Petroleum Reservoir Simulation Using 3-D Finite Element Method with Parallel Implementation
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Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1999 Petroleum Reservoir Simulation Using 3-D Finite Element Method With Parallel Implementation. Husam M. Yaghi Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Yaghi, Husam M., "Petroleum Reservoir Simulation Using 3-D Finite Element Method With Parallel Implementation." (1999). LSU Historical Dissertations and Theses. 7025. https://digitalcommons.lsu.edu/gradschool_disstheses/7025 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. 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Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 800-521-0600 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PETROLEUM RESERVOIR SIMULATION USING 3-D FINITE ELEMENT METHOD WITH PARALLEL IMPLEMENTATION A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Department of Computer Science by Husam M. Yaghi B.S., Southern University, 1984 M.S., Southern University, 1986 August 1999 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9945752 UMI Microform 9945752 Copyright 1999, by UMI Company. AH rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedicated to my mother and father. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS To Dr. John Tyler, my research major advisor and mentor, I say thank you. I hope you know I am much more grateful than words can express for all you have done. Please accept my warmest sincere thanks. Also thanks to the rest of my com mittee members Dr. Ted Bourgoyne, Dr. S. Sitharama Iyengar, Dr. Bert Boyce, and Dr. Robert O’Connell. I am very grateful to my two times alma mater Southern University for its financial support and the exceptional opportunities that I was given. Special thanks to Dr. James Anderson for being my best friend and for all his assistance, also to Dr. James Cross, Dr. George Whitfield, Dr. Sane Yagi, Mr. Alonzo Johnson, and Mr. Rahman Tashakkori. Finally, but certainly no less important, I dedicate this work to my mother and father. I express sincere gratitude and love to my brothers, sisters, and my wife for their inspiration and support. Special thanks to my loving princesses Angel, Amber, and Amira, for their patience as I devoted my life for this venture. In conclusion, I pray the almighty for his great blessings. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS DEDICATION.................................................................................................................ii ACKNOWLEDGEMENTS......................................................................................... iii ABSTRACT................................................................................................ - ..................vi CHAPTER 1. INTRODUCTION.................................................................................1 1.1 Statement of the Problem ..................... 4 CHAPTER 2. LITERATURE REVIEW ..................................................................11 2.1 Current Reservoir Simulations ................................................................... 11 2.2 Well Models ................................................................................................. 12 2.3 Black-Oil Reservoir Model .........................................................................15 2.4 Domain Decomposition ..............................................................................16 2.5 Coupling of FDM and FEM ....................................................................... 17 2.6 Parallel Computing in Reservoir Simulation .............................................18 CHAPTER 3. FINITE ELEMENTS METHOD.....................................................20 3.1 FEM Introduction ........................................................................................ 20 3.2 Finite Element Discretization .....................................................................23 3.3 Convergence of the FEM ........................................................................... 25 3.4 Possible FEM Benefits ................................................................................26 CHAPTER 4. MESH SYSTEMS............................................................................... 28 4.1 Block Centered ............................................................................................ 28 4.2 Coarse Mesh.................................................................................................29 4.3 Cylindrical Mesh......................................................................................... 31 4.4 Treatment of Irregularly Shaped Elements ............................................... 31 4.5 Wellbore Vicinity Model ........................................................................... 33 CHAPTER 5. NUMERICAL MODEL.....................................................................35 5.1 Discretization of the Flow Equations ........................................................36 5.2 Finite Element Formulation .......................................................................57 CHAPTER 6. COMPUTATIONAL MODEL......................................................... 73 6.1 System Requirements ..................................................................................75 6.2 Simulation Process ......................................................................................75 6.3 Input Data Requirements ............................................................................ 76 6.4 Coupling of Well Region and Reservoir Simulators ............................... 76 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.5 Wellblock Pressure Distribution ................................................................ 80 6.6 Transmissibilities .........................................................................................84 6.7 Node Numbering ..........................................................................................87 CHAPTER 7. PARALLEL M ODEL ......................................................................... 90 7.1 Wellbore Vicinity Parallelization ...............................................................91 7.2 Other Parallel Implementations ..................................................................96 CHAPTER 8. MULTIMEDIA VISUALIZATION ................................................ 99 8.1 Wellbore Vicinity Prototype Model .........................................................100 8.2 Distributed Visualization .......................................................................... 102 CHAPTER 9. RESULTS............................................................................................105 9.1 Case 1........................................................................................................... 106 9.2 Case 2........................................................................................................... 117 9.3 Comparison of Results .............................................................................. 135 CHAPTER 10. SUMMARY.......................................................................................139