Characterization of a Non-Darcy Flow and Development of New Correlation of NON-Darcy Coefficient

Abstract

Darcy’s law has long been used to describe the flow in porous media. Despite the progress that took place in oil production industry research, it became clear that there is a loss of pressure, especially in the area near the wellbore region, where Darcy’s law is not applicable. For this reason, Forchheimer presented his equation in 1910, where he added a new term to Darcy’s law dealing with pressure loss due to inertial forces by introducing a new term, the β coefficient, into the equation. This paper presents a study of fluid flow through porous media, where water was used as a working fluid. Furthermore, the characteristics of the non-Darcy flow were analyzed by presenting the corresponding pressure and velocity gradient curves for each pressure. Extensive analysis indicates that many of the correlations available in the literature either have defective units or are the product of a small number of experiments. In this study, we benefit from relatively large samples, the radial flow, and the perforation in the middle of the samples. The properties of the samples were measured using mercury intrusion porosimetry. It was found that there is a direct relationship between the porosity and the grain’s size; the greater the size of the grains, the greater the porosity, and vice versa. The non-Darcy coefficient term, β, is found to be inversely proportional to the porosity and permeability. In a previous study, the β was investigated for compressible flow scenarios; however, this study calculated it for an incompressible flow. Finally, by analyzing the β values of both studies, we could deduce new novelty correlations for the β coefficient term, where the permeability, porosity, and tortuosity are included.