Generalized equations for the inertial coefficient in non-Darcy porous flow

It is well known that deviation from Darcy’s law occurs for fluid through porous media at high velocity. In this situation, we are faced with a change in the behavior of the flow, which is called non-Darcy flow. Non-Darcy flow regime is important for describing fluid flow in both consolidated or unconsolidated porous media and it is described by the Forchheimer’s equation by adding a quadratic term to Darcy’s equation. Numerous studies have been dedicated to finding a reliable and unique formula that can precisely predict Forchheimer’s coefficient (β) in high velocity flows. Many researchers have made significant efforts to find a criterion or generalized equation to understand this phenomenon, but finding a universally applicable equation remains challenging. In this thesis, we have tried to reach a general equation to predict Forchheimer’s parameters (β, k, and 𝜑 ) by collecting data from 125 papers and performing a universal fit. Despite efforts, eliminating outliers, and achieve a high R2(0.95) but results derived from the MATLAB fitter toolbox indicate dissatisfaction with an exponent of k ([1.05-1.11]) and low porosity [0-0.5].