2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics
- 1st Edition, Volume 70 - November 17, 2020
- Imprint: Elsevier
- Editor: Nobuo Morita
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 2 3 8 2 5 - 7
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 2 3 8 3 9 - 4
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 bounda… Read more
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Request a sales quote2D/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.
- Includes interactive 2D and 3D coding exercises that readers can modify based on need
- Features research on the most recent developments in indirect and dual boundary element methods
- Contains case studies showing examples and applications of the theories presented in the book
Petroleum geologists and engineers; graduate students in petroleum geology and engineering Oil and gas industry
- Cover image
- Title page
- Table of Contents
- Copyright
- Introduction
- Part One: Fundamentals
- 1: Fundamental elasticity equations
- Abstract
- 1.1: Fundamental elasticity equations
- 1.2: Boundary conditions
- 2: Fluid flow through porous media
- Abstract
- 2.1: Fundamental equations of fluid flow through porous media
- 2.2: Boundary condition
- 3: Tensor notation or index notation
- Abstract
- 4: Fundamental solutions
- Abstract
- 4.1: Fundamental solutions for boundary element methods
- 4.2: Fundamental solution for the fluid flow through porous media
- 4.3: Fundamental solutions for boundary element methods for various problems
- 5: Boundary element methods
- Abstract
- 5.1: Direct boundary element method (direct-BEM)
- 5.2: Indirect boundary element method (indirect-BEM)
- 5.3: Displacement discontinuity method (DDM)
- 5.4: Dual boundary element method (dual BEM)
- 5.5: Integral equation for poro-elasticity problems
- Part Two: Theoretical development
- 6: Discretization of integral equation
- Abstract
- 6.1: Discretization using the direct BEM with a constant strain
- 6.2: Stress and strain evaluations within domain
- 6.3: Boundary element method including volume integration with tetrahedral and eight-node solid elements
- 6.4: Higher-order elements
- 6.5: Corner nodes
- 6.6: High order discontinuous shape function
- 7: Numerical integration
- Abstract
- 7.1: Numerical integration suitable to boundary element methods
- 7.2: Gauss integration (for integration over the element without singular point)
- 7.3: Quasisingular and singular integrations
- 7.4: Comparison of accuracy of numerical integrations around a singular point
- 7.5: Methods to avoid singular integrations using the rigid body movement and no flow conditions
- 8: Solution of linear system of equations
- Abstract
- 8.1: Transformation from local coordinate to global coordinate
- 8.2: System of linear equations
- 9: Discretization of the system of equations for fluid flow through porous media
- Abstract
- 9.1: Equations for fluid flow through porous media
- 9.2: Fundamental solution for steady-state flow
- 9.3: Boundary element method for unsteady-state flow through porous media
- 10: 2D structure code (Direct BEM) with stiffness matrix without numerical integration
- Abstract
- 10.1: Simple 2D elasticity computer program (usinganalytical integration for constructing H and G matrix)
- 10.2: Coefficient matrix
- 10.3: Example code
- 11: 2D structure code (direct BEM) with stiffness matrix with numerical integration
- Abstract
- 11.1: Discontinuous quadratic element for 2D elasticity problems
- 11.2: Integration of stiffness matrix
- 11.3: Code example
- 12: 2D displacement discontinuity boundary element method (DDM) suitable for crack problems
- Abstract
- 12.1: Analytical formulation of 2D DDM
- 12.2: Flowchart
- 12.3: Example of input data for line crack problems
- 12.4: Results
- 13: 2D transient flow program using time-dependent fundamental solution
- Abstract
- 13.1: 2D transient flow program using 3-node discontinuous quadratic element
- 13.2: Coefficients of the integral equations
- 13.3: Example program
- 14: 3D boundary element code (direct BEM) for solid elasticity problems
- Abstract
- 14.1: 3D elasticity program with quadratic continuous element
- 14.2: Program flow-chart
- 15: Analytical 3D displacement discontinuity method: Stress disturbance induced by movement of fault planes and fracture opening
- Abstract
- 15.1: Displacement discontinuity method
- 15.2: Stress shadow problems for a specified fracture surface pressure
- 16: 3D static fracture model using the dual boundary element method
- Abstract
- 16.1: Basic modes of crack surface displacements
- 16.2: Dual boundary element method (DBEM)
- 16.3: Discretization of DBEM
- 16.4: Integrations
- 16.5: Computer program
- 16.6: Accuracy and applications
- 16.7: Shear-type borehole wall shifts induced during lost circulations
- 16.8: Conclusions
- Appendix A: Stress transformation for a slant fracture from an inclined borehole
- Appendix B: Main factors determining the lost circulation volume
- 17: 3D Fracture propagation code coupled with 2D finite element flow and 3D DDM fracture code
- Abstract
- 17.1: Flow equations for 2D flow of frac-fluid
- 17.2: The variational method to discretize the flow equation
- 17.3: Galerkin approximation
- 17.4: Matrix form of fluid flow
- 17.5: Curved fracture problems for uniform formation without modulus contrast
- 17.6: Planer fracture for layered formation with modulus contrast
- 17.7: Flow chart and input example
- 17.8: Results
- References
- Author Index
- Subject Index
- Online Appendix A: Derivation of analytical equation for a rectangular element
- Online Appendix B: Fundamental solution for 3D bimaterial problems
- B.1: Fundamental solution for isotropic bimaterials(L. Rongved, 1955)
- B.2: Calculation of Tkα⁎ 11
- Online Appendix C: Example codes
- Chapter 10. Example code
- Chapter 11. Code example
- Chapter 12. Crouch method
- Chapter 13. Example program
- Chapter 14. Elast3D
- Chapter 15. Analytical 3D displacement discontinuous method for stress shadow problem induced by fracturing
- Chapter 16. 3D Curved static fracture with a Borehole
- Chapter 17. 3D fracture propagation program
- Chapter 18. Mesh generation preprocessing code
- Edition: 1
- Volume: 70
- Published: November 17, 2020
- Imprint: Elsevier
- No. of pages: 478
- Language: English
- Paperback ISBN: 9780128238257
- eBook ISBN: 9780128238394
NM
Nobuo Morita
Nobuo Morita is a professor at the Harold Vance Department of Petroleum Engineering, Texas A&M University, College Station, Texas. He teaches courses on boundary element methods for application to petroleum engineering problems, non-linear mechanics and finite element methods for geomechanics. He is a supervising professor of the Texas A&M Geomechanics Joint Industry Project. He holds sand control, borehole stability and hydraulic fracturing workshops twice per year around the world and has provided consulting services in major oil companies around the world. He was previously employed by ConocoPhillips for 14 years.
Affiliations and expertise
Professor, Texas A&M University, USARead 2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics on ScienceDirect