Differential Transform Approaches to Solve One DimensionalOil-Water Flow Problem in Homogeneous Porous Medium

Abstract

The current work investigates the instability (fingering) phenomenon in an immiscible flow of oil and water through a homogeneous porous medium. When residual oil is recovered by injecting water into an oil-formatted zone in the secondary oil recovery process, instability phenomena are most commonly observed. The injected water shoots at great speed through the porous material in the shape of fingers, which are unstable due to the injecting force. The partial differential equation that governs this phenomenon is non-linear and obtaining exact solution is sometimes difficult. It is proposed to solve this equation by using two Differential Transform approaches, namely Reduced Differential Transform Method (RDTM) and Hybrid Differential Transform Finite Difference Method (HDTFDM). The solution represents saturation of injected water occupied by schematic fingers, which is obtained in the form of an infinite series. To obtain the numerical solution, a simple iterative strategy is used, which reduces computing time as compared to the traditional Differential Transform Method. The numerical solution of the governing equation and the graphical representation have been obtained using MATLAB. The results obtained by both methods are compared and analysed.