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Experimental and modeling study of Pitch Pyrolysis kinetics Yue, Chengqing 1995

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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  degree at the  thesis  in  University of  partial  fulfilment  of  of  department  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  by  his  or  her  representatives.  an advanced  Library shall make it  agree that permission for extensive  this thesis for scholarly purposes may be granted or  for  It  is  by the  understood  that  head of my 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  DE-6 (2/88)  April  , m £ >  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 group yield was strongly influenced by heating rates. Higher 0  molecular weight components C n , 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 T A B L E S  viii  LIST OF FIGURES  x  NOMENCLATURE  xvi  ACKNOWLEDGMENTS  xviii  Chapter 1. INTRODUCTION  1  Chapter 2. Literature Review  4  2.1. Chemical Structure of Pitch 2.1.1 The Carbon-Hydrogen Structure 2.1.2 Solvent Fractionation of Pitches 2.2 Chemistry of Pyrolysis and Secondary Reaction 2.2.1 Chemical Thermodynamics of the Pyrolytic Reactions 2.2.3 Pyrolysis of Unsubstituted Aromatics 2.2.4 Pyrolysis of Mixture of Hydrocarbons 2.2.4.1 Pyrolysis of Crude Oil Fractions to Volatile Products 2.2.4.2 Pyrolysis of SARA Fractions 2.3 Pyrolysis Models and Comparison 2.3.1 Constant Evaporation Rate Model 2.3.2 Single Overall Reaction Model 2.3.3 Two Competing Reaction Model 2.3.4 Three Reaction Models 2.3.5 Multiple Parallel Reaction Model 2.3.6 Complex Models 2.3.7 Detailed Models 2.3.8 The Application of Models in Pyrolysis Kinetics 2.4 Compensation Effect of Kinetic Parameters 2.4.1 Effect of Sample Physico-Chemical Properties on the Kinetic Compensation Effect 2.4.2 Effect of Experimental Conditions on the Kinetic Compensation Effect 2.4.3 Analysis of One T G A Experiment with Different Models or Methods 2.4.4 Interaction of the Causes Chapter 3. Experimental Procedures and Apparatus 3.1 Introduction 3.2 Sample Preparation and Characterization 3.3 Experimental Apparatus 3.3.1 Thermogravimetric Analysis (TGA) Setup and Operation  4 5 6 7 7 10 11 11 12 13 14 16 16 17 20 22 23 24 25 27 28 29 30 32 32 32 33 34 v  3.3.2 Pyroprobe-GC .3.3.3 Peak Identification and Quantification  38 45  Chapter 4 Experimental Results 4.1 TGA Experimental Results 4.1.1 TGA Pyrolysis of CANMET Pitch. 4.1.1.1 Effect of Sample Weight 4.1.12 Effect of Heating Rate 4.1.1.3 Effect of Final Temperature 4.1.2 TGA Pyrolysis of Syncrude Pitch 4.1.2.1 Effect of Sample Weight 4.1.2.2 Effect of Heating Rate 4.1.2.3 Effect of Final Temperature 4.1.3 TGA Pyrolysis Characteristics 4.1.4 Discussion and Conclusion 4.2 Pyroprobe-GC Pyrolysis of CANMET and Syncrude Pitch 4.2.1 Pyroprobe-GC Pyrolysis of CANMET Pitch 4.2.1.1 Effect of Experimental Conditions on the Total Weight Loss 4.2.1.2 Effect of Experimental Conditions on the C Yield 4.2.1.3 Effect of Experimental Conditions on the Cio Yield 4.2.1.4 Effect of Experimental Conditions on the Cn Yield 4.2.1.5 Effect of Experimental Conditions on the Cn Yield 4.2.1.6 Effect of Experimental Conditions on the C i Yield 4.2.1.7 Effect of Experimental Conditions on the C i Yield 4.2.2 Pyroprobe-GC Pyrolysis of Syncrude Pitch 4.2.2.1 Effect of Experimental Conditions on the Total Weight Loss 4.2.2.2 Effect of Experimental Conditions on the C Yield 4.2.2.3 Effect of Experimental Conditions on the Cio, Cn, Cn, Cn, and C H Yield 4.2.3 Discussion and Conclusion 7  3  4  7  Chapter 5 Modeling of Experimental Results 5.1 Introduction of Pyrolysis Kinetic Models 5.1.1 Overall First Order Reaction Model 5.1.1.1 Integral Method.. 5.1.1.2 Friedman Method 5.1.1.3 Coats-Redfern Method 5.1.1.4 Chen-Nuttall Method 5.1.2 Multi-First-Order Reaction Model 5.1.3 Mathematical Methods for Overall Single First Order Reaction Model 5.2 Testing of the Basic Models 5.3 2-Stage First Order Reaction Model 5.3.1 Multi-Stage First Order Reaction Model and its Assumptions 5.3.2 Application of the Multi-Stage Model 5.4 2-Stage First Order Reaction Model for Pitch Pyrolysis 5.5 Testing of the 2-Stage Integral Method 5.6 Discussion and Conclusion  48 48 48 48 51 54 55 56 58 59 60 67 71 71 ........72 74 77 79 80 81 82 84 84 85 86 87 89 89 90 90 91 92 93 93 96 96 101 106 107 114 120 124 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 7.1 Summary of Findings 7.2 Recommendations  147 147 150  REFERENCES  152  APPENDICES APPENDIX A: Methods Available for Computing Kinetic Parameters APPENDIX B: G C Computer Station Method Parameters APPENDIX C: Comparison of Equation 5.5 and Equation 5.6 Evaluated with Different Numbers of Terms of Integral E;(-E/RT) APPENDIX D: F O R T R A N Programs and Calculation Results for T G A Experimental Results Modeling APPENDIX E : F O R T R A N Program for Two-Stage First Order Reaction Model APPENDIX F: Summary of Kinetic Parameters of the 2-Stage Model APPENDDC G: Kinetic Reaction Rate Constant Ink - 1/T for C A N M E T and Syncrude Pitches APPENDDC H : Volatile Yield Predicted via the Single Set Kinetic Parameters for Different Heating Rates APPENDIX I: The Effect of the Number of Significant Digits and Sample Weight Analysis  162 163 166 169 170 187 209 211 217 220  LIST OF T A B L E S Chapter 2 Table 2.1 Bond Energies Obtained from Thermodynamic Data and from Quantum Mechanical Calculations [22] Table 2.2 Resonance Energies of Cyclic Compounds [22] Table 2.3 Summary of the Methods Used in Constant Heating Rate Pitch Pyrolysis  8 9 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 Table 4.2.1 Experimental Conditions for Runs at Different Holding Times  70 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 G C 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 Chapter 4  44  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 Figure 4.1.8 Sample weight effect on Syncrude pitch pyrolysis with T G A at 100 °C/min at 10 min  57 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  Figure 4.2.2  Figure 4.2.3  Figure 4.2.4  Figure 4.2.5  Figure 4.2.6  Figure 4.2.7  Figure 4.2.8  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  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  C A N M E T pitch pyrolysis total loss vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min  74  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  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  C A N M E T pitch pyrolysis C yield vs. temperature at different pyrolysis holding times with heating rate 3000 °C/min  76  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  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  7  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 C u 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  Ill  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  NOMENCLATURE a  kinetic compensation constant in Chapter 2 fitting parameter in Chapter 5  B  maximum possible devolatilization rate, S"  b  kinetic compensation constant in Chapter 2 fitting parameter in Chapter 5, b=-E/R  C  heating rate, °C/min  1  E, E  activation energy, J/mol  0  E;  activation energy of ith stage of reaction, J/mol  f(E)  distribution function of activation energy  Hp  rate of heat supply for volatile evaporation per unit mass, kJ/s.kg coal  h  total heat of volatile evaporation per unit mass of coal, kJ/kg coal  T  LV  k, k i , k , k 2  3  rate constant represented by an Arrhenius expression, min"  ko, k o i , ko2  pre-exponential constant of Arrhenius equation, min"  koi  pre-exponential factor of ith stage reaction, min'  k  nominal rates  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  mass of tar, kg  T  ~k = (dV / dt) / (v*-V), min"  no. of reaction stages which are first order reaction  R  gas constant, 8.314 J/mol.K  s  2  1  1  n  R  1  linear regression constant standard deviation of activation energy, J/mol  1  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  coal particle temperature, °C (K)  P  Tv  volatile evaporation temperature, °C (or K)  V  volatile released at time t, % (or kg)  V=o  volatile yield at t=0 minutes, %  V =io  volatile yield at t=10 minutes, %  V*  total volatile yield, % (or kg)  X  reciprocal of temperature 1/T, K"  t  t  X  1  fraction of volatile material to be released  v  Y  L H S of each of the single overall first order reaction methods  a, cti, 0C2  kinetic compensation constant  cti, a  mass stoichiometric factors representing the extents of devolatilization via reaction 1 and 2 respectively in Chapter 2  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, U B C , 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  C H A P T E R 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 and catalysts 2  are added in to upgrade bitumen at temperature 375-530 °C and pressure 1100-1600 psi, and currently operating at 715 m /D of bitumen. About 4% of the feed ends up as pitch [15]. 3  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 T G A , and at rapid heating rates with a Pyroprobe-equipped gas chromatograph. With T G A , 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 G C 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 N M R in pitch characterization. For measurements on pitch solutions, the main problem is the fact that pitches are not completely soluble in solvents suitable for N M R . 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 C NMR. Well1 3  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, npentane 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 ObtainedfromThermodynamic Data and from Quantum Mechanical Calculations [22] From quantum mech. calculations From thermodynamic data Force Mean Mean constant Distance bond bond dynes between energy energy cm'SclO" nuclei, A kJ/mol kJ/mdl Compound Bond 5  C—C C==C  C2H5  325.10  —  C2FI4  585.76  C^C  C2H2  C—C  C^is  808.77 517.98  597.89 811.70  C—H  CH4  o—a  C=0  HO-H CH 0 2  410.87 457.73 683.25  —  —  1.337  9.8 15.6  1.205  —  —  —  412.96  1.094 0.98 1.21  4.88  462.75 694.54  7.6 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 kJ/mol Compound kJ/mol Compound 288.70 Quinoline 150.62 Benzene 299.16 Biphenyl 255.22 Naphthalene 167.36 Aniline 351.46 Anthracene 92.05 Furan 384.93 Phenanthrene 102.51 Pyrrole 146.44 Toluene 205.02 Indole 158.99 Styrene 117.15 Thiophene 150.62 Phenol 25.10 Cyclooctatraene 179.91 Pyridine  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 afractureof 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 smallfragmentsdown 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 S A R A Fractions Evidence from G C , HPLC, and FTIR analysis [23-29] suggests that S A R A 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 S A R A 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 JIT  —^=0;  T <TvorXv=1.0  dt  dt  (2.2a)  P  =-  /h  lv  ;  dX = -B; dt Where h  T >Tv and X <1.0, H < B h  lv  (2.2b)  T >Tv and X <1.0, Hpr>Bh,v  (2.2c)  P  P  V  PT  V  is total heat of volatile evaporation per unit mass of coal, kJ/kg coal, H  LV  PT  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" did not appreciably change the predicted temperature [36]. 1  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  mMz3L  .  v=  (2 2d)  w (0) c  and the total volatile yield is  ,  m (o)-m ( final) r  r  and the fraction of volatile material Xv to be released is  15  m -m ( final) r  *v=  r  (2.20  f.v  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 = k exp[-E/RT ] a  (2.3b)  p  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 C  ^ aiVi+(l-ai)Ri  "  caV2+(l-a2)R2  16  The rate of weight loss of the coal (maf basis) is given by  dm  c  dt  (2.4a)  -{k +k )m x  2  c  so that at any time t the mass of material yet to be pyrolyzed is  -J'(A, + k )dt'  m = m (0) exp c  O  c  (2.4b)  2  Where the rate of devolatilization at any time is  —=  (2.4c)  {a k +a k )m x  x  2  2  c  Where a i and cc are mass stoichiometric factors representing the extents of devolatilization via 2  reaction 1 and 2 respectively. The extent of devolatilization at time t is obtained as  F(/) = i» (0)J '(a * + a k )exp[-I> +^)^'}/r' c  o  I  2  I  2  1  (2.4d)  The rate constants ki and k have Arrhenius form, and are such that reaction 1 has a lower 2  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:  C  The rate of weight loss of the coal particle is given by  17  ^ =-*,'"c  (2.5a)  L  By integration, then m (t) = (0)exp[-i' k dt>] c  mc  o  (2.5b)  l  The net rate of production of tar is ^ - = a k m -(k l  l  c  2  + k )m 3  (2.5c)  T  Where mx is the mass of tar, then the yield of tar at any time is given by integration of the above equation.  m (t) = a T  lWc  (0)exr[-J ' 0  (* +*s)*]Jo a  J 'K >-^i)*']* + k  0  (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  ^Sffft --(-V)]-^h*p(-M<)]} 1  (2.50  which further simplifies to (by assuming ki much smaller than k , k ) 2  3  ™-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  a i Vi+(1 - ai)I  la ^  V2  The rate of decomposition of the coal particle is given by the equation ^ - = -k m x  (2.6a)  c  the rate of production of the volatile and the intermediate is then given as  dt  =akm x  x  (2.6b)  c  (\-a )k m -(k x  x  c  2  +k )m i  (2.6c)  I  ^=k m 3  (2.6d)  1  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  c H - C2 —  :  ^ V 2  ^Vi'+R'  +R  Coal particle C is assumed to consist of two distinct components, C i and C , of different ease of 2  pyrolysis. In their analysis, Nsakala et al. [48] ignored the secondary cracking of V i . If, therefore, components Ci and C decompose isothermally by independent first order reactions 2  C , = C e x p (-*,/)  (2 7a)  C = C exp(-V)  (27b)  0I  2  02  Where C i and C02 are the initial mass of Ci and C . The total weight loss is obtained from 0  2  V = V +V X  2  (2.7c)  where V i and V are volatile product from Ci and C 2 components respectively and 2  19  V =C -C X  QX  (2.7d)  X  (2.7e)  V = C -C -R 2  02  V =C  0 1  2  [l-exp(-^/)] ^r[l-exp(-^r)] +I  (2.7f)  At infinite time  V  *  =  C +  C  °  (2.7g)  2  or l - - ^ = (^r)exp(-^r) (l-C /F*)exp(-V) +  0 1  (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  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  V_ V* = 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  (2s )\ 2  (2.8b)  Where E is the mean activation energy and s the standard deviation. 0  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  forE^y, rt>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/kaRT  2  = e~  , then employ the averaged  B/RT  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 +  j(I  (1 - 0C6) R6  - ou) Rz + CX2T2  k2 k 7  '  k i C  — A C  ^  a? V 7 + (1  -  OCT)  R7  k 4 •  OO V 3  CX4  V4  + (1 - CM) R4  + (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: ^ Coal  tar formed  coke + light hydrogencarbons  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-T =Ct where C is heating rate. 0  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  J" c{ <t  \  r  4 {-W)}  eirt  e  -  (2  9)  Friedman Method The values of dV/dT is calculated by using two adjacent pairs of the volatile and temperature data: W _ **- i v  dT  CoatsRedfern Method  In  Chen-Nuttall Method  In  AnthonyHoward Model (1976)  (2.10a)  v  T -T M  t  -Clnll-^J  I  V  —  =x M x -  RT  2  E \  2  E  R  T  \  ) RT  RT i -v-)r °-RT 2  l l  nk  r= l - J exp_ -l' k(E)dt o  E  (2.11)  \  '  (212)  f{E)dE  (2.8a)  exp[-(E-E y/(2s )]  (2.8b)  o  2  0  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:  \nk = aE+0 o  (2.13)  The above equation indicates the linear dependence between the values of the logarithmic pre-exponential factor  lnko  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»H 0, with various 2  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 04*H 0, under 2  2  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 physicochemical 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 U B C , 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 C A N M E T 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 Maya[106] Suncor Syncrude C A N M E T Pitch As received Residuum Pitch Pitch [8] This Work Lim [10] 83.6 82.8 82.72 86.2 85.32 Carbon % 9.3 7.9 10.35 7.1 9.33 Hydrogen % 0.52 1.0 0.5 1.1 0.82 Nitrogen % 5.8 5.8 4.73 2.8 2.39 Sulfur % — 0.5 0.97 1.0 1.12 Oxygen % — — 0.71 1.8 1.02 Others % 99.7 97.5 100.00 100.00 100.00 H/C N/C  o/c s/c  Volatile Fixed Carbon Ash Pentane insolubles Asphaltene Benzene insolubles  1.50 0.99 1.31 0.0054 0.011 0.0082 0.0088 0.0087 0.0098 0.021 0.0012 0.011 Proximate Analysis % — 90.11 81.17 — 8.65 18.65 — 1.24 0.18 Solvent Fractionation % — 33.58 45.15 — 25.77 35.65 — 7.81 9.50  1.145 0.0104  —  0.0263  1.335 0.0051 0.0045 0.026  —  —  — —  1.6  —  39.5  — —  — —  The ultimate analysis results of C A N M E T 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 TGS2 T G A . 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 C A L I B R A T E and R E S E T 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 anticonvection 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. Nitrogenflowratewas 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 G C 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 G C 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 G C 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 innersurface 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 G C station as shown in Figure 3.3. The pyrolysis product is purged into the G C 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 G C is controlled using the computer workstation. The G C and the Pyroprobe were started at the same time for each run. The G C 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.  •  G C 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. 1 2 3 4 5  Retention Time min. 0.01- 4.73 8.84-15.86 19.17-23.97 24.24-31.72 32.11 -36.01  6  37.49 - 42.66  Mid-point min. 2.370 12.350 21.570 27.980 34.060 40.070  43  Chart Speed -* Start Time » M C M  0.35 cm/min 8.000 min  Attenuation 12 End Time •> 65.000 min  Zero Offset - -57t Kin / Tick « 1.00  x:  at o co O to o  El  40i  *i  « B C 3 « 3 o n n o s  a  0  B  IS CC a.  i , iiii(iiiiitiiitiiiiiiiiiii iiiiiiiiiiiii i  O M M O. -4 0> OU « Ot —CO  0 E«f< 0 H to « a  o0 Ufa  0 c S •0  O h *J 3  O H 6  (  0 0 f0 a  O *i -* C  , I l lt 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 l l I I I t l l l l l l i i i i i 1  i  | <H  0B c 0 M0 0 0 0 M  0.0 C £ O <E H U  .d-P u w  Figure 3.4 Chromatogram of C A N M E T pitch volatiles  Chart Speed « Start Time **  0  X a o  %4 T*  M <  £« 0 00 M M« 0 OB e 4 0J 00 c  0.3 5 cm/min 9.000 min  Attenuation « 28 End Time =• 65.000 min  Zero Offset - -SOt Min / Tick - 1.00  „,  U C  0«H  £< o *>  H  a o  5n  0  CL  3 a f f l a K  a &,  e  3  J H  O Z  0  (XM M  w  B  3-1  4J -O  uox a H A P .  00 0  *i  I I I I f I I I < I I I fI I I I I I I I I I I I I I I I I I I I I I I f  0  1  1  a  M M  ££ H  0  TJ -"-"-CO C  Efa3 I  •rt  «0  « k O H  *> c 5 -< 3  §•  0«  0 0e  00 0 00  O *J «H C tl *i 0 B<H *J *i 3 M C  l t I I I I I I I i I I I• I• < I I<I < I II II I I I 1  O  co H *  uu  O U  00  Figure 3.5 Chromatogram of standard sample  I t I I iI I | I iiiiii i  3.3.3 Peak Identification and Quantification In order to identify species from the chromatograms, standard samples of paraffin and aromatics  C6-C14  C6-C16  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, C n , C n , 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.  Paraffins Hexane C6 Heptane C7  fable 3.3 Retention Time of Each Component Retention Time min Aromatics Retention Time min 1.780 Benzene C6 1.489  Octane Cg Nonane C9 Decane C10 Undecane C n Dodecane C12  1.933 2.959 6.208 12.025 20.882 27.894  Tridecane C13 Tetradecane C14  34.051 40.030  Toluene C7 Xylene Cg Cumene C9 Butylbenzene C10  4.684 (p) 6.473 13.500  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; F A C T O R 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 T G A , Pyroprobe and G C are summarized in Table 3.4.  GC  Pyroprobe  TGA Purge Time min Purge Gas/Flow Rate mL/min  20 100  20 1  20 1  Initial Temperature  50 (5 min)  50  40 (10 min)  Heating Rate °C/min Final Temperature °C Holding Time  25, 50, 100, 150  2  700, 750, 800, 850, 900, 950  600, 3000, 30000, 300000 500, 600, 700, 800, 900, 1000  10 min  0, 5, 10 s  10 min  120  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 atfinaltemperature.  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. V=o and t  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 release from solid char, 2  but the amount is very small. This is in good agreement with the analysis of Nguyen [107], where only 1.56% of Ff content was observed in the delayed coke. It is generally believed that the 2  weight loss at this stage is caused by the H release from the remaining char [9, 17, 30]. At lower 2  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 •  88-  100°C/min, Oirin 100°C/mh. 10rrin  86-  to 84-  3 •  i  £ 82-  J  °• ^: >  80-  o  781  1  r  1  1  1  I  '  Sample Weight mg 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  90 - r o •  88-  50 °C/min, 0 min 50°C/min, 10 min  •  86-  to 84-  v>  3 • £ 82-  |  \ 80O  7876-  4  '  r—>6  8  10  12  14  16  18  Sample Weight mg  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  4.1.1.2 Effect of Heating Rate To study the heating rate effect on the pyrolysis total weight loss with T G A , 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 T G A , 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.  800 °C 700 °C  50-  40-  °^ 30to  3  i  CD  >  104  OH 1  100  1—i  i i i 11|  1000  1  l — • I I I I 11  r—l—i  10000  I  '  1  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 -m— 100°C/min, Omin - » — 100°C/tnin, 10 min  81.5 81.0-1 v o 80.54,  w cj 80.0-1 .£> 79.5-^ J  79.0-j  785-1 780  I— 700  750  I— 850  I—  800  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.  1004  •  800 °c  904 804 704  "g  3020-  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  750  1  1  800  •  1  850  •  1  900  •  1  1  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 C A N M E T 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 C A N M E T 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  0  1  1  5  <  1  10  1  1  15  >  1  20  '  1  25  1  r  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 200300400500600 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  0  1  1  5  1  1  10  •  1  15  1  1  20  "  1  25  1  T  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 T G A , 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 V M Final Temp Sample Weight mg Heating Rate °C wt% "C/min 900 4.406 82.8 100 900 5.702 82.51 100 900 6.441 82.05 100 900 7.074 80.60 100 900 7.774 79.80 100 900 7.981 81.65 100 900 10.719 80.27 100 11.162 79.33 900 100 12.034 79.59 900 100 13.680 78.70 900 100 900 15.784 79.85 100  Run* Canll Can20 Canl8 Can45 Canl5 Canl6 Canl7 Can8 Can38 Can 19 Canl4  Run* Can28 Can21 Can7 Can27 Can27 CanlO Can25 Can23 Can35 Can22 Canl3 Can31 Can24 Can30 Canl2  v . M  wt% 83.64 82.82 83.50 81.55 80.47 81.79 80.50 79.57 79.83 79.03 80.03  Table 4.1.2 Experimental Conditions for Runs at Different Sample Weight with TGA Sample Weight V« Final Temp Heating Rate °C mg wt% wt% "C/min 4.979 82.89 84.38 900 50 900 6.360 82.76 83.32 50 6.723 82.48 86.29 900 50 8.011 80.51 80.65 900 50 900 8.943 81.12 81.38 50 900 10.179 80.60 81.82 50 11.162 80.25 80.45 900 50 900 11.735 80.88 81.02 50 900 12.022 80.43 80.74 50 900 12.699 79.97 80.35 50 900 13.157 80.84 81.71 50 900 14.042 78.47 78.87 50 900 14.729 77.85 78.26 50 900 15.596 78.49 78.87 50 17.175 79.10 80.07 900 50  Table 4.1.3 Exoerimental Conditions for Runs at Different Heating Rates with TGA Final Temp. °C Sample Weight mg Volatile Heating Rate "C/min wt% Run# 700 9.368 81.78 25 Can54 700 8.835 80.66 50 Can61 700 7.896 79.74 100 Can53 700 8.923 79.93 150 Can60 800 8.878 80.84 25 Can48 800 8.224 80.79 50 Can33 800 10.304 79.30 100 Can41 800 9.109 77.59 150 Can58 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 12.00 5.0 700 600 Cam069 700 5.6 10.71 3,000 Cam051 30,000 700 5.2 9.62 Cam033 300,000 700 5.3 1.88 Cam015 800 5.3 49.06 600 Cam070 3,000 800 5.8 29.31 Cam052 30,000 800 5.2 7.69 Cam034 300,000 800 5.0 2.00 Cam016  Rimtf Can53 Can42 Can41 Can40 Can38 Can52  Table 4.1.5 Experimental Conditions for Runs at Different Final Temperature with TGA Heating Rate Final Temp. "C Sample Weight mg Vt-o "C/min wt% 100 700 7.896 79.74 100 750 9.171 79.54 100 800 10.304 79.30 100 850 10.723 79.01 100 900 12.034 79.59 100 950 8.199 81.23  Vc-io wt% 80.20 79.81 79.72 79.39 79.83 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 "C/min wt% 100 700 3.010 92.73 100 700 7.852 90.54 100 700 11.029 90.28 100 700 13.932 89.83 100 800 4.321 91.63 100 800 6.797 91.10 100 800 11.376 90.58 100 800 15.534 90.29 M  Run# Synl3 Synl4 Synl6 Synl5 Synl7 Synl9 Synl8 Syn20  Table 4.1.7 Experimental Conditions for Runs at Different Heating Rates with TGA and Pyroprobe Heating Rate Final Temp Sample Weight V "C/min mg wt% 25 800 10.477 91.03 50 800 11.708 90.70 100 800 11.376 90.59 150 800 10.053 90.62 600 800 4.600 8.70 3,000 800 2.400 8.33 30,000 800 3.600 2.78 300,000 800 4.900 £08  •  V wt% 93.51 90.84 90.60 90.40 91.89 91.39 90.94 91.36  M 0  M  Runtf Syn43 Syn29 Synl8 Syn8 Syn070 Syn052 Syn034 Syn016  Run# Syn27 Syn32 Syn33 SynlO Syn5 Syn4  Equipment TGA TGA TGA TGA Pyroprobe Pyroprobe Pyroprobe 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 "C/min wt% 50 750 7.604 90.96 50 850 7.134 90.61 50 950 6.942 91.01 150 750 7.606 90.18 150 850 6.920 91.19 150 950 7.262 92.66  Run# Can48 Can33 Can41 Can58 Syn43 Syn29 Synl8 Syn8  Table 4.1.9 The Pyrolysis Conditions for CANMET Pitch and Syncrude Pitch at Different Temperature and Heating Rates Heating Rate Final Temp. "C/min *C CANMET Pitch 800 25 50 800 100 800 800 150 Syncrude Pitch 800 25 50 800 100 800 . 150 800  V io wt% 91.02 90.87 91.21 90.51 91.22 93.05 P  V* wt% 80.84 80.79 79.30 77.59 91.03 90.70 90.58 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 Heating Rate °C/min Holding Time s 300,000 10.0 300,000 5.0 300,000 0.0 30,000 10.0 30,000 5.0 30,000 0.0 3,000 10.0 3,000 5.0 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  6D-  -R=Q05ams,t=10s 0  -R=a05°C/rrE,t=5s -R=aC6°C/nrB,t=0s  SD-  g 40^ 3)1 32 >-  2D  OH  —I—  3D  800  833  TOO  —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 yield is 54.46%, 27.92% and 0% at 1000 °C for holding time 7  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 yield at 10 7  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 yield reached 47.77% and 39.19% at 1000 °C for 10 7  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 yield vs. temperature at different pyrolysis holding times with heating rate 30,000 °C/min 7  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 yield is reached at different 7  temperature for different holding times. Maximum C yield is reached at a lower temperature for a 7  longer holding time. Maximum C yield, 43.75%, is reached at 700 °C for 10 second holding time, 7  while maximum C yield, 40.14% and 41,75%, is reached at 800 °C and 1000 °C for holding time 7  5 and 0 s respectively. Secondary pyrolysis is clearly observed for the C lump of compounds. At 7  temperature lower than 750 °C, it is observed that longer holding time resulted in higher C yield, 7  while at temperature higher than 900 °C, longer holding time resulted in lower C yield. It is also 7  observed that C yield increased dramatically at temperatures above 700 °C for 0 second holding 7  time and 41.75% is obtained at 1000 °C for holding time 0 s. The maximum C yields at different 7  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-R=005 C/rfE,t=10s c  -R=QC6 C/rrB,t=5s 0  25  -R=O05 C/m5,t=0s o  20H 15-  ? 1.0' Q5H  QOH  —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 C n Yield Figure 4.1.10 shows that the C n yield generally increases to 800 °C and then decreases as temperature at the heating rate of 300,000 °C/min, with maximum C n yield observed at 800 °C. Maximum C n yield of 2.7% and 1% is obtained at 800 °C for holding time 10 and 0 s respectively. There is no C n 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 C n lump depleted due to further pyrolysis (i.e. secondary reactions).  79  —»—R=50°C/ms,t=10s —A— R=50°CArs,t=Os 4H  !  3H  H oH 3D  833  TOO  833  3D  1003  Figure 4.2.10 C A N M E T pitch pyrolysis C n 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 C  n  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  — • — R= 5JO°CAIB, t- 10s  —A—R=5jO°C/tTB,t=OS  4H  3H  I 32  2 H OH 333  eoo  700  933  833  •KEO  T°C Figure 4.2.11 C A N M E T pitch pyrolysis C yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min u  4.2.1.6 Effect of Experimental Conditions on the C n 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. C n 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-R=50°C/ms,t=10s -F*=S0°C/ms,t=5s -R=5i0°C/ms,t=0s  15H  |,1.<H  8 >  0.5  -1— 700  eoo  3D  1033  933  833  Figure 4.2.13 CANMET pitch pyrolysis C i yield vs. temperature at different pyrolysis holding times with heating rate 300,000 °C/min 4  —«—R=05 C/mi,t=10s 0  —»—R=05°CATB,t=5s —A—R=05°C/m»,t 0s 3  4H  H  *  •r •  533  •  eoo  ••  •  i  1  700  1  833  1  1  933  1  "1  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 Heating Rate °C/min Holding Time s 300,000 10.0 300,000 5.0 300,000 0.0 30,000 10.0 30,000 5.0 30,000 0.0 3000 10.0 3000 5.0 3000 0.0 600 10.0 5.0 0.0  600 600  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  500  1  1  600  >  1  1  700  1  1  800  l  900  '  l  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  —1 500  1  1 600  •——I 700  1  1 800  "  1 900  1  1 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, C u , C , C13, and C i Yield 1 2  4  Fligher yield of Cio and C n 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 C n 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 C n 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 C n , 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 C n , 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: (5.1) 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;  T=Ct+T  a  (5.2)  where T is the initial temperature of the experiment. Substituting time term dt with temperature 0  dT, i.e. dT=C*dt, the general expression is then given as:  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  5.1.1  E  activation energy of the single overall first order reaction, J/mol  ko  pre-exponential factor of the single overall first order reaction, min" .  R  gas constant, 8.314 J/mol.K  C  pyrolysis heating rate, K/min.  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: (5.4)  v-v~c  e  v  Integrating the above expression in the temperature range of interest, we then get (5.5) where T is the initial temperature. In the current study the T is chosen as 50 °C, and the rate as 0  G  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 assumed to be 0 K . 0  (5.6) The exponential integral E (-E/RT) can be approximated by (Appendix C): ;  90  -E/RT  E\ -  E/RT  RTJ  1!  2!  E/RT  (E/RT)  (5.7)  1  If the first three terms of the approximation are used, the above integration becomes:  -id  (V_-v\  kRT (  V  CE  2RT E J  2  1—  -E/RT  (5.8)  Dividing both sides of the above equation by RT (1-2RTVE)/C and taking the logarithm, 2  then  -C\r[l-  V  Id  (  2RT)  \  E  •In 1 — —  RT  2  , k l*ln-=Q  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 F O R T R A N 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  KRT  (  2  V=V*\ 1-exp  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 V'dT~°  /RT  (V- V) V*  (5.11)  91  Taking the logarithm and rearranging,  (C  dV\  -ln[l~]=ln*.-  {.V* dTJ  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  .dTJ,  (5.13)  T -T, M  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 2RT/E«1.  -Clnf In  v  1  RT  V)  = , En 4RT -  £  (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 J  o  v -V  0  (  5.i5)  c  Integration of the above equation gives:  ^  k RT ,-E/RT -e C E+2RT 2  (5.16)  Multiplying both sides of the above equation by -C(E+2RT)/RT and taking logarithms gives: 2  (-CiE+lRVf^V^ iJ RT "X 2  V'l  1=1"^-^  (5.17)  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 F O R T R A N 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 ) from a wide range of 2  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 5(2^)  f«  E-E^  0 5 J  .  \kjtt  1  6XP  1  CE  (5.18)  2  exp  dE  Due to the complex and nonlinear nature of the model function, nonlinear regression must be used to fit the experimental data for E , ko and s. The Levenberg-Marquart method is thus used in 0  this work. This method adjusts ko, E and s within the calculation. Some authors [52] used a fixed 0  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 and s. In order to use the Levenberg-Marquart method, the derivatives with 0  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 E -4s to E +4s. Further increases in the 0  0  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:  V*  dV dE  .r*^  J k RT  .  2  a  V  1  2RT\  J  E-E  2  0.5  s(2x)  0  E-E (  ^  J  n  )  ^  +  e  x  p  (  kRT  e  X  p  -  (  8  )  e  JE„+A,  V*  s\27tf  5  S(2TT)  0.5  X  e  5(2^")'  P  (  " ^  2RT  l - ^  T  T T )  (5.19)  J  ]  ^  X  - ^ r - e x p ( - — X 1 - — )\^P) - 0 - 5 ( — )  RT'  CE  kRT  , E + 4s^  2  _ e x p ( - 8 ) e x p | - ^  0.5  X  X  2RT.  0  l - ^ ^ J  4V*  4F*  0  expi-  ) ^M E  P  T  ^ e x p ( - - ^  , E -4s^  2  -  , E +4s^  2  _ 8 ) e x p | - ^  k„RT  dV ds  £  / W  exp(-8)exp^  T  £ -45 0  • P(~ eX  D T  ;  dE  2RT\  0  ^ e x p ( - —  2  r  tf-^j  2i?r  XI - ^E -4s'IT) I 0  (5.20)  dV dk„  S(2K)  0.5  j ,E -4s a  CE  RT'  (5.21)  A F O R T R A N program was written to solve the above ODEs and the procedures outlined in Numerical Recipe [110] were followed. The F O R T R A N 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.  Integral  a a = InftyE)  Y  Methods  (5.23a)  r=in  RT  2  J a = In k  0  (5.24a)  Friedman  ( Coats-Redfern  -Cln  Y= In V  Chen-Nuttall  (  v V  1--7  \ VJ RT 2  a = \n(k</E) (5.25)  (5.25a)  >  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 Integral Friedman Coats-Redfern Chen-Nuttall Coats-Redfern Chen-Nuttall Anthony-Howard Anthony-Howard [m]  11111  11111  Feed Pitch Pitch Pitch Pitch Shale Shale Pitch Shale  k» min.' 151.0 130.0 59.1 104.0 56.4 37.7 5.0xl0 5.8x10 8  s  1  E kJ/mol 33.1 32.5 30.8 32.0 32.9 31.6 114.9 90.4  s kJ/mol  14.9  s.e.e. 6.57 6.12 9.33 5.40 5.3 5.4 6.22 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  •  Experimental resits Fitting restits  -10-11-12-  >-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 hC  1  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  •  *  Experimental resiits Fitting results  -15  0.0310 0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026  1/T rC  1  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-  Experimental results Fitting resiits  0-1-  >-  -2\ #  -3-  -51—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  0.0012  1  1 1 1 1 1 1—-1 1 1 1 1 1 1 1 0.0014 0.0016 0.0018 0.0020 0.0022 0.0024 0.0026  1/T rC  1  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-  • o  0.8-  A °  P  A/  0.6 H  0.4H  A  V A  25°C/min 50°C/min 1CX) amin 150°C/min 0  v •o  o  v D  A T  0  0.2-\  o.o H 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 • o A V  0.8 A  0.6 H  0  A *  0.44  A  o A  0.24  25°C/rr«n 50 C/rnri 1Q0°C/min 150°C/min  •  V  "OA •  o  0.0 4 —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 25°Cymin 50°C/min 100°C/min 150°amin  908070605040302010010  I 20  30  40  50  60  "T 70  80  90  V -V %  Figure 5.7b The devolatilization rate dV/dt vs. the remaining volatile at different heating rates and 800 °C for Syncrude pitch  100  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: ,-E,/RT  -T = La k e at t=i i  oi  (V-V)  (5.27)  (5.28)  T=Ct+32316 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:  ^ = tc k e-^(v'-V) ai  where  oi  cti=l, a =0  when T < 450 °C  cti=0, a = l  when T > 450 °C  2  2  (5.30)  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 F O R T R A N 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 Second stage First stage ko min' koi min" E kJ/mol E i kJ/mol C A N M E T Pitch 4.448* 10 71.34 5.534 21.89 2.865*10 69.93 1.207 18.31 4.004* 10 70.91 2.663 19.81 2.221*10 39.42 2.169 18.35 2  Run# Can48 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman Run# Syn43 2-Integral 2-Coats-Redfern 2-Chen-Nuttall 2-Friedman  s.e.e.  2  4  4  4  2  Syncrude Pitch 67.66 51.80 66.14 22.28 67.18 38.04 101.5 7.251  30.82 28.92 29.96 22.43  2.555*10 1.597*10 2.271 *10 3.875*10  4  4  4  6  1.42 8.66 4.46 5.68 1.94 5.23 2.06 9.74  The values of the E i , koi, E , ko2, i.e. the kinetic parameters determined by each of the 22  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 R T 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 R T 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.  (5.31)  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.  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 C A N M E T 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' o  -1H  v  Experimental data with 2-Integral Fitting results with 2-lnt6gral Experimental data with 2-Coats-Redfern Fitting results with 2-Coats-Redfem  -124 >- -13-^  -144  -154 — i  0.0010  1 0.0012  1  1 i i > I • i • i • 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  o  A  -1  Experimental data with 2-Chen-Nuttall Fitting results with 2-Chen-Nuttall Experimental data with 2-Frtedman Fitting results with 2-Friedman  -2 ^ 6 ,  >- -3" -4-5-6-7-  0.0010  T  0.0012  0.0014  0.0016  0.0018  1 —r^—T 0.0020 0.0022  0.0024  1/T K"  1  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 o -11  v  Experimental data with 2-Integral Fitting results With 2-Integral Experimental data with 2-Coats-Redfem Fitting results with 2-Coats-Redfem  -12H -13  -14H -15'  -16-  1 ' 1 0.0012 0.0014  r  1 • 1 ' 1 0.0016 0.0018 0.0020  1/T IC  1-  1 0.0022  1  1 0.0024  1  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 , k o , and s.e.e. were computed using iterative techniques for a 2  2  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 First stage Second stage Run# °C/min. E i kJ/mol k o i min." E kJ/mol k o min.' s.e.e. 1  1  2  Can48 Can33 Can41 Can58  25 50 100 150  21.89 20.90 26.91 46.64  C A N M E T Pitch 5.534 71.34 7.649 64.47 39.63 72.11 552.3 96.65  Syn43 Syn29 Synl8 Syn8  25 50 100 150  30.82 37.57 44.16 46.14  Syncrude Pitch 51.80 67.66 298.2 76.57 1.326*10 65.51 2.549* 10 69.80 3  3  2  4.448* 10 2.444* 10 1.111*10 3.511*10*  1.42 2.12 1.44 0.97  2.554*10 1.964*10 3.523*10 1.031*10  1.94 2.07 2.97 2.85  4  4  5  4  5  4  5  114  Having obtained the values of E i , k o i , E , k o 2 , from this table, the volatile content and the 2  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 2stage 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 0.0010  1  1  1  1  1  0.0012  0.0014  1  1  1  0.0016  1  1  0.0018  1  0.0020  r 0.0022  0.0024  1/T rC  1  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  •  25 °C/min experimental results 25 °C/minfittingresults (2-lntegral) ® 50 °C/mln experimental results SO "C/min fitting results (2-)ntegral) K 100 °C/min experimental results 100 °C/minfittingresults (2-Integral) O 150 °C/min experimental results - 150 °C/minfittingresults (2-lntegral)  -9 -10-11 -  >-  -12 -13  4  -14. -15-16 —i 1 0.0010 0.0012  1  1  0.0014  1  1  1  0.0016  1  0.0018 -1  1  1  0.0020  1  1  0.0022  1  1  0.0024  1/T K"  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  0  •  1 5  •  1 10  >  1 15  t min  •  1 20  •  1 25  • r 30  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  110100-  • 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/mlnfittingresults (2-lntegraO 100 °C/mln fitting results (2-lntegral) ISO "C/minfittingresults (2-lntegrar)  9080706050403020100I 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  Can42 Can40 Can52  750 850 950  Syn27 Syn32 Syn33  750 850 950  V* Integral C-R C A N M E T Pitch at 100 °C/min 79.54 2.05 4.24 79.01 4.87 2.70 81.23 1.39 5.25 Syncrude Pitch at 50 °C/min 90.96 2.57 5.38 90.61 2.04 5.15 91.01 4.49 8.75  C-N  FM  1.95 4.09 2.28  4.60 3.12 4.94  2.63 2.01 5.26  9.07 8.64 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 200300400500600700800900  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, CoatsRedfern, 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 nonaromatic 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: \nk = a + 0 E 0  B)  (6.1)  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 preexponential 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 C A N M E T 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  lnk = -8.781 +0.4184E 0  Friedman method -•-Integral method  Chen-Nuttall method Coats-Redfern method  30.0  -•—i—• 30.5  1 31.0  •—I—i—|—i—i 31.5 320 325  •—I—i—| 33.0 33.5  •—| 34.0  1  1 34.5  1-  . 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 andfinaltemperature 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 and p , are listed in Tables 6.1 and 6.2 for C A N M E T 2  2  and Syncrude pitch. The square of the regression coefficients, R , are also listed in these tables 2  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 Second stage First stage 4 R Method PinO" P^IO" ct CCi 0.008 1.558 0.952 1.711 -1.544 Integral -0.406 1.586 0.959 1.930 -2.824 Coats-Redfern 1.566 -0.087 0.956 1.826 -2.128 Chen-Nuttall -1.169 1.693 0.984 1.980 -2.444 Friedman 1.650 -0.789 0.957 1.903 -2.360 All methods 2  4  2  R 0.978 0.980 0.979 0.999 0.991 2  Table 6.2 Compensation Parameters for Syncrude Pitch Pyrolysis at Different Heatin g Rates and 800 °C Second stage First stage Method Integral Coats-Redfern Chen-Nuttall Friedman All methods  <Xi  Pi*™"  -3.718 -4.367 -3.923 -4.361 -3.308  2.492 2.591 2.530 2.852 2.384  4  R  2  0.998 0.998 0.998 0.998 0.979  a -1.220 -1.554 -1.278 0.705 0.516 2  P^IO" 1.761 1.781 1.765 1.471 1.497  4  R  2  0.795 0.809 0.801 0.977 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 coefficient is greater than 0.95, whereas for Syncrude pitch the R is greater than 0.998 for 2  2  the first stage and greater than 0.795 for the second stage.  131  20  •  18  o ©  A A V  C  10  1 st stage Integral 2nd stage Integral 1st stage Coats-Redfern 2nd stage Coats-Redfern 1 st stage Chen-Nuttall 2nd stage Chen-Nuttall 1 st stage Friedman 2nd stage Friedman  'E  >•*  . J§r^  &'  1— —  i  20000  1  1  1  y  1  40000  j»  60000  1  i  80000  100000  120000  E J/mol 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  20 18161412-  c E  10  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  :i 4 2-j  I 40000  —  20000  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-  o •  1st stage reaction 2nd stags reaction  1614-  Ink =-0.7886 + 1.650*1 ( P E O  1210-  E  ±?  864lnk = -2.360 + 1.903*1 O^E  2-  0  0— i — i  0  \  |—r—T'"i  20000  i  |  i  40000  i  i  i—[—  1  —  1  — r ~ T —J — l " •  60000  I " I  80000  I  I  I  100000  I  1  "T  "1  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  2018-  O •  1st stage reaction 2nd stage reaction  161412•  c  Ink =0.5161 + 1.496*1 O^E  ^  O  /  108H 642-  lnk =-3.308 +2.384*1 O^E 0  080000  100000  120000  E J/mol Figure 6.6 Syncrude pitch T G A 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 coefficient is greater than 0.957 for all the cases 2  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 coefficient of the first stage of Syncrude pitch is the highest in all the cases studied. 2  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 of 0.986. When the pyrolysis experimental results were fitted with 2-stage model, 2  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 coefficient is smaller than that obtained from the 2  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 coefficient. Similarly the lower R coefficient derived 2  2  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- *K1  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-  20T  c  E  -2A  .  -8-10-  1/T 1000 - * K ' 1  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 C A N M E T 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' , E =86.6 kJ/mol, ko =7.31* 10 min' . 1  s  2  1  2  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*10 min' , E =67.6 kJ/mol, ko =4.19*10 min' . 3  1  4  2  1  2  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  • e  Rrststagie reaction Secondstags reaction  a  •\  V*  •  B  • ft^ 20000  40000  60000  80000  a 100000  12D000  E J/mol 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 Integral One set k o Heating s.e.e E, s.e.e Rate°C/min V*% Run# Can48 Can33 Can41 Can58 Syn43 Syn29 Synl8 Syn8  C A N M E T pitch at 800 °C 4.10 80.84 25 5.62 80.79 50 8.69 79.30 100 1.57 77.59 150 Syncrude Pitch at 800 °C 10.45 91.03 25 5.62 90.07 50 4.01 90.58 100 9.98 90.62 150  1.42 2.12 1.44 0.97 1.94 2.07 2.97 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  100  90 80 7060-  O  >  30-I 2o4 10 OH  •  25 CArin, cDfjuiutaU data  9  50°C/rrin, efxrirrerfe] data  •  103°C/mn operimerta! data  O  150°C/rrin, aperimerti data fitting resiits  0  I 10  15  -r— 20  25  30  t min  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  Run# Can42 Can40 Can52 Syn27 Syn32 Syn33  10090-  O  One set k o T °C V*% E , s.e.e. C A N M E T Pitch at 100 °C/min 750 79.54 8.13 850 79.01 4.34 950 81.23 8.93 Syncrude Pitch at 50 °C/min 750 90.96 5.40 850 90.61 5.94 950 91.01 5.97  750°C. Experimental dat 750°C. Model prediction  O  850°C, Experiment oldat )°C. Model prediction  O  Integral s.e.e 2.05 4.87 1.39 2.57 2.04 4.49  950°C. Experiment oldat 950°C, Model prediction  ooo  807060-  ^  50-  |  4030' 20'  10  0 I • I ' I I . 250 500 750 1000 0 250 500 750 1000 1  250 500 750 1000 0  T °C 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 0  1  I ' I • I 250  500  • I  750 1000  'l • 0  I ' I • I 250  500  ' I  750 1000  1 ' I  1  0  1  250  I ' I 500  1  750  I 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 C n , 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 C n , C12 and C i . C14 is the heaviest group of compounds detected in the Pyroprobe-GC pyrolysis, 3  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 preexponential 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 R E C O M M E N D A T I O N S The following recommendations are offered for further work and future application: 1. To achieve more detailed G C 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 G C 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. The use of a pilot-scale pyrolyzer is needed to explore the applicability of the 2-stage mechanism and the related 2-stage first order integral method.  150  The application of the kinetic parameters of pitch pyrolysis should be concerned with the methods used to derived these values and the accuracy of the model predictions. The kinetic parameters k„ and E should be compared with and used as a pair. The magnitude of one of these parameters may not be adequate to describe the characteristics of a pitch pyrolysis process.  151  REFERENCES 1.  Solomon, P. and G . Hamblen, 'Pyrolysis", in 'Chemistry of Coal Conversion", Richard H . Schlosberg, Eds., Plenum Press, New York and London (1985), pp. 122.  2.  Solomon, P. and G. Hamblen, 'Pyrolysis", in 'Chemistry of Coal Conversion", Richard H . Schlosberg, Eds., Plenum Press, New York and London (1985), pp. 121.  3.  Solomon, P. and G. Hamblen, 'Pyrolysis", in 'Chemistry of Coal Conversion", Richard H . Schlosberg, Eds., Plenum Press, New York and London (1985), pp. 127.  4.  Howard, J. B . , 'Chemistry of Coal Utilization", Secondary Supplementary Volume, M . A . Elliott, Eds., Wiley Press, New York (1981), pp. 625-784.  5.  Serio, M . A . , W. A . Peters and J. B. Howard, 'Kinetics of Vapor Phase Secondary Reactions of Prompt Coal Pyrolysis Tars", Ind. Eng. Chem. Res. 26, 1831-1838 (1987).  6.  Hebden, D. and Henry J. F. Strout, 'Chemistry of Coal Utilization", Secondary Supplementary Volume, M . A . Elliott, Eds., Wiley Press, New York (1981), pp. 15991800.  7.  Maa, P. S., Ken L . Trachete and Richard D. Williams, 'Solvent Effects in Exxon DonorSolvent Coal Liquefaction", in 'Chemistry of Coal Conversion", Richard H . Schlosberg, Eds., Plenum Press, New York and London (1985), pp. 317-330.  8.  Furimsky, E . , 'Pyrolysis of Virgin Pitch and Thermally Hydrocracked Pitch Derived from Athabasca Bitumen", Ind. Eng. Chem. Prod. Res. Dev. 22, 637-642 (1983).  9.  Howard, J. B., 'Chemistry of Coal Utilization", Secondary Supplementary Volume, M . A. Elliott, Eds., Wiley Press, New York (1981), pp. 669.  10.  Legros, R, J. R. Grace, C. M . H . and C. J. Lim, 'Circulating Fluidized Bed Combustion of Pitches", Research Report, Department of Chemical Engineering, U B C (1990).  11.  Watkinson, A. P., Personal File, (1992).  12.  Menzies, M . A . , A. E . Siliva and J. M . Denis, 'Hydrocracking without Catalysis Upgrades Heavy Oil", Chem. Eng. 88(4) 46-47 (1981).  13.  Pruden, B. B., 'Hydrocracking of Bitumen and Heavy Oils at CANMET", Can. J. Chem. Eng. 56, 277-280 (1978).  14.  Pruden, B. B., 'Upgrading of Cold Lake Heavy Oil in the C A N M E T Hydrocracking Demonstration Plant", The Fourth Unitar/UNDP International Conference on Heavy Crude and Tar Sands", Proceedings volume 5, Extraction, Upgrading, Transportation, August 712, Edmonton, Alberta, Canada (1988) pp. 249-254.  152  15.  Reich, A . , W. Bishop and M . Veljkovic, 'LC-Finer Commercial Experience and Hydroprocessing Future Direction", Oil Sands:Our Petroleum Future Conference April 4-7, Edmonton, Alberta, Canada (1993)  16.  Lowry, H . H . , Eds., 'The Chemistry of Coal Utilization", Supplementary Volume, John Wiley and Sons, Inc., New York (1963).  17.  Van Krevelen, D. W., "Coal", Elsevier, Amsterdam (1981), pp. 514-516.  18.  Komatsu, N and T. Nishizawa, 'Ext. Abstracts 17th Biennial Conference on Carbon", Lexington, Kentucky, 16-21 June 1985 pp. 342-343.  19.  Mazza, A . G . , 'Modeling of the Liquid Phase Thermal Cracking Kinetics of Athabasca Bitumen and Its Major Chemical Fractions", Ph.D. Thesis, Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Canada (1987).  20.  Reynolds, J. G., 'Effect of Prehydrogenation on Hydroconversion of Maya Residuum, Part HI: Predicting Residuum Processibility by the SARA Separation Method". AIChE Symp. Ser. 87, 62-71 (1991).  21.  Sanford, E . , 'Molecular Approach to Understanding Residuum Conversion", Ind. Eng. Chem. Res. 33, 109-117 (1994).  22.  Fitzer, E . , K . Mueller and W. Schaefer, 'Conversion of Organic Compounds to Carbon", in "Chemistry and Physics of Carbon" 7, 238-283 (1971).  23.  Mazza, A. G. and Donald E . Cormack, 'Thermal Cracking of the Major Chemical Fractions of Athabasca Bitumen", A O S T R A J. Res. 4, 193-208 (1988).  24.  Selucky, M . L . , S. S. Kim, K . Skinner and 0. P. Strausz, 'Structure-Related Properties of Athabasca Asphaltenes and Resins as Indicated by Chromatographic Separation", in 'The Chemistry of Asphaltenes", J. W. Bunger and N . L i , Eds., Am. Chem. Soc. Advances in Chemistry Series 195 (1981), pp. 83.  25.  Gould, K . A . , 'Influence of Thermal Processing  on the Properties of Cold Lake  Asphaltenes, 2. Effect of Steam Treatment During Oil Recovery",  Fuel 62, 370- 372  (1983). 26.  Speight, J. G., 'Thermal Cracking of Athabasca Bitumen, Athabasca Asphaltenes and Athabasca Deasphalted Heavy Oil", Fuel 49, 134-145 (1970).  27.  Mojelsky, T. W., and O. P. Strausz, 'Detection of Alkylated Fluorenes in Athabasca Oil Sand Bitumens", Organic Geochemistry 9, 39-45 (1986).  28.  Selucky, M . L . , Y . Chu, T. Ruo and O. P. Strausz, 'Chemical Composition of Athabasca Bitumen", Fuel 56, 369-381 (1977).  29.  Hayashitani, M . , Ph.D. Thesis, University of Calgary, Calgary, Alberta, Canada (1978). 153  30.  Anthony, D. B. and J. B. Howard, 'Coal Devolatilization and Hydrogasification" AIChE 22, 625-656 (1976).  31.  Smoot, L . D . , 'Pulverized Coal Diffusion Flames, A perspective through Modeling", 18th Symposium (international) on Combustion, The Combustion Institute (1981), pp. 11851202.  32.  Smoot, L . D. and D. T. Pratt, 'Pulverized Coal Combustion and Gasification", Plenum Press, New York (1979).  33.  Trimm, D . L . and C. J. Turner, 'The Pyrolysis of Propane. I. Production of Gases, Liquids and Carbon", J. Chem. Tech. Biotechnol. 31, 195-204 (1981).  34.  Sundaram, K . M . and G . F. Froment, 'Kinetics of Coke Deposition in Thermal Cracking of Propane", Chem. Eng. Sci. 34, 635-644 (1979).  35.  Kumar, P. and D. Kunzru, 'Modeling of Naphtha Pyrolysis", Ind. Eng. Chem. Process Des. Dev. 24, 774-782 (1985).  36.  Jamaluddin, A. S., T. F. Wall and J. S. Truelove, 'Modeling of Devolatilization and Combustion of Pulverized Coal under Rapid Heating Condition", in 'Coal Science and Chemistry", A. Volborth, Eds., Elsevier Science Publishers B. V . , Amsterdam (1987), pp. 61-106.  37.  Suuberg, E . M . , 'Mass Transfer Effects in Pyrolysis of Coals: A Review of Experimental Evidence and Models", in 'Chemistry of Coal Conversion", R. H . Schlosberg, Eds., Plenum Press (1985), pp. 67-117.  38.  Baum, M . M . and P. J. Street, 'Predicting the Combustion Behavior of Coal Particles", Combustion Science and Technology 3, 231-243 (1971).  39.  Lochwood, F. C , S. M . A. Rizvi, G. K. Lee and H . Whaley, 'Coal Combustion Model Validation Using Cylindrical Furnace Data", 20th Symposium (International) on Combustion, The Combustion Institute (1984), pp. 513-522.  40.  Badzioch, S. and P. G . W. Hawksley, 'Kinetics of Thermal Decomposition of Pulverized Coal Particles", Ind. Eng. Chem. Process Des. Dev. 9, 521-530 (1970).  41.  Kobayashi, H . , J. B. Howard and A. F. Sarofim, 'Coal Devolatilization  at High  Temperatures", 16th Symposium (international) on Combustion, The Combustion Institute (1977), pp. 411-425. 42.  Ubhayakar, S. K., D. B. Stickler, C. W. V. Rosenberg and R. E . Gannon, 'Rapid Devolatilization of Pulverized Coal in Hot Combustion Gases", 16th Symposium (International) on Combustion, The Combustion Institute (1977), pp. 427-436.  154  43.  Wen, C. Y . and S. Dutta, 'Rates of Coal Pyrolysis and Gasification Reactions", in 'Coal Conversion Technology", C. Y . Wen and E . S. Lee, Eds., Addison Wesley Publishing Co., New York (1979).  44.  Niksa, S., H . E . Heyd, W. B . Russel and D. A . Saville, 'On the Role of Heating Rate and Rapid Coal Devolatilization", 20th Symposium (International) on Combustion, The Combustion Institute (1984), pp. 1445-1453.  45.  Juntgen, H . and K. H . Van Heek, 'Gas Release from Coal as a Function of the Rate of Heating", Fuel 47, pp. 103-117 (1968).  46.  Juntgen, H . and K . H . van Heek, "An Update of German Non-Isothermal Coal Pyrolysis Work", Fuel Processing Technology 2, 261-293 (1979).  47.  Nsakala, N . Y . , R. H . Essenhigh and P. L . Walker Jr., 'Studies on Coal Reactivity: Kinetics of Lignite Pyrolysis in Nitrogen at 808 °C" Combustion Science and Technology 16, 153163 (1977).  48.  Pitt, G. J., 'The Kinetics of the Evolution of Volatile Products from Coal", Fuel 41, 267276 (1962).  49.  Anthony, D. B . , J, B . Howard, H . C. Hottel and H . P. Meissner, 'Rapid Devolatilization and Hydrogasification of Bituminous Coal", Fuel 55, 121-128 (1976).  50.  Anthony, D . B . and J. B. Howard, 'Coal Devolatilization and Hydrogasification", AIChE 22, 625-656(1976).  51.  Lakshmanan, C. C. and N . White, "A New Distribution Activation Energy Model Using Weibull Distribution for the Representation of Complex Kinetics", Energy & Fuels 8, 11581167 (1994).  52.  Miura, K . , "A New and Simple Method to Estimate rTE) and ko(E) in the Distributed Activation Energy Model from Three Sets of Experimental Data", Energy & Fuels 9, 302307 (1995).  53.  Antal, M . J., E . G . Plett, T. P. Chung and Summerfield, 'Recent Progress in Kinetic Models for Coal Pyrolysis", ACS Divn. of Fuel Chemistry Prprints 22, 137-148 (1977).  54.  Reidelbach, H . and M . Summerfield, 'Kinetic Model for Coal Pyrolysis Optimization", ACS Divn. of Fuel Chemistry Preprints 20, 161-202 (1975).  55.  Antal, M . J., E . G. Plett, T. P. Chung and M . Summerfield, 'Recent Progress in Kinetic Models for Coal Pyrolysis", ACS Div. of Fuel Chemistry Preprints 22, 137-148 (1977).  56.  Suuberg, E . M . , W. M . Peters and J. B. Howard, 'Product Composition and Kinetics of Lignite Pyrolysis", Ind. Eng. Chem. Process Des. Dev. 17, 37 (1978).  155  57.  Suuberg, E . M . , 'Rapid Pyrolysis and Hydropyrolysis of Coal", Sc.D. Thesis, Department of Chemical Engineering, MIT, Cambridge, Mass (1977).  58.  Suuberg, E . M . , W. A . Peters and J. B. Howard, 'Product Compositions and Formation Kinetics in Rapid Pyrolysis of Pulverized Coal Implications for Combustion", Symposium (International) on Combustion, The Combustion Institute (1979), pp. 117-130.  59.  Hajaligol, M . , J. B . Howard and W. A . Peters, 'Product Composition and Kinetics for Rapid Pyrolysis of Cellulose", I&EC Process Des. Dev. 21, 457- 567 (1982).  60.  Kizler, F. J. and A . Broidio, 'Speculation on the Nature of Cellulose Pyrolysis", Pyrodynamics 2, 151-162 (1965).  61.  Milosavljevic, I. and E . Suuberg, 'Cellulose Thermal Decomposition Kinetics: Global Mass Loss Kinetics", Ind. Eng. Chem. Res. 34, 1081-1091 (1995).  62.  Carrasco, F., 'The Evaluation of Kinetic Parameters from Thermogravimetric Data: Comparison between Established Methods and the General Analytical Equation", Thermochim Acta 213, 115-134 (1993).  63.  Pysiak, J. and B. J. Sabalski, 'Compensation Effect and Isokinetic Temperature in Thermal Dissociation Reactions of the Type A^iid <-> B iod + Cgas: Interpretation of the Arrhenius Equation as a Projection Correlation", J. Therm. Anal. 17, 287-303 (1979). s  64.  Constable, F. H . , 'The Mechanism of Catalytic Decomposition", Proc. Roy. Soc. London, Ser. A 108, 355-385 (1925).  65.  Muraishi, K . and H . Yokobayashi, 'Kinetic Compensation Effect for the Thermal Solid State Reactions of Lanthanide Oxalate, Malonate and Succinate Hydrates and their Anhydrides", Thermochim. Acta 209, 175-188 (1992).  66.  Galwey, A . K . , 'Compensation Effect in Heterogeneous Catalysis", Advance in Catalysis 26, 247-322 (1977).  67.  Koga, N . , "A Review of the Mutual Dependence of Arrhenius Parameters Evaluated by the Thermoanalytical Study of Solid Reactions: the Kinetic Compensation Effect", Thermochim Acta 244, 1-20 (1994).  68.  Krai, H , 'Thermal Deactivation of Heterogeneous Catalysts, Part 1. The Theta-Rule, A Critical Review", Chem. Eng. Technol. 11, 113-119 (1988).  69.  Krai, H , 'Thermal Deactivation of Heterogeneous Catalysts, Part 2. The Compensation Effect and the Catalytic Paradox", Chem. Eng. Technol. 11, 228-236 (1988).  70.  Lesnikovich, A. I. and S. Levchik, 'Isoparametric Kinetic Relations for Chemical Transformations in Condensed Substances (Analytical Survey). I. Theoretical Fundamentals ", J. Therm. Anal. 30, 237-262 (1985). 156  71.  Norwisz, J., Z. Smieszek and Z. Kolenda, "Apparent Linear Relationship, Compensation Law and Others: Part I", Thermochim Acta 156, 313-320 (1989).  72.  Zawadski, J. and S. Bretzsnajder, 'The Temperature Increament of the Reaction Velocity of Reactions of the Type A Solid - » B Solid + C Gas", Z. Elektrochem. 41, 215-223 (1935).  73.  Gallagher, P. K. and D. W. Johnson, 'The Effects of Sample Size and Heating Rate on the Kinetics of the Thermal Decomposition of CaC0 ", Thermochim. Acta 6, 67-83(1973). 3  74.  Pavlyuchenko, M . M . and E . A. Prodan, 'The Role of Chemical and Crystallization Processes in Reversible Topochemical Reactions", Doklady Akad. Nauk. S.S.S.R. 136, 651-653 (1961).  75.  Wist, A . O., in R. F. Schwenker, Jr. and P. D. Gam, Eds., 'Thermal Analysis (Proc. 2nd ICTA)", Academic Press, New York (1969), pp. 1095.  76.  Roginski, S. Z. and J. L . Chatji, Izv. Acad. Sci. USSR Ser. Khim (1961), pp. 771.  77.  Pysiak, J., 'Influence of Some Factors on Thermal Dissociation of Solids", Thermochim Acta 148, 165-171 (1989).  78.  Zsako, J. and H . E . Arz, 'Kinetic Analysis of the Thermogravimetric Data: VII Thermal Decomposition of Calcium Carbonate", J. Therm. Anal. 6, 651-656 (1974).  79.  Zsako, J., C. Varhelyi and G. Liptay, 'Kinetic Analysis of Thermogravimetric Data. XXVIII. Thermal Decomposition of Some Metal and Ammonium Salts of Hexabromoplatinic Acid", J. Therm. Anal. 38, 2301-2310 (1992).  80.  Muraishi. K . and H . Yokobayashi, 'Kinetic Compensation Effect for the Thermal Solid State Reactions of Lanthanide Oxalate, Malonate and Succinate Hydrates and Their Anhydrides", Thermochim. Acta 209, 175-188 (1992).  81.  Dollimore, D. and P. F. Rogers, 'The Appearance of a Compensation Effect in the Thermal Decomposition of Manganese (II) Carbonates, Prepared in the Presence of Other Metal Ions", Thermochim. Acta 30, 273-280 (1979).  82.  Bordas, S., M . T. Clavaguera-Mora and N . Clavaguera, 'Glass Formation and Crystallization Kinetics of Some Germanium-Antimony-Selenium Glasses", J. Non-Cryst. Solids 107, 232-237 (1990).  83.  MacCallum, J. R. and M . V . Munro, 'The Kinetic Compensation Effect for the Thermal Decomposition of Some Polymers", Thermochim. Acta 203, 457-463 (1992).  84.  Guarini, G. G. T., R. Spinicci, F. M . Carlini and D. Donati, 'Some Experimental Aspects of D S C Determination of Kinetic Parameters in Thermal Decomposition of Solids", J. Therm. Anal. 5, 307-314(1973).  157  85.  Simon, J., 'Some Considerations Regarding the Kinetics of Solid-State Reactions", J. Therm. Anal. 5, 271-284 (1973).  86.  Szekely, T., G. Varhegyi, F. Till, P. Szabo and E . Jakab, 'The Effects of Heat and Mass Transport on the Results of Thermal Decomposition Studies. Part 1. the Three Reactions of Calcium Oxalate Monohydrate", J. Anal. Appl. Pyrol. 11, 71-81 (1987).  87.  Tanaka, H . and N . Koga, 'Kinetics of Thermal Decomposition of M C 0 to M C O 3 (M=Ca, Sr and Ba)", J. Therm. Anal. 32, 1521-1529 (1987).  88.  Ninan, K. N . , 'Kinetics of Solid State Thermal Decomposition Reactions", J. Therm. Anal. 35, 1267-1278 (1989).  89.  Flynn, J., 'Thermal Analysis Kinetics: Problems, Pitfalls and How to Deal with Them", J. Therm. Anal. 34, 367-381 (1988).  90.  Czarnecki, J. P., N . Koga, V . Sestak and J. Sestak, 'Factors Affecting the Experimentally Resolved Shapes of T G Curves", J. Therm. Anal. 38, 575-582 (1992).  91.  Criado, J. M . and M . Gonzalez, 'The Method of Calculation on Kinetic Parameters as a Possible Cause of Apparent Compensation Effects", Thermochim. Acta 46, 201-207 (1981).  92.  Criado, J. M . , D. Dollimore and G. R. Heal, "A Critical Study of the Suitability of the Freeman and Carroll Method for the Kinetic Analysis of Reactions of Thermal Decomposition of Solids", Thermochim. Acta 54, 159-165 (1982).  93.  Criado, J. M . and A Ortega, 'Errors in the Determination of Activation Energies of SolidState Reactions by the Piloyan Method, as a Function of the Reaction Mechanism", J. Therm. Anal. 29, 1075-1082 (1984).  94.  Vyazovkin, S. V . and A. I. Lesnikovich, 'Errors in Determining Activation Energy Caused by the Wrong Choice of Process Model", Thermochim. Acta 165, 11-15 (1990).  95.  Somasekharan, K . M . and V. Kalpagam, 'Use of a Compensation Parameter in the Thermal Decomposition of Copolymers", Thermochim. Acta 107, 379-382 (1986).  96.  Arnold, M . , G. E . Veress, J. Paulik and F. Paulik, 'Problems of the Characterization of Thermoanalytical Process be Kinetic Parameters, Part T\ J. Therm. Anal. 17, 507-528 (1979).  97.  Hulett, J. R., "Deviations from the Arrhenius Equations", Q. Rev 18, 227-230 (1964).  98.  Sestak, J., 'Errors of Kinetics Data Obtained from Thermogravimetric Curves at Increasing Temperature", Talanta 13, 567-579 (1966).  99.  Zsako, J., "The Kinetic Compensation Effect", J. Therm. Anal. 9, 101-108 (1976).  2  4  158  100. Exner, O., "Determination of the Isokinetic Temperature", Nature 227, 366-367 (1970). 101. Agrawal, R. K . , 'Compensation Effect: a Fact or a Fiction" J. Therm. Anal. 35, 909-917 (1989). 102. Sestak, J. and Z. Chvoj, 'Thermodynamics and Thermochemistry of Kinetic (Real) Phase Diagram Involving Solids", J. Therm. Anal. 32, 1465-1650 (1987). 103. Zsako, J. and K. N . Somasekharan, 'Critical Remarks on "On the Compensation Effect"", J. Therm. Anal. 32, 1277-1281 (1987). 104. Garn, P. D., "Kinetic Parameters", J. Therm. Anal. 13, 581-593 (1978). 105. Tanaka, H . , N . Koga and J. Sestak, 'Thermoanalytical Kinetics for Solid State Reactions as Examplified by the Thermal Dehydration of Li S0 .H 0", Thermochim. Acta 203, 203-220 (1992). 2  4  2  106. Heck, R. H . , L . A . Rankel and F. T. DiGuiseppi, 'Conversion of Petroleum Resid from Maya Crude: Effects of H-donors, Hydrogen Pressure and Catalyst", Fuel Process Technology 30, 69-81 (1992). 107. Nguyen, Q. T., 'Kinetics of Gasification and Sulphur Capture of Oil Sand Cokes", Ph.D. Thesis, Department of Chemical Engineering, University of British Columbia, Canada, 1988 108. Shin, S. M . and H . Y: Sohn, 'Nonisothermal Determination of the Intrinsic Kinetics of Oil Generation from Oil Shale", Ind. Eng. Chem. Process. Des. Dev. 19, 426-431 (1980). 109. Guo, D., Eds., 'University Mathematics Handbook", Shandong Science and Technology Press, Jinan (1985), pp. 202. 110. Press, W. H . , S. A- Teukolsky, W. T. Vetterling and B. P. Flannery, 'Numerical Recipes in F O R T R A N , The Art of Scientific Computing " 2nd. Ed., Cambridge University Press (1992), pp. 678-683. 111. Thakur, D. S. and H . E . Eric Nuttall Jr., 'Kinetics of Pyrolysis of Moroccan Oil Shale by Thermogravimetry", Ind. Eng. Chem. Res. 26, 1351-1356 (1987). 112. Braun, R. L . and A. Rothman, 'Oil Shale Pyrolysis Kinetics and Mechanism of Oil Production", J. Fuel 54, 129-131 (1975). 113. Rajeshwar, K . , 'Kinetics of Thermal Decomposition of Green River Shale Kerogen by Nonisothermal Thermogravimetry", Thermochim. Acta 40, 253-263 (1981). 114. Haddadin, R. A. and F. A. Mizyet, 'Thermogravimetric Analysis Kinetics of Jordan Oil Shale", Ind. Eng. Chem. Process Des. Dev. 13, 332-336 (1974). 115. Haddadin, R. A. and K. M . Tawarah, ' D T A Derived Kinetics of Jordan Oil Shale", Fuel 59, 539-545 (1980). 159  116. Schucher, R., 'Thermogravemetric Determination of the Coking Kinetics of Arab Vacuum Residuum", Ind. Eng. Chem. Process. Des. Dev. 22, 615-619 (1983). 117. Campbell, J. H . , George H Koskinas and Norman D. Stout, 'Kinetics of Oil Generation from Colorado Oil Shale", Fuel 57, 372-376 (1978). 118. Herrell, A . Y . and C. Arnold, Jr., 'Preliminary Studies on the Recovery of Oil from Chattanooga Shale", Thermochim. Acta 17, 165-175 (1976). 119. Jacobs, P. W. M . and F. C. Tompkins, Chap. 7 in 'Chemistry of Solid State", W. E . Garner Eds., Butterworths, London (1995), pp. 184-211. 120. Coats, A . W. and J. P. Redfern, 'Kinetic Parameters from Thermogravimetric Data", Nature (London) 201, 68-69 (1964). 121. Caballero, J. A., R. Font, A . Marcilla and J. A. Conesa, 'New Kinetic Model for Thermal Decomposition of Heterogeneous Materials", Ind. Eng. Chem. Res. 34, 806-812 (1995). 122. Dahr, P. S., "A Comparative Study of Different Methods for the Analysis of T G A Curves " Computers and Chemistry 10, 293-297 (1986). 123. Natu, G. N . , S. B. Kulkarni and P. S. Dahr, 'Thermal Studies on Tris-Chelate Complex of Nickel", J. Therm. Anal. 23, 101-109 (1982). 124. Heck, R. H . and F. T. DiGuiseppi, 'Kinetic Effects in Resid Hydrocracking", Energy & Fuels 8, 557-560(1994). 125. Gray, M . R., et al., 'Role of Catalyst in Hydrocracking of Residues from Alberta Bitumens", Energy & Fuels 6, 478-485 (1992). 126. Stubington, J. F. and S. Aiman, 'Pyrolysis Kinetics of Bagasse at High Heating Rates", Energy & Fuels 8, 194-203 (1994). 127. Lau, C. W. and S. Niksa, 'Impact of Soot on the Combustion Characteristics of Coal Particles of Various Types", Combust. Flame 95, 1-21 (1993) 128. Audouin, L . and J. Verdu, 'Comments on the Electrotechnical Ageing Compensation Effect", Polymer Degradation and Stability 31, 335-346 (1991). 129. Budrugeac, P. and E . Segal, 'The Ageing Compensation Effect on the Thermal Degradation of Some Electrical Insulators", Thermochim. Acta 202, 121-131 (1992). 130. Budrugeac, P. and E . Segal, 'On the Kinetics of the Thermal Degradation of Polymers with Compensation Effect and the Dependence of Activation Energy on the Degree of Conversion", Polymer Degradation and Stability 46, 203-210 (1994).  160  131. Gam, P. D., "An Examination of the Kinetic Compensation Effect", J. Therm. Anal. 7, 475-  478 (1975). 132. Garn, P. D., 'Kinetics of Decomposition of the Solid State", Thermochim. Acta 135, 71-77  (1988). 133. Garn, P. D . , 'Kinetics of Thermal Decomposition of the Solid State, n. Delimiting the Homogeneous-Reaction Model", Thermochim. Acta 160, 135-145 (1990). 134. 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] Method  Author  i-(i-/r  id  (l-n)7*2i(-ir»-!  Analytical solution id  i-i  In  = lnl  l-n  _,/^U> \PE) RT'  RT i-i  =ld  E  i  1  -RT'  n  =  1  (2.9b)  E/RT  m  RT van Krevelen etal. (1951)  '  100%  AR \BEj  X* [ 0.368  (2.9a)  v  -+1  (2.10a)  \nT:n*l  RT„  J  l n [ - l n ( l - / ) ] = ln  4:  E/RT  m  0368  108%  RT  (2.10b)  -+1 ln7/;n=l  J  U*R\  Id  1  ——; n*l  (2.11a)  R T'  Kissinger (1957)  Id  E  E  y 2  1  1  1  1  i  80% (2.11b)  163  Table A.1 (Continued)  id Horowitz and Metzger (1963)  (2.12a)  0 ;n±l  RT:  l-n  (2.12b)  ln[-ln(l-/)] = — 9 , n = \  RT? T  116%  where: 9=T-T, (T, is T at which f=(l-l/e) for n=l and T,=T for n*l m  A= Coats and Redfern (1965) (zero-order reaction)  , ex  iT  f  T  1-  A^ KBEj  r  / 2  (2.12c)  RT  RT;  Id  2RT  Id  liJ  Freeman and Carroll (1958)  (2.13a)  E . vBEj  94%  -^j;(when  Id  dT  = id  RT«E)  £1  RT  (1-/)' Multiple linear regression  E_\_ RT  (2.13b)  Table A.2 Summary of Differential Methods [62] Method  Author  Classical  BE  l  A  <dT)  Aln(l-/)  E  1  (2.14)  Close  (2.15)  Close  (2.16)  90% to 110%  i?Aln(l-/)  2 / Y  Vachusca and Voboril (1971)  E  VdT)  (2.17)  110%  dT)  164  Table A.3 Summary of Special Methods [62] Method  Author  Rlii Reich (1964)  E=  P , P 2 W j__J_  (2.18)  82%  T  r  Ti and T are measured at the same conversion value 1 2 of two different heating rate runs. 2  J  (dfldT)  K  In Friedman (1969)  dfjdT  T (T -T)(df/dT) m  m  f  (2.19a)  -Id  T(l-f ) EjTl(dfldT) m  m  R  l-/ df dTJ  (2.19b)  m  E  m  (2.19c)  A= 2  w*l  1  Id Reich and Stivala (1978)  107%  .V ln(l-/.)fy Id ln(l-/ )UJJ~*  (2.20a)  (2.20b)  a  2  W*I  (2.20c)  98%  where InK is the intercept of the line:  Id  i-(i-/r  E=  f  TT  R-^r\H  *0j  (2.20d)  Y  AT,Ax P  *0i  AT=T -T I  Popescu and Segal (1983)  i  vs — T  (2.21a)  2  (2.21b)  0  T and Ti are characteristic temperatures 0  ,  Eh-C  80% (2.21c)  PE \RT )  R(ATY  (2.21d)  EX  0  165  APPENDIX B G C Computer Station Method Parameters  ************************************************************** V a r i a n GC S t a r W o r k s t a t i o n - Method L i s t i n g Thu Jan 05 17:15:06 1995 Method: C:\STAR\PHILIP\PHILIPC.MTH *****************************************************************************  *********************************  ADC Board ********************************* Module A d d r e s s :  16  65.00 minutes Yes PID FID 10 VOLTS 10 VOLTS  End Time Autozero a t S t a r t Channel A Name Channel B Name Channel A F u l l S c a l e Channel A F u l l S c a l e GC  3600  Module Address : 17 GC I n j e c t o r A I n j e c t o r Type I n i t i a l GC I n j e c t o r Temperature I n i t i a l GC I n j e c t o r H o l d Time GC I n j e c t o r Oven On?  Isothermal 220 degree C 0.00 minutes Yes  GC I n j e c t o r B I n j e c t o r Type I n i t i a l GC I n j e c t o r Temperature I n i t i a l GC I n j e c t o r Hold Time GC I n j e c t o r Oven On?  Isothermal 220 degree C 0.00 minutes Yes  C o o l a n t To I n j e c t o r V a l u e On? C o o l a n t Timeout  : No : INFINITE  GC A u x i l i a r y I n j e c t o r 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 H o l d 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  C o o l a n t To I n j e c t o r V a l u e On? C o o l a n t Timeout GC Column Program 1 F i n a l Temperature Rate H o l d Time GC Column A Parameters Installed? Length Diameter C a r r i e r Gas GC Column B Parameters Installed?  : No : INFINITE 120 degree C 2.0 degrees C/minute 15.00 minutes Yes 30 meters 255 microns Helium Yes  166  30 meters 255 microns Helium  Length Diameter C a r r i e r Gas GC D e t e c t o r Heater A D e t e c t o r Heater On? D e t e c t o r Temperature  : Yes : 300 degrees C  GC D e t e c t o r Heater B D e t e c t o r Heater On? D e t e c t o r Temperature  : Yes : 250 degrees C  GC D e t e c t o r A D e t e c t o r Type D e t e c t o r On? Attenuation D e t e c t o r Range A u t o z e r o a t GC Ready?  PID Yes 1 12 Yes  GC D e t e c t o r B D e t e c t o r Type D e t e c t o r On? Attenuation D e t e c t o r Range A u t o z e r o a t GC Ready?  FID Yes 1 12 Yes  Autosampler Autosampler Type GC R e l a y s R e l a y Time Program GC S t r i p c h a r t S t r i p c h a r t On?  ***********************  :  Not used  :  Do Not Use  : No *********  ADC Board *********************** Module Address : 16 I n t e g r a t i o n Parameters Run Mode Multiplier Divisor Amount S t a n d a r d U n i d e n t i f i e d Peak F a c t o r Measurement Calculation Report U n i d e n t i f i e d Peaks S u b t r a c t Blank B a s e l i n e Peak R e j e c t i o n V a l u e S/N R a t i o Tangent H e i g h t % I n i t i a l Peak Width Response f a c t o r T o l e r a n c e Minimum Reference Window P e r c e n t Reference Window Minimum NbnReference Window P e r c e n t NonReference Window U n r e t a i n e d Peak Time  Analysis 1.000000 1.000000 1.000000 0.000000 Peak A r e a E x t e r n a l Standard NO Yes 0 Counts 5 5% 2 sec Update A l l Response F a c t o r s 0.10 minutes 2.0% 0.10 minutes 2.0% 0.000 minutes  167  Peak T a b l e Name C7 CIO Cll C12 C13 C14  Time 2.370 12.350 21.569 27.979 34.059 40.075  Factor 0.0028412 0.0094076 0.0098415 0.0134153 0.0128364 0.0209216  Ref. N N N N N N  Amount 0.5700000 0.6083000 0.6175000 0.6258000 0.6308000 0.6357000  TimeEvents T a b l e 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  Report Format Title S t a r t R e t e n t i o n Time End R e t e n t i o n Time I n i t i a l Attenuation I n i t i a l Zero O f f s e t Length i n Pages I n i t i a l Chart Speed Minutes p e r T i c k Autoscale Time Events Chromatogram Events R e t e n t i o n Times Peak Names Baseline Units Number o f Decimal D i g i t s Run Log E r r o r Log Notes ASCII F i l e Convert P r i n t Chromatogram P r i n t Results Copies  Standard Sample GC A n a l y s i s 0.00 minutes 65.00 minutes 32 0 1 O f f cm/min 1.0 On Off Off On On Off mg 4 Off On Off Off On On 1  Sample I n f o r m a t i o n D e t e c t o r Bunch M o n i t o r Length Data F i l e Name Channel  8 points 64 p o i n t s stan FID 10 VOLTS  Blank B a s e l i n e B a s e l i n e Compression F a c t o r Baseline Points B a s e l i n e Bunch S i z e B a s e l i n e Frequency  : 128 : 152 : 8 : 40.00  until until until until until until until  Std. N N N N N N  RRT N N N N N N  4.73 15.86 23.97 31.72 36.01 42.66 60.00  Hz  168  A P P E N D I X 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 C A N M E T 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= cu  90 80 70 H  —o— 3 term E (Equation 5.6) (  - -o - 4 term E,- (Equation 5.6) --A-- 5 term E (Equation 5.6) (  6 term E (Equation 5.6) s  - O — 7 term E,- (Equation 5.6)  60 H  — i — 8 term Ej (Equation 5.6)  50'  —•— Integration (Equation 5.5)  40' 30 H 20-  u ro o —I—  100  200  —I—  300  400  • 500  600  I  700  800  T °C  Figure C l Comparison of V evaluated for Equation 5.5 and Equation 5.6  169  APPENDIX D F O R T R A N Programs and Calculation Results for T G A Experimental Results Modeling Single Overall First Order Reaction Model Fitting Program C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C  M N LI L2 M1L1 R VO C  NO OF EXPERIMENTAL DATA POINTS NO OF COEFFICIENTS FOR LINEAR REGRESSION NO OF DATA POINTS OMITTED AT THE BEGINNING OF DV/DT NO OF DATA POINTS OMITTED AT THE END OF DV/DT NO OF DATA POINTS OMITTED AT THE END OF DV/DT AFTER L I GAS CONSTANT MAX VOLATILE AT CERTAIN HEATING RATE AND FINAL TEMPERATURE HEATING RATE  FOLLOWING ARRAYS WITH 1 ARE THOSE WITH SOME END POINTS OMITTED FROM EXPERIMENTAL DATA FOR DIFFERENT MODEL V, V I T X, XI VD  ARRAY ARRAY ARRAY ARRAY  OF OF OF OF  INTEGRAL METHOD Y, Y l ARRAY YFIT, YFIT1 ARRAY A ARRAY VFIT, VFIT1 ARRAY FRIEDMAN METHOD XD ARRAY OF YD. ARRAY OF YDD ARRAY OF YDDF ARRAY OF AD ARRAY OF VDD ARRAY OF  EXPERIMENTAL VOLATILE CONTENTS TEMPERATURE IN C 1/T IN 1/K EXPERIMENTAL DV/DT OF OF OF OF  EXPERIMENTAL DATA FITTED Y FITTED COEFFICIENTS FITTED VOLATILE CONTENTS V  X WITH END POINTS OMITTED EXPERIMENTAL DATA YD WITH END POINTS OMITTED FITTED YDD FITTED COEFFICIENTS FITTED VOLATILE CONTENTS V  COATS-REDFERN METHOD YCR, YCR1 ARRAY OF ACR ARRAY OF YCRF,YCRF1 ARRAY OF VCR, VCR1 ARRAY OF  EXPERIMENTAL DATA FITTED COEFFICIENTS FITTED YCR FITTED VOLATILE CONTENTS V  CHEN-NUTTALL METHOD YCN, YCN1 ARRAY OF EXPERIMENTAL DATA ACN ARRAY OF FITTED COEFFICIENTS YCNF, YCNF1 ARRAY OF FITTED YCN VCN, VCN1 ARRAY OF FITTED VOLATILE CONTENTS V  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 C  INTERGRAL METHOD 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.D01 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 C  FRIEDMAN METHOD 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.D01 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 C  COATS AND REDFERN METHOD 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.D01 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 VCR1(I)=VO*(1.DO-EXP(-RCR1*R*T(I)*T(I)*EXP(-ECR1/(R*T(I))) 1 *(l.D0-2.D0*R*T(I)/ECR1)/(C*ECR1) )) 136 CONTINUE C C C  C H E N - N U T T A L METHOD  140  ECN=E EOLD=ECN DO 150 1=1,M YCN (I) =DLOG ( - C * (ECN+2 . D 0 * R * T (I)  ) * D L O G ( 1 . D O - V ( I ) / V O ) / (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) VCN(I)=VO*(1.D0-EXP(-RCN*R*T(I)*T(I)*EXP(-ECN/(R*T(I)))*(1.D01 2.D0*R*T(I)/ECN)/(C*ECN))) 160 CONTINUE ECN1=E1 162 EOLD=ECNl DO 164 I=1+MM,M YCN1(I-MM)=DLOG(-C*(ECN1+2.D0*R*T(I))*DLOG(1.D0-V ( I ) / V O ) / ( T ( I ) * 1 T(I)*R)) 164 CONTINUE C A L L FLSQP ( X I , Y C N 1 , M l , N , A C N , VAR) ECN1=-R*ACN(2) IF(DABS(ECN1-EOLD).GE.0.1D-4) GOTO 162 RCN1=EXP(ACN(1) ) DO 166 1 = 1 , M l YCNF1(I)=ACN(1)+ACN(2)*X1(I) 166 CONTINUE DO 168 1=1,M VCNl(I)=VO*(l.D0-EXP(-RCNl*R*T(I)*T(I)*EXP(-ECNl/(R*T(I)))* 1 (l.D0-2.D0*R*T(I)/ECNl)/(C+ECN1))) 168 CONTINUE  C WRITE(3,200) 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 8X,'VD') 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 FORMAT(F7.2,6F10.6) 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 7X,'YCNF') 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 FORMAT(F10.5,6F11.6) 250 CONTINUE WRITE(3,260) 260 FORMAT(1OX,'X',13X,'YDD',11X,'YDDF') DO 280 I = M L , 1 , - 1 WRITE(3,270) XD(I),YDD(I),YDDF(I) 270 FORMAT(3F15.8) 280 CONTINUE 200  1  1  290  WRITE(3,290) FORMAT(35X,'A',14X,'E'),  173  WRITE(3,300) R A , E FORMAT('INTEGRAL M E T H O D ' , 1 0 X , 2 D 1 5 . 3 ) WRITE(3,310) RAD,ED 310 FORMAT('FRIEDMAN M E T H O D ' , 1 0 X , 2 D 1 5 . 3 ) WRITE(3,320) RCR,ECR 320 F O R M A T ( ' C O A T S - R E D F E R N M E T H O D ' , 5 X , 2 D 1 5 . 3 ) WRITE(3,330) RCN,ECN 330 F O R M A T ( ' C H E N - N U T T A L L M E T H O D ' , 6 X , 2 D 1 5 . 3 ) 300  WRITE(3>340) F O R M A T ( / / ' A N A L Y S I S WITHOUT T H E ABNORMAL END DATA P O I N T S ' ) 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 = M 1 , 1 , - 1 WRITE(3,240) X1(I),Y1(I),YFIT1(I),YCR1(I),YCRF1(I),YCN1(I), 1 YCNFl(I) 360 CONTINUE W R I T E ( 3 , 260) DO 370 I = M L 1 , 1 , - 1 WRITE(3,270) XD1(I),YDD1(I),YDDF1(I) 370 CONTINUE WRITE(3,290) WRITE(3,300) RA1,E1 WRITE(3,310) RAD1,EDI WRITE(3,320) RCR1,ECR1 W R I T E ( 3 , 330) R C N 1 , E C N 1  340  E N D F I L E ( U N I T = 3) CLOSE(UNIT =3) STOP END SUBROUTINE G A U S S ( A , N , N D R , N D C , X , R N O R M , I R E E O R ) 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  10 20  30  DO 20 1 = 1 , N DO 10 J = 1 , N P B (I, J) = A ( I , J) CONTINUE CONTINUE DO 70 K=1,NM KP=K+1 BIG=ABS(B(K,K)) IPIVOT=K DO 30 I = K P , N AB=ABS (B ( I , K) ) I F ( A B . G T . B I G ) THEN BIG=AB IPIVOT=I ENDIF CONTINUE I F ( I P I V O T . N E . K ) THEN DO 40 J = K , N P 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 = K P , N Q U O T = B ( I , K ) / B ( K , K) B(I,K)=0.D0 DO 50 J = K P , N P B ( I , J ) = B ( I , J ) - Q U O T * B ( K , J) 50 CONTINUE 60 CONTINUE 70 CONTINUE IF(B(N,N).EQ.0.D0) THEN IERROR=2 RETURN ENDIF X(N)=B(N,NP)/B(N,N) DO 90 I = N M , 1 , - 1 SUM=0.DO 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 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 ( 1 1 ) , C O E F F ( 1 0 , 11) ,SUMU(18)  10  20  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 ) ) 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 CONTINUE  30  40  50  60 70  80 90  100  110  120 130  10  DO 30 L=1,NM2 SUMU(L)=0.D0 CONTINUE DO 40 1=1,N COEFF(I,NP)=0.D0 CONTINUE DO 70 K=1,M TERMU=U(K) DO 50 L=1,NM2 SUMU(L)=SUMU(L)+TERMU TERMU=TERMU*U(K) CONTINUE TERMV=V(K) DO 60 1=1,N COEFF(I,NP)=COEFF(I,NP)+TERMV TERMV=TERMV*U(K) CONTINUE 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(1+J-2) ENDIF CONTINUE 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 SUM=SUM+NOMIAL(IM,J-l)*(-XP/XM)**(J-I)*B(J) CONTINUE ENDIF A ( I ) = Y M * ( 2 . D 0 / X M ) * * I M * S U M / 2 . DO 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 CONTINUE SSUM=SSUM+(Y(K)-SUM)**2 CONTINUE YAR=SSUM/(M-N) RETURN END FUNCTION N O M I A L ( I , J ) NOMIAL=l IF(J.LE.I.OR.I.EQ.O) RETURN DO 10 I C O U N T = l , I NOMIAL=NOMIAL*(J-ICOUNT+1)/ICOUNT CONTINUE RETURN END  Fitting Results for Run#61 with Single Overall First Order Reaction Models T 2 7 3 . 16 0. 3 2 3 . 01 0. 0. 3 9 7 . 66 0. 4 1 6 . 31 4 4 9 . 51 1. 4 7 4 . 36 3. 4. 4 9 9 . 26 6. 5 2 4 . 16 8. 5 4 8 . 16 5 7 1 . 81 1 1 . 5 9 8 . 81 1 4 . 6 2 1 . 61 1 7 . 6 4 8 . 56 2 1 . 6 7 5 . 51 2 6 . 6 9 8 . 31 3 1 . 7 1 0 . 76 3 4 . 7 2 5 . 26 3 8 . 7 3 9 . 76 4 4 . 7 5 0 . 16 4 9 . 7 5 8 . 46 5 3 . 7 6 8 . 81 5 9 . 7 7 7 . 11 6 4 . 7 8 5 . 41 6 9 . 7 9 7 . 86 7 4 . 8 1 0 . 26 7 7 . 8 2 2 . 71 7 8 . 8 4 9 . 66 8 0 . 8 7 4 . 56 8 0 . 9 4 9 . 21 8 0 . 9 7 3 . 16 8 0 . X 0 . 00103 0 . 00105 0 . 00114 0 . 00118 0 . 00122 0 . 00123 0 . 00125 0 . 00127 0 . 00129 0 . 00130 0 . 00132 0 . 00133 0 . 00135 0 . 00138 0 . 00141 0 . 00143 0 . 00148 0 . 00154 0 . 00161 0 . 00167 0 . 00175 0 . 00182 0 . 00191 0 . 00200 0 . 00211 0 . 00222 0 . 00240 0 . 00251  VCR VCN VDD VFIT 0. 002148 0 . 002148 001835 0 . 002088 0. 023518 0 . 025587 023641 0 . 025793 0. 290610 0 . 344936 345736 0 . 361193 0. 476451 0 . 575114 0 . 606667 585664 1. 042352 1. 291552 348438 1. 378113 1. 747062 2 . 201061 335505 2 . 365809 3 . 559491 2 . 785390 831136 3 . 849982 4 . 245088 5 . 488858 980990 5 . 967688 8 . 000267 6 . 133121 8 . 732291 805194 8. 524594 1 1 . 187995 411952 1 2 . 245013 595572 1 7 . 272655 1 1 . 962289 1 5 . 756300 839938 2 2 . 346199 1 5 . 476020 2 0 . 384440 925783 2 9 . 196143 2 0 . 332535 2 6 . 678746 688713 3 6 . 712478 2 5 . 870783 3 3 . 669396 476911 4 3 . 311675 3 0 . 979525 3 9 . 903756 156937 4 6 . 905714 3 3 . 886906 4 3 . 346999 337141 5 1 . 007448 3 7 . 339291 4 7 . 326756 333893 5 4 . 953606 4 0 . 825516 5 1 . 215466 050742 5 7 . 653200 4 3 . 324175 5 3 . 915945 113169 5 9 . 713761 4 5 . 305721 5 6 . 002775 538995 6 2 . 152120 4 7 . 748745 5 8 . 505153 358755 6 3 . 993571 4 9 . 676613 6 0 . 422057 061108 6 5 . 727472 5 1 . 569099 6 2 . 251570 387621 6 8 . 118229 5 4 . 327247 6 4 . 819982 430956 7 0 . 242956 5 6 . 960587 6 7 . 156536 211498 7 2 . 118937 5 9 . 473007 6 9 . 272460 196155 7 5 . 337198 64. 396759 7 3 . 063267 041713 7 7 . 401913 68. 261742 7 5 . 662338 292291 8 0 . 117552 7 5 . 953570 7 9 . 566076 485864 8 0 . 384632 7 7 . 371350 8 0 . 041927 YCR YCRF YFIT Y 0. - 9 . 850486 - 1 0 . 057252 179704 - 9 . 481708 0. - 9 . 800649 - 1 0 . 153178 153117 - 9 . 584969 0. 464879 - 9 . 943113 - 1 0 . 043230 - 1 0 . 485878 0. 566304 - 1 0 . 076571 - 1 0 . 122604 - 1 0 . 609854 0. 778232 - 1 0 . 230119 - 1 0 . 311201 - 1 0 . 752494 0. 936654 - 1 0 . 304503 - 1 0 . 459026 - 1 0 . 821594 0. 132381 - 1 0 . 380896 - 1 0 . 644309 - 1 0 . 892559 -0. 3 6 1 9 6 3 - 1 0 . 460023 - 1 0 . 863514 - 1 0 . 966065 -0. 541413 - 1 0 . 514183 - 1 1 . 036105 - 1 1 . 016377 -0. 712212 - 1 0 . 569512 - 1 1 . 200091 - 1 1 . 067776 -0. 904251 - 1 0 . 640204 - 1 1 . 383700 - 1 1 . 133445 -0. 035355 - 1 0 . 698303 - 1 1 . 508095 - 1 1 . 187417 -0. 181704 - 1 0 . 772943 - 1 1 . 646099 - 1 1 . 256753 -1. 345282 - 1 0 . 880580 - 1 1 . 798158 - 1 1 . 356744 -1. 494671 - 1 0 . 992609 - 1 1 . 936160 - 1 1 . 460814 -1. 586662 - 1 1 . 092512 - 1 2 . 018476 - 1 1 . 553619 -1. 743532 - 1 1 . 285013 - 1 2 . 157867 - 1 1 . 732445 -1. 917910 - 1 1 . 530008 - 1 2 . 311971 - 1 1 . 960034 -1. 085959 - 1 1 . 796246 - 1 2 . 460149 - 1 2 . 207358 -1. 2 3 2 5 9 9 - 1 2 . 040200 - 1 2 . 590281 - 1 2 . 433980 -2. 426729 - 1 2 . 354252 - 1 2 . 765208 - 1 2 . 725721 -2. 632724 - 1 2 . 654757 - 1 2 . 954679 - 1 3 . 004877 -2. 839908 - 1 2 . 987432 - 1 3 . 145370 - 1 3 . 313918 -2. 132499 - 1 3 . 366387 - 1 3 . 421133 - 1 3 . 665951 -3. 477522 - 1 3 . 785127 - 1 3 . 749606 - 1 4 . 054942 -3. 968892 - 1 4 . 249277 - 1 4 . 224727 - 1 4 . 486117 -4. 914993 - 1 4 . 955857 - 1 5 . 149524 - 1 5 . 142499 -4. 283782 - 1 5 . 404530 - 1 5 . 506541 - 1 5 . 559297  V 390000 390000 390000 610000 780000 160000 810000 890000 990000 610000 820000 790000 770000 490000 200000 130000 870000 290000 160000 500000 620000 660000 340000 190000 140000 750000 010000 340000 640000 640000 -9. -9. -9. -9. -9. -9. -10. -10. -10. -10. -10. -11. -11. -11. -11. -11. -11. -11. -12. -12. -12. -12. -12. -13. -13. -13. -14. -15.  0. 0. 0. 0. 1. 2. 3. 5. 8. 12. 17. 22. 29. 37. 44. 48. 52. 56. 59. 61. 63. 65. 67. 69. 71. 73. 76. 78. 80. 80.  VD 0 . 000000 0 . 000000 0 . 011796 0 . 035241 0 . 055533 0 . 066265 0 . 083534 0 . 087500 0 . 110782 0 . 118889 0 . 130263 0. 147681 0 . 175139 0 . 206579 0. 235341 0 . 326897 0 . 373793 0 . 468269 0 . 522892 0 . 591304 0 . 607229 0 . 563855 0 . 389558 0. 237903 0 . 129317 0 . 046753 0 . 013253 0 . 004019 0 . 000000 0 . 000000 YCN YCNF 931758 0 . 694442 973291 0 . 594723 0 . 248866 704377 616063 0 . 119986 417698 - 0 . 028295 265328 - 0 . 100127 075499 - 0 . 173899 148292 - 0 . 250311 323952 - 0 . 302613 491018 - 0 . 356045 - 0 . 424311 678478 - 0 . 480417 805974 947876 - 0 . 552496 105396 - 0 . 656441 - 0 . 764627 248887 - 0 . 861103 335942 484068 - 1 . 047000 648598 - 1 . 283590 - 1 . 540695 807311 - 1 . 776279 946443 - 2 . 079558 132134 - 2 . 369754 331130 531581 - 2 . 691016 817570 - 3 . 056972 156376 - 3 . 461346 641916 - 3 . 909573 580806 - 4 . 591914 - 5 . 025195 945827  177  X 0. 00123417 0. 00125335 0. 00127322 0. 00128682 0. 00130071 0. 00131846 0. 00133305 0. 00135179 0. 00137882 0. 00140694 0. 00143203 0. 00148036 0. 00154188 0. 00160873 0. 00166998 0. 00174883 0. 00182428 0. 00190781 0. 00200296 0. 00210810 0. 00222464 0. 00240206 0. 00251471  0. 0. 0. 0. 0. 0. -0. -0. -0. -1. -1. -1. -1. -2. -2. -2. -2. -2. -2. -3. -3. -3. -4.  INTEGRAL METHOD FRIEDMAN METHOD COATS-REDFERN METHOD CHEN-NUTTALL METHOD  YDD 60807557 60895559 54271001 56647688 36674818 08485328 18634571 44043312 80468691 04618577 43585946 65717687 90582279 14174758 31340313 45237380 56023804 82504563 89923461 15234745 34667896 81617456 91334683  YDDF 0. 04009520 - 0 . 03490237 - 0 . 11258481 - 0 . 16575592 - 0 . 22007510 - 0 . 28947602 - 0 . 34651452 - 0 . 41979110 - 0 . 52546313 - 0 . 63544672 - 0 . 73352542 - 0 . 92251219 - 1 . 16303342 - 1 . 42441033 - 1 . 66390972 - 1 . 97222821 - 2 . 26724630 - 2 . 59384664 - 2 . 96588292 - 3 . 37697689 - 3 . 83265228 - 4 . 52633118 - 4 . 96681167 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 F O R T R A N Program with L - M Nonlinear Regression  c c  C  10  100  200  300 400  INTEGER N D A T A , M A , M F I T , N C A 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, YFIT(NDATA),T, 2 EO,S,Z COMMON / Z D A T A / T , E O , S , Z EXTERNAL M R Q M I N , M R Q C O F , G A U S S J , C O V S R T , F U N C S , F U N C O , F U N C 1 , 1 FUNC2,FUNC3,QROMB,TRAPZD,POLINT INTEGER L I S T A ( M A ) 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 / DATA FOR RUN 6 1 : C A N 6 1 . D A T X=T (C) + 2 7 3 . 1 6 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 , 1 499.26D0,524.16D0,548.16D0,571.81D0,598.81D0,621.61D0, 2 648.56D0,675.51D0,689.31D0,710.76D0,725.26D0,739.76D0, 3 750.16D0,758.46D0,768.81D0,777.11D0,785.41D0,797.86D0, 4 810.26D0,822.71D0,849.66D0,874.56D0,949.21D0,973.16D0/ DATA Y / 0 . 3 9 D 0 , 0 . 3 9 D 0 , 0 . 3 9 D 0 , 0 . 6 1 D 0 , 1 . 7 8 D 0 , 3 . 1 6 D 0 , 4 . 8 1 D 0 , 1 6.89D0, 8.99D0,11.61D0,14.82D0,17.79D0,21.77D0,26.49D0, 2 31.20D0,34.13D0,38.87D0,44.29D0,49.16D0,53.50D0,59.62D0, 3 64.66D0,69.34D0,74.19D0,77.14D0,78.75D0,80.01D0,80.34D0, 4 80.64D0,80.64D0/ OPEN(UNIT=3,FILE='SLM61.DAT',ACCESS='SEQUENTIAL', 1 STATUS='OLD') DO 10 1=1,NDATA X(I)=X(I)-273.16D0 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 FORMAT(5X,3F20.6) VSTAR=Y (NDATA) AF=A(1)-4.D0*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) YFIT(I)=VSTAR*(1.D0-YF/(2.506628D0*A(2))) CONTINUE DO 400 1=1,NDATA WRITE(3,300) X(I),Y(I),YFIT(I) FORMAT(5X,3F20.5) 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, A L P H A , N C A , C H I S Q , 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 L I S T A ( M A ) DOUBLE P R E C I S I O N X ( N D A T A ) , Y ( N D A T A ) , S I G ( N D A T A ) , A ( M A ) , ALAMDA, C H I S Q , * 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 I F (IHIT.EQ.O) THEN LISTA(KK)=J KK=KK+1 ELSE I F (IHIT.GT.l) THEN PAUSE 'Improper p e r m u t a t i o n i n LISTA* ENDIF 12 CONTINUE I F (KK.NE.(MA+1)) PAUSE 'Improper p e r m u t a t i o n 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  170  180 C C  DO 170 K = 1 , M F I T A L P H A ( J , K ) = C O V A R ( J , K) CONTINUE BETA(J)=DA(J) A ( L I S T A ( J ) )=ATRY(LISTA(J) ) CONTINUE ENDIF WRITE(*,*) CHISQ=',CHISQ,' OCHISQ= ,OCHISQ WRITE {*,*)• A GOTO 100 RETURN END I  11 12  13 14 15  16 17  1  SUBROUTINE MRQCOF (X, Y , S I G , NDATA, A , M A , L I S T A , M F I T , A L P H A , B E T A , N A L P , * 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 I S T A ( M F I T ) DOUBLE P R E C I S I O N X (NDATA) , Y (NDATA) , S I G (NDATA) , A L P H A ( N A L P , NALP) , * BETA(MA),DYDA(3),A(3),XI,DY,SIG2I,WT,CHISQ DO 12 J = 1 , M F I T DO 11 K = 1 , J ALPHA(J,K)=0.D0 CONTINUE BETA(J)=0.DO CONTINUE CHISQ=0.D0 DO 15 1=1,NDATA XI=X(I) C A L L F U N C S ( X I , A , Y M O D , D Y D A , 3) SIG2I=1.D0/(SIG(I)*SIG(I)) DY=Y(I)-YMOD DO 14 J = 1 , M F I T WT=DYDA(LISTA(J))*SIG2I DO 13 K = 1 , J ALPHA(J,K)=ALPHA(J,K)+WT* DYDA(LISTA(K)) CONTINUE BETA (J)=BETA(J)+DY*WT 'CONTINUE CHISQ=CHISQ+DY*DY* SIG21 CONTINUE DO 17 J = 2 , M F I T DO 16 K = l , J - l A L P H A ( K , J ) = A L P H A ( J , K) CONTINUE CONTINUE RETURN END  C  11  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 P R E C I S I O N 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 IPIV(J)=0 CONTINUE DO 22 1=1,N BIG=0.D0 DO 13 J = 1 , N IF(IPIV(J).NE.1)THEN DO 12 K=1,N I F ( I P I V ( K ) . E Q . 0 ) THEN  IF  12 13  14  15  16 17  18 19 21 22  23 24  (ABS(A(J,K)).GE.BIG)THEN BIG=ABS(A(J,K)) IROW=J ICOL=K ENDIF ELSE I F (IPIV(K).GT.l) THEN PAUSE ' S i n g u l a r m a t r i x ' ENDIF CONTINUE ENDIF CONTINUE IPIV(ICOL)=IPIV(ICOL)+l I F (IROW.NE.ICOL) THEN DO 14 L=1,N DUM=A(IROW,L) A(IROW,L)=A(ICOL,L) A(ICOL,L)=DUM CONTINUE DO 15 L=1,M DUM=B(IROW,L) B(IROW,L)=B(ICOL,L) B(ICOL,L)=DUM CONTINUE ENDIF INDXR(I)=IROW INDXC(I)=ICOL I F (A(ICOL,ICOL).EQ.O.DO) PAUSE ' S i n g u l a r m a t r i x . PIVINV=l./A(ICOL,ICOL) A(ICOL,ICOL)=1. DO 16 L=1,N A(ICOL,L)=A(ICOL,L)*PIVINV CONTINUE DO 17 L=1,M B(ICOL,L)=B(ICOL,L)*PIVINV 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 CONTINUE DO 19 L=1,M B(LL,L)=B(LL,L)-B(ICOL,L)*DUM CONTINUE ENDIF CONTINUE 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 CONTINUE ENDIF CONTINUE RETURN END SUBROUTINE COVSRT(COVAR,NCVM,MA,LISTA,MFIT) INTEGER NCVM,MA,LISTA,MFIT, I, J INTEGER LISTA(MFIT)  182  11 12  13 14  15  16  17 18  DOUBLE P R E C I S I O N COVAR(NCVM,NCVM),SWAP DO 12 J = 1 , M A - 1 DO 11 I = J + 1 , M A COVAR(I, J)=0.DO CONTINUE CONTINUE DO 14 I = 1 , M F I T - 1 DO 13 J = I + 1 , M F I T IF(LISTA(J).GT.LISTA(I)) THEN COVAR(LISTA(J),LISTA(I))=COVAR(I,J) ELSE COVAR ( L I S T A ( I ) , L I S T A ( J ) ) =COVAR ( I , J ) ENDIF CONTINUE CONTINUE SWAP=COVAR(l,1) DO 15 J = 1 , M A COVAR(1,J)=COVAR(J,J) COVAR(J,J)=0.DO CONTINUE COVAR(LISTA(l),LISTA(1))=SWAP DO 16 J = 2 , M F I T COVAR(LISTA(J),LISTA(J))=COVAR(l,J) CONTINUE DO 18 J = 2 , M A DO 17 1 = 1 , J - 1 COVAR(I,J)=COVAR(J,I) CONTINUE CONTINUE RETURN END SUBROUTINE F U N C S ( X X , A , Y , D Y D A , N A ) INTEGER N A , N A A DOUBLE P R E C I S I O N 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 , * Y1,Y2,Y3 EXTERNAL F U N C O , F U N C 1 , F U N C 2 , F U N C 3 , Q R O M B , P O L I N T , TRAPZD COMMON / Z D A T A / T , E O , S , Z NAA=NA VSTAR=80.64D0 R=8.314D0 B=50.0D0 AA=A(1)-4.D0*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=VSTAR*(1.DO-YY/(2.506628D0*S)) CALL QROMB(FUNC1,AA,BB, Y l ) DYDA(1)=Y1+DEXP(-Z*R*T**2/(B*(EO+4.D0*S))*DEXP(-(EO+4.D0*S)/(R*T) * )*(l.D0-2.D0*R*T/(EO+4.D0*S)))*DEXP(-8.DO)-DEXP(-Z*R*T**2 * /(B*(EO-4.D0*S))*DEXP(-(EO-4.D0*S)/(R*T))*(1.D0-2.D0*R*T/ * (EO-4.D0*S)))*DEXP(-8.D0) DYDA(1)=-DYDA(1)*VSTAR/(2.506628D0*S) CALL QROMB(FUNC2,AA,BB,Y2) DYDA(2)=Y2+4.D0*DEXP(-Z*R*T**2/(B*(EO+4.D0*S))*DEXP(-(EO+4.D0*S)/ * (R*T))*(l.D0-2.D0*R*T/(EO+4.D0*S)))*DEXP(-8.DO)+4.D0*DEXP * (-Z*R*T**2/(B*(EO-4.D0*S))*DEXP(-(EO-4.D0*S)/(R*T))*(1.D0 * -2.D0*R*T/(EO-4.D0*S)))*DEXP(-8.D0) DYDA(2)=-VSTAR*(YY/S-DYDA(2))/(2.506628D0*S)  183  CALL QROMB(FUNC3, AA,BB, Y3) DYDA(3)=-Y3*VSTAR/(2.506628D0*S) RETURN END  11  11  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) I F (J.GE.K) THEN L=J-KM CALL POLINT(H(L),S(L),K,0.DO,SS,DSS) I F (DABS(DSS).LT.EPS*DABS(SS)) RETURN ENDIF S(J+1)=S(J) H(J+1)=0.25D0*H(J) CONTINUE PAUSE 'Too many s t e p s . ' END SUBROUTINE TRAPZD(FUNC,A,B, S,N) INTEGER N,IT,J DOUBLE PRECISION A, B,S,DEL,TNM,SUM,X I F (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 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)) I F (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 IF(DEN.EQ.0.DO)PAUSE DEN=W/DEN D(I)=HP+DEN C(I)=HO*DEN CONTINUE I F (2*NS.LT.N-M)THEN DY=C(NS+1) ELSE DY=D(NS) NS=NS-1 ENDIF Y=Y+DY CONTINUE RETURN END DOUBLE P R E C I S I O N FUNCTION FUNCO(E) DOUBLE P R E C I S I O N T , E O , S , Z , E COMMON/Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 FUNC0=DEXP(-Z*R*T**2/(B*E)*DEXP(-E/(R*T))*(1.DO-2.DO*R*T/E)) 1 *DEXP(-0.5D0*((E-EO)/S)**2) RETURN END DOUBLE P R E C I S I O N FUNCTION F U N C l ( E ) DOUBLE P R E C I S I O N T , E O , S , Z , E COMMON / Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 FUNC1=DEXP(-Z*R*T**2/(B*E)*DEXP(-E/(R*T))*(1.D0-2.D0*R*T/E)) 1 *DEXP(-0.5D0*((E-EO)/S)**2)*(E-EO)/S**2 RETURN END DOUBLE P R E C I S I O N FUNCTION FUNC2(E) DOUBLE P R E C I S I O N T , E O , S , Z , E COMMON / Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 FUNC2=DEXP(-Z*R*T**2/(B*E)*DEXP(-E/(R*T))*(1.D0-2.D0*R*T/E))* 1 DEXP(-0.5D0*((E-EO)/S)**2)*(E-EO)**2/S**3 RETURN END DOUBLE P R E C I S I O N FUNCTION FUNC3(E) DOUBLE P R E C I S I O N T , E O , S , Z , E COMMON / Z D A T A / T , E O , S , Z R=8.314D0 B=50.0D0 FUNC3=DEXP(-Z*R*T**2/(B*E)*DEXP(-E/(R*T))*(1.DO-2.D0*R*T/E))*(* *T**2/(B*E))*DEXP(-E/(R*T))*(1.DO-2.D0*R*T/E)*DEXP(-0.5D0 * EO)/S)**2) RETURN END  Fitting Result with Anthony-Howard Model for RUN#61 E J/mol 114999.999951 T °C  .00000 49.85000 124.50000 143.15000 176.35000 201.20000 226.10000 251.00000 275.00000 298.65000 325.65000 348.45000 375.40000 402.35000 416.15000 437.60000 452.10000 466.60000 477.00000 485.30000 495.65000 503.95000 512.25000 524.70000 537.10000 549.55000 576.50000 601.40000 676.05000 700.00000  s J/mol 14999.998064 V  e x p  .39000 .39000 .39000 .61000 1.78000 3.16000 4.81000 6.89000 8.99000 11.61000 14.82000 17.79000 21.77000 26.49000 31.20000 34.13000 38.87000 44.29000 49.16000 53.50000 59.62000 64.66000 69.34000 74.19000 77.14000 78.75000 80.01000 80.34000 80,64000 80.64000  i  -1  k s 500000004.536339 Vmod  -.00868 -.00783 .04946 .10393 .34987 .82673 1.69501 3.04457 5.27093 8.66743 13.68217 18.60192 26.42453 36.10305 41.01006 47.87946 52.29991 56.74668 59.87655 62.26663 65.02800 67.00712 68.74093 70.88771 72.60551 74.08491 76.79565 78.57816 80.37077 80.52666  186  APPENDIX E F O R T R A N Program for Two-Stage First Order Reaction Model C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C C  C  O r i g i n a l experimental data: V(M) E x p e r i m e n t a l v o l a t i l e content % VD(M) Experimental dV/dT,VD(I)=(V(I+1)-V(I))/(T(I+l)-T(I)) T(M) E x p e r i m e n t a l temperature X(M) 1/T(M) i n K M No. o f e x p e r i m e n t a l d a t a p o i n t s LN No. o f e x p e r i m e n t a l d a t a p o i n t s o m i t t e d a t t h e b e g i n n i n g f o r fitting VF  F i t t i n g results  i n t h e e n t i r e temperature  range  F i r s t r e a c t i o n f i t t i n g parameters ( S e c t i o n below temperature 450 oC) N No. o f f i r s t r e a c t i o n data p o i n t s VI(N) E x p e r i m e n t a l v o l a t i l e content % VD1(N) E x p e r i m e n t a l dV/dT Tl(N) E x p e r i m e n t a l temperature XI(N) 1/T1(N) Al(2) F i t t i n g a r r a y used i n FLSQP s u b r o u t i n e f o r f i r s t r e a c t i o n Yl(N) F i t t i n g parameter d e r i v e d from VI (N) u s i n g r e l a t i v e method Y1F(N) F i t t e d v a l u e f o r Yl(N) u s i n g r e l a t i v e method V1F(N) F i t t e d v o l a t i l e u s i n g r e l a t i v e method F i r s t r e a c t i o n f i t t i n g parameters ( S e c t i o n below temperature 450 oC) MN No. o f second r e a c t i o n d a t a p o i n t s V2(MN) E x p e r i m e n t a l v o l a t i l e content % VD2(MN) E x p e r i m e n t a l dV/dT T2(MN) E x p e r i m e n t a l temperature X2(MN) 1/T2(MN) A2(2) F i t t i n g a r r a y used i n FLSQP s u b r o u t i n e f o r second r e a c t i o n Y2(MN) F i t t i n g parameter d e r i v e d from V2(MN) u s i n g r e l a t i v e method Y2F(MN) F i t t e d v a l u e f o r Y2(MN) u s i n g r e l a t i v e method V2F(MN) F i t t e d v o l a t i l e u s i n g r e l a t i v e method S u b s c r i p t f o r each method NT CR CN FM  I n t e g r a l method Coats-Redfern method C h e n - N u t t a l l method Friedman method  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) 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 C C C  INTERGRAL METHOD First  reaction  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.D01 2.D0*R*T1(I)/E1)/(C*E1))) 70 CONTINUE C C C  Second  reaction  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 C C C  C C C  C C C C C C  C o a t s - R e d f e r n method First  reaction  DO 110 1=1,N Y1CR(I)=DLOG(-C* D L O G ( 1 . D 0 - V 1 ( I ) / V O ) / ( R * T l ( I ) * T l ( 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 Second  reaction  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 h e n - N u t t a l l method First  reaction  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 C  Second  reaction  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 C  Friedman Method 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  C C C  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 Second r e a c t i o n 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 a l c u l a t e t h e v o l a t i l e c o n t e n t i n t h e e n t i r e temperature range 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 C  C a l c u l a t e t h e r a t e a t e n t i r e temperature range 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 C  C C C  C a l c u l a t e t h e a b s o l u t e average d e v i a t i o n ERROR 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 P r i n t i n g r e s u l t s o f V I , V2, V1F and V2F 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 s e l e c t e d temperature range')  WRITE(3, 600) 600 FORMAT (4X, 'T',8X, 'V',8X, 'VFNT',5X, 'VFCR',6X, 'VFCN',6X, ' VFFM , 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 1  C C C  C C C  C C C  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 e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r b o t h 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) P r i n t i n g t h e r e s u l t s o f Y l , Y2, Y1F and Y2F WRITE(3,701) 701 FORMAT(//'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') 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 P r i n t i n g t h e r e s u l t s i n the e n t i r e temperature range 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 P r i n t i n g the standard d e v i a t i o n  WRITE(3,742) 742 FORMAT(//'standard d e v i a t i o n f o r each method above') C WRITE(3,746) SEENT,SEECR,SEECN,SEEFM 746 FORMAT(17X,4F10.6)  192  C C  P r i n t i n g the rates  i n t h e e n t i r e temperature range  WRITE(3,750) 750 F O R M A T ( / / ' F i t t i n g r a t e dV/dT i n t h e e n 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  10 20  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) CONTINUE CONTINUE DO 70 K=1,NM KP=K+1  30  40  50 60 70  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 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 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) CONTINUE CONTINUE 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  10  20  30 40  50  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)) 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 CONTINUE DO 30 L=1,NM2 SUMU(L)=0.D0 CONTINUE DO 40 1=1,N COEFF(I,NP)=0.DO CONTINUE DO 70 K=1,M TERMU=U(K) DO 50 L=1,NM2 SUMU(L)=SUMU(L)+TERMU TERMU=TERMU*U(K) CONTINUE TERMV=V(K) DO 60 1=1,N COEFF(I,NP)=COEFF(I,NP)+TERMV TERMV=TERMV*U(K)  194  60 70  80 90  100 110  120 130  CONTINUE 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 CONTINUE 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) CONTINUE ENDIF A(I)=YM*(2.D0/XM)**IM*SUM/2.DO 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 CONTINUE SSUM=SSUM+(Y(K)-SUM)**2 CONTINUE VAR=SSUM/(M-N) RETURN END  C  10  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 . 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 E x p e r i m e n t a l 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 YFCN YCN YFCR YCR YFNT YNT T 556 412 .001177 -10. 718 -10. 575 -10. 939 -10. 794 297 251 .001213 -10. 836 -10. 882 -11. 049 -11. 095 081 176 .001233 -10. 958 -11. 053 -11. 168 -11. 263 073 031 414 310 -11. 208 -11. . -11. 104 -11. .001251 208 -. 132 .001267 -11. 268 -11. 344 -11. 471 -11. 548 324 -.297 .001280 -11. 434 -11. 460 -11. 635 -11. 662 435 -. 432 .001293 -11. 570 -11. 572 -11. 768 -11. 771 539 -.598 .001306 -11. 736 -11. 676 -11. 932 -11. 873 661 745 .001320 -11. 884 -11. 800 -12. 078 -11. 994 898 ' -.812 .001338 -12. 037 -11. 951 -12. 228 -12. 143 967 .001356 -12. 170 -12. 107 -12. 358 -12. 296 -1. 029 -1. 099 -1. 126 426 453 -12. -12. 240 267 -12. -12. .001371 .001387 -12. 354 -12. 377 -12. 538 -12. 560 -1. 213 -1. 235 .001407 -12. 455 -12. 545 -12. 636 -12. 725 -1. 313 -1. 402 .001430 -11. 979 -12. 050 -12. 736 -12. 779 -2. 380 -2. 429 .001455 -12. 100 -12. 114 -12. 839 -12. 832 -2. 489 -2. 487 .001483 -12. 199 -12. 190 -12. 916 -12. 896 -2. 573 -2. 556 .001513 -12. 307 -12. 269 -13. 004 -12. 962 -2. 668 -2. 628 .001541 -12. 392 -12. 341 -13. 071 -13. 022 -2. 742 -2. 693 .001573 -12. 485 -12. 426 -13. 144 -13. 093 -2. 822 -2. 770 .001603 -12. 551 -12. 504 -13. 193 -13. 158 -2. 878 -2. 840 -3. 000 .001670 -12. 705 -12. 680 -13. 312 -13. 306 -3. O i l .001742 -12. 853 -12. 872 -13. 425 -13. 466 -3. 138 -3. 173 .001822 -13. 018 -13. 081 -13. 558 -13. 642 -3. 285 -3. 363 .001909 -13. 231 -13. 311 -13. 738 -13. 834 -3. 480 -3. 571 .002005 -13. 487 -13. 563 -13. 963 -14. 045 -3. 719 -3. 799 .002111 -13. 792 -13. 843 -14. 238 -14. 279 -4. 009 -4. 052 .002229 -14. 299 -14. 153 -14. 716 -14. 538 -4. 502 -4. 333 Fitting T 50. 22 100. 32 135. 40 153. 77 175. 47 200. 52 225. 60 250. 65 275. 70 300. 75 325. 80 350. 85 362. 55 375. 90 387. 60 400. 95 414. 32 426. 00 437. 70 447. 72 456. 07 464. 42 474. 45 484. 45 492. 80  r e s u l t s i n t h e e n t i r e temperature range VFCN VFCR VFNT V 173164 143757 155567 040000 583486 446609 585928 060000 . 842096 1. 151879 500000 1. 231859 1. 020000 1. 733712 1. 126916 1. 574572 2. 170000 2. 504867 1. 541807 2. 204314 3. 860000 3. 671561 2. 135001 3. 126396 5. 570000 5. 172992 2. 858170 4. 276503 7. 590000 7. 032889 3. 711836 5. 662237 9. 830000 9. 265615 4. 693808 7. 285796 12. 080000 11. 867032 5. 795725 9. 138123 14. 480000 14. 815040 7. 003953 11. 200199 17. 330000 18. 070076 8. 299930 13. 443768 18. 700000 19. 680585 8. 928980 14. 543901 20. 650000 21. 577142 9. 660695 15. 832638 22. 550000 23. 282974 10. 311053 16. 986420 25. 090000 25. 269189 11. 059527 18. 324429 27. 590000 27. 289795 11. 811514 19. 680511 30. 750000 29. 071447 12. 466628 20. 872552 34. 040000 30. 863205 13. 117667 22. 068282 37. 350000 32. 397342 13. 668495 23. 089827 40. 310000 41. 062072 35. 863390 40. 231548 43. 670000 45. 481618 39. 961255 44. 595503 48. 260000 50. 810762 45. 020628 49. 878827 53. 520000 55. 999556 50. 100606 55. 050838 58. 430000 60. 121639 54. 273443 59. 184363  YFM -1. 242 723 299 195 112 089 331 239 620 907 -1. 178 -1. 393 -1. 591 -1. 735 -1. 964 -2. 063 -2. 479 -2. 506 -2. 696 -2. 834 -3. 077 -3. 150 -3. 357 -3. 454 -3. 489 -3. 620 -3. 810 -3. 843  YFFM 179 -. 349 443 529 -. 604 -. 668 -.730 788 -. 856 -. 940 -1. 026 -1. 099 -1. 175 -1. 267 -2. 384 -2. 437 -2. 501 -2. 567 -2. 628 -2. 699 -2. 764 -2. 912 -3. 073 -3. 249 -3. 441 -3. 653 -3. 887 -4. 147  VFFM 254039 .789804 1. 488240 1. 990044 2. 719006 3. 756867 5. 014856 6. 489252 8. 170753 10. 038886 12. 064187 14. 209525 15. 240696 16. 431792 17. 482892 18. 683748 19. 880750 20. 915811 21. 937321 22. 796086 52. 110546 54. 815420 57. 945213 60. 904851 63. 232246  196  500. 00 507. 85 516. 20 526. 22 537. 90 551. 27 576. 32 601. 37 649. 80 699. 90 750. 00 800. 12  63. 510000 67. 420000 71. 520000 74. 860000 77. 160000 78. 620000 79. 700000 80. 030000 80. 290000 80. 520000 80. 720000 80. 840000  63. 449886 66. 779021 69. 922558 73. 101714 75. 971799 78. 230589 80. 249327 80. 759516 80. 839754 80. 840000 80. 840000 80. 840000  57. 755135 61. 365837 64. 928926 68. 744113 72. 468759 75. 729994 79. 254115 80. 506863 80. 836274 80. 839998 80. 840000 80. 840000  62. 541985 65. 923123 69. 142386 72. 433783 75. 450494 77. 874822 80. 124226 80. 733312 80. 839570 80. 840000 80. 840000 80. 840000  65. 122477 67. 051542 68. 945288 70. 996004 73. 078863 75. 066625 77. 755774 79. 351849 80. 575569 80. 812883 80. 838394 80. 839947  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range VDFM VDCN VDCR VDNT VD T .007594 .005420 .004289 .005196 .000399 50. 22 .018972 .014563 .010694 .015487 .012543 100. 32 .031347 .025052 .017650 .028220 .028307 135. 40 .039298 .031991 .022115 .036999 .052995 77 153. .049740 .041305 .027976 .049144 .067465 175. 47 .063140 .053529 .035494 .065595 .068182 200. 52 .078044 .067409 .043850 .084826 .080639 225. 60 .093857 .082443 .052710 .106264 .089421 250. 65 .110288 .098369 .061912 .129585 .089820 275. 70 .127292 .115130 .071431 .154713 .095808 300. 75 .144295 .132188 .080943 .180904 .113772 325. 80 .160123 .148424 .089793 .206557 .117094 85 350. .155798 .167211 .093755 .218426 .146067 362. 55 .173957 .163007 .097522 .230390 .162393 375. 90 .178925 .168466 .100294 .239737 .190262 387. 60 .182836 .173057 .102472 .248123 .186986 400. 95 .186123 .177062 .104300 .255705 .270548 414. 32 .184728 .176486 .103506 .256427 .281197 00 426. .181803 .174410 .101856 .254908 .330339 437. 70 .176398 .169807 .098818 .249397 .354491 447. 72 .539964 .539926 .454728 .558800 .402395 456. 07 .533028 .565276 .475201 .585505 .457627 464. 42 .509290 .578632 .485379 .599901 .526000 474. 45 .464358 .564076 .472178 .585343 .588024 484. 45 .407799 .523123 .437149 .543249 .705556 492. 80 .334071 .448745 .374454 .466302 .498089 500. 00 .275146 .388251 .323475 .403712 .491018 507. 85 .203760 .302658 .251757 .314930 .333333 516. 20 .140963 .222364 .184618 .231569 .196918 526. 22 .094482 .159569 .132199 .166329 .109200 537. 90 .062666 .114163 .094357 .119123 .043114 27 551. .038128 .079540 .065462 .083148 .013174 576. 32 .031788 .075349 .061765 .078905 .005369 601. 37 .028688 .085356 .069471 .089660 .004591 649. 80 .021745 .079924 .064620 .084197 .003992 699. 90 .010352 .046039 .037002 .048626 .002394 750. 00 .000000 .000000 .000000 .000000 .002394 800. 12  C A N M E T pitch 50 °C/min, 800 °C final temperature RUN#33 E x p e r i m e n t a l 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 YFCN YCN YFCR YCR YFNT YNT T .983 .939 .001169 -10.078 -10.036 -10.328 -10.283 .693 .824 .001207 -10.197 -10.328 -10.437 -10.568 .567 .716 -10.692 -10.543 -10.455 .001223 -10.306 .437 .574 .001240 -10.450 -10.587 -10.683 -10.820 .248 .300 .001265 -10.725 -10.776 -10.953 -11.005  YFM -.645 -.131 '.429 .488 .437  YFFM .522 .277 .171 ,061 -.098  197  . 001290 .001309 .001328 .001344 .001360 .001369 .001386 .001407 .001430 .001453 .001486 .001542 .001603 .001669 .001746 .001824 .001910 .002003 .002117 .002232 Fitting T 50. 10 99. 10 125. 80 152. 50 174. 80 199. 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  -11. 035 -11. 231 -11. 406 -11. 526 -11. 642 -11. 695 -11. 800 -11. 916 -12. 030 -12. 137 -12. 249 -11. 846 -11. 993 -12. 123 -12. 277 -12. 453 -12. 645 -12. 885 -13. 206 -13. 656  -10. 973 -11. 119 -11. 269 -11. 393 -11. 519 -11. 583 -11. 714 -11. 882 -12. 056 -12. 235 -12. 496 -11. 792 -11. 945 -12. 109 -12. 305 -12. 501 -12. 716 -12. 951 -13. 237 -13. 527  -11. 258 -11. 450 -11. 622 -11. 739 -11. 852 -11. 904 -12. 006 -12. 118 -12. 229 -12. 332 -12. 440 -12. 571 -12. 678 -12. 770 -12. 885 -13. 026 -13. 184 -13. 391 -13. 677 -14. 096  -11. 197 -11. 340 -11. 487 -11. 607 -11. 730 -11. 793 -11. 920 -12. 085 -12. 254 -12. 429 -12. 684 -12. 495 -12. 623 -12. 761 -12. 924 -13. 089 -13. 269 -13. 466 -13. 704 -13. 948  008 203 377 496 611 664 768 883 995 -1. 101 -1. 212 -2. 271 -2. 393 -2. 499 -2. 629 -2. 784 -2. 956 -3. 178 -3. 481 -3. 916  r e s u l t s i n the e n t i r e temperature range VFCN VFCR VFNT V 171486 138895 159415 320000 539215 404340 556368 310000 650541 971510 400000 . 898298 986978 1. 405702 1. 060000 1. 585018 2. 010000 2. 282442 1 .345596 1. 961703 3. 370000 3. 271052 1 .826008 2. 724890 4. 960000 4.650494 2 .459542 3. 756319 6. 640000 6.202251 3 .136557 4.883752 8.420000 8.042902 3 .904061 6.188210 10. 430000 10. 164493 4 .752172 7. 658213 12. 620000 12. 776137 5 .753620 9.429510 14. 760000 15. 416117 6 .726081 11. 185607 17. 410000 18. 248549 7 .729867 13. 037547 20. 810000 21. 219655 8 .740720 14. 948457 23. 700000 23. 166671 9 .379280 16. 184024 26. 510000 24. 573239 9 .828113 17. 068403 29. 700000 25. 979937 10 .265765 17. 945754 33. 180000 27. 394181 10 .693524 18. 820292 36. 470000 39. 517420 33 .781513 38. 494790 38. 200000 41. 620283 35 .681101 40. 558965 42. 010000 45. 875263 39 .583898 44. 747626 46. 100000 50. 133976 43 .581692 48. 958655 52. 050000 55. 353100 48 .633913 54. 150658 58. 550000 60. 295076 53 .615079 59. 107162 67. 700000 66. 450372 60 .191753 65. 355186 74. 020000 71. 494238 66 .051103 70. 566098 76. 480000 74. 320833 69 .637644 73. 542262 77. 950000 76. 495891 72 .644783 75. 875617 79. 280000 79 517704 77 .569040 79. 235903 79 950000 80 709446 80 .389877 80. 675051 80 150000 80 789924 80 .787785 80. 789835 80 790000 80 790000 80 .790000 80. 790000  053 092 241 363 488 552 682 849 -1. 021 -1. 199 -1. 458 -2. 843 -3. 038 -3. 251 -3. 509 -3. 772 -4. 039 -4. 397 -4. 806 -5. 734  -.  VFFM 591272 1.. 242183 1. 709785 2. 241225 2. 718060 3. 253745 3. 823297 4.293595 4.678267 4. 934511 5. 013092 4.845490 4.388759 3. 578859 2. 842789 2. 197203 1. 445455 570909 35.. 907049 37. 622476 41. 113278 44. 651810 49. 087966 53. 445751 59. 225680 64. 475386 67. 790289 70. 678095 75. 862118 79. 724209 80. 758907 80 789999  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range VDFM VDCN VDCR VDNT VD T 014815 .005205 .004026 ,005149 50.10 -.000204 026812 .013161 .009492 .014337 .003371 99.10 034799 .019799 .013844 .022507 .024719 125.80 043396 .028094 .019120 .033148 .042601 152.50 050842 .036234 .024167 .043952 .055624 174.80  280 014 262 523 688 824 946 -1. 186 -1. 329 -1. 511 -1. 868 -2. 210 -2. 502 -2. 748 -2. 842 -2. 870 -3. 016 -3. 094 -3. 260 -3. 344  -. -. -. -.  263 385 511 614 720 773 883 -1. 024 -1. 169 -1. 320 -1. 539 -2. 429 -2. 517 -2. 613 -2. 726 -2. 840 -2. 964 -3. 100 -3. 265 -3. 434  -. -. -. -. -.  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 E x p e r i m e n t a l 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 YFCN YCN YFCR YCR YFNT YNT T 1. 036 1. 162 .001215 -9. 982 -10. 109 -10. 192 -10. 319 937 1. 019 .001227 -10. 127 -10. 209 -10. 335 -10. 417 857 834 .001239 -10. 289 -10. 311 -10. 495 -10. 517 730 697 .001251 -10. 449 -10. 416 -10. 653 -10. 620 624 548 .001263 -10. 600 -10. 523 -10. 801 -10. 725 516 416 .001276 -10. 732 -10. 632 -10. 931 -10. 832 245 349 .001295 -10. 904 -10. 800 -11. 100 -10. 996 177 105 .001315 -11. 045 -10. 973 -11. 238 -11. 166 053 059 .001342 -11. 204 -11. 210 -11. 392 -11. 398 370 222 705 558 -11. 523 -11. -11. 375 .001378 -11. .001424 -11. 148 -11. 131 -11. 716 -11. 686 -1. 195 -1. 903 .001482 -11. 340 -11. 317 -11. 879 -11. 853 -1. 370 -2. 145 .001544 -11. 521 -11. 519 -12. 032 -12. 033 -1. 535 -2. 371 .001602 -11. 693 -11. 706 -12. 181 -12. 201 -1. 695 -2. 661 .001664 -11. 888 -11. 908 -12. 352 -12. 381 -1. 877 -2. 934 .001743 -12. 146 -12. 164 -12. 583 -12. 609 -2. 121 -3. 288 .001817 -12. 383 -12. 404 -12. 799 -12. 824 -2. 348 -3. 626 .001912 -12. 691 -12. 711 -13. 081 -13. 099 -2. 643 -4. 065 .002001 -13. 050 -12. 999 -13.. 419 -13. 357 -2. 992 -6. 243  .  .  -. -.  Fitting results i n V T .090000 51. 20 .250000 148. 60 .570000 175. 80 199. 20 1.250000 226. 50 2.410000 249. 80 3.670000 277. 10 5.330000 300. 50 7.100000  the e n t i r e temperature range VFCN VFCR VFNT .041788 .037196 .037815 .571244 .449749 .590487 .977237 .750431 1.038072 1.603755 1.113857 1.478432 2.532160 1.686924 2.283696 3.599821 2.323655 3.192784 5.226674 3.265426 4.555680 6.980181 4.255858 6.004666  YFM 1. 132 1. 252 1. 184 1. 023 815 567 260 064 377 695 -1. 067 -1. 370 -1. 625 -1. 754 -1. 879 -2. 041 -2. 280 -2. 521 -2. 655  .  -.  YFFM 1. 357 1. 207 1. 052 893 732 568 315 054 304 776 -1. 216 -1. 367 -1. 531 -1. 684 -1. 848 -2. 056 -2. 251 -2. 501 -2. 736  .  VFFM 089455 885730 1. 416064 2. 031820 2. 965834 3. 966103 5. 392814 6. 840918  .  199  327.70 351.10 374.50 401.70 429.00 452.40 471.90 487.40 499.10 510.80 518.60 526.40 534.20 542.00 549.70 565.30 584.80 612.10 651.00 701.60 752.30 799.00  9.650000 12.140000 14.860000 18.310000 22.540000 27.110000 32.190000 37.200000 41.820000 47.510000 51.880000 56.710000 61.610000 66.120000 69.670000 74.330000 77.000000 78.280000 78.820000 78.970000 79.150000 79.300000  9.465350 11.997734 14.888488 18.668993 22.858725 24.023730 32.039011 39.156521 44.774625 50.417374 54.098071 57.645267 61.002373 64.118252 66.915944 71.624776 75.640965 78.362692 79.242162 79.299799 79.300000 79.300000  5.632465 7.015564 8.581675 10.623569 12.894257 20.524340 27.552988 33.951636 39.137117 44.497372 48.095553 51.656872 55.130548 58.466153 61.576999 67.164201 72.531486 76.972609 79.033522 79.296617 79.299996 79.300000  8.035294 10.086823 12.415906 15.452627 18.818725 23.460954 31.302714 38.293751 43.836819 49.432639 53.101808 56.655377 60.037606 63.197157 66.054835 70.925638 75.178599 78.178239 79.221177 79.299639 79.300000 79.300000  8.783387 10.667295 12.731221 15.326578 18.101062 12.033339 19.205596 26.792290 33.573404 41.053280 46.260754 51.486260 56.570802 61.348836 65.613673 72.426814 77.215667 79.134416 79.299688 79.300000 79.300000 79.300000  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range VDFM VDCN VDCR VDNT VD T .002970 .001541 .001318 .001454 .001643 51. 20 .019344 .013569 .010325 .014541 .011765 148. 60 .028129 .020970 .015584 .023057 .029060 175. 80 .037294 .029134 .021262 .032670 .042491 20 199. .049829 .040884 .029274 .046802 .054077 226. 50 .061992 .052823 .037273 .061441 .060806 249. 80 .077848 .069056 .047974 .081694 .075641 277. 10 .092374 .084558 .058032 .101366 .093750 300. 50 .109705 .103839 .070346 .126246 .106410 327. 70 .124680 .121176 .081254 .148975 .116239 351. 10 .139336 .138785 .092180 .172396 .126838 374. 50 .155372 .158895 .104463 .199582 .154945 401. 70 .168297 .176369 .114859 .223821 .195299 429. 00 .240177 .360559 .304524 .372701 .260513 452. 40 .347618 .444225 .373598 .460019 .323226 471. 90 .444381 .502595 .421329 .521182 .394872 487. 40 .513459 .531302 .444351 .551505 .486325 499. 10 .560853 .532368 .444231 .553150 .560256 510. 80 .570239 .511745 .426392 .532058 .619231 518. 60 .552005 .468866 .390098 .487780 .628205 526. 40 .506336 .407489 .338550 .424184 .578205 534. 20 .440551 .336273 .278993 .350260 .461039 542. 00 .374077 .271267 .224756 .282713 .298718 549. 70 .259549 .170142 .140595 .177523 .136923 565. 30 .171268 .099474 .081937 .103931 .046886 584. 80 .121581 .060145 .049333 .062954 .013882 612. 10 .106607 .042650 .034788 .044749 .002964 651. 00 .152880 .047596 .038566 .050080 .003550 701. 60 .134973 .033506 .026987 .035344 .003212 752. 30 .000000 .000000 .000000 .000000 .003212 799. 00  C A N M E T pitch 150 °C/min, 800 °C final temperature RUN# CAN58 E x p e r i m e n t a l 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 .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 .001192 .001209 .001226 .001244 .001262 .001291 .001321 .001363 .001419 .001480 .001753 Fitting T 51. 80 203. 75 297. 20 402. 35 431. 60 460. 70 484. 10 501. 65 519. 20 530. 90 542. 60 554. 15 566. 00 577. 55 595. 10 612. 65 624. 35 653. 60 723. 65 799. 55  -10. 008 -10. 245 -10. 483 -10. 704 -10. 895 -11. 155 -11. 380 -11. 702 -11. 895 -12. 285 -13. 148 -14. 167  -10. 073 -10. 261 -10. 459 -10. 658 -10. 866 -11. 079 -11. 411 -11. 759 -12. 082 -12. 398 -12. 742 -14. 274  -10. 167 -10. 401 -10. 637 -10. 855 -11. 044 -11. 302 -11. 523 -11. 841 -12. 198 -12. 574 -13. 424 -14. 395  -10. 231 -10. 417 -10. 613 -10. 810 -11. 015 -11. 226 -11. 554 -11. 898 -12. 383 -12. 688 -13. 021 -14. 500  1 .446 1 .382 1 .194 1 .210 .973 .997 .798 .752 .591 .562 .379 .303 .047 .078 - .243 - .300 -1 .225 -2 .063 -1 .610 -3 .575 -2 .468 -5 .479 -3 .470 -10 .911  r e s u l t s i n t h e e n t i r e temperature range VFCN VFCR VFNT V .000159 .000154 .000151 .060000 .073340 .063126 .074681 .000000 .672535 .555184 .701829 .780000 .986740 3 .194776 3 .237655 .850000 4 2 7 .050000 6 .330544 4 .732698 5 .934912 10 .840000 9 .115970 8 .027129 8 .983551 15 .870000 15 .080683 13 .282723 14 .852779 21 .770000 21 .204772 18 .726693 20 .883108 27 .110000 28 .796499 25 .568963 28 .370146 33 .840000 34 .576969 30 .867080 34 .082948 39 .520000 40 .770361 36 .649493 40 .218947 46 .400000 47 .076315 42 .676873 46 .486832 53 .900000 53 .464116 48 .967499 52 .863180 60 .980000 59 .309409 54 .942318 58 .729828 66 .750000 66 .854625 63 .119819 66 .368983 72 .410000 72 .240913 69 .523827 71 .899768 75 .110000 74 .582095 72 .607495 74 .342314 75 .950000 77 .155327 76 .597077 77 .095814 76 . 820000 77 .589951 77 .589461 77 .589928 77 .590000 77 .590000 77 .590000 77 .590000  1 .088 1 .356 1 .113 .853 .510 .536 .201 - .202 - .728 -1 .284 -1 .244 -3 .259  -  1 .337 1 .158 .969 .779 .582 .379 .062 - .269 - .731 -1 .089 -1 .479 -3 .216  VFFM .000068 .070851 .866054 6 .378226 9 .894506 9 .795881 15 .812360 21 .863492 29 .251362 34 .821159 40 .756949 46 .786606 52 .903960 58 .537902 65 .934092 71 .411071 73 .913015 76 .930663 77 .589731 77 .590000  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range VDCN VDFM VDCR VDNT VD 1 .000005 .000009 .000009 .000009 .000395 51. 80 .002333 .002159 .001826 .002221 .008347 203. 75 .020546 .014342 .011640 .015110 .019686 297. 20 .113490 .063308 .049723 .067985 .143590 402. 35 .158347 .083982 .065475 .090575 .130241 431. 60 .213433 .202428 .178311 .206107 .214957 460. 70 .314499 .304952 .267476 .310924 .336182 484. 10 .396048 .390105 .341129 .398138 .304274 501. 65 .491444 .491390 .428456 .501982 .575214 519. 20 .521913 .526912 .458575 .538596 .485470 530. 90 .553269 .563825 .489815 .576667 .595671 542. 60 .547803 .563295 .488506 .576449 .632911 554. 15 .502590 .521455 .451440 .533933 .612987 566. 00 .421484 .441036 .381193 .451831 .328775 577. 55 .357799 .379098 .326871 .388681 .322507 595. 10 .220097 .236009 .203026 .242157 .230769 612. 65 .124013 .134011 .115110 .137569 .028718 624. 35 .121026 .133220 .114024 .136916 .012420 653. 60 .131517 .150649 .127955 .155215 .010145 723. 65 .000000 .000000 .000000 .000000 .010145 799. 55  -  Syncrude pitch 25 "C/min, 800 °C final temperature RUN# Syn43 E x p e r i m e n t a l 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 .001206 .001220 .001233 .001243 .001251 .001262 .001275 .001294 .001314 .001335 .001359 .001381 .001430 .001484 .001541 .001603 .001670 .001743 .001822 .001910 .002005 .002112 .002230 .002361  YNT -10. -10. -10. -11. -11. -11. -11. -11. -11. -11. -11. -12. -11. -11. -12. -12. -12. -12. -13. -13. -13. -14. -14. -15.  639 774 937 111 227 350 487 647 773 873 964 027 847 970 u i 292 504 765 063 399 761 233 714 242  YFNT -10. -10. -11. -11. -11. -11. -11. -11. -11. -11. -12. -12. -11. -11. -12. -12. -12. -12. -13. -13. -13. -14. -14. -15.  787 907 009 093 156 242 351 509 671 837 035 213 692 889 102 331 580 850 145 469 824 218 655 144  F i t t i n g r e s u l t s i n the e n t i i VFNT V T 5 0 . 05 7 5 . 12 1 0 0 . 17 1 2 5 . 22 1 5 0 . 30 1 7 5 . 35 2 0 0 . 40 2 2 5 . 47 2 5 0 . 52 2 7 5 . 57 3 0 0 . 62 3 2 5 . 70 3 5 0 . 75 3 7 5 . 80 4 0 0 . 87 4 2 5 . 92 4 5 0 . 97 4 6 2 . 67 4 7 6 . 05 4 8 7 . 72 4 9 9 . 42 5 1 1 . 12 5 1 9 . 47 5 2 6 . 15 5 3 1 . 17 5 3 7 . 85 5 4 6 . 20 5 5 6 . 22 5 7 4 . 60 5 9 9 . 65 6 2 4 . 72 6 5 1 . 45 6 7 4 . 82 6 9 9 . 90 7 2 4 . 95  100000 150000 190000 .600000 1. 000000 1 . 860000 3 . 270000 5 . 630000 8 . 600000 1 2 . 650000 1 7 . 690000 2 3 . 580000 2 9 . 640000 3 5 . 840000 4 1 . 510000 4 6 . 950000 5 2 . 400000 5 5 . 440000 5 9 . 570000 6 3 . 810000 6 8 . 730000 7 4 . 310000 7 8 . 470000 8 1 . 640000 8 4 . 140000 8 6 . 990000 8 8 . 850000 8 9 . 870000 9 0 . 460000 9 0 . 560000 9 0 . 580000 9 0 . 750000 9 0 . 800000 9 0 . 950000 9 0 . 900000  045729 119218 • 274938 573755 1. 102366 1. 971729 3 . 317881 5 . 293673 8 . 048237 1 1 . 715766 1 6 . 384554 2 2 . 079089 2 8 . 709136 3 6 . 099426 4 3 . 975909 5 1 . 972562 4 6 . 345424 5 3 . 099613 6 0 . 768890 6 7 . 125449 7 2 . 929307 7 7 . 960176 8 1 . 002113 8 3 . 089095 8 4 . 454969 8 6 . 011279 8 7 . 563757 8 8 . 918606 9 0 . 308221 9 0 . 918100 9 1 . 020123 9 1 . 029652 9 1 . 029991 9 1 . 030000 9 1 . 030000  YCN  YFCR  YCR -10. -10. -11. -11. -11. -11. -11. -11. -11. -12. -12. -12. -12. -12. -12. -12. -12. -13. -13. -13. -14. -14. -14. -15.  867 999 159 331 446 566 701 857 980 077 164 223 320 422 542 703 894 136 414 731 074 528 991 502  -11. -11. -11. -11. -11. -11. -11. -11. -11. -12. -12. -12. -12. -12. -12. -12. -12. -13. -13. -13. -14. -14. -14. -15.  014 132 232 313 375 459 566 720 878 041 234 409 146 330 530 745 978 232 509 812 146 516 926 385  -. -. -. -. -. -. -. -. - 1-. . -1. -1. -2. -2. -2. -2. -3. -3. -3. -4. -4.  YFCN 435 301 139 034 150 272 409 567 692 791 881 943 684 796 927 097 299 551 840 168 522 987 461 983  temperature range VFCN VFCR 041916 103723 228622 458602 851063 1. 476784 2 . 420624 3 . 776935 5 . 638572 8 . 094285 1 1 . 214130 1 5 . 044083 1 9 . 576469 2 4 . 769893 3 0 . 533683 3 6 . 716279 4 0 . 187785 4 6 . 439729 5 3 . 788245 6 0 . 146397 6 6 . 244810 7 1 . 854825 7 5 . 458219 7 8 . 061344 7 9 . 842218 8 1 . 970639 8 4 . 241244 8 6 . 412761 8 9 . 019474 9 0 . 551567 9 0 . 955365 9 1 . 024145 9 1 . 029642 9 1 . 029991 9 1 . 030000  047220 120245 271701 556947 1. 053327 1. 858037 3 . 088735 4 . 876388 7 . 348210 1 0 . 620223 1 4 . 773021 1 9 . 839594 2 5 . 762834 3 2 . 422129 3 9 . 617613 4 7 . 067418 4 5 . 322347 5 1 . 985524 5 9 . 598577 6 5 . 959294 7 1 . 822067 7 6 . 963617 8 0 . 110255 82. 291746 8 3 . 732460 8 5 . 390236 8 7 . 067081 8 8 . 558719 9 0 . 140012 9 0 . 878470 9 1 . 014822 9 1 . 029359 9 1 . 029980 9 1 . 030000 9 1 . 030000  • 287 • 168 • 067 016 079 164 273 429 590 755 951 - 1 . 129 - 2 . 380 - 2 . 644 - 2 . 930 - 3 . 245 - 3 . 590 - 3 . 973 - 4 . 398 - 4 . 874 - 5 . 410 - 6 . 017 - 6 . 711 - 7 . 514  -. -. -.  VFFM 183638 379017 712813 1. 242274 2 . 032195 3 . 146510 4 . 648328 6. 592209 9 . 012339 1 1 . 926517 1 5 . 326583 1 9 . 182983 2 3 . 426576 2 7 . 979782 3 2 . 748024 3 7 . 615765 2 2 . 184007 2 8 . 545636 3 7 . 089753 4 5 . 439528 5 4 . 279365 6 3 . 075784 6 8 . 995159 7 3 . 348936 7 6 . 333647 7 9 . 863493 8 3 . 504374 8 6 . 728488 8 9 . 881430 9 0 . 944794 9 1 . 028241 9 1 . 029996 9 1 . 030000 9 1 . 030000 9 1 . 030000  YFM  -. - 1-. . -1. -1. -2. -2. -2. -2. -2. -2. -2. -3. -3. -3. -4. -4.  YFFM 368 155 321 437 282 057 294 626 951 242 529 783 092 211 278 295 412 525 746 015 361 619 149 653  -. -. -. -. -. - 1-. . -1. -1. -1. -2. -2. -2. -2. -2. -2. -3. -3. -3. -4. -4.  449 269 116 009 104 233 397 633 876 126 422 690 879 023 177 344 525 722 937 172 431 718 036 392  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 r a t e dV/dT i n t h e e n t i r e temperature range VDCN VDFM VDGR VDNT VD T .006238 .001984 .001713 .001964 .001994 50. 05 .004425 .011371 .003716 .004483 .001597 75. 12 .019116 .008858 .007260 .009153 .016367 100. 17 .029980 .016182 .012987 .017014 .015949 125. 22 .044581 .027532 .021687 .029395 .034331 150. 30 .063032 .043869 .033988 .047477 .056287 175. 35 .085283 .066049 .050421 .072355 .094136 200. 40 .094241 .110524 .070989 .104373 .118563 225. 47 .138203 .128543 .095669 .143776 .161677 250. 52 .166266 .167355 .123200 .188875 .201198 275. 57 .192835 .208607 .152042 .237368 .234848 300. 62 .215958 .249594 .180256 .286149 .241916 325. 70 .235538 .289273 .207161 .333937 .247505 350. 75 .250227 .325032 .230969 .377615 .226167 375. 80 .358567 .262075 .252973 .419042 .217166 400. 87 .386595 .269273 .270933 .454277 .217565 425. 92 .285043 .499692 .417385 .518990 .259829 450. 97 .343355 .549754 .457946 .571709 .308670 462. 67 .591258 .408191 .491032 .615731 .363325 476. 05 .603604 .453461 .500008 .629331 .420513 487. 72 .473687 .580793 .479920 .606242 .476923 499. 42 .449582 .509003 .419588 .531899 .498204 511. 12 .397909 .426201 .350744 .445717 .474551 519. 47 .338350 .346972 .285167 .363080 .498008 526. 15 .273100 .271176 .222655 .283894 .426647 531. 17 .181460 .172724 .141638 .180931 .222754 537. 85 .114152 .103164 .084465 .108144 .101796 546. 20 .072722 .061841 .050539 .064882 .032100 556. 22 .049169 .037535 .030575 .039440 .003992 574. 60 .061295 .040689 .033005 .042837 .000798 599. 65 .086728 .050450 .040760 .053212 .006360 624. 72 .079952 .040720 .032767 .043029 .002139 651. 45 .090944 .041490 .033276 .043910 .005981 674. 82 .044086 .017978 .014370 .019056 699 90 -.001996 .098155 .035983 .028670 .038199 724 95 -.000399 .142614 .047247 .037529 .050227 .005988 750 00 -.004076 --.013548 -.003228 775 05 -.000399 -.004339 .000000 .000000 .000000 .000000 800 12 -.000399  Syncrude pitch 50 °C/min, 800 °Cfinaltemperature RUN# Syn29 E x p e r i m e n t a l 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 YFCN YCN YFCR YCR YFNT YNT T .826 .929 .001230 -10. 282 -10. 384 -10. 476 -10. 578 .697 .748 705 -10. 655 .001244 -10. 463 -10. 514 -10. .531 .512 .001262 -10. 700 -10. 681 -10. 888 -10. 869 .361 .282 .001281 -10. 930 -10. 852 -11. 116 -11. 038 .167 .256 .001292 -11. 047 -10. 957 -11. 231 -11. 141 .113 .035 283 -11. 360 101 -11. -11. .001308 -11. 179 -.070 -.095 .001328 -11. 309 -11. 285 -11. 488 -11. 463 -.375 -.239 .001361 -11. 455 -11. 592 -11. 629 -11. 765 -1.148 -.921 493 718 -11. -11. 124 .001391 -11. 336 -11. .001442 -11. 480 -11. 354 -11. 846 -11. 713 -1.057 -1.384 .001492 -11. 625 -11. 578 -11. 977 -11. 927 -1.196 -1.637 .001545 -11. 795 -11. 818 -12. 132 -12. 157 -1.359 -1.938 .001602 -11. 997 -12. 076 -12. 321 -12. 404 -1.556 -2.266  YFM .683 .855 .651 .440 .210 -.076 -.410 -.870 -1.216 -1.451 -1.547 -1.630 -1.720  YFFM .962 .775 .533 .285 .133 -.076 -.342 -.787 -1.112 -1.275 -1.434 -1.605 -1.788  203  .001670 .001743 .001824 .001896 .002001 .002107 .002285 Fitting T 51. 65 100. 00 164. 50 201. 35 226. 70 254. 35 275. 10 300. 40 325. 75 351. 10 374. 15 397. 20 420. 20 445. 55 461. 65 480. 10 491. 60 500. 85 507. 75 519. 25 530. 80 540. 00 553. 80 574. 55 599. 90 650. 55 698. 95 749. 60 800. 30  -12. 257 -12. 570 -12. 944 -13. 300 -13. 861 -14. 375 -15. 392  -12. 382 -12. 716 -13. 079 -13. 404 -13. 878 -14. 361 -15. 162  -12. 565 -12. 863 -13. 222 -13. 566 -14. 111 -14. 611 -15. 608  -1. 809 -2. 116 -2. 484 -2. 836 -3. 391 -3. 900 -4. 911  -12. 698 -13. 018 -13. 366 -13. 677 -14. 131 -14. 594 -15. 362  r e s u l t s i n the e n t i r e temperature range VFCN VFCR VFNT V 010091 .009251 009799 140000 076391 .066885 076477 190000 585025 .489475 603673 480000 1. 520000 1. 542227 1 .209491 1. 474579 2. 760000 2. 716734 2 .089952 2. 577077 5. 230000 4.728916 3 .574526 4.452674 7. 850000 6.892639 5 .154681 6.459578 11. 990000 10. 464453 7 .749320 9.761545 17. 060000 15. 226500 11 .209405 14. 156507 22. 760000 21. 261362 15 .629579 19. 730895 28. 370000 27. 825962 20 .516929 25. 816720 34. 000000 35. 271960 26 .202357 32. 765722 39. 550000 43. 319420 32 .574092 40. 353804 45. 630000 52. 465639 40 .203254 49. 112623 49. 930000 45. 544597 40 .142579 44. 732081 56. 230000 57. 049162 51 .010700 56. 134667 61. 490000 64. 046787 57 .913998 63. 119553 66. 500000 69. 320859 63 .320820 68. 418263 70. 620000 72. 949788 67 .174942 72. 086372 77. 790000 78. 265718 73 .090112 77. 503543 83. 510000 82. 552398 78 .202721 81. 925942 86. 620000 85. 182659 81 .583735 84. 676348 88. 850000 87. 920141 85 .456989 87. 589287 89. 660000 89. 941164 88 .853273 89. 808968 89. 980000 90. 609394 90 .362395 90. 584542 90. 220000 90. 699888 90 .698331 90. 699812 90. 400000 90. 700000 90 .700000 90. 700000 90. 570000 90. 700000 90 .700000 90. 700000 90. 700000 90. 700000 90 .700000 90. 700000  .  -2. 624 -2. 943 -3. 409 -3. 884 -4. 673 -6. 428 -8. 201  -1. 879 -2. 063 -2. 315 -2. 606 -2. 980 -3. 596 -4. 158  -2. 006 -2. 243 -2. 502 -2. 732 -3. 069 -3. 413 -3. 983  VFFM 069018 315460 1. 453963 2. 903798 4.403386 6. 612174 8.712572 11. 826934 15. 572819 19. 927271 24. 368376 29. 197021 34. 309169 40. 152213 25. 361219 37. 631151 46. 535234 54. 065860 59. 693159 68. 630844 76. 428641 81. 413289 86. 580788 89. 957255 90. 669984 90. 700000 90. 700000 90. 700000 90. 700000  .  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range VDFM VDCN VDCR VDNT VD T .002632 .000497 .000446 .000490 .001034 51. 65 .009479 .002925 .002509 .002968 .004496 100. 00 .033618 .016868 .013835 .017630 .028223 164. 50 .058773 .036688 .029491 .038858 .048915 35 201. .081707 .058174 .046199 .062112 .089331 226. 70 .090106 .111234 .070713 .096965 .126265 254. 35 .135785 .120147 .093525 .129992 .163636 275. 10 .167061 .163208 .125892 .177651 .200000 300. 40 .198132 .211965 .162139 .232004 .224852 325. 75 .227298 .264330 .200647 .290795 .243384 351. 10 .250483 .312477 .235665 .345237 .244252 374. 15 .270272 .359941 .269833 .399266 .241304 397. 20 .285841 .404580 .301601 .450452 .239842 420. 20 .296595 .446924 .331252 .499500 .267081 445. 55 .371255 .560143 .476958 .577103 .341463 461. 65 .489652 .642807 .545310 .663253 .457391 480. 10 .541543 .654083 .553640 .675488 .541622 60 491. .552650 .625343 .528390 .646257 .597101 500. 85 .533992 .576110 .486170 .595681 .623478 507. 75 .439180 .439911 .369847 .454474 .495238 519. 25 .288809 .312035 .242723 .299108 .338043 530. 80  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 E x p e r i m e n t a l 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 1. 534 1. 722 .001127 -9. 308 -9. 498 -9. 564 -9. 751 1. 291 517 990 1. 764 -9. -9. 743 -9. 516 .001158 -9. 1. 146 1. 250 .001176 -9. 785 -9. 889 -10. 028 -10. 132 1. 035 1. 029 .001191 -10. 007 -10. 001 -10. 247 -10. 241 921 822 354 -10. -10. 452 116 -10. .001205 -10. 215 641 • 803 .001220 -10. 398 -10. 235 -10. 631 -10. 469 487 683 .001236 -10. 552 -10. 356 -10. 782 -10. 587 560 364 .001251 -10. 677 -10. 480 -10. 904 -10. 708 435 270 .001267 -10. 772 -10. 606 -10. 996 -10. 831 305 192 958 -10. 071 -11. .001284 -10. 850 -10. 737 172 126 089 -11. 135 -11. 871 -10. 918 -10. .001301 Oil 049 .001324 -10. 997 -11. 056 -11. 209 -11. 269 152 009 .001343 -11. 055 -11. 199 -11. 264 -11. 408 347 084 .001368 -11. 131 -11. 396 -11. 337 -11. 599 811 489 .001393 -11. 100 -10. 908 -11. 415 -11. 214 973 598 388 518 -11. -11. .001427 -11. 212 -11. 087 700 -1. 143 .001455 -11. 318 -11. 236 -11. 617 -11. 532 832 -1. 319 .001492 -11. 453 -11. 432 -11. 744 -11. 722 956 -1. 503 881 863 -11. 596 -11. .001523 -11. 579 -11. .001555 -11. 720 -11. 768 -11. 997 -12. 047 -1. 094 -1. 696 .001589 -11. 868 -11. 946 -12. 139 -12. 220 -1. 239 -1. 950 .001624 -12. 032 -12. 133 -12. 295 -12. 401 -1. 400 -2. 218 .001661 -12. 210 -12. 327 -12. 467 -12. 589 -1. 576 -2. 562 .001709 -12. 463 -12. 584 -12. 712 -12. 838 -1. 826 -2. 998 .001760 -12. 760 -12. 855 -13. 000 -13. 101 -2. 120 -3. 473 .001826 -13. 145 -13. 204 -13. 376 -13. 438 -2. 502 -4. 077 .001909 -13. 593 -13. 644 -13. 813 -13. 865 -2. 946 -5. 319 .001999 -14. 121 -14. 124 -14. 330 -14. 330 -3. 471 -6. 997 .002114 -15. 006 -14. 735 -15. 203 -14. 922 -4. 353 -9. 207  .  -.  -.  -. -. -.  Fitting T 50. 40 101. 40 152. 30 199. 90 227. 10 250. 80 274. 60 295. 00 312. 0.0 329. 00 342. 60 356. 20 369. 80 383. 40 397. 00 414. 00 427. 50  r e s u l t s i n the e n t i VFNT V 001540 010000 • 018878 000000 • 129853 080000 550585 420000 1. 120000 1. 116204 2. 050000 1. 948625 3. 440000 3. 247629 5. 330000 4. 856552 7. 450000 6. 635186 9. 930000 8. 884788 12. 160000 11. 066733 14. 630000 13. 618970 17. 290000 16. 562265 20. 210000 19. 907563 23. 230000 23. 653224 26. 990000 28. 871191 30. 220000 33. 395664  temperature range VFCN VFCR 001588 001496 018978 017085 128043 111371 „ 535174 453851 902845 1. 077492 1. 553575 1. 871033 2. 557005 3. 103598 3. 789285 4. 624784 5. 144724 6. 302401 6. 854845 8. 420862 8. 513106 10. 473818 10. 455958 12. 874559 12. 704596 15. 643977 15. 275332 18. 794581 18. 177902 22. 328055 22. 274075 27. 264504 25. 885633 31. 561762 #  VFFM • 016485 105664 442528 1. 293837 2. 185278 3. 301432 4. 816467 6. 483361 8. 163141 10. 127888 11. 914502 13. 896846 16. 076091 18. 449990 21. 012616 24. 466045 27. 389481  YFM  232 • 996 1. 482 1. 452 1. 225 947 653 336 • 016 242 435 639 724 830 882 973 977 -1. 114 -1. 153 -1. 228 -1. 357 -1. 463 -1. 593 -1. 740 -1. 922 -2. 241 -2. 719 -3. 127 -3. 556  .  -. -. -. -. -. -. -. -.  YFFM 1. 444 1. 152 978 • 844 • 707 • 566 • 422 • 273 • 123 033 193 413 583 818 689 818 924 -1. 064 -1. 182 -1. 304 -1. 432 -1. 565 -1. 704 -1. 888 -2. 082 -2. 331 -2. 646 -2. 989 -3. 426  .  -. -. -. -. -. -. -. -.  444. 50 458. 10 471. 70 481. 90 495. 50 505. 70 515. 90 526. 00 536. 20 546. 40 556. 60 566. 80 577. 00 590. 60 614. 40 644. 90 699. 30 801. 20  34. 100000 37. 280000 40. 440000 42. 920000 46. 340000 49. 260000 52. 570000 56. 470000 61. 340000 67. 070000 73. 250000 79. 270000 84. 200000 88. 020000 89. 670000 90. 020000 90. 270000 90. 580000  39 .480515 30 .294054 36 .300444 41 .121766 47 .837747 52 .973813 58 .079517 62 .995823 67 .710001 72 .070023 75 .990181 79 .408748 82 .293013 85 .308779 88 .564528 90 .176356 90 .574109 90 .580000  30.848632 25.465104 30.645522 34.873027 40.887724 45.607671 50.426936 55.214767 59.976033 64.570176 68.907305 72.906769 76.502948 80.594647 85.747974 89.132030 90.516899 90.579999  37. 371937 29. 445278 35. 289245 39. 993312 46. 571202 51. 626478 56. 678531 61. 574160 66. 304153 70. 718213 74. 728841 78. 269233 81. 298659 84. 526661 88. 135044 90. 041295 90. 569747 90. 580000  31. 268862 17. 320647 21. 944588 25. 922760 31. 885258 36. 804164 42. 037160 47. 440367 53. 008302 58. 555721 63. 938346 69. 011118 73. 641053 78. 944401 85. 506564 89. 407948 90. 561938 90. 580000  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range VDFM VDCN VDCR VDNT VD T .000721 .000091 .000084 .000089 50. 40 -.000196 .003566 .000829 .000734 .000832 .001572 101. 40 .011985 .004433 .003793 .004537 .007143 152. 30 .029320 .015295 .012761 .015877 .025735 199. 90 .045017 .027756 .022876 .029010 .039241 227. 10 .062805 .044166 .036052 .046410 .058403 250. 80 .084707 .067202 .054374 .070968 .092647 274. 60 .106299 .092766 .074537 .098349 .124706 00 295. .125877 .118330 .094563 .125836 .145882 312. 00 .146683 .147911 .117598 .157746 .163971 329. 00 .163949 .174379 .138102 .186382 .181618 60 342. .181427 .203072 .160227 .217506 .195588 356. 20 .198912 .233795 .183810 .250916 .214706 369. 80 .215849 .265870 .208314 .285889 .222059 383. 40 .232321 .299315 .233749 .322448 .221176 397. 00 .252370 .343077 .266876 .370407 .239259 414. 00 .266473 .377325 .292643 .408066 .228235 427. 50 .283511 .421681 .325871 .456957 .233824 444. 50 .235294 .376596 .311918 .392638 .232353 458. 10 .279832 .430556 .355393 .449670 .243137 471. 70 .315379 .471541 .388258 .493090 .251471 481. 90 .364805 .525615 .431395 .550524 .286275 495. 50 .399845 .560798 .459198 .588064 .324510 505. 70 .429851 .587278 .479789 .616536 .386139 515. 90 .448357 .597254 .486870 .627702 .477451 526.00 .445692 .579092 .471047 .609276 .561765 536. 20 .414022 .525030 .426173 .552983 .605882 546. 40 .351351 .435121 .352468 .458760 .590196 556. 60 .263082 .318359 .257369 .335994 .483333 566. 80 .169709 .200783 .162001 .212114 .280882 577. 00 .081032 .093104 .074930 .098484 .069328 590. 60 .038554 .042177 .033800 .044710 .011475 614. 40 .033719 .034769 .027721 .036952 .004596 644. 90 .033079 .030979 .024494 .033062 .003042 699. 30 .000000 .000000 .000000 .000000 .003042 801. 20  Syncrude pitch 150 T/min, 800 °C final temperature RUN# Syn08 E x p e r i m e n t a l 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 .001129 -8.944 -9.092 -9.181 -9.327 2.158 2.011  YFM .7  .001153 .001171 .001190 .001203 .001217 .001230 .001244 .001258 .001273 .001288 .001311 .001335 .001368 .001394 .001421 .001449 .001489 .001530 .001574 .001620 .001682 .001749 .001821 .001900 .001986 .002120 Fitting 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  -9. 102 -9. 317 -9. 581 -9. 764 -9. 942 -10. 107 -10. 243 -10. 351 -10. 437 -10. 513 -10. 610 -10. 695 -10. 808 -10. 787 -10. 892 -11. 001 -11. 162 -11. 349 -11. 553 -11. 784 -12. 125 -12. 481 -12. 947 -13. 438 -13. 882 -14. 878  -9. 290 -9. 445 -9. 605 -9. 715 -9. 828 -9. 941 -10. 058 -10. 177 -10. 300 -10. 426 -10. 619 -10. 818 -11. 098 -10. 634 -10. 784 -10. 938 -11. 158 -11. 387 -11. 630 -11. 888 -12. 231 -12. 603 -13. 004 -13. 442 -13. 916 -14. 663  -9. 333 -9. 544 -9. 804 -9. 984 -10. 160 -10. 322 -10. 456 -10. 560 -10. 644 -10. 717 -10. 810 -10. 892 -10. 999 -11. 086 -11. 184 -11. 287 -11. 439 -11. 617 -11. 813 -12. 036 -12. 366 -12. 711 -13. 167 -13. 648 -14. 083 -15. 064  2. 002 1. 788 1. 526 1. 344 1. 166 1. 003 867 760 675 600 504 420 309 124 227 334 491 674 876 -1. 104 -1. 440 -1. 793 -2. 255 -2. 743 -3. 185 -4. 176  -9. 521 -9. 672 -9. 829 -9. 936 -10. 046 -10. 157 -10. 272 -10. 387 -10. 508 -10. 631 -10. 820 -11. 014 -11. 288 -10. 926 -11. 072 -11. 222 -11. 434 -11. 657 -11. 893 -12. 145 -12. 477 -12. 839 -13. 228 -13. 654 -14. 115 -14. 840  .  -.  r e s u l t s i n the e n t i r e temperature range VFCN VFCR VFNT V 000917 000867 000891 020000 034164 030388 034308 070000 386644 330372 396712 320000 907488 764888 938068 970000 563176 306550 1. 1. 623374 1. 630000 1. 2. 850000 2. 694018 2. 143508 2. 583332 4. 820000 4. 276303 3. 369713 4. 085792 7. 260000 6. 553257 5. 123781 6. 242050 10. 660000 9. 663453 7. 513555 9. 182153 13. 840000 12. 900822 10. 003840 12. 240464 17. 410000 16. 819236 13. 031557 15. 943453 21. 390000 21. 474008 16. 658307 20. 348467 25. 520000 26. 901856 20. 942446 25. 498709 28. 720000 31. 342672 24. 502038 29. 726985 32. 080000 36. 156700 28. 427027 34. 329008 35. 380000 28. 033573 23. 801644 27. 333528 39. 830000 36. 320795 31. 011915 35. 421705 43. 350000 43. 062424 37. 006635 42. 024491 47. 390000 50. 205200 43. 520235 49. 050957 50. 520000 55. 048013 48. 054191 53. 837831 54. 040000 59. 830187 52. 646333 58. 587362 58. 280000 64. 382933 57. 147460 63. 134447 63. 460000 68. 766400 61. 629215 67. 541374 69. 320000 72. 755015 65. 867186 71. 582191 75. 110000 76. 412080 69. 927104 75. 320122 80. 170000 79. 617170 73. 668578 78. 629972 85. 600000 83. 505731 78. 543562 82. 705429 88. 350000 86. 344521 82. 480538 85. 744533 89. 590000 88. 711449 86. 251528 88. 354415 89. 970000 90 211576 89. 281375 90. 095072 90. 300000 90 613468 90. 562245 90. 609490 90. 620000 90 620000 90 620000 90. 620000  .  .  1. 814 1. 660 1. 501 1. 392 1. 280 1. 168 1. 051 934 812 687 494 297 019 269 486 714 954 -1. 210 -1. 549 -1. 918 -2. 314 -2. 748 -3. 218 -3. 957 -6. 081 -9. 310  .  -.  -.  VFFM 007966 134342 896348 1. 746136 2. 669480 3. 949116 5. 642770 7. 845678 10. 591947 13. 249213 16. 286221 19. 723079 23. 578196 26. 655275 29. 947086 18. 612215 25. 296279 31. 104254 37. 654348 42. 353987 47. 227206 52. 111450 57. 077576 61. 864936 66. 530691 70. 894557 76. 659233 81. 356480 85. 839815 89. 313126 90. 585096 90. 620000  F i t t i n g r a t e dV/dT i n t h e e n t i r e temperature range  .  1 .507 1 .795 1 .742 1 .677 1 .494 1 .280 .965 .658 .364 .171 .063 .261 .415 .479 .517 .605 .715 .800 .956 -1 .121 -1 .309 -1 .676 -1 .906 -2 .406 -3 .021 -3 .387  -  -  1. 643 1. 473 1. 297 1. 176 1. 052 928 • 798 • 668 • 533 • 394 • 182 037 345 297 409 525 690 862 -1. 044 -1. 238 -1. 496 -1. 775 -2. 076 -2. 405 -2. 761 -3. 321  .  -. -. -. -. -. -. -.  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  VDCR  VDCN  VDFM  .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  .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  .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  .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, s.e.e  ko2  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 e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r s f o r both r e a c t i o n s E k2 k i Ei 71347.395 44484.445 5.534 2-Integral 21895.871 69931.248 28659.014 1.207 2-Coats-Redfern 18317.044 70918.682 2.663 40047.550 2-Chen-Nuttall 19815.807 39422.571 2.169 222.056 2-Friedman 18356.762 2  0  D  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 e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r b o t h r e a c t i o n s E k k i Ei 64473.015 24448.637 7.649 2-Integral 20907.935 62943.175 15044.712 1.688 2-Coats-Redfern 17507.079 63977.704 3.717 21585.114 2-Chen-Nuttall 18939.224 0.833 54006.641 3350.699 2-Friedman 12109.801 2  0  o2  s.e.e 2.128091 8.270525 4.639823 11.413135  C A N M E T pitch 100 °C/min., 800 °C  Activation  e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r both r e a c t i o n s k E Ei ki 111143.981 72117.918 26914.040 39.637 2-Integral 72034.563 70720.507 12.482 24063.137 2-Coats-Redfern 100310.634 24.221 71699.067 25429.522 2-Chen-Nuttall 31432193.146 12.635 21904.369 108819.449 2-Friedman o2  2  0  s.e.e. 1.446535 4.703861 1.899520 5.279363  C A N M E T pitch 150 °C/min., 800 °C Activation  e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r both E k i Ei 96651.309 552.339 2-Integral 46648.168 95534.758 304.766 2-Coats-Redfern 45065.482 96377.125 463.684 2-Chen-Nuttall A 46065.844 92011.326 2804.999 2-Friedman 52896.511  reactions k 3510920.010 2529475.085 3296730.811 1699475.805  s.e.e 0.975426 2.908742 1.027556 1.499851  e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r both r e a c t i o n s k E k i Ei 25546.591 67665.168 51.805 30825.690 2-Integral 15973.274 66149.761 22.282 28925.970 2-Coats-Redfern 22714.511 67185.904 38.048 29969.525 2-Chen-Nuttall 101506.600 3875272.258 22436.425 7.251 2-Friedman  s.e.e. 1.941470 5.238812 2.066038 9.746673  2  0  o2  Syncrude Pitch 25 °C/min., 800 °C  Activation  2  0  o2  Syncrude pitch 50 °C/min., 800 °C  A c t i v a t i o n e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r both r e a c t i o n s k ki E Ei 196413.926 298.225 76570.633 2-Integral 37574.160 131230.169 152.170 75271.326 2-Coats-Redfern 36007.909 179430.028 240.377 76200.343 2-Chen-Nuttall 36950.208 34882245.211 28.783 110908.304 2-Friedman 26717.957 Q  2  o2  s.e.e 2.079083 4.555376 1.827761 8.003341  209  Syncrude pitch 100 °C/min., 800 °C  Activation  e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r b o t h r e a c t i o n s Ei k i E2 k2 2-Integral 44166.789 1326.666 65511.067 35233.527 2-Coats-Redfern 42786.603 750.710 63799.493 21122.231 2-Chen-Nuttall 43670.266 1126.495 64938.056 30754.384 2-Friedman 31580.121 99.840 78074.842 166743.612 c  0  s.e.e 2.970666 4.667832 2.683058 8.111536  Syncrude pitch 150 °C/min., 800 °C  Activation  e n e r g i e s and p r e - e x p o n e n t i a l f a c t o r f o r both r e a c t i o n s Ei k i E k 2-Integral 46141.423 2549.212 69808.233 103113.970 2-Coats-Redfern 44831.086 1485.078 68221.838 64209.953 2-Chen-Nuttall 45685.309 2194.201 69303.236 91513.836 2-Friedman 34645.511 248.057 76752.670 216684.308 0  2  o2  S.e.e 2.859655 4.405498 2.586208 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 kineticreactionrate Ink-1/T Integral method 25 "C/min 50°C/min 100 °C/min 150 °C/min 1/T K' 800 - 450 °C 4.23878 3.53565 2.87824 2.70633 0.93183 3.14066 3.70941 2.52511 2.31555 0.97736 2.70507 3.12564 2.13570 1.88462 1.02758 2.22230 2.47863 1.70410 1.40700 1.08324 1.68424 1.75753 1.22308 0.87469 1.14527 1.08081 0.94883 0.68362 0.27771 1.21483 0.39933 0.03553 0.07438 -0.39649 1.29339 -0.37638 -1.00407 -0.61910 -1.16391 1.38282 450 - 50 °C -1.44292 -0.79669 -1.44456 -1.93090 1.38282 -1.12919 -2.02085 -1.70122 -2.20140 1.48553 -1.51504 -2.68962 -2.00096 -2.51531 1.60472 -1.96822 -3.47507 -2.35301 -2.88399 1.74471 -2.50801 -4.41066 -2.77234 -3.32314 1.91146 -3.16189 -5.54398 -3.28030 -3.85510 2.11345 -3.90830 -3.97029 -6.94512 -4.51277 2.36317 -4.99532 -8.72174 ^.70459 -5.34669 2.67982 -6.33755 -11.04810 -5.74729 -6.43866 3.09444  Coats-Redfern method 25 "C/min 1/T K"' 800-450 "C 2.42538 0.93183 2.04236 0.97736 1.61998 1.02758 1.15184 1.08324 0.63009 1.14527 0.04496 1.21483 -0.61585 1.29339 -1.36804 1.38282 450 - 50'C -2.85843 1.38282 -3.08472 1.48553 -3.34732 1.60472 -3.65574 1.74471 -4.02311 1.91146 -4.46812 2.11345 -5.01830 2.36317 -5.71592 2.67982 -6.62940 3.09444  Chen-Nuttall method 25 "C/min 1/T K" 800-450 °C 2.64931 0.93183 2.26088 0.97736 1.83253 1.02758 1.35779 1.08324 0.82867 1.14527 0.23528 1.21483 -0.43486 1.29339 -1.19767 1.38282 450 - 50 °C -2.31640 1.38282 -2.56120 1.48553 -2.84529 1.60472 -3.17894 1.74471 -3.57637 1.91146 -4.05780 2.11345 -4.65299 2.36317 -5.40769 2.67982 -6.39592 3.09444  Friedman method 25 "C/min 1/T K" 800-450 °C 0.98447 0.93183 0.76855 0.97736 0.53044 1.02758 0.26654 1.08324 -0.02759 1.14527 -0.35744 1.21483 -0.72997 1.29339 -1.15400 1.38282 450 - 50'C -2.27891 1.38282 -2.50569 1.48553 -2.76886 1.60472 -3.07795 1.74471 -3.44611 1.91146 -3.89209 2.11345 ^t.44346 2.36317 -5.14259 2.67982 -6.05806 3.09444  1  50°C/min  100 "C/min 150 "C/min  2.80918 2.45877 2.07235 1.64407 1.16674 0.63142 0.02687 -0.66128  3.48004 3.08734 2.65428 2.17431 1.63938 1.03945 0.36194 -0.40927  4.20656 3.67869 3.09658 2.45141 1.73235 0.92594 0.01523 -1.02141  -1.83714 -2.07111 -2.34263 -2.66153 -3.04138 -3.50150 -4.07037 -4.79168 -5.73620  -1.04233 -1.35648 -1.72105 -2.14923 -2.65925 -3.27706 -4.04087 -5.00937 -6.27756  -1.52266 -2.09176 -2.75218 -3.52783 -4.45174 -5.57091 -6.95456 -8.70900 -11.00630  CANMET SINGLE OVERALL MODEL lnk-1/T 700 - 50 °C C-N C-R Integral 1/T K' 0.68931 0.27246 0.92624 1.02758 0.47509 0.06628 0.70466 1.08324 0.23635 -0.16351 0.45771 1.14527 -0.03141 -0.42122 0.18075 1.21483 -0.33379 -0.71227 -0.13202 1.29339 -0.67799 -1.04356 -0.48805 1.38282 -1.07331 -1.42406 -0.89697 1.48553 -1.53208 -1.86562 -1.37151 1.60472 -2.07089 -2.38423 -1.92884 1.74471 -2.71269 -3.00196 -2.59270 1.91146 -3.49013 -3.75024 -3.39686 2.11345 -4.45129 -4.67536 -4.39107 2.36317 -5.67003 -5.84840 -5.65170 2.67982 -7.26590 -7.38442 -7.30243 3.09444  Friedman 0.85065 0.63309 0.39061 0.11868 -0.18843 -0.53800 -0.93951 -1.40544 -1.95267 -2.60450 -3.39409 -4.37027 -5.60805 -7.22885  1  1  1  50 "C/min  100 "C/min 150 "C/min  2.56415 2.21941 1.83923 1,41788 0.94827 0.42161 -0.17317 -0.85019  3.25860 2.87125 2.44410 1.97069 1.44305 0.85132 0.18305 -0,57763  4.03605 3.51280 2.93577 2.29624 1.58347 0.78411 -0.11864 -1.14622  •2.38831 -2.60459 -2.85558 -3.15036 -3.50149 -3.92682 -4.45267 -5.11944 -5.99253  -1.47800 -1.77527 -2.12025 -2.52542 -3.00804 -3.59265 -4.31542 -5.23188 -6.43193  -1.77594 -2.33268 -2.97876 -3.73756 -4.64140 -5.73627 -7.08987 -8.80622 -11.05370  50 "C/min  100 °C/min 150 "C/min  2.06390 1.76810 1.44190 1.08037 0.67743 0.22555 -0.28479 -0.86569  5.06693 4.47092 3.81365 3.08520 2.27331 1.36279 0.33451 -0.83597  4.03326 3.52931 2.97356 2.35762 1.67114 0.90126 0.03180 -0.95788  -2.19688 -2.34648 -2.52009 -2.72399 -2.96687 -3.26108 -3.62481 -4.08602 -4.68995  -1.10676 -1.37736 -1.69139 -2.06022 -2.49953 -3.03170 -3.68963 -4.52387 -5.61626  -0.85881 -1.51230 -2.27065 -3.16131 -4.22221 -5.50733 -7.09615 -9.11074 -11.74870  211  SYNCRUDE PITCH 2-STAGE M O D E L KINETIC reaction rate Ink-1/T Integral method 25 "C/min 50 "C/min 100 "C/min 150 "C/min 1/T K" 800 - 450°C 3.71953 3.12732 3.60600 2.56439 0.93183 3.33718 2.76851 3.18661 2.19378 0.97736 2.91555 2.37282 2.72413 1.78509 1.02758 2.44824 1.93428 2.21155 1.33213 1.08324 1.92741 1.44551 1.64027 0.82729 1.14527 1.34330 0.89736 0.99958 0.26112 1.21483 0.68366 0.27832 0.27603 -0.37828 1.29339 -0.06721 -0.42633 -0.54757 -1.10610 1.38282 450-50°C 0.16910 -0.15558 -0.55165 -1.17957 1.38282 -0.40093 -0.70122 -1.01584 -1.56039 1.48553 -1.06243 -1.33442 -1.55452 -2.00232 1.60472 -1.83935 -2.07809 -2.18718 -2.52136 1.74471 -2.76478 -2.96391 -2.94078 -3.13961 1.91146 -3.88578 -4.03694 -3.85364 -3.88852 2.11345 -5.27170 -5.36355 -4.98224 -4.81441 2.36317 -7.02903 -7.04567 -6.41327 -5.98842 2.67982 -9.33014 -9.24830 -8.28713 -7.52573 3.09444  Coats-Redfern method 25 "C/min 1/T K" 800 - 450 "C 0.93183 2.26465 0.97736 1.90234 1.02758 1.50280 1.08324 1.05998 1.14527 0.56645 1.21483 0.01296 1.29339 -0.61212 1.38282 -1.32364 450 - 50 °C 1.38282 -1.70731 1.48553 -2.06466 1.60472 -2.47936 1.74471 -2.96641 1.91146 -3.54655 2.11345 -4.24931 2.36317 -5.11814 2.67982 -6.21980 3.09444 -7.66237  Chen-Nuttall method 25 "C/min 1/T K' 800 - 450•c 2.50061 0.93183 2.13262 0.97736 1.72683 1.02758 1.27707 1.08324 0.77580 1.14527 0.21364 1.21483 -0.42123 1.29339 -1.14389 1.38282 450 - 50'C -1.34581 1.38282 -1.71605 1.48553 -2.14571 1.60472 -2.65033 1.74471 -3.25141 1.91146 -3.97952 2.11345 -4.87969 2.36317 -6.02110 2.67982 -7.51571 3.09444  Friedman method 1/T K 25°C/min 800-450 °C 0.93183 3.79334 0.97736 3.23737 1.02758 2.62428 1.08324 1.94477 1.14527 1.18745 1.21483 0.33812 1.29339 -0.62106 1.38282 -1.71288 450 - 50 °C 1.38282 -1.75058 1.48553 -2.02776 1.60472 -2.34942 1.74471 -2.72720 1.91146 -3.17719 2.11345 -3.72228 2.36317 -4.39619 2.67982 -5.25070 3.09444 -6.36962  1  1  50 "C/min  100 "C/min 150 °C/min  3.55706 3.13970 2.67945 2.16935 1.60083 0.96325 0.24320 -0.57642  3.05557 2.69990 2.30768 1.87297 1.38848 0.84513 0.23150 -0.46699  3.65679 3.27720 2.85862 2.39469 1.87763 1.29775 0.64287 -0.10256  -0.66351 -1.11999 -1.64973 -2.27188 -3.01297 -3.91067 -5.02052 -6.42779 -8.27053  -0.23656 -0.77606 -1.40214 -2.13745 -3.01331 -4.07428 -5.38598 -7.04918 -9.22706  0.09500 -0.46940 -1.12436 -1.89360 -2.80988 -3.91980 -5.29202 -7.03197 -9.31034  1  50 "C/min  100 "C/min  3.34835 2.93608 2.48145 1.97756 1.41598 0.78616 0.07489 -0.73474  2.80748 2.45804 2.07270 1.64561 1.16961 0.63578 0.03291 -0.65332  3.42366 3.05000 2.63794 2.18125 1.67226 1.10143 0.45677 -0.27703  -0.96399 -1.40883 -1.92506 -2.53135 -3.25353 -4.12835 -5.20989 -6.58128 -8.37702  -0.49543 -1.02402 -1.63742 -2.35786 -3.21599 -4.25550 -5.54065 -7.17020 -9.30401  -0.15327 -0.70712 -1.34984 -2.10469 -3.00384 -4.09301 -5.43957 -7.14699 -9.38275  50 "C/min  100 "C/min  4.93696 4.32950 3.65962 2.91718 2.08971 1.16171 0.11369 -1.07925  3.27364 2.84601 2.37445 1.85180 1.26929 0.61602 -0.12174 -0.96153  3.68381 3.26343 2.79985 2.28605 1.71341 1.07120 0.34593 -0.47963  -1.08406 -1.41413 -1.79717 -2.24704 -2.78291 -3.43202 -4.23453 -5.25210 -6.58455  -0.64897 -1.03911 -1.49186 -2.02360 -2.65698 -3.42422 -4.37277 -5.57551 -7.15044  -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-  25°C/rrnfin*stage SD°C/rrin, First stage 1CD°C/rrirv First stage 150°C/mi\firststage 25°C/mn Second stage 5D°Orrin, Second stage 100°arrin,Secord stage 1S)C/rrir\ Second stage  3 0-  0  V  -2-  £  -6-8-10-12-  -1— 1.0  I  1.5  20  25  1/T 1000- *K' 1  3.0  1  Figure G. 1 C A N M E T pitch pyrolysis kinetic reaction rate as a function of temperature at different heating rates andfinaltemperature 800 °C with 2-stage Coats-Redfern method  213  1/T 1000- *K 1  _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' *K" 1  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  25C/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 1S0C/rrin, Second stage 0  420-  o  V  c  E  -2-  .4-6•8-10-12-  1.0  1.5  25  20  1/T 1000- *K' 1  1  -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-  25°(7nin, First stage go^amn, First stage 1ffl°C/rrin, First stage 1SD°C/rrin, First stage 25°arrin Second stage SOC/mt\ Second stage •KD'Onin, Second stage 150°CArin, Secondstage  4-  2H  0  0 V c  -2  1  -10J  -12  1.0  I—  - I — 20  1.5  1fl-  lOOO-^K  25  3.0  -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  1.0  .  1  1.5  .  1  .  !  20  25  1/T 1000- *K1  .  1  3.0  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 t min 0.01 2.01 3.42 4.15 5.02 6.02 7.02 8.03 9.03 10.03 11.03 12.03 12.50 13.04 13.50 14.04 14.57 15.04 15.51 15.91 16.24 16.58 16.98 17.38 17.71 18.00 18.31 18.65 19.05 19.52 20.05 21.05 22.05 23.99 26.00 28.00 30.00  Vexp 0.04 0.06 0.50 1.02 2.17 3.86 5.57 7.59 9.83 12.08 14.48 17.33 18.70 20.65 22.55 25.09 27.59 30.75 34.04 37.35 40.31 43.67 48.26 53.52 58.43 63.51 67.42 71.52 74.86 77.16 78.62 79.70 80.03 80.29 80.52 80.72 80.84  Vmod 0.00 0.04 0.13 0.24 0.45 0.88 1.60 2.75 4.49 7.00 10.45 14.97 17.47 20.63 23.64 27.36 31.32 34.95 38.69 41.95 44.60 49.98 56.32 62.24 66.67 70.01 73.09 75.69 77.93 79.52 80.40 80.81 80.84 80.84 80.84 80.84 80.84  Syncnide pitc 1 800 °C 25°C/min tmin 0.00 1.00 2.01 3.01 4.01 5.01 6.02 7.02 8.02 9.02 10.02 11.03 12.03 13.03 14.03 15.04 16.04 16.51 17.04 17.51 17.98 18.44 18.78 19.05  Vexp 0.10 0.15 0.19 0.60 1.00 1.86 3.27 5.63 8.60 12.65 17.69 23.58 29.64 35.84 41.51 46.95 52.40 55.44 59.57 63.81 68.73 74.31 78.47 81.64  Vmod 0.00 0.02 0.06 0.18 0.46 1.04 2.18 4.23 7.67 13.01 20.71 30.93 43.21 56.42 68.85 78.83 62.72 69.40 76.10 80.89 84.61 87.27 88.59 89.37  50°C/min tmin 0.00 0.98 1.52 2.05 2.50 2.99 3.52 4.01 4.50 4.99 5.52 6.01 6.50 6.99 7.30 7.53 7.75 7.97 8.15 8.24 8.42 8.60 8.82 9.04 9.35 9.66 9.89 10.11 10.64 11.49 12.78 15.00  Vexp 0.32 0.31 0.40 1.06 2.01 3.37 4.96 6.64 8.42 10.43 12.62 14.76 17.41 20.81 23.70 26.51 29.70 33.18 36.47 38.20 42.01 46.10 52.05 58.55 67.70 74.02 76.48 77.95 79.28 79.95 80.15 80.79  Vmod 0.00 0.02 0.05 0.12 0.22 0.43 0.81 1.38 2.25 3.50 5.43 7.84 10.96 14.84 17.73 19.99 22.40 24.96 27.39 29.60 34.30 39.31 45.84 52.43 61.14 68.59 72.78 75.92 79.80 80.77 80.79 80.79  50°C/min tmin 0.03 1.00 2.29 3.03 3.53 4.09 4.50 5.01 5.52 6.02 6.48 6.94 7.40 7.91 8.23 8.60 8.83 9.02 9.16 9.39 9.62 9.80 10.08 10.49  Vexp 0.14 0.19 0.48 1.52 2.76 5.23 7.85 11.99 17.06 22.76 28.37 34.00 39.55 45.63 49.93 56.23 61.49 66.50 70.62 77.79 83.51 86.62 88.85 89.66  Vmod 0.00 0.03 0.37 1.12 2.20 4.26 6.67 10.94 17.02 25.09 34.08 44.25 54.88 66.08 45.92 56.23 62.52 67.33 70.70 75.77 80.08 82.90 86.12 88.98  100°C/min Vexp tmin 0.01 0.09 0.99 0.25 1.26 0.57 1.49 1.25 1.77 2.41 2.00 3.67 2.27 5.33 2.51 7.10 2.78 9.65 3.01 12.14 3.25 14.86 3.52 18.31 3.79 22.54 4.02 27.11 4.22 32.19 4.37 37.20 4.49 41.82 4.61 47.51 4.69 51.88 4.76 56.71 4.84 61.61 4.92 66.12 5.00 69.67 5.15 74.33 5.35 77.00 5.62 78.28 6.01 78.82 6.52 78.97 7.02 79.15 7.49 79.30  Vmod 0.00 0.05 0.11 0.21 0.40 0.67 1.16 1.77 2.78 3.97 5.52 7.85 10.83 13.38 19.52 25.62 30.90 36.67 40.71 44.85 49.01 53.12 57.04 64.27 71.35 76.99 79.15 79.30 79.30 79.30  100°C/min tmin Vexp 0.00 0.01 0.51 0.00 1.02 0.08 1.50 0.42 1.77 1.12 2.01 2.05 2.25 3.44 2.45 5.33 2.62 7.45 2.79 9.93 2.93 12.16 3.06 14.63 3.20 17.29 3.33 20.21 3.47 23.23 3.64 26.99 3.78 30.22 3.95 34.10 4.08 37.28 4.22 40.44 4.32 42.92 4.46 46.34 4.56 49.26 4.66 52.57  Vmod 0.00 0.02 0.12 0.54 1.12 1.98 3.36 5.08 7.00 9.45 11.84 14.64 17.88 21.57 25.69 31.42 36.37 42.97 25.56 31.05 35.55 41.98 47.01 52.14  150°C/min tmin 0.01 1.03 1.65 2.35 2.54 2.74 2.89 3.01 3.13 3.21 3.28 3.36 3.44 3.52 3.63 3.75 3.83 4.02 4.49 5.00  Vexp 0.06 0.00 0.78 2.85 7.05 10.84 15.87 21.77 27.11 33.84 39.52 46.40 53.90 60.98 66.75 72.41 75.11 75.95 76.82 77.59  Vmod 0.00 0.15 1.09 5.25 7.45 10.68 16.75 22.70 29.85 35.18 40.82 46.53 52.33 57.70 64.88 70.40 73.05 76.57 77.59 77.59  150°C/min tmin Vexp 0.00 0.02 0.51 0.07 0.99 0.32 1.20 0.97 1.35 1.63 1.51 2.85 1.66 4.82 1.81 7.26 1.96 10.66 2.08 13.84 2.20 17.41 2.32 21.39 2.45 25.52 2.54 28.72 2.63 32.08 2.72 35.38 2.84 39.83 2.93 43.35 3.02 47.39 3.08 50.52 3.14 54.04 3.20 58.28 3.26 63.46 3.32 69.32  Vmod 0.00 0.03 0.35 0.81 1.40 2.32 3.67 5.61 8.27 11.04 14.41 18.45 23.21 27.14 31.45 17.86 23.56 28.44 33.91 37.85 41.96 46.13 50.44 54.69  217  19.25 19.51 19.85 20.25 20.98 21.99 22.99 24.06 24.99 26.00 27.00 28.00 29.00 30.00  84.14 86.99 88.85 89.87 90.46 90.56 90.58 90.75 90.80 90.95 90.90 90.89 91.04 91.03  89.81 90.25 90.60 90.84 91.00 91.03 91.03 91.03 91.03 91.03 91.03 91.03 91.03 91.03  11.00 12.01 12.98 13.99 15.01  89.98 90.22 90.40 90.57 90.70  90.34 90.70 90.70 90.70 90.70  4.76 4.86 4.96 5.07 5.17 5.27 5.41 5.64 5.95 6.49 7.51  56.47 61.34 67.07 73.25 79.27 84.20 88.02 89.67 90.02 90.27 90.58  57.21 62.21 66.98 71.41 75.41 78.91 82.76 87.26 89.80 90.56 90.58  3.39 3.45 3.54 3.63 3.75 3.93 4.26 4.99  75.11 80.17 85.60 88.35 89.59 89.97 90.30 90.62  58.97 63.13 68.98 74.24 80.05 86.01 90.11 90.62  Volatile Yield Predicted via the Single Set Kinetic Parameters for Different Final Temperature 100 "C/min CANMET pitch 750 °C 50.6 0.16 034 151.8 1.04 202.4 1.90 225.8 2.85 249.2 276.4 4.37 6.02 299.8 8.47 327.0 10.95 350.4 14.05 377.6 17.09 401.0 20.48 424.3 25.64 451.6 31.58 474.9 490.5 36.67 502.2 41.70 510.0 45.81 53.18 521.7 55.86 525.6 61.28 533.3 66.20 541.1 71.47 552.8 568.4 75.54 77.50 583.9 78.67 607.3 78.88 626.8 79.06 650.1 79.40 700.7 79.60 750.0  V^.%  0.00 0.06 0.23 0.40 0.67 1.15 1.75 2.76 3.95 5.78 7.81 10.30 13.22 20.70 27.07 32.51 36.40 42.51 44.59 48.72 52.85 58.78 65.81 71.34 76.62 78.64 79.44 79.60 79.60  850 °C 49.3 150.6 197.4 232.5 252.0 291.0 322.1 349.4 376.7 400.1 423.5 446.9 466.3 481.9 497.5 509.2 520.9 532.6 540.4 548.2 556.0 563.8 571.6 591.0 610.6 649.5 700.2 750.8 801.5 850.8  0.00 0.00 0.50 1.35 2.26 4.26 6.55 9.00 11.98 14.61 17.82 21.57 25.85 29.96 34.59 39.07 44.43 50.68 55.22 59.87 64.33 68.12 71.21 75.40 77.19 78.02 78.38 78.58 78.74 79.01  850 °C 51.6 102.2 164.4 201.3 228.9 252.0 277.3 300.4 325.7 348.7 374.1 399.4 424.8 447.8 466.2 482.3 493.8 503.1  Ve,%  V„d%  0.06 0.02 0.48 1.36 2.80 4.80 7.88 11.70 16.76 21.89 28.07 34.44 40.76 46.75 52.50 59.46 65.60 71.20  0.00 0.03 0.37 1.12 2.32 4.03 6.97 10.92 16.99 24.21 34.00 45.21 56.91 66.92 48.40 57.39 63.63 68.36  V.,,%  V„„,%  0.00 0.05 0.20 0.46 0.70 1.49 2.53 3.86 5.67 7.67 10.14 13.10 17.52 23.25 30.04 35.73 41.77 47.98 52.09 56.08 59.87 63.40 66.58 72.79 76.52 78.84 79.01 79.01 79.01 79.01  950 °C 51.1 152.2 175.6 202.8 222.2 249.5 276.7 300.1 327.3 350.6 377.9 401.2 424.6 447.9 467.4 482.9 494.6 506.3 517.9 525.7 533.5 541.3 545.2 552.9 564.6 580.2 595.7 623.0 650.2 751.4 852.5 949.8  V^o/o  V^'/o  0.29 0.53 1.45 2.55 3.79 5.43 7.28 9.17 11.47 13.82 16.81 19.67 23.09 27.46 32.51 37.44 41.67 46.50 52.13 56.46 60.85 65.12 67.09 70.59 74.52 77.73 79.05 80.06 80.33 80.77 81.07 81.23  0.00 0.06 0.11 0.24 0.38 0.68 1.18 1.80 2.83 4.04 5.92 7.99 10.55 13.61 18.39 24.32 29.51 35.24 41.33 45.56 49.82 54.04 56.10 60.04 65.53 71.61 75.98 79.98 81.07 81.23 81.23 81.23  950 °C 51.1 99.7 148.3 182.4 206.7 233.5 257.8 277.2 301.5 325.8 350.2 376.9 401.2 425.5 447.4 464.5 476.6 486.3  V«p%  Vmo.1%  0.21 0.29 0.56 1.52 2.71 5.31 8.42 11.62 16.41 22.06 28.00 34.79 40.74 46.39 52.04 57.61 62.93 67.86  0.00 0.03 0.21 0.65 1.31 2.61 4.61 6.99 11.20 17.09 24.83 35.36 46.24 57.50 67.07 47.64 54.46 59.86  50 "C/min Syncrude pitch 750 °C 50.4 99.9 158.1 190.4 224.9 250.8 276.6 300.3 326.2 349.9 375.8 399.5 425.3 449.0 462.0 474.9 483.5 492.0  V„p%  Va.o.1%  0.03 0.10 0.56 1.46 3.35 5.88 9.79 14.02 19.16 24.83 30.94 36.59 42.40 47.91 51.12 54.96 58.00 61.50  0.00 0.03 0.30 0.82 2.11 3.94 6.90 10.95 17.19 24.73 34.85 45.41 57.38 67.69 46.22 53.45 58.28 62.92  498.6 507.2 515.8 526.6 535.2 546.0 561.1 574.0 599.8 651.6 750.7  64.42 69.23 74.30 80.25 84.12 87.41 89.45 89.93 90.38 90.53 90.96  66.35 70.64 74.54 78.82 81.72 84.68 87.61 89.19 90.59 90.96 90.96  514.6 526.1 537.6 549.1 567.6 599.8 650.5 701.2 749.5 800.2 850.9  78.24 83.85 87.32 88.80 89.49 89.78 90.03 90.23 90.39 90.50 90.61  73.71 78.33 82.14 85.07 88.16 90.24 90.61 90.61 90.61 90.61 90.61  496.1 505.8 513.1 520.4 530.1 542.3 556.8 600.6 651.7 700.3 751.4 800.0 851.1 897.3 952.9  73.42 78.51 82.10 85.05 87.68 88.98 89.49 90.17 90.27 90.65 90.88 90.75 90.97 90.89 91.01  65.09 69.98 73.38 76.48 80.10 83.79 86.97 90.66 91.01 91.01 91.01 91.01 91.01 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 F O R T R A N 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 the entire temperature range with the change of significant digits V V5 V4 V3 V2 T  50.22 100.32 135.40 153.77 175.47 200.52 225.60 250.65 275.70 300.75 325.80 350.85 362.55 375.90 387.60 400.95 414.32 426.00 437.70 447.72 456.07 464.42 474.45 484.45 492.80 500.00 507.85 516.20 526.22 537.90 551.27 576.32 601.37 649.80 699.90 750.00 800.12  040000 060000 500000 1. 020000 2 . 170000 3 . 860000 5 . 570000 7 . 590000 9 . 830000 1 2 . 080000 1 4 . 480000 1 7 . 330000 1 8 . 700000 2 0 . 650000 2 2 . 550000 2 5 . 090000 2 7 . 590000 3 0 . 750000 3 4 . 040000 3 7 . 350000 4 0 . 310000 4 3 . 670000 4 8 . 260000 5 3 . 520000 5 8 . 430000 6 3 . 510000 6 7 . 420000 7 1 . 520000 7 4 . 860000 7 7 .,160000 7 8 .,620000 7 9 .,700000 80.,030000 8 0 .,290000 80..520000 8 0 .,720000 80..840000  .155612 .586071 1.232127 1.734067 2.505345 3.672206 5.173826 7.033928 9.266864 11.868485 14.816680 18.071870 19.682439 21.579050 23.284918 25.271160 27.291778 29.073425 30.865168 32.399281 41.063754 45.483339 50.812486 56.001230 60.123230 63.451378 66.780378 69.923750 73.102690 75.972522 78.231054 80.249473 80.759543 80.839754 80.840000 80.840000 80.840000  .155925 .587093 1.234082 1.736689 2.508926 3.677123 5.180311 7.042167 9.276985 11.880535 14.830612 18.087541 19.698846 21.596222 23.302686 25.289514 27.310609 29.092580 30.884554 32.418790 41.020945 45.439130 50.767717 55.957289 60.081089 63.411572 66.743855 69.891393 73.075913 75.952435 78.217958 80.245260 80.758742 80.839749 80.840000 80.840000 80.840000  .155187 .148259 .584630 .561560 1.229293 1.184507 1.730211 1.669683 2.499990 2.416585 3.664705 3.548955 5.163737 5.009436 7.020847 6.822622 9.250461 9.004178 11.848537 11.551843 14.793103 14.445798 18.044737 17.648988 19.653715 19.236753 21.548593 21.108932 23.253032 22.795035 25.237764 24.760882 27.257016 26.763636 29.037604 28.531953 30.828418 30.312592 32.361847 31.839053 40.747694 42.488916 45.158472 46.936603 50.485304 52.261405 55.681786 57.400808 59.818183 61.447106 63.164263 64.686734 66.517930 67.898483 69.692140 70.899546 72.911869 73.895247 75.830062 76.553672 78.138651 78.599589 80.219989 80.361467 80.753972 80.779498 80.839723 80.839849 80.840000 80.840000 80.840000 80.840000 80.840000 80.840000 220  standard deviation for each method above 1.425523  1.417689  the s.e.e. relative change in % with 5, 4, 3, 2 digits .005239 .554801  1.400758  1.742416 2 6 . 6 6 3 7 0 9  Fitting results in the entire temperature range with the change of k T 50. 22 100. 32 135. 40 153. 77 175. 47 200. 52 225. 60 250. 65 275. 70 300. 75 325. 80 350. 85 362. 55 375. 90 387. 60 400. 95 414. 32 426. 00 437. 70 447. 72 456. 07 464. 42 474. 45 484. 45 492. 80 500. 00 507. 85 516. 20 526. 22 537. 90 551. 27 576. 32 601. 37 649 80 699 90 750 00 800 12  V 040000 060000 500000 1. 020000 2. 170000 3. 860000 5. 570000 7. 590000 9.830000 12. 080000 14. 480000 17. 330000 18. 700000 20. 650000 22. 550000 25. 090000 27. 590000 30. 750000 34. 040000 37. 350000 40. 310000 43. 670000 48. 260000 53. 520000 58. 430000 63. 510000 67. 420000 71. 520000 74. 860000 77. 160000 78. 620000 79. 700000 80 030000 80 290000 80 520000 80 720000 80 840000  VM2 152449 574217 1. 207336 1. 699306 2. 455396 3. 599583 5. 072560 6.898025 9.090637 11. 647051 14. 546404 17. 750740 19. 337387 21. 206920 22. 889470 24. 849839 26. 845596 28. 606588 30. 378797 31. 897207 40. 493876 44. 891975 50. 210075 55. 406352 59. 549749 62. 907169 66. 278446 69 476530 72 729934 75 690399 78 045114 80 188263 80 747584 80 839682 80 840000 80 840000 80 840000  VM1 154003 580055 1.219562 1. 716460 2. 480063 3. 635475 5. 122645 6.965290 9.177923 11. 756806 14. 680464 17. 910142 19. 508723 21. 391776 23. 085980 25. 059293 27. 067503 28. 838855 30. 620875 32. 147183 40. 778982 45. 188016 50. 511906 55. 704705 59. 837641 63. 180613 66. 530923 69 701777 72 918005 75 833076 78 139443 80 219546 80 753756 80 839720 80 840000 80 840000 80 840000  standard deviation for each method above 1.477343  1.440612  VFT 155557 •585893 1. 231787 1. 733611 2. 504722 3. 671350 5. 172698 7. 032493 9.265102 11. 866387 14. 814254 18. 069141 19. 679582 21. 576059 23. 281823 25. 267963 27. 288498 29. 070089 30. 861791 32. 395883 41. 062074 45. 481620 50. 810763 55. 999558 60. 121640 63. 449888 66. 779023 69. 922559 73. 101715 75. 971800 78. 230589 80. 249327 80 759516 80 839754 80 840000 80 840000 80 840000  VP1 157111 591731 1. 244009 1. 750758 2. 529373 3. 707208 5. 222717 7. 099636 9.352175 11. 975795 14. 947773 18. 227739 19. 849964 21. 759771 23. 477003 25. 475853 27. 508585 29. 300295 31. 101552 32. 643312 41. 343165 45. 772805 51. 106675 56. 290952 60. 401799 63. 715057 67. 022820 70. 138965 73. 281164 76. 106680 78. 318659 80. 277679 80. 764891 80. 839783 80 840000 80 840000 80 840000  VP 2 158665 597568 1. 256230 1. 767901 2. 554017 3. 743050 5. 272703 7. 166718 9.439143 12. 085028 15. 081021 18. 385936 20. 019872 21. 942914 23. 671520 25. 682965 27. 727767 29. 529477 31. 340163 32. 889478 41. 622269 46. 061593 51. 399671 56. 578928 60. 678169 63. 976182 67. 262391 70. 351080 73. 456452 76. 237823 78. 403756 80. 304670 80 769907 80 839809 80 840000 80 840000 80 840000  1.425819  1.432991  1.461189  .518604  2.496592  the s.e.e. relative change in % with k: -/+1% and -1+2% 3.629687  1.053194  1.805715  .015486  .  .  100 •  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  90807060'  CD  S° o >  50-l 40-\ 30 H 20 H 10 OH —I  0  100  200  300  807060'  0)  JS o  1 —  500  600  700  800  900  500  600  700  800  900  T °C  10090-  '  400  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  50 40-  > 30' 20100100  200  300  400  T °C 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 8.011-13.157 mg at 7.774-12.034 mg at heating rate 50 °C/min heating rate 100 °C/min Vt=io% Vt=o% Vt=o% Vt=io% 81.01 80.57 80.43 80.12 Average V yield 0.5 0.3 0.7 0.8 Standard Deviation 8 8 5 5 No. of Data Points  223  

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