2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics, Volume 72, is designed to make it easy for researchers, engineers and students to begin writing boundary element programs. This reference covers the fundamentals, theoretical developments, programming and applications. Both fluid flow through porous media and structural problems are used for coding exercises. Included computer programs may be used as starting codes; after modifications, they can be applied to real world problems. The book covers topics around mesh generation, 3D boundary element coding, and interface coding for controlling mesh generation, and plotting results.
1. Introduction - p. page_ix 2. Part One: Fundamentals - p. page_x 3. 1: Fundamental elasticity equations - p. page_3 4. 2: Fluid flow through porous media - p. page_9 5. 3: Tensor notation or index notation - p. page_13 6. 4: Fundamental solutions - p. page_15 7. Abstract - p. page_15 8. 4.1: Fundamental solutions for boundary element methods - p. page_15 9. 4.2: Fundamental solution for the fluid flow through porous media - p. page_31 10. 4.3: Fundamental solutions for boundary element methods for various problems - p. page_37 11. 5: Boundary element methods - p. page_41 12. Abstract - p. page_41 13. 5.1: Direct boundary element method (direct-BEM) - p. page_41 14. 5.2: Indirect boundary element method (indirect-BEM) - p. page_61 15. 5.3: Displacement discontinuity method (DDM) - p. page_65 16. 5.4: Dual boundary element method (dual BEM) - p. page_89 17. 5.5: Integral equation for poro-elasticity problems - p. page_97 18. Part Two: Theoretical development - p. page_104 19. 6: Discretization of integral equation - p. page_107 20. Abstract - p. page_107 21. 6.1: Discretization using the direct BEM with a constant strain - p. page_107 22. 6.2: Stress and strain evaluations within domain - p. page_111 23. 6.3: Boundary element method including volume integration with tetrahedral and eight-node solid elements - p. page_113 24. 6.4: Higher-order elements - p. page_120 25. 6.5: Corner nodes - p. page_157 26. 6.6: High order discontinuous shape function - p. page_177 27. 7: Numerical integration - p. page_183 28. Abstract - p. page_183 29. 7.1: Numerical integration suitable to boundary element methods - p. page_183 30. 7.2: Gauss integration (for integration over the element without singular point) - p. page_193 31. 7.3: Quasisingular and singular integrations - p. page_202 32. 7.4: Comparison of accuracy of numerical integrations around a singular point - p. page_239 33. 7.5: Methods to avoid singular integrations using the rigid body movement and no flow conditions - p. page_244 34. 8: Solution of linear system of equations - p. page_249 35. 9: Discretization of the system of equations for fluid flow through porous media - p. page_261 36. 10: 2D structure code (Direct BEM) with stiffness matrix without numerical integration - p. page_273 37. 11: 2D structure code (direct BEM) with stiffness matrix with numerical integration - p. page_295 38. 12: 2D displacement discontinuity boundary element method (DDM) suitable for crack problems - p. page_309 39. Abstract - p. page_309 40. 12.1: Analytical formulation of 2D DDM - p. page_309 41. 12.2: Flowchart - p. page_317 42. 12.3: Example of input data for line crack problems - p. page_318 43. 12.4: Results - p. page_322 44. 13: 2D transient flow program using time-dependent fundamental solution - p. page_329 45. 14: 3D boundary element code (direct BEM) for solid elasticity problems - p. page_351 46. 15: Analytical 3D displacement discontinuity method: Stress disturbance induced by movement of fault planes and fracture opening - p. page_371 47. 16: 3D static fracture model using the dual boundary element method - p. page_381 48. Abstract - p. page_381 49. 16.1: Basic modes of crack surface displacements - p. page_381 50. 16.2: Dual boundary element method (DBEM) - p. page_385 51. 16.3: Discretization of DBEM - p. page_388 52. 16.4: Integrations - p. page_397 53. 16.5: Computer program - p. page_398 54. 16.6: Accuracy and applications - p. page_400 55. 16.7: Shear-type borehole wall shifts induced during lost circulations - p. page_406 56. 16.8: Conclusions - p. page_423 57. Appendix A: Stress transformation for a slant fracture from an inclined borehole - p. page_425 58. Appendix B: Main factors determining the lost circulation volume - p. page_425 59. 17: 3D Fracture propagation code coupled with 2D finite element flow and 3D DDM fracture code - p. page_429 60. Abstract - p. page_429 61. 17.1: Flow equations for 2D flow of frac-fluid - p. page_429 62. 17.2: The variational method to discretize the flow equation - p. page_432 63. 17.3: Galerkin approximation - p. page_435 64. 17.4: Matrix form of fluid flow - p. page_436 65. 17.5: Curved fracture problems for uniform formation without modulus contrast - p. page_437 66. 17.6: Planer fracture for layered formation with modulus contrast - p. page_442 67. 17.7: Flow chart and input example - p. page_453 68. 17.8: Results - p. page_454 69. References - p. page_459 70. Author Index - p. page_461 71. Subject Index - p. page_463 72. Online Appendix A: Derivation of analytical equation for a rectangular element - p. page_463 73. Online Appendix B: Fundamental solution for 3D bimaterial problems - p. page_463 74. Online Appendix C: Example codes - p. page_e1 75. Chapter 10. Example code - p. page_e1 76. Chapter 11. Code example - p. page_e17 77. Chapter 12. Crouch method - p. page_e47 78. Chapter 13. Example program - p. page_e57 79. Chapter 14. Elast3D - p. page_e84 80. Chapter 15. Analytical 3D displacement discontinuous method for stress shadow problem induced by fracturing - p. page_e146 81. Chapter 16. 3D Curved static fracture with a Borehole - p. page_e151 82. Chapter 17. 3D fracture propagation program - p. page_e219 83. Chapter 18. Mesh generation preprocessing code - p. page_e287
2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics, Volume 72, is designed to make it easy for researchers, engineers and students to begin writing boundary element programs. This reference covers the fundamentals, theoretical developments, programming and applications. Both fluid flow through porous media and structural problems are used for coding exercises. Included computer programs may be used as starting codes; after modifications, they can be applied to real world problems. The book covers topics around mesh generation, 3D boundary element coding, and interface coding for controlling mesh generation, and plotting results.
1. Introduction - p. page_ix 2. Part One: Fundamentals - p. page_x 3. 1: Fundamental elasticity equations - p. page_3 4. 2: Fluid flow through porous media - p. page_9 5. 3: Tensor notation or index notation - p. page_13 6. 4: Fundamental solutions - p. page_15 7. Abstract - p. page_15 8. 4.1: Fundamental solutions for boundary element methods - p. page_15 9. 4.2: Fundamental solution for the fluid flow through porous media - p. page_31 10. 4.3: Fundamental solutions for boundary element methods for various problems - p. page_37 11. 5: Boundary element methods - p. page_41 12. Abstract - p. page_41 13. 5.1: Direct boundary element method (direct-BEM) - p. page_41 14. 5.2: Indirect boundary element method (indirect-BEM) - p. page_61 15. 5.3: Displacement discontinuity method (DDM) - p. page_65 16. 5.4: Dual boundary element method (dual BEM) - p. page_89 17. 5.5: Integral equation for poro-elasticity problems - p. page_97 18. Part Two: Theoretical development - p. page_104 19. 6: Discretization of integral equation - p. page_107 20. Abstract - p. page_107 21. 6.1: Discretization using the direct BEM with a constant strain - p. page_107 22. 6.2: Stress and strain evaluations within domain - p. page_111 23. 6.3: Boundary element method including volume integration with tetrahedral and eight-node solid elements - p. page_113 24. 6.4: Higher-order elements - p. page_120 25. 6.5: Corner nodes - p. page_157 26. 6.6: High order discontinuous shape function - p. page_177 27. 7: Numerical integration - p. page_183 28. Abstract - p. page_183 29. 7.1: Numerical integration suitable to boundary element methods - p. page_183 30. 7.2: Gauss integration (for integration over the element without singular point) - p. page_193 31. 7.3: Quasisingular and singular integrations - p. page_202 32. 7.4: Comparison of accuracy of numerical integrations around a singular point - p. page_239 33. 7.5: Methods to avoid singular integrations using the rigid body movement and no flow conditions - p. page_244 34. 8: Solution of linear system of equations - p. page_249 35. 9: Discretization of the system of equations for fluid flow through porous media - p. page_261 36. 10: 2D structure code (Direct BEM) with stiffness matrix without numerical integration - p. page_273 37. 11: 2D structure code (direct BEM) with stiffness matrix with numerical integration - p. page_295 38. 12: 2D displacement discontinuity boundary element method (DDM) suitable for crack problems - p. page_309 39. Abstract - p. page_309 40. 12.1: Analytical formulation of 2D DDM - p. page_309 41. 12.2: Flowchart - p. page_317 42. 12.3: Example of input data for line crack problems - p. page_318 43. 12.4: Results - p. page_322 44. 13: 2D transient flow program using time-dependent fundamental solution - p. page_329 45. 14: 3D boundary element code (direct BEM) for solid elasticity problems - p. page_351 46. 15: Analytical 3D displacement discontinuity method: Stress disturbance induced by movement of fault planes and fracture opening - p. page_371 47. 16: 3D static fracture model using the dual boundary element method - p. page_381 48. Abstract - p. page_381 49. 16.1: Basic modes of crack surface displacements - p. page_381 50. 16.2: Dual boundary element method (DBEM) - p. page_385 51. 16.3: Discretization of DBEM - p. page_388 52. 16.4: Integrations - p. page_397 53. 16.5: Computer program - p. page_398 54. 16.6: Accuracy and applications - p. page_400 55. 16.7: Shear-type borehole wall shifts induced during lost circulations - p. page_406 56. 16.8: Conclusions - p. page_423 57. Appendix A: Stress transformation for a slant fracture from an inclined borehole - p. page_425 58. Appendix B: Main factors determining the lost circulation volume - p. page_425 59. 17: 3D Fracture propagation code coupled with 2D finite element flow and 3D DDM fracture code - p. page_429 60. Abstract - p. page_429 61. 17.1: Flow equations for 2D flow of frac-fluid - p. page_429 62. 17.2: The variational method to discretize the flow equation - p. page_432 63. 17.3: Galerkin approximation - p. page_435 64. 17.4: Matrix form of fluid flow - p. page_436 65. 17.5: Curved fracture problems for uniform formation without modulus contrast - p. page_437 66. 17.6: Planer fracture for layered formation with modulus contrast - p. page_442 67. 17.7: Flow chart and input example - p. page_453 68. 17.8: Results - p. page_454 69. References - p. page_459 70. Author Index - p. page_461 71. Subject Index - p. page_463 72. Online Appendix A: Derivation of analytical equation for a rectangular element - p. page_463 73. Online Appendix B: Fundamental solution for 3D bimaterial problems - p. page_463 74. Online Appendix C: Example codes - p. page_e1 75. Chapter 10. Example code - p. page_e1 76. Chapter 11. Code example - p. page_e17 77. Chapter 12. Crouch method - p. page_e47 78. Chapter 13. Example program - p. page_e57 79. Chapter 14. Elast3D - p. page_e84 80. Chapter 15. Analytical 3D displacement discontinuous method for stress shadow problem induced by fracturing - p. page_e146 81. Chapter 16. 3D Curved static fracture with a Borehole - p. page_e151 82. Chapter 17. 3D fracture propagation program - p. page_e219 83. Chapter 18. Mesh generation preprocessing code - p. page_e287
