =real(abs(Y_3(:,4))); CD_5 CR_5 CC_5 CI_5  =real(abs(Y_5(:,1))); =real(abs(Y_5(:,2))); =real(abs(Y_5(:,3))); =real(abs(Y_5(:,4)));  CD_6 CR_6 CC_6 CI_6  =real(abs(Y_6(:,1))); =real(abs(Y_6(:,2))); =real(abs(Y_6(:,3))); =real(abs(Y_6(:,4)));  CD=[CD_3; CR=[CR_3; CC=[CC_3; CI=[CI_3;  CD_5; CR_5; CC_5; CI_5;  CD_6]; CR_6]; CC_6]; CI_6];  %extracting experimental data CDX=[CDX_3 CDX_5 CDX_6]; CRX=[CRX_3 CRX_5 CRX_6]; CCX=[CCX_3 CCX_5 CCX_6]; CIX=[CIX_3 CIX_5 CIX_6]; %calculating objective function OBJ=sum((CD-CDX').^2+(CR-CRX').^2+(CC-CCX').^2+(CI-CIX').^2);  174  %This function evaluates the ODE functions function dC = ODE_FUN_Thesis(t,C,flag,p,CHX, T, Tref,m, V1) %KHC: Equilibrium constant for adsorption on Ir steps %KHHD: Equilibrium constant for hyd/dehyd steps and hydrogen reactions %ki: reaction rate const %Keq: equil const for Do=Io step R=8.314472e-3; %kJ/K mol dC=zeros(4,1); k1=p(1); k2=p(2); k4=p(3); Keq=p(4); KHC=p(5); KHHD=p(6); k3=p(7); CD=C(1); CR=C(2); CC=C(3); CI=C(4); %CH=CHX; %CH=mean(CHX)*ones(9,1); CH=CHX(1)*ones(9,1); if t==0 i=1; elseif t<=15 i=2; elseif t<=30 i=3; elseif t<=45 i=4; elseif t<=60 i=5; elseif t<=120 i=6; elseif t<=180 i=7; elseif t<=240 i=8; elseif t<=300 i=9; end CDo=CD./(KHHD*CH(i)); CIo=CI./(KHHD*CH(i));  175  CRo=CR./(KHHD*CH(i)); CCo=CC./(KHHD*CH(i)); CRoo=CR./(KHHD^2*CH(i).^2); CCoo=CC./(KHHD^2*CH(i).^2); den=1+KHC*(CDo+CIo+CRo+CCo+CRoo+CCoo); r1=k1*KHC*(CDo-CIo./Keq)/den; r2=k2*KHC*CIo/den; r3=k3*KHC*CRoo/den; r4=k4*KHC*CRo/den; %decalin density = 0.896 g/cc V=m./896; cat_den=0.5./V1*1000; %g cat/L dC(1)=cat_den(i)*-r1; % decalin D dC(4)=cat_den(i)*(r1-r2); % isomers I dC(2)=cat_den(i)*(r2-r3-r4); % RO product R dC(3)=cat_den(i)*2*(r4+r3); %cracked products C  176  %This funciton is used to calculate the objective function for... %data at T=325C since some values at P= 3 MPa are unavailalbe function OBJ=OBJECTIVE_FUN_MLE_Thesis_325(p, T,CDX_5,CRX_5,CCX_5,... CIX_5,CHX_5, CDX_6,CRX_6,CCX_6,CIX_6,CHX_6,T_5, T_6,Tref,... m_5, m_6,V_5, V_6) %Extracting initial conditions C_0_5 = [CDX_5(1);CRX_5(1);CCX_5(1);CIX_5(1)]; C_0_6 = [CDX_6(1);CRX_6(1);CCX_6(1);CIX_6(1)]; %calculating model predictions using current parameters [Tm,Y_5]=ode45('ODE_FUN_Thesis',T,C_0_5,[],p,CHX_5, T_5, Tref,... m_5,V_5); [Tm,Y_6]=ode45('ODE_FUN_Thesis',T,C_0_6,[],p,CHX_6, T_6, Tref,... m_6,V_6); %extracting model predictions CD_5 =real(abs(Y_5(:,1))); CR_5 =real(abs(Y_5(:,2))); CC_5 =real(abs(Y_5(:,3))); CI_5 =real(abs(Y_5(:,4))); CD_6 CR_6 CC_6 CI_6  =real(abs(Y_6(:,1))); =real(abs(Y_6(:,2))); =real(abs(Y_6(:,3))); =real(abs(Y_6(:,4)));  CD=[CD_5; CR=[CR_5; CC=[CC_5; CI=[CI_5;  CD_6]; CR_6]; CC_6]; CI_6];  %extracting experimental data CDX=[CDX_5 CDX_6]; CRX=[CRX_5 CRX_6]; CCX=[CCX_5 CCX_6]; CIX=[CIX_5 CIX_6]; %calculating objective function OBJ=sum((CD-CDX').^2+(CR-CRX').^2+(CC-CCX').^2+(CI-CIX').^2);  177  Appendix C Arrhenius equation calculations  178  The reaction constants can be expressed using Arrhenius law as following:   Ea j   k j  A j  exp  R T   (C1)  The natural logarithm of Equation C1 gives the following equation:   E aj ln k j   ln A j     R   1    T  (C2)     1 By plotting ln k j versus   as shown in Figure 74, the pre-exponential factors T   A j and activation energies Eaj can be obtained from the intercept and the slope as following:    Ea1  slope     19221  R  Ea1  19221 0.008314472  159.81 kJ / mol Intercept  ln A1   35.583 A1  exp 35.583  2.84 1015  1 min  g  179  y = -19221x + 35.58  6  y = -16288x + 29.29 y = -17315x + 29.98  4  y = -27621x + 45.75  ln(k)  2  k1 k2 k3 k4  0  -2 -4  -6 1.60E-03 1.65E-03 1.70E-03 1.75E-03 1.80E-03 1.85E-03 1/T, 1/K     1 Figure 74. Arrhenius plot of ln k j versus   for all k j at all temperatures tested. T   180  Appendix D Experimental error analysis  181  Equations: The average error in the conversion was calculated as following:  𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 % =  𝑥𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝑥 × 100% 𝑥𝐴𝑣𝑒𝑟𝑎𝑔𝑒  where 𝑥𝐴𝑣𝑒𝑟𝑎𝑔𝑒 is the average conversion of experiments 1 and 2, and 𝑥 is the conversion of experiments 1 or 2.  The total error in the conversion was calculated as following:  𝑇𝑜𝑡𝑎𝑙 𝐸𝑟𝑟𝑜𝑟 % =  𝑥𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝑥 × 100% 𝑥𝑇𝑜𝑡𝑎𝑙  where 𝑥𝑇𝑜𝑡𝑎 𝑙 is the average total decalin conversion at the end of experiment (at 300 min). The average error in the concentrations was determined by injecting the same sample twice using the GC-MS and then calculated as following:  𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐸𝑟𝑟𝑜𝑟 % =  𝐶𝑖,𝐴𝑣𝑒𝑟𝑎𝑔𝑒 − 𝐶𝑖 × 100% 𝐶𝑖,𝐴𝑣𝑒𝑟𝑎𝑔𝑒  where 𝐶𝑖,𝐴𝑣𝑒𝑟𝑎𝑔𝑒 is the average concentration of species i of injections 1 and 2, and 𝐶𝑖 is the concentration of species i of injections 1 or 2.  182  Tables and figures: Table 16 shows the error analysis for decalin conversion at T=350°C and P=6MPa. Figure 75 shows a plot of the conversions with error bars. Table 16. Error analysis for two experiment runs performed at T=350°C and P=6 MPa. Time, min  Conversion, wt% Experiment 1  Error, %  Experiment 2 Average Difference  Average  Total  0  65.17  62.87  64.02  1.15  1.80  1.26  15  73.87  70.81  72.34  1.53  2.12  1.68  30  78.79  77.18  77.99  0.81  1.03  0.89  45  83.01  79.85  81.43  1.58  1.94  1.74  60  84.49  81.77  83.13  1.36  1.64  1.50  120  87.09  87.89  87.49  0.40  0.46  0.44  180  89.35  89.29  89.32  0.03  0.03  0.03  240  90.12  90.06  90.09  0.03  0.03  0.03  300  91.05  90.80  90.92  0.13  0.14  0.14  95.00  Conversion, wt%  90.00 85.00 80.00 75.00 70.00 65.00 60.00 0  50  100  150 Time, min  200  250  300  Figure 75. Average decalin conversions at T=350°C and P=6 MPa. 183  Table 17 shows the error analysis for decalin conversion at T=275°C and P=3MPa. Figure 76 shows a plot of the conversions with error bars. Table 17. Error analysis for two experiment runs performed at T=275°C and P=3 MPa Time, min  Conversion, wt% Experiment 1 Experiment 2 Average  Error, % Difference  Average  Total  0  12.08  12.21  12.14  0.07  0.55  0.11  15  19.59  16.28  17.94  1.66  9.23  2.63  30  26.54  21.40  23.97  2.57  10.72  4.08  45  28.87  24.62  26.74  2.13  7.95  3.37  60  31.97  28.72  30.34  1.62  5.35  2.58  120  43.45  40.68  42.06  1.38  3.29  2.20  180  53.03  50.30  51.67  1.36  2.64  2.16  240  59.67  56.57  58.12  1.55  2.67  2.46  300  64.40  61.60  63.00  1.40  2.22  2.22  70.00  Conversion, wt%  60.00 50.00 40.00 30.00 20.00 10.00 0.00 0  50  100  150 Time, min  200  250  300  Figure 76. Average decalin conversions at T=275°C and P=3 MPa.  184  Table 18 shows the error analysis for decalin (D), ring opened product (R), cracked product (C), and isomers (I) concentrations.  Table 18. Error analysis for three GC-MS injections of the same sample for decalin (D), ring opened product (R), cracked product (C), and isomers (I) concentrations. Injection  Concentration, mol/l D  R  C  I  1  4.57E-03  3.94E-03  6.89E-04  2.97E-03  2  4.75E-03  3.95E-03  5.54E-04  3.15E-03  3  4.49E-03  4.09E-03  5.20E-04  3.14E-03  Average  4.62E-03  4.02E-03  5.37E-04  3.14E-03  Difference  1.32E-04  6.76E-05  1.69E-05  6.86E-06  Error, % 3.22  2.33  17.25  3.65  185  Appendix E GC-MS scan sample  186  Figure 77 shows a GC-MS scan for a liquid sample collected at 120 min for the reaction performed at T=350°C and P=6MPa. The GC-MS detected 242 peaks for this specific sample corresponding to 242 chemical species.  Figure 77. MS scan for a liquid sample collected at 120 min for the reaction performed at T=350°C and P=6MPa.  187  The area under each peak was used to calculate the mass fraction of the chemical species. The mass of the chemical species was determined by multiplying the mass fraction with the mass of the sample. The number of moles was calculated by dividing the mass of the chemical species by its molar mass. The number of moles of each group identified, decalin (D), isomers (I), ring-opened products (R), cracked products (C), and heavy products (HP), was calculated by summing the number of moles of chemical species belonging to these groups. The concentration of each group was calculated by dividing the number of moles by the volume of the sample.  188  

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