Seminar title. Two-phase Flow models to understand enhanced oil recovery
This lecture introduces mathematical governing equations for flow through porous media, flow through oil reservoirs etc. where the solid skeleton is assumed to be a rigid non- deformable matrix. This then introduces multi-phase flow models applied to enhanced oil recovery. We then discuss two-phase flow model in a highly heterogeneous porous column consisting of homogeneous blocks with periodically changing porosity and permeability. In order to capture the effective behavior, upscaled equations for the average saturation are derived via homogenization. This technique relies on a notion of periodicity and allows averaging over any number of blocks that may have any internal distributions of the rock parameters. Numerical experiments will be shown to gain insights on how these show a good agreement between the averaged solutions of the original micro-scale equations and the solutions of the upscaled equations. Finally, numerical investigation of spontaneous imbibition in an anisotropic reservoir will be discussed with few test cases.