THE EFFECT OF COUNTER CURRENT IMBIBITION IN FLUID MOVEMENT THROUGH HOMOGENEOUS AND FRACTURED POROUS MEDIA UNDER SPECIFIC CONDITIONS IS THOROUGHLY COMPARED

Abstract

In this article, we address a one-dimensional mathematical model that describes the reverse movement of water through an oil-saturated, irregularly shaped rock or soil porous matrix. During the secondary oil recovery process, water is injected into the reservoir, which consists of a mixture of various materials containing oil. This initiates a phenomenon known as counter-current imbibition at the interface where oil and water converge. Due to the differing viscosities of water and oil, they satisfy the condition for imbibition, meaning the volume of water (Vi) is equal to the negative volume of oil (Vn). This situation is best represented by a complex equation, specifically a nonlinear partial differential equation. By employing a similarity transformation, we simplified it to a nonlinear ordinary differential equation. We resolved this issue using an Ascending Power series and compared the outcome with a Homogeneous porous medium by applying the appropriate conditions at the common interface. A graph is generated, and the final solution is explained in straightforward terms.