Numerical Methods for Including the Effect of Capillary Pressure Forces on Two-phase, Immiscible Flow in a Layered Porous Medium

摘要

This mathematical doctoral thesis contains the theory, algorithms and numerical simulations for a heterogeneous oil reservoir. It presents the equations, which apply to immiscible and incompressible two-phase fluid flow in the reservoir, including the effect of capillary pressure forces, and emphasises in particular the interior boundary conditions at the interface between two sediments. Two different approaches are discussed. The first approach is to decompose the computational domain along the interior boundary and iterate between the subdomains until mass balance is achieved. The second approach accounts for the interior boundary conditions in the basis in which the solution is expanded, the basis being discontinuous over the interior boundaries. An overview of the construction of iterative solvers for partial differential equations by means of Schwartz methods is given, and the algorithm for local refinement with Schwartz iterations as iterative solver is described. The theory is then applied to a core plug problem in one and two space dimensions and the results of different methods compared. A general description is given of the computer simulation model, which is implemented in C++. 64 refs., 49 figs., 7 tabs.