One-Dimensional Modeling of Imbibition in Porous Media Using an Approximate Analytical Method

This paper is concerned with solving the problem of one-dimensional counter-current imbibition in a homogeneous porous medium. In this research, water and oil are treated as two distinct liquid phases, in which the water is the wetting phase while the oil is the non-wetting phase. This is the common scenario during secondary recovery of oil. During this phase, the fluid behavior is characterized by a nonlinear partial differential equation. To find the solution of this equation, we utilize the Homotopy Analysis Method (HAM), which is a powerful analytical method. Proper boundary conditions are chosen according to the physical phenomenon of the problem. The results are visualized and interpreted with the help of Mathematica 12.0 using graphical plots.