From Pre‐Darcy Flow to Darcy Flow in Porous Media: A Simple Unified Model

Extensive experiments have demonstrated that fluid flow in low‐permeability media deviates from Darcy's law at low pressure gradients, which is called pre‐Darcy flow. Although numerous pre‐Darcy flow models have been proposed, these models generally contain one or more empirical parameters with no clear physical meaning. In this paper, we present a simple unified model to describe pre‐Darcy flow in porous media by introducing the concept of loss permeability. The physical meaning of the loss permeability parameter and its relationship to permeability are analyzed. Based on the statistics of the loss permeability parameter results of 24 core samples, we found that there is a good positive correlation between the loss permeability parameter and the absolute permeability. A smaller loss permeability indicates a stronger fluid‐solid interaction and a stronger nonlinearity between the flow velocity and the pressure gradient. Taking a one‐dimensional linear unsteady flow of a slightly compressible fluid in a homogeneous porous medium as an example, we solve the pressure diffusion equation based on the proposed model using a finite difference method. Our results demonstrate that the rate of pressure propagation for pre‐Darcy flow is slower than that for Darcy flow for the entire observation period, which corrects previous conclusions. This study is highly important for improving the understanding of fluid flow in low‐permeability media. Plain Language Summary Pre‐Darcy flow usually occurs in low‐permeability media when the pressure gradient is very low. As the pressure gradient increases, the flow gradually transitions from the pre‐Darcy flow to Darcy flow. For a long time, pre‐Darcy flow and Darcy flow were described using two relatively independent equations, which is highly inconvenient. Because it is very difficult to accurately determine the critical pressure gradient between the pre‐Darcy flow and the Darcy flow, especially for the fluid flow in natural low‐permeability reservoirs. How to perfectly unify the pre‐Darcy flow and the Darcy flow in a simple and easy‐to‐use model is a scientific problem that has been researched for decades. Although several unified models have been proposed in recent years, they all contain one or more empirical parameters with no clear physical meaning. In this study, we propose a simple unified model to describe the flow from the pre‐Darcy flow to the Darcy flow in a porous medium by introducing the concept of loss permeabilit