Finite Element Programming in Non-linear Geomechanics and Transient Flow
- 1st Edition - August 21, 2021
- Imprint: Gulf Professional Publishing
- Author: Nobuo Morita
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 1 1 1 2 - 2
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 1 1 1 3 - 9
Finite Element Programming in Non-linear Geomechanics and Transient Flow delivers a textbook reference for both students and practitioners alike, with provided codes to understan… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteFinite 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.
- Helps users understand finite element programs such as Flow3D and Geo3D to solve geomechanics problems, including casing stability, reservoir compaction challenges, and sand production
- Bridges the gap between theory, applications and source codes to help readers develop or modify their own computer programs with provided source codes
- Includes cases studies and practice examples that illustrate real-world applications
Doctorate-level petroleum engineering students; petroleum engineers, mechanical engineers, petroleum researchers
- Cover image
- Title page
- Table of Contents
- Copyright
- Introduction
- I: Basics of the finite element method
- Chapter 1. Fundamental equations of poro-elasticity and fluid flow through porous media
- Abstract
- 1.1 Force, displacement, stress, strain, and displacement–strain relations
- 1.2 Equation of equilibrium and stress–strain relation
- 1.3 Fluid flow through porous media
- 1.4 Matrix expression
- Chapter 2. Finite element methods
- Abstract
- 2.1 Discretization using the virtual work principle
- 2.2 Discretization using the minimization of total potential energy
- 2.3 Discretization using the residual method
- 2.4 Discretization of the set of flow equations through porous media using the residual method
- Chapter 3. Finite element method with analytical integration using simple elements
- Abstract
- 3.1 Discretization using 3D tetrahedral elements
- 3.2 Analytical integrations
- 3.3 Assembling the elements
- 3.4 Nodal forces
- 3.5 Body forces
- Chapter 4. Finite element method with isoparametric elements
- Abstract
- 4.1 Isoparametric elements
- 4.2 Brick elements
- 4.3 Infinite element
- Chapter 5. Numerical integration
- Abstract
- 5.1 Gaussian integration
- 5.2 Integration formula for triangle and tetrahedron shape functions
- Chapter 6. Solution of linear simultaneous equations
- Abstract
- 6.1 Matrix transformation for the boundary condition given by local coordinates
- 6.2 Solution of linear simultaneous equations
- Chapter 7. Convergence and error analysis
- Abstract
- 7.1 Theoretical estimation of error
- 7.2 Numerical evaluation of error
- Chapter 8. Application of the finite element method to nonlinear geological materials
- Abstract
- 8.1 Standard triaxial rock test equipment and typical test results
- 8.2 Nonlinearity at a low-stress state
- 8.3 Shear-type nonlinear strain
- 8.4 Yield envelope fitted to real polyaxial stress–strain empirical data
- 8.5 Incremental form of nonlinear stress strain for application of the finite element method
- 8.6 Application of the Newton–Raphson method to nonlinear problems
- 8.7 Calculation method of λ, Dep
- 8.8 Implementation
- 8.9 Construction of constitutive relations from triaxial data
- Chapter 9. Coupling geomechanics and transient fluid flow
- Abstract
- 9.1 Fundamental equations for isotropic poro-elasticity problems
- 9.2 Discretization using the virtual work principle
- 9.3 Discretization of transient flow equations through porous media
- 9.4 Coupling geomechanics and transient fluid flow
- 9.5 Stability of the sequential methods
- 9.6 Sequential coupling with commercially available reservoir models
- Further reading
- II: Applications of Flow3D and Geo3D to real field problems
- Chapter 10. Pressure profile around perforations—field problems using Flow3D
- Abstract
- 10.1 Pressure profile around a single perforation
- 10.2 Numerical solution for pressure distribution around a single perforation
- 10.3 Pressure distribution around a perforation for gravel packed well
- 10.4 Quantitative analysis of the effect of perforation interaction on flow efficiency
- Nomenclature
- References
- Chapter 11. Evaluation of mechanical stability of perforations using Geo3D
- Abstract
- 11.1 Stability of perforations during oil and gas production
- 11.2 Field observation of sand-production problems
- 11.3 A quick method to forecast the possibility of sand problems: Perforation stability analysis using TWC or TPS test equipment
- 11.4 Concluding remarks
- Nomenclature
- Further reading
- Chapter 12. Numerical methods for the borehole breakout problems using Geo3D
- Abstract
- 12.1 Rock failure and failure theories
- 12.2 Failure envelopes from empirical results
- 12.3 Stress state around an inclined well drilled through inclined formation
- 12.4 Comprehensive analysis of stress state around a borehole with temperature, swelling, and pore pressure change for layered and orthotropic formations
- 12.5 Failure theories to predict breakout angle around a borehole
- 12.6 Effect of controllable parameters on safe mud window design
- 12.7 Conclusion
- Nomenclature
- References
- Further reading
- Chapter 13. Casing collapse for hydrostatic and geotechnical loads—Geo3D analysis
- Abstract
- 13.1 Casing collapse for hydrostatic load
- 13.2 Concluding remarks
- Nomenclature
- Further reading
- Chapter 14. Three-dimensional reservoir compaction problems with coupled Geo3D code
- Abstract
- 14.1 Introduction of reservoir compaction problems
- 14.2 Strain nuclei method
- 14.3 Analytical solution at the center of a reservoir for a radial reservoir
- 14.4 Subsidence, pore pressure, and stress change in the overburden formation using the finite element method coupled with transient flow and geomechanics models
- 14.5 Parametric analysis of subsidence and compaction
- References
- Further reading
- Appendix A. Apparent elastic modulus with pore fluid
- III: Programming of the finite element methods
- Appendix B. Computer program structure for transient fluid flow problems through porous media
- B.1 Program Flow3D
- B.2 Input example FLOW3D
- Appendix C. Program Geo3D
- C.1 Input example for Geo3D
- C.2 Input example for Geo3D
- Appendix D. Program COEFI for determining the parameters of the nonlinear constitutive relations from a set of triaxial test results
- D.1 Calculation procedure
- D.2 Input file “Coefi.inp”
- Index
- Edition: 1
- Published: August 21, 2021
- Imprint: Gulf Professional Publishing
- No. of pages: 550
- Language: English
- Paperback ISBN: 9780323911122
- eBook ISBN: 9780323911139
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 Finite Element Programming in Non-linear Geomechanics and Transient Flow on ScienceDirect