2D/3D boundary element programming in petroleum engineering and geomechanics
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| Format: | eBook Book |
| Language: | English |
| Published: |
Amsterdam
Elsevier
2020
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| Edition: | 1 |
| Subjects: | |
| ISBN: | 9780128238257, 0128238259 |
| Online Access: | Get full text |
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Table of Contents:
- 15.2. Stress shadow problems for a specified fracture surface pressure -- Chapter 16: -- 16.1. Basic modes of crack surface displacements -- 16.1.1. Stress and displacement around a crack tip -- 16.1.2. Stress intensity factors -- 16.2. Dual boundary element method (DBEM) -- 16.3. Discretization of DBEM -- 16.3.1. Hyper singular integration -- 16.3.2. Special crack tip element -- 16.3.3. Evaluation of the fracture intensity factor -- 16.4. Integrations -- 16.5. Computer program -- 16.5.1. Flow chart -- 16.6. Accuracy and applications -- 16.6.1. 3D fracture model around an inclined borehole using the dual boundary element method -- 16.6.1.1. Model calibrations -- 16.6.1.2. Penny shaped crack -- 16.6.1.3. Slant elliptical-shaped crack -- 16.6.1.4. Borehole displacement -- 16.7. Shear-type borehole wall shifts induced during lost circulations -- 16.7.1. Abstract -- 16.7.2. Introduction -- 16.7.2.1. Fracture model -- 16.7.2.2. Borehole wall shift calculations -- 16.7.2.3. Analysis and discussion for practical applications -- 16.8. Conclusions -- Appendix A Stress transformation for a slant fracture from an inclined borehole -- Appendix B Main factors determining the lost circulation volume -- Chapter 17: -- 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 -- 17.6.1. Shape functions for crack elements -- 17.6.2. Coupling and solution procedures -- 17.6.3. Advancement of a fracture tip -- 17.7. Flow chart and input example -- 17.7.1. Test input -- 17.7.2. Initial mesh -- 17.8. Results -- References -- Author index -- Subject index -- Online Appendix A -- Online Appendix B
- 6.4.4. Assembling GH matrix without crack elements -- 6.5. Corner nodes -- 6.6. High order discontinuous shape function -- Chapter 7: -- 7.1. Numerical integration suitable to boundary element methods -- 7.1.1. Five types of singular boundary integrations -- 7.1.2. Definition of the Cauchy principal-value integral -- 7.1.2.1. 2D problems -- 7.1.2.2. 3D problems -- 7.1.3. Definition of the Hadamard finite part integral -- 7.1.3.1. 2D problems -- 7.1.3.2. 3D problems -- 7.1.4. Standard procedure for singular integrations -- 7.2. Gauss integration (for integration over the element without singular point) -- Integration formula for triangle and tetrahedron shape functions -- 7.3. Quasisingular and singular integrations -- 7.3.1. Domain refinement -- 7.3.2. Coordinate transformation-1 (polynomial transformation) -- 7.3.3. Coordinate transformation-2: A self-adaptive coordinate transformation for quasisingular or singular integrations -- 7.3.4. Coordinate transformation-3 Lachat-Watson transformation for weak singularity -- 7.3.5. Coordinate transformation-4 PART method: Projection and Angular & -- Radial Transformation for quasisingular integrat ... -- Tangential integration with the Gaussian quadrature -- Radial integration with the Gaussian quadrature after radial transformation -- Application example -- Analytical solution -- 7.3.6. Radial transformation similar to the PART method described by S.G. Mikhlin -- 7.3.7. Cauchy principal-value integral for strong singularity O(1/r2) -- Application example -- 7.3.8. Hadamard finite part integral: singular subtraction method for the finite part integral of the hypersingularity O( ... -- 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
- B.1. Fundamental solution for isotropic bimaterials(L. Rongved, 1955) -- B.2. Calculation of Tkα11 -- References -- 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
- 7.5.1. Finite region rigid-body-motion constraint -- 7.5.2. Semiinfinite region rigid-body-motion constraint -- 7.5.3. Flow problems -- Chapter 8: -- 8.1. Transformation from local coordinate to global coordinate -- 8.2. System of linear equations -- 8.2.1. Gaussian elimination -- 8.2.2. Variable bandwidth elimination method -- 8.2.3. Conjugate gradient method -- Chapter 9: -- 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 -- Chapter 10: -- 10.1. Simple 2D elasticity computer program (usinganalytical integration for constructing H and G matrix) -- 10.2. Coefficient matrix -- 10.2.1. Nondiagonal matrix -- 10.2.2. Diagonal coefficients -- 10.3. Example code -- 10.3.1. Input data for a simple structural problem -- Chapter 11: -- 11.1. Discontinuous quadratic element for 2D elasticity problems -- 11.2. Integration of stiffness matrix -- 11.3. Code example -- 11.3.1. Input data for a simple structural problem -- Chapter 12: -- 12.1. Analytical formulation of 2D DDM -- 12.1.1. Displacement and the stresses within the domain -- 12.2. Flowchart -- 12.3. Example of input data for line crack problems -- 12.3.1. Input example -- 12.3.2. Circle without crack -- 12.3.3. Input data -- 12.4. Results -- Chapter 13: -- 13.1. 2D transient flow program using 3-node discontinuous quadratic element -- 13.2. Coefficients of the integral equations -- 13.3. Example program -- 13.3.1. Example input data -- Chapter 14: -- 14.1. 3D elasticity program with quadratic continuous element -- 14.1.1. Construct GH Matrix -- 14.2. Program flow-chart -- 14.2.1. Descriptions of the subroutines -- 14.2.2. Model around a borehole -- Chapter 15: -- 15.1. Displacement discontinuity method
- Front Cover -- 2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics -- Copyright -- Contents -- Introduction -- Part One: Fundamentals -- Chapter 1: -- 1.1. Fundamental elasticity equations -- 1.2. Boundary conditions -- Chapter 2: -- 2.1. Fundamental equations of fluid flow through porous media -- 2.2. Boundary condition -- Chapter 3: -- Chapter 4: -- 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 -- Chapter 5: -- 5.1. Direct boundary element method (direct-BEM) -- 5.1.1. Stress evaluation -- 5.2. Indirect boundary element method (indirect-BEM) -- 5.3. Displacement discontinuity method (DDM) -- 5.3.1. Derivation of displacement discontinuity method -- 5.3.1.1. Alternative method to reduce the singularity. -- 5.3.2. Other expression of the generalized displacement discontinuity method for 3-D fracture problems -- 5.3.3. 2D fracture problems -- 5.3.3.1. Analytical method to obtain Eq. (5.143) -- 5.3.4. 3D problems originally proposed by Crouch -- 5.4. Dual boundary element method (dual BEM) -- 5.4.1. Alternative method to reduce the degree of singularity -- 5.5. Integral equation for poro-elasticity problems -- 5.5.1. Fundamental equations -- 5.5.1.1. Derivation of Eq. (5.208) using divergence theorem -- Part Two: Theoretical development -- Chapter 6: -- 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 -- 6.4.1. Interpolation function -- 6.4.2. Discontinuous element -- 6.4.3. Discretization using shape functions with high order polynomials