http://www.ucalgaryreservoirsimulation.ca/wp-content/uploads/2014/07/J27-1-s2.0-S0009250907003144-main.pdf

Critical review of the impact of tortuosity on diffusion

DuMux: DUNE for multi-{phase,component,scale,physics,…} flow and transport in porous media

This book provides a self-contained introduction to the simulation of flow and transport in porous media, written by a developer of numerical methods. The reader will learn how to implement reservoir simulation models and computational algorithms in a robust and efficient manner. The book contains a large number of numerical examples, all fully equipped with online code and data, allowing the reader to reproduce results, and use them as a starting point for their own work. All of the examples in the book are based on the MATLAB Reservoir Simulation Toolbox (MRST), an open-source toolbox popular popularity in both academic institutions and the petroleum industry. The book can also be seen as a user guide to the MRST software. It will prove invaluable for researchers, professionals and advanced students using reservoir simulation methods. This title is also available as Open Access on Cambridge Core.

An Introduction to Reservoir Simulation Using MATLAB/GNU Octave: User Guide for the MATLAB Reservoir Simulation Toolbox (MRST)

Adjoint-based optimization of multi-phase flow through porous media – A review

The flow of water in partially saturated porous media is of importance in fields such as hydrology, agriculture, environment and waste management. It is also one of the most complex flows in nature. The Richards’ equation describes the flow of water in an unsaturated porous medium due to the actions of gravity and capillarity neglecting the flow of the non-wetting phase, usually air. Analytical solutions of Richards’ equation exist only for simplified cases, so most practical situations require a numerical solution in one- two- or three-dimensions, depending on the problem and complexity of the flow situation. Despite the fact that the first reasonably complete conservative numerical solution method was published in the early 1990s, the numerical solution of the Richards’ equation remains computationally expensive and in certain circumstances, unreliable. A universally robust and accurate solution methodology has not yet been identified that is applicable across the range of soils, initial and boundary conditions found in practice. Existing solution codes have been modified over years to attempt to increase robustness. Despite theoretical results on the existence of solutions given sufficiently regular data and constitutive relations, our numerical methods often fail to demonstrate reliable convergence behavior in practice, especially for higher-order methods. Because of robustness, the lack of higher-order accuracy and computational expense, alternative solution approaches or methods are needed. There is also a need for better documentation of improved solution methodologies and benchmark test problems to facilitate consistent advances and avoid re-inventing of the wheel.

Numerical Solution of Richards' Equation: A Review of Advances and Challenges

Preface 1. Introduction 2. Flow and transport equations 3. Rock and fluid properties 4. Numerical methods 5. Solution of linear systems 6. Single phase flow 7. Two-phase flow 8. The Black Oil model 9. The Compositional model 10. Nonisothermal flow 11. Chemical flooding 12. Flows in fractured porous media 13. Welling modeling 14. Special topics 15. Nomenclature 16. Units Bibliography Index.

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Chʿang-hsin Chʿen

Papers

Computational Methods for Multiphase Flows in Porous Media