Modelling Two-phase Flow through Porous Media: Using Finite Difference Method

This work presents mathematical models for pressure and saturation distributions of oil and water flow through semi-infinite porous media. The mathematical models were developed from the popular Darcy’s equation and the continuity equation. The mathematical model, which contains simultaneously saturation and pressure gradients, was decoupled to have a pure pressure and saturation differential equations. The Crank-Nicolson Finite Difference Method was used to provide solution to the partial differential equations. System of linear equations resulted from the discretized partial differential equations were solved for saturation and pressure distributions using the Modified Gaussian Elimination Method algorithm, which was implemented in Microsoft Excel Visual Basic for Application. The solution was tested using hypothetical oil/water well production data. The solution scheme and computer language adopted in this work are easy to apply and use as opposed to the sophisticated and expensive computer software used by most researchers in the area.