,.t· o-,. !-->. - C''-~ ' .. I ' A THEORETICAL STUDY OF THE KINETICS OF POLYETHYLENE REACTOR DECOMPOSITIONS by GARY MILO GARDNER, B.S. in Ch.E. A THESIS IN CHEMICAL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN CHEMICAL ENGINEERING Approved Accepted August, 1975 AC ~0~ 13 _,. I{; 7~ No,~~ Cnp. )... ACKNOWLEDGMENT The author wishes to express his sincere appreciation to Dr. W. J. Huffman for his guidance and expertise in this endeavor. His assistance in research and academic affairs was the most anyone could hope for. Special thanks to Dr. D. C. Bonner for giving a lot of extra time when it was desperately needed. The author acknowledges the Gulf Oil Foundation for their financial support. i i TABLE OF CONTENTS Page ACKNOWLEDGEMENT. ii LIST OF TABLES . v LIST OF FIGURES. vi CHAPTER I INTRODUCTION. 1 Industrial Process ... 1 Investigations On Reactor Stability . 3 Effects of Operating Variables ... 4 CHAPTER II MATHEMATICAL MODELING TECHNIQUE ... 8 Reactions Affecting the Overall Polymerization Rate . 8 The Polymerization Rate Expression. 9 Polymerization Rate Constants . 11 Values of Kinetic Parameters .. 13 Material and Energy Balances. • • . 16 Genera 1 Fonn of the Materia 1 and Energy Equations. 16 Linearization of the Material and Energy Balances. 17 Analytical Solution and Stability Criteria. 21 Computer Simulation ........ 25 CHAPTER III APPLICATION TO A POLYETHYLENE REACTOR . • • • • • 27 Steady States of a Polymerization Reaction .. • • 29 Transient Responses of the Stability Regions. 34 Transient Responses in the General Operating Region . 41 Perturbation Analysis .......... 47 Effect of Feed Stream Impurities . 53 iii Page Effect of Initiator Choice on Stability .... 56 Effect of Thermal Decomposition of Ethylene .. 58 Reactor Response to Changes in Viscosity and Pressure 59 Effect of Viscosity and Diffusion-Limited Termination . 59 Effect of Pressure ..... 67 CHAPTER IV CONCLUSIONS AND RECOMMENDATIONS .. 72 Conclusions .. 72 Recommendations . 73 Reactor Operation. 73 Future Investigations .. 73 LIST OF REFERENCES . 74 NOMENCLATURE . 78 APPENDIX A ULTIMATE REACTION CONDITIONS ATTAINED DURING A POLYETHYLENE REACTOR DECOMPOSITION ........ 81 APPENDIX B REACTOR OPERATING PARAMETERS AND KINETIC DATA. 83 Reactor Operating Conditions and Physical Constants . 84 APPENDIX C FUNCTIONAL RELATIONSHIP OF THE TERMINATION RATE CONSTANT TO VISCOSITY AND PRESSURE EFFECTS . 88 Viscosity Effect on Initiator Concentration . 89 Effect of Pressure on Feed Variations ... 91 Viscosity Effect to the Transient Responses . 92 APPENDIX D STEADY STATES FOR A POLYMERIZATION REACTION. 94 APPENDIX E COMPUTER SIMULATIONS . 96 iv LIST OF TABLES Table Page I PARAMETERS FOR THE STABILITY REGIONS. • 40 II PARAMETERS FOR TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS CONCENTRATIONS. • . • . 46 III PARAMETERS FOR TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS TEMPERATURES. 52 IV EFFECT OF ACETYLENE CONCENTRATION ON THE STEADY­ STATE PARAMETERS ................• . 55 v EFFECT OF VISCOSITY CHANGES ON THE INITIATOR CONCENTRATION . 62 VI EFFECTS OF CHANGES IN OPERATING PRESSURE ON THE STEADY -STATE PARAMETERS . 68 A-I ULTIMATE REACTION CONDITIONS ATTAINED DURING A POLYETHYLENE REACTOR DECOMPOSITION ...... 82 B-I REACTION CHEMISTRY AND KINETICS OF POLYETHYLENE DECOMPOSITIONS ................ 85 v LIST OF FIGURES Figure Page 1 POSSIBLE SEQUENCE FOR INITIATION OF A POLYETHLYENE DECOMPOSITION. 6 2 SOLUTION OF MATERIAL AND ENERGY BALANCES FOR REVERSIBLE EXOTHERMIC REACTION. 22 3 UNSTEADY STATE ANALOG SCHEME . 26 4 STEADY STATES OF A POLYMERIZATION REACTION . 30 Sa TRANSIENT RESPONSES OF THE STABILITY REGIONS . 36 Sb TRANSIENT RESPONSES OF THE STABILITY REGIONS . 37 Sc TRANSIENT RESPONSES OF THE STABILITY REGIONS . 38 Sd TRANSIENT RESPONSES OF THE STABILITY REGIONS . 39 6a TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS CONCENTRATIONS . 42 6b TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS CONCENTRATIONS . 43 6c TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS CONCENTRATIONS . 44 6d TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS CONCENTRATIONS . 45 7a TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS TEMPERATURES . • • • 48 7b TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS TEMPERATURES . • . • • • 49 7c TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS TEMPERATURES . 50 7d TRANSIENT RESPONSES IN THE OPERATING REGION AT VARIOUS TEMPERATURES . • • • 51 8 ACETYLENE DECOMPOSITION .. • • • 54 vi Figure Page 9 EFFECT OF TEMPERATURE SENSITIVE INITIATORS ... 57 10 VISCOSITY AND PRESSURE EFFECTS ON THE TRANSIENT RESPONSES . 65 B-1 COMPARISON OF DATA FOR DECOMPOSITION OF ETHANE •. • • • 87 D-1 EXTENDED PLOT OF THE STEADY STATES FOR A POLYMERIZATION REACT I ON • • • • • • • • • • • • • • • • • • • • • • • • 9 5 vii CHAPTER I INTRODUCTION Industrial Process The stability and control of the free-radical polymerization of ethylene at high pressures has become an important area of commercial and theoretical interest. Presently, low density polyethylene (LDPE) is produced commercially in a variety of high pressure industrial re­ actors. These processes have been described by Raff and Allison (1956), and Smith (1965). They include continuous stirred tank re­ actors (CSTR), tubular reactors, and several modifications of these basic designs. A high-pressure industrial reactor operates between 15,000 and 45,000 pounds per square inch of pressure. Normal operating tem­ peratures are between 100°C and 300°C (Miles and Briston, 1965). The process requires a feed stream purity in excess of 99.9 percent ethylene (Hahn, Chaptal, and Sialelli, 1974). The initiation of the polymerization process requires primary free radicals. The ethylene feed is accompanied by an initiator which has the ability to generate these free radicals. Oxygen was employed almost exclu­ sively as the pioneer initiator (Ehrlich, Pittilo, and Cotman, 1958; Ehrlich and Pittilo, 1960); however, modern industrial initiators are usually organic compounds (Brandrup and Immergut, 1958). Free-radical polymer chains react to form inactive polymer molecules in the termination step of the process. Termination can 1 2 proceed by recombination or disproportionation, although it is widely recognized in the polyethylene industry that recombination dominates (Woodbrey and Ehrlich, 1963). Chain termination as a result of poisoning reactions can usually be ignored because of the purity of the ethylene feed. The frequency with which polymeric chains terminate is described by the termination rate constant. The value of this term is usually assumed to be constant over moderate ranges of tem­ peratures, densities, and viscosities. The effect of the termination rate constant increases in importance as large deviations of these process parameters are witnessed. Because of the dangers involved, polyethylene decompositions have received significant attention by industrial personnel. The disasterous effects of a decomposition have been monitored, and the magnitude of the explosions is astounding. It is reported that the detonation of an ethylene-air mixture at a pressure of 2.6 kg/cm2 causes explosive damage equivalent to an equal weight of TNT ( 11 Safety in High Pressure Polyethylene Plants .. , 1974). Huffman and Bonner (1974) have provided_th~oret~cal calculations which indicate that the maximum temperatures and pressures resulting from a decomposition could reach 100,000 pounds per square inch and 1950°C. These values were shown to be. dependent upon initial reactor conditions, but were independent of reactor volumes. On the basis of these calculations, the decomposition gas was predicted to contain large percentages of methane, carbon, and possibly ethane. The numerical results of this study are found in Appendix A. 3 Investigations On Reactor Stability Several studies have been undertaken in an effort to analyze the stability of LOPE systems. Important studies have included Hoftyzer and Zwietering (1961), Warden and Amundson (1962), Goldstein and Amundson (1965), Matsuura and Kato (1966), Goldstein and Hwa (1966), Knorr and O'Driscoll (1970), and Agrawal and Han (1974). Hoftyzer and Zwietering (1961) analyzed stability and control of a high-pressure polymerization reactor which was limited by a half-order reaction rate step. Warden and Amundson (1962) evaluated a CSTR with terminated addition polymerization. Knorr and O'Driscoll (1970) utilized a theoretical study by Matsuura and Kato {1966) to analyze the stability of a concentration-dependent, isothermal re­ actor. The Matsuura and Kato {1966) analysis considered the con­ centration stability of liquid-phase autooxidation of isopropyl alcohol. The Goldstein and Amundson (1965) model investigated sta­ bility in two immiscible phases. The effects on product properties of important reactor variables were studied by Goldstein and Hwa (1966). The Agrawal and Han (1974) model is an application to tubular reactors. Polymer reactor designs are generally based on the steady-state analysis of a reactor system, coupled with the transient response of the system to a perturbation in one of the operating parameters. The steady-state character of a homogeneous reactor is generally obtained by simultaneous solutions of the non-linear material and energy balances. The free-radical polymerization kinetics make 4 algebraic manipulation of these equations cumbersome. It is customary, therefore, to linearize the equations utilizing