EXPERIMENTAL AND MODELING STUDY OF PITCH PYROLYSIS KINETICS by CHENGQING YUE B.Eng. China University of Mining and Technology, 1984 M.Sc. Beijing Coal Chemistry Research Institute, 1987 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Chemical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November 1995 ©Chengqing Yue, 1995 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada Date A p r i l , m £ > DE-6 (2/88) ABSTRACT Kinetics of thermal pyrolysis of both C A N M E T and Syncrude pitches from heavy oil upgrading have been studied with Thermogravimetric Analysis (TGA), and with Pyroprobe-Gas Chromatography (Pyroprobe-GC). In the latter technique samples are pyrolyzed at high heating rates and products analyzed with in-line gas chromatography. Experiments with T G A were carried out at atmospheric pressure and at temperatures between 700 and 950 °C. The heating rates were 25, 50 100 and 150 °C/min. The sample weight was varied between 3 and 17.2 mg. The effects of sample weight, heating rate and final temperature on the weight loss as a function of time were examined. Experiments with Pyroprobe-GC were carried out at atmospheric pressure and at temperatures between 500 and 1000 °C. The heating rates were 600, 3000, 30000, 300000 °C/min, using a sample weight of about 5 mg. The accumulated pyrolysis products were analyzed and lumped into major groups for yield estimation based on number of carbon atoms. The final weight of residue was also determined. The effects of the final temperatures on the yield of each major group were examined. At temperatures below 150 °C, there is little pyrolysis of either pitch. At higher temperatures, the pyrolysis takes place in two following stages, with a first stage of low activation energy barrier and low pre-exponential factor, and the second stage of higher activation energy and pre-exponential factor. Higher conversion to volatiles was achieved with Syncrude pitch than with C A N M E T pitch. Heating rates had a minor effect on the weight loss. The total weight loss decreased slightly with the increase of sample weight, and final temperatures. The most abundant components of the pyrolysis products were species lighter than Cy, which are primarily gases. The C i 0 group yield was strongly influenced by heating rates. Higher molecular weight components Cn, Cn, C 1 3 , and C14 were also detected. The pyrolysis products ii from Syncrude pitch consisted of higher yields of lighter components (C7) than those from C A N M E T pitch. A general first order equation for the kinetics of volatile release under temperature programmed conditions is widely used in the pyrolysis literature. Interpretation of results via the single stage integral method and methods due to Coats-Redfern, Chen-Nuttall and Friedman were tested with the T G A data and found inadequate. The single stage first order model of Anthony and Howard, which incorporates a Gaussian distribution of activation energies also failed. An adequate description of the pitch pyrolysis kinetics was achieved using a 2-stage first order model with the integral analysis method. The 2-stage model reflects changes in the chemical constitution or structure as conversion proceeds using two sets of kinetic parameters. This feature is essential to describe the dependence of devolatilization rates on remaining volatile content. The transition between these two stages is a sharp one, occurring at about 450 °C for both C A N M E T and Syncrude pitches. The magnitude of the activation energies suggested that both stages are kinetically controlled. The analysis methods of Coats-Redfern, Chen-Nuttall, and Friedman were also tested as two stage methods and found to be inadequate to describe the pitch pyrolysis kinetics in the temperature range studied. The pre-exponential factors and activation energies from the different kinetic methods exhibited the compensation effect, in which the values of the derived pre-exponential factors and activation energies are related. This mutual dependence prompted an the examination of the accuracy of these kinetic parameters, and a search for a single set of parameters for each stage of the pitch pyrolysis. It was found that the accuracy of these kinetic parameters derived by different analysis procedures are not identical, and a single set of kinetic parameters for each stage can be obtained with adequate fitting of the experimental data. iii Indexing terms: Pitch, Residuum, TGA, Pyroprobe-GC, Pyrolysis, Kinetics, Modeling, Kinetic Compensation Effect. T A B L E OF CONTENTS ABSTRACT ii T A B L E OF CONTENTS v LIST OF TABLES viii LIST OF FIGURES x N O M E N C L A T U R E xvi ACKNOWLEDGMENTS xviii Chapter 1. INTRODUCTION 1 Chapter 2. Literature Review 4 2.1. Chemical Structure of Pitch 4 2.1.1 The Carbon-Hydrogen Structure 5 2.1.2 Solvent Fractionation of Pitches 6 2.2 Chemistry of Pyrolysis and Secondary Reaction 7 2.2.1 Chemical Thermodynamics of the Pyrolytic Reactions 7 2.2.3 Pyrolysis of Unsubstituted Aromatics 10 2.2.4 Pyrolysis of Mixture of Hydrocarbons 11 2.2.4.1 Pyrolysis of Crude Oil Fractions to Volatile Products 11 2.2.4.2 Pyrolysis of SARA Fractions 12 2.3 Pyrolysis Models and Comparison 13 2.3.1 Constant Evaporation Rate Model 14 2.3.2 Single Overall Reaction Model 16 2.3.3 Two Competing Reaction Model 16 2.3.4 Three Reaction Models 17 2.3.5 Multiple Parallel Reaction Model 20 2.3.6 Complex Models 22 2.3.7 Detailed Models 23 2.3.8 The Application of Models in Pyrolysis Kinetics 24 2.4 Compensation Effect of Kinetic Parameters 25 2.4.1 Effect of Sample Physico-Chemical Properties on the Kinetic Compensation Effect 27 2.4.2 Effect of Experimental Conditions on the Kinetic Compensation Effect 28 2.4.3 Analysis of One T G A Experiment with Different Models or Methods 29 2.4.4 Interaction of the Causes 30 Chapter 3. Experimental Procedures and Apparatus 32 3.1 Introduction 32 3.2 Sample Preparation and Characterization 32 3.3 Experimental Apparatus 33 3.3.1 Thermogravimetric Analysis (TGA) Setup and Operation 34 v 3.3.2 Pyroprobe-GC .- 38 3.3.3 Peak Identification and Quantification 45 Chapter 4 Experimental Results 48 4.1 TGA Experimental Results 48 4.1.1 TGA Pyrolysis of CANMET Pitch. 48 4.1.1.1 Effect of Sample Weight 48 4.1.12 Effect of Heating Rate 51 4.1.1.3 Effect of Final Temperature 54 4.1.2 TGA Pyrolysis of Syncrude Pitch 55 4.1.2.1 Effect of Sample Weight 56 4.1.2.2 Effect of Heating Rate 58 4.1.2.3 Effect of Final Temperature 59 4.1.3 TGA Pyrolysis Characteristics 60 4.1.4 Discussion and Conclusion 67 4.2 Pyroprobe-GC Pyrolysis of CANMET and Syncrude Pitch 71 4.2.1 Pyroprobe-GC Pyrolysis of CANMET Pitch 71 4.2.1.1 Effect of Experimental Conditions on the Total Weight Loss ........72 4.2.1.2 Effect of Experimental Conditions on the C 7 Yield 74 4.2.1.3 Effect of Experimental Conditions on the Cio Yield 77 4.2.1.4 Effect of Experimental Conditions on the Cn Yield 79 4.2.1.5 Effect of Experimental Conditions on the Cn Yield 80 4.2.1.6 Effect of Experimental Conditions on the Ci 3 Yield 81 4.2.1.7 Effect of Experimental Conditions on the C i 4 Yield 82 4.2.2 Pyroprobe-GC Pyrolysis of Syncrude Pitch 84 4.2.2.1 Effect of Experimental Conditions on the Total Weight Loss 84 4.2.2.2 Effect of Experimental Conditions on the C 7 Yield 85 4.2.2.3 Effect of Experimental Conditions on the Cio, Cn, Cn, Cn, and C H Yield 86 4.2.3 Discussion and Conclusion 87 Chapter 5 Modeling of Experimental Results 89 5.1 Introduction of Pyrolysis Kinetic Models 89 5.1.1 Overall First Order Reaction Model 90 5.1.1.1 Integral Method.. 90 5.1.1.2 Friedman Method 91 5.1.1.3 Coats-Redfern Method 92 5.1.1.4 Chen-Nuttall Method 93 5.1.2 Multi-First-Order Reaction Model 93 5.1.3 Mathematical Methods for Overall Single First Order Reaction Model 96 5.2 Testing of the Basic Models 96 5.3 2-Stage First Order Reaction Model 101 5.3.1 Multi-Stage First Order Reaction Model and its Assumptions 106 5.3.2 Application of the Multi-Stage Model 107 5.4 2-Stage First Order Reaction Model for Pitch Pyrolysis 114 5.5 Testing of the 2-Stage Integral Method 120 5.6 Discussion and Conclusion 124 vi Chapter 6 Compensation Effect of the Kinetic Parameters 128 6.1 Compensation Effect of Kinetic Parameters Derived from Overall First Order Reaction Model 129 6.2 Compensation Effect of Kinetic Parameters Derived from 2-Stage Reaction Model... 131 6.3 The Relationship of Standard Errors and Kinetic Parameters 137 6.4 Discussion and Conclusion..... 143 Chapter 7 Conclusions and Recommendations 147 7.1 Summary of Findings 147 7.2 Recommendations 150 REFERENCES 152 APPENDICES 162 APPENDIX A: Methods Available for Computing Kinetic Parameters 163 APPENDIX B: GC Computer Station Method Parameters 166 APPENDIX C: Comparison of Equation 5.5 and Equation 5.6 Evaluated with Different Numbers of Terms of Integral E;(-E/RT) 169 APPENDIX D: FORTRAN Programs and Calculation Results for T G A Experimental Results Modeling 170 APPENDIX E: FORTRAN Program for Two-Stage First Order Reaction Model 187 APPENDIX F: Summary of Kinetic Parameters of the 2-Stage Model 209 APPENDDC G: Kinetic Reaction Rate Constant Ink - 1/T for C A N M E T and Syncrude Pitches 211 APPENDDC H: Volatile Yield Predicted via the Single Set Kinetic Parameters for Different Heating Rates 217 APPENDIX I: The Effect of the Number of Significant Digits and Sample Weight Analysis 220 LIST OF TABLES Chapter 2 Table 2.1 Bond Energies Obtained from Thermodynamic Data and from Quantum Mechanical Calculations [22] 8 Table 2.2 Resonance Energies of Cyclic Compounds [22] 9 Table 2.3 Summary of the Methods Used in Constant Heating Rate Pitch Pyrolysis 25 Chapter 3 Table 3.1 Pitch Characterization Analysis 33 Table 3.2 Retention Time of Each Component 43 Table 3.3 Important Peaks on the Pyrolysis-GC Chromatograms 45 Table 3.4 The Summary of Operation Parameters Used by TGA, Pyroprobe and G C 47 Chapter 4 Table 4.1.1 Experimental Conditions for Runs at Different Sample Weight with T G A 69 Table 4.1.2 Experimental Conditions for Runs at Different Sample Weight with T G A 69 Table 4.1.3 Experimental Conditions for Runs at Different Heating Rates with T G A 69 Table 4.1.4 Experimental Conditions for Runs at Different Heating Rates with Pyroprobe 69 Table 4.1.5 Experimental Conditions for Runs at Different Final Temperature with T G A 69 Table 4.1.6 Experimental Conditions for Runs at Different Sample Weight with T G A .....70 Table 4.1.7 Experimental Conditions for Runs at Different Heating Rates with T G A and Pyroprobe 70 Table 4.1.8 Experimental Conditions for Runs at Different Final Temperature with T G A 70 Table 4.1.9 The Pyrolysis Conditions for C A N M E T Pitch and Syncrude Pitch at Different Temperature and Heating Rates 70 Table 4.2.1 Experimental Conditions for Runs at Different Holding Times 71 Table 4.2.2 Experimental Conditions for Runs at Different Holding Times 84 Chapter 5 Table 5.1 Y and a Formulas for Each of the Overall Single First Order Reaction Methods 96 Table 5.2 Kinetic Parameters for the Nonisothermal Pyrolysis of C A N M E T Pitch at 50 °C/min. and 700 °C 97 Table 5.3 Kinetic Parameters for the Nonisothermal Pyrolysis of C A N M E T Pitch and Syncrude Pitch at 25 °C/min. and 800 °C 108 Table 5.4 Kinetic Parameters for the Nonisothermal Pyrolysis of C A N M E T Pitch and Syncrude Pitch at 800 °C and Different Heating Rates with 2-Integral Model 114 Table 5.4 Experimental Conditions and Model Predicted Results of C A N M E T Pitch and Syncrude Pitch Pyrolysis 120 Chapter 6 Table 6.1 Compensation Parameters for C A N M E T Pitch Pyrolysis at Different Heating Rates and 800 °C 131 Table 6.2 Compensation Parameters for Syncrude Pitch Pyrolysis at Different Heating Rates and 800 °C 131 Table 6.3 Experimental Conditions and Model Predicted Results of C A N M E T Pitch and Syncrude Pitch Pyrolysis 140 Table 6.4 Experimental Conditions and Model Predicted Results of C A N M E T Pitch and Syncrude Pitch Pyrolysis 142 LIST OF FIGURES Chapter 3 Figure 3.1 The relative position of the furnace and sample pan on the left and the T G A furnace on the right 36 Figure 3.2 The Pyroprobe-GC setup 39 Figure 3.3 The installation of Pyroprobe interface into the GC injection port 40 Figure 3.3 a The sketch of Pyroprobe with pitch sample applied on the inner surface of quartz tube 40 Figure 3.4 Chromatogram of C A N M E T pitch volatiles 44 Figure 3.5 Chromatogram of standard sample 44 Chapter 4 Figure 4.1.1 Sample weight effect on C A N M E T pitch pyrolysis with T G A at 900 °C and 100 °C/min 50 Figure 4.1.2 Sample weight effect on C A N M E T pitch pyrolysis with T G A at 900 °C and 50 °C/min 50 Figure 4.1.3 Heating rate effect on C A N M E T pitch pyrolysis with T G A 52 Figure 4.1.4 Heating rate effect on C A N M E T pitch pyrolysis with Pyroprobe-GC 53 Figure 4.1.5 Heating rate effect on C A N M E T pitch pyrolysis with T G A and Pyroprobe-GC 54 Figure 4.1.6 Final temperature effect on C A N M E T pitch pyrolysis with T G A at 100 °C/min 55 Figure 4.1.7 Sample weight effect on Syncrude pitch pyrolysis with T G A at 100 °C/min and 0 min 57 Figure 4.1.8 Sample weight effect on Syncrude pitch pyrolysis with T G A at 100 °C/min at 10 min 57 Figure 4.1.9 Heating rate effect on Syncrude pitch pyrolysis with T G A and Pyroprobe-GC (0 minute after reaching 800 °C) 58 Figure 4.1.10 Final temperature effect on Syncrude pitch pyrolysis with T G A at 0 min 59 Figure 4.1.11 Final temperature effect on Syncrude pitch pyrolysis with T G A at 10 min 60 x Figure 4.1.12 C A N M E T pitch weight loss vs. temperature at different heating rates and final temperature 800 °C measured via T G A 63 Figure 4.1.13 C A N M E T pitch weight loss vs. time at different heating rates and final temperature 800 °C measured via T G A 64 Figure 4.1.14 C A N M E T pitch weight loss rate vs. time at different heating rates and final temperature 800 °C measured via T G A 64 Figure 4.1.15 C A N M E T pitch weight loss dW/dT vs. temperature at different heating rates and final temperature 800 °C measured via T G A 65 Figure 4.1.16 Syncrude pitch weight loss vs. temperature at different heating rates and final temperature 800 °C measured via T G A 65 Figure 4.1.17 Syncrude pitch weight loss vs. time at different heating rates and final temperature 800 °C measured via T G A 66 Figure 4.1.18 Syncrude pitch weight loss rate vs. time at different heating rates and final temperature 800 °C measured via T G A 66 Figure 4.1.19 Syncrude pitch weight loss dW/dT vs. temperature at different heating rates and final temperature 800 °C measured via T G A 67 Figure 4.2.1 C A N M E T pitch pyrolysis total loss vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 73 Figure 4.2.2 C A N M E T pitch pyrolysis total loss vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 73 Figure 4.2.3 C A N M E T pitch pyrolysis total loss vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min 74 Figure 4.2.4 C A N M E T pitch pyrolysis C7 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 75 Figure 4.2.5 C A N M E T pitch pyrolysis C7 yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 75 Figure 4.2.6 C A N M E T pitch pyrolysis C 7 yield vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min 76 Figure 4.2.7 C A N M E T pitch pyrolysis C10 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 78 Figure 4.2.8 C A N M E T pitch pyrolysis C10 yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 78 Figure 4.2.9 C A N M E T pitch pyrolysis Cio yield vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min 79 Figure 4.2.10 C A N M E T pitch pyrolysis Cu yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 80 Figure 4.2.11 C A N M E T pitch pyrolysis C12 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 81 Figure 4.2.12 C A N M E T pitch pyrolysis C B yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 82 Figure 4.2.13 C A N M E T pitch pyrolysis C14 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min. 83 Figure 4.2.14 C A N M E T pitch pyrolysis C14 yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 83 Figure 4.2.15 Syncrude pitch pyrolysis total weight loss vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 85 Figure 4.2.16 Syncrude pitch pyrolysis C 7 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 86 Chapter 5 Figure 5.1 Comparison of model prediction and experimental volatile for C A N M E T pitch at 50 °C/min. and 700 °C with first order reaction methods 99 Figure 5.2 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with integral method 99 Figure 5.3 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with Coats-Redfern method 100 Figure 5.4 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with Chen-Nuttall method 100 Figure 5.5 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with Friedman method 101 Figure 5.6 The devolatilization ratio dV/dT vs. the remaining volatile at different heating rates and 800 °C for C A N M E T pitch 104 Figure 5.6b The devolatilization rate dV/dt vs. the remaining volatile at different heating rates and 800 °C for C A N M E T pitch 104 Figure 5.7 The devolatilization ratio dV/dT vs. the remaining volatile at different heating rates and 800 °C for Syncrude pitch 105 Figure 5.7b The devolatilization rate dV/dt vs. the remaining volatile at different heating rates and 800 °C for Syncrude pitch 105 Figure 5.8 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 25 °C/min. and 800 °C with 2-stage methods I l l Figure 5.9 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 25 °C/min. and 800 °C with 2-stage methods 112 Figure 5.10 Comparison of model prediction and experimental volatile for C A N M E T pitch at 25 °C/min. and 800 °C with each 2-stage first order reaction methods 112 Figure 5.11 Comparison of model predicted Y results and experimental Y results for Syncrude pitch at 25 °C/min. and 800 °C with 2-stage methods 113 Figure 5.12 Comparison of model predicted Y results and experimental Y results for Syncrude pitch at 25 °C/min. and 800 °C with 2-stage methods 113 Figure 5.13 Comparison of model prediction and experimental volatile for Syncrude pitch at 25 °C/min. and 800 °C with each 2-stage first order reaction methods 114 Figure 5.14 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method 116 Figure 5.15 Comparison of model predicted Y results and experimental Y results for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 116 Figure 5.16 Comparison of model prediction and experimental volatile for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method 117 Figure 5.17 Comparison of model prediction and experimental volatile for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 117 Figure 5.18 Comparison of model prediction and experimental volatile for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method 118 Figure 5.19 Comparison of model prediction and experimental volatile for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 118 Figure 5.20 Comparison of model prediction dV/dt and experimental dV/dt for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method 119 Figure 5.21 Comparison of model prediction dV/dt and experimental dV/dt for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 119 xiii Figure 5.22 Comparison of model prediction and experimental volatile for C A N M E T pitch at 100 °C/min and 750 °C with 2-stage integral method 121 Figure 5.23 Comparison of model prediction and experimental volatile for C A N M E T pitch at 100 °C/min and 850 °C with 2-stage integral method 122 Figure 5.24 Comparison of model prediction and experimental volatile for C A N M E T pitch at 100 °C/min and 950 °C with 2-stage integral method 122 Figure 5.25 Comparison of model prediction and experimental volatile for Syncrude pitch at 50 °C/min and 750 °C with 2-stage integral method 123 Figure 5.26 Comparison of model prediction and experimental volatile for Syncrude pitch at 50 °C/min and 850 °C with 2-stage integral method 123 Figure 5.27 Comparison of model prediction and experimental volatile for Syncrude pitch at 50 °C/min and 950 °C with 2-stage integral method 124 Chapter 6 Figure 6.1 C A N M E T pitch T G A pyrolysis kinetic parameters at 50 °C/min and 700 °C with different overall first order model 130 Figure 6.2 C A N M E T pitch pyrolysis reaction rate constant as a function of temperature at heating rate 50 °C/min and final temperature 700 °C 130 Figure 6.3 C A N M E T pitch T G A pyrolysis kinetic parameters at different heating rates and 800 °C with different 2-stage first order methods 132 Figure 6.4 Syncrude pitch T G A pyrolysis kinetic parameters at different heating rates and 800 °C with different 2-stage first order methods 132 Figure 6.5 C A N M E T pitch T G A pyrolysis kinetic parameters at different heating rates and 800 °C with different 2-stage first order methods 133 Figure 6.6 Syncrude pitch T G A pyrolysis kinetic parameters at 800 °C with different 2-stage first order methods 133 Figure 6.7 C A N M E T pitch pyrolysis reaction rate constant as a function of temperature at different heating rates and final temperature 800 °C with 2-stage integral method.... 136 Figure 6.8 Syncrude pitch pyrolysis reaction rate constant as a function of temperature at different heating rates and final temperature 800 °C with 2-stage integral method.... 137 Figure 6.9 C A N M E T pitch T G A pyrolysis s.e.e. as a function of E at different conditions and with different methods 139 xiv Figure 6.10 Syncrude pitch T G A pyrolysis s.e.e. as a function of E at different conditions and different methods 139 Figure 6.11 Comparison of experimental data and model prediction for C A N M E T pitch at different heating rates and 800 °C with a single set of kinetic parameters 141 Figure 6.12 Comparison of experimental data and model prediction for Syncrude pitch at different heating rates and 800 °C with a single set of kinetic parameters 141 Figure 6.13 Comparison of model prediction and experimental volatile content for C A N M E T pitch at 100 °C/min and 750 °C, 850 °C, and 950 °C respectively 142 Figure 6.14 Comparison of model prediction and experimental volatile content for Syncrude pitch at 50 °C/min and 750 °C, 850 °C and 950 °C respectively 143 xv N O M E N C L A T U R E a kinetic compensation constant in Chapter 2 fitting parameter in Chapter 5 B maximum possible devolatilization rate, S"1 b kinetic compensation constant in Chapter 2 fitting parameter in Chapter 5, b=-E/R C heating rate, °C/min E, E 0 activation energy, J/mol E; activation energy of ith stage of reaction, J/mol f(E) distribution function of activation energy HpT rate of heat supply for volatile evaporation per unit mass, kJ/s.kg coal hLV total heat of volatile evaporation per unit mass of coal, kJ/kg coal k, k i , k 2, k 3 rate constant represented by an Arrhenius expression, min"1 k o , k o i , k o 2 pre-exponential constant of Arrhenius equation, min"1 k o i pre-exponential factor of ith stage reaction, min'1 k nominal rates ~k = (dV / dt) / (v*-V), min"1 mc(0) initial mass of coal, kg mc mass of coal at any time t, kg mc(final) mass of coal at the end of pyrolysis reaction, kg mi mass of the reactive intermediate, kg m T mass of tar, kg n no. of reaction stages which are first order reaction R gas constant, 8.314 J/mol.K R 2 linear regression constant s standard deviation of activation energy, J/mol s.e.e. standard deviation error T temperature, °C (or K) T; critical temperature, at which reaction behavior is undergoing visible change in terms of the ratio dV/dT or rate dV/dt due to the change of reacting residue, K To initial temperature for TGA, 50 °C T P coal particle temperature, °C (K) Tv volatile evaporation temperature, °C (or K) V volatile released at time t, % (or kg) Vt=o volatile yield at t=0 minutes, % Vt=io volatile yield at t=10 minutes, % V * total volatile yield, % (or kg) X reciprocal of temperature 1/T, K" 1 X v fraction of volatile material to be released Y LHS of each of the single overall first order reaction methods a, cti, 0C2 kinetic compensation constant cti, a 2 mass stoichiometric factors representing the extents of devolatilization via reaction 1 and 2 respectively in Chapter 2 cti constant used to characterize the gradual change of the chemical structure of reacting residue, cti = 1 when Ti„i<T<Tj, otherwise cti =0 P shape parameter of Weibull distribution P, Pi, P2 kinetic compensation constant r\ scale parameter of Weibull distribution y threshold or location parameter of Weibull distribution xvii ACKNOWLEDGMENTS I am grateful to my supervisor, Professor A. P. Watkinson, for his guidance and interest in this research. I am also indebted to many others who helped during the course of this work: To the University of British Columbia which contributed financial support in the form of University Graduate Fellowships. To the Natural Science and Engineering Research Council of Canada which provided financial support in the form of research grants. To the Combustion Group of the Department of Chemical Engineering, UBC, which provided the C A N M E T pitch sample. To Syncrude Canada Ltd. which provided the Syncrude pitch sample. Special thanks are due to my mother, sisters and younger brother for their encouragement, understanding and patience. xviii CHAPTER 1 INTRODUCTION Pyrolysis of high molecular mass carbon and hydrogen containing materials is viewed as depolymerization in parallel with thermal decomposition of functional groups. The primary products compete for the donatable hydrogen for stabilization [1]. Pyrolysis is the first step in some conversion processes for hydrocarbon containing materials such as coal, heavy petroleum, and oil shale. It is the step which is most dependent on the properties of the hydrocarbons [2]. In combustion and gasification, pyrolysis precedes reaction by oxygen, steam, hydrogen or carbon dioxide [3]. In coking processes, pyrolysis of petroleum, semi-solids (mainly residua) and solids (mainly coals) results in the formation of a complete range of products from solids to gas. In addition to its importance in the hydrocarbon conversion process, analysis of pyrolysis products can supply important clues to the structure of the parent hydrocarbon. The last several decades have seen an improvement in the understanding of coal and biomass pyrolysis in processes such as gasification, combustion, and liquefaction [1-4]. More rigorous information has also been developed for the light hydrocarbons. For complex feedstocks such as above, the approach taken to pyrolysis has been mainly semi-empirical. The literature contains relatively fewer attempts to deal with moderately heavy hydrocarbon feedstocks and the related mechanism involved, especially the secondary reactions which are often ignored in coal pyrolysis. Secondary reaction refers to the cyclization and condensation of the pyrolysis volatiles before leaving the reacting hydrocarbon matrix. For coal, secondary reactions are complex, being influenced by coal type, heating rate, residence time, temperature, intra- and extra-particle heat and mass transfer, and physical structure of the reacting coal. Further, these reactions can be heterogeneous (vapor-solid, vapor-liquid, or liquid-solid) or homogeneous (vapor phase or liquid phase) [5]. 1 The pyrolysis of coal and biomass has been widely investigated since the late 1970's to maximize the liquid product yield in order to find a substitute for petroleum or for generation of chemicals. This has resulted in the development of several coal conversion processes [6, 7] in which the knowledge of pyrolysis is used to predict the product yields and distribution quite reasonably and successfully. For biomass, the complexity of the liquid products generally defies prediction. The knowledge of pitch pyrolysis is also quite limited and has been borrowed from that for coal. Most known technology for processing of bitumen, coal, petroleum, and oil sands produces pitch. Pitch is commonly used to describe the liquid or semi-liquid fraction of a reaction product that boils above 524 °C and which arises as a by-product from processing of crude oil or bitumen. Its relatively high H/C atomic ratio (about 1.0 compared to about 0.5 for coke and 0.3 to 0.9 for coal) [8, 9] suggests that it should be possible to produce liquids by additional processing. Furthermore an appreciation of pitch pyrolysis might lead to new methods of pitch utilization. Thus, there is a clear need for further study in this field, to clarify the behavior of pitch in pyrolysis, which will improve the understanding of the processes and mechanisms involved, and hopefully lead to a proper way to process pitch, and generate economic and environmental profit. As Canada, and other countries rely increasingly on heavy oils, residues from upgrading will become more of a disposal problem. Hydrogen or fuel gas production via gasification is a possible route to utilization. When pitches are heated prior to gasification their large volatile content is released, leaving a char. To understand kinetics, information on volatile yields and composition as function of temperature, atmosphere and pitch type is essential [10, 11]. Syncrude and C A N M E T processes represent two major bitumen processes which subsequently produce pitch as by-product. C A N M E T pitch is the residue of Cold Lake bitumen from C A N M E T hydrocracking process, where an additive is used to inhibit coke formation. This process was demonstrated at 5000 bpd in Petro-Canada's Montreal refinery and about 10% of the feed ends up as pitch during the upgrading process [12-14]. This demonstration was successful and the technology is ready for commercialization. Syncrude pitch is the residue of Athabasca bitumen from Syncrude LC-Fining process. LC-Fining is a hydroprocessing process where H 2 and catalysts are added in to upgrade bitumen at temperature 375-530 °C and pressure 1100-1600 psi, and currently operating at 715 m3/D of bitumen. About 4% of the feed ends up as pitch [15]. The objectives of this study were to investigate the pyrolysis reaction mechanism and product distribution for different pitch types, and to formulate a model for the mechanism under conditions of different heating rates, final temperatures and reaction times. The study is concerned with pitch pyrolysis over a range of heating rates and for final temperatures from 700 to 1000 °C, and under normal pressure in an inert atmosphere, so that the first step in atmospheric pressure gasification, pyrolysis and combustion processes can be simulated. Pitch pyrolysis at low heating rates is studied using a TGA, and at rapid heating rates with a Pyroprobe-equipped gas chromatograph. With TGA, the weight loss rate is investigated quantitatively at different final temperatures and heating rates less than 150 °C/min. Diffusional effects inside the pitch samples are studied by changing the initial pitch sample weight (or pitch sample thickness inside the T G A sample holder). Thus pyrolysis kinetics and relative parameters can be derived from the data. With the Pyroprobe-equipped chromatograph, weight loss is also obtained at different final temperatures and heating rates up to 300,000 °C/min. The Pyroprobe equipped chromatograph permits in situ GC analysis, in which the volatile composition is investigated as a function of reaction conditions. With the two procedures, pyrolysis kinetics and reaction parameters can be investigated under a wide range of conditions. 3 Chapter 2 Literature Review 2.1 Chemical Structure of Pitch The pyrolysis of relatively simple hydrocarbon compounds is complex and only partly understood. Therefore, it comes as little surprise that the knowledge of chemical mechanisms for pyrolysis of relatively undefined materials such as pitch or coal is lacking. The characterization of pyrolysis products of coal and/or pitch is a sizable task, as these are usually present as gases, liquids and solids. The number of distinct chemical species is very large, and to facilitate data analysis one must usually resort to judiciously grouping the products into a few key classes of compounds. With pitch, the characterization of the reactant is as difficult, if not more difficult than, the characterization of the products of the process. Because pitch is a somewhat heterogeneous and only partially soluble in most solvents, many of the traditional chemical and spectroscopic techniques for organic structure determination can not be applied easily or unambiguously. Therefore there is still a fair amount of debate over what constitutes a representative structure for a pitch 'rnolecule". The chemical structures of the pitches studied have not been determined directly in this work. Rather, the structural characteristics must be inferred from a knowledge of the more traditional classification parameters for pitch. The literature on the structure determination of petroleum derived pitch also contains information on 'boal extracts" and other solvated coal and pitch fractions. However, the fraction that is soluble in a given solvent does not represent the total pitch or coal, since solubilization is unlikely to preserve its basic structure. The information is therefore difficult to apply. 4 2.1.1 The Carbon-Hydrogen Structure It is generally accepted that an important characteristic of pitch or coal structure is its aromaticity, defined as the fraction of carbon in the pitch or coal which is aromatic in nature. A large number of approaches have been employed to determine the aromaticity and the average number of rings in the condensed polycyclic aromatic 'blusters", as a function of carbon content. Various physical techniques [16] have been employed in studying the structure of coal/pitch structure. From empirical studies on many hydrocarbons Van Krevelen [17] and several coworkers developed several ingenious correlations between measurable physical properties and some much more difficult to measure structural parameters. Great advances have been achieved during the last decade in the application of NMR in pitch characterization. For measurements on pitch solutions, the main problem is the fact that pitches are not completely soluble in solvents suitable for NMR. Solid state N M R has the disadvantage of insufficient spectral results. As has been shown by Komatsu [18], these disadvantages can be overcome by measuring the spectrum at a temperature above the softening point of the pitch. The method has been applied to various types of pitches using 1 3 C NMR. Well-resolved spectra characterized by a high signal to noise ratio were obtained. Moreover, the measuring time could be markedly shorted compared with the measuring time necessary in organic solutions. 1 3 C N M R not only provides the important aromaticity figure but also detailed information on the aliphatic functional groups present in pitches. Of course aromaticity alone does not completely characterize the carbon skeletal structure. Information on the distribution of aromatic and nonaromatic carbon is also necessary. It should also certainly be noted that using the total carbon content for the coals or pitch masks 5 potentially significant differences among the maceral fractions in coals, or the difference among fractions of different solubility in pitches. Unfortunately data on total hydrogen distribution is not plentiful and its reliability is frequently questioned. Chemical techniques have provided some of the necessary data (such as that for hydroaromatic hydrogen and phenolic hydrogen), while spectroscopic techniques, such as *H N M R and JJR, have provided others. 2.1.2 Solvent Fractionation of Pitches Solvent fractionation is the most widely used method in pitch characterization. Solvent fractionation uses organic solvents of increasing polarity such as w-pentane, benzene and tetrahydrofuran (THF) to give fractions of increasing molar mass and heteroatom content. Three typical fractions are: w-pentane solubles, benzene insolubles and asphaltenes (benzene soluble, n-pentane insoluble). The fractions can be separated further by chromatographic methods and characterized by a variety of spectroscopic and chemical methods to provide details of individual components and average structures. Chromatography is widely used in the separation, fractionation and characterization of complex mixtures of organic molecules. Size exclusion chromatography provides a separation mainly on the basis of molecular size which corresponds to separation on the basis of molar mass. It has been extensively used for coal and petroleum derivatives. However, separation occurs partially on the basis of functionality when THF is used as solvent, as well as on molecular size. This makes determination of molar mass distributions unreliable with high concentrations of pitch or tar present. SARA (saturates, aromatics, resins and asphaltenes) separation is a traditional characterization method for hydrocarbon residuum, based on solubility/polarity of compounds. A 6 discussion of the chemical structures found in the SARA fractions can be found [19]. In general, the components are alkyl-substituted polycyclic structures related to steranes and hopanes derived from squalene precursors, or to terpenoid skeletons. Following the progression from saturates to aromatics to resins to asphaltenes, these fractions show increased aromaticity, average molecular weight, and heteroatomic content. There is also some overlap of structures and properties between neighboring fractions. Furthermore, variations in the relative amounts of the SARA fractions are accompanied by variations in the physical properties of bitumen. The chemical structures in the different fractions are believed to be related through various diagenetic processes such biodegradation and thermal maturation. However, each SARA fraction is fundamentally different to the extent that it can exhibit some specific chemical attributes. The studies of SARA fractions have led to insights into the processing of petroleum residuum (pitch etc.). However, attempts to correlate SARA fractions with the processibility of residua have generally also been unsuccessful [20]. The determination of average molecular structures held some promise of providing insight into residuum conversion chemistry. A promising approach to gain some understanding of the complex chemistry of residuum upgrading [21] by coking, hydrocracking and hydrotreating appears to be to use a combination of yield data obtained over a wide range of conversions, together with average molecular structural data and the extensive knowledge of molecular structures in residua. 2.2 Chemistry of Pyrolysis and Secondary Reaction 2.2.1 Chemical Thermodynamics of the Pyrolytic Reactions To understand the chemistry of the pyrolysis reaction and the criteria for its chemical control, it is necessary to compare the thermodynamic stability of the various carbon compounds. The comparative stability of the various hydrocarbon groups may serve as a basis for discussing 7 the probable sequence of a decomposition reaction. Among the three major groups of hydrocarbons, i.e., paraffins, olefins and aromatics, the low molecular weight paraffins are the most stable hydrocarbons up to about 500 °C and among these, methane exhibits the greatest stability. Above 800 °C, the aromatics become the most stable hydrocarbons. In this temperature range (500-800 °C), the thermodynamic stability of the olefins lies between that of the paraffins and aromatics. The stability of paraffins decreases with increasing chain length. In the higher temperature region (>800 °C), the same holds true for the olefins. The alkylated aromatics compounds are less stable than the pure aromatics. With increasing length of the side chain, the stability decreases. Contrary to this, the stability of aromatics increases with increasing number of rings, i.e. with increasing molecular size. The mean bond energies of organic compounds are obtained by referring the energies of formation to the gaseous elements involved, i.e. carbon and hydrogen, and by then dividing by the number of bonds. Table 2.1 gives bonds energies obtained from thermodynamic data, as compared with those derived from quantum mechanical calculations based on bond length and force constants. Both methods give approximately the same values for the individual bond types. Table 2.1 Bond Energies Obtained from Thermodynamic Data and from Quantum Mechanical Calculations [22] From thermodynamic data From quantum mech. calculations Mean Mean Force bond bond Distance constant Bond Compound energy kJ/mdl energy kJ/mol between nuclei, A dynes cm'SclO"5 C — C C2H5 325.10 — — — C==C C2FI4 585.76 597.89 1.337 9.8 C ^ C C 2 H 2 808.77 811.70 1.205 15.6 C — C C^is 517.98 — — — C — H CH4 410.87 412.96 1.094 4.88 o—a H O - H 457.73 462.75 0.98 7.6 C = 0 C H 2 0 683.25 694.54 1.21 12.1 8 A comparative consideration shows that the C - H bond is more stable than the C-C bond. Also shown is the higher bond energy of the C-C double bond and the C-C triple bond, which explains the dehydrogenation tendency towards olefins and the stability of acetylene at high temperature. The high stability of ring compounds and especially of aromatics is due to the resonance energy. The resonance energy increases with increasing molecular size of the ring system, thus explaining the driving force for the chemical condensation of low molecular weight aromatics to polycyclic aromatic systems with the accompanying release of hydrogen. Examples are given in the following Table 2.2. Table 2.2 Resonance Energies of Cyclic Compounds [22] Energy Energy Compound kJ/mol Compound kJ/mol Benzene 150.62 Quinoline 288.70 Naphthalene 255.22 Biphenyl 299.16 Anthracene 351.46 Aniline 167.36 Phenanthrene 384.93 Furan 92.05 Toluene 146.44 Pyrrole 102.51 Styrene 158.99 Indole 205.02 Phenol 150.62 Thiophene 117.15 Pyridine 179.91 Cyclooctatraene 25.10 This qualitative thermodynamic consideration suggests the following trends for the course of pyrolysis of hydrocarbons with the increase of temperature [22]: 1. Cracking of all nonaromatic hydrocarbons to smaller molecules (cracking and dehydrogenation reactions). 2. Cyclization of all hydrocarbon chains to form aromatics. The first and the second reaction trends apply in the same way to aromatics with side chains which can undergo cracking or cyclization. 3. Condensation reactions of aromatics to form polycyclic aromatic systems. 9 These three principal types of reactions occur in all known technical processes dealing with the formation of carbon via pyrolysis reactions. 2.2.2 Pyrolysis of Unsubstituted Aromatics Unsubstituted aromatics primarily exhibit direct ring condensation, i.e., the formation of diarenes and triarenes. Whenever sterically possible, chemical condensation can proceed to polycyclic products. Unsubstituted aromatics having the anthracene configuration are more reactive with respect to chemical condensation. In summary [22], the pyrolysis of hydrocarbons takes place via aromatic intermediates. Results on the pyrolysis of well-defined, pure aromatics have shown the following effects: 1. Unsubstituted aromatics react by chemical condensation to form polynuclear aromatics, the aromatics having an anthracene configuration being the most reactive. 2. Alkyl-substituted aromatics are more reactive than unsubstituted ones, the effect being more pronounced the greater the number and the length of the alkyl groups. 3. The alkyl groups are the positions where the formation of the new aromatic systems takes place. 4. The highest reactivity is exhibited by aromatics containing five-numbered ring systems. The existing investigations, pertaining to gas phase pyrolysis in a flow system, show that in the early stages the order of reaction is approximately unity for benzene, naphthalene and biphenyl. The apparent first order rate constants fox these three aromatics are found to be of the same order of magnitude. The apparent activation energies amount to approximately 292.88 kJ/mol to 334.72 kj/mol. 10 2.2.3 Pyrolysis of Mixture of Hydrocarbons The great complexity of chemical reactions occurring during the pyrolysis of hydrocarbons can be recognized not only from thermodynamic considerations but also from technological experiences gained in different processes. In view of the various mixtures of hydrocarbons used as raw materials and because of the insufficient analytical control of a technical pyrolysis, these processes do not reveal the chemistry in detail. Nevertheless, they provide a fair picture as to process parameters such as temperature, residence time and yield upon pyrolysis. Free radical reactions control the pyrolysis of most organic substances. 2.2.3.1 Pyrolysis of Crude Oil Fractions to Volatile Products It has been found that the tendency to pyrolysis increases from the paraffins to the olefins and further to the naphthalene and the alkylated aromatics, up to the nonsubstituted aromatics. In case of purely thermal pyrolysis, mild conditions around 400 °C lead primarily to a fracture of the C-C bond, preferentially in the middle of the molecule chain. With increasing temperatures, the position of the fracture shifts towards the chain end, thus producing long chain olefins and increased portions of highly volatile fragments. Paraffins undergo pyrolysis leading to the formation of saturated and nonsaturated fragments between 400 °C and 600 °C. Depending on the length of the main chain, isoparaffins primarily lose their branches and then behave like straight chain paraffins. Ring paraffins lose parts of their side chains, thus leading to unsaturated fragments. At temperatures above 600 °C, naphthalene rings can be broken to form straight chain olefins. Cycloparaffins containing three carbon atoms are broken most easily, whereas cyclopentane is most stable. Cycloparaffins containing six carbon atoms in the ring become stabilized by aromatization. In the case of 11 alkylated aromatics, the rupture of the side chains is promoted with increasing length of these chains. With rising temperature, the rupture of the C - H bond is more strongly enhanced than rupture of the C-C bond. Thus the formation of very small fragments down to hydrogen is favored and diolefrns and triolefins with good thermal stability are formed. Above 550 °C, long chain olefins disintegrate, leading to shorter molecules and partial aromatization. The first step of the hydrocarbon pyrolysis, namely, the decomposition to nonaromatic hydrocarbons takes place in the low temperature region between 400 and 700 °C, whereas the aromatization occurs between 700 and 900 °C. These results are however valid only for short contact times at the described temperature. Similar experiences pertain to the coal coking processes. The volatile hydrocarbons released at pyrolysis temperatures between 400 and 500 °C consist mainly of noncyclic compounds. In the high temperature range, however, the volatile products found in the coal tar are extremely aromatic. 2.2.3.2 Pyrolysis of SARA Fractions Evidence from GC, HPLC, and FTIR analysis [23-29] suggests that SARA fractions (saturates, aromatics, resins, and asphaltenes) from heavy hydrocarbon undergo dealkalyation and aromatization when pyrolyzed at temperatures 362 °C to 418 °C. Aromatization and dealkylation of the polycyclic, saturated structures in the saturate fraction lead directly to the production of aromatic compounds. Further aromatization and dealkylation of the aromatic fraction result in resin production. Resins and asphaltenes have chemical and structural similarities. The thermal pyrolysis of the resins and asphaltenes results in further condensation of the polycyclic structure and fragmentation and finally leads to the formation of coke. This process was proven to involve 12 bond scission and radical reactions. The pyrolysis of each of the SARA fractions appeared first order. The observed apparent activation energy of pyrolysis for aromatics, resins and asphaltenes is 108, 135, 150 kJ/mol respectively [23]. These values fall in the wide range of values 29.1 kJ/mol and 286 kJ/mol [29] for bitumen pyrolysis. Observed values of apparent activation energies depend upon many factors, including the structure and complexity of the kinetic model. The method used to prepare a particular fraction will influence both its chemical composition and behavior, and consequently the values for any kinetic parameters that characterize it. The more chemically-varied the species contained in a particular fraction, the greater will be the number of reactions within the fraction and consequently, the lower will be the observed globe kinetic parameters [13, 30]. 2.3 Pyrolysis Models and Comparison One aim of modeling is to predict the pyrolysis behavior a priori in a conversion system as . a function of parameters (temperature, heating rate, pressure, particle size etc.) thus facilitating the design of conversion reactors. Systematic research to this end during recent decades has advanced our knowledge to a stage where reasonable predictions are possible through modeling [31, 32]. These studies have provided valuable insight into the kinetics and the mechanism of the pyrolysis process. The modeling of pyrolysis is relatively straightforward when the chemical reaction is the only process occurring within the reactor and the feed species is simple. There are, of course, different levels of complexity of kinetic models. For simple hydrocarbons, pyrolysis models are based on the free radical mechanism. For propane pyrolysis, for example, the scheme of Trimm and Turner [33] includes one initiation reaction, thirty one propagation reactions, and nine termination reactions. These involved no species of greater molecular weight than C4H10, and no coke formation. At a less complex level, Sundaram and Froment [34] describe propane 13 cracking by ten reactions using molecular species rather than free radicals. This reaction scheme yields information on product distributions, but does not represent the mechanism as such. For higher molecular weight hydrocarbon feeds, or complex mixtures such as pitch, it is not feasible to write a kinetic model which reflects all steps in the actual mechanism. For example, the Kumar and Kunzru [35] scheme for naphtha pyrolysis incorporates twenty two reactions which are written in terms of molecular species. Each reaction requires a specified pre-exponential factor and activation energy. However, pyrolysis can involve extra transport steps which introduce complexity. The review by Jamaludin et al. [36] considers the present understanding of kinetic models, and the review by Suuberg [37] considers the present understanding of general pyrolysis models including the mass transfer limitations of coal pyrolysis. Analogous models are applied to biomass pyrolysis. At the time of writing, no accurate model has been developed to completely describe pitch pyrolysis. The following work which primarily involves coal pyrolysis is reviewed as that which bears most relevance to the system under investigation. Rather than dealing with individual species, this approach deals with the volatile matter as one or two components. The application of the models to pitch involves some changes, and certain steps which are valid for coal, would not apply to pitch. The two competing reaction model of pyrolysis is shown to be a simple, but effective method for predicting the weight loss due to devolatilization at high temperature and high heating rates for coal pyrolysis. 2.3.1 Constant Evaporation Rate Model The constant evaporation model is probably the simplest existing pyrolysis model. Proposed by Baum and Street [38], it assumes that pyrolysis does not begin until the particle 14 temperature exceeds a vaporization temperature Ty, taken as 327 °C. Above TV, the rate of pyrolysis is controlled by the total heat of evaporation of the volatile, up to an empirically determined maximum value. The rate of pyrolysis in terms of the fraction of volatile material Xv to be released, can be expressed as J I T —^=0; TP<TvorXv=1.0 (2.2a) dt = - /hlv ; TP>Tv and XV<1.0, H P T <Bh l v (2.2b) dt dX = -B; TP>Tv and XV<1.0, Hpr>Bh,v (2.2c) dt Where hLV is total heat of volatile evaporation per unit mass of coal, kJ/kg coal, HPT is rate of heat supply for volatile evaporation per unit mass, kJ/s.kg coal. B is the maximum possible devolatilization rate. Tp is the coal particle temperature and T v the volatile evaporation temperature. Lochwood et al. [39] observed that good predictions are obtained only for coal when B<Hpr/hiv, while Jamaludin found that using considerably higher values of B compared to the recommended value of 10 s"1 did not appreciably change the predicted temperature [36]. By defining mc(0) as the initial mass of coal (kg), mc as the mass of coal at any time t (kg), mc(final) as the mass of coal at the end of pyrolysis reaction (kg), then the volatile released at time t is v=mMz3L (2.2d) wc(0) and the total volatile yield is , mr(o)-mr( final) and the fraction of volatile material Xv to be released is 15 mr-mr( final) *v= f . v (2.20 2.3.2 Single Overall Reaction Model This model, proposed first by Badzioch and Hawksley [40] for coal pyrolysis, has been widely used due to its simplicity and effectiveness. It is based on the following simplified reaction scheme C—^->V + R coal C pyrolyzes to produce volatiles V and solid residue R. The reaction is assumed first order, the pyrolysis rate being proportional to the volatile matter yet to be released (V*-V) ^. = k(v'-V) (2.3a) Where V * is the total volatile fraction, and the rate constant k is represented by an Arrhenius expression: k = kaexp[-E/RTp] (2.3b) The fractional devolatilization at any time is obtained by integrating the above equation, then |r=l-ex{-J><*] (2-3c) 2.3.3 Two Competing Reaction Model This model, proposed by Kobayashi et al. [41], and Ubhahayakar et al. [42], represents the overall coal pyrolysis process by two mutually competing first order reactions as: ki ^ aiVi+(l-ai)Ri C " caV2+(l-a2)R2 16 The rate of weight loss of the coal (maf basis) is given by dmc dt -{kx+k2)mc (2.4a) so that at any time t the mass of material yet to be pyrolyzed is mc = mc(0) exp -JO'(A, + k2)dt' (2.4b) Where the rate of devolatilization at any time is —= {axkx+a2k2)mc (2.4c) Where a i and cc2 are mass stoichiometric factors representing the extents of devolatilization via reaction 1 and 2 respectively. The extent of devolatilization at time t is obtained as The rate constants ki and k 2 have Arrhenius form, and are such that reaction 1 has a lower activation energy than reaction 2, with the effect that secondary reaction becomes operational only at higher temperature to effect volatile yields in excess of cti. 2.3.4 Three Reaction Models The three reaction models, first proposed by Wen and Dutta [43], considers of three parts representing devolatilization, cracking and deposition. The pyrolysis products are gases, tar and solid residual. Tars are defined as species heavier than and gases those lighter than C6. The proposed reaction scheme is: F(/) = i»c(0)Jo'(aI*I + a2k2 )exp[-I>1+^)^'}/r' (2.4d) C The rate of weight loss of the coal particle is given by 17 ^ L = - * , ' " c (2.5a) By integration, then mc(t) = mc(0)exp[-i'okldt>] (2.5b) The net rate of production of tar is ^ - = alklmc-(k2 + k3)mT (2.5c) Where mx is the mass of tar, then the yield of tar at any time is given by integration of the above equation. mT(t) = a l W c (0)exr [ -J 0 ' (*a +*s)*]Jo J 0 'K + k>-^i)*']* (2.5d) The corresponding rate of production of volatile is dV , _ _ . By integration the above equation, with mr given by the previous equation, gives the volatile yield at any time t. For isothermal conditions, the expression for the volatile yield simplifies to ^Sffft1--(-V)]-^h*p(-M<)]} (2.50 which further simplifies to (by assuming ki much smaller than k2, k3) ™-3£l !M-^] (Z5g) A reaction scheme similar to the above was proposed by Niksa et al. [44], using a nonisothermal kinetic analysis, similar to that of Jiintgen and Van Heek [45, 46], to show that faster devolatilization rates were obtained at higher heating rates and they adopted the following competitive scheme to account for the enhanced yield at high heating rates as: 18 la C ai Vi+(1 - ai)I la ^ V 2 The rate of decomposition of the coal particle is given by the equation ^ - = -kxmc (2.6a) the rate of production of the volatile and the intermediate is then given as dt = axkxmc (2.6b) c H (\-ax)kxmc-(k2 +ki)mI (2.6c) ^=k3m1 (2.6d) Where mi is the mass of the reactive intermediate. Nsakala et al. [47] proposed the following parallel consecutive reactions scheme based on pyrolysis of lignite at 800 °C as: • Ci ^ V i ^ V i ' + R ' - C 2 — : ^ V 2 + R Coal particle C is assumed to consist of two distinct components, C i and C 2 , of different ease of pyrolysis. In their analysis, Nsakala et al. [48] ignored the secondary cracking of V i . If, therefore, components Ci and C 2 decompose isothermally by independent first order reactions C,=C 0 I exp (-*,/) (2 7a) C 2 = C 0 2exp(-V) (27b) Where C 0 i and C02 are the initial mass of Ci and C 2 . The total weight loss is obtained from V = VX+V2 (2.7c) where V i and V 2 are volatile product from Ci and C 2 components respectively and 19 VX=CQX-CX (2.7d) V2 = C02-C2-R (2.7e) V = C 0 1 [ l-exp(-^/)] + I ^r[l-exp(-^r)] (2.7f) At infinite time V * = C + C ° 2 (2.7g) or l - - ^ = (^ r )exp ( -^ r ) + ( l -C 0 1 /F*)exp ( -V) (2.7h) 2.3.5 Multiple Parallel Reaction Model The powerful multiple parallel reaction model, originally proposed by Pitt [48], was later adopted by Anthony and Howard [49, 50] to fit their data. The merit of this model is that it only needs one more adjustable parameter than the single reaction model. The reactions envisaged were V_ V* Coal -> Eq. — (=1 /=1 The reactions are assumed to have the same pre-exponential factor but different activation energies. The weight loss due to devolatilization at any time is = l-\\x^-\lk{E)dt^f(E)dE (2.8a) fTE), denoting the distribution function of activation energy, is assumed to be Gaussian and given by f(E)= -j= exp \-(E-E 0 ) 2 (2s2)\ (2.8b) Where E 0 is the mean activation energy and s the standard deviation. 20 Instead of using a Gaussian distribution, Laskshmannan [51] used the Weibull distribution to model the kinetics of petroleum generation over a geological time scale. The probability density function f(E) (as applied to describe the distribution of activation energies) for this distribution is given by: 'E-yY f o r E ^ y , r t>0andp>0 =0 for all other values of E , rj and P (2.8c) where E is the activation energy expressed in kcal/mol. There are three parameters, namely, r\, the scale parameter; B, the shape parameter; and y, the threshold or location parameter characterizing the distribution. A number of different distributions can be generated by a suitable choice of these parameters. For 0=1, the Weibull distribution coincides with the exponential distribution. For B>1, the distribution becomes 'bell shaped", but becomes positively skewed. As B increases, the Weibull distribution approaches the Gaussian distribution more and more closely. In fact, for P=4, the Weibull and Gaussian distributions become almost indistinguishable. This model may be useful for process chemical engineering applications, such as combustion and pyrolysis of coal, oil shale, bitumen and pitch. Unlike the Gaussian distribution, the Weibull distribution is well suited to represent many empirical distributions. Noting the limitation of these distributions, Miura [52] proposed a mathematical procedure to estimate f(E) from experimental data without assuming any form of distribution. This procedure requires only three sets of experimental data. The procedure to estimate f(E) and k o is summarized as follows: 1. Measure V / V * vs T relationships at three different heating rates at least. 21 2. Calculate nominal rates k = (dV I dt) I (v* -V) at several but same V / V * values at different heating rates, then make Arrhenius plots of k at the same V / V * values. 3. Determine activation energies from the Arrhenius plots at different levels of V / V * and then plot V / V * against the activation energy E . 4. Differentiate V / V * by E to obtain rTE). 5. Calculate k o corresponding to each E value at all the heating rates using equation 0.5447 a E/kaRT2 = e~B/RT, then employ the averaged k o value as a true k o value. 2.3.6 Complex Models In order to model more accurately the gross fundamental mechanism involved, Reidelbelbach and Summerfield [53, 54] formulated a model which included six competitive /consecutive reactions. This was later modified by Antal et al. [55] to correct the abnormally high activation energy for the activation step. The reaction scheme is expressed as follows: CX6 V 6 + (1 - 0C6) R6 j(I - ou) Rz + CX2T2 k2 k i C — A C k 7 ' ^ a? V 7 + (1 - O C T ) R7 k 4 • C X 4 V4 + (1 - CM) R4 OO V3 + (1 - CO) R3 *-oc5V5 + (l -as)R5 Several consideration went into the model, e.g. reaction 1 was proposed to limit decomposition of coal at low temperature. Further decomposition can then proceed by two routines depending on the heating rate and the temperature. The tar production step (reaction 2) was assigned a low activation energy as tar evolves at comparatively low temperatures. Similarly, 22 the experimental observation for increased gas/tar ratios and increased yield at high temperature, etc., were also accommodated. Reidelbach and Summerfield achieved good agreement with the experiment data of Badzioch and Hawsley [40] using a simplified version of the model. 2.3.7 Detailed Models Detailed models of coal pyrolysis attempt to describe the evolution of individual volatile species. One such model is that formulated by Suuberg et al. [56-58] assuming nine volatile products to be formed via fifteen different reactions. The activation energies of the individual reactions when synthesized into a composite distribution function, were found to agree well with the corresponding Gaussian distribution obtained by Anthony et al. [49] solely from the total weight loss data. Tar was assumed to be either converted to coke and light hydrocarbons by secondary reactions, or evolve from the coal particles, as in the two competitive reactions below: ^ coke + light hydrogencarbons Coal tar formed v , ^ ^ k tar evolved Soloman and coworkers [1-3] have been working towards providing a fundamental basis for pyrolysis reactions though the concept of'functional groups'. The overall reaction is: la w tar evolved tar "~ j^""""^ secondary gas pnmary gas Thus a representative sample of the functional groups evolves without decomposition leaving coal molecule to form tar, while light primary gases are formed by decomposition of some functional groups. These two processes are assumed to be competitive. A single rate is used for tar evolution, and a separate rate for each gaseous species. Distributed (Gaussian) rate kinetics 23 are used for the gaseous species evolution, and secondary reaction of tar and tar evolution are represented by a separate set of competing reactions. The evolution of ten species (excluding tar) are represented by 15 reactions. Time and temperature dependent devolatilization of coal was predicted by the model using a coal independent set of kinetic parameters and the structural composition. 2.3.8 The Application of Models in Pyrolysis Kinetics The global pyrolysis kinetics applied to pitch or any other hydrocarbon is generally intended to predict the overall rate and yield of volatile release (i.e. mass loss) from the sample. For a first order process this is given as Equation 2.3: dV/dt=k(V*-V), where for temperature programmed experiments, T=f(t). For linear rise in temperature T-T0=Ct where C is heating rate. It has been reported that different volatile products are released depending on the temperature ranges [59] or the temperature histories [60]. This fact has not diminished the interest in the global kinetics for various reasons. One reason is that under certain conditions, tar is a dominant product of pyrolysis for a significant part of the process [59], so that prediction of total mass loss would allow prediction of tar release rate. A second reason is that global kinetics are looked to as offering a clue to the key mechanistic steps in the overall pyrolysis process [61]. Carrasco [62] conducted an extensive review of the different computing methods (used to analyze Equation 2.3) in the literature leading to the determination of the kinetic parameters of thermal decomposition reactions and compared the results obtained by using those methods for coal. Those methods do not reproduce the values of activation energy and reaction order when the same data are taken for computation. Due to the above mentioned shortcomings of these methods listed in Appendix A, these methods are of little use for pitch or bitumen pyrolysis studies, except for the integral method. Table 2.3 summarizes some of the methods used for 24 analyzing data via Equation 2.3 and the Anthony-Howard model (Equation 2.8). However, there is no comparison of the kinetic parameters derived from the methods listed in Table 2.3 reported yet for pitch. A detailed description of these methods is found in Chapter 5. Table 2.3 Summary of the Analysis Methods Used in Constant Heating Rate Pyrolysis Integral Method \ r J" c {t<-eirt4e{-W)} (2-9) Friedman Method The values of dV/dT is calculated by using two adjacent pairs of the volatile and temperature data: W _v**-vi (2.10a) dT TM-Tt Coats-Redfern Method In - C l n l l - ^ J RT2 = x M x - 2 R T \ E (2.11) E \ E ) RT \ ' Chen-Nuttall Method In I RT2 lil-v-)rnk°-RT (212) Anthony-Howard Model (1976) V r -— = l - J o exp_ -l'ok(E)dt f{E)dE (2.8a) exp[-(E-E0y/(2s2)] (2.8b) where the heating rate C=dT/dt in the above table. 2.4 Compensation Effect of Kinetic Parameters On determining the kinetic parameters from the thermoanalytical curves with the single overall reaction model (Equation 2.3), variations in the kinetic parameters are encountered due to the variation in physico-chemical properties (such as sample size), measuring conditions and the mathematical methods employed to derive the kinetic parameters. Thus high values of activation energy would be compensated by high values of the pre-exponential factors to give the same rate 25 constant k value. Further analysis of the variation of the kinetic parameters for a series of reactions leads to a general result of a mutual dependence of the kinetic parameters, termed as the kinetic compensation effect expressed by: \nko = aE+0 (2.13) The above equation indicates the linear dependence between the values of the logarithmic pre-exponential factor l n k o and the activation energy E with the constants a and p. The simple relationship of the above equation is reproduced on the Arrhenius coordinates, Ink vs. 1/T, with an intersection point called the isokinetic points (l/Tbo, lnk^) [63]. Using the isokinetic relationship, the above equation is rewritten as: \nk = a + bj (2.14) The kinetic compensation effect was first identified by Constable [64] from studies of dehydrogenation of ethanol on copper. Subsequently, a large number of further examples of comparable patterns of kinetic behavior have been described for many diverse surface heterogeneous catalytic reactions. Occurrence of such a compensation behavior between lnko and E has been widely investigated in recent years. In particular, the existence of the compensation effect in thermal dehydration and decomposition reactions of solid inorganic and organic materials has been reported [65]: Numerous papers have dealt with the variation of the apparent kinetic parameters using Equations 2.13 and 2.14. In addition, comparable relationships were found during these analyses of reported kinetic data. Additional trends could be also recognized if the survey was extended further or experimental measurements obtained for additional systems [66]. However, despite these many and various examples of compensation behavior, there remain important difficulties in establishing the range of meaningful application and the usefulness of Equations 2.13 and 2.14 in the understanding of the significance of kinetic observation. Although 26 the present state of understanding of the kinetic compensation effect can be found in many historical surveys [66-71], no single theoretical explanation of compensation behavior has been recognized as having general application. The factors to which references are made most frequently are surface heterogeneity in catalytic reactions and the occurrence of two or more concurrent and/or consecutive reactions in thermal decomposition processes. The causes of the kinetic compensation effect in thermal decomposition reactions may be classified into the three categories discussed below: sample physico-chemical properties, measuring conditions, and the mathematical methods used to derive the kinetic parameters. At present time, however, doubt remains concerning the general theoretical implications of the compensation relation despite the very many reported instances of obedience of Equation 2.13. Accordingly, this short review emphasizes the interrelation between kinetic characteristics and the chemistry of thermal decomposition processes. 2.4.1 Effect of Sample Physico-Chemical Properties on the Kinetic Compensation Effect A typical example of the physico-chemical interpretation of the kinetic compensation effect is seen for the thermal decomposition of CaCC>3, under various partial pressures of C O 2 . In 1935, Zawadski and Bretzsnajder [72] originally pointed out the variation in E with C O 2 partial pressure. Another example is seen for the thermal decomposition of CaC204»H20, with various sample sizes. The activation energy was found to decrease with the increase of sample size [73]. A theoretical interpretation for this effect was attempted by Pavlyuchenko and Prodan [74]. The kinetic behavior was reinvestigated experimentally by Wist [75] and analyzed by Roginski and Chatji [76] from a viewpoint of chemical statistics. Attempts have been made to explain the empirical kinetic compensation effect by using the physico-chemical variables, such as partial pressure of a gas [77], bond energy due to the different metals and ligands [78-80], defect 27 concentration [81], chemical composition [82], impurities [83] etc., other than reaction rate and temperature. Guarini et al. [84] pointed out that nonlinearity of the Arrhenius plot increases with the sample size, and recommended extrapolation to zero mass to avoid the kinetic compensation effect. Sample size dependent variations in the Arrhenius parameters have been explained by the effect of gradients in temperature and gaseous pressure [73]. In thermal analysis, however, the physico-chemical properties are difficult to identify quantitatively, because of the macroscopic character of the kinetic data derived from T G A curves. Without quantitative identification of the physico-chemical properties, estimation of the linear interdependence of Equation 2.13 does not provide meaningful kinetic interpretation, but only shows an empirical observation of the mutual dependence of the kinetic parameters. 2.4.2 Effect of Experimental Conditions on the Kinetic Compensation Effect One of the examples is also seen for the thermal decomposition of CaC 204*H 20, under various heating rates [73, 85, 86]. It was found that the activation energy E decreased with the increase of heating rate. It is generally accepted that the experimentally resolved shape of a T G A curve changes with the measuring conditions applied, such as heating rates, atmosphere, etc. [85]. In many cases, the kinetic parameters obtained from such a T G A curve are also dependent on the measuring conditions applied, showing empirically the kinetic compensation effect. The kinetic compensation effect caused by the effect of heating rate is rather common for the thermal decomposition of solids with gaseous products [87,88]. On discussing the kinetic compensation effect obtained from different measuring conditions, both effects of heating rate on the sample physico-chemical properties and the changes in the sample caused by reaction itself should be taken into consideration. The latter is closely connected with the reliability of the experimentally resolved shape of the T G A curve as a source of kinetic data [89, 90], because such changes in the 28 sample is not controlled, in a strict sense, in conventional T G A measurements. A typical example can be seen for hydrocarbon pyrolysis in which the chemical structure and makeup is undergoing constant change. 2.4.3 Analysis of One T G A Experiment with Different Models or Methods Discussion of the mutual dependence of the kinetic parameters has also been attempted from the mathematical and statistical points of view. Because the kinetic parameters have meaning only in relation to the mathematical functions of the kinetic model, these are distorted by an inappropriate kinetic model function. Criado and Gonzalez [91] reported that sets of kinetic parameters calculated using inappropriate kinetic model functions show mutual dependence. The degree of the distortion was further discussed on the basis of an empirical analysis [92, 93] and a mathematical approximation [94]. Reexamination of the kinetic compensation effect of this type was performed by Somasekharan and Kalpagam [95], who suggested the correspondence between the isokinetic temperature and the maximum T G A peak. However, application of the Arrhenius equation to complicated solid-state processes has been questioned [96]. Hulett [97] made a search for the nonlinearity of the Arrhenius plot, determining that any derivations from a straight line in the plot of lnk(T) vs. 1/T are to be considered as almost certain evidence that the observed process is complex. Drawing the theoretical T G A curves, correlation of the kinetic parameters and its effect on the T G A curves were noticed by Sestak [98] and further analyzed by Zsako [99]. Exner [100] first suggested that it is not correct to determine the kinetic compensation effect by a linear regression of E vs. lnko, because these quantities are mutually dependent. Agrawal [101] proposed dividing the kinetic compensation effect into two groups by the existence of an isokinetic point: one arising from physico-chemical factors and the other from computational and experimental artifacts. Because 29 k(T) and T can be determined independently, the plot of lnk(T) vs. 1/T is statistically correct. However, Agrawal's procedure of distinguishing a false kinetic compensation effect from a true one was criticized by Sestak [102] and was shown by Zsako and Somasekharan [103] to be incorrect. Gam's view is that the kinetic compensation effect is simply a consequence of trying to describe a complex process by computing one of the kinetic parameters in Equation 2.3 and dumping the results of computed variations into the remaining 'constant', accepting changes of many orders of magnitude without question or test [ 104]. 2.4.4 Interaction of the Causes According to the procedure of T G A kinetics of thermal decomposition reactions, the sample physico-chemical properties, experimental conditions and the resulting mutual dependence of the kinetic parameters seem to be interpreted separately [105]. However, the causes seem to be interrelated and inseparable. The T G A curve is a response of a certain averaged behavior of the respective reaction steps involved for the case of the thermal decomposition. The mutual relationship of the consecutive and/or concurrent steps may change with the experimental conditions applied (such as heating rates) and the changes in the sample, influencing the overall characteristics of the reaction. The variation in the overall behavior for a reaction is only detected as changes in the position and shapes of the experimentally resolved T G A curves. The kinetic parameters calculated from these macroscopic data are projected on the Arrhenius coordinates through a particular projection system, i.e., the general kinetic equation. The variation in the respective kinetic parameters apparently results from changes in the experimental and physico-chemical factors. However, the resulting mutual dependence of the kinetic parameters, usually stated as the kinetic compensation effect, seems to be connected with the properties of the mathematical methods used to analyzed the general kinetic equation (Equation 2.3). In such a 30 case, not knowing the properties of the general kinetic equation concerning the kinetic compensation effect, interpretation of the mutually dependent variation of the Arrhenius parameters connected with the physico-chemical properties of the kinetic process is likely to lead to a speculative conclusion. However, recognition of the kinetic compensation effect would give some insights to the relationship between the logarithm of pre-exponential factor, Ink,,, and activation energy E , and further give guidelines of application and explanation of the kinetic parameters. The magnitude of the rate constant is therefore of more importance than that of each of the kinetic parameters ko and E . 31 Chapter 3 Experimental Procedures and Apparatus 3.1 Introduction In this chapter, the experimental procedures which outline each operational step employed in the present work are discussed. The first part of this chapter deals with the materials, sample preparation and characterization. This is followed by the description of the experimental apparatus. Finally, the experimental techniques are presented. 3.2 Sample Preparation and Characterization The C A N M E T pitch was obtained from Combustion Group of Department of Chemical Engineering at UBC, which obtained the pitch sample from C A N M E T in barrels for combustion study. The Syncrude pitch was obtained from the sample bank of Syncrude Canada Ltd. in 10kg containers. Representative samples were then taken from C A N M E T pitch barrels and Syncrude pitch containers and stored in a refrigerator for the subsequent characterization analysis, T G A study and Pyroprobe-GC study. Each of the two pitch samples was used as received. Representative samples of CANMET and Syncrude pitches were sent to MicroAnalytical of Delta, Vancouver for ultimate analysis. Results are given in Table 3.1, along with the proximate analysis determined by T G A and solvent fractionation with pentane and benzene. The latter were determined by dissolving 5 mg of pitch sample into 200 ml pentane and benzene respectively in an ultrasonic bath (~ 25 °C for 30 min). The pentane or benzene soluble fractions were clarified over filter paper and the insolubles washed and dried at room temperature for 12 hours. The weight of the insolubles was recorded. The atomic ratios were also calculated and given in the same table. It is evident that the chemical structure and makeup of Syncrude pitch are different from those of C A N M E T pitch. Syncrude pitch has higher H/C, S/C atomic ratios and lower N/C, O/C atomic ratios. This observation is in 32 good agreement with the low pentane and benzene insolubles. It is expected that the pyrolysis behavior of these two pitches might be different due to those chemical differences. Both pitches contain limited amounts of ash and oxygen. Syncrude pitch contains more sulfur than the C A N M E T pitch. Table 3.1 Pitch Characterization Analysis — Ultimate Analysis As received C A N M E T Pitch Syncrude Suncor Maya[106] This Work Lim [10] Pitch Pitch [8] Residuum Carbon % 85.32 86.2 82.72 82.8 83.6 Hydrogen % 9.33 7.1 10.35 7.9 9.3 Nitrogen % 0.82 1.1 0.52 1.0 0.5 Sulfur % 2.39 2.8 4.73 5.8 5.8 Oxygen % 1.12 1.0 0.97 — 0.5 Others % 1.02 1.8 0.71 — — 100.00 100.00 100.00 97.5 99.7 H/C 1.31 0.99 1.50 1.145 1.335 N/C 0.0082 0.011 0.0054 0.0104 0.0051 o/c 0.0098 0.0087 0.0088 — 0.0045 s/c 0.011 0.0012 0.021 0.0263 0.026 Proximate Analysis % Volatile 81.17 — 90.11 — — Fixed Carbon 18.65 — 8.65 — — Ash 0.18 — 1.24 1.6 — Solvent Fractionation % Pentane insolubles 45.15 — 33.58 39.5 Asphaltene 35.65 — 25.77 — — Benzene insolubles 9.50 — 7.81 — — The ultimate analysis results of CANMET and Syncrude pitch samples in this research are similar to those reported by previous workers [8, 10, 106]. 3.3 Experimental Apparatus The C A N M E T pitch and Syncrude pitch were pyrolyzed with T G A at low heating rates using U.H.P. Nitrogen as purge gas, and with Pyroprobe-GC at high heating rates using U.H.P. Helium as carrier gas. The volatile yield (or the weight loss) was recorded with T G A dynamically as a function of temperature via a computer. The weight of the pitch sample and the residue of 33 Pyroprobe-GC pyrolysis was recorded before and after each run at the selected operating conditions. The weight loss in the Pyroprobe pyrolysis can then be calculated by subtracting the residue weight from the initial sample weight. The volatiles were swept into the on-line G C for analysis of the chemical composition. 3.3.1 Thermogravimetric Analysis (TGA) Setup and Operation The pyrolysis of C A N M E T and Syncrude pitches was performed on a Perkin-Elmer TGS-2 TGA. The model TGS-2 (referred to as the T G A in the following text) is designed for accurately recording the weight loss (or volatile content) of a sample as it is subject to a precisely controlled temperature environment. It is capable of controlled heating rates of 0.31 to 320 °C/min. It is a completely modular system consisting of the following units: the thermo-balance analyzer; the electronic balance control unit; the heater control unit; the temperature program control unit, data acquisition computer, plotter and purge gas system. The balance system consists of a Perkin-Elmer AR-2 recording balance (including an analyzer and balance control unit) which can be used together with a recorder as a recording balance independently of the other components. The temperature program control is the unit which provides the control over the starting temperature, heating rate, stopping temperature and holding time. The heater control unit is a power supply source which provides the controls for calibrating the furnace so that the sample temperature is that temperature indicated on the programmer readout. It provides thermocouple circuitry for monitoring the temperature of the sample environment. In order to record the weight loss versus temperature information, the temperature was calibrated each two weeks and when the furnace was changed. An inert purge gas was also used to avoid oxidation of samples and volatiles during each run. 34 The T G A temperature is controlled through a closed-loop, heater-sensor resistance thermometer circuit, using the furnace winding as both sensor and heater. Reproducible, linear temperature programs are thus achieved. A calibration must be performed, however, to make sure that the temperature at any given moment is that specified during experimental runs. The calibration is first performed at the factory, where adjustments are made to assure the temperature of the sample agrees with the program temperature. After operating the instrument for a period of time, calibration is also necessary to assure best temperature control accuracy. The calibration can be accomplished by changing the heater control unit range and zero settings to force agreement between the program temperatures and the thermocouple temperatures (or a magnetic transition standard, a Curie point calibration standard). However, a more convenient method was used, employing a calibration routine built in the heater control unit. This routine automatically checks and corrects the thermocouple temperature at three program temperature points. The calibration routine forces correspondence between the program and sensor temperature at T MTN (50 °C), T M A X (1000 °C) and the temperature midway between T MTN and T M A X . The calibration sequence is begun by pressing the CALIBRATE and RESET keys on the control unit keypad. The control unit then programs to T MTN, waits for thermal equilibrium, and measures the difference between the sample temperatures and program temperatures. It then corrects the furnace set-point, allows equilibrium, and again checks for agreement. This procedure is repeated until the discrepancy is less than 0.5 °C. The above procedure is repeated for the intermediate temperature and T M A X and the T G A is then considered calibrated. The control unit forces the sample temperature and the program temperature to agree exactly at 3 points, and approximates a correction for the rest of the scale. The control unit 35 interpolates correction between T MIN and T M A X , so that the T G A is calibrated for the whole temperature range. When the calibration is completed, the program temperature and actual temperature agrees within 2 °C or better [8, 62]. The positions of the furnace and the sample pan are very important for correct temperature control. The position of the furnace itself can be changed horizontally or vertically by using the adjustments under the furnace support assembly. The ideal position of the furnace is in the center of the furnace assembly as shown in Figure 3.1. A more detailed sketch of the T G A furnace is also shown in the same figure. The top of the furnace should be 10 mm below the anti-convection shield and the top of the stirrup should be recessed by about 1 to 2 mm into the furnace. The bottom of the sample pan should be 2 mm above the tip of the thermocouple. If it is not, another hangdown wire should be prepared, having the appropriate length in order to obtain the best performance. To Microbalance Figure 3.1 The relative position of the furnace and sample pan on the left and the T G A furnace sketch on the right 36 The thermal balance was continuously purged with inert U.H.P. Nitrogen gas when samples were being pyrolyzed in order to prevent decomposition products from flowing up and contaminating the balance mechanism and oxidation. A 20 minute purge was also applied before each run. The U.H.P. Nitrogen flowrate was set 100 mL/min and checked before each run. The T G A had been calibrated at the factory so that when the instrument is set up using the proper configuration of furnace height, hangdown wire length, the temperature accuracy should be within one percent over the temperature range of the instrument. Temperature calibration was always made using a U.H.P. Nitrogen gas to achieve the same conductivity as an experimental run. The pitch sample was applied to the sample pan carefully into a thin layer to achieve a better temperature uniformity and therefore temperature readings. Once the temperature calibration was achieved, the temperature control unit was used to control the pyrolysis temperature. Different heating rates and final temperatures were used to study their effects on the pyrolysis of C A N M E T and Syncrude pitches. The heating rates employed in this study are 25, 50, 100, and 150 °C/min, the final temperatures 700, 750, 800, 850, 900, 950 °C. The following temperature program was used to achieve this conditions: • Purge the T G A system for 20 minutes at room temperature before starting the run and then increase the furnace temperature to 50 °C. • Hold at 50 °C for 5 minutes and then ramp to the final temperature at each selected heating rate. • Hold at that final temperature for 10 minutes, then terminate the run and decrease the temperature to room temperature. The sample temperature and weight (of sample as well as residue after certain pyrolysis) at any time was recorded using a computer data logger. The weight of sample was also recorded 37 at the beginning of each run. At any time, the remaining sample weight was recorded as the percentages of the original sample weight. The information of weight and temperature was then recorded into the computer, printed out as hardcopies, and converted into data files. The data files were used in the subsequent analysis and modeling. 3.3.2 Pyroprobe-GC The pyroprobe-GC is a relatively new type of equipment constructed for dynamic analysis of pyrolysis products from the probe by using in-line Gas Chromatography. The main advantages of this piece of equipment are the temperature programmable probe, high temperature ramping rates and small quantity of samples required in the GC analysis. The Pyroprobe-GC consists of the following modular units: Pyroprobe 1000 controller, Pyroprobe interface, Varian G C 3600, Computer Workstation, and gas system, as shown in Figure 3.2. The CDS Instruments Pyroprobe 1000 is a resistively heated platinum filament pyrolyzer which prepares samples for analysis by gas chromatography. The Pyroprobe 1000 controller calculates the resistance of the filament and supplies the proper voltage needed to achieve the setpoint temperature. Heating rates are selectable in increments of 0.01 °C per millisecond to 20 °C per millisecond. Final temperature ranges in 1 °C increments to a maximum of 1400 °C. Final holding time may be selected from 0.01 seconds to 99.99 seconds. All parameters are entered by simple key strokes on the front panel of the controller module. Samples may be pyrolyzed using a variety of filament designs. The standard model Pyroprobe 1000 includes a coil element and a ribbon element. The coil element, which heats samples held in a quartz tube, was used to pyrolyze the pitch samples in order to record the weight of the sample and the residue to calculate the volatile yield. 38 The gas chromatograph interface for the Pyroprobe is a heated chamber which houses the probe during pyrolysis. This chamber attaches to the injection port of the gas chromatograph by means of a welded needle nut assembly which replaces the septum retainer. Carrier gas is brought into the interface, sweeps through the heated chamber containing the probe and exits through the needle nut assembly into the injection port of the gas chromatograph. Autosampler Pyroprobe Interface Chromatograph Printer Varian Star Computer System Pyroprobe 1000 Varian GC 3600 Figure 3.2 The Pyroprobe-GC setup All flow entering the injection port comes from the interface. It is important to remember that the Pyroprobe interface is plumbed upstream from the column, and opening the chamber for probe placement permits air to enter the chromatographic system. Therefore, probe placement and removal should be performed when the column is cool to prevent oxidation of the column liquid phase. The Pyroprobe interface was installed (Figure 3.3) by inserting it between the gas chromatograph carrier gas flow controller and the injection port. The standard interface has three gas fittings and one electrical connection. The electrical connector attaches to the rear of the Pyroprobe controller to supply current to heat the interface and permits temperature monitoring. The three gas fittings are: 1) a large opening in the front for the interface to accept the probe; 2) a 39 1/8" Swagelok fitting which attaches the interface to the welded needle nut assembly of the injection port of the gas chromatograph; and 3) a length of stainless steel tubing with a 1/16" Swagelok fitting to connect to GC carrier flow. The large opening for the probe may be sealed with an interface retainer to permit syringe injections directly into the interface. A more detailed sketch of the pyroprobe head is shown in Figure 3.3 a. (T) Interface (7) NeedkNutAssenHey ( ? ) GC Injection Port (7) Injection Port Wet Plug ( ? ) 1/8" to 1/16" Reducer (7) 1/16" Union (7) Opening for the Probe (7) Coa Rlament Probe to GC Column Figure 3.3 The installation of Pyroprobe interface into the GC injection port. Probe head Heating coil Pitch sample Quartz tube Figure 3.3 a The sketch of Pyroprobe with pitch sample applied on the inner surface of quartz tube The 1/16" stainless steel tubing must be connected to the carrier gas for the GC column. Flow is disconnected from the injection port and the inlet there capped while the flow is connected to the Swagelok fitting on the end of the 1/16" tubing. This will bring G C flow into the 40 interface, where it proceeds through the probe chamber and then into the injection port through the needle nut assembly. For pyrolysis, the probe seal in the collar of the probe makes a gas tight connection while the probe is in the interface. This seal was checked and replaced regularly to insure sealing. A sample of around 5 mg was applied uniformly onto the middle section of the inner-surface of the quartz tube which then was inserted into the Pyroprobe heating coil. The quartz tube is T'long and 1/8" in diameter. The heating coil is interfaced with the GC station as shown in Figure 3.3. The pyrolysis product is purged into the GC injection port by Helium carrier gas. Proper sample handling plays a very important role in achieving reproducible pyrolysis. Best results are obtained by using as small a sample as possible to prevent thermal gradient effects and to insure that the sample is completely pyrolyzed. It is important to remember that the Pyroprobe is being used as a sample introduction device for the gas chromatograph and the sample size should be consistent with what is generally injected onto the column. The best reproducibility was obtained using samples of about 5 mg. The Pyroprobe 1000 was used to control the heating rates and final temperature. The temperature was calibrated according to the calibration number of the heating coil supplied by the manufacturer. Heating rates employed in this study are 600, 3000, 30 000 and 300 000 °C/min, and final temperatures are 500, 600, 700, 800, 900, 1000 °C. Pyrolysis times used are 0, 5, 10 seconds. The following temperature program was used: • Purge the Interface for 20 minutes at room temperature with U.H.P. Helium. • Ramp to the final temperature at the selected heating rate. • Hold at that final temperature for the selected pyrolysis time, then terminate the run and decrease the temperature to room temperature. • Through the experiments, the interface temperature was kept at 50 °C. 41 In the GC, a J&W DB-5HT fused silica capillary column was used. It is comprised of three major parts. Polymide is used to coat the exterior of the fused silica tubing to protect the fused silica tubing from breaking. The stationary phase is a polymer that is evenly coated onto the inner wall of the tubing. The predominant stationary phases are silicon based polymers (polysiloxanes), polyethlene glycols (PEG, Carbowax™) and solid adsorbents. The liquid phase in this column is DB-5HT. The column is 30 meters long with a diameter of 0.255 mm, and a film thickness of 0.10 um. The column can be operated from -60 °C to 400 °C. In this setup the column was installed to FID and PID detectors. U.H.P. Helium is selected as the carrier gas for this capillary column. The carrier gas flow rate was then optimized during test runs as 1 mL/min. The operation of the GC is controlled using the computer workstation. The GC and the Pyroprobe were started at the same time for each run. The GC analysis results were also gathered through this computer. The results can be printed out as hardcopies (including chromatograph and analysis results). Due to the fact that this piece of equipment had not been widely used in the pyrolysis kinetic studies, a great deal of effort was required to configure the equipment and optimize the experimental conditions. This step consumed some four months of experimental time. The optimal conditions for pitch pyrolysis were found to be: • Purging the interface chamber for 20 min. before starting a run. • G C column temperature program: 40 °C for 10 min., ramping to 120 °C at the rate of 2 °C/min. and holding the final temperature for 10 min. • GC column carrier gas flow rate 1 mL/min U.H.P. Helium. • The Hydrogen flow rate is 20 mL/min, and the air flow rate is 375 mL/min. 42 A summary of the Pyroprobe-GC parameters used by the computer program is listed in Appendix B. The weights of the sample and residue were recorded before and after each run. The volatile yield was then calculated by subtracting the residue weight from original sample weight at each condition. The FED analysis results of the released volatiles were logged with the computer workstation and used for subsequent recalculation and analysis for both pitches. A typical Chromatogram is shown in Figure 3.4. The insert is the enlargement of the chromatogram for the period 8 to 45 min. The peaks indicate the major products. As can be seen, most of the pyrolysis products elutes within 5 min. Other products were also identified between retention time 8 and 45 min as shown in Figure 3.4. Syncrude pitch pyrolysis volatile analysis showed a similar chromatogram. It is clear that it is difficult to identify each of the large number of peaks in Figure 3.4. A grouping scheme was therefore employed to simplify the identification and quantification processes. Similar lumping schemes have been successfully used in coal pyrolysis to estimate the yields of tar and gases [1, 17, 50]. Inseparable peaks were therefore grouped into six single peaks. The retention time of those groups are listed in Table 3.2 for the volatile of both pitches. The identification of species and quantification of yields are discussed in the following section. Lump No. Retention Time min. Mid-point min. 1 0.01- 4.73 2.370 2 8.84-15.86 12.350 3 19.17-23.97 21.570 4 24.24-31.72 27.980 5 32.11 -36.01 34.060 6 37.49 - 42.66 40.070 43 El CC a. O M M O. -4 0> OU « Ot —CO 0 E«f< 0 H to « a 4i « B C 0 3 « 3 o n n o s M C M x: at o co O to o * i a 0 B IS Chart Speed -* 0.35 cm/min Attenuation - 12 Start Time » 8.000 min End Time •> 65.000 min Zero Offset - -57t Kin / Tick « 1.00 i , i i i i ( i i i i i t i i i t i i i i i i i i i i i i i i i i i i i i i i i i i ( , I l l t l l l i i i l l i l i l i l l i l l l l t l l l l l I l l I I l I I 1 l l I I I t l l l l l l i i i i i i 0 O h O H *J c S 6 3 • 0 O * i - * C Ufa o 0 | <H 0 B M c 0 M 0 0 0 . 0 C £ O <E H U 0 0 0 fa 0 0 . d - P u w Figure 3.4 Chromatogram of C A N M E T pitch volatiles a o H 5 a &, n J O Z H u o x a H A P . (XM M 0 0 M M a w £ £ H TJ -"-"-CO 0 C E fa 3 0 X a o %4 T* M U C < 0 « H Chart Speed « 0.3 5 cm/min Attenuation « 28 Start Time ** 9.000 min End Time =• 65.000 min Zero Offset - -SOt Min / Tick - 1.00 „, £« 0 £< o *> 0 0 M M « 0 OB e 0 CL 4J 0 e c 0 3 0 3 a f f l a K * i 0 0 B 3 - 1 0 4J -O I I I I f I 1 I I < I I I f I I I I I I I I I I I I I I I I I I I I I I 1 I f I I I l t I 1 I I I I I I i I I I I I I I I I I • • < < < I I I I I I t I I i I I | I i i i i i i i •rt « 0 « k O H *> c 5 §• -< 3 0 « O *J «H C t l * i 0 0 0 B<H *J * i 3 0 0 0 M C 0 O 0 e co H u u 0 0 * O U Figure 3.5 Chromatogram of standard sample 3.3.3 Peak Identification and Quantification In order to identify species from the chromatograms, standard samples of paraffin C6-C16 and aromatics C6-C14 were obtained and analyzed individually for retention time. The retention times of the peaks of interest for both C A N M E T and Syncrude pitch volatiles match those of paraffin: n-Heptane, n-Decane, n-Undecane, n-Dodecane, n-Tridecane, and n-Tetradecane. A standard sample was then designed according to the individual retention time of each standard sample and the characteristics of the chromatogram obtained for C A N M E T pitch and Syncrude pitch pyrolysis products. The standard sample consists of equal amount of n-Heptane, n-Decane, n-Uhdecane, n-Dodecane, n-Tridecane, and n-Tetradecane ( C 7 , C10, Cn , Cn, C13, C14 ). The standard sample analysis chromatogram is shown in Figure 3.5. The insert is the enlargement of the chromatogram from 9 to 45 min. The retention times of aromatics were detected separately and listed in Table 3.3 for comparison. As can be seen, the retention times fall into those of the volatile lumps and close to that of each paraffin component with the same carbon number. The retention time of each component in this standard sample is listed in Table 3.3. fable 3.3 Retention Time of Each Component Paraffins Retention Time min Aromatics Retention Time min Hexane C6 1.489 Benzene C6 1.780 Heptane C7 1.933 Toluene C7 Octane Cg 2.959 Xylene Cg 4.684 (p) Nonane C9 6.208 Cumene C9 6.473 Decane C10 12.025 Butylbenzene C10 13.500 Undecane Cn 20.882 Dodecane C12 27.894 Tridecane C13 34.051 Tetradecane C14 40.030 Octylbenzene C14 43.212 The peak identification was based on two criteria: • the time at which the peak elutes (retention time) and • the size of the peak (response) 45 Both these criteria were used to identify not only peaks of interest, but also to eliminate from consideration those peaks that are not analytically significant (because of retention time or relative size). The quantification was then performed according to an external standard. External standard calculation allows one to determine the absolute amount of the compounds of interest, without regard to the total area or height, or the area or height of any other peaks in the chromatogram. The peaks of interest must be identified in a peak table, and the detector response is calibrated to these peaks by injecting a known amount of each compound in a run to determine the Calibration Factor. Peak lump to 4.73 minutes may contain lighter gases up to Ce>. However, it was impossible to separate this lump into detailed peaks in a practical time scale with the column being used since the wide spectrum of the components in the volatile. It was therefore lumped as one peak and estimated using the response factor of C 7 . The yield therefore obtained is a rough estimation. The heavier components were lumped in the same fashion. The yield of each is also an estimation. Following identification of the peaks in the chromatogram, the yields were calculated according to the parameters specified through the computer station. The results can be calculated to meet the analytical requirements. The yields of each component were then calculated using an external standard as outlined in the Varian Star Computer System User Handbook. In the external standard calculations, peaks were reported in amounts. The calculation in this study gave results in weight (mg). External standard calculation was also done in two stages. First, Calibration Factors developed during a Calibration run are stored in the computer program, then, during an Analysis run, these factors are used to produce the final calculated results. Calibration Factors for External Standard calculation are absolute factors that are not relative to any component and are based upon an absolute amount injected. The following equation is the formula used to develop Calibration Factors for External Standard calculations: 46 AMOUNT, x AMT STD FACTOR, = ' x 10000 AREA, AMOUNTi: Peak; A M O U N T in Peak Table. A M T STD: Amount Standard 1.000, constant AREAj: the Peak; area. 10000: constant used to calculate the scale factor. The following equation shows the formula used for External Standard calculations during an analysis run. n r . „ r T r m , AREA, x FACTOR , „ ^ r n AREAj: Peak; area. DIVISOR: Divisor 1.000, constant FACTORj: Peak; FACTOR in Peak Table is used for identified Peaks MLTPLR: Multiplier 1.000, constant 10000: constant used to compensate for scaled factor. RESULTj: Final External Standard calculation results, mg. The operation parameters used with TGA, Pyroprobe and GC are summarized in Table 3.4. T G A Pyroprobe GC Purge Time min 20 20 20 Purge Gas/Flow Rate mL/min 100 1 1 Initial Temperature 50 (5 min) 50 40 (10 min) Heating Rate °C/min 25, 50, 100, 150 600, 3000, 30000, 300000 2 Final Temperature °C 700, 750, 800, 850, 900, 950 500, 600, 700, 800, 900, 1000 120 Holding Time 10 min 0, 5, 10 s 10 min 47 Chapter 4 Experimental Results 4.1 T G A Experimental Results 4.1.1 T G A Pyrolysis of C A N M E T Pitch The T G A pyrolysis of C A N M E T pitch was performed under different experimental conditions to study the effects of sample weight, heating rate, and final pyrolysis temperature. The sample weight was varied between 4.4 and 17.2 mg. The heating rates employed were 25, 50, 100 and 150 °C/min and final temperatures of 700 to 950 °C in 50 °C increments. Each run was performed with a 10 minute holding time at final temperature. 4.1.1.1 Effect of Sample Weight The sample weight effect on C A N M E T pitch pyrolysis was investigated under heating rates of 50 °C/min and 100 °C/min and final temperature 900 °C for different sample weights ranging from 4.4 to 17.2 mg. The operating conditions and experimental results are provided in Tables 4.1.1 and 4.1.2. Vt=o and V,=io refer to the total volatile yield (or weight loss) in percentage of the original sample weight at 0 minute and 10 minutes pyrolysis reaction time at the final temperature. For this pitch, some 80% is converted into volatiles, and about 20% is left as solid residue under these conditions. The shapes of the chromatograms will be discussed in Section 4.1.3. Here just the final residue numbers are discussed. Figures 4.1.1 and 4.1.2 show that the weight loss decreased (the solid residue increased) with increases in sample weight. This may indicate an internal mass transfer effect. With larger sample sizes, the volatile release from the residue matrix may be hindered, resulting in more char. It appears that the decrease is not linear and the weight loss exhibited a shallow minimum at a sample weight of about 14 mg for runs at 100 °C/min and 15 mg at 50 °C/min, at both zero and ten minute holding times. Since the slight increase appears at both heating rates, a polynomial 48 rather than a straight line fit was done to illustrate the general trend of data. The weight loss reduced from 82.89% at sample weight 4.406 mg to 79.85% at sample weight 15.78 mg for t=0 minute, while the weight loss reduced from 83.64% at sample weight 4.406 mg to 80.03% at sample weight 15.78 mg for t=10 minutes for runs at 100 °C/min heating rate. For runs at 50 °C/min heating rate, the weight loss reduced from 84.38% at sample weight 4.979 mg to 80.07% at sample weight 17.17 mg for t=0 minute, while the weight loss reduced from 82.89% at sample weight 4.979 mg to 79.9% at sample weight 17.17 mg for t=10 minutes. It is also clearly shown that the effect of holding time at any sample weight on the total weight loss is not significant for C A N M E T pitch, i.e. essentially all the reaction occurs during heating to the final temperature for each heating rate. A longer holding time may result in more residual H 2 release from solid char, but the amount is very small. This is in good agreement with the analysis of Nguyen [107], where only 1.56% of Ff2 content was observed in the delayed coke. It is generally believed that the weight loss at this stage is caused by the H 2 release from the remaining char [9, 17, 30]. At lower heating rate, the results appear more scattered (Figure 4.1.2), and it may be caused by the longer pyrolysis time. It is expected that at sample weights below 14 mg, the pyrolysis process may be dominated by chemical reaction processes while at higher sample weights diffusional effect may occur. For reference, a single spherical particle of pitch of 14 mg would have a diameter of 1.5 mm. The statistical analysis of the sample size is shown no mass transfer effect in the range of 7.774-12.034 mg at 100 °C/min and 8.011-13.157 mg at 50 °C/min (Appendix I). The difference of weight loss as shown in Figures 4.1.1 and 4.1.2 (and figures in the following sections) is believed not the consequences of experimental errors. For the remaining work, the size of about 9 mg is used. It is believed that the results reflect the intrinsic kinetics and are not significantly affected by mass transfer. As will be subsequently shown, the calculated activation energy is greater than the range 8-24 kJ/mol typical of diffusion processes. 49 90-T o 100°C/min, Oirin 88- • 100°C/mh. 10rrin 86-to 84-3 • £ 82-i J 80-° • > ^ : o 78-1 1 r 1 1 1 I ' Sample Weight mg Figure 4.1.1 Sample weight effect on CANMET pitch pyrolysis with T G A at 900 °C and 100 °C/min 90 - r 88-o 50 °C/min, 0 min • 50°C/min, 10 min 86- • to 84-v> 3 • £ 82-| \ 80-78-O 76- ' r—>-4 6 8 10 12 14 16 18 Sample Weight mg Figure 4.1.2 Sample weight effect on CANMET pitch pyrolysis with T G A at 900 °C and 50 °C/min 4.1.1.2 Effect of Heating Rate To study the heating rate effect on the pyrolysis total weight loss with TGA, the heating rates were set at 25, 50, 100 and 150 °C/min with final temperatures of 700 °C and 800 °C. The sample weight was held constant around 8.216 to 9.668 mg in order to nrinimize the sample size effect. The operating conditions for the experiments are provided in Table 4.1.3. The volatile yield is the weight loss which occurred when the final temperature was reached, i.e. the holding time was zero. Figure 4.1.3 shows the heating rate results with different final set temperatures. From this plot, it is observed that the total weight loss decreases weakly as heating rate is increased at both temperatures. At the same heating rate, the weight loss (volatile yield) is essentially the same for both temperatures, especially at heating rates smaller than 100 °C/min. The total weight loss reached 80.84% and 77.92% at 25 °C/min and 150 °C/min for 800 °C respectively. A decrease of 3% is observed due to the increase of the heating rate by a factor of six. The weight loss at 700 °C decreased to 79.93% at 150 °C/min from 81.59% at 25 °C/min. However, the decrease in total weight loss caused by either the temperature and heating rates is marginal. This indicates that the pyrolysis process is nearly complete at the temperature of 700 °C and further increase of the temperature does not significantly increase the total weight loss. In the range of low heating rates studied with TGA, the volatile 'precursors" apparently have enough time to decompose and evolve from the sample, therefore no significant difference of weight loss is observed. The effect of heating rate was also studied at much higher level with the Pyroprobe using heating rates of 600, 3000, 30,000 and 300,000 °C/min and final temperatures of 700 °C and 800 °C. The sample weight was held around 5.02 to 5.58 mg. The operating conditions are provided in Table 4.1.4. The volatile yield is the weight loss occurred when the final temperature is reached. 51 Heating rate °C/min Figure 4.1.3 Heating rate effect on C A N M E T pitch pyrolysis with T G A Figure 4.1.4 shows that with the Pyroprobe, the weight loss decreases nonlinearly with the increase of heating rate. The weight loss decreased from 49.06% for heating rate 600 °C/min to 2% for 300,000 °C/min at 800 °C, while the weight loss decreased from 12% for heating rate 600 °C/min to 1.89% for 300,000 °C/min at 700 °C. At very high heating rates, the weight loss is essentially the same for the two final temperatures. This suggests that the reaction time is an important factor. At high heating rates (>10,000 °C/min), the reaction time is extremely short, and the difference of weight loss is small. At low heating rates, the reaction time is long, the difference of weight loss is therefore greater. At very low heating rates, the components have enough time to undergo chemical changes, then the same weight loss would be observed. This is shown in T G A results at < 100 °C/min. Figure 4.1.5 compares the results using the T G A and the Pyroprobe. Results using the two procedures appear consistent. The weight loss decreased with increased heating rates over the full range studied, i.e., 25 °C/min to 300,000 T/min. The weight loss decreased from 81.79% for 52 heating rate 25 °C/min to 1.8% for 300,000 °C/min at 700 °C and decreased from 80.84% for heating rate 25 °C/min to 2% for 300,000 °C/min at 800 °C. It is also observed that the temperature is a significant parameter between heating rate 100 °C/min to 30,000 "C/min, which indicates the pyrolysis is reaction controlled. At heating rates higher than 30,000 °C/min, the weight loss is much less than that at heating rate lower than 150 °C/min. The effect of heating rate may be due to pyrolysis reaction times. At heating rates above 30,000 °C/min, it takes less than 1.6 seconds to reach the final temperature of 800 °C, while it takes 320 seconds to reach the same temperature at 150 °C/min. The rapid drop-off in Figures 4.1.5 and 4.1.9 which occurs for C A N M E T pitch heated to 700 °C and for Syncrude pitch may be caused by some combination of time and temperature effect. However, the reasons that it did not occur for C A N M E T pitch heated to 800 °C are not obvious. 50-40-°^ 30-to 3 CD i > 104 OH 800 °C 700 °C 1 1—i i i i 11| 1 l — • I I I I 11 r — l — i I ' 1 100 1000 10000 100000 Heating rate °C/min Figure 4.1.4 Heating rate effect on C A N M E T pitch pyrolysis with Pyroprobe-GC 53 Heating rate °C/min Figure 4.1.5 Heating rate effect on C A N M E T pitch pyrolysis with T G A and Pyroprobe-GC 4.1.1.3 Effect of Final Temperature The effect of final temperature was studied at the heating rate 100 °C/min and final temperatures of 700, 750, 800, 850, 900 and 950 °C with 10 minute holding time. The sample weight was held roughly constant (8.13-11.31 mg) for all the runs. The operating conditions are provided in Table 4.1.5. Volatile yields are reported for both zero and ten minute holding time. Figure 4.1.6 is the weight loss at zero and ten minute holding times vs. final temperature plot. It is observed that the weight loss decreased slightly, reached a minimum and then increased with the increase of temperature. At 0 min holding time, the weight loss decreased from 79.74% at 700 °C to minimal weight loss 79.01% at 850 °C and then increased to 81.58% at 950 °C. While it decreased from 80.20% at 750 °C to minimal weight loss 79.39% at 850 °C and then increased to 81.58% at 950 °C for 10 minute holding time. An increase of weight loss of less than 0.5% was observed over the 10 minute holding time. The residue is already solid char at the temperature 700 °C. That may indicate that pyrolysis of the pitch samples is nearly complete and 54 that further weight loss may be caused by the release of residue hydrogen in the char matrix at high temperature. The minimal weight loss at 850 °C reflects the complexity of the pitch pyrolysis chemistry. Similar phenomena was also observed by van Krevelen [17]. However, it is yet to be investigated. 4.1.2 T G A Pyrolysis of Syncrude Pitch The T G A pyrolysis of Syncrude pitch was performed under different experimental conditions to study the effects of heating rate, pyrolysis temperature and sample weight. The sample weight was controlled between 3 and 16 mg. The heating rates employed are 25, 50, 100 and 150 °C/min and predefined final temperatures of 700, 750, 800, 850, 900 and 950 °C. Each run was also performed with a 10 minute holding time. 820 81.5 81.0-1 v o 80.54, w cj 80.0-1 .£> 79.5-^  J 79.0-j 785-1 780 -m— 100°C/min, Omin - » — 100°C/tnin, 10 min I— 700 750 I— 800 I— 850 900 - 1 — 950 T°C Figure 4.1.6 Final temperature effect on C A N M E T pitch pyrolysis with T G A at 100 °C/min 55 4.1.2.1 Effect of Sample Weight The sample weight effect on Syncrude pitch pyrolysis was investigated under the final temperatures of 700, 800 °C and heating rate 100 °C/min for different sample weight from 3 mg to 16 mg. The operating conditions are provided in Table 4.1.6. Volatile yields are about 90%, leaving 10% of the pitch as non-volatile residue under these conditions. Figures 4.1.7 and 4.1.8 show that the weight loss decreased as the increase of sample weight for Syncrude pitch, as also observed for C A N M E T pitch. It is also observed that only slightly higher weight loss is obtained at 10 minute holding time over 0 minute (Table 4.1.6), i.e., almost all reactions occur during the heatup period. These results are in good agreement with those of C A N M E T pitch. With sample weight increasing from 3 to 14 mg, the weight loss decreased from 92.73% to 89.89% for 0 minute holding time while it decreased from 93.51% to 90.4% for 10 minute holding time for runs at 700 °C. For runs at 800 °C, the weight loss decreased from 91.63% to 90.29% for 0 minute holding time, while it decreased from 91.89% to 91.36% for 10 minutes. The decrease of weight loss happened mostly with sample weights from 3 to 8 mg. Only a very slight decrease of volatile yield was observed with further increases of sample weight. A comparison of the above results in Figures 4.1.7 and 4.1.8 show that higher weight loss is obtained under higher final pyrolysis temperature for the sample weight higher than 6 mg, while lower weight loss is observed under higher final pyrolysis temperature for a sample size less than 6 mg. This indicated a very complex reaction mechanism and the temperature plays a very important role. 56 Figure 4.1.7 Sample weight effect on Syncrude pitch pyrolysis with T G A at 100 °C/min and 0 min Figure 4.1.8 Sample weight effect on Syncrude pitch pyrolysis with T G A at 100 °C/min at 10 min 4.1.2.2 Effect of Heating Rate The heating rate was varied from 25 to 300,000 °C/min while that final temperature was held constant at 800 °C (Table 4.1.7). The volatile yield is the weight loss which had occurred when the final temperature was reached. Figure 4.1.9 is the comparison of the weight loss results of T G A and Pyroprobe. It is observed that the weight loss decreased with the heating rates over the range studied. The weight loss decreased from 90.6% for heating rates less than 150 °C/min to below 9% above 600 °C/min at a final temperature of 800 °C. The trend of results observed is in rough agreement with those of C A N M E T pitch pyrolysis shown in Figure 4.1.5. At heating rates higher than 3000 °C/min, the weight loss is much less than that at heating rates lower than 150 °C/min due to the different pyrolysis reaction times. The slower the heating rate, the longer the reaction time, and the more weight loss occurs. 1 0 0 4 • 800 °c 904 804 704 "g 30-20-104 Figure 4.1.9 Heating rate effect on Syncrude pitch pyrolysis with T G A and Pyroprobe-GC (0 minute after reaching 800 °C) 58 4.1.2.3 Effect of Final Temperature The effect of final temperature on weight loss was studied at the heating rates of 50 and 150 °C/min and final temperatures of 750, 850 and 950 °C for holding time 0 and 10 minutes. The sample weight was held in a range of 6.9 to 7.5 mg for runs under those conditions (Table 4.1.8). Figures 4.1.10 and 4.1.11 are the weight loss vs. final temperature plots for runs at different heating rates and holding times. At zero holding time, the weight loss increased slightly with the increase of temperature at the higher heating rate. The weight loss increased from 90.18% at 750 °C to 92.66% at 950 °C for the heating rate 150 °C/min, while the weight loss remained essentially constant at 91 % from 750 °C to 950 °C for the heating rate 50 °C/min. More total weight loss is observed at 150 °C/min than 50 °C/min at temperature higher than 800 °C. At 50 °C/min and 850 °C, the weight loss was lowest, but the sample size was larger, and from Figure 4.1.2 with C A N M E T pitch, one should expect a lower weight loss. For 10 minute holding time (Figure 4.1.11), the results are essentially similar to those of at zero holding time. 93.0 -r- • • 1 90.04 -I 1 1 1 • 1 • 1 • 1 1 750 800 850 900 950 T°C Figure 4.1.10 Final temperature effect on Syncrude pitch pyrolysis with T G A at 0 min 59 33.5 — 1 5 0 ° a m i n , 10 rrin — 5 0 ° C / m i n , 10 rrin 925 H 1 • 91.0-905 H 750 800 850 900 950 T °C Figure 4.1.11 Final temperature effect on Syncrude pitch pyrolysis with T G A at 10 min From Table 4.1.8, slightly higher weight loss was observed at 10 minute holding time. The effect of final temperature, as well as holding time, is in accordance with those of CANMET pitch. 4.1.3 T G A Pyrolysis Characteristics In experiments presented in this section, the pyrolysis heating rate was varied while other parameters such as the final temperature and the sample weight were held constant. The sample weight for C A N M E T pitch is 8.129 to 10.12 mg and the sample weight for Syncrude pitch is 9.904 to 11.90 mg to permit a direct comparison (Table 4.1.9). The total weight loss (V*) is also listed in the table for each run. The volatile yield (V*) is obtained when the final temperature is reached. The dynamic weight change during the time of heating is discussed. C A N M E T and Syncrude pitches both showed similar patterns in the T G A pyrolysis plots. This pattern differs from results found with oil shale or coals. Figures 4.1.12 to 4.1.18 show the nonisothermal devolatilization T G A curves of CANMET pitch and Syncrude pitch at 800 °C final 60 temperature and heating rates of 25, 50, 100 and 150 °C/min. The nonisothermal devolatilization weight loss vs. temperature behavior is shown in Figures 4.1.12 and 4.1.16 for each pitch respectively. It is observed that a slightly higher weight loss is obtained at a lower heating rate at a given temperature, or a higher temperature is required to reach the same amount of weigh loss for a higher heating rate. However, the effect of the heating rates is not systematic, nor significant. For C A N M E T pitch, weight loss at 25 and 50 °C/min is noticeably higher than those at 100, and 150 °C/min, while the weight loss is roughly the same for heating rates 25 and 50 °C/min at the same temperature as shown in Figure 4.1.12. For Syncrude pitch (Figure 4.1.16), the weight loss is almost the same at heating rates 25 and 50 °C/min. Also the weight loss is roughly the same at 100 and 150 °C/min. However the weight loss at 25 and 50 °C/min is generally higher that that at 100 and 150 °C/min at the same temperature. Similar behavior was also observed by Milosavljevic [61], but heating rate as such was not considered to be the main reason for the difference. He claimed that the chemical reaction itself caused the change and difference. This seems reasonable in the present case as well. Heating rates do affect the temperature history, however, it is the chemical reaction at the specific temperature which causes formation of volatiles and the weight loss. This is also observed in Figures 4.1.13 and 4.1.17, which show the weight loss results vs. time. As can be seen, the heating rate changed the reaction time, but it did not change the volatile evolution pattern with temperature of either C A N M E T pitch or Syncrude pitch. Figures 4.1.15 and 4.1.19 showed the weight loss per degree of temperature rise dW/dT vs. temperature for each pitch. This derivative was calculated with the following formula: 61 The above equation indicates that dW/dT is the average value of weight loss in a very small temperature interval and represents the weight loss rate divided by the heating rate. dW/dT is also negative because the pyrolysis is a weight loss process with temperature. It is clearly shown that the dW/dT changes with the temperature in a nonlinear manner, passing through three major stages for each type of pitch. At temperatures lower than 150 °C, dW/dT is roughly equal to 0 as observed in Figures 4.1.15 and 4.1.19 for C A N M E T and Syncrude pitches respectively. This indicates that there is no chemical or physical reaction taking place below this temperature, and that the content of water and low molecular components is negligible. At temperatures between 150 °C to about 400 °C, the weight loss dW/dT slowly decreased to a steady value, which is more evident for the Syncrude pitch results, then dW/dT decreased rather dramatically to its minimum, which occurs at temperatures between 500 °C and 600 °C. The ratio dW/dT then went through the last stage of changing, increasing from its minimum to a very small absolute value at approximately 600 °C. At this condition pyrolysis is nearly complete and further increases of the temperature did not affect the total weight loss significantly. This indicated that the temperature is an important parameter and the change of temperature affects the behavior of the pitch pyrolysis process. It is clearly shown that the pyrolysis process takes place as a two stage process and therefore there are two weight loss peaks as observed in these two plots. However these two stages of pyrolysis overlap and this feature can be easily missed in Figure 4.1.15 for C A N M E T pitch as they are not clearly separated. This two-peak weight loss feature, i.e. two-stage reaction characteristics is more clearly shown in Figure 4.1.19 for Syncrude pitch. The peak weight loss temperature is also very close to a fixed value for all the heating rates studied for each pitch as shown in Figures 4.1.15 and 4.1.19. This further suggests the chemical nature of the pyrolysis. The first peak temperature is not clearly identifiable for C A N M E T pitch, but lies in the range of 400 °C and 450 °C for Syncrude pitch. The second maximum weight loss rate temperature is 62 clearly identifiable for both C A N M E T pitch and Syncrude pitch. The second peak temperature for C A N M E T pitch is between 500 °C to 600 °C. It is even better defined for Syncrude pitch in the temperature range of 500 °C and 550 °C. The weight loss for C A N M E T pitch at 400 °C is between 5% and 25% depending on the heating rate, while the weight loss for Syncrude pitch is between 20% and 40% at the same temperature. The total weight loss for C A N M E T pitch and Syncrude pitch is 80% and 90% at 800 °C respectively. The most weight loss therefore occurred at temperatures between 400 °C and 600 °C. The weight loss in this temperature range is 65% to 75% for C A N M E T pitch and 50% to 70% for Syncrude pitch respectively. Figures 4.1.13 and 4.1.17 showed the weight loss vs. time for each pitch at different heating rates. Figures 4.1.14 and 4.1.18 showed the weight loss rate dW/dt vs. time for each pitch at different heating rate. It is also observed that the pyrolysis occurs in stages at different time scales with changes in heating rate. The two peak weight loss character is also identified in these two plots, attesting the results in Figures 4.1.15 and 4.1.19. 63 time Figure 4.1.13 C A N M E T pitch weight loss vs. time at different heating rates and final temperature 800 °C measured via T G A 10 -100 4 1 1 1 < 1 1 1 > 1 ' 1 1 r 0 5 10 15 20 25 30 tmin Figure 4.1.14 C A N M E T pitch weight loss rate vs. time at different heating rates and final temperature 800 °C measured via T G A 0.1 - 0 . 7 - I — | — i — | — i — | — i — | — i — | — i — | — i — | — i — | — i — | — i — | 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 700 800 900 T°C Figure 4.1.15 C A N M E T pitch weight loss dW/dT vs. temperature at different heating rates and final temperature 800 °C measured via T G A T°C Figure 4.1.16 Syncrude pitch weight loss vs. temperature at different heating rates and final temperature 800 °C measured via T G A t min Figure 4.1.17 Syncrude pitch weight loss vs. time at different heating rates and final temperature 800 °C measured via T G A 10 T 1 1 1 1 • 1 1 1 " 1 1 T 0 5 10 15 20 25 30 tmin Figure 4.1.18 Syncrude pitch weight loss rate vs. time at different heating rates and final temperature 800 °C measured via T G A - 0 . 7 - 1 — i — i — i — i — | — i — | — i — i — i — | — i — | — i — | — i — | — i — | 0 100 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 T°C Figure 4.1.19 Syncrude pitch weight loss dW/dT vs. temperature at different heating rates and final temperature 800 °C measured via T G A 4.1.4 Discussion and Conclusion It is shown that the heating rates slightly affect the weight loss, however, it is believed that the temperature history, not the heating rate as such causes the difference. Temperature is the significant factor causing the reactions to take place and produce the weight loss. The devolatilization step is not instantaneous, as little weight loss occurred at the highest heating rate. The importance of the temperature history is more significantly noticed among the runs of Pyroprobe experiments where total reaction time in the heatup was short, i.e. a few seconds. Low heating rates produce longer reaction times of the order of minutes, caused more extensive pyrolysis reaction, and therefore resulted in a higher weight loss (or volatile yield). At temperatures below 150 °C, there is little weight loss, suggesting that no pyrolysis take place. The weight loss takes place in two following stages with two different, distinct patterns of chemical and physical change. In the first stage, a low peak weight loss rate was observed, while 67 in the second stage a higher peak weight loss rate was observed. These features appear unique to pitch pyrolysis, as they have not been reported for coal or shale pyrolysis. The total weight loss (volatile yield) decreases slightly with the increase of sample weight over the range studied for both C A N M E T pitch and Syncrude pitch. With TGA, more than 80% of residue conversion can be achieved for C A N M E T pitch, while more than 90% of residue conversion can be achieved for Syncrude pitch. 68 Table 4 11 Experimental Conditions for Runs at Different Sample Weight with TGA Heating Rate Final Temp Sample Weight mg V M vM . Run* "C/min °C wt% wt% Canll 100 900 4.406 82.8 83.64 Can20 100 900 5.702 82.51 82.82 Canl8 100 900 6.441 82.05 83.50 Can45 100 900 7.074 80.60 81.55 Canl5 100 900 7.774 79.80 80.47 Canl6 100 900 7.981 81.65 81.79 Canl7 100 900 10.719 80.27 80.50 Can8 100 900 11.162 79.33 79.57 Can38 100 900 12.034 79.59 79.83 Can 19 100 900 13.680 78.70 79.03 Canl4 100 900 15.784 79.85 80.03 Table 4.1.2 Experimental Conditions for Runs at Different Sample Weight with TGA Heating Rate Final Temp Sample Weight V « Run* "C/min °C mg wt% wt% Can28 50 900 4.979 82.89 84.38 Can21 50 900 6.360 82.76 83.32 Can7 50 900 6.723 82.48 86.29 Can27 50 900 8.011 80.51 80.65 Can27 50 900 8.943 81.12 81.38 CanlO 50 900 10.179 80.60 81.82 Can25 50 900 11.162 80.25 80.45 Can23 50 900 11.735 80.88 81.02 Can35 50 900 12.022 80.43 80.74 Can22 50 900 12.699 79.97 80.35 Canl3 50 900 13.157 80.84 81.71 Can31 50 900 14.042 78.47 78.87 Can24 50 900 14.729 77.85 78.26 Can30 50 900 15.596 78.49 78.87 Canl2 50 900 17.175 79.10 80.07 Table 4.1.3 Exoerimental Conditions for Runs at Different Heating Rates with TGA Heating Rate Final Temp. °C Sample Weight mg Volatile Run# "C/min wt% Can54 25 700 9.368 81.78 Can61 50 700 8.835 80.66 Can53 100 700 7.896 79.74 Can60 150 700 8.923 79.93 Can48 25 800 8.878 80.84 Can33 50 800 8.224 80.79 Can41 100 800 10.304 79.30 Can58 150 800 9.109 77.59 Table 4.1.4 Experimental Conditions for Runs at Different Heating Rates with Pyroprobe Heating Rate Final Temp. °C Sample Weight mg Volatile Run# °C/min Cam069 600 700 5.0 12.00 Cam051 3,000 700 5.6 10.71 Cam033 30,000 700 5.2 9.62 Cam015 300,000 700 5.3 1.88 Cam070 600 800 5.3 49.06 Cam052 3,000 800 5.8 29.31 Cam034 30,000 800 5.2 7.69 Cam016 300,000 800 5.0 2.00 Table 4.1.5 Experimental Conditions for Runs at Different Final Temperature with TGA Heating Rate Final Temp. "C Sample Weight mg Vt-o Vc-io Rimtf "C/min wt% wt% Can53 100 700 7.896 79.74 80.20 Can42 100 750 9.171 79.54 79.81 Can41 100 800 10.304 79.30 79.72 Can40 100 850 10.723 79.01 79.39 Can38 100 900 12.034 79.59 79.83 Can52 100 950 8.199 81.23 81.58 69 Table 4.1,6 Experimental Conditions for Runs at Different Sample Weight with TGA Heating Rate Final Temp. °C Sample Weight mg V M V M 0 Run# "C/min wt% wt% Synl3 100 700 3.010 92.73 93.51 Synl4 100 700 7.852 90.54 90.84 Synl6 100 700 11.029 90.28 90.60 Synl5 100 700 13.932 89.83 90.40 Synl7 100 800 4.321 91.63 91.89 Synl9 100 800 6.797 91.10 91.39 Synl8 100 800 11.376 90.58 90.94 Syn20 100 800 15.534 90.29 91.36 Table 4.1.7 Experimental Conditions for Runs at • Different Heating Rates with TGA and Pyroprobe Heating Rate Final Temp Sample Weight V M Runtf "C/min mg wt% Equipment Syn43 25 800 10.477 91.03 TGA Syn29 50 800 11.708 90.70 TGA Synl8 100 800 11.376 90.59 TGA Syn8 150 800 10.053 90.62 TGA Syn070 600 800 4.600 8.70 Pyroprobe Syn052 3,000 800 2.400 8.33 Pyroprobe Syn034 30,000 800 3.600 2.78 Pyroprobe Syn016 300,000 800 4.900 £08 Pyroprobe Table 4.1.8 Experimental Conditions for Runs at Different Final Temperature with TGA Heating Rate Final Temp. °C Sample Weight mg Vt=o VPio Run# "C/min wt% wt% Syn27 50 750 7.604 90.96 91.02 Syn32 50 850 7.134 90.61 90.87 Syn33 50 950 6.942 91.01 91.21 SynlO 150 750 7.606 90.18 90.51 Syn5 150 850 6.920 91.19 91.22 Syn4 150 950 7.262 92.66 93.05 Table 4.1.9 The Pyrolysis Conditions for CANMET Pitch and Syncrude Pitch at Different Temperature and Heating Rates Heating Rate Final Temp. V* Run# "C/min *C wt% CANMET Pitch Can48 25 800 80.84 Can33 50 800 80.79 Can41 100 800 79.30 Can58 150 Syncrude Pitch 800 77.59 Syn43 25 800 91.03 Syn29 50 800 90.70 Synl8 100 800 90.58 Syn8 . 150 800 90.62 70 4.2 Pyroprobe-GC Pyrolysis of C A N M E T and Syncrude Pitch C A N M E T and Syncrude pitches were studied with the Pyroprobe-GC. The yield of volatiles was determined by the difference between the sample weight and residue weight after pyrolysis. The yield of each major group of components was determined following the method outlined in the experiment techniques section in Chapter 3. The experimental conditions are summarized in each of the following sections. The mass balance of each run in this section is in the range of 95 to 105%. 4.2.1 Pyroprobe-GC Pyrolysis of C A N M E T Pitch The Pyroprobe-GC pyrolysis of C A N M E T pitch was performed under different experimental conditions to study the effects of heating rates, pyrolysis reaction temperatures and holding times. The sample weight was kept relatively constant around 5 mg in order to limit the sample size effects. The heating rates are 300000, 30000, 3000 "C/min, the holding times are 10, 5 and 0 s. The combinations of these operating parameters are listed in Table 4.2.1. Each combination of these parameters was performed at the final temperatures of 500, 600, 700, 800, 900, 1000 °C. Table 4.2.1 Experimental Conditions for Runs at Different Holding Times Holding Time s Heating Rate °C/min 10.0 300,000 5.0 300,000 0.0 300,000 10.0 30,000 5.0 30,000 0.0 30,000 10.0 3,000 5.0 3,000 0.0 3,000 71 4.2.1.1 Effect of Experimental Conditions on the Total Weight Loss The total weight loss vs. holding time is an important characteristic in hydrocarbon pyrolysis. The effect of holding times on the total weight loss is shown in Figures 4.2.1 to 4.2.3. Figures 4.2.1 to 4.2.3 show that the weight loss (volatile yield) generally increases as the increase of temperature, with maximum weight loss observed at heating rate 30,000 and 3,000 °C/min. At the heating rate of 300,000 °C/min as shown in Figure 4.2.1, higher weight loss is observed for a longer holding time at temperatures below 800 °C, i. e., more weight loss is observed after 10 s than 5 or 0 s. At temperatures higher than 800 °C, however, about the same amount of weight loss is observed at 10 and 5 s. That may indicate that the pyrolysis is nearly complete at these conditions. Little weight loss is observed at 0 s. At heating rate of 30,000 °C/min as shown in Figure 4.2.2, it is observed that the weight loss vs. temperature at different holding times is not linear. The maximum weight loss is reached at 900 °C for holding time 10 and 5 s. Higher weight loss is also observed under longer holding time. About 5% more weight loss is observed at 10 s holding time than 5 s holding time. At heating rate of 3000 °C/min as shown in Figure 4.2.3, it is observed that the weight loss vs. temperature at different holding times is not linear. The maximum weight loss is observed at 700 °C for holding time 10 s, and at 800 °C for 5 s. At temperatures lower than 800 °C, more weigh loss is observed under a longer holding time. At temperatures higher than 900 °C, weight loss becomes less sensitive to the holding time. More weight loss is observed at 0 s for heating rate 3000 °C/min than that for 300,000 and 30,000 °C/min. 50.9% weight loss is observed at 1000 °C and 0 s for heating rate 3000 °C/min, while less than 5% weight loss is observed for both 300,000 and 30,000 °C/min at the same temperature. This further indicates the importance of holding times. To reach 1000 °C, it takes 19, 1.9 and 0.19 s for 3000, 30,000 and 300,000 °C/min respectively. 72 Figure 4.2.2 C A N M E T pitch pyrolysis total loss (yield) vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 70 6 D -SD-g 40-^ 3)1 32 >- 2D O H -R=Q050ams,t=10s -R=a05°C/rrE,t=5s -R=aC6°C/nrB,t=0s 3D 800 TOO —I— 833 —I— 3D — I — 1000 J°C Figure 4.2.3 C A N M E T pitch pyrolysis total loss (yield) vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min 4.2.1.2 Effect of Experimental Conditions on the C7 Yield Figures 4.2.4 to 4.2.6 show that the C7 yield generally increases as the increase of temperature, while maximum yield was observed at 3000 °C/min. At the heating rate of 300,000 °C/min as shown in Figure 4.2.4, higher C7 yield is observed at a longer holding time in the temperature range studied. The C 7 yield is 54.46%, 27.92% and 0% at 1000 °C for holding time 10, 5 and 0 s respectively. At heating rate 30,000 °C/min as shown in Figure 4.2.5, it is observed that the C7 yield vs. temperature at different holding times is not linear. It is also observed that the C 7 yield at 10 second holding time is very close to that at 5 second holding time. A maximum C7 yield, 40.94%, is observed at 900 °C for holding time 5 s. C 7 yield reached 47.77% and 39.19% at 1000 °C for 10 and 5 second holding time respectively. The C7 yield at 0 s is negligible, as also observed in Figure 4.2.4. 74 Figure 4.2.5 C A N M E T pitch pyrolysis C 7 yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min Figure 4.2.6 C A N M E T pitch pyrolysis C 7 yield vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min At heating rate of 3000 °C/min as shown in Figure 4.2.6, it is observed that the C 7 yield vs. temperature is not linear. It is also observed that maximum C 7 yield is reached at different temperature for different holding times. Maximum C 7 yield is reached at a lower temperature for a longer holding time. Maximum C 7 yield, 43.75%, is reached at 700 °C for 10 second holding time, while maximum C 7 yield, 40.14% and 41,75%, is reached at 800 °C and 1000 °C for holding time 5 and 0 s respectively. Secondary pyrolysis is clearly observed for the C 7 lump of compounds. At temperature lower than 750 °C, it is observed that longer holding time resulted in higher C 7 yield, while at temperature higher than 900 °C, longer holding time resulted in lower C 7 yield. It is also observed that C 7 yield increased dramatically at temperatures above 700 °C for 0 second holding time and 41.75% is obtained at 1000 °C for holding time 0 s. The maximum C 7 yields at different conditions is essentially the same and may indicate the secondary reactions of some of the components in the sample. 76 4.2.1.3 Effect of Experimental Conditions on the Cio Yield Figures 4.2.7 to 4.2.9 show that Cio yield generally increases as temperature, with the maximum yield observed at 800 to 900 °C. At heating rate 300,000 °C/min as shown in Figure 4.2.7, higher Cio yield is observed at higher heating rate in the temperature range studied. The Cio yield is not sensitive to temperatures lower than 600 °C. As also observed in Figure 4.2.5, Cio yield is negligible for 0 s in the temperature range studied. Maximum Cio yield is also observed at 800 °C for holding time 10 s. At heating rate 30,000 °C/min as shown in Figure 4.2.8, it is observed that the Cio yield vs. temperature at different holding times is not linear. It is also observed that the Cio yield at 10 second holding time is very close to that at 5 second holding time. A maximum Cio yield, 2.3% and 2.2%, is observed at 900 °C for holding time 10 and 5 s respectively. The Cio yield at 0 s is, as also observed in Figure 4.2.7, negligible. At heating rate of 3000 °C/min as shown in Figure 4.2.9, it is observed that the Cio yield vs. temperature is not linear. It is also observed that maximum Cio yield is reached at different temperature for different holding times. Maximum Cio yield is reached at about the same temperature 900 °C for holding time 10 and 5 s respectively. The maximum Cio yield is 1.8% and 1.7% for holding time 10 and 5 s respectively. At temperature lower than 600 °C, it is observed that Cio yield is not sensitive to the temperature. It is also observed that Cio yield for holding time 10 s is close to that for holding time 5 s in the temperature range from 600 to 900 °C. Cio yield increased significantly at temperature higher than 800 °C and reached maximum yield 1.6% at 900 °C for holding time 0 s. Secondary pyrolysis of Cio lump is also evident as shown in Figures 4.2.7, 4.2.8 and 4.2.9. 77 Figure 4.2.8 C A N M E T pitch pyrolysis Cio yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 30-25 20H 15-? 1.0' Q5H QOH -R=005 cC/rfE,t=10s -R=QC6 0C/rrB,t=5s -R=O05oC/m5,t=0s —I— 333 eoo —i— 700 800 933 1000 T°C Figure 4.2.9 CANMET pitch pyrolysis Cio yield vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min 4.2.1.4 Effect of Experimental Conditions on the Cn Yield Figure 4.1.10 shows that the Cn yield generally increases to 800 °C and then decreases as temperature at the heating rate of 300,000 °C/min, with maximum Cn yield observed at 800 °C. Maximum Cn yield of 2.7% and 1% is obtained at 800 °C for holding time 10 and 0 s respectively. There is no Cn observed at temperatures lower than 600 °C for holding time 10 s, and 700 °C for holding time 0 s. It is worth noting that the C n yield is negligible at 1000 °C for holding time 10 s and temperatures higher than 900 °C for holding time 0 s, indicating that the Cn lump depleted due to further pyrolysis (i.e. secondary reactions). 79 4H ! 3H H oH —»—R=50°C/ms,t=10s —A— R=50°CArs,t=Os 3D 833 TOO 833 3D 1003 Figure 4.2.10 C A N M E T pitch pyrolysis Cn yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 4.2.1.5 Effect of Experimental Conditions on the Cn Yield Figure 4.2.11 shows that the Cn yield generally increases to 800 °C and then decreases as temperature at the heating rate of 300,000 °C/min, with maximum Cn yields observed at 800 °C. Maximum C12 yield of 3.7% and 1% is obtained at 800 °C for holding times 10 and 0 s respectively. There is no Cn observed at temperature lower than 600 °C for holding time 10 s, 700 °C for holding time 0 s. It is also worth noting that the Cn yield depleted at 900 °C due to its further pyrolysis at 0 second holding time and also significantly decreased at temperatures above 800 °C for 10 second holding time. 80 4H I 32 2 3H H OH — • — R= 5JO°CAIB, t- 10s —A—R=5jO°C/tTB,t=OS 333 eoo 700 833 T°C 933 •KEO Figure 4.2.11 C A N M E T pitch pyrolysis Cu yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 4.2.1.6 Effect of Experimental Conditions on the Cn Yield Figure 4.2.12 shows the C13 yield generally increases to 700 °C and then decreases as temperature at the heating rate of 30,000 °C/min, with the maximum C13 yield observed 700 °C for the holding time studied. Higher C13 yield is also observed at a longer holding time. The maximum C13 yield, observed at 700 °C, is 2.9%, 2.4% and 2.1% for holding times 10, 5 and 0 s. Cn yield decreased as further increase of temperature. This again indicates secondary pyrolysis of C13 lump at higher temperature. 81 3S 600 TOO 833 333 1000 Figure 4.2.12 C A N M E T pitch pyrolysis C13 yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 4.2.1.7 Effect of Experimental Conditions on the C14 Yield Figures 4.1.13 and 4.1.14 show that the C14 yield generally increases to certain temperatures and then decreases as temperature. At.the heating rate of 300,000 °C/min as shown in Figure 4.2.13, maximum C u yield is obtained at 800 °C for holding time 10 s and 900 °C for holding time 5 s. The maximum yields are 1.7% and 1.3% respectively. There is no C14 observed at the temperature range studied for holding time 0 s. At heating rate 30,000 °C/min as shown in Figure 4.2.14, it is observed that the C14 yield vs. temperature at different holding times is not linear. Maximum C14 yield is observed at 700 °C for holding times 10 and 5 s. The maximum yields are 3.89% and 3.91% respectively. C14 yield increased as temperature in the range from 500 to 700 °C, decreased in the range from 700 to 1000 °C. C14 yield for holding time 10 s is close to that for holding time 5 s at the same temperature. Secondary reaction is also evident for C14 as shown in Figures 4.2.13 and 4.2.14. 82 20-15H | ,1 .<H 8 > 0.5 -R=50°C/ms, t=10s -F*=S0°C/ms,t=5s -R=5i0°C/ms,t=0s 3D eoo - 1 — 700 833 933 1033 Figure 4.2.13 CANMET pitch pyrolysis Ci 4 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 4H H — « — R = 0 5 0 C / m i , t = 1 0 s —»—R=05°CATB,t=5s — A — R = 0 5 ° C / m » , t 3 0 s •r * • • •• • i 1 1 1 1 1 " 1 533 eoo 700 833 933 1000 T^C Figure 4.2.14 C A N M E T pitch pyrolysis C u yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 4.2.2 Pyroprobe-GC Pyrolysis of Syncrude Pitch The Pyroprobe-GC pyrolysis of Syncrude pitch was again performed under different experimental conditions to study the effects of heating rates, pyrolysis reaction temperatures and holding times. The sample weight was kept relatively constant around 5 mg in order to limit the sample size effect. The heating rates are 300,000, 30,000, 3000, 600 °C/min, the holding time is 10, 5 and 0 s. The combinations of these operating parameters are listed in Table 4.2.2. Each combination of these parameters was performed at the final temperatures of 500, 600, 700, 800, 900, 1000 °C. Table 4.2.2 Experimental Conditions for Runs at Different Holding Times Holding Time s Heating Rate °C/min 10.0 300,000 5.0 300,000 0.0 300,000 10.0 30,000 5.0 30,000 0.0 30,000 10.0 3000 5.0 3000 0.0 3000 10.0 600 5.0 600 0.0 600 4.2.2.1 Effect of Experimental Conditions on the Total Weight Loss The total weight loss vs. holding time is an important character for Syncrude pitch pyrolysis as well. The effect of holding times on the total weight loss is shown in Figure 4.2.15. Figure 4.2.15 shows that the weight loss generally increases as the increase of temperature at 300,000 °C/min, with maximum yield observed for 5 s holding time. Higher weight loss is observed for 10 s than 5 s or 0 s. It is also noted that the weight loss is not significant at holding time 0 s. 84 90 —i 1 1 > 1 1 1 1 l ' l 500 600 700 800 900 1000 T ° C Figure 4.2.15 Syncrude pitch pyrolysis total weight loss vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 4.2.2.2 Effect of Experimental Conditions on the C 7 Yield Figure 4.16 shows that the C 7 yield increases as temperature at the heating rate of 300,000 °C/min, with maximum yield observed for 5 s holding time. Higher C? yield is observed at a longer holding time. The C 7 yield reached 75% and 60% at 10 and 5 s holding time respectively, while no C 7 was detected at all at 0 s. Comparison with Figure 4.1.5 shows that at high heating rates the C 7 lump comprises essentially all the weight loss. 85 —1 1 1 • — — I 1 1 " 1 1 1 500 600 700 800 900 1000 T °C Figure 4.2.16 Syncrude pitch pyrolysis C 7 yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 4.2.2.3 Effect of Experimental Conditions on the Cio, Cu, C 1 2 , C13, and C i 4 Yield Fligher yield of Cio and Cn is generally obtained at a lower holding time and higher temperature at the heating rate of 300,000 °C/min. However, the yields of these lumps are rather small. The Cio yield reached only 0.7% and 0.5% at holding time of 10 and 5 s respectively, while the Cn yield reached only 0.225% and 0.07% for holding time 10 and 5 s. At heating rate 600, 3000, 30,000 °C/min, little C w and Cn was detected. The heating rate effect is not an important parameter for C12, C13, C M yield. The increase of heating rates did not show any significant effect on C12, C13, C M yield as observed in the C A N M E T pitch pyrolysis. The quantity of each of the lumps is not abundant to determine accurately. 86 4.2.3 Discussion and Conclusion It is shown that under Pyroprobe pyrolysis conditions, the pyrolysis reaction time is a very important operating parameter. At the highest heating rate (300,000 °C/min) employed in this study, there is little pyrolysis, i.e. weight loss, is observed for both C A N M E T and Syncrude pitches, while at heating rate of 3000 °C/min, the weight loss is rather significant when the final temperature is just reached (0 s isothermal reaction time). In the latter case, some 10 to 50% of volatile yield was observed at different final temperature. The latter case is somewhat similar to the T G A experiment results, and the effect of the heating period on the pyrolysis of either C A N M E T or Syncrude pitch should not be ignored. At heating rate of 30,000 "C/min, the weight loss results are rather close to those at 300,000 °C/min, while they are generally higher than those at 3000 °C/min. The effect of the heating rate combined with the final temperature is therefore expected to be interrelated and remains as a topic of research for high heating rate pyrolysis. However, a different pyrolysis mechanism is also expected for the high heating rate pyrolysis. The most abundant component of the volatile is shown experimentally the hydrocarbons with less than 10 carbons, which is grouped as single lump as C7 in this study. At each heating rate and final temperature, the amount of C7 is becoming significant at temperatures higher than 700 °C. As high as 50% volatile yield of this group was detected for C A N M E T pitch and secondary reaction is observed at heating rate 3000 °C/min. At the Pyroprobe pyrolysis conditions, the volatile may undergo secondary pyrolysis when being purged through the quartz tube. Similar trend is also observed for Syncrude pitch pyrolysis with Pyroprobe-GC. The yield of Cio compounds is very strongly influenced by the heating rates. At the highest heating rate (300,000 °C/min), less than 5% volatile yield of this group of components was detected, while as high as 23% volatile yield of the group was detected at 30,000 °C/min. This again attests the influence of the reaction time and heating rates. The amount of Cio detected from 87 Syncrude pitch pyrolysis with Pyroprobe-GC is much less than that of C A N M E T pitch. This is in agreement with the difference of 'chemical structure" or 'chemical makeup" of these two pitches, where proximate analysis, ultimate analysis and fractionation also show that Syncrude pitch contains more low molecular components than C A N M E T pitch. Higher yields of Cn, C12, C » and C n groups was also detected at lower heating rates, a similar trend as that of Cio group. While the yield of C14 is much less that those of Cn, C12 and C13. C14 is the heaviest group of compound detected in the Pyroprobe-GC pyrolysis. This may indicate that the volatile is mostly compounds lighter than C M . The yield of these groups from Syncrude pitch pyrolysis with Pyroprobe-GC is also significantly less than those from C A N M E T pitch pyrolysis. This is in agreement with the Cio yield. The different yields of each lumped group between C A N M E T pitch and Syncrude pitch is in good agreement with the difference of the chemical nature of these two pitch samples. This is also in agreement with the T G A pyrolysis results in which the T G A pyrolysis curves showed different patterns between the above two samples. Secondary reaction of the product lumps is evident for both C A N M E T and Syncrude pitch. At high temperatures, heavy lumps such as C M , are prone to pyrolysis into smaller molecules before leaving the quartz tube. 88 Chapter 5 Modeling of Experimental Results 5.1 Introduction of Pyrolysis Kinetic Models A number of mechanisms which have been proposed in the literature for pyrolysis were described in the literature review. However, the single overall first order reaction mechanism has been accepted most widely due to its simplicity and adequacy to explain the pyrolysis behavior and to model the process mathematically. The single overall first order reaction model assumed that de-volatilization takes place as a single first order reaction and the mechanism does not change during pyrolysis process. It is widely used to describe and explain the pyrolysis processes of coal, oil shale, bitumen, biomass and other hydrocarbons, due to its mathematical simplicity. A number of first order reaction models were thus proposed to that effect. The general expression for the first order mechanism is given as: Under nonisothermal conditions, such as those in the T G A experiments, the temperature at any time during the heating period is given by the following expression; where T 0 is the initial temperature of the experiment. Substituting time term dt with temperature dT, i.e. dT=C*dt, the general expression is then given as: (5.1) T=Ct+Ta (5.2) dV_ dT (5.3) where: maximum volatile content released at the final temperature, wt% T pyrolysis temperature, K V volatile content released at temperature T, wt% t pyrolysis reaction time, min. 89 E activation energy of the single overall first order reaction, J/mol ko pre-exponential factor of the single overall first order reaction, min"1. R gas constant, 8.314 J/mol.K C pyrolysis heating rate, K/min. 5.1.1 Overall First Order Reaction Model A number of methods have been suggested to extract values of k o and E for Equation 5.3 from experiments in which V is measured as a function of T at constant heating rate. Since they use the experimental data in different forms, they tend to give different results for the reaction parameters. 5.1.1.1 Integral Method This method estimates the values of E and k o of a reaction from the overall volatile yield vs. temperature curves. Shih and Sohn [108] used this method to determine the kinetic parameters for oil shale pyrolysis. The general expression is rearranged as: where T 0 is the initial temperature. In the current study the T G is chosen as 50 °C, and the rate as well as the total volatile yield at this temperature is negligible; therefore the temperature limit T 0 can be by replaced by 0. Integration of the above equation gives, with T 0 assumed to be 0 K. v-v~ce v Integrating the above expression in the temperature range of interest, we then get (5.4) (5.5) (5.6) The exponential integral E ; (-E/RT) can be approximated by (Appendix C): 90 E\ -RTJ -E/RT E/RT 1! 2! E/RT (E/RT)1 (5.7) If the first three terms of the approximation are used, the above integration becomes: - i d (V_-v\ V kRT2( 2RT CE 1— E J -E/RT (5.8) Dividing both sides of the above equation by RT2(1-2RTVE)/C and taking the logarithm, then Id -C\r[l-V RT2 ( 2RT) , kQ E •In 1 — — l*ln-=-\ E E RT (5.9) The values of E and k o can be obtained by repeated least squares fit of the above equation to the experimental data. By first using an approximate E in the left hand side of the above equation, the least squares fit can therefore be performed with the FORTRAN program in Appendix D. The value of E thus obtained is then used as the new value on the left hand side and successively a more accurate value of E is obtained until no improvement in the value of E takes place. The values of E and k o are therefore obtained. From the above equation, the volatile yield V (Appendix C) can be obtained as V=V*\ 1-exp KRT2 E/RT( 2Rr CE (5.10) 5.1.1.2 Friedman Method This method determines the values of E and k o from the ratio dV/dT vs. temperature. Rewriting the general expression (Equation 5.3) as: £_^L_u /RT (V- V) V'dT~° V* (5.11) 91 Taking the logarithm and rearranging, (C dV\ {.V* dTJ - l n [ l ~ ] = l n * . - RT (5.12) The values of E and k o can be obtained by fitting the above equation to the experimental data, using least squares fitting program in Appendix D. The values of dV/dT are calculated by using two adjacent pairs of the volatile and temperature data: dV V -V (5.13) .dTJ, TM-T, Where i=l, n-l. The number of data points in a run is n, and (dV/dT^^dV/dT)^. The volatile yield can then be calculated from Equation 5.10 with the values of E and k o obtained. 5.1.1.3 Coats-Redfern Method This method is the same as the integral method except that the term of 2RT/E is ignored in Equation 5.9. This simplifies the mathematical procedure, and is based on the assumption of 2 R T / E « 1 . - C l n f In v1 V) RT = , n 4 - £ E RT (5.14) The values of E and k o can be obtained by fitting the above equation to the experimental data, using the program in Appendix D. The volatile yield can be obtained from Equation 5.10 by using the E and k o values thus obtained. 92 5.1.1.4 Chen-Nuttall Method This method assumed the initial temperature to be zero K. The initial temperature of this investigation (50 °C) was taken to be close enough to 0 such that the rate as well as the volatile yield was negligible. The general expression is then given as: yw^^^ar ( 5 . i 5 ) J o v -V 0 c Integration of the above equation gives: ^ k RT2 -e ,-E/RT (5.16) C E+2RT Multiplying both sides of the above equation by -C(E+2RT)/RT2 and taking logarithms gives: iJ (-CiE+lRVf^V^ 1 = 1 " ^ - ^ (5.17) RT2 "X V'l The values of E and k o can be obtained by repeated least squares fit of the above equation to the experimental data with the same procedure as that of the integral method. By first using an approximate E in the left hand side of the above equation, the least squares fit can therefore be performed with the FORTRAN program in Appendix D and the value of E thus obtained is used in the calculation of the values of the left hand side of the equation and successively a more accurate value of E is obtained until no improvement in the value of E takes place. The values of E and k o are therefore obtained. The volatile yield can also be calculated from Equation 5.10 with the values of E and k> obtained. 5.1.2 Multi-First-Order Reaction Model One of the principal shortcomings of the above four methods is the tacit assumption that a single activation energy and a single pre-exponential factor can adequately describe the evolution of the pyrolysis products. For the case of fossil fuel and especially pitch pyrolysis it is physically 93 realistic to expected evolution of products (for example CH4 and H 2 ) from a wide range of chemically nonequivalent sources. Hence more than one rate constant would be required to describe the pyrolysis process. Anthony and Howard [30] proposed a model to deal with this situation in an attempt to explain the coal devolatilization mechanism. Their model describes the evolution of products by a number of parallel, first order rate processes, each represented by a rate constant k. To simplify the problem, Anthony and Howard [30] assumed that the rate constants have the same pre-exponential factor, and differ only in activation energy, and that the number of parallel reactions is sufficiently large for the activation energies to be described by a Gaussian distribution function. The model and its assumptions have been described in the literature review section in more detail. Integration of the general expression in the activation range of 0 to 00 gives: 1 f « \kjtt1 5 ( 2 ^ ) 0 5 J . 6XP1 CE exp E-E^2 (5.18) dE Due to the complex and nonlinear nature of the model function, nonlinear regression must be used to fit the experimental data for E 0 , ko and s. The Levenberg-Marquart method is thus used in this work. This method adjusts ko, E 0 and s within the calculation. Some authors [52] used a fixed ko value to simplify the mathematical process and reduce the computing time. However their approach resulted in questionable kinetic parameters. This Levenberg-Marquart method is proven a good nonlinear method. It requires the derivatives of V with respect to each of the three parameters: ko, E 0 and s. In order to use the Levenberg-Marquart method, the derivatives with respect of each parameter must be derived in a specific range of activation energy, using the following general mathematical formula [109]: 94 The range of the activation energy is selected as E0-4s to E0+4s. Further increases in the range of activation energy did not improve the precision of parameters and the accuracy of the volatile prediction. These derivatives have been derived as part of this work as is shown below: dV dE0 s(2x) V* . r * ^ J kaRT2 . £ V 1 2RT\ J E-E 2 0.5 E-En J kRT2 , E0+4s^ 2RT ( ^ ) ^ + e x p ( _ 8 ) e x p | - ^ T ^ e x p ( - - ^ X l - ^ T T T ) J k„RT2 , E0-4s^ 2RT. - e X p ( - 8 ) e X P l - ^ ^ J e X P ( " ^ X ^ ] (5.19) dV V* JE„+A, ds s\27tf5 expi -S(2TT) 0.5 )E^M - ^ r - e x p ( - — X 1 - — )\^P) - 0 - 5 ( — ) r ; dE CE RT' 4V* kRT2 , E0 + 4s^ 2RT\ _ e x p ( - 8 ) e x p | - ^ T ^ e x p ( - — tf-^j 4F* 5(2^")' 0.5 exp(-8)exp^ / W 2 £ 0 - 4 5 2i?r • e X P ( ~ D T XI - ^ IT) I E0-4s' dV dk„ S(2K) 0.5 j , Ea-4s CE RT' (5.20) (5.21) A FORTRAN program was written to solve the above ODEs and the procedures outlined in Numerical Recipe [110] were followed. The FORTRAN program is listed in Appendix D. 95 5.1.3 Mathematical Methods for Overall Single First Order Reaction Model In order to use the first order model to fit the parameters, the experimental data, i.e. the measured volatile contents need to be converted according to each method into the form: Y=a+bX (5.22) 7 is the LHS of each of the single overall first order reaction methods, b is equal to -E/R, and X is the reciprocal of temperature 1/T in K. The Y and a for each method are listed in Table 5.1. Methods Y a Integral r=in RT2 J a = InftyE) (5.23a) Friedman a = In k0 (5.24a) Coats-Redfern Y= In ( ( v V - C l n 1 - - 7 \ V J RT2 V > (5.25) a = \n(k</E) (5.25a) Chen-Nuttall 7 = ln a = ln^„ (5.26a) The Y values for the integral method and Chen-Nuttall method were calculated with the first guess of E , and then iterated for the best fit for the activation E and pre-exponential factor k o . The values of E and k o for the Friedman and Coats-Redfern methods are obtained by using least squares to fit the above equations to experimental data. 5.2 Testing of the Basic Models The volatile yield was checked against the prediction of the four different methods and one model described in the previous section. Each method was used to fit to the experimental data for the pre-exponential factor, the activation energy as well as standard activation energy distribution 96 for the Anthony and Howard model. The values of the k o , E , as well as s were then used to predict the volatile yield. These values are listed for C A N M E T pitch, along with the results of kinetic parameters for Moroccan oil shale pyrolysis [111] in Table 5.2. Table 5.2 Kinetic Parameters for the Nonisothermal Pyrolysis of C A N M E T Pitch al . 50 °C/min. and 700 °C Compared with Literature Model/Method Feed k» min.'1 E kJ/mol s kJ/mol s.e.e. Integral Pitch 151.0 33.1 6.57 Friedman Pitch 130.0 32.5 6.12 Coats-Redfern Pitch 59.1 30.8 9.33 Chen-Nuttall Pitch 104.0 32.0 5.40 Coats-Redfern [ m ] Shale 56.4 32.9 5.3 Chen-Nuttall11111 Shale 37.7 31.6 5.4 Anthony-Howard Pitch 5.0xl08 114.9 14.9 6.22 Anthony-Howard11111 Shale 5.8x10s 90.4 4.6 There is a close agreement between the values obtained in this study and those obtained by Thakur and Nuttall [111] except for the k o value of the Anthony Howard model. The kinetic parameters also compare favorably with the literature [112-115] for kerogen pyrolysis to bitumen. Having obtained the kinetic parameters, the volatile yields can then be predicted using Equation 5.10, which were computed using the program in the Appendix D. The predicted and experimental results are plotted in Figure 5.1. It is clear that these models all failed to predict the volatile contents at temperatures higher than 200 °C even though the values of the kinetic parameters are well within the expected range for hydrocarbon pyrolysis and agree well with the literature, and the standard deviation (s.e.e.) is small enough. However, the s.e.e. is misleading because it is the average error (Equation 5.31). The difference between experimental data and the model prediction, is up to 30 % as is observed in Figure 5.1. It comes as no surprise that these models failed. The fact that the chemical nature of the "pitch" is changing continuously as the pyrolysis progresses has long been overlooked. Schuckler [116] reported that the activation energy increases markedly with the increase of fractional volatilization V/V*. This drastic change 97 in activation energies coupled with the unusually high preexponential factors at V/V* of 0.8 and 0.9 suggested a significant change in the pyrolysis mechanism at high volatile levels. The discrepancy at high temperature in Figure 5.1 is also supported by Thakur and Nuttall [111], who reported that two sets of kinetic parameters are required to fit their experimental data over the whole range. The Anthony and Howard [30] model takes account of the expected change of activation energy in the fashion of a Gaussian distribution with a constant pre-exponential factor. Although this assumption reflects the fact that the activation energy increases in the pyrolysis process, it does not adequately reflect the rate constant change of either C A N M E T pitch or Syncrude pitch pyrolysis quantitatively and mechanistically. The additional parameter, s, is insufficient to fit the experimental results. In examining the Y values for each overall single reaction model, it is clear that the assumption of the linear relation between Y values and X is not valid for each of the methods, as shown in Figures 5.2, 5.3, 5.4, and 5.5. Inflection points are observed at X value of 0.0014 (450 °C). This observation is in accordance to the fact that the ratio of pyrolysis dV/dT is dramatically increased at 450 °C as shown in Figures 4.1.15 and 4.1.19 in Chapter 4. Single step reaction models applied to C A N M E T pitch over the whole temperature range failed to predicted this basic feature. The fitting results of these models to Syncrude pitch showed similar results, in that the single step model failed to predict the change of pyrolysis rate and volatile yield. The results obtained in the present study indicate that the thermal pyrolysis reactions of pitches are complex to the extent that they can not be described as a single overall first order reaction. Hence the above models (the overall single reaction model analyzed with four different mathematical methods, the Anthony and Howard model analyzed with the Levenberg-Marquart nonlinear 98 regression method) can not be used to fit the T G A data of C A N M E T and Syncrude pitch pyrolysis. 0 100 200 300 400 500 600 700 800 T °C Figure 5.1 Comparison of model prediction and experimental volatile for C A N M E T pitch at 50 °C/min. and 700 °C with first order reaction models -10-• Experimental resits Fitting restits -11--12->--13--14--15--16- 1 1 1 1 1 1 1 ' r~ — • 1 1 1 1 1 1 1 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0023 1/T hC1 Figure 5.2 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with integral method 99 -15 • Experimental resiits * Fitting results 0.0310 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026 1/T rC1 Figure 5.3 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with Coats-Redfern method 1-0-• Experimental results Fitting resiits -1--2->--3- \ # -5-1 — 1 1 1 1 1 1 I T—l 1 1 1 1 — 1 ' 1 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0033 m rC 1 Figure 5.4 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with Chen-Nuttall method 4 1 1 1 1 1 1 1 1—-1 1 1 1 1 1 1 1 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026 1/T rC1 Figure 5.5 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 50 °C/min. and 700 °C with Friedman method 5.3 2-Stage First Order Reaction Model Multi-step behavior has been clearly identified in the present data as well as results of Rajeshwar [113], Thakur and Nuttall [111] and Schuckler [116]. Rajeshwar [113], Thakur and Nuttall [111] analyzed their oil shale pyrolysis data with the assumption that the thermal decomposition proceeds in two consecutive steps via a soluble bitumen intermediate, while Schuckler [116] analyzed pyrolysis data of heavy residuum fractions within several volatile conversion intervals to evaluate the kinetic parameters, which indicated a multiple step mechanism instead. Campbell et al. [117] employed nonlinear least squares fit of nonisothermal thermogravimetry data to derive kinetic parameters for a Colorado oil shale sample. Herrell and Arnold [118] report the use of nonisothermal T G A for the study of Chattanooga shale. In both these studies the kinetic data have been interpreted in terms of single step decomposition mechanisms. Such an interpretation, however seems to be contradictory to the conclusions 101 reached in most of the early studies which indicate that the thermal decomposition of oil shale kerogen proceeds in two consecutive steps. It is noted however, that the concept of reaction order and pre-exponential factor in solid-state kinetics assumes a different significance from that adopted in homogenous reaction kinetics. Topochemical considerations restrict values of the reaction order to 0, 1/2, 2/3, and 1 in solid state kinetics [119, 120]. Normally the order of pyrolysis of a sufficiently small sample is considered to be unity [121]. However, a model for a multi-step process such as that identified in the pyrolysis/thermal decomposition process is not yet available. In order to describe the pitch pyrolysis and take into account the activation energy change in the model, it is important that the model reflect those features as shown in Figures 5.6 and 5.7. Figure 5.6 shows the ratio dV/dT and the rate dV/dt vs. the remaining volatile content V*-V for different heating rates at the final temperature 800 °C for C A N M E T pitch. It is shown that the ratio dV/dT increase linearly with the increase of the remaining volatile content, up to 25% remaining volatile content, and then decreases approximately linearly with the increase of the remaining volatile content. It is also noted that the heating rate does not show any influence on the volatile yield rate, i.e. the reaction mechanism. The same value of maximum dV/dT is reached at about 25% remaining volatile content for each heating rate. This suggests that the pyrolysis process of C A N M E T pitch is chemically controlled. This further indicates that the pyrolysis takes place in two stages with differing mechanisms. In the beginning of the pyrolysis, the rate increases with temperature, and the decrease of the remaining volatile content, up to the maximum value which occurs at the remaining volatile content of 25%. Then the ratio dV/dT decreases with increasing temperature, and the decrease of remaining volatile content. Figure 5.7 shows the ratio dV/dT and the rate dV/dt vs. the remaining volatile content V*-V for different heating rates at the final temperature 800 °C for Syncrude pitch. The ratio dV/dT 102 increases roughly linearly with the increase of the remaining volatile content, up to about 25% remaining volatile content, which is the amount of the remaining volatile content also observed for the C A N M E T pitch pyrolysis. However unlike the C A N M E T pitch pyrolysis, the ratio dV/dT vs. the remaining V * - V does not show a single linear relationship to the end of the pyrolysis process. Instead, the ratio dV/dT vs. the remaining volatile content V * - V decreases approximately linearly to 55% remaining volatile content, then maintains a steady value dV/dT up to 75% remaining volatile content, and then decreases to nil. This is because there are more lower molecular weight components in the Syncrude pitch than in the C A N M E T pitch shown by the lower pentane solubles and higher H/C atomic ratio in Table 3.1. At the beginning of pyrolysis of the Syncrude pitch, the value increases with the temperature and the decrease of the remaining of the volatile content, then the ratio dV/dT maintains a steady value in the range of remaining volatile content of 55% to 70%. This suggests that lower molecular components undergo mild and rather quick chemical changes in the narrow temperature interval of 300 °C to 450 °C. The steady value in dV/dT is unlikely to be caused by physical changes, such as distillation, because the temperature is too high for distillation of most components existing in pitch samples. The relationship of dV/dT vs. V * - V of Syncrude pitch shows some similarities to that of C A N M E T pitch, suggesting a similar pyrolysis pathway, at least up to remaining volatile content of 45%. Similar patterns as that observed from results of dV/dT are also observed in the pyrolysis rate dV/dt plots Figure 5.6b and Figure 5.7b. The difference in these two graphs as a function of heating rate is as expected, and is caused by the difference of time scale of the pyrolysis process. 103 1.0-0.8-P 0.6 H 0.4H 0.2-\ o.o H • 25°C/min o 50°C/min A 1CX)0amin ° V 150°C/min A o v A/ A v • o D A T 0 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100 V * - V % Figure 5.6 The devolatilization ratio dV/dT vs. the remaining volatile at different heating rates and 800 °C for C A N M E T pitch 100 T — • — i — i — i — • — i — • — i — • — i — • — i — • — i — • — i — • — i — • — I 0 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100 V - V % Figure 5.6b The devolatilization rate dV/dt vs. the remaining volatile at different heating rates and 800 °C for C A N M E T pitch 1.0 0.8 A 0.6 H 0.44 0.24 0.0 4 A * o A o A V • " O A • • 25°C/rr«n o 500C/rnri A 1Q0°C/min V 150°C/min —j—i—|—i—|—i—|—i——|—i—|—i—i—i—|—i—i—i—i • 0 10 20 30 40 50 60 70 80 90 100 V - V % Figure 5.7 The devolatilization ratio dV/dT vs. the remaining volatile at different heating rates and 800 °C for Syncrude pitch 100-r 90-80-70-60-50-40-30-20-10-0-25°Cymin 50°C/min 100°C/min 150°amin 10 I 20 30 40 50 60 "T 70 80 90 100 V - V % Figure 5.7b The devolatilization rate dV/dt vs. the remaining volatile at different heating rates and 800 °C for Syncrude pitch 5.3.1 Multi-Stage First Order Reaction Model and its Assumptions In order to model the pitch pyrolysis data, it is assumed that the pyrolysis of the pitch samples takes place as a multi-step first order thermal decomposition with regard to the volatile content remaining in the 'residue" and is a chemically controlled process. It is also assumed that at some critical temperature, the kinetic parameters undergo change as the "reaction" shifts from one stage to the other stage of the pyrolysis process. In each stage, only one type of reaction dominates, and the kinetics parameters remain relatively constant. Therefore each stage of the reaction can be modeled as a single overall first order reaction. As the reaction proceeds and the temperature increases, the chemical nature of the 'active reacting matrix" gradually undergoes change due to the depletion of the 'bomponent" which dominated the reaction behavior in that stage. This causes the significant change of the reaction behavior. The critical temperatures at which the subsequent stage begins should be identifiable from the pyrolysis rate or weight loss ratio in the case of T G A experiments, such as are shown in Figures 5.6 and 5.7. With these assumptions in mind, the total volatile content can therefore be given by the following expression: -T = Laikoie at t=i ,-E,/RT (V-V) (5.27) T=Ct+32316 (5.28) therefore: (5.29) where: n no. of reaction stages which are first order reaction constant used to characterize the gradual change of the chemical structure of reacting residue. 106 cti =1 when Tj.i<T<Tj, otherwise cti =0 Tj critical temperature, at which reaction behavior is undergoing visible change in terms of the ratio dV/dT or rate dV/dt due to the change of reacting residue, K Ei activation energy of ith stage of reaction, J/mol koi pre-exponential factor of ith stage reaction, min"1. 5.3.2 Application of the Multi-Stage Model As observed in the T G A results of C A N M E T and Syncrude pitch pyrolysis, the pyrolysis behavior is shifted at about 450 °C into a second stage as shown in the rate plots and weight loss plot. This two step feature is also observed by Rajeshwar [113] and Thakur and Nuttall [111] for oil shale pyrolysis, and Schuckler [116] for vacuum residuum pyrolysis. The need for a two stage reaction analysis was evident by their results, but two stage analysis was not implemented. The multi-stage expression can therefore be simplified to a 2-stage pyrolysis mechanism as follows: ^ = tcaikoie-^(v'-V) (5.30) where cti=l, a2=0 when T < 450 °C cti=0, a 2=l when T > 450 °C This approach which was developed in this work, differs from the multi-parallel reactions discussed in Section 2.3: previous works have assumed that the reactions take place as mutually competing first order reactions. The 2-stage first order reaction model was applied to the overall single first order reaction methods described earlier, and fitted to experimental data of both C A N M E T and Syncrude pitch. The T G A data have been divided into two stages: stage 1 corresponding to the first stage of the pyrolysis reaction in the temperature range 50 °C (initial 107 T G A pyrolysis temperature) to 450 °C, and stage 2 corresponding to the second stage of pyrolysis reaction in the temperature range of 450 °C to the final pyrolysis temperature. Each stage was fitted to the model for the kinetic parameters for C A N M E T pitch and Syncrude pitch pyrolysis with the FORTRAN program, listed in Appendix E . One run was initially chosen for each pitch. The kinetic parameters are listed in Table 5.3 for runs at 25 °C/min and 800 °C: Table 5.3 Kinetic Parameters for the Nonisothermal Pyrolysis First stage Second stage E i kJ/mol koi min" E 2 kJ/mol ko 2 min' s.e.e. Run# Can48 C A N M E T Pitch 2-Integral 21.89 5.534 71.34 4.448* 104 1.42 2-Coats-Redfern 18.31 1.207 69.93 2.865*104 8.66 2-Chen-Nuttall 19.81 2.663 70.91 4.004* 104 4.46 2-Friedman 18.35 2.169 39.42 2.221*102 5.68 Run# Syn43 Syncrude Pitch 2-Integral 30.82 51.80 67.66 2.555*104 1.94 2-Coats-Redfern 28.92 22.28 66.14 1.597*104 5.23 2-Chen-Nuttall 29.96 38.04 67.18 2.271 *104 2.06 2-Friedman 22.43 7.251 101.5 3.875*106 9.74 The values of the E i , koi, E 2 , ko2, i.e. the kinetic parameters determined by each of the 2-stage reaction methods, are in reasonable agreement except for Friedman method. The 2-stage integral method gives the best fit for both C A N M E T and Syncrude pitch. Table 5.3 also indicates the significant change of kinetic parameters between the first stage and second stage reactions, as expected. The activation energies of the second stage are about 2 to 4 times those of the first stage. Having obtained these parameters, the volatile contents were calculated according to each method and the predicted results (Appendices E and F) were plotted, along with experimental results in Figures 5.10 and 5.13. Only the 2-stage integral method gave good predictions of the volatile content over the complete range. The other three 2-stage methods failed to predict the volatile content reasonably. The effect of the number of significant digits and a change of k in the range of ±2% was examined (Appendix I). A change of the number of significant digits or k did not affect the fitting results and the superiority of integral method to other methods. The kinetic parameters were then reported in four significant digits and the s.e.e. in three significant digits. 108 Examination of the fitted Y values for each 2-stage reaction method revealed that only the 2-stage integral method fitted the Y value calculated from experimental results as shown in Figures 5.8, 5.9, 5.11 and 5.12. The 2-stage Coats-Redfern method analysis was performed by fitting Equation 5.14 to the 2 stages of T G A experimental data, with the term 2RT/E ignored. This term, ranging from 0.293 to 0.656 for the first stage reaction and from 0.172 to 0.255 for the second stage reaction of C A N M E T pitch pyrolysis and from 0.186 to 0.416 for the first stage reaction and from 0.182 to 0.270 for the second reaction of Syncrude pitch pyrolysis, is not small enough to be ignored in the linear regression fitting for the kinetic parameters. To do so, introduces a large error, and results in erroneous kinetic parameters and therefore wrong volatile yield predictions. Given a small value of 2RT/E of 0.05, the activation energy E is 423.4 kJ/mol at 1000 °C, and 107.4 kJ/mol at 50 °C. The error thus introduced to the predicted volatile content would be negligible for this case. However, the obtained activation energy of 423.4 kJ/mol is unrealistically high. The simplification may be quite satisfactory when the thermal energy RT is significantly less than the activation energy. This case is often found for thermal decomposition of solids where either the temperature is low or the activation energy of the process is greater than RT. However, if RT tends to E , as is observed in this study, i.e., with low activation barriers and high temperatures, it is necessary to take a great number of terms in the integral analytical solution. It is clearly indicated that the assumption of 2 R T / E « 1 is not valid for the case of pitch pyrolysis. The results obtained in the present study indicate that the thermal pyrolysis reactions of pitches are complex to the extent that they can not be described by the 2-stage Coats-Redfern method. The 2-stage Friedman method analysis was performed by fitting Equation 5.15 to the 2 stages of the T G A experimental data, with the dV/dT calculated with experimental data in each stage by Equation 5.13. However the value of dV/dT has been noted to be a sensitive index of the 109 reaction rate. The error introduced into the method is even significant at the second stage of reaction. Nonlinear behavior was observed for both C A N M E T pitch and Syncrude pitch as shown in Figures 5.9 and 5.12. In the second stage, the rate of the weight loss changes dramatically as the temperature is increased, and the ratio dV/dT is less accurate. The standard error of deviation is observed as high as 5.68 for C A N M E T pitch and 9.74 for Syncrude pitch. The difference between the predicted and experimental volatile content is observed as high as 20% for C A N M E T pitch and 25% for Syncrude pitch as shown in Figures 5.10 and 5.13. The Friedman method is handicapped by the necessity of differentiating the raw T G A data, which is prone to error. Application of this method for the analysis of nonisothermal T G A data for pitch pyrolysis would lead, therefore, to incomplete, even wrong, information on the pyrolysis parameters. The 2-stage Chen-Nuttall method analysis was performed by fitting Equation 5.17 to the 2 stages of the T G A experimental data, with the iterative linear regression technique. However, the Y values for this method are rather sensitive to the activation energy. The results indicate less satisfactory fitting than the integral method, even though the standard deviation s.e.e. of this method is rather close to that of 2-stage integral method for Syncrude pitch pyrolysis. In the derivation of the Least Squares Fitting Equation 5.22, it is assumed that all measurements have the same standard deviation, s.e.e., and that the equation does fit well, then fitting for the parameters to minimize this deviation error and finally recomputing the standard deviation s.e.e. Where V i i s the experimental volatile content, Vj fit is the model predicted volatile content at data point i and n is the total number of data points. (5.31) 110 Obviously, this approach prohibits assessment of goodness-of-fit, a fact frequently missed. When the standard deviation is too large, it indicates that the fitting is not successful, as can be seen in Table 5.2 and Figure 5.1. However, a small s.e.e. does not suggest any goodness-of-fit when the standard deviation is well within the experimental error. Further examination is always necessary to ensure the validity of the modeling results, as well as of the kinetic parameters. The 2-stage integral method does not have the shortcomings mentioned above. The Y values calculated from the experimental data fitted linearly to 1/T for both C A N M E T and Syncrude pitches, as shown in Figures 5.8 and 5.11. The predicted volatile contents compare closely to the experimental results for both CANMET pitch and Syncrude pitch at all the temperature investigated in this study as shown in Figures 5.10 and 5.13, with s.e.e. 1.4 and 1.9 respectively. The results obtained therefore suggest that the thermal pyrolysis reactions of these pitches can best be described by a 2-stage integral method. This analysis method is further tested for different pyrolysis conditions for its validity. -10' - 1 H -124 >- -13-^ -144 -154 o Experimental data with 2-Integral Fitting results with 2-lnt6gral v Experimental data with 2-Coats-Redfern Fitting results with 2-Coats-Redfem — i 1 1 1 i i > I • i • i • 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 1/T K'1 Figure 5.8 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 25 °C/min. and 800 °C with 2-stage model 111 H o -1 -2 >- -3" -4--5--6--7- T o Experimental data with 2-Chen-Nuttall Fitting results with 2-Chen-Nuttall A Experimental data with 2-Frtedman Fitting results with 2-Friedman ^ 6 , 0.0010 0.0012 0.0014 0.0016 0.0018 1/T K"1 1 —r^—T 0.0020 0.0022 0.0024 Figure 5.9 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at 25 °C/min. and 800 °C with 2-stage model 90 900 T °C Figure 5.10 Comparison of model prediction and experimental volatile for C A N M E T pitch at 25 °C/min. and 800 °C with 2-stage first order reaction model 112 -10 -11 -12H -13 -14H -15' -16-o Experimental data with 2-Integral Fitting results With 2-Integral v Experimental data with 2-Coats-Redfem Fitting results with 2-Coats-Redfem 1 ' 1 r 1 • 1 ' 1 1- 1 1 1 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 1/T IC1 Figure 5.11 Comparison of model predicted Y results and experimental Y results for Syncrude pitch at 25 °C/min. and 800 °C with 2-stage model Figure 5.12 Comparison of model predicted Y results and experimental Y results for Syncrude pitch at 25 °C/min. and 800 °C with 2-stage model 100 Figure 5.13 Comparison of model prediction and experimental volatile for Syncrude pitch at 25 °C/min. and 800 °C with 2-stage first order reaction model 5.4 2-Stage First Order Reaction Model for Pitch Pyrolysis Using the least squares curve fitting of experimental data to the 2-stage integral method, the kinetic parameters E i , k o i , E 2 , k o 2 , and s.e.e. were computed using iterative techniques for a number of different experiments. The values of these parameters are listed in Table 5.4. Table 5.4 Kinetic Parameters for the Nonisothermal Pyrolysis of C A N M E T Pitch and Syncrude Pitch at 800 °C and Different Heating Rates with 2-Integral Method Run# °C/min. First stage E i kJ/mol ko i min."1 Second stage E 2 kJ/mol k o 2 min.'1 s.e.e. CANMET Pitch Can48 25 21.89 5.534 71.34 4.448* 104 1.42 Can33 50 20.90 7.649 64.47 2.444* 104 2.12 Can41 100 26.91 39.63 72.11 1.111*105 1.44 Can58 150 46.64 552.3 96.65 3.511*10* 0.97 Syncrude Pitch Syn43 25 30.82 51.80 67.66 2.554*104 1.94 Syn29 50 37.57 298.2 76.57 1.964*105 2.07 Synl8 100 44.16 1.326*103 65.51 3.523*104 2.97 Syn8 150 46.14 2.549* 103 69.80 1.031*105 2.85 114 Having obtained the values of E i , k o i , E 2 , k o 2 , from this table, the volatile content and the Y values for both C A N M E T pitch and Syncrude pitch predicted by the 2-stage integral method were computed using Equation 5.22 and Equation 5.23 respectively. The Y values obtained experimentally and predicted by the 2-stage integral method for runs at different heating rates are plotted in Figures 5.14 and 5.15, as a function of 1/T. The 2-stage integral method fits adequately and linearly the Y versus 1/T data for both C A N M E T pitch and Syncrude pitch. It is also noted that it is not safe to fit all the data from different runs to find a set of unique activation energy E and pre-exponential factor k o , regardless of the heating rates. The scatter of the data points prohibits this. It is more evidently noted in Figure 5.14 for C A N M E T pitch pyrolysis at low temperatures. However the heating rate did not show a systematic influence. Similarly, the prediction of the 2-stage integral method for the volatile content is shown in Figures 5.16 and 5.17 as a function of pyrolysis time and in Figures 5.18 and 5.19 as a function of pyrolysis temperature for runs at different heating rates, for C A N M E T pitch and Syncrude pitch respectively. The experimental data fitted the 2-stage integral method well at different heating rates over the entire temperature range. The close agreement between the experimental volatile contents and the predicted volatile contents suggests that the 2-stage integral method describes the pitch pyrolysis adequately. The magnitude of the standard deviation also supports this observation. The volatile yield rate dV/dt is also computed with the kinetic parameters obtained as shown in Table 5.4 and compared with the yield rate dV/dt calculated from the experimental data. The results are plotted in Figures 5.20 and 5.21. The close agreement between the predicted volatile yield rate and the rate calculated from experimental data is in accordance with that of the volatile content versus t curve, but is a more rigorous test. 115 -15 -t 1 1 1 1 1 1 1 1 1 1 1 r 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 1/T rC1 Figure 5.14 Comparison of model predicted Y results and experimental Y results for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method >--8 -9 -10--11 --12 -13 4 -14. -15--16 • 25 °C/min experimental results 25 °C/min fitting results (2-lntegral) ® 50 °C/mln experimental results SO "C/min fitting results (2-)ntegral) K 100 °C/min experimental results 100 °C/min fitting results (2-Integral) O 150 °C/min experimental results - 150 °C/min fitting results (2-lntegral) — i 1 1 1 1 1 1 1 1 1 1 1 1 1 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 1/T K" -1 Figure 5.15 Comparison of model predicted Y results and experimental Y results for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 116 90 T • 1 • 1 > 1 • 1 • 1 • r 0 5 10 15 20 25 30 t min Figure 5.16 Comparison of model prediction and experimental volatile for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method Figure 5.17 Comparison of model prediction and experimental volatile for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 90 Figure 5.18 Comparison of model prediction and experimental volatile for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method 100 T °C Figure 5.19 Comparison of model prediction and experimental volatile for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method Figure 5.20 Comparison of model prediction dV/dt and experimental dV/dt for C A N M E T pitch at different heating rates and 800 °C with 2-stage integral method 110-100-90-80-70-60-50-40-30-20-10-0-• 25 "C/mln experimental results © 50 °C/mln experimental results ta 100 "C/min experimental results O 150 °C/mln experimental results 25 °C/mIn fitting resutls (2-lntograO 50 °C/mln fitting results (2-lntegraO 100 °C/mln fitting results (2-lntegral) ISO "C/min fitting results (2-lntegrar) I 10 1 15 t min i 20 25 -1— 30 Figure 5.21 Comparison of model prediction dV/dt and experimental dV/dt for Syncrude pitch at different heating rates and 800 °C with 2-stage integral method 5.5 Testing of the 2-Stage Integral Method In order to further examine the validity of the 2-stage integral method, it was used to predict the volatile yield at different pyrolysis conditions, other than the runs used to fit for the kinetic parameters. The kinetic parameters obtained at conditions of 25, 50, 100 and 150 °C/min and final temperature 800 °C were used to fit runs at the same heating rates but different final temperature ranging from 750 °C to 950 °C for C A N M E T pitch and Syncrude pitch respectively. The kinetic parameters at heating rate 100 °C/min and final temperature 800 °C were used to predict the volatile yield for C A N M E T pitch runs at the same heating rate but different final temperature 750, 850 and 950 °C, while the kinetic parameters at heating rate 50 °C/min and 800 °C were used to predict the volatile yield for Syncrude pitch runs at the same heating rate but final temperature of 750, 850 and 950 °C. The experimental conditions are listed in Table 5.5. The s.e.e. values are also listed in the table as the indication of the goodness of the model prediction. The s.e.e values calculated with other methods are also listed in the table for comparison. Table 5.5 Experimental Conditions and Model Predicted Results of C A N M E T Pitch and Syncrude Pitch Pyrolysis s.e.e. Run# T °C V* Integral C-R C-N F M C A N M E T Pitch at 100 °C/min Can42 750 79.54 2.05 4.24 1.95 4.60 Can40 850 79.01 4.87 2.70 4.09 3.12 Can52 950 81.23 1.39 5.25 2.28 4.94 Syncrude Pitch at 50 °C/min Syn27 750 90.96 2.57 5.38 2.63 9.07 Syn32 850 90.61 2.04 5.15 2.01 8.64 Syn33 950 91.01 4.49 8.75 5.26 12.19 Integral=2-stage integral method, C-R=2-stage Coats-Redfern method, C-N= 2-stage Chen-Nuttall method, FM= 2-stage Friedman method It is observed from the s.e.e. values that the prediction is in good agreement with the experimental volatile content. Further examination of Figure 5.22 to Figure 5.27 proved that the 120 model indeed predicted the volatile content well. The prediction of C A N M E T pitch pyrolysis volatile content was calculated with the kinetic parameters obtained at 100 °C/min and 800 °C and plotted in Figures 5.22, 5.23, and 5.24, along with the experimental volatile content for comparison. The prediction of Syncrude pitch pyrolysis volatile content was calculated with the kinetic parameters obtained at 50 °C/min and 800 °C and plotted in Figures 5.25, 5.26, 5.27, along with the experimental volatile contents for comparison. It is shown that the agreement between the prediction and experimental data is very good, which is supported by the s.e.e. values. This indicates that the 2-stage integral method can describe the pitch pyrolysis, and the kinetic parameters derived from this model are independent of pyrolysis conditions such as final temperature. The results thus support the assumption that pyrolysis is a chemical reaction controlled process. 90 Figure 5.22 Comparison of model prediction and experimental volatile for C A N M E T pitch at 100 °C/min and 750 °C with 2-stage integral method 121 90 T °C Figure 5.23 Comparison of model prediction and experimental volatile for C A N M E T pitch at 100 °C/min and 850 °C with 2-stage integral method 90 T 03 Figure 5.24 Comparison of model prediction and experimental volatile for C A N M E T pitch at 100 °C/min and 950 °C with 2-stage integral method 4 — i — • — i — • — i — • — j — • — i — • — i — • — i — • — i — • — i — i — | 0 100 2 0 0 3 0 0 4 0 3 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 T °C Figure 5.25 Comparison of model prediction and experimental volatile for Syncrude pitch at 50 °C/min and 750 °C with 2-stage integral method 100 A—l—i—i—•—i—•—i—•—i—•—i—•—i—•—i—•—i—>—i—•—| 0 100 2 0 0 3 0 0 4 0 3 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1000 T <C Figure 5.26 Comparison of model prediction and experimental volatile for Syncrude pitch at 50 °C/min and 850 °C with 2-stage integral method A—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—|—i—| 0 100 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1000 1100 T °C Figure 5.27 Comparison of model prediction and experimental volatile for Syncrude pitch at 50 °C/min and 950 °C with 2-stage integral method 5.6 Discussion and Conclusions Although the pattern of volatile release for pitches pyrolyzed under T G A conditions is complex, an adequate description of the kinetics is possible. The pyrolysis takes place in 2 stages, with a first stage of low activation energy barrier and lower pre-exponential factor, and the second stage of higher activation energy and pre-exponential factor. It is recommended that the process be modeled with a 2-stage reaction model with the integral method analysis. It is demonstrated that the overall single stage reaction model with analysis by the integral, Coats-Redfern, Chen-Nuttall and Friedman methods, as well as Anthony and Howard's distributed activation energy model, are not sufficient to fit the T G A pyrolysis data and predict the course of the pitch pyrolysis process. It is also found that the single stage reaction model analyzed with these methods does not reproduce the values of activation energy and pre-exponential factors when the pitch T G A pyrolysis data at different conditions are taken for computation. This 124 phenomena has also been observed by Dahr [122], Natu [123] and Carrasco [62]. By contrast, the two-stage first order model with constants fitted by the integral analysis method provides a good description of the volatilization behavior. The kinetic expressions obtained represent the global process, and are intended for numerical modeling or engineering calculations. These parameters have only limited validity and can not be used to pin-point the rate controlling mechanism. The true reaction chemistry undoubtedly is much more complex than the multiple stage first order reactions assumed above. It is known that the pyrolysis of any hydrocarbon residual is a very intricate and complex phenomena composed of various elementary reactions that are different to analyze separately and whose quantitative contributions to the global pyrolysis process are virtually impossible to evaluate. For these reasons, even if the overall process has no ideal significance with regard to the reaction mechanism, it is useful as a means of quantifying the rate of reaction and for design purposes. Caution must therefore be used to avoid over-interpreting these rate equations in terms of the fundamental microscopic chemistry of the system. The apparent activation energies calculated from this study for pitch fall approximately midway between values reported by others for oil shale decomposition. Values of 31.6 kJ/mol, 38.4 kJ/mol and 62.3 kJ/mol [111], 108.1^kJ/mol and 209.5^ kJ/mol [113] are reported. Since the strength of typical single bonds to carbon are about 335-420 kJ/mol, the question often arises as to why the activation energies for thermal decomposition of such residues are so much lower. The answer is that the activation energies for decomposition of heterogeneous organic material can not generally be interpreted in terms of a specific bond-breaking process (e.g. C-C vs. C-H vs. C-0 etc.). Often, activation energies in the ranges of 42-84 kJ/mol are reported with an indication that these are essentially effective activation energies for a sum of different reactions that occur simultaneously. When there are radicals involved in the pyrolysis, the activation energy 125 can be reduced to as low as 21-42 kJ/mol [22]. The activation energies for each reaction may be much higher. As a result, the development of a detailed mechanistic picture on the basis of a few effective activation energies is usually fruitless. Heck and DiGuiseppi [124] observed that the critical element of 2-stage hydrocracking of residuum is believed to be the balancing of the cracking and hydrogenation activities during the initial 50% conversion. It is during this initial conversion that the residuum is most active, free radicals are formed at the highest rate and hydrogen demand is highest. Gray et al. [125] found that the initial conversion of asphaltenes occurs largely as a result of cracking relatively long aliphatic fragments away from a largely aromatic core. The aliphatic/aromatic bonds broken during this initial conversion process are relatively facile, especially when the aliphatic chains are longer than one or two carbon atoms. The conversion path is best illustrated [124] by the relatively rapid decrease in average molecular size and increase in aromaticity that occurs during the initial cracking of the large aliphatic moieties away from the largely aromatic core. The remaining conversion, which proceeds more slowly, involves the cracking away of smaller aliphatic moieties. Stubington's results [126] using bagasse suggested that the pyrolysis mechanism changed at certain pyrolysis level, which can be expressed as time, conversion of carbon or the remaining volatile content. At a certain devolatilization level, a set of different kinetic parameters is required to describe the change of the pyrolysis mechanism. These findings support the 2-stage pitch pyrolysis mechanism with the low activation energy barrier for the first stage and high activation energy barrier for the second stage. The 2-stage model reflects changes in the chemical constitution or structures as conversion proceeds by using two values of activation energy and pre-exponential factor. This feature is essential to describe pitch dependence of devolatilization rates on the remaining volatile content. The abundance of radicals in the bridges of non-aromatics accelerates their conversion 126 rates, which has two ramifications: First, gases are expelled rapidly at low temperature and, second, extensive cross-linking inhibits the production of tar precursors [127]. In contrast, bridges in aromatics have very little radical content, so they decompose at relatively high temperatures at significantly slower rates. The transition between these two limiting cases is a sharp one, occurring at a certain temperature (remaining volatile content) level. Consequently for non-aromatic and aromatic components, small differences in the radical content causes appreciable difference in rates and yields, compounding the acute sensitivity of the labile bridge fraction to carbon content. These findings in the present study clearly demonstrated that the chemical constitution of pitch affects product evolution rates and yield at any stage of devolatilization. The magnitude of the activation energies in both stages suggests that the pyrolysis of pitch was kinetically controlled under the reaction conditions studied. The dependence of dV/dT on V * - V is also in accordance with that. In summary, the overall single first order model and the Gaussian distributed activation energy model are not adequate to describe pyrolysis of C A N M E T and Syncrude pitches due to the mechanism change of the pitch pyrolysis at an intermediate temperature, and high volatile yield. These models have been developed for relatively low volatile content material and processes such as coal pyrolysis. The 2-stage first order reaction model with the integral analysis method is proven adequate to describe the pitch pyrolysis process and gives lower activation energy and preexponential factor for the first stage, and higher activation energy and preexponential factor for the second stage of pyrolysis. These kinetic parameters can be extrapolated to different temperature range. However, the compensation effect of the kinetic parameters is observed and is discussed in the next chapter. J 127 Chapter 6 Compensation Effect of the Kinetic Parameters It was noted in applying the different analysis methods to the pyrolysis kinetics, that when the activation energy was low, the pre-exponential factor was also low. The mutual dependence of the activation energy E and the pre-exponential factor k„, termed the compensation effect, has been reported for catalytic kinetics [68, 69], thermal aging process of polymers [128-130], and some CaC204*H.20 pyrolysis processes [86] as described in Chapter 2. The mutual dependence of the kinetic parameters does not occur in simple reactions. The compensation effect is associated with the following two criteria: A) The logarithm of the pre-exponential factor, lnko, is linearly proportional to the activation energy E , given by the following equation, where the a and P are the compensation constants: \nk0 = a + 0 E (6.1) B) The logarithm of the reaction rate constant, Ink, is linearly proportional to the reciprocal of the reaction temperature 1/T, and all the Ink vs. 1/T lines generated in different temperature programmed experiments intersect at one point Ti, the isokinetic temperature. This results in the following equation, where the a and b are isokinetic constants: \nk = a + bj (6.2) As pointed out in the literature review, the second criterion is a special case of the first one. The existence of the second criterion guarantees the existence of the first criterion and the compensation effect. However, the existence of the first criterion guarantees the existence of the compensation effect, but not the second criterion. The most common identification of a compensation effect comes from the observation of a linear correlation between the activation energy and the logarithm of the pre-exponential factor 128 [66]. The application of statistical methods to the recognition of a linear relationship between values of the activation energy and the logarithm of the pre-exponential factor has been described by Exner [100], who suggests that a single point of intersection in the Ink vs. 1/T plots could be used for a sound statistical test, since Ink and T are statistically independent. This is the basis of the isokinetic relationship. It is evident that for a set of experimental data one may infer from such a point of intersection the linearity between the activation energy and the logarithm of the pre-exponential factor, but the reverse may not be true. In this work, the compensation effect was investigated at different pyrolysis conditions and for different single overall first reaction models and 2-stage first order model for both CANMET and Syncrude pitch. The accuracy of the kinetic parameters was also examined, comparing the resulting standard deviation error (s.e.e.). The possibility of the existence of one unique set of these kinetic parameters was therefore investigated. 6.1 Compensation Effect of Kinetic Parameters Derived from Overall First Order Model Since the single overall first order reaction model (analyzed with integral, Coats-Redfern, Chen-Nuttall and Friedman methods) was inadequate to describe the pyrolysis kinetics, results on compensation effect are not discussed in detail. Figures 6.1 and 6.2 show that a good linear correlation of Equation 6.1 was obtained, however, Equation 6.2 was not met since an isokinetic temperature within the operating temperature range was not found. This compensation effect has also been observed in the studies of thermal degradation of polymers with different mathematical methods [130]. The single overall first order model analyzed by the different mathematical methods in this work did not reproduce the kinetic parameters, and these parameters derived from each of these methods follow the compensation effect. 129 8 • Canmet pitch TGA Pyrolysis Friedman method lnk0 = -8.781 +0.4184E -•-Integral method Chen-Nuttall method Coats-Redfern method - • — i — • 1 • — I — i — | — i — i • — I — i — | • — | 1 1 1- . 30.0 30.5 31.0 31.5 320 325 33.0 33.5 34.0 34.5 35.0 EkJ/mol Figure 6.1 C A N M E T pitch T G A pyrolysis kinetic parameters at 50 °C/min and 700 °C with different methods (overall first order) Figure 6.2 C A N M E T pitch pyrolysis reaction rate constant as a function of temperature at heating rate 50 °C/min and final temperature 700 °C 6.2 Compensation Effect of Kinetic Parameters Derived from 2-Stage Reaction Model The compensation effect for the 2-stage reaction model analyzed with different methods, at different heating rates such as 25, 50, 100 and 150 °C/min and final temperature of 800 °C, was investigated and the values of the compensation effect parameters (Equation 6.1) for the first stage: a! and Pi, for the second stage a 2 and p 2, are listed in Tables 6.1 and 6.2 for C A N M E T and Syncrude pitch. The square of the regression coefficients, R 2 , are also listed in these tables indicting the linearity of the fitting. Four data points derived via each 2-stage method were used in the fitting of each run. Table 6.1 Compensation Parameters for C A N M E T Pitch Pyrolysis at Different Heatin g Rates and 800 °C First stage Second stage Method CCi PinO"4 R 2 ct2 P^IO"4 R 2 Integral -1.544 1.711 0.952 0.008 1.558 0.978 Coats-Redfern -2.824 1.930 0.959 -0.406 1.586 0.980 Chen-Nuttall -2.128 1.826 0.956 -0.087 1.566 0.979 Friedman -2.444 1.980 0.984 -1.169 1.693 0.999 All methods -2.360 1.903 0.957 -0.789 1.650 0.991 Table 6.2 Compensation Parameters for Syncrude Pitch Pyrolysis at Different Heatin g Rates and 800 °C First stage Second stage Method <Xi Pi*™"4 R 2 a 2 P^IO"4 R 2 Integral -3.718 2.492 0.998 -1.220 1.761 0.795 Coats-Redfern -4.367 2.591 0.998 -1.554 1.781 0.809 Chen-Nuttall -3.923 2.530 0.998 -1.278 1.765 0.801 Friedman -4.361 2.852 0.998 0.705 1.471 0.977 All methods -3.308 2.384 0.979 0.516 1.497 0.961 Figures 6.3 and 6.4 show that the compensation effect Equation 6.1 fits data for each method at each stage of pyrolysis adequately. For all the cases investigated for C A N M E T pitch the R 2 coefficient is greater than 0.95, whereas for Syncrude pitch the R 2 is greater than 0.998 for the first stage and greater than 0.795 for the second stage. 131 20 18 C 'E 10 • 1 st stage Integral 2nd stage Integral j» o 1st stage Coats-Redfern >•* © 2nd stage Coats-Redfern A 1 st stage Chen-Nuttall A 2nd stage Chen-Nuttall . V 1 st stage Friedman J§r^ 2nd stage Friedman y &' — i 1 1 1 1 1 i 1— 20000 40000 60000 80000 E J/mol 100000 120000 Figure 6.3 C A N M E T pitch T G A pyrolysis kinetic parameters at different heating rates and 800 °C with 2-stage first order model analyzed with different methods c E 20 18-16-14-12-10 : i 4 2-j A V 1st stage Integral 2nd stage Integral 1 st stage Coats-Redfern 2nd stage Coats-Redfern 1st stage Chen-Nuttall 2nd stae Chen-Nuttall 1 st stage Friedman 2nd stage Friedman 20000 I — 40000 60000 E J/mol 80000 I 100000 120000 Figure 6.4 Syncrude pitch T G A pyrolysis kinetic parameters at different heating rates and 800 °C with 2-stage first order model analyzed with different methods 20-1 18-16-14-12-10-E 8-±? 6-4-2-0-o 1st stage reaction • 2nd stags reaction Ink =-0.7886 + 1.650*1 ( P E O lnk0 = -2.360 + 1.903*1 O^E — i — i \ | — r — T ' " i i | i i i i — [ — 1 — 1 — r ~ T — J — l " • I " I I I I I 1 "T "1 0 20000 40000 60000 80000 100000 120000 E J/mol Figure 6.5 C A N M E T pitch T G A pyrolysis kinetic parameters at different heating rates and 800 °C with 2-stage first order model 20-18-16-14-12-• c 10-8H 6-4-2-0-O 1st stage reaction • 2nd stage reaction Ink =0.5161 + 1.496*1 O^E ^ O / lnk0 =-3.308 +2.384*1 O^E 80000 100000 120000 E J/mol Figure 6.6 Syncrude pitch TGA pyrolysis kinetic parameters at different heating rates and at 800 °C with 2-stage first order model The regression results for parameters via 2-stage model are plotted in Figure 6.5 and Figure 6.6 for C A N M E T and Syncrude pitch respectively. Clearly one set of constants fits data from all methods in each stage, with R 2 coefficient is greater than 0.957 for all the cases investigated. The physical meaning of the compensation effect parameters a and P has been a topic of research and it is beyond the scope of this research to explore it in detail. However, it is noticed that the parameter p is rather constant for each stage of the pyrolysis and the parameter p of the first stage is larger than the P parameter of the second stage, for both of the two pitches studied. By contrast the parameter a changes with the model over a large range. For decarboxylation of solids, Muraishi [65] has stated that whereas the parameter P is related to the bond strength of the metal leaving group in the three dicarboxylates investigated in his work, the parameter a is related to the structure of and defects in the starting material or to the mobility of the crystal lattice in the dicarboxylate thermal decomposition. The parameter a obtained in the present work showed complex tendencies among the 2-stage of pyrolysis process and different mathematical methods used with the 2 stage model to derive the kinetic parameters. However, the parameter a of the first stage of the pyrolysis process of both pitches studied is smaller than that of the second stage of the pyrolysis process, which may suggest the chemical structure difference between these two stages. This difference of the chemical structure at different level of pyrolysis has been also observed experimentally [125]. Although there are slight differences in the parameter p obtained from the different methods, the parameter P obtained may indicate similar " bond strength" and therefore suggest there is one type of reaction dominant in each stage. The bond strength is therefore different according to the parameter P between the first stage and second stage. 134 The R 2 coefficient of the first stage of Syncrude pitch is the highest in all the cases studied. This is in good agreement with the results as shown in Figure 5.7 in Chapter 5. The experimental results clearly show a consecutive pyrolysis process: at the beginning of the pyrolysis, the ratio dV/dT increases with the decrease of the V * - V and up to a point where dV/dT kept roughly the same before going into the next stage of pyrolysis. In the modeling process, this consecutive process was not divided into more detailed stages for the simplicity of modeling and limiting the parameters introduced into the kinetic model due to the fact that the yield of volatile at this stage is much less than that at lower V * - V . This experimental evidence supports a common belief that a consecutive process is one of causes of the compensation effect. This is further supported by the results with C A N M E T pitch. When the pyrolysis process was fitted with the overall single first order model, the linear regression of the kinetic parameter k o and E to the compensation equation resulted in a R 2 of 0.986. When the pyrolysis experimental results were fitted with 2-stage model, the linear regression of the kinetic parameter k o and E for each stage and each method resulted in R 2 coefficient from 0.952 to 0.999. The R 2 coefficient is smaller than that obtained from the overall single first order model, except for the second stage of the Friedman method for C A N M E T pitch pyrolysis. It is, therefore, evident that the 2 stage behavior in the overall single first order model resulted in the higher R 2 coefficient. Similarly the lower R 2 coefficient derived for the second stage kinetic parameters k o and E of Syncrude pitch pyrolysis suggests a lesser degree of multi-stage behavior, i.e., lesser heterogeneity of reactions. The activation energy of the second stage of Syncrude pitch pyrolysis changes over a very small range with changes of pyrolysis conditions and methods used to derive this parameter. The compensation effect was also assessed via Equation 6.2, and the results calculated with the kinetic parameters derived from 2-stage reaction model analyzed with integral method are shown in Figure 6.7 and Figure 6.8 for C A N M E T and Syncrude pitch respectively, as a 135 function of the reciprocal of the pyrolysis temperature 1/T. The logarithm of reaction rate constants at different heating rates shows linear relationship with the reciprocal temperature 1/T in each temperature range, however the lines of Ink ~ 1/T do not intersect at one single point for either pitch in both stages. The isokinetic temperature was therefore not observed. This suggests that the second criterion for the compensation effect does not hold for C A N M E T and Syncrude pitch pyrolysis. As described by Krai [68, 69], the second criterion is a special case, and the existence of the compensation effect does not guarantee it to be true. Similarly, calculations were done with the kinetic parameters derived from Coats-Redfern, Chen-Nuttall and Friedman methods as found in Appendix G. As before, the isokinetic temperature was not clearly observed. The inaccuracy of these methods used to derive the kinetic parameters has been cited as a cause of the compensation effect, however the less accurate models did not result in an isokinetic temperature. It is worth noting that although the Ink ~ 1/T lines appeared to intersect at a single point during the first stage pyrolysis of Syncrude pitch, with all 2-stage methods, a narrow temperature range was observed rather than a single point. 1/T1000-1*K-1 Figure 6.7 C A N M E T pitch pyrolysis reaction rate constant as a function of temperature at different heating rates and final temperature 800 °C with 2-stage reaction model analyzed with integral method 136 6 T 4-2-0 -T -2-c E A . -8--10-1/T 1000 - 1 * K ' 1 Figure 6.8 Syncrude pitch pyrolysis reaction rate constant as a function of temperature at different heating rates and final temperature 800 °C with 2-stage reaction model analyzed with integral method 6.3 The Relationship of Standard Errors and Kinetic Parameters Even though the kinetic parameters Inko and E follow a linear relationship, the standard deviation errors (s.e.e.) of the experimental volatile content and the model predicted volatile yield via different pairs of the kinetic parameters were not identical. The standard deviation error was calculated with the related model and the kinetic parameters (Appendix E), and is plotted against the activation energy obtained with the different analysis methods and at different pyrolysis conditions in Figures 6.9 and 6.10. For CANMET pitch (Figure 6.9), the s.e.e. for the first stage decreases with the increase of the activation energy and passes through a weak minimum. This minimum is not really well defined. For the second stage pyrolysis of C A N M E T pitch pyrolysis, a minimum was also observed. It is evident that there is an optimal value of activation energy for each stage of pyrolysis reaction at which minimum s.e.e. can be achieved. Because lnko is linearly 137 proportional to E , there exists a relative value of k o . Therefore there is an unique set of optimal values of E and k o for the first and second stage reaction which minimize the s.e.e. For C A N M E T pitch these minimal values for the pyrolysis kinetic parameters obtained from Figure 6.9 are: E,=40.2 kJ/mol, koi=197.4 min'1, E2=86.6 kJ/mol, ko2=7.31* 10s min'1. It should be noted that for the first stage, a range of values of E could be applied. For Syncrude pitch pyrolysis process as shown in Figure 6.10, the trends are different in that no minima are evident, but optimal values for the pyrolysis kinetic parameters can be obtained as: E,=45.7 kJ/mol, koi=1.96*103 min'1, E2=67.6 kJ/mol, ko2=4.19*104 min'1. The activation energy values are within the wide range of published kinetic parameters [127] in which an activation energy range of 42-84 kJ/mol was reported for kerogen-to-bitumen pyrolysis. It is also worth noting that these values are very close to the kinetic parameter values derived with integral method for each stage. With the above kinetic parameters, the volatile yields were calculated for different pyrolysis conditions with Equation 5.10 in Chapter 5 and the results are listed in Appendix H and plotted in Figures 6.11 to 6.14. With the predicted volatile yield, the s.e.e. can therefore be calculated. The results are listed in Tables 6.3 and 6.4 are plotted in Figures 6.11 to 6.14. 138 • Rrststag ie reaction e Seconds tags reaction • \ a V * • B • ft^ a 20000 40000 60000 E J/mol 80000 100000 12D000 Figure 6.9 C A N M E T pitch T G A pyrolysis s.e.e. as a function of E at different conditions and with different methods Figure 6.10 Syncrude pitch T G A pyrolysis s.e.e. as a function of E at different conditions and different methods Figures 6.11 and 6.12 show that the predicted volatile contents at high heating rates and high temperature are in very good agreement with the experimental values, while the prediction at low temperatures for both samples and at the low heating rate of 25 °C/min for C A N M E T pitch is acceptable. Figures 6.13 and 6.14 also show that at different final temperatures the predicted volatile contents at high temperature for each run are in very good agreement with the experimental volatile yields. The prediction is generally better than that shown in Figures 6.11 and 6.12, and much better than the prediction of the overall single reaction model as shown in Figure 5.1. It is therefore possible to predict the volatile content with one set of unique kinetic parameters for the 2 stage reaction model regardless of the pyrolysis conditions and the methods used to fit the experimental results. Table 6.3 Experimental Conditions and Model Predicted Results of C A N M E T Pitch and Syncrude Pitch Pyrolysis Heating One set k o Integral Run# Rate°C/min V * % E , s.e.e s.e.e C A N M E T pitch at 800 °C Can48 25 80.84 4.10 1.42 Can33 50 80.79 5.62 2.12 Can41 100 79.30 8.69 1.44 Can58 150 77.59 1.57 0.97 Syncrude Pitch at 800 °C Syn43 25 91.03 10.45 1.94 Syn29 50 90.07 5.62 2.07 Synl8 100 90.58 4.01 2.97 Syn8 150 90.62 9.98 2.85 140 90H t min Figure 6.11 Comparison of experimental data and model prediction for C A N M E T pitch at different heating rates and 800 °C with a single set of kinetic parameters 1 0 0 90 80 70-60-O > 30-I 2o4 10 OH 0 • 25 CArin, cDfjuiutaU data 9 50°C/rrin, efxrirrerfe] data • 103°C/mn operimerta! data O 150°C/rrin, aperimerti data fitting resiits I 10 15 t min -r— 20 25 30 Figure 6.12 Comparison of experimental data and model prediction for Syncrude pitch at different heating rates and 800 °C with a single set of kinetic parameters Table 6.4 Experimental Conditions and Model Predicted One set k o Integral Run# T °C V * % E , s.e.e. s.e.e C A N M E T Pitch at 100 °C/min Can42 750 79.54 8.13 2.05 Can40 850 79.01 4.34 4.87 Can52 950 81.23 8.93 1.39 Syncrude Pitch at 50 °C/min Syn27 750 90.96 5.40 2.57 Syn32 850 90.61 5.94 2.04 Syn33 950 91.01 5.97 4.49 100-90-80-70-60-^ 50-| 40-30' 20' 10 0 O 750°C. Experimental dat 750°C. Model prediction 250 500 750 1000 O 850°C, Experiment oldat )°C. Model prediction 0 O 950°C. Experiment oldat 950°C, Model prediction o o o 250 500 750 1000 T °C I • I ' I 1 I . 0 250 500 750 1000 Figure 6.13 Comparison of model prediction and experimental volatile content for C A N M E T pitch at 100 °C/min and 750 °C, 850 °C, and 950 °C respectively 'l 1 I ' I • I • I 'l • I ' I • I ' I 11 ' I 1 I ' I 1 I 0 250 500 750 1000 0 250 500 750 1000 0 250 500 750 1000 T °C Figure 6.14 Comparison of model prediction and experimental volatile content for Syncrude pitch at 50 °C/min and 750 °C, 850 °C and 950 °C respectively 6.4 Discussion and Conclusion Clearly for both C A N M E T and Syncrude pitches, evidence for the compensation effect Equation 6.1 was obtained for the kinetic parameters derived from the single first order reaction model, and the kinetic parameters derived from each stage of the 2-stage kinetic model with different mathematical methods. It seems that the compensation effect is caused by the heating rates for each method used to analyzed the kinetic model equation, as shown in Figures 6.3 and 6.4. Since for these experiments were performed at the same atmosphere and roughly the same sample weight for each pitch type, these physico-chemical factors are therefore excluded. However, one set of compensation effect constants was found to be able to fit all the kinetic parameters derived from the 2-stage kinetic model with all the mathematical methods, as shown in Figures 6.5 and 6.6. This further indicates that the effects of heating rates and mathematical 143 methods are inseparable factors causing the kinetic compensation effect. Equation 6.2 was not met in the temperature range studied. The isokinetic temperature T; was therefore not observed as a result. Such an isokinetic temperature was not observed either for TVC-70 polymer thermal degradation [129]. The isokinetic temperature is more commonly observed in the catalysis kinetics and is often explained in terms of the temperature at which the catalyst was prepared [68, 69]. It is not surprising that the isokinetic temperature is not observed in pitch pyrolysis kinetics, since the temperature at which the pitch was prepared, has a totally different meaning. It seems safe to say that the measuring conditions and the methods used to analyze the kinetic models cause the kinetic compensation effect in this work and these factors are inseparable. This work however is not intended to investigate this effect in detail and identify the underlying factors as well as the mechanism of the kinetic compensation effect. The Arrhenius equation of the kinetic parameters, which is rigorously valid for homogeneous reactions, is widely used for heterogeneous reactions, such as hydrocarbon pyrolysis, although such an extrapolation is not justified. Indeed, heterogeneous systems are characterized by supplementary problems due to complication of heterogeneous reactions. It has been shown [130] that for a series of related heterogeneous reactions, the compensation effect holds between the activation energy and pre-exponential factors. Compensation effects occur either for a series of reactions or for a given reaction when the operational parameters are changed. According to Garn [131-133], the common element of the reported cases of compensation effects is the existence of a main reaction which remains unaltered, in which a parameter regarded as a secondary factor changes the modification of the reaction rate with temperature. Audouin and Verdu [128] reported that a compensation effect appears only when the overall kinetic equation for thermal degradation is composed of many steps. It has been suggested that for such system at each moment a new material undergoes degradation and that 144 each reaction is characterized by a specific value of the activation energy. In catalytic reactions, the reaction rates have been proven associated with the distribution and concentration of active sites [134, 135]. For pyrolysis, the activation energy E value has been observed to change with its conversion in nonisothermal experiments with oil shale [116], and in the two stages of pyrolysis in the present study. Pitch pyrolysis is such a process in which a series of reactions occur consecutively and/or concurrently, in the meantime the concentration of the active radicals decreases with the extent of reaction. When an inappropriate method is used to derive the two kinetic parameters, the error of one parameter caused by the method would be dumped to the other. However, these two parameters are related through the Arrhenius relationship. Since the pyrolysis rate is dependent on the remaining volatile content (or the reactive residue structure), the pyrolysis rate constants should be independent of the mathematical methods. The change of one parameter would be compensated to give the same rate. The existence of the compensation effect can therefore be attested. Similarly at different heating rates, the same "component" may undergo pyrolysis at different temperatures under T G A conditions. When one method is used to derive the kinetic parameters, the accuracy of the parameters to reflect the "true kinetics of that component" may be affected. Again the average kinetic behavior is retained by the Arrhenius relationship and consequently causing the compensation effect. However, the importance of the compensation effect may lie in the fact that the kinetic parameters ko and E are interrelated for the pitch pyrolysis. This requires that the kinetic parameters of pitch pyrolysis be interpreted and compared with as a pair. One of the parameters may not be able to describe the whole picture of the pitch pyrolysis process. Care must also be exercised when using the reported kinetic parameters in research or design work. 145 It is also noted that these methods did not reproduce the kinetic parameters ko and E at the operating conditions studied. The standard deviation caused by each pair of these parameters is not identical and it is possible to minimize the standard deviation through choosing the best pair of kinetic parameters ko and E . 146 Chapter 7 Conclusions and Recommendations At the onset of the research, no adequate data were available for the kinetics of the pitch pyrolysis and no mathematical models were available for the pitch pyrolysis mechanism. The primary goal of this research has been fulfilled in that the kinetic data for these processes have been outlined and a relevant kinetic model proposed. 7.1 S U M M A R Y OF FINDINGS The principal observations and conclusions resulting from this study are listed below: 1. Heating rates were found to slightly affect the weight loss at a given temperature. The temperature history is the significant factor governing the extent to which the reactions take place and produce the weight loss. The devolatilization step is not instantaneous, as little weight loss occurred at the highest heating rates where the heating time took of the order of a few seconds. 2. The pyrolysis takes place in stages. At temperatures below 150 °C, there is little weight loss. The weight loss takes place in two following stages with two different, distinct patterns of chemical and physical change. In the first stage, the rate of the total weight loss increased with the temperature. In the second stage, the rate decreased with the temperature. These features appear unique to pitch pyrolysis, as they have not been reported for coal or shale pyrolysis. 3. The total weight loss (volatile yield) using thermogravimetric analysis decreased slightly with the increase of sample weight over the range of 3 to 17 mg for both C A N M E T pitch and Syncrude pitch. More than 80% of residue conversion was achieved for C A N M E T pitch, while more than 90% of residue conversion was achieved for Syncrude pitch. 147 4. Under Pyroprobe pyrolysis conditions, the pyrolysis time is a very important operating parameter. At the highest heating rate (300,000 °C/min) employed in this study, little pyrolysis was observed for both C A N M E T and Syncrude pitches up to 700 °C, while at heating rate of 600 °C/min, the weight loss was rather significant when the final temperature was just reached (0 min isothermal reaction time). Higher heating rates exhibit complex effects on the weight loss and the secondary pyrolysis of the volatiles. 5. The most abundant component of the volatiles is shown experimentally to be hydrocarbons with less than the 10 carbons, which is grouped as single lump, C 7 , in this study. At each heating rate and final temperature, the amount of C 7 became significant at temperatures higher than 700 °C. As high as 50% volatile yield of this group in the total volatiles was detected for C A N M E T pitch and secondary reaction is observed at heating rate 3000 °C/min. At the Pyroprobe pyrolysis conditions, the volatiles may undergo secondary pyrolysis when being purged through the quartz tube. A similar trend is also observed for Syncrude pitch pyrolysis with the Pyroprobe-GC. 6. The yield of Cio compounds is very strongly influenced by the heating rates. At the highest heating rate (300,000 °C/min), less than 5% volatile yield of this group of components was detected, while as high as 25% volatile yield of Cio was detected at lower heating rates. This again attests to the influence of the reaction time and heating rates. The amount of Cio detected from Syncrude pyrolysis with Pyroprobe-GC is much less than that of C A N M E T pitch, which is in agreement with the differences of chemical structure or makeup of these two pitches. Higher yields of Cn, Cn, C13 and C14 groups were also detected at lower heating rates, a similar trend as that of Cio group. The yield of C14 is much less that those of Cn, C12 and Ci 3 . C14 is the heaviest group of compounds detected in the Pyroprobe-GC pyrolysis, which suggests that the volatiles are mostly compounds lighter than C14. The yield of these 148 groups from Syncrude pitch pyrolysis with Pyroprobe-GC is also significantly less than those from C A N M E T pitch pyrolysis. This is in agreement with the Cio yield. 7. Although the pattern of volatile release for pitches pyrolyzed under T G A conditions is complex, an adequate description of the kinetics is possible by methods developed in this work. The pyrolysis takes place in 2 stages, with a first stage of low activation energy barrier and lower pre-exponential factor, and the second stage of higher activation energy and pre-exponential factor. It is recommended that the process be modeled with a 2-stage first order reaction model using integral analysis method. It is demonstrated that the overall single stage reaction model using integral, Coats-Redfern, Chen-Nuttall and Friedman methods as well as Anthony and Howard's distributed activation energy model, are not sufficient to fit the T G A pyrolysis data and predict the course of the pitch pyrolysis process over the full range of conversion. It is also found that these single stage methods do not give similar values of activation energy and pre-exponential factors when data at different T G A conditions are taken for computation. 8. The 2-stage model reflects changes in the chemical constitution or structures as conversion proceeds by using two sets of activation energy. This feature is essential to describe pitch dependence of devolatilization rates on the remaining volatile content. The transition between these two stages is a sharp one, occurring at 450 °C for both C A N M E T and Syncrude pitches. The magnitude of the activation energies suggests that the pyrolysis of pitch was kinetically controlled under the reaction conditions studied. The dependence of dV/dT on V * - V is also in accordance with that. The activation energy of the second stage is higher than that of the first stage. 9. For both C A N M E T and Syncrude pitches, correlation between k o and E values obtained via the different methods was observed. One set of compensation effect constants was found to 149 be able to fit all the kinetic parameters derived from all the 2-stage kinetic analysis methods. An isokinetic temperature Ti was not observed. These methods did not give similar kinetic parameters k o and E at the operating conditions studied. The standard deviation caused by each pair of these parameters was not identical and it was possible to minimize the standard deviation through choosing the best pair of kinetic parameters k o and E . 7.2 RECOMMENDATIONS The following recommendations are offered for further work and future application: 1. To achieve more detailed GC analysis of the Pyroprobe pyrolysis products, a longer column should be used and the gaseous and liquid components should be analyzed separately using cryogenic focus. The C 7 should also be analyzed in detail with GC for gas components since it is the major lump for both C A N M E T and Syncrude Pitch. 2. To correlate the volatile yield with operating conditions such as heating rates, final temperature, and sample weights, a wider heating rate range should be used, such as heating rates as low as a few degrees per minute. Large sample weight (>18mg) should also be used to study the internal mass transfer effect. 3. The critical temperature, dividing the two pyrolysis stage of pitch pyrolysis should be further studied with a variety of pitch samples of different origin. This temperature may be dependent on the pitch sample used. 4. To achieve a higher conversion and more light volatile yields, reactive pyrolysis environments such as hydrogen or steam should be used. 5. 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Yoneda, Y. , 'Linear Free Energy Relationships in Heterogeneous Catalysis: T V Regional Analysis for Solid Acid Catalysis", J. Catal. 9, 51-56 (1967). 135. Li-Quin, S, H. Su, and L. Xuan-Wen, 'Stud. Surf. Sci. Catal", in 'Catalysis by Acids and Bases", B. Imelik, Eds., Elsevier, Amsterdam (1985) pp. 335. 161 APPENDICES 162 APPENDIX A Methods Available for Computing Kinetic Parameters Carrasco [62] has compared the activation energy results obtained by using the general analytical solution with those evaluated by means of established methods which were classified in three categories: integral (Table A.1), differential (Table A.2), and special methods (Table A.3). The comparison of the results and the related methods are summarized in the following tables. The accuracy (inaccuracy) of these methods was considered as the consequences of the simplification. These methods are however of no use due to the inaccuracy and their oversimplification for pitch pyrolysis. Table A. 1 Summary of the Integral Methods [62] Author Method id Analytical solution i-(i-/r id (l-n)7*2i(-ir»-! RT i-i _,/^ U> (2.9a) \PE) RT' v ' i-i =ld AR \BEj E 1 i -RT'n = 1 In l-n = lnl X* [ 0.368 E/RTm RT - + 1 van Krevelen etal. (1951) RT„ \nT:n*l J ln [ - ln ( l - / ) ] = ln 4 : 0368 E/RTm RT -+1 ln7/;n=l J (2.9b) (2.10a) (2.10b) 100% 108% Kissinger (1957) Id Id y 2 1 1 1 U*R\ E 1 i E 1 — — ; n * l R T' (2.11a) (2.11b) 80% 163 Table A.1 (Continued) id l-n RT: 0 ;n±l Horowitz and Metzger (1963) ln[- ln(l- / )] = — T 9 , n = \ RT? where: 9=T-T, (T, is T at which f=(l-l/e) for n=l and T,=Tm for n*l BE f iT A= , ex RT; RT (2.12a) (2.12b) (2.12c) 116% Coats and Redfern (1965) (zero-order reaction) Id Id / T2 1-2RT E . vBEj liJ rA^ KBEj E_\_ RT -^j;(when RT«E) (2.13a) (2.13b) 94% Table A.2 Summary of Differential Methods [62] Author Method Classical Id dT (1- / ) ' = id £ 1 RT (2.14) Close Multiple linear regression <dT) l A E 1 (2.15) Close Freeman and Carroll (1958) A l n ( l - / ) i ? A l n ( l - / ) (2.16) 90% to 110% Vachusca and Voboril (1971) 2 / Y dT) E VdT) (2.17) 110% 164 Table A.3 Summary of Special Methods [62] Author Method Rlii Reich (1964) E = P , P 2 W j__J_ r T 1 J 2 Ti and T 2 are measured at the same conversion value of two different heating rate runs. (2.18) 82% Friedman (1969) In (dfldT)K dfjdT Tm(Tm-T)(df/dT)f T(l-fm) EjTl(dfldT)m R -Id A = l - / m df dTJm E (2.19a) (2.19b) (2.19c) 107% Reich and Stivala (1978) Id Id 12 . V ln(l-/.)fya ln(l-/ 2)UJJ~* w*l W*I where InK is the intercept of the line: Id i - ( i - / r i vs — T (2.20a) (2.20b) (2.20c) (2.20d) 98% T T E = R-^r\H *0j *0i f AT, Y Ax P 2 Popescu and Segal (1983) AT=TI-T0 T 0 and Ti are characteristic temperatures Eh-C , PE R(ATY EX \RT0) (2.21a) (2.21b) (2.21c) (2.21d) 80% 165 APPENDIX B GC Computer Station Method Parameters ************************************************************** Varian GC Star Workstation - Method L i s t i n g Thu Jan 05 17:15:06 1995 Method: C:\STAR\PHILIP\PHILIPC.MTH * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ********************************* ADC Board ********************************* Module Address: 16 End Time Autozero at Start Channel A Name Channel B Name Channel A F u l l Scale Channel A F u l l Scale 65.00 minutes Yes PID FID 10 VOLTS 10 VOLTS GC 3600 Module Address : 17 GC Injector A Injector Type I n i t i a l GC Inject o r Temperature I n i t i a l GC Inject o r Hold Time GC Injector Oven On? Isothermal 220 degree C 0.00 minutes Yes GC Injector B Injector Type I n i t i a l GC Injector Temperature I n i t i a l GC Inject o r Hold Time GC Injector Oven On? Isothermal 220 degree C 0.00 minutes Yes Coolant To Injector Value On? : No Coolant Timeout : INFINITE GC A u x i l i a r y Injector Type Not used GC Column Column Oven On? I n i t i a l Column Temperate I n i t i a l Column Hold Time Thermal S t a b i l i z a t i o n Time Yes 40 degree C 10.00 minutes 3.00 minutes Coolant To Injector Value On? : No Coolant Timeout : INFINITE GC Column Program 1 F i n a l Temperature Rate Hold Time 120 degree C 2.0 degrees C/minute 15.00 minutes GC Column A Parameters Installe d ? Length Diameter C a r r i e r Gas GC Column B Parameters Installe d ? Yes 30 meters 255 microns Helium Yes 166 Length Diameter C a r r i e r Gas 30 meters 255 microns Helium GC Detector Heater A Detector Heater On? : Yes Detector Temperature : 300 degrees C GC Detector Heater B Detector Heater On? : Yes Detector Temperature : 250 degrees C GC Detector A Detector Type Detector On? Attenuation Detector Range Autozero at GC Ready? GC Detector B Detector Type Detector On? Attenuation Detector Range Autozero at GC Ready? Autosampler Autosampler Type GC Relays Relay Time Program GC St r i p c h a r t S t r i p c h a r t On? * * * * * * * * * * * * * * * * * * * * * * * ADC Board *********************** Module Address : 16 PID Yes 1 12 Yes FID Yes 1 12 Yes : Not used : Do Not Use : No ********* Integration Parameters Run Mode M u l t i p l i e r D i v i s o r Amount Standard U n i d e n t i f i e d Peak Factor Measurement C a l c u l a t i o n Report U n i d e n t i f i e d Peaks Subtract Blank Baseline Peak Rejection Value S/N Ratio Tangent Height % I n i t i a l Peak Width Response f a c t o r Tolerance Minimum Reference Window Percent Reference Window Minimum NbnReference Window Percent NonReference Window Unretained Peak Time Analysis 1.000000 1.000000 1.000000 0.000000 Peak Area External Standard NO Yes 0 Counts 5 5% 2 sec Update A l l Response Factors 0.10 minutes 2.0% 0.10 minutes 2.0% 0.000 minutes 167 Peak Table Name Time Factor C7 2.370 0.0028412 CIO 12.350 0.0094076 C l l 21.569 0.0098415 C12 27.979 0.0134153 C13 34.059 0.0128364 C14 40.075 0.0209216 Amount Ref. Std. RRT 0.5700000 N N N 0.6083000 N N N 0.6175000 N N N 0.6258000 N N N 0.6308000 N N N 0.6357000 N N N TimeEvents Table Group Event Group Event Group Event Group Event Group Event Group Event I n h i b i t Integrate 0.01 8.84 19.17 24.24 32.11 37.49 42.67 u n t i l u n t i l u n t i l u n t i l u n t i l u n t i l u n t i l 4.73 15.86 23.97 31.72 36.01 42.66 60.00 Report Format T i t l e Start Retention Time End Retention Time I n i t i a l Attenuation I n i t i a l Zero Offset Length i n Pages I n i t i a l Chart Speed Minutes per Tick Autoscale Time Events Chromatogram Events Retention Times Peak Names Baseline Units Number of Decimal D i g i t s Run Log Error Log Notes ASCII F i l e Convert P r i n t Chromatogram P r i n t Results Copies Standard Sample GC Analysis 0.00 minutes 65.00 minutes 32 0 1 Off cm/min 1.0 On Off Off On On Off mg 4 Off On Off Off On On 1 Sample Information Detector Bunch Monitor Length Data F i l e Name Channel 8 points 64 points stan FID 10 VOLTS Blank Baseline Baseline Compression Factor : 128 Baseline Points : 152 Baseline Bunch Size : 8 Baseline Frequency : 40.00 Hz 168 APPENDIX C Comparison of Equation 5.5 and Equation 5.6 Evaluated with Different Numbers of Terms of Integral E;(-E/RT) The accuracy of term V from Equation 5.6 was compared with that from Equation 5.6, using the kinetic parameters derived from CANMET pitch pyrolysis at 50 °C/min and 700 °C. The V term was integrated with Equation 5.5 and calculated with Equation 5.6, in which different numbers of terms of integral (Equation 5.7) were used. The results of V were plotted in Figure C l . As can be seen that the V term calculated with 3 to 8 terms of integral (Equation 5.7) is very close to that from the integration of Equation 5.5. It is therefore reasonable to use 3 terms of integral to estimate Equation 5.6 and simplify the mathematical process of Equation 5.5, and the accuracy of V thus obtained will not significantly affected. 100 CD tO t_ o in m' w c o ro zs cr 111 E o i= 30 H cu u ro o 90 80 70 H 60 H 50' 40' 20-—o— 3 term E ( (Equation 5.6) - -o - 4 term E,- (Equation 5.6) - -A- - 5 term E ( (Equation 5.6) 6 term E s (Equation 5.6) - O — 7 term E,- (Equation 5.6) — i — 8 term Ej (Equation 5.6) —•— Integration (Equation 5.5) — I — 100 200 — I — 300 400 T °C • 500 600 I 700 800 Figure C l Comparison of V evaluated for Equation 5.5 and Equation 5.6 169 APPENDIX D FORTRAN Programs and Calculation Results for T G A Experimental Results Modeling Single Overall First Order Reaction Model Fitting Program C M NO OF EXPERIMENTAL DATA POINTS C N NO OF COEFFICIENTS FOR LINEAR REGRESSION C LI NO OF DATA POINTS OMITTED AT THE BEGINNING OF DV/DT C L2 NO OF DATA POINTS OMITTED AT THE END OF DV/DT C M1L1 NO OF DATA POINTS OMITTED AT THE END OF DV/DT AFTER LI C R GAS CONSTANT C VO MAX VOLATILE AT CERTAIN HEATING RATE AND FINAL TEMPERATURE C C HEATING RATE C C C FOLLOWING ARRAYS WITH 1 ARE THOSE WITH SOME END POINTS OMITTED C FROM EXPERIMENTAL DATA FOR DIFFERENT MODEL C C V, VI ARRAY OF EXPERIMENTAL VOLATILE CONTENTS C T ARRAY OF TEMPERATURE IN C C X, XI ARRAY OF 1/T IN 1/K C VD ARRAY OF EXPERIMENTAL DV/DT C C INTEGRAL METHOD C Y, Y l ARRAY OF EXPERIMENTAL DATA C YFIT, YFIT1 ARRAY OF FITTED Y C A ARRAY OF FITTED COEFFICIENTS C VFIT, VFIT1 ARRAY OF FITTED VOLATILE CONTENTS V C C FRIEDMAN METHOD C XD ARRAY OF X WITH END POINTS OMITTED C YD. ARRAY OF EXPERIMENTAL DATA C YDD ARRAY OF YD WITH END POINTS OMITTED C YDDF ARRAY OF FITTED YDD C AD ARRAY OF FITTED COEFFICIENTS C VDD ARRAY OF FITTED VOLATILE CONTENTS V C C COATS-REDFERN METHOD C YCR, YCR1 ARRAY OF EXPERIMENTAL DATA C ACR ARRAY OF FITTED COEFFICIENTS C YCRF,YCRF1 ARRAY OF FITTED YCR C VCR, VCR1 ARRAY OF FITTED VOLATILE CONTENTS V C C CHEN-NUTTALL METHOD C YCN, YCN1 ARRAY OF EXPERIMENTAL DATA C ACN ARRAY OF FITTED COEFFICIENTS C YCNF, YCNF1 ARRAY OF FITTED YCN C VCN, VCN1 ARRAY OF FITTED VOLATILE CONTENTS V C C IMPLICIT REAL*8(A-H,0-Z) PARAMETER (M=30,L1M1=3) EXTERNAL NOMIAL DIMENSION V(M) ,T(M) ,X(M) ,X1 (M) ,VD(M) , VD1 (M) , YD (M) , 1 Y (M) , Y l (M) ,A(2) , YFIT(M) , YFIT1 (M) ,VFIT(M) , 2 VFIT1 (M) ,XD(M) , AD (2) , YDD (M) , YDDF (M) ,VDD(M) , 3 XD1 (M) , YDD1 (M) , YDDF1 (M) , VDD1 (M) , 4 YCR(M) ,YCRF(M) ,VCR(M) ,ACR(2) , 5 YCR1 (M) , YCRF1 (M) , VCR1 (M) , 6 YCN (M) , YCNF (M) , VCN (M) , ACN (2) , 7 YCNl(M),YCNF1(M),VCN1(M) DATA V/99.61D0,99.61D0,99.61D0,99.39D0,98.22D0,96.84D0, 1 95.19D0,93.11D0,91.OlD0,88.39D0,85.18D0,82.21D0, 2 78.23D0,73.51D0,68.8D0,65.87D0,61.13D0,55.71D0, 3 50.84D0,46.5D0,40.38D0,35.34D0,30.66D0,25.81D0, 4 22.86D0,21.25D0,19.99D0,19.66D0,19.36D0,19.36D0/ DATA T/0.D0,49.85D0,124.5D0,143.15D0,176.35D0,201.2D0, 1 226.1D0,251.D0,275.D0,298.65D0,325.65D0, 2 348.45D0,375.4D0,402.35D0,425.15D0,437.6D0,452.1D0, 3 466.6D0,477.D0,485.3D0,495.65D0,503.95D0,512.25D0, 4 524.700,537.100,549.5500,576.500,601.400,676.0500,700.00/ DATA MM,N,Ll,L2,R,VO,C/2,2,2,2,8.314D0,80.66D0,50.D0/ OPEN(UNIT = 3, FILE = 'FIT.DAT', 1 ACCESS = 'SEQUENTIAL', STATUS = 'NEW') E=250.D3 DO 10 1=1,M V(I)=100.D0-V(I) T(I)=T(I)+273.16D0 X(I)=1.D0/T(I) 10 CONTINUE DO 12 I=1+MM,M XI(I-MM)=X(I) 12 CONTINUE C C INTERGRAL METHOD C 20 E0LD=E DO 30 1=1,M Y(I)=DLOG(-C*DLOG(l.D0-V(I)/VO)/(R*T(I)*T(I))) 1 -DLOG(l.D0-2.D0*R*T(I)/E) 30 CONTINUE CALL FLSQP(X,Y,M,N,A,VAR) E=-A(2)*R IF(DABS(E-EOLD).LT.0.1D-4) THEN RA=EXP (A(l ) ) * E GOTO 40 ENDIF GOTO 20 40 CONTINUE DO 60 1=1,M YFIT(I)=A(1)+A(2) *X(I) VFIT(I)=VO*(1.D0-EXP(-RA*R*T(I)*T(I)*EXP(-E/(R*T(I)))*(1.D0-1 2.D0*R*T(I)/E)/(C*E))) 60 CONTINUE M1=M-MM E1=E 62 E0LD=E1 DO 64 I=1+MM,M Yl(I-MM)=DLOG(-C*DL0G(1.DO-V(I)/V0)/(R*T(I)*T(I))) 1 -DLOG(l.D0-2.D0*R*T(I)/El) 64 CONTINUE CALL FLSQP(XI,Y1,M1,N,A,VAR) El=-A(2)*R IF(DABS(E1-E0LD).GE.0.1D-4) GOTO 62 RA1=EXP(A(1))*E1 DO 66 1=1,Ml YFIT1(I)=A(1)+A(2)*X1(I) 66 CONTINUE DO 68 1=1,M VFIT1(I)=V0*(1.D0-EXP(-RA1*R*T(I)*T(I)*EXP(-E1/(R*T(I))) 1 *(l.D0-2.D0*R*T(I)/El)/(C*E1))) 68 CONTINUE 171 C FRIEDMAN METHOD C MD=M-1 DO 70 1=1,MD VD(I)=(V(I+1)-V(I))/(T(I+l)-T(I)) 70 CONTINUE VD(M)=VD(MD) DO 80 I=1+L1,M-L2 YD(I)=DLOG(C/VO*VD(I))-DLOG(1.DO-V(I) /VO) 80 CONTINUE ML=M-L1-L2 DO 90 1=1,ML XD(I)=X(I+L1) YDD(I)=YD(I+L1) 90 CONTINUE CALL FLSQP(XD,YDD,ML,N,AD,VARD) ED=-AD(2)*R RAD=EXP(AD(1)) DO 100 1=1,ML YDDF(I)=AD(1)+AD(2)*XD(I) 100 CONTINUE DO 110 1=1,M VDD(I)=VO*(1.D0-EXP(-RAD*R*T(I)*T(I)*EXP(-ED/(R*T(I)))*(1.D0-1 2.D0*R*T(I)/ED)/(C*ED))) 110 CONTINUE ML1=ML-L1M1 DO 112 1=1,ML1 XD1(I)=XD(I) YDD1(I)=YDD(I) 112 CONTINUE CALL FLSQP(XD1,YDD1,ML1,N,AD,VARD) ED1=-AD(2)*R RAD1=EXP(AD(1)) DO 114 1=1,ML1 YDDF1(I)=AD(1)+AD(2)*XD1(I) 114 CONTINUE DO 116 1=1,M VDD1(I)=VO*(1.D0-EXP(-RAD1*R*T(I)*T(I)*EXP(-ED1/(R*T(I)))* 1 (1.D0-2.D0*R*T(I)/ED1)/(C*ED1))) 116 CONTINUE C C COATS AND REDFERN METHOD C DO 120 1=1,M YCR(I)=DLOG(-C*DLOG(1.D0-V(I)/VO)/(R*T(I)*T(I))) 120 CONTINUE CALL FLSQP (X, YCR, M,N,ACR,VAR) ECR=-R*ACR(2) RCR=ECR*EXP(ACR(1)) DO 130 1=1,M YCRF(I)=ACR(1)+ACR(2) *X(I) VCR(I)=VO*(1.D0-EXP(-RCR*R*T(I)*T(I)*EXP(-ECR/(R*T(I)))*(1.D0-1 2.D0*R*T(I)/ECR)/(C*ECR))) 130 CONTINUE DO 132 I=1+MM,M YCR1(I-MM)=DLOG(-C*DLOG(l.D0-V(I)/VO)/(R*T(I)*T(I))) 132 CONTINUE CALL FLSQP(X1,YCR1,M1,N,ACR,VAR) ECR1=-R*ACR(2) RCR1=ECR1*EXP(ACR(1)) DO 134 1=1,Ml YCRF1(I)=ACR(1)+ACR(2)*X1(I) 134 CONTINUE 172 DO 136 1=1,M V C R 1 ( I ) = V O * ( 1 . D O - E X P ( - R C R 1 * R * T ( I ) * T ( I ) * E X P ( - E C R 1 / ( R * T ( I ) ) ) 1 * ( l . D 0 - 2 . D 0 * R * T ( I ) / E C R 1 ) / ( C * E C R 1 ) ) ) 136 CONTINUE C C CHEN-NUTTAL METHOD C ECN=E 140 EOLD=ECN DO 150 1=1,M YCN (I) =DLOG ( - C * (ECN+2 . D 0 * R * T (I) ) *DLOG (1. DO-V( I ) /VO) / (T ( I ) * T ( I ) *R)') 150 CONTINUE CALL FLSQP (X, Y C N , M , N , A C N , VAR) ECN=-R*ACN(2) I F ( D A B S ( E C N - E O L D ) . G E . 0 . 1 D - 4 ) GOTO 140 RCN=EXP(ACN(1)) DO 160 1=1,M YCNF( I )=ACN(1)+ACN(2) *X( I ) V C N ( I ) = V O * ( 1 . D 0 - E X P ( - R C N * R * T ( I ) * T ( I ) * E X P ( - E C N / ( R * T ( I ) ) ) * ( 1 . D 0 -1 2 . D 0 * R * T ( I ) / E C N ) / ( C * E C N ) ) ) 160 CONTINUE ECN1=E1 162 EOLD=ECNl DO 164 I=1+MM,M Y C N 1 ( I - M M ) = D L O G ( - C * ( E C N 1 + 2 . D 0 * R * T ( I ) ) * D L O G ( 1 . D 0 - V ( I ) / V O ) / ( T ( I ) * 1 T ( I ) * R ) ) 164 CONTINUE CALL FLSQP (X I , Y C N 1 , M l , N , ACN, VAR) ECN1=-R*ACN(2) I F ( D A B S ( E C N 1 - E O L D ) . G E . 0 . 1 D - 4 ) GOTO 162 RCN1=EXP(ACN(1) ) DO 166 1=1,Ml YCNF1( I )=ACN(1)+ACN(2) *X1( I ) 166 CONTINUE DO 168 1=1,M V C N l ( I ) = V O * ( l . D 0 - E X P ( - R C N l * R * T ( I ) * T ( I ) * E X P ( - E C N l / ( R * T ( I ) ) ) * 1 ( l . D 0 - 2 . D 0 * R * T ( I ) / E C N l ) / ( C + E C N 1 ) ) ) 168 CONTINUE C WRITE(3,200) 200 FORMAT(4X, ' T ' , 8 X , ' V ' ^ X , ' V F I T ' , 6 X , ' V D D ' ^ X , ' V C R ' , 7 X , ' V C N 1 , 1 8 X , ' V D ' ) DO 220 1=1,M WRITE(3,210) T ( I ) , V ( I ) , V F I T ( I ) , V D D ( I ) , V C R ( I ) , V C N ( I ) , V D ( I ) 210 F O R M A T ( F 7 . 2 , 6 F 1 0 . 6 ) 220 CONTINUE WRITE(3,230) 230 FORMAT(6X, ' X ' , 1 0 X , ' Y ' , 8 X , ' Y F I T ' , 7 X , ' Y C R ' , 7 X , ' Y C R F ' , 8 X , ' Y C N 1 , 1 7 X , ' Y C N F ' ) DO 250 I=M,1 , -1 WRITE(3,240) X ( I ) , Y ( I ) , Y F I T ( I ) , Y C R ( I ) , Y C R F ( I ) , Y C N ( I ) , Y C N F ( I ) 240 F O R M A T ( F 1 0 . 5 , 6 F 1 1 . 6 ) 250 CONTINUE WRITE(3,260) 260 F O R M A T ( 1 O X , ' X ' , 1 3 X , ' Y D D ' , 1 1 X , ' Y D D F ' ) DO 280 I = M L , 1 , - 1 WRITE(3 ,270) X D ( I ) , Y D D ( I ) , Y D D F ( I ) 270 FORMAT(3F15.8) 280 CONTINUE WRITE(3,290) 290 F O R M A T ( 3 5 X , ' A ' , 1 4 X , ' E ' ) , 173 WRITE(3,300) R A , E 300 FORMAT( ' INTEGRAL METHOD' ,10X ,2D15 .3 ) WRITE(3,310) RAD,ED 310 FORMAT('FRIEDMAN METHOD' ,10X ,2D15 .3 ) WRITE(3,320) RCR,ECR 320 FORMAT( 'COATS-REDFERN METHOD' ,5X ,2D15 .3 ) WRITE(3,330) RCN,ECN 330 FORMAT( 'CHEN-NUTTALL M E T H O D ' , 6 X , 2 D 1 5 . 3 ) WRITE(3>340) 340 F O R M A T ( / / ' A N A L Y S I S WITHOUT THE ABNORMAL END DATA POINTS' ) WRITE(3,200) DO 350 1=1,M WRITE(3,210) T ( I ) , V ( I ) , V F I T 1 ( I ) , V D D 1 ( I ) , V C R 1 ( I ) , V C N 1 ( I ) , V D ( I ) 350 CONTINUE WRITE(3,230) DO 360 I=M1,1 , -1 WRITE(3,240) X 1 ( I ) , Y 1 ( I ) , Y F I T 1 ( I ) , Y C R 1 ( I ) , Y C R F 1 ( I ) , Y C N 1 ( I ) , 1 Y C N F l ( I ) 360 CONTINUE WRITE(3 , 260) DO 370 I = M L 1 , 1 , - 1 WRITE(3,270) X D 1 ( I ) , Y D D 1 ( I ) , Y D D F 1 ( I ) 370 CONTINUE WRITE(3,290) WRITE(3,300) RA1 ,E1 WRITE(3,310) RAD1,EDI WRITE(3,320) RCR1,ECR1 WRITE(3, 330) RCN1,ECN1 ENDFILE(UNIT = 3) CLOSE(UNIT = 3 ) STOP END SUBROUTINE GAUSS(A,N,NDR,NDC,X,RNORM,IREEOR) IMPLICIT R E A L * 8 ( A - H , 0 - Z ) DIMENSION A ( N D R , N D C ) , X ( N ) , B ( 5 0 , 5 1 ) NM=N-1 NP=N+1 DO 20 1=1,N DO 10 J=1,NP B ( I , J) =A( I , J) 10 CONTINUE 20 CONTINUE DO 70 K=1,NM KP=K+1 BIG=ABS(B(K,K) ) IPIVOT=K DO 30 I=KP,N AB=ABS (B ( I , K) ) I F ( A B . G T . B I G ) THEN BIG=AB IPIVOT=I ENDIF 30 CONTINUE I F ( I P I V O T . N E . K ) THEN DO 40 J=K,NP TEMP=B( IPIVOT,J) B ( I P I V O T , J ) = B ( K , J) B (K ,J )=TEMP 40 CONTINUE ENDIF I F ( B ( K , K ) . E Q . 0 . D 0 ) THEN IERROR=2 RETURN ENDIF DO 60 I=KP,N Q U O T = B ( I , K ) / B ( K , K) B ( I , K ) = 0 . D 0 DO 50 J=KP,NP B ( I , J ) = B ( I , J ) - Q U O T * B ( K , J) 50 CONTINUE 60 CONTINUE 70 CONTINUE I F ( B ( N , N ) . E Q . 0 . D 0 ) THEN IERROR=2 RETURN ENDIF X ( N ) = B ( N , N P ) / B ( N , N ) DO 90 I=NM,1 , -1 SUM=0.DO DO 80 J=I+1,N SUM=SUM+B(I ,J)*X(J) 80 CONTINUE X ( I ) = ( B ( I , N P ) - S U M ) / B ( I , I ) 90 CONTINUE RSQ=0.D0 DO 110 1=1,N SUM=0.DO DO 100 J=1,N SUM=SUM+A(I ,J)*X(J) 100 CONTINUE RSQ=RSQ+(A( I ,NP) -SUM)**2 110 CONTINUE RNORM=DSQRT(RSQ) IERROR=l RETURN END SUBROUTINE F L S Q P ( X , Y , M , N , A , V A R ) IMPLICIT R E A L * 8 ( A - H , O - Z ) DIMENSION X ( M ) , U ( 5 1 ) , Y ( M ) , V ( 5 1 ) , A ( N ) ,B (11 ) , C O E F F ( 1 0 , 11) ,SUMU(18) NP=N+1 NM2=2*(N-1) XMIN=X(1) XMAX=X(1) YMIN=Y(1) YMAX=Y(1) DO 10 K=2,M XMIN=DMIN1(XMIN,X(K)) XMAX=DMAX1(XMAX,X(K)) YMIN=DMIN1(YMIN,Y(K)) YMAX=DMAX1(YMAX, Y(K) ) 10 CONTINUE XP=XMIN+XMAX XM=XMAX-XMIN YP=YMIN+YMAX YM=YMAX-YMIN DO 20 K=1,M U ( K ) = ( 2 . D 0 * X ( K ) - X P ) / X M V ( K ) = ( 2 . D 0 * Y ( K ) - Y P ) / Y M 20 CONTINUE DO 30 L=1,NM2 SUMU(L)=0.D0 30 CONTINUE DO 40 1=1,N C O E F F ( I , N P ) = 0 . D 0 40 CONTINUE DO 70 K=1,M TERMU=U(K) DO 50 L=1,NM2 SUMU(L)=SUMU(L)+TERMU TERMU=TERMU*U(K) 50 CONTINUE TERMV=V(K) DO 60 1=1,N COEFF( I ,NP)=COEFF( I ,NP)+TERMV TERMV=TERMV*U(K) 60 CONTINUE 70 CONTINUE DO 90 1=1,N DO 80 J=1,N I F ( I . E Q . 1 . A N D . J . E Q . 1 ) THEN C O E F F ( I , J ) = M E L S E COEFF( I ,J )=SUMU(1+J-2 ) ENDIF 8 0 CONTINUE 90 CONTINUE CALL GAUSS(COEFF,N ,10 ,11 ,B ,RNORM, IERROR) DO 110 1=1,N IM=I-1 SUM=B(I) I F ( I . N E . N ) THEN DO 100 J=I+1,N S U M = S U M + N O M I A L ( I M , J - l ) * ( - X P / X M ) * * ( J - I ) * B ( J ) 100 CONTINUE ENDIF A( I )=YM* (2.D0/XM) * * IM*SUM/2 . DO 110 CONTINUE A ( 1 ) = A ( 1 ) + Y P / 2 . D 0 SSUM=0.D0 DO 130 K=1,M SUM=A(1) TEMP=1.D0 DO 120 J=2 ,N TEMP=TEMP*X(K) SUM=SUM+A(J)*TEMP 120 CONTINUE SSUM=SSUM+(Y(K)-SUM)**2 130 CONTINUE YAR=SSUM/(M-N) RETURN END FUNCTION NOMIAL( I ,J ) NOMIAL=l I F ( J . L E . I . O R . I . E Q . O ) RETURN DO 10 ICOUNT=l , I NOMIAL=NOMIAL*(J-ICOUNT+1)/ ICOUNT 10 CONTINUE RETURN END Fitting Results for Run#61 with Single Overall First Order Reaction Models T V V F I T VDD VCR VCN VD 273 . 16 0. 390000 0. 001835 0. 002088 0. 002148 0. 002148 0. 000000 323 . 01 0. 390000 0. 023641 0. 025793 0. 023518 0. 025587 0. 000000 397 . 66 0. 390000 0. 345736 0. 361193 0. 290610 0. 344936 0. 011796 416. 31 0. 610000 0. 585664 0. 606667 0. 476451 0. 575114 0. 035241 449 . 51 1. 780000 1. 348438 1. 378113 1. 042352 1. 291552 0. 055533 474. 36 3 . 160000 2 . 335505 2 . 365809 1. 747062 2 . 201061 0. 066265 499. 26 4 . 810000 3 . 831136 3. 849982 2 . 785390 3 . 559491 0. 083534 524. 16 6. 890000 5. 980990 5 . 967688 4. 245088 5. 488858 0. 087500 548. 16 8. 990000 8. 805194 8. 732291 6. 133121 8. 000267 0. 110782 571 . 81 11 . 610000 12 . 411952 12. 245013 8. 524594 11 . 187995 0. 118889 598. 81 14. 820000 1 7 . 595572 17 . 272655 11. 962289 15. 756300 0. 130263 621. 61 17 . 790000 22 . 839938 22 . 346199 15. 476020 20 . 384440 0. 147681 648. 56 2 1 . 770000 2 9 . 925783 29 . 196143 20 . 332535 26 . 678746 0. 175139 675. 51 2 6 . 490000 3 7 . 688713 36 . 712478 25 . 870783 33 . 669396 0. 206579 698. 31 31 . 200000 44 . 476911 43 . 311675 30. 979525 39 . 903756 0. 235341 710 . 76 34 . 130000 48 . 156937 46. 905714 33. 886906 43 . 346999 0. 326897 725 . 26 38 . 870000 52 . 337141 51 . 007448 37. 339291 4 7 . 326756 0. 373793 739 . 76 44 . 290000 56 . 333893 54. 953606 40. 825516 5 1 . 215466 0. 468269 750 . 16 4 9 . 160000 5 9 . 050742 57. 653200 43. 324175 53 . 915945 0. 522892 758. 46 53 . 500000 61 . 113169 59. 713761 45. 305721 56 . 002775 0. 591304 768. 81 59 . 620000 63 . 538995 62. 152120 47. 748745 58 . 505153 0. 607229 777 . 11 64. 660000 65 . 358755 63. 993571 49. 676613 60. 422057 0. 563855 785 . 41 69 . 340000 67 . 061108 65. 727472 51 . 569099 62. 251570 0. 389558 797 . 86 74 . 190000 69. 387621 68. 118229 54. 327247 64. 819982 0. 237903 810 . 26 7 7 . 140000 7 1 . 430956 70 . 242956 56. 960587 67 . 156536 0. 129317 822. 71 78 . 750000 7 3 . 211498 72 . 118937 59. 473007 69 . 272460 0. 046753 849. 66 80 . 010000 76 . 196155 75 . 337198 64. 396759 7 3 . 063267 0. 013253 874. 56 80 . 340000 78 . 041713 77 . 401913 68. 261742 7 5 . 662338 0. 004019 949. 21 80 . 640000 80. 292291 80. 117552 75. 953570 7 9 . 566076 0. 000000 973. 16 80 . 640000 80. 485864 80. 384632 77. 371350 80 . 041927 0. 000000 X Y YF IT YCR YCRF YCN YCNF 0. 00103 - 9 . 179704 - 9 . 481708 - 9 . 850486 - 1 0 . 057252 0. 931758 0. 694442 0. 00105 - 9 . 153117 - 9 . 584969 - 9 . 800649 - 1 0 . 153178 0. 973291 0. 594723 0. 00114 - 9 . 464879 - 9 . 943113 - 1 0 . 043230 - 1 0 . 485878 0. 704377 0. 248866 0. 00118 - 9 . 566304 - 1 0 . 076571 - 1 0 . 122604 - 1 0 . 609854 0. 616063 0. 119986 0. 00122 - 9 . 778232 - 1 0 . 230119 - 1 0 . 311201 - 1 0 . 752494 0. 417698 - 0 . 028295 0. 00123 - 9 . 936654 - 1 0 . 304503 - 1 0 . 459026 - 1 0 . 821594 0. 265328 - 0 . 100127 0. 00125 - 1 0 . 132381 - 1 0 . 380896 - 1 0 . 644309 - 1 0 . 892559 0. 075499 - 0 . 173899 0. 00127 - 1 0 . 361963 - 1 0 . 460023 - 1 0 . 863514 - 1 0 . 966065 - 0 . 148292 - 0 . 250311 0. 00129 - 1 0 . 541413 - 1 0 . 514183 - 1 1 . 036105 - 1 1 . 016377 - 0 . 323952 - 0 . 302613 0. 00130 - 1 0 . 712212 - 1 0 . 569512 - 1 1 . 200091 - 1 1 . 067776 - 0 . 491018 - 0 . 356045 0. 00132 - 1 0 . 904251 - 1 0 . 640204 - 1 1 . 383700 - 1 1 . 133445 - 0 . 678478 - 0 . 424311 0. 00133 - 1 1 . 035355 - 1 0 . 698303 - 1 1 . 508095 - 1 1 . 187417 - 0 . 805974 - 0 . 480417 0. 00135 - 1 1 . 181704 - 1 0 . 772943 - 1 1 . 646099 - 1 1 . 256753 - 0 . 947876 - 0 . 552496 0. 00138 - 1 1 . 345282 - 1 0 . 880580 - 1 1 . 798158 - 1 1 . 356744 - 1 . 105396 - 0 . 656441 0. 00141 - 1 1 . 494671 - 1 0 . 992609 - 1 1 . 936160 - 1 1 . 460814 - 1 . 248887 - 0 . 764627 0. 00143 - 1 1 . 586662 - 1 1 . 092512 - 1 2 . 018476 - 1 1 . 553619 - 1 . 335942 - 0 . 861103 0. 00148 - 1 1 . 743532 - 1 1 . 285013 - 1 2 . 157867 - 1 1 . 732445 - 1 . 484068 - 1 . 047000 0. 00154 - 1 1 . 917910 - 1 1 . 530008 - 1 2 . 311971 - 1 1 . 960034 - 1 . 648598 - 1 . 283590 0. 00161 - 1 2 . 085959 - 1 1 . 796246 - 1 2 . 460149 - 1 2 . 207358 - 1 . 807311 - 1 . 540695 0. 00167 - 1 2 . 232599 - 1 2 . 040200 - 1 2 . 590281 - 1 2 . 433980 - 1 . 946443 - 1 . 776279 0. 00175 - 1 2 . 426729 - 1 2 . 354252 - 1 2 . 765208 - 1 2 . 725721 - 2 . 132134 - 2 . 079558 0. 00182 - 1 2 . 632724 - 1 2 . 654757 - 1 2 . 954679 - 1 3 . 004877 - 2 . 331130 - 2 . 369754 0. 00191 - 1 2 . 839908 - 1 2 . 987432 - 1 3 . 145370 - 1 3 . 313918 - 2 . 531581 - 2 . 691016 0. 00200 - 1 3 . 132499 - 1 3 . 366387 - 1 3 . 421133 - 1 3 . 665951 - 2 . 817570 - 3 . 056972 0. 00211 - 1 3 . 477522 - 1 3 . 785127 - 1 3 . 749606 - 1 4 . 054942 - 3 . 156376 - 3 . 461346 0. 00222 - 1 3 . 968892 - 1 4 . 249277 - 1 4 . 224727 - 1 4 . 486117 - 3 . 641916 - 3 . 909573 0. 00240 - 1 4 . 914993 - 1 4 . 955857 - 1 5 . 149524 - 1 5 . 142499 - 4 . 580806 - 4 . 591914 0. 00251 - 1 5 . 283782 - 1 5 . 404530 - 1 5 . 506541 - 1 5 . 559297 - 4 . 945827 - 5 . 025195 177 X YDD YDDF 0. 00123417 0. 60807557 0. 04009520 0. 00125335 0. 60895559 - 0 . 03490237 0. 00127322 0. 54271001 - 0 . 11258481 0. 00128682 0. 56647688 - 0 . 16575592 0. 00130071 0. 36674818 - 0 . 22007510 0. 00131846 0. 08485328 - 0 . 28947602 0. 00133305 - 0 . 18634571 - 0 . 34651452 0. 00135179 - 0 . 44043312 - 0 . 41979110 0. 00137882 - 0 . 80468691 - 0 . 52546313 0. 00140694 - 1 . 04618577 - 0 . 63544672 0. 00143203 - 1 . 43585946 - 0 . 73352542 0. 00148036 - 1 . 65717687 - 0 . 92251219 0. 00154188 - 1 . 90582279 - 1 . 16303342 0. 00160873 - 2 . 14174758 - 1 . 42441033 0. 00166998 - 2 . 31340313 - 1 . 66390972 0. 00174883 - 2 . 45237380 - 1 . 97222821 0. 00182428 - 2 . 56023804 -2 . 26724630 0. 00190781 - 2 . 82504563 - 2 . 59384664 0. 00200296 - 2 . 89923461 - 2 . 96588292 0. 00210810 - 3 . 15234745 - 3 . 37697689 0. 00222464 - 3 . 34667896 - 3 . 83265228 0. 00240206 - 3 . 81617456 -4 . 52633118 0. 00251471 - 4 . 91334683 - 4 . 96681167 INTEGRAL METHOD FRIEDMAN METHOD COATS-REDFERN METHOD CHEN-NUTTALL METHOD A 0.151D+03 0.130D+03 0.591D+02 0.104D+03 E 331D+05 325D+05 308D+05 320D+05 178 Anthony-Howard Model FORTRAN Program with L - M Nonlinear Regression c c INTEGER NDATA,MA,MFIT ,NCA PARAMETER(NDATA=3 0,MA=3,MFIT=3,NCA=3) DOUBLE PRECISION X ( N D A T A ) , Y ( N D A T A ) , A ( M A ) , S I G ( N D A T A ) , A F , B F , Y F , 1 COVAR(NCA,NCA) ,ALPHA(NCA,NCA) ,CHISQ,ALAMDA, Y F I T ( N D A T A ) , T , 2 E O , S , Z COMMON / Z D A T A / T , E O , S , Z EXTERNAL MRQMIN,MRQCOF,GAUSSJ,COVSRT,FUNCS,FUNCO,FUNC1, 1 FUNC2,FUNC3,QROMB,TRAPZD,POLINT INTEGER LISTA(MA) DATA L I S T A / 1 , 2 , 3 / DATA S I G / 1 2 * 1 . D - 1 , 6 * 1 . D - 5 , 1 2 * 1 . D - l / DATA A / 1 1 5 0 0 0 . D O , 1 5 0 0 0 . D O , 5 0 0 0 0 0 0 0 0 . 0 D 0 / C DATA FOR RUN 61:CAN61.DAT X=T (C) + 273 .16 K DATA X / 2 7 3 . 1 6 D 0 , 3 2 3 . 0 1 D 0 , 3 9 7 . 6 6 D 0 , 4 1 6 . 3 1 D 0 , 4 4 9 . 5 1 D 0 , 4 7 4 . 3 6 D 0 , 1 4 9 9 . 2 6 D 0 , 5 2 4 . 1 6 D 0 , 5 4 8 . 1 6 D 0 , 5 7 1 . 8 1 D 0 , 5 9 8 . 8 1 D 0 , 6 2 1 . 6 1 D 0 , 2 6 4 8 . 5 6 D 0 , 6 7 5 . 5 1 D 0 , 6 8 9 . 3 1 D 0 , 7 1 0 . 7 6 D 0 , 7 2 5 . 2 6 D 0 , 7 3 9 . 7 6 D 0 , 3 7 5 0 . 1 6 D 0 , 7 5 8 . 4 6 D 0 , 7 6 8 . 8 1 D 0 , 7 7 7 . 1 1 D 0 , 7 8 5 . 4 1 D 0 , 7 9 7 . 8 6 D 0 , 4 8 1 0 . 2 6 D 0 , 8 2 2 . 7 1 D 0 , 8 4 9 . 6 6 D 0 , 8 7 4 . 5 6 D 0 , 9 4 9 . 2 1 D 0 , 9 7 3 . 1 6 D 0 / DATA Y / 0 .39D0, 0 .39D0, 0 .39D0, 0 .61D0, 1 .78D0, 3 .16D0 , 4 .81D0 , 1 6 .89D0, 8 . 9 9 D 0 , 1 1 . 6 1 D 0 , 1 4 . 8 2 D 0 , 1 7 . 7 9 D 0 , 2 1 . 7 7 D 0 , 2 6 . 4 9 D 0 , 2 3 1 . 2 0 D 0 , 3 4 . 1 3 D 0 , 3 8 . 8 7 D 0 , 4 4 . 2 9 D 0 , 4 9 . 1 6 D 0 , 5 3 . 5 0 D 0 , 5 9 . 6 2 D 0 , 3 6 4 . 6 6 D 0 , 6 9 . 3 4 D 0 , 7 4 . 1 9 D 0 , 7 7 . 1 4 D 0 , 7 8 . 7 5 D 0 , 8 0 . 0 1 D 0 , 8 0 . 3 4 D 0 , 4 8 0 . 6 4 D 0 , 8 0 . 6 4 D 0 / O P E N ( U N I T = 3 , F I L E = ' S L M 6 1 . D A T ' , A C C E S S = ' S E Q U E N T I A L ' , 1 STATUS='OLD' ) DO 10 1=1,NDATA X ( I ) = X ( I ) - 2 7 3 . 1 6 D 0 10 CONTINUE ALAMDA=-0.001D0 CALL M R Q M I N ( X , Y , S I G , N D A T A , A , M A , L I S T A , M F I T , C O V A R , 1 A L P H A , N C A , C H I S Q , F U N C S , ALAMDA) WRITE(3,100) A 100 FORMAT(5X,3F20.6) VSTAR=Y (NDATA) A F = A ( 1 ) - 4 . D 0 * A ( 2 ) BF=A(1)+4.D0*A(2) EO=A(1) S=A(2) Z=A(3) DO 200 1=1,NDATA T=X(I )+273.16D0 CALL QROMB(FUNCO,AF,BF,YF) Y F I T ( I ) = V S T A R * ( 1 . D 0 - Y F / ( 2 . 5 0 6 6 2 8 D 0 * A ( 2 ) ) ) 200 CONTINUE DO 400 1=1,NDATA WRITE(3,300) X ( I ) , Y ( I ) , Y F I T ( I ) 300 FORMAT(5X,3F20.5) 400 CONTINUE ENDFILE(UNIT=3) CLOSE(UNIT=3) STOP END SUBROUTINE M R Q M I N ( X , Y , S I G , N D A T A , A , M A , L I S T A , M F I T , * COVAR, ALPHA,NCA, CHISQ, FUNCS, ALAMDA) INTEGER M M A X , M A , M F I T , N C A , K K , K , J , I H I T PARAMETER (MMAX=20) INTEGER LISTA(MA) DOUBLE PRECISION X(NDATA) ,Y (NDATA) ,S IG(NDATA) ,A(MA) , ALAMDA, CHISQ, * COVAR (NCA, NCA) , ALPHA (NCA, NCA) , ATRY (MMAX) , BETA(MMAX) , DA(MMAX) , * OCHISQ EXTERNAL FUNCS IF(ALAMDA.LT.O.DO) THEN KK=MFIT+1 DO 12 J=1,MA IHIT=0 DO 11 K=1,MFIT IF(LISTA(K).EQ.J)IHIT=IHIT+1 11 CONTINUE IF (IHIT.EQ.O) THEN LISTA(KK)=J KK=KK+1 ELSE IF (IHIT.GT.l) THEN PAUSE 'Improper permutation i n LISTA* ENDIF 12 CONTINUE IF (KK.NE.(MA+1)) PAUSE 'Improper permutation i n LISTA' ALAMDA=0.001D0 CALL MRQCOF (X,Y,SIG, NDATA, A, MA, LISTA, MFIT, ALPHA, BETA, NCA, CHISQ, F * UNCS) OCHISQ=CHISQ DO 13 J=1,MA ATRY(J)=A(J) 13 CONTINUE ENDIF 100 DO 15 J=1,MFIT DO 14 K=1,MFIT COVAR(J,K)=ALPHA(J,K) 14 CONTINUE COVAR(J,J)=ALPHA(J,J)*(1.DO+ALAMDA) DA(J)=BETA(J) 15 CONTINUE CALL GAUSSJ(COVAR,MFIT,NCA, DA, 1,1) IF(ALAMDA.EQ.0.DO)THEN CALL COVSRT(COVAR,NCA,MA,LISTA,MFIT) RETURN ENDIF DO 16 J=1,MFIT C WRITE(3,*) 'DA( ' , J , ') = ',DA(J) IF((DABS(DA (1))+DABS(DA(2))+DABS(DA(3))) .LT.1.D1) THEN ATRY(LISTA(J))=A(LISTA(J))+DA(J) ELSE ATRY(LISTA(J))=A(LISTA(J))+DA(J)*1.0D-60 ENDIF 16 CONTINUE IF((DABS(DA(1))+DABS(DA(2))+DABS(DA(3))).LT.l.D-250) RETURN CALL MRQCOF (X, Y, SIG, NDATA, ATRY, MA, LI STA, MFIT, COVAR, DA, NCA, CHISQ, * FUNCS) C IF((DABS(CHISQ-OCHISQ)/CHISQ).LT.1D-3) RETURN IF(CHISQ.LT.OCHISQ) THEN ALAMDA=0.1D0*ALAMDA OCHISQ=CHISQ DO 18 J=1,MFIT DO 17 K=1,MFIT ALPHA (J,K)=COVAR(J, K) 17 CONTINUE BETA(J)=DA(J) A (LISTA (J) )=ATRY(LISTA(J) ) 18 CONTINUE ELSE ALAMDA=10.DO*ALAMDA CHISQ=OCHISQ DO 180 J=1,MFIT 180 DO 170 K=1,MFIT A L P H A ( J , K ) = C O V A R ( J , K) 170 CONTINUE BETA(J )=DA(J ) A ( L I S T A ( J ) )=ATRY(LISTA(J) ) 180 CONTINUE ENDIF C W R I T E ( * , * ) I C H I S Q = ' , C H I S Q , ' OCHISQ= 1 ,OCHISQ C WRITE {*,*)• A GOTO 100 RETURN END SUBROUTINE MRQCOF (X, Y , S I G , NDATA, A , M A , L I S T A , M F I T , ALPHA, BETA, NALP, * CHISQ,FUNCS) INTEGER N D A T A , M A , M F I T , N A L P , I , J , K , M M A X PARAMETER (MMAX=3) INTEGER L ISTA(MFIT) DOUBLE PRECISION X (NDATA) , Y (NDATA) , SIG (NDATA) , ALPHA (NALP, NALP) , * B E T A ( M A ) , D Y D A ( 3 ) , A ( 3 ) , X I , D Y , S I G 2 I , W T , C H I S Q DO 12 J=1,MFIT DO 11 K = 1 , J A L P H A ( J , K ) = 0 . D 0 11 CONTINUE BETA(J )=0 .DO 12 CONTINUE CHISQ=0.D0 DO 15 1=1,NDATA XI=X(I) CALL FUNCS(XI ,A ,YMOD,DYDA, 3) S I G 2 I = 1 . D 0 / ( S I G ( I ) * S I G ( I ) ) DY=Y(I)-YMOD DO 14 J=1,MFIT WT=DYDA(L ISTA(J) ) *S IG2 I DO 13 K = 1 , J ALPHA(J ,K )=ALPHA(J ,K )+WT* DYDA(LISTA(K)) 13 CONTINUE BETA (J)=BETA(J)+DY*WT 14 'CONTINUE CHISQ=CHISQ+DY*DY* SIG21 15 CONTINUE DO 17 J=2,MFIT DO 16 K = l , J - l A L P H A ( K , J ) = A L P H A ( J , K) 16 CONTINUE 17 CONTINUE RETURN END C SUBROUTINE G A U S S J ( A , N , N P , B , M , M P ) INTEGER N M A X , N , N P , M , M P , I , J , K , I R O W , I C O L , L , L L PARAMETER (NMAX=50) INTEGER IPIV(NMAX),INDXR(NMAX),INDXC(NMAX) DOUBLE PRECISION A ( N P , N P ) , B ( N P , M P ) , D U M , B I G , P I V I N V DO 11 J=1,N IP IV (J )=0 11 CONTINUE DO 22 1=1,N BIG=0.D0 DO 13 J=1,N I F ( I P I V ( J ) . N E . 1 ) T H E N DO 12 K=1,N I F ( I P I V ( K ) . E Q . 0 ) THEN IF (ABS(A(J,K)).GE.BIG)THEN BIG=ABS(A(J,K)) IROW=J ICOL=K ENDIF ELSE IF (IPIV(K).GT.l) THEN PAUSE 'Singular matrix' ENDIF 12 CONTINUE ENDIF 13 CONTINUE IPIV(ICOL)=IPIV(ICOL)+l IF (IROW.NE.ICOL) THEN DO 14 L=1,N DUM=A(IROW,L) A(IROW,L)=A(ICOL,L) A(ICOL,L)=DUM 14 CONTINUE DO 15 L=1,M DUM=B(IROW,L) B(IROW,L)=B(ICOL,L) B(ICOL,L)=DUM 15 CONTINUE ENDIF INDXR(I)=IROW INDXC(I)=ICOL IF (A(ICOL,ICOL).EQ.O.DO) PAUSE 'Singular matrix. PIVINV=l./A(ICOL,ICOL) A(ICOL,ICOL)=1. DO 16 L=1,N A(ICOL,L)=A(ICOL,L)*PIVINV 16 CONTINUE DO 17 L=1,M B(ICOL,L)=B(ICOL,L)*PIVINV 17 CONTINUE DO 21 LL=1,N IF(LL.NE.ICOL)THEN DUM=A(LL,ICOL) -A(LL,ICOL)=0.D0 DO 18 L=1,N A(LL,L)=A(LL,L)-A(ICOL,L)*DUM 18 CONTINUE DO 19 L=1,M B(LL,L)=B(LL,L)-B(ICOL,L)*DUM 19 CONTINUE ENDIF 21 CONTINUE 22 CONTINUE DO 24 L=N,1,-1 IF(INDXR(L).NE.INDXC(L))THEN DO 23 K=1,N DUM=A(K,INDXR(L)) A(K,INDXR(L))=A(K,INDXC(L)) A(K,INDXC(L))=DUM 23 CONTINUE ENDIF 24 CONTINUE RETURN END SUBROUTINE COVSRT(COVAR,NCVM,MA,LISTA,MFIT) INTEGER NCVM,MA,LISTA,MFIT, I, J INTEGER LISTA(MFIT) 182 DOUBLE PRECISION COVAR(NCVM,NCVM),SWAP DO 12 J=1 ,MA-1 DO 11 I=J+1,MA COVAR( I , J )=0.DO 11 CONTINUE 12 CONTINUE DO 14 I=1 ,MFIT-1 DO 13 J=I+1,MFIT I F ( L I S T A ( J ) . G T . L I S T A ( I ) ) THEN C O V A R ( L I S T A ( J ) , L I S T A ( I ) ) = C O V A R ( I , J ) E L S E COVAR (L ISTA( I ) , L I S T A ( J ) ) =COVAR ( I , J) ENDIF 13 CONTINUE 14 CONTINUE SWAP=COVAR(l,1) DO 15 J=1,MA C O V A R ( 1 , J ) = C O V A R ( J , J ) C O V A R ( J , J ) = 0 . D O 15 CONTINUE C O V A R ( L I S T A ( l ) , L I S T A ( 1 ) ) = S W A P DO 16 J=2,MFIT C O V A R ( L I S T A ( J ) , L I S T A ( J ) ) = C O V A R ( l , J ) 16 CONTINUE DO 18 J=2,MA DO 17 1 = 1 , J - 1 C O V A R ( I , J ) = C O V A R ( J , I ) 17 CONTINUE 18 CONTINUE RETURN END SUBROUTINE F U N C S ( X X , A , Y , D Y D A , N A ) INTEGER NA,NAA DOUBLE PRECISION A ( 3 ) , D Y D A ( 3 ) , X X , Y , T , E O , S , Z , V S T A R , Y Y , A A , B B , * Y 1 , Y 2 , Y 3 EXTERNAL FUNCO,FUNC1,FUNC2,FUNC3,QROMB, POLINT, TRAPZD COMMON / Z D A T A / T , E O , S , Z NAA=NA VSTAR=80.64D0 R=8.314D0 B=50.0D0 A A = A ( 1 ) - 4 . D 0 * A ( 2 ) BB=A(1)+4.D0*A(2) EO=A(l) S=A(2) Z=A(3) T=XX+273.13D0 CALL QROMB(FUNCO,AA,BB,Y) YY=Y Y = V S T A R * ( 1 . D O - Y Y / ( 2 . 5 0 6 6 2 8 D 0 * S ) ) CALL QROMB(FUNC1,AA,BB, Y l ) D Y D A ( 1 ) = Y 1 + D E X P ( - Z * R * T * * 2 / ( B * ( E O + 4 . D 0 * S ) ) * D E X P ( - ( E O + 4 . D 0 * S ) / ( R * T ) * ) * ( l . D 0 - 2 . D 0 * R * T / ( E O + 4 . D 0 * S ) ) ) * D E X P ( - 8 . D O ) - D E X P ( - Z * R * T * * 2 * / ( B * ( E O - 4 . D 0 * S ) ) * D E X P ( - ( E O - 4 . D 0 * S ) / ( R * T ) ) * ( 1 . D 0 - 2 . D 0 * R * T / * ( E O - 4 . D 0 * S ) ) ) * D E X P ( - 8 . D 0 ) DYDA(1 )= -DYDA(1) *VSTAR/ (2 .506628D0*S) CALL QROMB(FUNC2,AA,BB,Y2) D Y D A ( 2 ) = Y 2 + 4 . D 0 * D E X P ( - Z * R * T * * 2 / ( B * ( E O + 4 . D 0 * S ) ) * D E X P ( - ( E O + 4 . D 0 * S ) / * ( R * T ) ) * ( l . D 0 - 2 . D 0 * R * T / ( E O + 4 . D 0 * S ) ) ) * D E X P ( - 8 . D O ) + 4 . D 0 * D E X P * ( - Z * R * T * * 2 / ( B * ( E O - 4 . D 0 * S ) ) * D E X P ( - ( E O - 4 . D 0 * S ) / ( R * T ) ) * ( 1 . D 0 * - 2 . D 0 * R * T / ( E O - 4 . D 0 * S ) ) ) * D E X P ( - 8 . D 0 ) D Y D A ( 2 ) = - V S T A R * ( Y Y / S - D Y D A ( 2 ) ) / ( 2 . 5 0 6 6 2 8 D 0 * S ) 183 CALL QROMB(FUNC3, AA,BB, Y3) DYDA(3)=-Y3*VSTAR/(2.506628D0*S) RETURN END SUBROUTINE QROMB(FUNC,A,B,SS) INTEGER JMAX,JMAXP,J,K, KM, L DOUBLE PRECISION EPS,A,B,SS,DSS PARAMETER(EPS=5.D-3,JMAX=500,JMAXP=JMAX+1,K=5,KM=4) DOUBLE PRECISION S(JMAXP),H(JMAXP) EXTERNAL FUNC H( l ) = l . DO 11 J=l,JMAX CALL TRAPZD(FUNC, A, B, S(J) , J) IF (J.GE.K) THEN L=J-KM CALL POLINT(H(L),S(L),K,0.DO,SS,DSS) IF (DABS(DSS).LT.EPS*DABS(SS)) RETURN ENDIF S(J+1)=S(J) H(J+1)=0.25D0*H(J) 11 CONTINUE PAUSE 'Too many steps.' END SUBROUTINE TRAPZD(FUNC,A,B, S,N) INTEGER N,IT,J DOUBLE PRECISION A, B,S,DEL,TNM,SUM,X IF (N.EQ.l) THEN S=0.5D0*(B-A)*(FUNC(A)+FUNC(B)) IT=1 ELSE TNM=IT DEL=(B-A)/TNM X=A+0.5D0*DEL SUM=0.DO DO 11 J=1,IT SUM=SUM+FUNC(X) X=X+DEL 11 CONTINUE S=0.5D0*(S+(B-A) *SUM/TNM) IT=2*IT ENDIF RETURN END SUBROUTINE POLINT(XA,YA,N,X,Y,DY) INTEGER I,M,N,NS,NMAX PARAMETER (NMAX=10) DOUBLE PRECISION XA (N),YA (N),C(NMAX),D(NMAX),X,Y,DY,DIFT,HO,HP,W, * DEN NS=1 DIF=DABS(X-XA(l)) DO 11 1=1,N DIFT=DABS(X-XA(I)) IF (DIFT.LT.DIF) THEN NS=I DIF=DIFT ENDIF C(I)=YA(I) D(I)=YA(I) 11 CONTINUE Y=YA(NS) 184 NS=NS-1 DO 13 M=1,N-1 DO 12 1=1,N-M HO=XA(I ) -X HP=XA(I+M)-X W=C(I+1)-D(I ) DEN=HO-HP I F ( D E N . E Q . 0 . D O ) P A U S E DEN=W/DEN D(I)=HP+DEN C( I )=HO*DEN CONTINUE I F ( 2 * N S . L T . N - M ) T H E N DY=C(NS+1) E L S E DY=D(NS) NS=NS-1 ENDIF Y=Y+DY CONTINUE RETURN END DOUBLE PRECISION FUNCTION FUNCO(E) DOUBLE PRECISION T , E O , S , Z , E COMMON/Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 F U N C 0 = D E X P ( - Z * R * T * * 2 / ( B * E ) * D E X P ( - E / ( R * T ) ) * ( 1 . D O - 2 . D O * R * T / E ) ) 1 * D E X P ( - 0 . 5 D 0 * ( ( E - E O ) / S ) * * 2 ) RETURN END DOUBLE PRECISION FUNCTION FUNCl(E) DOUBLE PRECISION T , E O , S , Z , E COMMON / Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 F U N C 1 = D E X P ( - Z * R * T * * 2 / ( B * E ) * D E X P ( - E / ( R * T ) ) * ( 1 . D 0 - 2 . D 0 * R * T / E ) ) 1 * D E X P ( - 0 . 5 D 0 * ( ( E - E O ) / S ) * * 2 ) * ( E - E O ) / S * * 2 RETURN END DOUBLE PRECISION FUNCTION FUNC2(E) DOUBLE PRECISION T , E O , S , Z , E COMMON / Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 F U N C 2 = D E X P ( - Z * R * T * * 2 / ( B * E ) * D E X P ( - E / ( R * T ) ) * ( 1 . D 0 - 2 . D 0 * R * T / E ) ) * 1 D E X P ( - 0 . 5 D 0 * ( ( E - E O ) / S ) * * 2 ) * ( E - E O ) * * 2 / S * * 3 RETURN END DOUBLE PRECISION FUNCTION FUNC3(E) DOUBLE PRECISION T , E O , S , Z , E COMMON / Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 F U N C 3 = D E X P ( - Z * R * T * * 2 / ( B * E ) * D E X P ( - E / ( R * T ) ) * ( 1 . D O - 2 . D 0 * R * T / E ) ) * ( -* * T * * 2 / ( B * E ) ) * D E X P ( - E / ( R * T ) ) * ( 1 . D O - 2 . D 0 * R * T / E ) * D E X P ( - 0 . 5 D 0 * E O ) / S ) * * 2 ) RETURN END Fitting Result with Anthony-Howard Model for RUN#61 E J/mol s J/mol i -1 k s 114999.999951 14999.998064 500000004.536339 T ° C V e x p Vmod .00000 .39000 -.00868 49.85000 .39000 -.00783 124.50000 .39000 .04946 143.15000 .61000 .10393 176.35000 1.78000 .34987 201.20000 3.16000 .82673 226.10000 4.81000 1.69501 251.00000 6.89000 3.04457 275.00000 8.99000 5.27093 298.65000 11.61000 8.66743 325.65000 14.82000 13.68217 348.45000 17.79000 18.60192 375.40000 21.77000 26.42453 402.35000 26.49000 36.10305 416.15000 31.20000 41.01006 437.60000 34.13000 47.87946 452.10000 38.87000 52.29991 466.60000 44.29000 56.74668 477.00000 49.16000 59.87655 485.30000 53.50000 62.26663 495.65000 59.62000 65.02800 503.95000 64.66000 67.00712 512.25000 69.34000 68.74093 524.70000 74.19000 70.88771 537.10000 77.14000 72.60551 549.55000 78.75000 74.08491 576.50000 80.01000 76.79565 601.40000 80.34000 78.57816 676.05000 80,64000 80.37077 700.00000 80.64000 80.52666 186 APPENDIX E FORTRAN Program for Two-Stage First Order Reaction Model C O r i g i n a l experimental data: C V(M) Experimental v o l a t i l e content % C VD(M) Experimental dV/dT,VD(I)=(V(I+1)-V(I))/(T(I+l)-T(I)) C T(M) Experimental temperature C X(M) 1/T(M) i n K C M No. of experimental data points C LN No. of experimental data points omitted at the beginning f o r C f i t t i n g C C VF F i t t i n g r e s u l t s i n the e n t i r e temperature range C C F i r s t reaction f i t t i n g parameters (Section below temperature 450 oC) C N No. of f i r s t reaction data points C VI(N) Experimental v o l a t i l e content % C VD1(N) Experimental dV/dT C Tl(N) Experimental temperature C XI(N) 1/T1(N) C Al(2) F i t t i n g array used i n FLSQP subroutine for f i r s t reaction C Yl(N) F i t t i n g parameter derived from VI (N) using r e l a t i v e method C Y1F(N) F i t t e d value for Yl(N) using r e l a t i v e method C V1F(N) F i t t e d v o l a t i l e using r e l a t i v e method C C F i r s t reaction f i t t i n g parameters (Section below temperature 450 oC) C MN No. of second reaction data points C V2(MN) Experimental v o l a t i l e content % C VD2(MN) Experimental dV/dT C T2(MN) Experimental temperature C X2(MN) 1/T2(MN) C A2(2) F i t t i n g array used i n FLSQP subroutine f o r second r e a c t i o n C Y2(MN) F i t t i n g parameter derived from V2(MN) using r e l a t i v e method C Y2F(MN) F i t t e d value f o r Y2(MN) using r e l a t i v e method C V2F(MN) F i t t e d v o l a t i l e using r e l a t i v e method C C Subscript for each method C C NT Integral method C CR Coats-Redfern method C CN Chen-Nuttall method C FM Friedman method C IMPLICIT REAL*8(A-H,0-Z) PARAMETER (M=37,N=14,MN=14,LN=4) EXTERNAL NOMIAL DIMENSION V(M),T(M),X(M),A1(2),A2(2),VD(M) DIMENSION VI(N),T1(N),X1(N),V2(MN),T2(MN),X2(MN),VD1(N),VD2(MN), 1 Y1NT(N),Y1FNT(N), V1FNT(N),Y2NT(MN),Y2FNT(MN),V2FNT(MN),VFNT(M), 2 Y1CR(N),Y1FCR(N),V1FCR(N),Y2CR(MN),Y2FCR(MN),V2FCR(MN),VFCR(M), 3 Y1CN(N),YIFCN(N),V1FCN(N),Y2CN(MN),Y2FCN(MN),V2FCN(MN),VFCN(M), 4 Y1FM(N),Y1FFM(N),V1FFM(N),Y2FM(MN),Y2FFM(MN),V2FFM(MN),VFFM(M) DIMENSION VDNT(M),VDCR(M),VDCN(M),VDFM(M) C canmet p i t c h 25 oC/min and 800 oC DATA V/99.96D0,99.94D0,99.50D0,98.98D0,97.83D0,96.14D0,94.43D0, 1 92.41D0,90.17D0,87.92D0,85.52D0,82.67D0,81.30D0,79.35D0,77.45D0, 2 74.91D0,72.41D0,69.25D0,65.96D0,62.65D0,59.69D0,56.33D0,51.74D0, 3 46.48D0,41.57D0,36.49D0,32.58D0,28.48D0,25.14D0,22.84D0,21.38D0, 4 20.30D0,19.97D0,19.71D0,19.48D0,19.28D0,19.16D0/ DATA T/ 50.22D0,100.32D0,135.40D0,153.77D0,175.47D0,200.52D0, 1 225.60D0,250.65D0,275.70D0,300.75D0,325.80D0,350.85D0,362.55D0, 2 375.90D0,387.60D0,400.95D0,414.32D0,426.00D0,437.70D0,447.72D0, 3 456.07D0,464.42D0,474.45D0,484.45D0,492.80D0,500.00D0,507.85D0, 4 516.20D0,526.22D0,537.90D0,551.27D0,576.32D0,601.37D0,649.80D0, 5 699.90D0,750.00D0,800.12D0/ DATA R,VO,C/8.314D0,80.84D0,25.DO/ OPEN(UNIT = 3, FILE = 'FIT2RN1.DAT', 1 ACCESS = 'SEQUENTIAL', STATUS = 'OLD') E1=250.D3 DO 10 1=1,M V(I)=100.D0-V(I) T(I)=T(I)+273.16D0 X(I)=1.D0/T(I) 10 CONTINUE DO 20 1=1,N VI (I)=V(LN+I) T1(I)=T(LN+I) XI (I)=X(LN+I) 20 CONTINUE DO 30 1=1,MN V2(I)=V(LN+N+I) T2(I)=T(LN+N+I) X2(I)=X(LN+N+I) 30 CONTINUE C C INTERGRAL METHOD C C F i r s t reaction C 4 0 E10LD=E1 DO 50 1=1,N Y1NT(I)=DLOG(-C*DLOG(1.D0-V1(I)/VO)/(R*T1(I)*T1(I))) 1 -DLOG(1.DO-2.DO*R*T1(I)/E1) 50 CONTINUE CALL FLSQP(X1,Y1NT,N,2,A1,VAR) E1=-A1(2)*R IF(DABS(El-EIOLD).LT.1.0D-8) THEN RK1=EXP(Al(1))*E1 VAR1=VAR GOTO 60 ENDIF GOTO 40 60 CONTINUE DO 70 1=1,N Y1FNT(I)=A1(1)+A1(2)*X1(I) VlFNT(I)=VO*(1.D0-EXP(-RK1*R*T1(I)*T1(I)*EXP(-E1/(R*T1(I)))*(1.D0-1 2.D0*R*T1(I)/E1)/(C*E1))) 70 CONTINUE C C Second reaction C E2=E1 80 E20LD=E2 DO 90 1=1,MN Y2NT(I)=DLOG(-C*DLOG(1.D0-V2(I)/VO)/(R*T2(I)*T2(I))) 1 -DLOG(l.D0-2.D0*R*T2(I)/E2) 90 CONTINUE CALL FLSQP(X2,Y2NT,MN,2,A2,VAR) E2=-A2(2)*R IF(DABS(E2-E20LD).GE.1.0D-8) GOTO 80 RK2=EXP(A2(1))*E2 DO 100 1=1,MN Y2FNT(I)=A2(1)+A2(2)*X2(I) 188 V2FNT(I)=VO*(l.DO-EXP(-RK2*R*T2(I)*T2(I)*EXP(-E2/(R*T2 (I))) 1 *(l.D0-2.D0*R*T2(I)/E2)/(C*E2)) ) 100 CONTINUE WRITE(*,*) * INTEGRAL METHOD SUCCESSFUL" C C Coats-Redfern method C C F i r s t reaction C DO 110 1=1,N Y1CR(I)=DLOG(-C* DLOG(1.D0-V1(I)/VO)/(R*Tl(I)*Tl(I))) 110 CONTINUE CALL FLSQP(X1,Y1CR,N,2,A1,VAR) E1CR=-A1(2)*R RK1CR=EXP(Al(1))*E1CR DO 120 1=1,N Y1FCR(I)=A1 (1)+A1 (2) *X1 (I) VlFCR(I)=VO*(l.DO-EXP(-RK1CR*R*T1(I)*T1(I)*EXP(-E1CR/(R*T1(I)))* 1 (l.D0-2.D0*R*Tl(I)/E1CR)/(C*E1CR))) 120 CONTINUE C C Second reaction C DO 130 I=1,MN Y2CR(I)=DLOG(-C*DLOG(l.D0-V2(I)/VO)/(R*T2(I)*T2(I))) 130 CONTINUE CALL FLSQP(X2,Y2CR,MN,2,A2,VAR) E2CR=-A2(2)*R RK2CR=EXP(A2(1))*E2CR DO 140 1=1,MN Y2FCR(I)=A2(1)+A2(2)*X2(I) V2FCR(I)=VO*(l.DO-EXP(-RK2CR*R*T2(I)*T2(I)*EXP(-E2CR/(R*T2(I))) 1 *(1.DO-2.D0*R*T2(I)/E2CR)/(C*E2CR))) 140 CONTINUE WRITE(*,*) "COATS-REDFERN METHOD SUCESSFUL" C C C Chen-Nuttall method C C F i r s t reaction C E1CN=E1CR 150 EOLD=ElCN DO 160 1=1,N YlCN(I)=DLOG(-C*(E1CN+2.D0*R*T1(I))* DLOG(1. D0-V1(I)/VO)/ 1 (T1(I)*T1(I)*R)) 160 CONTINUE CALL FLSQP(X1,Y1CN,N,2,A1,VAR) E1CN=-R*A1(2) IF(DABS(ElCN-EOLD).GE.1.0D-8) GOTO 150 RK1CN=EXP(Al (1)) DO 170 1=1,N Y1FCN(I)=A1(1)+A1(2)*X1(I) V1FCN(I)=VO*(l.DO-EXP(-RK1CN*R*T1(I)*T1(I)*EXP(-E1CN/(R*T1(I)))* 1 (1.D0-2.D0*R*T1(I)/E1CN)/(C*E1CN))) 170 CONTINUE C C Second reaction C E2CN=E1CN 180 EOLD=E2CN DO 190 1=1,MN Y2CN(I)=DLOG(-C*(E2CN+2.D0*R*T2(I))*DLOG(1.D0-V2(I)/VO)/(T2(I)* 189 1 T2(I)*R)) 190 CONTINUE CALL FLSQP(X2,Y2CN,MN,2,A2,VAR) E2CN=-R*A2(2) IF(DABS(E2CN-EOLD).GE.1.0D-8) GOTO 180 RK2CN=EXP(A2(1)) DO 200 1=1,MN Y2FCN(I)=A2(1)+A2(2)*X2(I) V2FCN(I)=VO*(1.D0-EXP(-RK2CN*R*T2(I)*T2(I)*EXP(-E2CN/(R*T2(I)))* 1 (l.D0-2.D0*R*T2(I)/E2CN)/(C*E2CN))) 200 CONTINUE WRITE(*,*) 'CHEN-NUTTAL METHOD SUCESSFUL' C C C Friedman Method C DO 210 1=1,M-l VD(I)=(V(I+1)-V(I))/(T(I+l)-T(I)) 210 CONTINUE VD(M)=VD(M-1) DO 220 1=1,N VD1(I)=VD(LN+I) 220 CONTINUE DO 230 1=1,MN VD2(I)=VD(LN+N+I) 230 CONTINUE C C C F i r s t reaction DO 240 1=1,N Y1FM(I)=DLOG(C/VO*VDl(I))-DLOG(1.D0-V1(I)/VO) 240 CONTINUE CALL FLSQP(X1,Y1FM,N,2,A1,VAR) E1FM=-A1(2)*R RK1FM=EXP(A1(1)) DO 250 1=1,N Y1FFM(I)=A1(1)+A1(2)*X1(I) VlFFM(I)=VO*(1.D0-EXP(-RK1FM*R*T1(I)*T1(I)*EXP(-E1FM/(R*T1(I)))* 1 (1.0D0-2.D0*R*T1(I)/E1FM)/(C*E1FM))) 250 CONTINUE C C Second reaction C DO 260 1=1,MN Y2FM(I)=DLOG(C/VO*VD2(I))-DLOG(1.D0-V2(I)/VO) 260 CONTINUE CALL FLSQP(X2,Y2FM,MN,2,A2,VAR) E2FM=-A2(2)*R RK2FM=EXP(A2(1)) DO 270 1=1,MN Y2FFM(I)=A2(1)+A2(2)*X2(I) V2FFM(I)=VO*(1.D0-EXP(-RK2FM*R*T2(I)*T2(I)*EXP(-E2FM/(R*T2(I)))* 1 (l.D0-2.D0*R*T2(I)/E2FM)/(C*E2FM))) 270 CONTINUE WRITE(*,*) 'FRIEDMAN METHOD SUCESSFUL' C C Calculate the v o l a t i l e content i n the en t i r e temperature range C DO 280 1=1,M IF((T(I)-273.16).LT.450.D0) THEN VFNT(I)=VO*(l.D0-EXP(-RKl*R*T(I)*T(I)*EXP(-El/(R*T(I)))*(1.D0-190 1 2.D0*R*T(I)/E1)/(C*E1))) VFCR(I)=V0*(1.DO-EXP(-RK1CR*R*T(I)*T(I)*EXP(-E1CR/(R*T(I)))* 1 (l.D0-2.D0*R*T(I)/E1CR)/(C*E1CR))) VFCN(I)=VO*(l.DO-EXP(-RK1CN*R*T(I)*T(I)*EXP(-E1CN/(R*T(I)))* 1 (1.D0-2.D0*R*T(I)/E1CN)/(C*E1CN))) VFFM(I)=VO*(l.DO-EXP(-RK1FM*R*T(I)*T(I)*EXP(-E1FM/(R*T(I)))* 1 (1.0D0-2.D0*R*T(I)/E1FM)/(C*E1FM))) ELSE VFNT(I)=VO*(l.D0-EXP(-RK2*R*T(I)*T(I)*EXP(-E2/(R*T(I))) 1 *(1.D0-2.D0*R*T(I)/E2)/(C*E2))) VFCR(I)=VO*(1.DO-EXP(-RK2CR*R*T(I)*T(I)*EXP(-E2CR/(R*T(I))) 1 *(l.D0-2.D0*R*T(I)/E2CR)/(C*E2CR))) VFCN(I)=VO*(l.DO-EXP(-RK2CN*R*T(I)*T(I)*EXP(-E2CN/(R*T(I)))* 1 (l.D0-2.D0*R*T(I)/E2CN)/(C*E2CN))) VFFM(I)=VO*(l.DO-EXP(-RK2FM*R*T(I)*T(I)*EXP(-E2FM/(R*T(I)))* 1 (l.D0-2.D0*R*T(I)/E2FM)/(C*E2FM))) ENDIF 280 CONTINUE C C Calculate the rate at e n t i r e temperature range C DO 290 1=1,M IF((T(I)-273.16D0).LT.450.D0) THEN VDNT(I)=RK1*EXP(-E1/R/T(I))*(VO-V(I))/C VDCR(I)=RK1CR*EXP(-E1CR/R/T(I))*(VO-V(I))/C VDCN(I)=RK1CN*EXP(-E1CN/R/T(I))*(VO-V(I))/C VDFM(I)=RK1FM*EXP(-E1FM/R/T(I))*(VO-V(I))/C ELSE VDNT(I)=RK2*EXP(-E2/R/T(I))*(VO-V(I))/C VDCR(I)=RK2CR*EXP(-E2CR/R/T(I))*(VO-V(I))/C VDCN(I)=RK2CN*EXP(-E2CN/R/T(I))*(VO-V(I))/C VDFM(I)=RK2FM*EXP(-E2FM/R/T(I))*(VO-V(I))/C ENDIF 290 CONTINUE C C Calculate the absolute average deviation ERROR C SEENT=0.D0 SEECR=0.DO SEECN=0.DO SEEFM=0.DO DO 450 1=1,M SEENT=SEENT+(V(I)-VFNT(I))**2 SEECR=SEECR+(V(I)-VFCR(I))**2 SEECN=SEECN+(V(I)-VFCN(I))**2 SEEFM=SEEFM+(V(I)-VFFM(I))**2 450 CONTINUE SEENT=SQRT((SEENT)/(DBLE(M)-2.DO)) SEECR=SQRT((SEECR)/(DBLE(M)-2.DO)) SEECN=SQRT((SEECN)/(DBLE(M)-2.DO)) SEEFM=SQRT((SEEFM)/(DBLE(M)-2.DO)) WRITE(*,*) SEENT,SEECR,SEECN,SEEFM C C P r i n t i n g r e s u l t s of VI, V2, V1F and V2F C DO 500 1=1,M T(I)=T(I)-273.16D0 500 CONTINUE WRITE(3, 550) 550 FORMAT(//'Fitting r e s u l t s i n the selected temperature range') WRITE(3, 600) 600 FORMAT (4X, 'T',8X, 'V',8X, 'VFNT',5X, 'VFCR',6X, 'VFCN',6X, ' VFFM1 , 1 8X,'VD') DO 620 1=1,N WRITE(3,610) T(LN+I),V(LN+I) ,V1FNT(I) ,V1FCR(I),V1FCN(I),V1FFM(I), 1 VD(LN+I) 610 FORMAT(F7.2,6F10.6) 620 CONTINUE DO 640 1=1,MN WRITE(3,630) T(LN+N+I),V(LN+N+I),V2FNT(I),V2FCR(I),V2FCN(I), 1 V2FFM(I),VD(LN+N+I) 630 FORMAT(F7.2,6F10.6) 640 CONTINUE WRITE(3, 650) 650 FORMAT(//'Activation energies and pre-exponential f a c t o r f o r both 1 reactions') WRITE(3, 660) 660 FORMAT(30X,'E1',10X,'K1',10X,'E2',10X,'K2') WRITE(3,670) E l , RK1,E2,RK2 670 FORMAT('Integral method',10X,4F12.3) WRITE(3,680) E1CR,RK1CR,E2CR, RK2CR 680 FORMAT('Coats-Redfern method', 5X, 4F12.3) WRITE(3,690) ElCN,RK1CN,E2CN,RK2CN 690 FORMAT('Chen-Nuttall method',6X,4F12.3) WRITE(3,700) E1FM,RK1FM,E2FM, RK2FM 700 FORMAT('Friedman method',10X,4F12.3) C C P r i n t i n g the r e s u l t s of Y l , Y2, Y1F and Y2F C WRITE(3,701) 701 FORMAT(//'Experimental re s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F') WRITE(3,702) 702 FORMAT(4X,'T',5X,'YNT',5X,'YFNT',4X,'YCR',5X,'YFCR',4X,'YCN',5X, 1 'YFCN',4X,'YFM',5X,'YFFM') DO 704 I=MN,1,-1 WRITE(3,703) X2(I),Y2NT(I),Y2FNT(I) , Y2CR(I) , Y2FCR(I),Y2CN(I), 1 Y2FCN(I),Y2FM(I),Y2FFM(I) 703 FORMAT(F8.6,8F8.3) 704 CONTINUE DO 705 I=N,1,-1 WRITE(3,703) X1(I),Y1NT(I),Y1FNT(I),Y1CR(I),Y1FCR(I),Y1CN(I), 1 YIFCN(I),Y1FM(I),Y1FFM(I) 705 CONTINUE C C P r i n t i n g the r e s u l t s i n the ent i r e temperature range C WRITE(3,710) 710 FORMAT(//'Fitting r e s u l t s i n the e n t i r e temperature range') WRITE(3,720) 720 FORMAT (4X, 'T',7X, 'V,7X, 'VFNT',6X, 'VFCR',6X, 'VFCN',6X, 'VFFM' ) DO 740 1=1,M WRITE(3,730) T(I),V(I),VFNT(I),VFCR(I),VFCN(I) ,VFFM(I) 730 FORMAT(F7.2,5F10.6) 740 CONTINUE C C P r i n t i n g the standard deviation C WRITE(3,742) 742 FORMAT(//'standard deviation f o r each method above') WRITE(3,746) SEENT,SEECR,SEECN,SEEFM 746 FORMAT(17X,4F10.6) C 192 C P r i n t i n g the rates i n the enti r e temperature range C WRITE(3,750) 750 FORMAT(//'Fitting rate dV/dT i n the en t i r e temperature reange') WRITE(3,760) 760 FORMAT (4X, 'T',6X, 'VD',7X, 'VDNT'^X, 'VDCR'^X, 'VDCN',6X, ' VDFM' ) DO 770 1=1,M WRITE(3,730) T(I),VD(I),VDNT(I),VDCR(I),VDCN(I),VDFM(I) 770 CONTINUE ENDFILE(UNIT = 3) CLOSE(UNIT =3) STOP END SUBROUTINE GAUSS(A,N,NDR,NDC,X,RNORM,IREEOR) IMPLICIT REAL*8(A-H,0-Z) DIMENSION A(NDR,NDC),X(N),B(50, 51) NM=N-1 NP=N+1 IREEOR=3 DO 20 1=1,N DO 10 J=1,NP B (I, J) =A(I, J) 10 CONTINUE 20 CONTINUE DO 70 K=1,NM KP=K+1 BIG=ABS(B(K,K)) IPIVOT=K DO 30 I=KP,N AB=ABS(B(I,K)) IF(AB.GT.BIG) THEN BIG=AB IPIVOT=I ENDIF 30 CONTINUE IF(IPIVOT.NE.K) THEN DO 40 J=K,NP TEMP=B(IPIVOT,J) B(IPIVOT,J)=B(K,J) B(K, J)=TEMP 40 CONTINUE ENDIF IF(B(K,K).EQ.0.D0) THEN IERROR=2 RETURN ENDIF DO 60 I=KP,N QUOT=B(I,K)/B(K,K) B(I,K)=0.D0 DO 50 J=KP,NP B(I, J)=B(I,J)-QUOT*B(K,J) 50 CONTINUE 60 CONTINUE 70 CONTINUE IF(B(N,N).EQ.0.D0) THEN IERROR=2 RETURN 193 ENDIF X(N)=B(N,NP)/B(N,N) DO 90 I=NM,1,-1 SUM=0.D0 DO 80 J=I+1,N SUM=SUM+B(I,J)*X(J) 80 CONTINUE X(I)=(B(I,NP)-SUM)/B(I,I) 90 CONTINUE RSQ=0.D0 DO 110 1=1,N SUM=0.DO DO 100 J=1,N SUM=SUM+A(I,J)*X(J) 100 CONTINUE RSQ=RSQ+(A(I,NP)-SUM)* * 2 110 CONTINUE RNORM=DSQRT(RSQ) IERROR=l RETURN END SUBROUTINE FLSQP(X,Y,M,N,A,VAR) IMPLICIT REAL*8(A-H,0-Z) DIMENSION X(M) , U(51),Y(M),V(51),A(N),B(11) , COEFF(10, 11) ,SUMU(18) NP=N+1 NM2=2*(N-1) XMIN=X(1) XMAX=X(1) YMIN=Y(1) YMAX=Y(1) DO 10 K=2,M XMIN=DMIN1(XMIN,X(K)) XMAX=DMAX1(XMAX,X(K)) YMIN=DMIN1(YMIN,Y(K)) YMAX=DMAX1(YMAX,Y(K)) 10 CONTINUE XP=XMIN+XMAX XM=XMAX-XMIN YP=YMIN+YMAX YM=YMAX-YMIN DO 20 K=1,M U(K)=(2.D0*X(K)-XP)/XM V(K)=(2.D0*Y(K)-YP)/YM 20 CONTINUE DO 30 L=1,NM2 SUMU(L)=0.D0 30 CONTINUE DO 40 1=1,N COEFF(I,NP)=0.DO 40 CONTINUE DO 70 K=1,M TERMU=U(K) DO 50 L=1,NM2 SUMU(L)=SUMU(L)+TERMU TERMU=TERMU*U(K) 50 CONTINUE TERMV=V(K) DO 60 1=1,N COEFF(I,NP)=COEFF(I,NP)+TERMV TERMV=TERMV*U(K) 194 60 CONTINUE 70 CONTINUE DO 90 1=1,N DO 80 J=1,N IF(I.EQ.1. AND.J.EQ.1) THEN COEFF(I,J)=M ELSE COEFF(I,J)=SUMU(I+J-2) ENDIF 80 CONTINUE 90 CONTINUE CALL GAUSS(COEFF,N,10,11,B,RNORM,IERROR) DO 110 1=1,N IM=I-1 SUM=B(I) IF(I.NE.N) THEN DO 100 J=I+1,N SUM=SUM+NOMIAL(IM,J-l)*(-XP/XM)**(J-I)*B(J) 100 CONTINUE ENDIF A(I)=YM*(2.D0/XM)**IM*SUM/2.DO 110 CONTINUE A(1)=A(1)+YP/2.D0 SSUM=0.D0 DO 130 K=1,M SUM=A(1) TEMP=1.D0 DO 120 J=2,N TEMP=TEMP*X(K) SUM=SUM+A(J)+TEMP 120 CONTINUE SSUM=SSUM+(Y(K)-SUM)**2 130 CONTINUE VAR=SSUM/(M-N) RETURN END C FUNCTION NOMIAL(I,J) NOMIAL=l IF(J.LE.I.OR.I.EQ.O) RETURN DO 10 ICOUNT=l,I NOMIAL=NOMIAL*(J-ICOUNT+1)/ICOUNT . 10 CONTINUE RETURN END 195 2-Stage First Order Reaction Model Fitting Results C A N M E T pitch 25 "C/min, 800 °C final temperature RUN# CAN48 Experimental r e s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM YFFM .001177 -10. 718 -10. 575 -10. 939 -10. 794 412 556 -1. 242 179 .001213 -10. 836 -10. 882 -11. 049 -11. 095 297 251 723 -. 349 .001233 -10. 958 -11. 053 -11. 168 -11. 263 176 081 299 443 .001251 -11. 104 -11. 208 -11. 310 -11. 414 . 031 073 195 529 .001267 -11. 268 -11. 344 -11. 471 -11. 548 -. 132 208 112 -. 604 .001280 -11. 434 -11. 460 -11. 635 -11. 662 -. 297 324 089 -. 668 .001293 -11. 570 -11. 572 -11. 768 -11. 771 -. 432 435 331 -. 730 .001306 -11. 736 -11. 676 -11. 932 -11. 873 -. 598 539 239 788 .001320 -11. 884 -11. 800 -12. 078 -11. 994 745 661 620 -. 856 .001338 -12. 037 -11. 951 -12. 228 -12. 143 898 ' -. 812 907 -. 940 .001356 -12. 170 -12. 107 -12. 358 -12. 296 -1. 029 967 -1. 178 -1. 026 .001371 -12. 267 -12. 240 -12. 453 -12. 426 -1. 126 -1. 099 -1. 393 -1. 099 .001387 -12. 354 -12. 377 -12. 538 -12. 560 -1. 213 -1. 235 -1. 591 -1. 175 .001407 -12. 455 -12. 545 -12. 636 -12. 725 -1. 313 -1. 402 -1. 735 -1. 267 .001430 -11. 979 -12. 050 -12. 736 -12. 779 -2. 380 -2. 429 -1. 964 -2. 384 .001455 -12. 100 -12. 114 -12. 839 -12. 832 -2. 489 -2. 487 -2. 063 -2. 437 .001483 -12. 199 -12. 190 -12. 916 -12. 896 -2. 573 -2. 556 -2. 479 -2. 501 .001513 -12. 307 -12. 269 -13. 004 -12. 962 -2. 668 -2. 628 -2. 506 -2. 567 .001541 -12. 392 -12. 341 -13. 071 -13. 022 -2. 742 -2. 693 -2. 696 -2. 628 .001573 -12. 485 -12. 426 -13. 144 -13. 093 -2. 822 -2. 770 -2. 834 -2. 699 .001603 -12. 551 -12. 504 -13. 193 -13. 158 -2. 878 -2. 840 -3. 077 -2. 764 .001670 -12. 705 -12. 680 -13. 312 -13. 306 -3. O i l -3. 000 -3. 150 -2. 912 .001742 -12. 853 -12. 872 -13. 425 -13. 466 -3. 138 -3. 173 -3. 357 -3. 073 .001822 -13. 018 -13. 081 -13. 558 -13. 642 -3. 285 -3. 363 -3. 454 -3. 249 .001909 -13. 231 -13. 311 -13. 738 -13. 834 -3. 480 -3. 571 -3. 489 -3. 441 .002005 -13. 487 -13. 563 -13. 963 -14. 045 -3. 719 -3. 799 -3. 620 -3. 653 .002111 -13. 792 -13. 843 -14. 238 -14. 279 -4. 009 -4. 052 -3. 810 -3. 887 .002229 -14. 299 -14. 153 -14. 716 -14. 538 -4. 502 -4. 333 -3. 843 -4. 147 F i t t i n g r e s u l t s i n the e n t i r e temperature range T V VFNT VFCR VFCN VFFM 50. 22 040000 155567 143757 173164 254039 100. 32 060000 585928 446609 . 583486 . 789804 135. 40 500000 1. 231859 842096 1. 151879 1. 488240 153. 77 1. 020000 1. 733712 1. 126916 1. 574572 1. 990044 175. 47 2. 170000 2. 504867 1. 541807 2. 204314 2. 719006 200. 52 3. 860000 3. 671561 2. 135001 3. 126396 3. 756867 225. 60 5. 570000 5. 172992 2. 858170 4. 276503 5. 014856 250. 65 7. 590000 7. 032889 3. 711836 5. 662237 6. 489252 275. 70 9. 830000 9. 265615 4. 693808 7. 285796 8. 170753 300. 75 12. 080000 11. 867032 5. 795725 9. 138123 10. 038886 325. 80 14. 480000 14. 815040 7. 003953 11. 200199 12. 064187 350. 85 17. 330000 18. 070076 8. 299930 13. 443768 14. 209525 362. 55 18. 700000 19. 680585 8. 928980 14. 543901 15. 240696 375. 90 20. 650000 21. 577142 9. 660695 15. 832638 16. 431792 387. 60 22. 550000 23. 282974 10. 311053 16. 986420 17. 482892 400. 95 25. 090000 25. 269189 11. 059527 18. 324429 18. 683748 414. 32 27. 590000 27. 289795 11. 811514 19. 680511 19. 880750 426. 00 30. 750000 29. 071447 12. 466628 20. 872552 20. 915811 437. 70 34. 040000 30. 863205 13. 117667 22. 068282 21. 937321 447. 72 37. 350000 32. 397342 13. 668495 23. 089827 22. 796086 456. 07 40. 310000 41. 062072 35. 863390 40. 231548 52. 110546 464. 42 43. 670000 45. 481618 39. 961255 44. 595503 54. 815420 474. 45 48. 260000 50. 810762 45. 020628 49. 878827 57. 945213 484. 45 53. 520000 55. 999556 50. 100606 55. 050838 60. 904851 492. 80 58. 430000 60. 121639 54. 273443 59. 184363 63. 232246 196 500. 00 63. 510000 63. 449886 57. 755135 62. 541985 65. 122477 507. 85 67. 420000 66. 779021 61. 365837 65. 923123 67. 051542 516. 20 71. 520000 69. 922558 64. 928926 69. 142386 68. 945288 526. 22 74. 860000 73. 101714 68. 744113 72. 433783 70. 996004 537. 90 77. 160000 75. 971799 72. 468759 75. 450494 73. 078863 551. 27 78. 620000 78. 230589 75. 729994 77. 874822 75. 066625 576. 32 79. 700000 80. 249327 79. 254115 80. 124226 77. 755774 601. 37 80. 030000 80. 759516 80. 506863 80. 733312 79. 351849 649. 80 80. 290000 80. 839754 80. 836274 80. 839570 80. 575569 699. 90 80. 520000 80. 840000 80. 839998 80. 840000 80. 812883 750. 00 80. 720000 80. 840000 80. 840000 80. 840000 80. 838394 800. 12 80. 840000 80. 840000 80. 840000 80. 840000 80. 839947 F i t t i n g rate dV/dT i n the en t i r e temperature range T VD VDNT VDCR VDCN VDFM 50. 22 .000399 .005196 .004289 .005420 .007594 100. 32 .012543 .015487 .010694 .014563 .018972 135. 40 .028307 .028220 .017650 .025052 .031347 153. 77 .052995 .036999 .022115 .031991 .039298 175. 47 .067465 .049144 .027976 .041305 .049740 200. 52 .068182 .065595 .035494 .053529 .063140 225. 60 .080639 .084826 .043850 .067409 .078044 250. 65 .089421 .106264 .052710 .082443 .093857 275. 70 .089820 .129585 .061912 .098369 .110288 300. 75 .095808 .154713 .071431 .115130 .127292 325. 80 .113772 .180904 .080943 .132188 .144295 350. 85 .117094 .206557 .089793 .148424 .160123 362. 55 .146067 .218426 .093755 .155798 .167211 375. 90 .162393 .230390 .097522 .163007 .173957 387. 60 .190262 .239737 .100294 .168466 .178925 400. 95 .186986 .248123 .102472 .173057 .182836 414. 32 .270548 .255705 .104300 .177062 .186123 426. 00 .281197 .256427 .103506 .176486 .184728 437. 70 .330339 .254908 .101856 .174410 .181803 447. 72 .354491 .249397 .098818 .169807 .176398 456. 07 .402395 .558800 .454728 .539926 .539964 464. 42 .457627 .585505 .475201 .565276 .533028 474. 45 .526000 .599901 .485379 .578632 .509290 484. 45 .588024 .585343 .472178 .564076 .464358 492. 80 .705556 .543249 .437149 .523123 .407799 500. 00 .498089 .466302 .374454 .448745 .334071 507. 85 .491018 .403712 .323475 .388251 .275146 516. 20 .333333 .314930 .251757 .302658 .203760 526. 22 .196918 .231569 .184618 .222364 .140963 537. 90 .109200 .166329 .132199 .159569 .094482 551. 27 .043114 .119123 .094357 .114163 .062666 576. 32 .013174 .083148 .065462 .079540 .038128 601. 37 .005369 .078905 .061765 .075349 .031788 649. 80 .004591 .089660 .069471 .085356 .028688 699. 90 .003992 .084197 .064620 .079924 .021745 750. 00 .002394 .048626 .037002 .046039 .010352 800. 12 .002394 .000000 .000000 .000000 .000000 C A N M E T pitch 50 °C/min, 800 °C final temperature RUN#33 Experimental r e s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM YFFM .001169 -10.078 -10.036 -10.328 -10.283 .939 .983 -.645 .522 .001207 -10.197 -10.328 -10.437 -10.568 .824 .693 -.131 .277 .001223 -10.306 -10.455 -10.543 -10.692 .716 .567 '.429 .171 .001240 -10.450 -10.587 -10.683 -10.820 .574 .437 .488 ,061 .001265 -10.725 -10.776 -10.953 -11.005 .300 .248 .437 -.098 197 . 001290 -11. 035 -10. 973 -11. 258 -11. 197 008 053 280 263 .001309 -11. 231 -11. 119 -11. 450 -11. 340 203 092 014 385 .001328 -11. 406 -11. 269 -11. 622 -11. 487 377 241 -. 262 -. 511 .001344 -11. 526 -11. 393 -11. 739 -11. 607 496 363 523 -. 614 .001360 -11. 642 -11. 519 -11. 852 -11. 730 611 488 -. 688 -. 720 .001369 -11. 695 -11. 583 -11. 904 -11. 793 664 -. 552 -. 824 -. 773 .001386 -11. 800 -11. 714 -12. 006 -11. 920 768 682 -. 946 -. 883 .001407 -11. 916 -11. 882 -12. 118 -12. 085 883 849 -1. 186 -1. 024 .001430 -12. 030 -12. 056 -12. 229 -12. 254 995 -1. 021 -1. 329 -1. 169 .001453 -12. 137 -12. 235 -12. 332 -12. 429 -1. 101 -1. 199 -1. 511 -1. 320 .001486 -12. 249 -12. 496 -12. 440 -12. 684 -1. 212 -1. 458 -1. 868 -1. 539 .001542 -11. 846 -11. 792 -12. 571 -12. 495 -2. 271 -2. 843 -2. 210 -2. 429 .001603 -11. 993 -11. 945 -12. 678 -12. 623 -2. 393 -3. 038 -2. 502 -2. 517 .001669 -12. 123 -12. 109 -12. 770 -12. 761 -2. 499 -3. 251 -2. 748 -2. 613 .001746 -12. 277 -12. 305 -12. 885 -12. 924 -2. 629 -3. 509 -2. 842 -2. 726 .001824 -12. 453 -12. 501 -13. 026 -13. 089 -2. 784 -3. 772 -2. 870 -2. 840 .001910 -12. 645 -12. 716 -13. 184 -13. 269 -2. 956 -4. 039 -3. 016 -2. 964 .002003 -12. 885 -12. 951 -13. 391 -13. 466 -3. 178 -4. 397 -3. 094 -3. 100 .002117 -13. 206 -13. 237 -13. 677 -13. 704 -3. 481 -4. 806 -3. 260 -3. 265 .002232 -13. 656 -13. 527 -14. 096 -13. 948 -3. 916 -5. 734 -3. 344 -3. 434 F i t t i n g r e s u l t s i n the e n t i r e temperature range T V VFNT VFCR VFCN VFFM 50. 10 320000 159415 138895 171486 . 591272 99. 10 310000 556368 404340 539215 1. 242183 125. 80 400000 971510 650541 . 898298 1. 709785 152. 50 1. 060000 1. 585018 986978 1. 405702 2. 241225 174. 80 2. 010000 2. 282442 1 .345596 1. 961703 2. 718060 199. 25 3. 370000 3. 271052 1 .826008 2. 724890 3. 253745 226. 00 4. 960000 4. 650494 2 .459542 3. 756319 3. 823297 250. 45 6. 640000 6. 202251 3 .136557 4. 883752 4. 293595 274. 95 8. 420000 8. 042902 3 .904061 6. 188210 4. 678267 299. 45 10. 430000 10. 164493 4 .752172 7. 658213 4. 934511 326. 15 12. 620000 12. 776137 5 .753620 9. 429510 5. 013092 350. 65 14. 760000 15. 416117 6 .726081 11. 185607 4. 845490 375. 15 17. 410000 18. 248549 7 .729867 13. 037547 4. 388759 399. 60 20. 810000 21. 219655 8 .740720 14. 948457 3. 578859 415. 20 23. 700000 23. 166671 9 .379280 16. 184024 2. 842789 426. 35 26. 510000 24. 573239 9 .828113 17. 068403 2. 197203 437. 45 29. 700000 25. 979937 10 .265765 17. 945754 1. 445455 448. 60 33. 180000 27. 394181 10 .693524 18. 820292 . 570909 457. 50 36. 470000 39. 517420 33 .781513 38. 494790 35. 907049 461. 95 38. 200000 41. 620283 35 .681101 40. 558965 37. 622476 470. 85 42. 010000 45. 875263 39 .583898 44. 747626 41. 113278 479. 75 46. 100000 50. 133976 43 .581692 48. 958655 44. 651810 490. 90 52. 050000 55. 353100 48 .633913 54. 150658 49. 087966 502. 05 58. 550000 60. 295076 53 .615079 59. 107162 53. 445751 517. 60 67. 700000 66. 450372 60 .191753 65. 355186 59. 225680 533. 20 74. 020000 71. 494238 66 .051103 70. 566098 64. 475386 544. 35 76. 480000 74. 320833 69 .637644 73. 542262 67. 790289 555. 45 77. 950000 76. 495891 72 .644783 75. 875617 70. 678095 582. 15 79. 280000 79 517704 77 .569040 79. 235903 75. 862118 624. 45 79 950000 80 709446 80 .389877 80. 675051 79. 724209 689 05 80 150000 80 789924 80 .787785 80. 789835 80. 758907 800 00 80 790000 80 790000 80 .790000 80. 790000 80 789999 F i t t i n g rate dV/dT i n the enti r e temperature range T 50.10 99.10 125.80 152.50 174.80 VD -.000204 .003371 .024719 .042601 .055624 VDNT ,005149 .014337 .022507 .033148 .043952 VDCR .004026 .009492 .013844 .019120 .024167 VDCN .005205 .013161 .019799 .028094 .036234 VDFM 014815 026812 034799 043396 050842 199.25 226.00 250.45 274.95 299.45 326.15 350.65 375.15 399.60 415.20 426.35 437.45 448.60 457.50 461.95 470.85 479.75 490.90 502.05 517.60 533.20 544.35 555.45 582.15 624.45 689.05 800.00 .059439 .068712 .072653 .082041 .082022 .087347 .108163 .139059 .185256 .252018 .287387 .312108 .369663 .388764 .428090 .459551 .533632 .582960 .588424 .405128 .220628 .132432 .049813 .015839 .003096 .005768 .005768 .057756 .075246 .093094 .112617 .133237 .156988 .179303 .200430 .218394 .226248 .228010 .227007 .223431 .532799 .545977 .563999 .570667 .549467 .492026 .352553 .220429 .160001 .119715 .085249 .072702 .098935 .000000 .030292 .037675 .044861 .052407 .060054 .068543 .076215 .083110 .088506 .090434 .090280 .089065 .086886 .421759 .431532 .444443 .448386 .430191 .383888 .273787 .170413 .123312 .091986 .065050 .054917 .073711 .000000 .046329 .058758 .071103 .084293 .097901 .113247 .127353 .140330 .150892 .155076 .155429 .153929 .150727 .510357 .522721 .539453 .545314 .524450 .469098 .335617 .209535 .151940 .113573 .080693 .068592 .092926 .000000 .059121 .068311 .076549 .084603 .092158 .100004 .106566 .111726 .114728 .114691 .112787 .109668 .105486 .408986 .414753 .419756 .416309 .391181 .342084 .237411 .143936 .102276 .074962 .050908 .040506 .050168 .000000 C A N M E T pitch 100 "C/min, 800 °C final temperature RUN# CAN41 Experimental r e s u l t s Y1,Y2 and f i t t e d r esults Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM YFFM .001215 -9. 982 -10. 109 -10. 192 -10. 319 1. 162 1. 036 1. 132 1. 357 .001227 -10. 127 -10. 209 -10. 335 -10. 417 1. 019 . 937 1. 252 1. 207 .001239 -10. 289 -10. 311 -10. 495 -10. 517 . 857 834 1. 184 1. 052 .001251 -10. 449 -10. 416 -10. 653 -10. 620 697 730 1. 023 . 893 .001263 -10. 600 -10. 523 -10. 801 -10. 725 548 624 . 815 732 .001276 -10. 732 -10. 632 -10. 931 -10. 832 416 516 567 568 .001295 -10. 904 -10. 800 -11. 100 -10. 996 245 349 260 315 .001315 -11. 045 -10. 973 -11. 238 -11. 166 105 177 064 054 .001342 -11. 204 -11. 210 -11. 392 -11. 398 -. 053 059 377 304 .001378 -11. 375 -11. 523 -11. 558 -11. 705 -. 222 370 -. 695 776 .001424 -11. 148 -11. 131 -11. 716 -11. 686 -1. 195 -1. 903 -1. 067 -1. 216 .001482 -11. 340 -11. 317 -11. 879 -11. 853 -1. 370 -2. 145 -1. 370 -1. 367 .001544 -11. 521 -11. 519 -12. 032 -12. 033 -1. 535 -2. 371 -1. 625 -1. 531 .001602 -11. 693 -11. 706 -12. 181 -12. 201 -1. 695 -2. 661 -1. 754 -1. 684 .001664 -11. 888 -11. 908 -12. 352 -12. 381 -1. 877 -2. 934 -1. 879 -1. 848 .001743 -12. 146 -12. 164 -12. 583 -12. 609 -2. 121 -3. 288 -2. 041 -2. 056 .001817 -12. 383 -12. 404 -12. 799 -12. 824 -2. 348 -3. 626 -2. 280 -2. 251 .001912 -12. 691 -12. 711 -13. 081 -13. 099 -2. 643 -4. 065 -2. 521 -2. 501 .002001 -13. 050 -12. 999 -13.. 419 -13. 357 -2. 992 -6. 243 -2. 655 -2. 736 F i t t i n g r e s u l t s i n the entire temperature range T V VFNT VFCR VFCN VFFM 51. 20 .090000 .037815 .037196 .041788 089455 148. 60 .250000 .590487 .449749 .571244 . 885730 175. 80 .570000 1.038072 .750431 .977237 1 416064 199. 20 1.250000 1.603755 1.113857 1.478432 2. 031820 226. 50 2.410000 2.532160 1.686924 2.283696 2. 965834 249. 80 3.670000 3.599821 2.323655 3.192784 3. 966103 277. 10 5.330000 5.226674 3.265426 4.555680 5. 392814 300. 50 7.100000 6.980181 4.255858 6.004666 6. 840918 199 327.70 9.650000 351.10 12.140000 374.50 14.860000 401.70 18.310000 429.00 22.540000 452.40 27.110000 471.90 32.190000 487.40 37.200000 499.10 41.820000 510.80 47.510000 518.60 51.880000 526.40 56.710000 534.20 61.610000 542.00 66.120000 549.70 69.670000 565.30 74.330000 584.80 77.000000 612.10 78.280000 651.00 78.820000 701.60 78.970000 752.30 79.150000 799.00 79.300000 9.465350 5.632465 11.997734 7.015564 14.888488 8.581675 18.668993 10.623569 22.858725 12.894257 24.023730 20.524340 32.039011 27.552988 39.156521 33.951636 44.774625 39.137117 50.417374 44.497372 54.098071 48.095553 57.645267 51.656872 61.002373 55.130548 64.118252 58.466153 66.915944 61.576999 71.624776 67.164201 75.640965 72.531486 78.362692 76.972609 79.242162 79.033522 79.299799 79.296617 79.300000 79.299996 79.300000 79.300000 8.035294 8.783387 10.086823 10.667295 12.415906 12.731221 15.452627 15.326578 18.818725 18.101062 23.460954 12.033339 31.302714 19.205596 38.293751 26.792290 43.836819 33.573404 49.432639 41.053280 53.101808 46.260754 56.655377 51.486260 60.037606 56.570802 63.197157 61.348836 66.054835 65.613673 70.925638 72.426814 75.178599 77.215667 78.178239 79.134416 79.221177 79.299688 79.299639 79.300000 79.300000 79.300000 79.300000 79.300000 F i t t i n g rate dV/dT i n the e n t i r e temperature range T VD VDNT VDCR VDCN VDFM 51. 20 .001643 .001454 .001318 .001541 .002970 148. 60 .011765 .014541 .010325 .013569 .019344 175. 80 .029060 .023057 .015584 .020970 .028129 199. 20 .042491 .032670 .021262 .029134 .037294 226. 50 .054077 .046802 .029274 .040884 .049829 249. 80 .060806 .061441 .037273 .052823 .061992 277. 10 .075641 .081694 .047974 .069056 .077848 300. 50 .093750 .101366 .058032 .084558 .092374 327. 70 .106410 .126246 .070346 .103839 .109705 351. 10 .116239 .148975 .081254 .121176 .124680 374. 50 .126838 .172396 .092180 .138785 .139336 401. 70 .154945 .199582 .104463 .158895 .155372 429. 00 .195299 .223821 .114859 .176369 .168297 452. 40 .260513 .372701 .304524 .360559 .240177 471. 90 .323226 .460019 .373598 .444225 .347618 487. 40 .394872 .521182 .421329 .502595 .444381 499. 10 .486325 .551505 .444351 .531302 .513459 510. 80 .560256 .553150 .444231 .532368 .560853 518. 60 .619231 .532058 .426392 .511745 .570239 526. 40 .628205 .487780 .390098 .468866 .552005 534. 20 .578205 .424184 .338550 .407489 .506336 542. 00 .461039 .350260 .278993 .336273 .440551 549. 70 .298718 .282713 .224756 .271267 .374077 565. 30 .136923 .177523 .140595 .170142 .259549 584. 80 .046886 .103931 .081937 .099474 .171268 612. 10 .013882 .062954 .049333 .060145 .121581 651. 00 .002964 .044749 .034788 .042650 .106607 701. 60 .003550 .050080 .038566 .047596 .152880 752. 30 .003212 .035344 .026987 .033506 .134973 799. 00 .003212 .000000 .000000 .000000 .000000 C A N M E T pitch 150 °C/min, 800 °C final temperature RUN# CAN58 Experimental r e s u l t s Y1,Y2 and f i t t e d results Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM YFFM .001129 -9.519 -9.531 -9.685 -9.696 1.934 1.922 1.899 1.852 .001152 -9.801 -9.796 -9.963 -9.958 1.652 1.657 1.496 1.600 200 .001175 -10. 008 -10. 073 -10. 167 -10. 231 1 .446 1 .382 1 .088 1 .337 .001192 -10. 245 -10. 261 -10. 401 -10. 417 1 .210 1 .194 1 .356 1 .158 .001209 -10. 483 -10. 459 -10. 637 -10. 613 .973 .997 1 .113 .969 .001226 -10. 704 -10. 658 -10. 855 -10. 810 .752 .798 .853 .779 .001244 -10. 895 -10. 866 -11. 044 -11. 015 .562 .591 .510 .582 .001262 -11. 155 -11. 079 -11. 302 -11. 226 .303 .379 .536 .379 .001291 -11. 380 -11. 411 -11. 523 -11. 554 .078 .047 -.201 .062 .001321 -11. 702 -11. 759 -11. 841 -11. 898 -.243 -.300 -.202 -.269 .001363 -11. 895 -12. 082 -12. 198 -12. 383 -1 .225 -2 .063 -.728 -.731 .001419 -12. 285 -12. 398 -12. 574 -12. 688 -1 .610 -3 .575 -1 .284 -1 .089 .001480 -13. 148 -12. 742 -13. 424 -13. 021 -2 .468 -5 .479 -1 .244 -1 .479 .001753 -14. 167 -14. 274 -14. 395 -14. 500 -3 .470 -10 .911 -3 .259 -3 .216 F i t t i n g r e s u l t s i n the e n t i r e temperature range T V VFNT VFCR VFCN VFFM 51. 80 .060000 .000151 .000154 .000159 .000068 203. 75 .000000 .074681 .063126 .073340 .070851 297. 20 .780000 .701829 .555184 .672535 .866054 402. 35 2 .850000 4 .237655 3 .194776 3 .986740 6 .378226 431. 60 7 .050000 6 .330544 4 .732698 5 .934912 9 .894506 460. 70 10 .840000 9 .115970 8 .027129 8 .983551 9 .795881 484. 10 15 .870000 15 .080683 13 .282723 14 .852779 15 .812360 501. 65 21 .770000 21 .204772 18 .726693 20 .883108 21 .863492 519. 20 27 .110000 28 .796499 25 .568963 28 .370146 29 .251362 530. 90 33 .840000 34 .576969 30 .867080 34 .082948 34 .821159 542. 60 39 .520000 40 .770361 36 .649493 40 .218947 40 .756949 554. 15 46 .400000 47 .076315 42 .676873 46 .486832 46 .786606 566. 00 53 .900000 53 .464116 48 .967499 52 .863180 52 .903960 577. 55 60 .980000 59 .309409 54 .942318 58 .729828 58 .537902 595. 10 66 .750000 66 .854625 63 .119819 66 .368983 65 .934092 612. 65 72 .410000 72 .240913 69 .523827 71 .899768 71 .411071 624. 35 75 .110000 74 .582095 72 .607495 74 .342314 73 .913015 653. 60 75 .950000 77 .155327 76 .597077 77 .095814 76 .930663 723. 65 76 . 820000 77 .589951 77 .589461 77 .589928 77 .589731 799. 55 77 .590000 77 .590000 77 .590000 77 .590000 77 .590000 F i t t i n g rate dV/dT i n the e n t i r e temperature range 1 VD VDNT VDCR VDCN VDFM 51. 80 - .000395 .000009 .000009 .000009 .000005 203. 75 .008347 .002221 .001826 .002159 .002333 297. 20 .019686 .015110 .011640 .014342 .020546 402. 35 .143590 .067985 .049723 .063308 .113490 431. 60 .130241 .090575 .065475 .083982 .158347 460. 70 .214957 .206107 .178311 .202428 .213433 484. 10 .336182 .310924 .267476 .304952 .314499 501. 65 .304274 .398138 .341129 .390105 .396048 519. 20 .575214 .501982 .428456 .491390 .491444 530. 90 .485470 .538596 .458575 .526912 .521913 542. 60 .595671 .576667 .489815 .563825 .553269 554. 15 .632911 .576449 .488506 .563295 .547803 566. 00 .612987 .533933 .451440 .521455 .502590 577. 55 .328775 .451831 .381193 .441036 .421484 595. 10 .322507 .388681 .326871 .379098 .357799 612. 65 .230769 .242157 .203026 .236009 .220097 624. 35 .028718 .137569 .115110 .134011 .124013 653. 60 .012420 .136916 .114024 .133220 .121026 723. 65 .010145 .155215 .127955 .150649 .131517 799. 55 .010145 .000000 .000000 .000000 .000000 Syncrude pitch 25 "C/min, 800 °C final temperature RUN# Syn43 Experimental r e s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F 201 T YNT YFNT .001206 - 1 0 . 639 - 1 0 . 787 .001220 - 1 0 . 774 - 1 0 . 907 .001233 - 1 0 . 937 - 1 1 . 009 .001243 - 1 1 . 111 - 1 1 . 093 .001251 - 1 1 . 227 - 1 1 . 156 .001262 - 1 1 . 350 - 1 1 . 242 .001275 - 1 1 . 487 - 1 1 . 351 .001294 - 1 1 . 647 - 1 1 . 509 .001314 - 1 1 . 773 - 1 1 . 671 .001335 - 1 1 . 873 - 1 1 . 837 .001359 - 1 1 . 964 - 1 2 . 035 .001381 - 1 2 . 027 - 1 2 . 213 .001430 - 1 1 . 847 - 1 1 . 692 .001484 - 1 1 . 970 - 1 1 . 889 .001541 - 1 2 . u i - 1 2 . 102 .001603 - 1 2 . 292 - 1 2 . 331 .001670 - 1 2 . 504 - 1 2 . 580 .001743 - 1 2 . 765 - 1 2 . 850 .001822 - 1 3 . 063 - 1 3 . 145 .001910 - 1 3 . 399 - 1 3 . 469 .002005 - 1 3 . 761 - 1 3 . 824 .002112 - 1 4 . 233 - 1 4 . 218 .002230 - 1 4 . 714 - 1 4 . 655 .002361 - 1 5 . 242 - 1 5 . 144 YCR YFCR YCN - 1 0 . 867 - 1 1 . 014 435 - 1 0 . 999 - 1 1 . 132 301 - 1 1 . 159 - 1 1 . 232 139 - 1 1 . 331 - 1 1 . 313 -. 034 - 1 1 . 446 - 1 1 . 375 -. 150 - 1 1 . 566 - 1 1 . 459 -. 272 - 1 1 . 701 - 1 1 . 566 -. 409 - 1 1 . 857 - 1 1 . 720 -. 567 - 1 1 . 980 - 1 1 . 878 -. 692 - 1 2 . 077 - 1 2 . 041 -. 791 - 1 2 . 164 - 1 2 . 234 -. 881 - 1 2 . 223 - 1 2 . 409 -. 943 - 1 2 . 320 - 1 2 . 146 - 1 . 684 - 1 2 . 422 - 1 2 . 330 - 1 . 796 - 1 2 . 542 - 1 2 . 530 - 1 . 927 - 1 2 . 703 - 1 2 . 745 - 2 . 097 - 1 2 . 894 - 1 2 . 978 - 2 . 299 - 1 3 . 136 - 1 3 . 232 - 2 . 551 - 1 3 . 414 - 1 3 . 509 - 2 . 840 - 1 3 . 731 - 1 3 . 812 - 3 . 168 - 1 4 . 074 - 1 4 . 146 - 3 . 522 - 1 4 . 528 - 1 4 . 516 - 3 . 987 - 1 4 . 991 - 1 4 . 926 - 4 . 461 - 1 5 . 502 - 1 5 . 385 - 4 . 983 YFCN YFM YFFM • 287 368 449 • 168 155 269 • 067 321 116 016 437 -. 009 079 282 -. 104 -. 164 057 -. 233 -. 273 -. 294 -. 397 -. 429 626 -. 633 590 -. 951 -. 876 755 - 1 . 242 - 1 . 126 951 - 1 . 529 - 1 . 422 - 1 . 129 - 1 . 783 - 1 . 690 - 2 . 380 - 2 . 092 - 1 . 879 - 2 . 644 - 2 . 211 - 2 . 023 - 2 . 930 - 2 . 278 - 2 . 177 - 3 . 245 - 2 . 295 - 2 . 344 - 3 . 590 - 2 . 412 - 2 . 525 - 3 . 973 - 2 . 525 - 2 . 722 - 4 . 398 - 2 . 746 - 2 . 937 - 4 . 874 - 3 . 015 - 3 . 172 - 5 . 410 - 3 . 361 - 3 . 431 - 6 . 017 - 3 . 619 - 3 . 718 - 6 . 711 - 4 . 149 - 4 . 036 - 7 . 514 - 4 . 653 - 4 . 392 F i t t i n g r e s u l t s i n the e n t i i T V VFNT 50 . 05 100000 045729 7 5 . 12 150000 119218 100. 17 190000 • 274938 125. 22 . 600000 573755 150. 30 1. 000000 1. 102366 175. 35 1. 860000 1. 971729 200 . 40 3 . 270000 3 . 317881 225 . 47 5 . 630000 5. 293673 250 . 52 8. 600000 8. 048237 275 . 57 12 . 650000 11 . 715766 300 . 62 17 . 690000 16. 384554 325 . 70 2 3 . 580000 22 . 079089 350 . 75 2 9 . 640000 28 . 709136 375 . 80 3 5 . 840000 36 . 099426 400. 87 4 1 . 510000 43 . 975909 425 . 92 46 . 950000 51 . 972562 450 . 97 52 . 400000 46 . 345424 462. 67 5 5 . 440000 53 . 099613 476 . 05 5 9 . 570000 60. 768890 487. 72 63 . 810000 67 . 125449 499. 42 68 . 730000 72 . 929307 511 . 12 74 . 310000 7 7 . 960176 519 . 47 7 8 . 470000 81 . 002113 526 . 15 81 . 640000 83 . 089095 531 . 17 84. 140000 84. 454969 537 . 85 86 . 990000 86. 011279 546 . 20 88 . 850000 87 . 563757 556 . 22 89 . 870000 88. 918606 574. 60 90 . 460000 90. 308221 599. 65 90 . 560000 90. 918100 624. 72 90. 580000 91. 020123 651. 45 90. 750000 91. 029652 674. 82 90. 800000 91. 029991 699. 90 90. 950000 91. 030000 724. 95 90. 900000 91. 030000 temperature range VFCR VFCN VFFM 041916 047220 183638 103723 120245 379017 228622 271701 712813 458602 556947 1. 242274 851063 1. 053327 2 . 032195 1. 476784 1. 858037 3 . 146510 2 . 420624 3 . 088735 4 . 648328 3 . 776935 4 . 876388 6. 592209 5. 638572 7. 348210 9 . 012339 8. 094285 10. 620223 11 . 926517 11. 214130 14. 773021 15 . 326583 15 . 044083 19 . 839594 19 . 182983 19 . 576469 2 5 . 762834 2 3 . 426576 24 . 769893 32 . 422129 2 7 . 979782 30 . 533683 39 . 617613 32 . 748024 36 . 716279 47 . 067418 3 7 . 615765 40. 187785 45 . 322347 2 2 . 184007 46. 439729 51 . 985524 2 8 . 545636 53 . 788245 59 . 598577 3 7 . 089753 60. 146397 65 . 959294 45 . 439528 66. 244810 7 1 . 822067 54 . 279365 71 . 854825 76 . 963617 63 . 075784 75 . 458219 80. 110255 68 . 995159 78 . 061344 82. 291746 7 3 . 348936 79 . 842218 83 . 732460 76 . 333647 81 . 970639 85 . 390236 7 9 . 863493 84. 241244 87 . 067081 83 . 504374 86. 412761 88. 558719 86. 728488 89. 019474 90. 140012 89 . 881430 90. 551567 90. 878470 90 . 944794 90. 955365 91. 014822 91 . 028241 91. 024145 91. 029359 91 . 029996 91. 029642 91. 029980 91 . 030000 91. 029991 91. 030000 91 . 030000 91. 030000 91. 030000 91 . 030000 750.00 90.890000 91.030000 91.030000 91.030000 91.030000 775.05 91.040000 91.030000 91.030000 91.030000 91.030000 800.12 91.030000 91.030000 91.030000 91.030000 91.030000 F i t t i n g rate dV/dT i n the enti r e temperature range T VD VDNT VDGR VDCN VDFM 50. 05 .001994 .001964 .001713 .001984 .006238 75. 12 .001597 .004483 .003716 .004425 .011371 100. 17 .016367 .009153 .007260 .008858 .019116 125. 22 .015949 .017014 .012987 .016182 .029980 150. 30 .034331 .029395 .021687 .027532 .044581 175. 35 .056287 .047477 .033988 .043869 .063032 200. 40 .094136 .072355 .050421 .066049 .085283 225. 47 .118563 .104373 .070989 .094241 .110524 250. 52 .161677 .143776 .095669 .128543 .138203 275. 57 .201198 .188875 .123200 .167355 .166266 300. 62 .234848 .237368 .152042 .208607 .192835 325. 70 .241916 .286149 .180256 .249594 .215958 350. 75 .247505 .333937 .207161 .289273 .235538 375. 80 .226167 .377615 .230969 .325032 .250227 400. 87 .217166 .419042 .252973 .358567 .262075 425. 92 .217565 .454277 .270933 .386595 .269273 450. 97 .259829 .518990 .417385 .499692 .285043 462. 67 .308670 .571709 .457946 .549754 .343355 476. 05 .363325 .615731 .491032 .591258 .408191 487. 72 .420513 .629331 .500008 .603604 .453461 499. 42 .476923 .606242 .479920 .580793 .473687 511. 12 .498204 .531899 .419588 .509003 .449582 519. 47 .474551 .445717 .350744 .426201 .397909 526. 15 .498008 .363080 .285167 .346972 .338350 531. 17 .426647 .283894 .222655 .271176 .273100 537. 85 .222754 .180931 .141638 .172724 .181460 546. 20 .101796 .108144 .084465 .103164 .114152 556. 22 .032100 .064882 .050539 .061841 .072722 574. 60 .003992 .039440 .030575 .037535 .049169 599. 65 .000798 .042837 .033005 .040689 .061295 624. 72 .006360 .053212 .040760 .050450 .086728 651. 45 .002139 .043029 .032767 .040720 .079952 674. 82 .005981 .043910 .033276 .041490 .090944 699 90 -.001996 .019056 .014370 .017978 .044086 724 95 -.000399 .038199 .028670 .035983 .098155 750 00 .005988 .050227 .037529 .047247 .142614 775 05 -.000399 -.004339 -.003228 -.004076 --.013548 800 12 -.000399 .000000 .000000 .000000 .000000 Syncrude pitch 50 °C/min, 800 °C final temperature RUN# Syn29 Experimental r e s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM YFFM .001230 -10. 282 -10. 384 -10. 476 -10. 578 .929 .826 .683 .962 .001244 -10. 463 -10. 514 -10. 655 -10. 705 .748 .697 .855 .775 .001262 -10. 700 -10. 681 -10. 888 -10. 869 .512 .531 .651 .533 .001281 -10. 930 -10. 852 -11. 116 -11. 038 .282 .361 .440 .285 .001292 -11. 047 -10. 957 -11. 231 -11. 141 .167 .256 .210 .133 .001308 -11. 179 -11. 101 -11. 360 -11. 283 .035 .113 -.076 -.076 .001328 -11. 309 -11. 285 -11. 488 -11. 463 -.095 -.070 -.410 -.342 .001361 -11. 455 -11. 592 -11. 629 -11. 765 -.239 -.375 -.870 -.787 .001391 -11. 336 -11. 124 -11. 718 -11. 493 -.921 -1.148 -1.216 -1.112 .001442 -11. 480 -11. 354 -11. 846 -11. 713 -1.057 -1.384 -1.451 -1.275 .001492 -11. 625 -11. 578 -11. 977 -11. 927 -1.196 -1.637 -1.547 -1.434 .001545 -11. 795 -11. 818 -12. 132 -12. 157 -1.359 -1.938 -1.630 -1.605 .001602 -11. 997 -12. 076 -12. 321 -12. 404 -1.556 -2.266 -1.720 -1.788 203 .001670 -12. 257 -12. 382 -12. 565 -12. 698 -1. 809 -2. 624 -1. 879 -2. 006 .001743 -12. 570 -12. 716 -12. 863 -13. 018 -2. 116 -2. 943 -2. 063 -2. 243 .001824 -12. 944 -13. 079 -13. 222 -13. 366 -2. 484 -3. 409 -2. 315 -2. 502 .001896 -13. 300 -13. 404 -13. 566 -13. 677 -2. 836 -3. 884 -2. 606 -2. 732 .002001 -13. 861 -13. 878 -14. 111 -14. 131 -3. 391 -4. 673 -2. 980 -3. 069 .002107 -14. 375 -14. 361 -14. 611 -14. 594 -3. 900 -6. 428 -3. 596 -3. 413 .002285 -15. 392 -15. 162 -15. 608 -15. 362 -4. 911 -8. 201 -4. 158 -3. 983 F i t t i n g r e s u l t s i n the e n t i r e temperature range T V VFNT VFCR VFCN VFFM 51. 65 140000 009799 .009251 010091 069018 100. 00 190000 076477 .066885 076391 . 315460 164. 50 480000 603673 .489475 . 585025 1 453963 201. 35 1. 520000 1. 542227 1 .209491 1 474579 2. 903798 226. 70 2. 760000 2. 716734 2 .089952 2. 577077 4. 403386 254. 35 5. 230000 4. 728916 3 .574526 4. 452674 6. 612174 275. 10 7. 850000 6. 892639 5 .154681 6. 459578 8. 712572 300. 40 11. 990000 10. 464453 7 .749320 9. 761545 11. 826934 325. 75 17. 060000 15. 226500 11 .209405 14. 156507 15. 572819 351. 10 22. 760000 21. 261362 15 .629579 19. 730895 19. 927271 374. 15 28. 370000 27. 825962 20 .516929 25. 816720 24. 368376 397. 20 34. 000000 35. 271960 26 .202357 32. 765722 29. 197021 420. 20 39. 550000 43. 319420 32 .574092 40. 353804 34. 309169 445. 55 45. 630000 52. 465639 40 .203254 49. 112623 40. 152213 461. 65 49. 930000 45. 544597 40 .142579 44. 732081 25. 361219 480. 10 56. 230000 57. 049162 51 .010700 56. 134667 37. 631151 491. 60 61. 490000 64. 046787 57 .913998 63. 119553 46. 535234 500. 85 66. 500000 69. 320859 63 .320820 68. 418263 54. 065860 507. 75 70. 620000 72. 949788 67 .174942 72. 086372 59. 693159 519. 25 77. 790000 78. 265718 73 .090112 77. 503543 68. 630844 530. 80 83. 510000 82. 552398 78 .202721 81. 925942 76. 428641 540. 00 86. 620000 85. 182659 81 .583735 84. 676348 81. 413289 553. 80 88. 850000 87. 920141 85 .456989 87. 589287 86. 580788 574. 55 89. 660000 89. 941164 88 .853273 89. 808968 89. 957255 599. 90 89. 980000 90. 609394 90 .362395 90. 584542 90. 669984 650. 55 90. 220000 90. 699888 90 .698331 90. 699812 90. 700000 698. 95 90. 400000 90. 700000 90 .700000 90. 700000 90. 700000 749. 60 90. 570000 90. 700000 90 .700000 90. 700000 90. 700000 800. 30 90. 700000 90. 700000 90 .700000 90. 700000 90. 700000 F i t t i n g rate dV/dT i n the e n t i r e temperature range T VD VDNT VDCR VDCN VDFM 51. 65 .001034 .000490 .000446 .000497 .002632 100. 00 .004496 .002968 .002509 .002925 .009479 164. 50 .028223 .017630 .013835 .016868 .033618 201. 35 .048915 .038858 .029491 .036688 .058773 226. 70 .089331 .062112 .046199 .058174 .081707 254. 35 .126265 .096965 .070713 .090106 .111234 275. 10 .163636 .129992 .093525 .120147 .135785 300. 40 .200000 .177651 .125892 .163208 .167061 325. 75 .224852 .232004 .162139 .211965 .198132 351. 10 .243384 .290795 .200647 .264330 .227298 374. 15 .244252 .345237 .235665 .312477 .250483 397. 20 .241304 .399266 .269833 .359941 .270272 420. 20 .239842 .450452 .301601 .404580 .285841 445. 55 .267081 .499500 .331252 .446924 .296595 461. 65 .341463 .577103 .476958 .560143 .371255 480. 10 .457391 .663253 .545310 .642807 .489652 491. 60 .541622 .675488 .553640 .654083 .541543 500. 85 .597101 .646257 .528390 .625343 .552650 507. 75 .623478 .595681 .486170 .576110 .533992 519. 25 .495238 .454474 .369847 .439180 .439911 530. 80 .338043 .299108 .242723 .288809 .312035 204 540.00 553.80 574.55 599.90 650.55 698.95 749.60 800.30 .161594 .039036 .012623 .004738 .003719 .003356 .002564 .002564 .193218 .105838 .078144 .074164 .088169 .090528 .062715 .000000 .156450 .085423 .062780 .059265 .069767 .071034 .048819 .000000 .186448 .102036 .075238 .071297 .084523 .086578 .059842 .000000 .213631 .127370 .106271 .116186 .179029 .229655 .196353 .000000 Syncrude pitch 100 "C/min, 800 °C final temperature RUN# Synl8 Experimental r e s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM YFFM .001127 -9. 308 -9. 498 -9. 564 -9. 751 1. 722 1. 534 232 1. 444 .001158 -9. 516 -9. 743 -9. 764 -9. 990 1. 517 1. 291 • 996 1. 152 .001176 -9. 785 -9. 889 -10. 028 -10. 132 1. 250 1. 146 1. 482 . 978 .001191 -10. 007 -10. 001 -10. 247 -10. 241 1. 029 1. 035 1. 452 • 844 .001205 -10. 215 -10. 116 -10. 452 -10. 354 . 822 921 1. 225 • 707 .001220 -10. 398 -10. 235 -10. 631 -10. 469 641 • 803 . 947 • 566 .001236 -10. 552 -10. 356 -10. 782 -10. 587 487 683 653 • 422 .001251 -10. 677 -10. 480 -10. 904 -10. 708 364 560 336 • 273 .001267 -10. 772 -10. 606 -10. 996 -10. 831 270 435 • 016 • 123 .001284 -10. 850 -10. 737 -11. 071 -10. 958 192 305 -. 242 -. 033 .001301 -10. 918 -10. 871 -11. 135 -11. 089 126 172 -. 435 -. 193 .001324 -10. 997 -11. 056 -11. 209 -11. 269 049 -. O i l -. 639 -. 413 .001343 -11. 055 -11. 199 -11. 264 -11. 408 009 152 -. 724 -. 583 .001368 -11. 131 -11. 396 -11. 337 -11. 599 084 347 -. 830 -. 818 .001393 -11. 100 -10. 908 -11. 415 -11. 214 489 -. 811 -. 882 -. 689 .001427 -11. 212 -11. 087 -11. 518 -11. 388 598 973 -. 973 -. 818 .001455 -11. 318 -11. 236 -11. 617 -11. 532 -. 700 -1. 143 -. 977 -. 924 .001492 -11. 453 -11. 432 -11. 744 -11. 722 -. 832 -1. 319 -1. 114 -1. 064 .001523 -11. 579 -11. 596 -11. 863 -11. 881 -. 956 -1. 503 -1. 153 -1. 182 .001555 -11. 720 -11. 768 -11. 997 -12. 047 -1. 094 -1. 696 -1. 228 -1. 304 .001589 -11. 868 -11. 946 -12. 139 -12. 220 -1. 239 -1. 950 -1. 357 -1. 432 .001624 -12. 032 -12. 133 -12. 295 -12. 401 -1. 400 -2. 218 -1. 463 -1. 565 .001661 -12. 210 -12. 327 -12. 467 -12. 589 -1. 576 -2. 562 -1. 593 -1. 704 .001709 -12. 463 -12. 584 -12. 712 -12. 838 -1. 826 -2. 998 -1. 740 -1. 888 .001760 -12. 760 -12. 855 -13. 000 -13. 101 -2. 120 -3. 473 -1. 922 -2. 082 .001826 -13. 145 -13. 204 -13. 376 -13. 438 -2. 502 -4. 077 -2. 241 -2. 331 .001909 -13. 593 -13. 644 -13. 813 -13. 865 -2. 946 -5. 319 -2. 719 -2. 646 .001999 -14. 121 -14. 124 -14. 330 -14. 330 -3. 471 -6. 997 -3. 127 -2. 989 .002114 -15. 006 -14. 735 -15. 203 -14. 922 -4. 353 -9. 207 -3. 556 -3. 426 F i t t i n g r e s u l t s i n the e n t i T V VFNT 50. 40 010000 001540 101. 40 000000 • 018878 152. 30 080000 • 129853 199. 90 420000 550585 227. 10 1. 120000 1. 116204 250. 80 2. 050000 1. 948625 274. 60 3. 440000 3. 247629 295. 00 5. 330000 4. 856552 312. 0.0 7. 450000 6. 635186 329. 00 9. 930000 8. 884788 342. 60 12. 160000 11. 066733 356. 20 14. 630000 13. 618970 369. 80 17. 290000 16. 562265 383. 40 20. 210000 19. 907563 397. 00 23. 230000 23. 653224 414. 00 26. 990000 28. 871191 427. 50 30. 220000 33. 395664 temperature range VFCR VFCN VFFM 001496 001588 • 016485 017085 018978 105664 111371 128043 442528 453851 „ 535174 1. 293837 # 902845 1. 077492 2. 185278 1. 553575 1. 871033 3. 301432 2. 557005 3. 103598 4. 816467 3. 789285 4. 624784 6. 483361 5. 144724 6. 302401 8. 163141 6. 854845 8. 420862 10. 127888 8. 513106 10. 473818 11. 914502 10. 455958 12. 874559 13. 896846 12. 704596 15. 643977 16. 076091 15. 275332 18. 794581 18. 449990 18. 177902 22. 328055 21. 012616 22. 274075 27. 264504 24. 466045 25. 885633 31. 561762 27. 389481 444. 50 34. 100000 39 458. 10 37. 280000 30 471. 70 40. 440000 36 481. 90 42. 920000 41 495. 50 46. 340000 47 505. 70 49. 260000 52 515. 90 52. 570000 58 526. 00 56. 470000 62 536. 20 61. 340000 67 546. 40 67. 070000 72 556. 60 73. 250000 75 566. 80 79. 270000 79 577. 00 84. 200000 82 590. 60 88. 020000 85 614. 40 89. 670000 88 644. 90 90. 020000 90 699. 30 90. 270000 90 801. 20 90. 580000 90 .480515 30.848632 .294054 25.465104 .300444 30.645522 .121766 34.873027 .837747 40.887724 .973813 45.607671 .079517 50.426936 .995823 55.214767 .710001 59.976033 .070023 64.570176 .990181 68.907305 .408748 72.906769 .293013 76.502948 .308779 80.594647 .564528 85.747974 .176356 89.132030 .574109 90.516899 .580000 90.579999 37. 371937 31. 268862 29. 445278 17. 320647 35. 289245 21. 944588 39. 993312 25. 922760 46. 571202 31. 885258 51. 626478 36. 804164 56. 678531 42. 037160 61. 574160 47. 440367 66. 304153 53. 008302 70. 718213 58. 555721 74. 728841 63. 938346 78. 269233 69. 011118 81. 298659 73. 641053 84. 526661 78. 944401 88. 135044 85. 506564 90. 041295 89. 407948 90. 569747 90. 561938 90. 580000 90. 580000 F i t t i n g rate dV/dT i n the e n t i r e temperature range T VD VDNT VDCR VDCN VDFM 50. 40 -.000196 .000089 .000084 .000091 .000721 101. 40 .001572 .000832 .000734 .000829 .003566 152. 30 .007143 .004537 .003793 .004433 .011985 199. 90 .025735 .015877 .012761 .015295 .029320 227. 10 .039241 .029010 .022876 .027756 .045017 250. 80 .058403 .046410 .036052 .044166 .062805 274. 60 .092647 .070968 .054374 .067202 .084707 295. 00 .124706 .098349 .074537 .092766 .106299 312. 00 .145882 .125836 .094563 .118330 .125877 329. 00 .163971 .157746 .117598 .147911 .146683 342. 60 .181618 .186382 .138102 .174379 .163949 356. 20 .195588 .217506 .160227 .203072 .181427 369. 80 .214706 .250916 .183810 .233795 .198912 383. 40 .222059 .285889 .208314 .265870 .215849 397. 00 .221176 .322448 .233749 .299315 .232321 414. 00 .239259 .370407 .266876 .343077 .252370 427. 50 .228235 .408066 .292643 .377325 .266473 444. 50 .233824 .456957 .325871 .421681 .283511 458. 10 .232353 .392638 .311918 .376596 .235294 471. 70 .243137 .449670 .355393 .430556 .279832 481. 90 .251471 .493090 .388258 .471541 .315379 495. 50 .286275 .550524 .431395 .525615 .364805 505. 70 .324510 .588064 .459198 .560798 .399845 515. 90 .386139 .616536 .479789 .587278 .429851 526.00 .477451 .627702 .486870 .597254 .448357 536. 20 .561765 .609276 .471047 .579092 .445692 546. 40 .605882 .552983 .426173 .525030 .414022 556. 60 .590196 .458760 .352468 .435121 .351351 566. 80 .483333 .335994 .257369 .318359 .263082 577. 00 .280882 .212114 .162001 .200783 .169709 590. 60 .069328 .098484 .074930 .093104 .081032 614. 40 .011475 .044710 .033800 .042177 .038554 644. 90 .004596 .036952 .027721 .034769 .033719 699. 30 .003042 .033062 .024494 .030979 .033079 801. 20 .003042 .000000 .000000 .000000 .000000 Syncrude pitch 150 T/min, 800 °C final temperature RUN# Syn08 Experimental r e s u l t s Y1,Y2 and f i t t e d r e s u l t s Y1F,Y2F T YNT YFNT YCR YFCR YCN YFCN YFM .001129 -8.944 -9.092 -9.181 -9.327 2.158 2.011 .7 .001153 -9. 102 -9. 290 -9. 333 -9. 521 2. 002 1. 814 1 .507 1. 643 .001171 -9. 317 -9. 445 -9. 544 -9. 672 1. 788 1. 660 1 .795 1. 473 .001190 -9. 581 -9. 605 -9. 804 -9. 829 1. 526 1. 501 1 .742 1. 297 .001203 -9. 764 -9. 715 -9. 984 -9. 936 1. 344 1. 392 1 .677 1. 176 .001217 -9. 942 -9. 828 -10. 160 -10. 046 1. 166 1. 280 1 .494 1. 052 .001230 -10. 107 -9. 941 -10. 322 -10. 157 1. 003 1. 168 1 .280 . 928 .001244 -10. 243 -10. 058 -10. 456 -10. 272 . 867 1. 051 .965 • 798 .001258 -10. 351 -10. 177 -10. 560 -10. 387 760 . 934 .658 • 668 .001273 -10. 437 -10. 300 -10. 644 -10. 508 675 812 .364 • 533 .001288 -10. 513 -10. 426 -10. 717 -10. 631 600 687 .171 • 394 .001311 -10. 610 -10. 619 -10. 810 -10. 820 504 494 -.063 • 182 .001335 -10. 695 -10. 818 -10. 892 -11. 014 420 297 -.261 -. 037 .001368 -10. 808 -11. 098 -10. 999 -11. 288 309 019 -.415 -. 345 .001394 -10. 787 -10. 634 -11. 086 -10. 926 124 -. 269 -.479 -. 297 .001421 -10. 892 -10. 784 -11. 184 -11. 072 -. 227 486 -.517 -. 409 .001449 -11. 001 -10. 938 -11. 287 -11. 222 334 714 -.605 -. 525 .001489 -11. 162 -11. 158 -11. 439 -11. 434 491 -. 954 -.715 -. 690 .001530 -11. 349 -11. 387 -11. 617 -11. 657 674 -1. 210 -.800 -. 862 .001574 -11. 553 -11. 630 -11. 813 -11. 893 876 -1. 549 -.956 -1. 044 .001620 -11. 784 -11. 888 -12. 036 -12. 145 -1. 104 -1. 918 -1 .121 -1. 238 .001682 -12. 125 -12. 231 -12. 366 -12. 477 -1. 440 -2. 314 -1 .309 -1. 496 .001749 -12. 481 -12. 603 -12. 711 -12. 839 -1. 793 -2. 748 -1 .676 -1. 775 .001821 -12. 947 -13. 004 -13. 167 -13. 228 -2. 255 -3. 218 -1 .906 -2. 076 .001900 -13. 438 -13. 442 -13. 648 -13. 654 -2. 743 -3. 957 -2 .406 -2. 405 .001986 -13. 882 -13. 916 -14. 083 -14. 115 -3. 185 -6. 081 -3 .021 -2. 761 .002120 -14. 878 -14. 663 -15. 064 -14. 840 -4. 176 -9. 310 -3 .387 -3. 321 F i t t i n g r e s u l t s i n the e n t i r e temperature range T V VFNT VFCR VFCN VFFM 50. 00 020000 000891 000867 000917 007966 125. 75 070000 034308 030388 034164 134342 198. 50 320000 396712 330372 386644 . 896348 230. 45 . 970000 938068 764888 . 907488 1. 746136 253. 10 1. 630000 1. 623374 1. 306550 1. 563176 2. 669480 275. 90 2. 850000 2. 694018 2. 143508 2. 583332 3. 949116 298. 55 4. 820000 4. 276303 3. 369713 4. 085792 5. 642770 321. 35 7. 260000 6. 553257 5. 123781 6. 242050 7. 845678 344. 00 10. 660000 9. 663453 7. 513555 9. 182153 10. 591947 362. 30 13. 840000 12. 900822 10. 003840 12. 240464 13. 249213 380. 45 17. 410000 16. 819236 13. 031557 15. 943453 16. 286221 398. 60 21. 390000 21. 474008 16. 658307 20. 348467 19. 723079 416. 90 25. 520000 26. 901856 20. 942446 25. 498709 23. 578196 430. 40 28. 720000 31. 342672 24. 502038 29. 726985 26. 655275 444. 05 32. 080000 36. 156700 28. 427027 34. 329008 29. 947086 457. 70 35. 380000 28. 033573 23. 801644 27. 333528 18. 612215 476. 00 39. 830000 36. 320795 31. 011915 35. 421705 25. 296279 489. 50 43. 350000 43. 062424 37. 006635 42. 024491 31. 104254 503. 15 47. 390000 50. 205200 43. 520235 49. 050957 37. 654348 512. 30 50. 520000 55. 048013 48. 054191 53. 837831 42. 353987 521. 45 54. 040000 59. 830187 52. 646333 58. 587362 47. 227206 530. 45 58. 280000 64. 382933 57. 147460 63. 134447 52. 111450 539. 60 63. 460000 68. 766400 61. 629215 67. 541374 57. 077576 548. 60 69. 320000 72. 755015 65. 867186 71. 582191 61. 864936 557. 75 75. 110000 76. 412080 69. 927104 75. 320122 66. 530691 566. 90 80. 170000 79. 617170 73. 668578 78. 629972 70. 894557 580. 55 85. 600000 83. 505731 78. 543562 82. 705429 76. 659233 594. 20 88. 350000 86. 344521 82. 480538 85. 744533 81. 356480 612. 35 89. 590000 88. 711449 86. 251528 88. 354415 85. 839815 639. 65 89. 970000 90 211576 89. 281375 90. 095072 89. 313126 689. 60 90. 300000 90 613468 90. 562245 90. 609490 90. 585096 798. 80 90. 620000 90 620000 90 620000 90. 620000 90. 620000 F i t t i n g rate dV/dT i n the ent i r e temperature range T 50.00 125.75 198.50 230.45 253.10 275.90 298.55 321.35 344.00 362.30 380.45 398.60 416.90 430.40 444.05 457.70 476.00 489.50 503.15 512.30 521.45 530.45 539.60 548.60 557.75 566.90 580.55 594.20 612.35 639.65 689.60 798.80 VD .000660 .003436 .020344 .029139 .053509 .086976 .107018 .150110 .173770 .196694 .219284 .225683 .237037 .246154 .241758 .243169 .260741 .295971 .342077 .384699 .471111 .566120 .651111 .632787 .553005 .397802 .201465 .068320 .013919 .006607 .002930 .002930 VDNT .000054 .001397 .011908 .024939 .039780 .060793 .088697 .125044 .168954 .210191 .255424 .303822 .355679 .394629 .433662 .389133 .473696 .537611 .596677 .627795 .647704 .644567 .608896 .534725 .435741 .327743 .184725 .097515 .053958 .045216 .035875 .000000 VDCR .000051 .001208 .009689 .019867 .031266 .047191 .068073 .094960 .127063 .156917 .189377 .223798 .260370 .287620 .314724 .314606 .380539 .429941 .475083 .498431 .512801 .508947 .479497 .420008 .341385 .256132 .143840 .075665 .041679 .034702 .027236 .000000 VDCN .000055 .001379 .011514 .023937 .038002 .057825 .084034 .118035 .158945 .197232 .239103 .283764 .331479 .367218 .402941 .375285 .455912 .516685 .572649 .601965 .620502 .616969 .582329 .510976 .416050 .312683 . 176034 .092822 .051288 .042890 . 033912 .000000 VDFM .000376 .004351 .021734 .037795 .053566 .073400 .096922 .124536 .154501 .180199 .206139 .231577 .256700 .274068 .290120 .260778 .326435 .377864 .427533 .455504 .475739 .479042 .457857 .406636 .335093 .254815 .145923 .078226 .044148 .038054 .031660 .000000 APPENDIX F Summary of Kinetic Parameters of the 2-Stage Model E,,E2 koi, k o 2 s.e.e Reaction activation energy J/mol pre-exponential factors min Standard deviation for each method, % C A N M E T pitch 25 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factors f o r both reactions 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman Ei 21895.871 18317.044 19815.807 18356.762 k 0i 5.534 1.207 2.663 2.169 E 2 71347.395 69931.248 70918.682 39422.571 kD2 44484.445 28659.014 40047.550 222.056 s.e.e 1.425598 8.666605 4.464558 5.683572 C A N M E T Pitch 50 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor for both reactions 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman Ei 20907.935 17507.079 18939.224 12109.801 k 0i 7.649 1.688 3.717 0.833 E 2 64473.015 62943.175 63977.704 54006.641 k o 2 24448.637 15044.712 21585.114 3350.699 s.e.e 2.128091 8.270525 4.639823 11.413135 C A N M E T pitch 100 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor f o r both reactions 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman Ei 26914.040 24063.137 25429.522 21904.369 k 0i 39.637 12.482 24.221 12.635 E 2 72117.918 70720.507 71699.067 108819.449 k o 2 111143.981 72034.563 100310.634 31432193.146 s.e.e. 1.446535 4.703861 1.899520 5.279363 C A N M E T pitch 150 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor f o r both reactions 2-Integral 2-Coats-Redfern 2-Chen-Nuttall A 2-Friedman Ei 46648.168 45065.482 46065.844 52896.511 k 0i 552.339 304.766 463.684 2804.999 E 2 96651.309 95534.758 96377.125 92011.326 k o 2 3510920.010 2529475.085 3296730.811 1699475.805 s.e.e 0.975426 2.908742 1.027556 1.499851 Syncrude Pitch 25 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor f o r both reactions 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman Ei 30825.690 28925.970 29969.525 22436.425 k 0i 51.805 22.282 38.048 7.251 E 2 67665.168 66149.761 67185.904 101506.600 k o 2 25546.591 15973.274 22714.511 3875272.258 s.e.e. 1.941470 5.238812 2.066038 9.746673 Syncrude pitch 50 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor for both reactions 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman Ei 37574.160 36007.909 36950.208 26717.957 k Qi 298.225 152.170 240.377 28.783 E 2 76570.633 75271.326 76200.343 110908.304 k o 2 196413.926 131230.169 179430.028 34882245.211 s.e.e 2.079083 4.555376 1.827761 8.003341 209 Syncrude pitch 100 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor for both reactions Ei k c i E2 k02 s.e.e 2-Integral 44166.789 1326.666 65511.067 35233.527 2.970666 2-Coats-Redfern 42786.603 750.710 63799.493 21122.231 4.667832 2-Chen-Nuttall 43670.266 1126.495 64938.056 30754.384 2.683058 2-Friedman 31580.121 99.840 78074.842 166743.612 8.111536 Syncrude pitch 150 °C/min., 800 °C A c t i v a t i o n energies and pre-exponential factor for both reactions Ei k 0 i E 2 k o 2 S.e.e 2-Integral 46141.423 2549.212 69808.233 103113.970 2.859655 2-Coats-Redfern 44831.086 1485.078 68221.838 64209.953 4.405498 2-Chen-Nuttall 45685.309 2194.201 69303.236 91513.836 2.586208 2-Friedman 34645.511 248.057 76752.670 216684.308 6.605246 210 APPENDIX G Kinetic Reaction Rate Constant Ink - 1/T for C A N M E T and Syncrude Pitches CANMET PITCH 2-stage model kinetic reaction rate Ink-1/T Integral method 1/T K'1 25 "C/min 50°C/min 100 °C/min 150 °C/min 800 - 450 °C 0.93183 2.70633 2.87824 3.53565 4.23878 0.97736 2.31555 2.52511 3.14066 3.70941 1.02758 1.88462 2.13570 2.70507 3.12564 1.08324 1.40700 1.70410 2.22230 2.47863 1.14527 0.87469 1.22308 1.68424 1.75753 1.21483 0.27771 0.68362 1.08081 0.94883 1.29339 -0.39649 0.07438 0.39933 0.03553 1.38282 -1.16391 -0.61910 -0.37638 -1.00407 450 - 50 °C 1.38282 -1.93090 -1.44292 -0.79669 -1.44456 1.48553 -2.20140 -1.70122 -1.12919 -2.02085 1.60472 -2.51531 -2.00096 -1.51504 -2.68962 1.74471 -2.88399 -2.35301 -1.96822 -3.47507 1.91146 -3.32314 -2.77234 -2.50801 -4.41066 2.11345 -3.85510 -3.28030 -3.16189 -5.54398 2.36317 -4.51277 -3.90830 -3.97029 -6.94512 2.67982 -5.34669 .^70459 -4.99532 -8.72174 3.09444 -6.43866 -5.74729 -6.33755 -11.04810 Chen-Nuttall method 1/T K"1 25 "C/min 50°C/min 100 "C/min 150 "C/min 800-450 °C 0.93183 2.64931 2.80918 3.48004 4.20656 0.97736 2.26088 2.45877 3.08734 3.67869 1.02758 1.83253 2.07235 2.65428 3.09658 1.08324 1.35779 1.64407 2.17431 2.45141 1.14527 0.82867 1.16674 1.63938 1.73235 1.21483 0.23528 0.63142 1.03945 0.92594 1.29339 -0.43486 0.02687 0.36194 0.01523 1.38282 -1.19767 -0.66128 -0.40927 -1.02141 450 - 50 °C 1.38282 -2.31640 -1.83714 -1.04233 -1.52266 1.48553 -2.56120 -2.07111 -1.35648 -2.09176 1.60472 -2.84529 -2.34263 -1.72105 -2.75218 1.74471 -3.17894 -2.66153 -2.14923 -3.52783 1.91146 -3.57637 -3.04138 -2.65925 -4.45174 2.11345 -4.05780 -3.50150 -3.27706 -5.57091 2.36317 -4.65299 -4.07037 -4.04087 -6.95456 2.67982 -5.40769 -4.79168 -5.00937 -8.70900 3.09444 -6.39592 -5.73620 -6.27756 -11.00630 CANMET SINGLE OVERALL MODEL lnk-1/T 700 - 50 °C 1/T K'1 Integral C-R C-N Friedman 1.02758 0.92624 0.27246 0.68931 0.85065 1.08324 0.70466 0.06628 0.47509 0.63309 1.14527 0.45771 -0.16351 0.23635 0.39061 1.21483 0.18075 -0.42122 -0.03141 0.11868 1.29339 -0.13202 -0.71227 -0.33379 -0.18843 1.38282 -0.48805 -1.04356 -0.67799 -0.53800 1.48553 -0.89697 -1.42406 -1.07331 -0.93951 1.60472 -1.37151 -1.86562 -1.53208 -1.40544 1.74471 -1.92884 -2.38423 -2.07089 -1.95267 1.91146 -2.59270 -3.00196 -2.71269 -2.60450 2.11345 -3.39686 -3.75024 -3.49013 -3.39409 2.36317 -4.39107 -4.67536 -4.45129 -4.37027 2.67982 -5.65170 -5.84840 -5.67003 -5.60805 3.09444 -7.30243 -7.38442 -7.26590 -7.22885 Coats-Redfern method 1/T K"' 25 "C/min 50 "C/min 100 "C/min 150 "C/min 800-450 "C 0.93183 2.42538 2.56415 3.25860 4.03605 0.97736 2.04236 2.21941 2.87125 3.51280 1.02758 1.61998 1.83923 2.44410 2.93577 1.08324 1.15184 1,41788 1.97069 2.29624 1.14527 0.63009 0.94827 1.44305 1.58347 1.21483 0.04496 0.42161 0.85132 0.78411 1.29339 -0.61585 -0.17317 0.18305 -0.11864 1.38282 -1.36804 -0.85019 -0,57763 -1.14622 450 - 50' C 1.38282 -2.85843 •2.38831 -1.47800 -1.77594 1.48553 -3.08472 -2.60459 -1.77527 -2.33268 1.60472 -3.34732 -2.85558 -2.12025 -2.97876 1.74471 -3.65574 -3.15036 -2.52542 -3.73756 1.91146 -4.02311 -3.50149 -3.00804 -4.64140 2.11345 -4.46812 -3.92682 -3.59265 -5.73627 2.36317 -5.01830 -4.45267 -4.31542 -7.08987 2.67982 -5.71592 -5.11944 -5.23188 -8.80622 3.09444 -6.62940 -5.99253 -6.43193 -11.05370 Friedman method 1/T K"1 25 "C/min 50 "C/min 100 °C/min 150 "C/min 800-450 °C 0.93183 0.98447 2.06390 5.06693 4.03326 0.97736 0.76855 1.76810 4.47092 3.52931 1.02758 0.53044 1.44190 3.81365 2.97356 1.08324 0.26654 1.08037 3.08520 2.35762 1.14527 -0.02759 0.67743 2.27331 1.67114 1.21483 -0.35744 0.22555 1.36279 0.90126 1.29339 -0.72997 -0.28479 0.33451 0.03180 1.38282 -1.15400 -0.86569 -0.83597 -0.95788 450 - 50 'C 1.38282 -2.27891 -2.19688 -1.10676 -0.85881 1.48553 -2.50569 -2.34648 -1.37736 -1.51230 1.60472 -2.76886 -2.52009 -1.69139 -2.27065 1.74471 -3.07795 -2.72399 -2.06022 -3.16131 1.91146 -3.44611 -2.96687 -2.49953 -4.22221 2.11345 -3.89209 -3.26108 -3.03170 -5.50733 2.36317 t^.44346 -3.62481 -3.68963 -7.09615 2.67982 -5.14259 -4.08602 -4.52387 -9.11074 3.09444 -6.05806 -4.68995 -5.61626 -11.74870 211 SYNCRUDE PITCH 2-STAGE M O D E L KINETIC reaction rate Ink-1/T Integral method Coats-Redfern method 1/T K"1 25 "C/min 50 "C/min 100 "C/min 150 "C/min 1/T K"1 25 "C/min 50 "C/min 100 "C/min 800 - 450 °C 800 - 450 "C 0.93183 2.56439 3.60600 3.12732 3.71953 0.93183 2.26465 3.34835 2.80748 0.97736 2.19378 3.18661 2.76851 3.33718 0.97736 1.90234 2.93608 2.45804 1.02758 1.78509 2.72413 2.37282 2.91555 1.02758 1.50280 2.48145 2.07270 1.08324 1.33213 2.21155 1.93428 2.44824 1.08324 1.05998 1.97756 1.64561 1.14527 0.82729 1.64027 1.44551 1.92741 1.14527 0.56645 1.41598 1.16961 1.21483 0.26112 0.99958 0.89736 1.34330 1.21483 0.01296 0.78616 0.63578 1.29339 -0.37828 0.27603 0.27832 0.68366 1.29339 -0.61212 0.07489 0.03291 1.38282 -1.10610 -0.54757 -0.42633 -0.06721 1.38282 -1.32364 -0.73474 -0.65332 450-50° C 450 - 50 °C 1.38282 -1.17957 -0.55165 -0.15558 0.16910 1.38282 -1.70731 -0.96399 -0.49543 1.48553 -1.56039 -1.01584 -0.70122 -0.40093 1.48553 -2.06466 -1.40883 -1.02402 1.60472 -2.00232 -1.55452 -1.33442 -1.06243 1.60472 -2.47936 -1.92506 -1.63742 1.74471 -2.52136 -2.18718 -2.07809 -1.83935 1.74471 -2.96641 -2.53135 -2.35786 1.91146 -3.13961 -2.94078 -2.96391 -2.76478 1.91146 -3.54655 -3.25353 -3.21599 2.11345 -3.88852 -3.85364 -4.03694 -3.88578 2.11345 -4.24931 -4.12835 -4.25550 2.36317 -4.81441 -4.98224 -5.36355 -5.27170 2.36317 -5.11814 -5.20989 -5.54065 2.67982 -5.98842 -6.41327 -7.04567 -7.02903 2.67982 -6.21980 -6.58128 -7.17020 3.09444 -7.52573 -8.28713 -9.24830 -9.33014 3.09444 -7.66237 -8.37702 -9.30401 Chen-Nuttall method Friedman method 1/T K'1 25 "C/min 50 "C/min 100 "C/min 150 °C/min 1/T K 25°C/min 50 "C/min 100 "C/min 800 - 450 •c 800-450 °C 0.93183 2.50061 3.55706 3.05557 3.65679 0.93183 3.79334 4.93696 3.27364 0.97736 2.13262 3.13970 2.69990 3.27720 0.97736 3.23737 4.32950 2.84601 1.02758 1.72683 2.67945 2.30768 2.85862 1.02758 2.62428 3.65962 2.37445 1.08324 1.27707 2.16935 1.87297 2.39469 1.08324 1.94477 2.91718 1.85180 1.14527 0.77580 1.60083 1.38848 1.87763 1.14527 1.18745 2.08971 1.26929 1.21483 0.21364 0.96325 0.84513 1.29775 1.21483 0.33812 1.16171 0.61602 1.29339 -0.42123 0.24320 0.23150 0.64287 1.29339 -0.62106 0.11369 -0.12174 1.38282 -1.14389 -0.57642 -0.46699 -0.10256 1.38282 -1.71288 -1.07925 -0.96153 450 - 50' C 450 - 50 °C 1.38282 -1.34581 -0.66351 -0.23656 0.09500 1.38282 -1.75058 -1.08406 -0.64897 1.48553 -1.71605 -1.11999 -0.77606 -0.46940 1.48553 -2.02776 -1.41413 -1.03911 1.60472 -2.14571 -1.64973 -1.40214 -1.12436 1.60472 -2.34942 -1.79717 -1.49186 1.74471 -2.65033 -2.27188 -2.13745 -1.89360 1.74471 -2.72720 -2.24704 -2.02360 1.91146 -3.25141 -3.01297 -3.01331 -2.80988 1.91146 -3.17719 -2.78291 -2.65698 2.11345 -3.97952 -3.91067 -4.07428 -3.91980 2.11345 -3.72228 -3.43202 -3.42422 2.36317 -4.87969 -5.02052 -5.38598 -5.29202 2.36317 -4.39619 -4.23453 -4.37277 2.67982 -6.02110 -6.42779 -7.04918 -7.03197 2.67982 -5.25070 -5.25210 -5.57551 3.09444 -7.51571 -8.27053 -9.22706 -9.31034 3.09444 -6.36962 -6.58455 -7.15044 3.42366 3.05000 2.63794 2.18125 1.67226 1.10143 0.45677 -0.27703 -0.15327 -0.70712 -1.34984 -2.10469 -3.00384 -4.09301 -5.43957 -7.14699 -9.38275 3.68381 3.26343 2.79985 2.28605 1.71341 1.07120 0.34593 -0.47963 -0.24873 -0.67674 -1.17343 -1.75679 -2.45165 -3.29336 -4.33399 -5.65348 -7.38128 212 Compensation Effect of Kinetic Parameters Derived other 2-Stage Methods The logarithms of reaction rate constants, calculated with the kinetic parameters derived from the 2-stage Coats-Redfern method, were plotted in Figures G . l and G.4 for C A N M E T and Syncrude pitch respectively. The logarithms of reaction rate constants, calculated with the kinetic parameters derived from the 2-stage Chen-Nuttall method, were plotted in Figures G.2 and G.5 for C A N M E T and Syncrude pitch respectively. The logarithms of reaction rate constants, calculated with the kinetic parameters derived from the 2-stage Friedman method, were plotted in Figures G.3 and G.6 for C A N M E T and Syncrude pitch respectively. Examination of these graphs reveals that the second criterion of compensation effect is not met. 6-3 0-V -2-£ -6--8--10-25°C/rrn fin* stage SD°C/rrin, First stage 1CD°C/rrirv First stage 150°C/mi\ first stage 25°C/mn Second stage 5D°Orrin, Second stage 100°arrin,Secord stage 1S)0C/rrir\ Second stage -12- -1— 1.0 I 1.5 20 25 1/T 1000- 1*K' 1 3.0 Figure G. 1 C A N M E T pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates and final temperature 800 °C with 2-stage Coats-Redfern method 213 1/T 1000- 1*K _ 1 Figure G.2 C A N M E T pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates and final temperature 800 °C with 2-stage Chen-Nuttall method 1/T 1000'1*K"1 Figure G.3 C A N M E T pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates and final temperature 800 °C with 2-stage Friedman method 214 6-r 4-2-0-V -2-c E .4--6-•8--10--12-250C/rrir\Rrst stage 50°arrirvRrst stage KD°Clmr\ First stage 1S0°C/rrin, First stage 25°CArin, Second stage SO °C/rrin, Second stage im°C/rrfn, Second stage 1S0oC/rrin, Second stage 1.0 1.5 2 0 1/T 1000- 1*K' 1 25 -r— ao Figure G.4 Syncrude pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates and final temperature 800 °C with 2-stage Coats-Redfern method 6-4-2H 0 V -2 c 1 - 1 0 J -12 25°(7nin, First stage go^amn, First stage 1ffl°C/rrin, First stage 1SD°C/rrin, First stage 25°arrin Second stage SO 0C/mt\ Second stage •KD'Onin, Second stage 150°CArin, Secondstage 1.0 1.5 - I — 2 0 I — 25 3.0 1fl- lOOO-^K -1 Figure G.5 Syncrude pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates and final temperature 800 °C with 2-stage Chen-Nuttall method 215 -10-j -124 1 . 1 . 1 . ! . 1 1.0 1.5 20 25 3.0 1/T 1000- 1*K- 1 Figure G.6 Syncrude pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates and final temperature 800 °C with 2-stage Friedman method 216 APPENDIX H Volatile Yield Predicted via the Single Set Kinetic Parameters for Different Heating Rates 800 °C C A N M E T pitch 25°C/min 50°C/min 100°C/min 150°C/min t min Vexp Vmod tmin Vexp Vmod tmin Vexp Vmod tmin Vexp Vmod 0.01 0.04 0.00 0.00 0.32 0.00 0.01 0.09 0.00 0.01 0.06 0.00 2.01 0.06 0.04 0.98 0.31 0.02 0.99 0.25 0.05 1.03 0.00 0.15 3.42 0.50 0.13 1.52 0.40 0.05 1.26 0.57 0.11 1.65 0.78 1.09 4.15 1.02 0.24 2.05 1.06 0.12 1.49 1.25 0.21 2.35 2.85 5.25 5.02 2.17 0.45 2.50 2.01 0.22 1.77 2.41 0.40 2.54 7.05 7.45 6.02 3.86 0.88 2.99 3.37 0.43 2.00 3.67 0.67 2.74 10.84 10.68 7.02 5.57 1.60 3.52 4.96 0.81 2.27 5.33 1.16 2.89 15.87 16.75 8.03 7.59 2.75 4.01 6.64 1.38 2.51 7.10 1.77 3.01 21.77 22.70 9.03 9.83 4.49 4.50 8.42 2.25 2.78 9.65 2.78 3.13 27.11 29.85 10.03 12.08 7.00 4.99 10.43 3.50 3.01 12.14 3.97 3.21 33.84 35.18 11.03 14.48 10.45 5.52 12.62 5.43 3.25 14.86 5.52 3.28 39.52 40.82 12.03 17.33 14.97 6.01 14.76 7.84 3.52 18.31 7.85 3.36 46.40 46.53 12.50 18.70 17.47 6.50 17.41 10.96 3.79 22.54 10.83 3.44 53.90 52.33 13.04 20.65 20.63 6.99 20.81 14.84 4.02 27.11 13.38 3.52 60.98 57.70 13.50 22.55 23.64 7.30 23.70 17.73 4.22 32.19 19.52 3.63 66.75 64.88 14.04 25.09 27.36 7.53 26.51 19.99 4.37 37.20 25.62 3.75 72.41 70.40 14.57 27.59 31.32 7.75 29.70 22.40 4.49 41.82 30.90 3.83 75.11 73.05 15.04 30.75 34.95 7.97 33.18 24.96 4.61 47.51 36.67 4.02 75.95 76.57 15.51 34.04 38.69 8.15 36.47 27.39 4.69 51.88 40.71 4.49 76.82 77.59 15.91 37.35 41.95 8.24 38.20 29.60 4.76 56.71 44.85 5.00 77.59 77.59 16.24 40.31 44.60 8.42 42.01 34.30 4.84 61.61 49.01 16.58 43.67 49.98 8.60 46.10 39.31 4.92 66.12 53.12 16.98 48.26 56.32 8.82 52.05 45.84 5.00 69.67 57.04 17.38 53.52 62.24 9.04 58.55 52.43 5.15 74.33 64.27 17.71 58.43 66.67 9.35 67.70 61.14 5.35 77.00 71.35 18.00 63.51 70.01 9.66 74.02 68.59 5.62 78.28 76.99 18.31 67.42 73.09 9.89 76.48 72.78 6.01 78.82 79.15 18.65 71.52 75.69 10.11 77.95 75.92 6.52 78.97 79.30 19.05 74.86 77.93 10.64 79.28 79.80 7.02 79.15 79.30 19.52 77.16 79.52 11.49 79.95 80.77 7.49 79.30 79.30 20.05 78.62 80.40 12.78 80.15 80.79 21.05 79.70 80.81 15.00 80.79 80.79 22.05 80.03 80.84 23.99 80.29 80.84 26.00 80.52 80.84 28.00 80.72 80.84 30.00 80.84 80.84 Syncn 25°C/min ide pitc 1 800 °C 50°C/min 100° C/min 150° C/min tmin Vexp Vmod tmin Vexp Vmod tmin Vexp Vmod tmin Vexp Vmod 0.00 0.10 0.00 0.03 0.14 0.00 0.00 0.01 0.00 0.00 0.02 0.00 1.00 0.15 0.02 1.00 0.19 0.03 0.51 0.00 0.02 0.51 0.07 0.03 2.01 0.19 0.06 2.29 0.48 0.37 1.02 0.08 0.12 0.99 0.32 0.35 3.01 0.60 0.18 3.03 1.52 1.12 1.50 0.42 0.54 1.20 0.97 0.81 4.01 1.00 0.46 3.53 2.76 2.20 1.77 1.12 1.12 1.35 1.63 1.40 5.01 1.86 1.04 4.09 5.23 4.26 2.01 2.05 1.98 1.51 2.85 2.32 6.02 3.27 2.18 4.50 7.85 6.67 2.25 3.44 3.36 1.66 4.82 3.67 7.02 5.63 4.23 5.01 11.99 10.94 2.45 5.33 5.08 1.81 7.26 5.61 8.02 8.60 7.67 5.52 17.06 17.02 2.62 7.45 7.00 1.96 10.66 8.27 9.02 12.65 13.01 6.02 22.76 25.09 2.79 9.93 9.45 2.08 13.84 11.04 10.02 17.69 20.71 6.48 28.37 34.08 2.93 12.16 11.84 2.20 17.41 14.41 11.03 23.58 30.93 6.94 34.00 44.25 3.06 14.63 14.64 2.32 21.39 18.45 12.03 29.64 43.21 7.40 39.55 54.88 3.20 17.29 17.88 2.45 25.52 23.21 13.03 35.84 56.42 7.91 45.63 66.08 3.33 20.21 21.57 2.54 28.72 27.14 14.03 41.51 68.85 8.23 49.93 45.92 3.47 23.23 25.69 2.63 32.08 31.45 15.04 46.95 78.83 8.60 56.23 56.23 3.64 26.99 31.42 2.72 35.38 17.86 16.04 52.40 62.72 8.83 61.49 62.52 3.78 30.22 36.37 2.84 39.83 23.56 16.51 55.44 69.40 9.02 66.50 67.33 3.95 34.10 42.97 2.93 43.35 28.44 17.04 59.57 76.10 9.16 70.62 70.70 4.08 37.28 25.56 3.02 47.39 33.91 17.51 63.81 80.89 9.39 77.79 75.77 4.22 40.44 31.05 3.08 50.52 37.85 17.98 68.73 84.61 9.62 83.51 80.08 4.32 42.92 35.55 3.14 54.04 41.96 18.44 74.31 87.27 9.80 86.62 82.90 4.46 46.34 41.98 3.20 58.28 46.13 18.78 78.47 88.59 10.08 88.85 86.12 4.56 49.26 47.01 3.26 63.46 50.44 19.05 81.64 89.37 10.49 89.66 88.98 4.66 52.57 52.14 3.32 69.32 54.69 217 19.25 84.14 89.81 11.00 89.98 90.34 4.76 56.47 57.21 3.39 75.11 58.97 19.51 86.99 90.25 12.01 90.22 90.70 4.86 61.34 62.21 3.45 80.17 63.13 19.85 88.85 90.60 12.98 90.40 90.70 4.96 67.07 66.98 3.54 85.60 68.98 20.25 89.87 90.84 13.99 90.57 90.70 5.07 73.25 71.41 3.63 88.35 74.24 20.98 90.46 91.00 15.01 90.70 90.70 5.17 79.27 75.41 3.75 89.59 80.05 21.99 90.56 91.03 5.27 84.20 78.91 3.93 89.97 86.01 22.99 90.58 91.03 5.41 88.02 82.76 4.26 90.30 90.11 24.06 90.75 91.03 5.64 89.67 87.26 4.99 90.62 90.62 24.99 90.80 91.03 5.95 90.02 89.80 26.00 90.95 91.03 6.49 90.27 90.56 27.00 90.90 91.03 7.51 90.58 90.58 28.00 90.89 91.03 29.00 91.04 91.03 30.00 91.03 91.03 Volatile Yield Predicted via the Single Set Kinetic Parameters for Different Final Temperature 100 "C/min CANMET pitch 750 °C V ^ . % 50.6 0.16 0.00 151.8 034 0.06 202.4 1.04 0.23 225.8 1.90 0.40 249.2 2.85 0.67 276.4 4.37 1.15 299.8 6.02 1.75 327.0 8.47 2.76 350.4 10.95 3.95 377.6 14.05 5.78 401.0 17.09 7.81 424.3 20.48 10.30 451.6 25.64 13.22 474.9 31.58 20.70 490.5 36.67 27.07 502.2 41.70 32.51 510.0 45.81 36.40 521.7 53.18 42.51 525.6 55.86 44.59 533.3 61.28 48.72 541.1 66.20 52.85 552.8 71.47 58.78 568.4 75.54 65.81 583.9 77.50 71.34 607.3 78.67 76.62 626.8 78.88 78.64 650.1 79.06 79.44 700.7 79.40 79.60 750.0 79.60 79.60 850 °C V . , , % V „ „ , % 49.3 0.00 0.00 150.6 0.00 0.05 197.4 0.50 0.20 232.5 1.35 0.46 252.0 2.26 0.70 291.0 4.26 1.49 322.1 6.55 2.53 349.4 9.00 3.86 376.7 11.98 5.67 400.1 14.61 7.67 423.5 17.82 10.14 446.9 21.57 13.10 466.3 25.85 17.52 481.9 29.96 23.25 497.5 34.59 30.04 509.2 39.07 35.73 520.9 44.43 41.77 532.6 50.68 47.98 540.4 55.22 52.09 548.2 59.87 56.08 556.0 64.33 59.87 563.8 68.12 63.40 571.6 71.21 66.58 591.0 75.40 72.79 610.6 77.19 76.52 649.5 78.02 78.84 700.2 78.38 79.01 750.8 78.58 79.01 801.5 78.74 79.01 850.8 79.01 79.01 950 °C V^o/o V ^ ' / o 51.1 0.29 0.00 152.2 0.53 0.06 175.6 1.45 0.11 202.8 2.55 0.24 222.2 3.79 0.38 249.5 5.43 0.68 276.7 7.28 1.18 300.1 9.17 1.80 327.3 11.47 2.83 350.6 13.82 4.04 377.9 16.81 5.92 401.2 19.67 7.99 424.6 23.09 10.55 447.9 27.46 13.61 467.4 32.51 18.39 482.9 37.44 24.32 494.6 41.67 29.51 506.3 46.50 35.24 517.9 52.13 41.33 525.7 56.46 45.56 533.5 60.85 49.82 541.3 65.12 54.04 545.2 67.09 56.10 552.9 70.59 60.04 564.6 74.52 65.53 580.2 77.73 71.61 595.7 79.05 75.98 623.0 80.06 79.98 650.2 80.33 81.07 751.4 80.77 81.23 852.5 81.07 81.23 949.8 81.23 81.23 50 "C/min Syncrude pitch 750 °C V „ p % Va.o.1% 50.4 0.03 0.00 99.9 0.10 0.03 158.1 0.56 0.30 190.4 1.46 0.82 224.9 3.35 2.11 250.8 5.88 3.94 276.6 9.79 6.90 300.3 14.02 10.95 326.2 19.16 17.19 349.9 24.83 24.73 375.8 30.94 34.85 399.5 36.59 45.41 425.3 42.40 57.38 449.0 47.91 67.69 462.0 51.12 46.22 474.9 54.96 53.45 483.5 58.00 58.28 492.0 61.50 62.92 850 °C V e , % V „ d % 51.6 0.06 0.00 102.2 0.02 0.03 164.4 0.48 0.37 201.3 1.36 1.12 228.9 2.80 2.32 252.0 4.80 4.03 277.3 7.88 6.97 300.4 11.70 10.92 325.7 16.76 16.99 348.7 21.89 24.21 374.1 28.07 34.00 399.4 34.44 45.21 424.8 40.76 56.91 447.8 46.75 66.92 466.2 52.50 48.40 482.3 59.46 57.39 493.8 65.60 63.63 503.1 71.20 68.36 950 °C V « p % Vmo.1% 51.1 0.21 0.00 99.7 0.29 0.03 148.3 0.56 0.21 182.4 1.52 0.65 206.7 2.71 1.31 233.5 5.31 2.61 257.8 8.42 4.61 277.2 11.62 6.99 301.5 16.41 11.20 325.8 22.06 17.09 350.2 28.00 24.83 376.9 34.79 35.36 401.2 40.74 46.24 425.5 46.39 57.50 447.4 52.04 67.07 464.5 57.61 47.64 476.6 62.93 54.46 486.3 67.86 59.86 498.6 64.42 66.35 507.2 69.23 70.64 515.8 74.30 74.54 526.6 80.25 78.82 535.2 84.12 81.72 546.0 87.41 84.68 561.1 89.45 87.61 574.0 89.93 89.19 599.8 90.38 90.59 651.6 90.53 90.96 750.7 90.96 90.96 514.6 78.24 73.71 526.1 83.85 78.33 537.6 87.32 82.14 549.1 88.80 85.07 567.6 89.49 88.16 599.8 89.78 90.24 650.5 90.03 90.61 701.2 90.23 90.61 749.5 90.39 90.61 800.2 90.50 90.61 850.9 90.61 90.61 496.1 73.42 65.09 505.8 78.51 69.98 513.1 82.10 73.38 520.4 85.05 76.48 530.1 87.68 80.10 542.3 88.98 83.79 556.8 89.49 86.97 600.6 90.17 90.66 651.7 90.27 91.01 700.3 90.65 91.01 751.4 90.88 91.01 800.0 90.75 91.01 851.1 90.97 91.01 897.3 90.89 91.01 952.9 91.01 91.01 219 APPENDIX I The Effect of the Number of Significant Digits and Sample Weight Analysis The effect of number of significant digits and change of reaction rate constant k ± 1 % and ± 2 % was checked. The following temperature T is in oC and the volatile content V is in % of the original sample weight. Each symbol is defined in the FORTRAN program. Run Can48 is fitted in the following results. The results show that a change of the number of significant digits from 5 to 2 caused 0.0052%, 0.005239%,0.5548%,1.742%,26.66% of s.e.e. but made no noticeable effect on the fitting of the volatile content vs temperature curve, as shown in Figure 1.1. The results also show that a change of k from the best fitting values caused 3.629%, 1.053%, 0.5186%, 2.496% for -2%, -1%, +1, +2% change of k, but the made no noticeable effect on the fitting of the volatiles vs temperature curve, as shown in Figure 1.1. Fitting results in T 5 0 . 2 2 100 .32 135 .40 153 .77 1. 175 .47 2 . 200 .52 3 . 2 2 5 . 6 0 5 . 2 5 0 . 6 5 7 . 2 7 5 . 7 0 9. 300 .75 1 2 . 325 .80 14 . 3 5 0 . 8 5 17 . 3 6 2 . 5 5 18 . 375 .90 2 0 . 387 .60 2 2 . 4 0 0 . 9 5 2 5 . 414 .32 2 7 . 426 .00 3 0 . 4 3 7 . 7 0 3 4 . 447 .72 37 . 456 .07 4 0 . 464 .42 4 3 . 474 .45 48 . 4 8 4 . 4 5 5 3 . 492 .80 58 . 500 .00 63 . 5 0 7 . 8 5 67 . 516 .20 7 1 . 526 .22 74 . 537 .90 77 . 5 5 1 . 2 7 78 . 576 .32 79 . 601 .37 80. 649 .80 80. 699 .90 80. 7 5 0 . 0 0 80. 800 .12 80. the entire temperature range with the change of significant digits V V5 V4 V3 V2 040000 .155612 .155925 .155187 .148259 060000 .586071 .587093 .584630 .561560 500000 1.232127 1.234082 1.229293 1.184507 020000 1.734067 1.736689 1.730211 1.669683 170000 2 .505345 2 .508926 2 .499990 2 .416585 860000 3 .672206 3 .677123 3 .664705 3 .548955 570000 5 .173826 5 .180311 5.163737 5 .009436 590000 7.033928 7 .042167 7 .020847 6 .822622 830000 9.266864 9 .276985 9 .250461 9 .004178 080000 11 .868485 11 .880535 11 .848537 11 .551843 480000 14 .816680 14 .830612 14 .793103 14 .445798 330000 18 .071870 18 .087541 18.044737 17 .648988 700000 19 .682439 19 .698846 19 .653715 19 .236753 650000 21 .579050 21 .596222 21 .548593 21 .108932 550000 23 .284918 23 .302686 23 .253032 22 .795035 090000 25 .271160 25 .289514 25 .237764 24 .760882 590000 27 .291778 27 .310609 27 .257016 26 .763636 750000 29 .073425 29 .092580 29 .037604 28 .531953 040000 30 .865168 30 .884554 30 .828418 30 .312592 350000 32 .399281 32 .418790 32.361847 31 .839053 310000 41.063754 41 .020945 40.747694 42 .488916 670000 45 .483339 45 .439130 45.158472 46 .936603 260000 50 .812486 50 .767717 50.485304 5 2 . 2 6 1 4 0 5 520000 56 .001230 55 .957289 55 .681786 57 .400808 430000 60 .123230 60 .081089 59 .818183 61 .447106 510000 63.451378 63.411572 63.164263 64.686734 420000 66.780378 66 .743855 66.517930 67 .898483 520000 69 .923750 69 .891393 69 .692140 70 .899546 860000 73 .102690 73 .075913 72 .911869 73 .895247 ,160000 75 .972522 75 .952435 75 .830062 76 .553672 ,620000 78 .231054 78 .217958 78 .138651 78 .599589 ,700000 80 .249473 80 .245260 80 .219989 80 .361467 ,030000 80 .759543 80 .758742 80.753972 80 .779498 ,290000 80.839754 80 .839749 80.839723 80 .839849 .520000 80 .840000 80 .840000 80 .840000 80 .840000 ,720000 80 .840000 80 .840000 80 .840000 80 .840000 .840000 80 .840000 80 .840000 80.840000 80 .840000 220 standard deviation for each method above 1.425523 1.417689 1.400758 1.805715 the s.e.e. relative change in % with 5, 4, 3, 2 digits .005239 .554801 1.742416 26.663709 Fitting results in the entire temperature range with the change of k T V VM2 VM1 VFT VP1 VP 2 50. 22 040000 152449 154003 155557 157111 158665 100. 32 060000 574217 580055 • 585893 . 591731 . 597568 135. 40 500000 1. 207336 1. 219562 1. 231787 1. 244009 1. 256230 153. 77 1. 020000 1. 699306 1. 716460 1. 733611 1. 750758 1. 767901 175. 47 2. 170000 2. 455396 2. 480063 2. 504722 2. 529373 2. 554017 200. 52 3. 860000 3. 599583 3. 635475 3. 671350 3. 707208 3. 743050 225. 60 5. 570000 5. 072560 5. 122645 5. 172698 5. 222717 5. 272703 250. 65 7. 590000 6. 898025 6. 965290 7. 032493 7. 099636 7. 166718 275. 70 9. 830000 9. 090637 9. 177923 9. 265102 9. 352175 9. 439143 300. 75 12. 080000 11. 647051 11. 756806 11. 866387 11. 975795 12. 085028 325. 80 14. 480000 14. 546404 14. 680464 14. 814254 14. 947773 15. 081021 350. 85 17. 330000 17. 750740 17. 910142 18. 069141 18. 227739 18. 385936 362. 55 18. 700000 19. 337387 19. 508723 19. 679582 19. 849964 20. 019872 375. 90 20. 650000 21. 206920 21. 391776 21. 576059 21. 759771 21. 942914 387. 60 22. 550000 22. 889470 23. 085980 23. 281823 23. 477003 23. 671520 400. 95 25. 090000 24. 849839 25. 059293 25. 267963 25. 475853 25. 682965 414. 32 27. 590000 26. 845596 27. 067503 27. 288498 27. 508585 27. 727767 426. 00 30. 750000 28. 606588 28. 838855 29. 070089 29. 300295 29. 529477 437. 70 34. 040000 30. 378797 30. 620875 30. 861791 31. 101552 31. 340163 447. 72 37. 350000 31. 897207 32. 147183 32. 395883 32. 643312 32. 889478 456. 07 40. 310000 40. 493876 40. 778982 41. 062074 41. 343165 41. 622269 464. 42 43. 670000 44. 891975 45. 188016 45. 481620 45. 772805 46. 061593 474. 45 48. 260000 50. 210075 50. 511906 50. 810763 51. 106675 51. 399671 484. 45 53. 520000 55. 406352 55. 704705 55. 999558 56. 290952 56. 578928 492. 80 58. 430000 59. 549749 59. 837641 60. 121640 60. 401799 60. 678169 500. 00 63. 510000 62. 907169 63. 180613 63. 449888 63. 715057 63. 976182 507. 85 67. 420000 66. 278446 66. 530923 66. 779023 67. 022820 67. 262391 516. 20 71. 520000 69 476530 69 701777 69. 922559 70. 138965 70. 351080 526. 22 74. 860000 72 729934 72 918005 73. 101715 73. 281164 73. 456452 537. 90 77. 160000 75 690399 75 833076 75. 971800 76. 106680 76. 237823 551. 27 78. 620000 78 045114 78 139443 78. 230589 78. 318659 78. 403756 576. 32 79. 700000 80 188263 80 219546 80. 249327 80. 277679 80. 304670 601. 37 80 030000 80 747584 80 753756 80 759516 80. 764891 80 769907 649 80 80 290000 80 839682 80 839720 80 839754 80. 839783 80 839809 699 90 80 520000 80 840000 80 840000 80 840000 80 840000 80 840000 750 00 80 720000 80 840000 80 840000 80 840000 80 840000 80 840000 800 12 80 840000 80 840000 80 840000 80 840000 80 840000 80 840000 standard deviation for each method above 1.477343 1.440612 1.425819 1.432991 1.461189 the s.e.e. relative change in % with k: -/+1% and -1+2% 3.629687 1.053194 .015486 .518604 2.496592 100 CD 90-80-70-60' 50-l S° 40-\ o > 30 H 20 H 10 • Experimental volatile results Fitting results with 5 significant digits Fitting results with 4 significant digits Fitting results with 3 significant digits -— Fitting results with 2 significant digits 0) OH 100-90-80-70-60' 50 JS 40-o > 30' 20-10-0 -0 100 200 300 — I ' 1 — 400 500 T °C 600 700 800 900 Experimental volatile results - Fitting results with 0.98k • Fitting results with 0.99k Fitting resutls with 1.00k Fitting results with 1.01k Fitting results with 1.02k 100 200 300 400 500 T °C 600 700 800 900 Figure 1.1 Effect of the number of significant digits (a) and the change of k in the range of+1% and +2% from the best fit values (b) 222 The Statistical Analysis of Sample Size Effect The statistical analysis of sample size effect is examined with results in Tables 4.1.1 and 4.1.2 and the analysis results are listed in the following Table 1.1. The results show that the volatile yield is roughly constant and the deviation is small in the sample size range for both heating rates. It is therefore believed that results reflect the intrinsic kinetics and are not significantly affected by mass transfer in these sample size ranges. Table IJ Statistical Analysis of Sample Size Effect 7.774-12.034 mg at heating rate 100 °C/min 8.011-13.157 mg at heating rate 50 °C/min Vt=o% Vt=io% Vt=o% Vt=io% Average V yield 80.12 80.43 80.57 81.01 Standard Deviation 0.8 0.7 0.3 0.5 No. of Data Points 5 5 8 8 223