The solution of the Problem Arising in the Displacement Process in Double Phase Due to Differential Wettability

This paper presents a numerical solution for the one-dimensional flow of two immiscible fluids, ‘oil’ and ‘water’, in a homogeneous porous medium. Water is injected uniformly at a constant velocity into the unsaturated section of this medium, causing it to displace the fluids over a short distance. Our objective is to obtain a numerical solution for phase saturation distribution. The mathematical analysis leads to a governing equation, a second-order linear partial differential equation, which is solved using an explicit scheme under suitable boundary conditions. The porosity and permeability of the medium are treated as constant. The numerical solutions to this governing equation are presented in tables and graphs generated using MATLAB.