Abstract
The study of fluid flow in porous media, differing from traditional pipe flow is crucial for developing efficient methods in oil extraction and minerals, considering the challenges associated with ambiguous flows and diverse porous structures. This paper addresses the complexity of investigating fluid flow in porous media, a phenomenon significantly distinct from fluid movement in pipes. Emphasis is placed on the absence of clearly defined flow tubes in porous media, complicating measurements, and analysis. The study introduces a new approach incorporating both analytical and numerical methods, applied to various porous media. The research proposes a mathematical model based on laws and correlations to describe systems, including concepts such as permeability, flow velocity potential, characteristics of single-phase and multiphase systems, and fluid compressibility. Special attention is given to the characteristics of oil reservoirs, determined based on fluid properties in the reservoir, including porosity and saturation, as assessed by engineers. Numerical results represent fluid displacement in a flat channel and a onedimensional problem in a porous medium, performed using finite-difference approximation of equations with an explicit scheme. The numerical results of this model were implemented in the Matlab software.