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KALIAPPAN Bachelor of Engin PREDICTION OF PRESSURE-TEMPERATURE PHASE ENVELOPES OF MULTICOMPONENT HYDROCARBON SYSTEMS By C .. S._ KALIAPPAN I/ Bachelor of Engineering University of Madras Madras, India 1961 Master of Engineering Indian Institute of Science Bangalore, India 1963 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY July, 1971 OKl.AHONll\ STATE Ut·.;!VERSITY LIBRARY APR 3 1975 PREDICTION OF PRESSURE-TEMPERATURE PHASE ENVELOPES OF MULTICOMPONENT HYDROCARBON SYSTEMS Thesis Approved: Dean of the Graduate College ACKNOWLEDGMENTS I wish to express my sincere gratitude to my thesis adviser, Dr. A. M. Rowe, Jr., for his encouragement and guidance throughout this study. He has been extremely helpful in solving various problems which arose during the course of this work. I am deeply indebted to my advisory committee members, Drs. J. A. Wiebelt, R. J. Schoppel, and R. L. Robinson, Jr., for their exceptional guidance and constructive suggestions. I am grateful to the School of Mechanical and Aerospace Engineering for the financial support during my attendance at Oklahoma State University. I offer my thanks to Margaret Estes for the typing of this manuscript. I would like to take this opportunity to express my appreciation to Watumull Foundation, Hawaii, for their financial aid to prepare this thesise Finally, I sincerely thank my wife, Padmavathi, and daughter, Sivakami, and my parents whose understanding, encouragement, and sacrifice were invaluable in the preparation of this dissertation. TABI.E OF CONTENTS Chapter Page I. INTRODUCTION • 1 II. PHASE DIAGRAMS 6 2.1 Phase Diagrams • • • • • 6 2.2 One Component Systems • • • • 6 2.3 Two Component Systems 7 2.4: Systems Containing Three or More Components 10 III. LITERATURE SURVEY 15 IV. DEVELOPMENT OF CORRELATIONS 22 4:. 1 Prerequisites for the Solution • 22 4:.2 K-f actors • • • • • • • • • • • • • • • • • 22 4:. 3 K-factors for the Heptane Plus Fraction 27 4:. 4: K-f actors for Intermediate Convergence Pressures • 29 4:.5 Critical Pressure and Critical Temperature Correlations • • • • 29 V. GENERATION OF PHASE ENVELOPES 5.1 General • • • • • • • 4:2 5.2 Two Component Systems 4:3 5.3 Three Component Systems 48 5. 4: Systems Containing More Than Three Components 53 5.5 Computer Program • 55 VI. RESULTS 59 6.1 Calculations Performed • 59 6.2 Binary Systems • , • • • • • • 59 6.3 Systems Containing Three or More Components 65 VII. CONCLUSIONS AND RECOMMENDATIONS 85 BIBLIOGRAPHY 88 APPENDIX A--SUBROUTINE FLASH APPENDIX B--SUBROUTINE AVALK 101 Chapter Page APPENDIX C--SUBROUTINE EXTRAP 105 APPENDIX D--SUBROUTINE CVPR 111 APPENDIX E--SUBROUTINE FRAN 115 APPENDIX F--SUBROUTINE VECTEM • 118 APPENDIX G--STEPS FOR THE CALCULATION OF CONVERGENCE PRESSURE BY CRITICAL COMPOSITION METHOD 12~ APPENDIX H--MATHEMATICAL PROOF SHOWING CONVERGENCE PRESSURE IS A PHASE RULE VARIABLE • • • • • • • • • • • 127 APPENDIX !--CALCULATED PRESSURE-TEMPERATURE PHASE ENVELOPES • 132 v LIST OF TABLES Table Page I. Summary of Experimental Work Done on Phase Behavior of Binary and Ternary Systems • • • • • • • • • • • 16 II. Constants for Critical Pressure Correlations 33 III. Binary Temperature Coefficients for the Critical Temperature Correlations 35 IV. Constants for Calculating the Critical Pressure of the Mixtures 39 V. Constants for Calculating the Critical Temperature of the Mixtures • • • • • • • • • • • • • • • 41 VI. Calculated Phase Envelope Data for Methane/Ethane System 61 VII. Calculated Phase Envelope Data for Methane/n Heptane System 62 VIII. Calculated Phase Envelope Data for Ethane/n Pentane System • • • • • • • • • • • • • • • • • • • • • 64 IX. Calculated Phase Envelope Data for Ethane/Propane/ n Pentane System • • • • • • • • • • • • • 67 x. Calculated Phase Envelope Data for Ethane/Propane/ n Butane/n Pentane System • • • • • • • • • • • • 70 XI. Calculated Phase Envelope Data for Ethane/Propane/ n Butane/n Pentane/n Hexane System • • • • • • • 72 XII. Calculated Phase Envelope Data for Methane/Ethane/ Propane/n Butane/n Pentane/n Hexane System 74 XIII. Calculated Phase Envelope Data for a Natural Gas System 76 XIV. Calculated Phase Envelope Data for a Mixture of Natural Gas and Natural Gasoline System • . 77 XV. Calculated Phase Envelope Data for a Natural Gas System (Molecular Weight of c7+ = 114.22) • • • • • • • • • 79 vi Table Page XVI. Calculated Phase Envelope Data for a Gas Condensate Reservoir Fluid (Molecular Weight of c7+ = 167) • • • • • Bo XVII. Calculated Phase Envelope Data for a Gas Condensate Reservoir Fluid (Molecular Weight of c7+ = 114) • • • • • 82 XVIII. Calculated Phase Envelope Data for a Naturally Occurring Hydrocarbon Mixture • • • • • • • • 83 LIST OF FIGURES Figure Page 1. Pressure-Temperature Phase Envelope of a Multicomponent System • • • • • • . 3 2~ Pressure-Temperature Diagram for One Component System - Ethane • • • • • • 8 3. Pressure-Temperature Diagram for a Two Component System 8 4. Pressure-Temperature-Composition Diagram of a Two Component System • • • • • • • • • • • • • 11 5. Phase Envelope for a Multicomponent System • 12 6. Critical Pressure Locus of Methane/Propane System 32 7. Locus of Slopes Joining A and Constant Weight Fraction Points . 32 8. Compositions for Determining Convergence Pressures for High Pressure States . 49 9. Compositions for Determining Convergence Pressures for Low Pressure States . 50 10. Vapor Pressure Chart • • 50 11. Effect of Convergence Pressure Error on Low Pressure K-factors • • • • • • • • • • • • • • • • • • • • • • 12. Probable Phase Diagram at Very High Pressure • . 13. General Flow Diagram for the Calculation of Phase Envelopes 56 14. Flow Diagram for the Calculation of Dew Point Pressure Corresponding to Critical Point - Method A • • 58 15. Flow Diagram for Calculating the Dew Point Locus • . 58 16. Flow Diagram for Calculating the Bubble Point Locus 58 17. Pressure-Temperature Phase Envelopes for Methane/Ethane System (Concentration of Methane = 0~7000; Concentration of Methane = 0.5002) • • • • • • • • • • • • • • • • • • 6o viii Figure Page 18. Pressure-Temperature Phase Envelope for Methane/n Heptane System • • • • • • 6o 19. Pressure-Temperature Phase Envelopes for Ethane/n Pentane System • • • • • • 63 20. Pressure-Temperature Phase Envelope for Ethane/Propane/ n Pentane System • • • • • • • • • • • • • • • • 66 21. Pressure-Temperature Phase Envelope for Ethane/Propane/ n Butane/n Pentane System • • • • • • • • • • • • • • 69 22. Pressure-Temperature Phase Envelope for Ethane/Propane/ n Butane/n Pentane/n Hexane System • • • • • • • • • • 71 2J. Pressure-Temperature Phase Envelope for Methane/Ethane/ Propane/n Butane/n Pentane/n Hexane System • • • • • • 73 24. Pressure-Temperature Phase Envelope for a Natural Gas System • 75 25. Pressure-Temperature Phase Envelope for a Mixture of Natural Gas and Natural Gasoline System • • • • • • • • • • • • • • 75 26. Pressure-Temperature Phase Envelope for a Natural Gas System (Molecular Weight of c7+ = 114.22) • • • • • • 78 27. Pressure-Temperature Phase Envelope for a Gas Condensate Reservoir Fluid (Molecular Weight of c7+ = 167) 78 28. Pressure-Temperature Phase Envelope for a Gas Condensate Reservoir Fluid (Molecular Weight of c7+ = 114) 81 29. Pressure-Temperature Phase Envelope for a Naturally Occurring Hydrocarbon Mixture . 81 JO. Composition Diagram Illustrating the Regions of Applicability of Flash Calculation . 98 J1. The Nature of the Function f(V) . 98 J2. K-factor Data for Methane/Ethane/n Pentane at 100°F 107 JJ. Ternary Phase Diagram of a Three Component System . 113 J4. Compositions Used by Subroutine VECTEM •• 120 35. Pressure-Temperature Phase Envelopes for Methane/Ethane System (Concentration of Methane = 0.9750; Concentration of Methane = 0.9250; Concentration of Methane = 0.8516) 1JJ Figure Page 36. Pressure-Temperature Phase Envelopes for Methane/Ethane System (Concentration of Methane = 0.3002; Concentration of Methane 0.1498; Concentration of Methane = 0.0500) . 133 37. Pressure-Temperature Phase Envelopes for Methane/Propane System . 134 38. Pressure-Temperature Phase Envelopes for Methane/n Butane System . 135 39. Pressure-Temperature Phase Envelopes for Methane/n Pentane System . 135 40. Pressure-Temperature Phase Envelopes for Ethane/Propane System . 136 41. Pressure-Temperature Phase Envelopes for Ethane/n Butane System . 136 42. Pressure-Temperature Phase Envelopes for Ethane/n Heptane System . 137 43. Pressure-Temperature Phase Envelopes for Propane/n Butane System . 13S 44. Pressure-Temperature Phase Envelopes for Propane/n Pentane System . 139 45. Pressure-Temperature Phase Envelopes for n Butane/n Heptane System . 140 46. Pressure-Temperature Phase Envelopes for n Pentane/n Heptane System . 141 47. Pressure-Temperature Phase Envelope for Methane/Ethane/ n Butane System . 142 48. Pressure-Temperature Phase Envelope for Ethane/n Pentane/ n Heptane System . 142 49. Pressure-Temperature Phase Envelope for Propane/n Butane/ n Pentane System . 143 50. Pressure-Temperature Phase Envelope for Propane/n Butane/ n Pentane/n Hexane System . 144 51. Pressure-Temperature Phase Envelope for Methane/Ethane/ Propane/n Butane/n Pentane System . 144 v NOMENCLATURE B = Boiling point C = Constant CP = Critical point F = Number of independent phase rule variables K = Equilibrium constant, K-factor M Molecular weight n Number of components in a mixture P System pressure PT = Operating pressure PK Assumed convergence pressure PKT = Calculated convergence pressure
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