Finite Element Programming in Non-linear Geomechanics and Transient Flow delivers a textbook reference for both students and practitioners alike, with provided codes to understand and modify. Starting with the fundamentals, the reference covers the basics of finite element methods, including coupling geomechanics and transient fluid flow. The next phase moves from theory into practical application from programs Flow3D and Geo3D, utilizing source codes to solve real field challenges. Stability of perforations during oil and gas production, sand production problems, rock failure, casing collapse, and reservoir compaction problems are just some examples.
Next, the reference elevates to hands-on experience, sharing source codes with additional problems engineers can work on independently. This gives students and engineers a starting point to modify their own code in a fraction of the time.
1. Introduction - p. ix 2. Chapter 1 Fundamental equations of poro-elasticity and fluid flow through porous media - p. 3 3. Chapter 2 Finite element methods - p. 17 4. Chapter 3 Finite element method with analytical integration using simple elements - p. 29 5. Chapter 4 Finite element method with isoparametric elements - p. 41 6. Chapter 5 Numerical integration - p. 63 7. Chapter 6 Solution of linear simultaneous equations - p. 69 8. Chapter 7 Convergence and error analysis - p. 87 9. Chapter 8 Application of the finite element method to nonlinear geological materials - p. 93 10. Chapter 9 Coupling geomechanics and transient fluid flow - p. 127 11. Keywords - p. 127 12. 9.1 Fundamental equations for isotropic poro-elasticity problems - p. 127 13. 9.2 Discretization using the virtual work principle - p. 130 14. 9.3 Discretization of transient flow equations through porous media - p. 133 15. 9.4 Coupling geomechanics and transient fluid flow - p. 136 16. 9.5 Stability of the sequential methods - p. 144 17. 9.5.1 One-dimensional compaction problem coupled with fluid flow and geomechanics - p. 144 18. 9.5.2 Stability analysis of the coupled problem - p. 145 19. 9.5.3 Stability of drained split method - p. 148 20. 9.5.4 Stability of undrained split method - p. 150 21. 9.5.5 Stability of fixed strain method - p. 152 22. 9.5.6 Stability of fixed total stress method - p. 156 23. 9.5.7 Numerical example of one-dimensional compaction problem using the fixed total stress method - p. 159 24. 9.6 Sequential coupling with commercially available reservoir models - p. 162 25. Further reading - p. 176 26. Chapter 10 Pressure profile around perforations—field problems using Flow3D - p. 179 27. Chapter 11 Evaluation of mechanical stability of perforations using Geo3D - p. 203 28. Chapter 12 Numerical methods for the borehole breakout problems using Geo3D - p. 241 29. Keywords - p. 241 30. 12.1 Rock failure and failure theories - p. 241 31. 12.2 Failure envelopes from empirical results - p. 248 32. 12.3 Stress state around an inclined well drilled through inclined formation - p. 270 33. 12.4 Comprehensive analysis of stress state around a borehole with temperature, swelling, and pore pressure change for layered and orthotropic formations - p. 281 34. 12.5 Failure theories to predict breakout angle around a borehole - p. 303 35. 12.6 Effect of controllable parameters on safe mud window design - p. 332 36. 12.7 Conclusion - p. 342 37. Nomenclature - p. 343 38. References - p. 344 39. Further reading - p. 344 40. Chapter 13 Casing collapse for hydrostatic and geotechnical loads—Geo3D analysis - p. 347 41. Chapter 14 Three-dimensional reservoir compaction problems with coupled Geo3D code - p. 393 42. Appendix A Apparent elastic modulus with pore fluid - p. 443 43. Appendix B Computer program structure for transient fluid flow problems through porous media - p. 459 44. Appendix C Program Geo3D - p. 479 45. Appendix D Program COEFI for determining the parameters of the nonlinear constitutive relations from a set of triaxial test results - p. 505 46. Index - p. 531
Finite Element Programming in Non-linear Geomechanics and Transient Flow delivers a textbook reference for both students and practitioners alike, with provided codes to understand and modify. Starting with the fundamentals, the reference covers the basics of finite element methods, including coupling geomechanics and transient fluid flow. The next phase moves from theory into practical application from programs Flow3D and Geo3D, utilizing source codes to solve real field challenges. Stability of perforations during oil and gas production, sand production problems, rock failure, casing collapse, and reservoir compaction problems are just some examples.
Next, the reference elevates to hands-on experience, sharing source codes with additional problems engineers can work on independently. This gives students and engineers a starting point to modify their own code in a fraction of the time.
1. Introduction - p. ix 2. Chapter 1 Fundamental equations of poro-elasticity and fluid flow through porous media - p. 3 3. Chapter 2 Finite element methods - p. 17 4. Chapter 3 Finite element method with analytical integration using simple elements - p. 29 5. Chapter 4 Finite element method with isoparametric elements - p. 41 6. Chapter 5 Numerical integration - p. 63 7. Chapter 6 Solution of linear simultaneous equations - p. 69 8. Chapter 7 Convergence and error analysis - p. 87 9. Chapter 8 Application of the finite element method to nonlinear geological materials - p. 93 10. Chapter 9 Coupling geomechanics and transient fluid flow - p. 127 11. Keywords - p. 127 12. 9.1 Fundamental equations for isotropic poro-elasticity problems - p. 127 13. 9.2 Discretization using the virtual work principle - p. 130 14. 9.3 Discretization of transient flow equations through porous media - p. 133 15. 9.4 Coupling geomechanics and transient fluid flow - p. 136 16. 9.5 Stability of the sequential methods - p. 144 17. 9.5.1 One-dimensional compaction problem coupled with fluid flow and geomechanics - p. 144 18. 9.5.2 Stability analysis of the coupled problem - p. 145 19. 9.5.3 Stability of drained split method - p. 148 20. 9.5.4 Stability of undrained split method - p. 150 21. 9.5.5 Stability of fixed strain method - p. 152 22. 9.5.6 Stability of fixed total stress method - p. 156 23. 9.5.7 Numerical example of one-dimensional compaction problem using the fixed total stress method - p. 159 24. 9.6 Sequential coupling with commercially available reservoir models - p. 162 25. Further reading - p. 176 26. Chapter 10 Pressure profile around perforations—field problems using Flow3D - p. 179 27. Chapter 11 Evaluation of mechanical stability of perforations using Geo3D - p. 203 28. Chapter 12 Numerical methods for the borehole breakout problems using Geo3D - p. 241 29. Keywords - p. 241 30. 12.1 Rock failure and failure theories - p. 241 31. 12.2 Failure envelopes from empirical results - p. 248 32. 12.3 Stress state around an inclined well drilled through inclined formation - p. 270 33. 12.4 Comprehensive analysis of stress state around a borehole with temperature, swelling, and pore pressure change for layered and orthotropic formations - p. 281 34. 12.5 Failure theories to predict breakout angle around a borehole - p. 303 35. 12.6 Effect of controllable parameters on safe mud window design - p. 332 36. 12.7 Conclusion - p. 342 37. Nomenclature - p. 343 38. References - p. 344 39. Further reading - p. 344 40. Chapter 13 Casing collapse for hydrostatic and geotechnical loads—Geo3D analysis - p. 347 41. Chapter 14 Three-dimensional reservoir compaction problems with coupled Geo3D code - p. 393 42. Appendix A Apparent elastic modulus with pore fluid - p. 443 43. Appendix B Computer program structure for transient fluid flow problems through porous media - p. 459 44. Appendix C Program Geo3D - p. 479 45. Appendix D Program COEFI for determining the parameters of the nonlinear constitutive relations from a set of triaxial test results - p. 505 46. Index - p. 531
