COEFFICIENT OF ISOTHERMAL OIL COMPRESSIBILITY FOR RESERVOIR FLUIDS BY CUBIC EQUATION-OF-STATE by OLAOLUWA OPEOLUWA ADEPOJU, B.Tech. Chem Engr. A THESIS IN PETROLEUM ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN PETROLEUM ENGINEERING Approved Lloyd Heinze Chairperson of the Committee Shameem Siddiqui Accepted John Borrelli Dean of the Graduate School December, 2006 ACKNOWLEDGEMENTS I extend my profound gratitude to Dr. Akanni Lawal for inspiring me into phase behavior and into this research. Special thanks to Dr. Lloyd Heinze, the chair of my Masters committee and Dr. Shameem Siddiqui for their support. I would like to acknowledge the African Development Bank for awarding me the 2005- 2006 ADB/Japan Fellowship award. I extend my profound appreciation to my family for their support and encouragement. I also acknowledge my colleagues in Texas Tech University for their support. To God be the glory. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS ii ABSTRACT v LIST OF TABLES vi LIST OF FIGURES viii LIST OF ABBREVIATIONS x CHAPTER 1 INTRODUCTION 1.1 Background Information 1 1.2 Importance of isothermal Oil Compressibility 4 1.3 Scope of the Project 9 1.4 Objectives of the Project 9 2 COEFFIECIENT OF ISOTHERMAL OIL COMPRESSIBILITY 2.1 Defining Equations for Isothermal Oil Compressibility 10 2.2 Isothermal Oil Compressibility Correlation and Computation Methods 24 3 DESIGN OF CUBIC EQUATION OF STATE 3.1 Generalized Cubic Equation of State 35 3.2 Characterization of Heavy Petroleum Fractions 43 3.3 Cubic EOS Based Isothermal Compressibility Equation 43 4 ANALYSIS OF PREDICTION RESULTS 4.1 Computing Isothermal Oil Compressibility from Reservoir Fluid Study Report 56 4.2 Predicted Molar Volume from Cubic Equation of State 56 4.3 Predicted Coefficient of Isothermal Oil Compressibility from Cubic iii Equation of State 66 4.4 Discussion of Results 74 5 CONCLUSIONS AND RECOMMENDATIONS 5.1 Conclusions 77 5.2 Recommendations 78 REFERENCES 79 APPENDIX A. DERIVATION OF PR EOS COMPRESSIBILITY FACTOR AND MOLAR VOLUME EQUATION. 83 B. DERIVATION OF PR EOS BASED ISOTHERMAL COMPRESSIBILITY EQUATION. 86 C. DERIVATION OF THE PR EOS ISOTHERMAL GAS COMPRESSIBILITY EQUATION. 88 D. DERIVATION OF THE FLASH CALCULATION ALGORITHM 90 E. MATHEMATICAL CONSISITENCY OF ISOTHERMAL COMPRESSIBILITY ADDITION BELOW BUBBLE POINT PRESSURE. 94 F. RESERVOIR FLUID STUDY REPORT AND ANALYSIS 97 G. RESERVOIR FLUIDS CRITICAL PROPERTIES TABLE 108 H. AVERAGE ABSOLUTE PERCENT DEVIATION (AAPD) 109 I. FORTRAN CODE DOCUMENTATION 116 J. DEVELOPED FORTRAN CODE 120 K. VITA 162 iv ABSTRACT Calculations of reservoir performance for petroleum reservoirs require accurate knowledge of the volumetric behavior of hydrocarbon mixtures, both liquid and gaseous. Coefficient of Isothermal oil compressibility is required in transient fluid flow problems, extension of fluid properties from values at the bubble point pressure to higher pressures of interest and in material balance calculations38, 35. Coefficient of Isothermal oil compressibility is a measure of the fractional change in volume as pressure is changed at constant temperature29. Coefficients of isothermal oil compressibility are usually obtained from reservoir fluid analysis. Reservoir fluid analysis is an expensive and time consuming operation that is not always available when the volumetric properties of reservoir fluids are needed. For this reason correlations have been developed and are being developed for predicting fluid properties including the coefficient of isothermal oil compressibility. This project developed a mathematical model for predicting the coefficient of isothermal oil compressibility based on Peng-Robinson Equation of State (PR EOS). A computer program was developed to predict the coefficient of isothermal compressibility using the developed model. The predicted coefficient of isothermal oil compressibility closely matches the experimentally derived coefficient of isothermal compressibility. v LIST OF TABLES 2.1 Coefficients for the co Correlations 34 4.1 Predicted Molar Volume for Oil Well No. 4, Good Oil Company, Samson, Texas, Bubble Point = 2619.7 psia 57 4.2 Predicted molar volume for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. Bubble Point = 2666.7 psia 60 4.3 Predicted molar volume for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas. Bubble Point = 1689.7 psia 63 4.4 Predicted Coefficient of Isothermal Oil Compressibility for Oil Well No. 4, Good Oil Company. Samson, Texas. Bubble Point = 2619.7 psia 66 4.5 Predicted Coefficient of Isothermal Oil Compressibility for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. Bubble Point = 2666.7 psia. 69 4.6 Predicted Coefficient of Isothermal Oil Compressibility for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas. Bubble Point = 1689.7 psia 72 F.1 Reservoir Fluid Composition for Oil Well No. 4 98 F.2 Molar Volume Determination from Pressure-Volume Relations for Oil Well No. 4 99 F.3 Differential Vaporization data for Oil Well No. 4 100 F.4 Reservoir Fluid Composition for Jehlicka 1A 101 F.5 Molar Volume Determination from Pressure-Volume Relations for Jehlicka 1A 102 F.6 Differential Vaporization data for Jehlicka 1A 103 F.7 Reservoir Fluid Composition for Jacques Unit #5603 104 F.8 Molar Volume Determination from Pressure-Volume Relations for Jacques Unit #5603 105 F.9 Differential Vaporization data for Jacques Unit #5603 106 G.1 Reservoir Fluids Critical Properties 107 vi H.1 The AAPD for the Predicted Molar Volume for Oil Well No. 4, Good Oil Company. Samson, Texas 108 H.2 The AAPD for the Predicted Coefficient of Isothermal Oil Compressibility For Oil Well No. 4, Good Oil Company. Samson, Texas. 109 H.3 The AAPD for the Predicted Molar Volume for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas. 110 H.4 The AAPD for the Predicted Coefficient of Isothermal Oil Compressibility for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas (Using 11 Components). 111 H.5 The AAPD for the Predicted Molar Volume for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. 112 H.6 The AAPD for the Predicted Coefficient of Isothermal Oil Compressibility for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. 113 H.7 The AAPD for the Predicted Coefficient of Isothermal Oil Compressibility for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas (Using 11 Components). 114 vii LIST OF FIGURES 1.1 Pressure-Volume/Compressibility Relationship 7 2.1 Typical Shape of the Isothermal Gas Compressibility of Gas as a Function of Pressure at Constant Reservoir Temperature 11 2.2 Standing and Katz compressibility factors chart 15 2.3 Variation of Reduced Compressibility with Reduced Pressures for Various Fixed values of Reduced Temperature for Natural Gases (0.1< cr <1.0) 18 2.4 Variation of Reduced Compressibility with Reduced Pressures for Various Fixed values of Reduced Temperature for Natural Gases (0.01< cr < 0.1) 18 2.5 Typical Shape of the Isothermal Oil Compressibility as a Function of Reservoir Pressure at Constant Temperatures at Pressures above the Bubble Point Pressure 20 2.6 Typical Shape of the Coefficient of Isothermal Oil Compressibility as a Function of Pressure at Constant Reservoir Temperature 24 2.7 Trube’s Pseudo Reduced Compressibility of Undersaturated Crude Oils 25 2.8 Coefficient of Isothermal Compressibility of Undersaturated Black Oils 27 2.9 Coefficient of Isothermal Compressibility of Saturated Black Oils 29 3.1 Volumetric Behavior of Pure Compounds by Van der Waal Cubic EOS 37 3.2 Reservoir Oil at Pressure above the Bubble Point Pressure 44 3.3 Reservoir Oil at Pressure below the Bubble Point Pressure 47 3.4 Schematic diagram of Flash Liberation Experiment 49 4.1 Predicted Molar Volume for Oil Well No- 4, Good Oil Company. Samson, Texas (Model Based on PR EOS). 58 4.2 Predicted Molar Volume for Oil Well No- 4, Good Oil Company. Samson, Texas (Model Based on MPR EOS). 59 4.3 Predicted Molar Volume for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. (Model Based on PR EOS). 61 viii 4.4 Predicted Molar Volume for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. (Model Based on MPR EOS). 62 4.5 Predicted Molar Volume for Jacques Unit #5603, Rough Ride Field, Fisher County, Texas. (Model Based on PR EOS). 64 4.6 Predicted Molar Volume for Jacques Unit #5603, Rough Ride Field, Fisher County, Texas. (Model Based on MPR EOS). 65 4.7 Predicted Coefficient of Isothermal Oil Compressibility for Oil Well No. 4, Good Oil Company. Samson, Texas. (Model Based on PR EOS) 67 4.8 Predicted Coefficient of Isothermal Oil Compressibility for Oil Well No. 4, Oil Company. Samson, Texas. (Model Based on MPR EOS). 68 4.9 Predicted Coefficient of Isothermal Oil Compressibility for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. (Model Based on PR EOS). 70 4.10 Predicted Coefficient of Isothermal Oil Compressibility for Jehlicka 1A, Wilshire Oil Co. of Texas, Beaver, Oklahoma. (Model Based on MPR EOS) 71 4.11 Predicted Coefficient of Isothermal Oil Compressibility for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas. (Model Based on PR EOS). 73 4.12 Predicted Coefficient of Isothermal Oil Compressibility for Jacques Unit #5603, Rough Ride Field, A.C.T. Operating Company, Fisher County, Texas. (Model Based on MPR EOS). 74