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.

中文翻译：

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从前达西流到多孔介质中的达西流：一个简单的统一模型


大量实验证明，低渗透介质中的流体流动在低压梯度下偏离达西定律，称为前达西流。尽管已经提出了许多前达西流模型，但这些模型通常包含一个或多个没有明确物理意义的经验参数。在本文中，我们通过引入渗透率损失的概念，提出了一个简单的统一模型来描述多孔介质中的前达西流动。分析了损失渗透率参数的物理意义及其与渗透率的关系。通过对24块岩心样品损失渗透率参数结果的统计，我们发现损失渗透率参数与绝对渗透率之间存在良好的正相关关系。损失渗透率越小，表明流固相互作用越强，流速和压力梯度之间的非线性越强。以均匀多孔介质中微可压缩流体的一维线性非定常流动为例，我们利用有限差分法求解基于所提出模型的压力扩散方程。我们的结果表明，在整个观测期间，前达西流的压力传播速率比达西流的压力传播速率慢，这纠正了之前的结论。这项研究对于提高对低渗透介质中流体流动的理解非常重要。