Numerical solution for subsurface reservoir simulation

Transport problems in porous media constitute an important field of scientific research in modern world, due to their broad applications in area such as petroleum engineering, water resources, pollutants transport and green- house gases sequestration to just mention few. The mathematical models that describe such problems have been developed and form one of the main classes of partial differential equations (PDEs) that scientists encounter in the real-world modeling. Nevertheless, in most of the cases, the exact solutions in the classical sense of those models are not available. The study of numerical approximation of PDEs is therefore an active research area and there is an extensive literature on numerical methods for PDEs. In this work, we review some numerical techniques, more precisely we present finite volume method with two-point flux approximation and mixed finite volume method for spatial discretization of elliptic and parabolic PDEs modeling transport flow in porous media. We then present some standard explicit and implicit methods, Rosenbrock schemes and exponential time stepping schemes for temporal discretization. We finally run some numerical simulations of advection-diffusion-reaction problems in a heterogeneous and an anisotropic porous media.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2017

Author dc:creator

• Etekpo, Kossi

Advisors dc:contributor.advisor

• Tambue, Antoine
• Reddy, Daya

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/25007

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/25007