Finite Element Programming in Non-linear Geomechanics and Transient Flow

Part 1 Basics of the finite element method1. Fundamental equations of poro-elasticity and fluid flow through porous media2. Finite element methods4. Finite element method with isoparametric elements5. Numerical integration6. Solution of linear simultaneous equations7. Convergence and error analysis8. Application of the finite element method to non-linear geological materials9. Coupling geomechanics and transient fluid flow

Part 2 Applications of Flow3D and Geo3D to real field problems10. Pressure profile around perforations - field problems using Flow3D11. Evaluation of mechanical stability of perforations using Geo3D12. Numerical methods for the borehole breakout problems using Geo3D13. Casing collapse for hydrostatic and geotechnical loads14. 3D reservoir compaction problems

Appendix A: Apparent elastic modulus with pore fluid

Part 3 Programming of the finite element methodsAppendix B: 2D and 3D finite element code for single phase transient porous fluid flow problemsAppendix C: Geo3D code

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10-node parabolic tetrahedron element; 12-node parabolic infinite element; 15-node parabolic wedge element; 20-node isoparametric element; Analytical integration; Areal coordinate; Biaxial compression test; Body force; Borehole breakout; Breakout angle; Casing collapse; Collapse presure; Conjugate gradient method; Constitutive relation; Continuity equation; Convergence; Critical drawdown; Darcy's law; Directional cosines; Displacement; Displacement measurement system; Drained split method; Drucke-Prager yield envelope; Drucker-Prager failure criterion; Drucker-Prager yield theory; Drucker-Prager failure; Drucker-Prager yield theory; Effective stress; Eight-node isoparametric element; Elastic cillapse; p-plane; Equilibrium; Error analysis; Finite element method; Flow performance; Fluid flow around a perforation; Force; Formation Micro Imager; Four-node infinite element; Frontal method; Full coupling; Gaussian elimination; Gaussian integration; Gravel pack; Infinite element; Initial nonlinearity; Isoparametric; Jacobian; Kinematic hardening; Lade model failure; Lade yield envelope; Lade yield theory; Lade's failure criterion; Line loading; Local coordinates; Maximum stress yield theory; Mogi failure; Mogi's failure criterion; Mohr yield theory; Mohr-Coulomb failure criterion; Mohr-Coulomb yield envelope; Mohr's nonlinear yield theory; Mohr-Coulomb failure; Mohr's nonlinear yield theory; Neutral stress; Newton-Raphson method; Newton-Raphson method; Nodal force; Non-staggered perforation; Nonlinear stress strain; Nonlinearity at low-stress state; Octahedral shear stress yield theory; Oriented perfoation; Osmosis effect; Perforation pattern; Phase behaviour equation; Plastic collapse; Polyaxial test; Pore collapse failure; Pore-collapse nonlinearity; Pore-collapse type nonlinearity; Poro-elasticity; Potential energy; Real triaxial test; Reservoir compaction; Residual method; Rock failure; Shale swelling effect; Shape function; Shear failue; Shear failure; Shear type nonliniarity; Shear-type nonlinearity; Simpson's integration; Six-node wedge element; Spiral perforation; Staggered perforation; Standard triaxial test; Strain; Strain energy