Porous media characterization is crucial to engineering projects where the pore shape has impact on performance gains. Membrane filters, sportswear fabrics, and tertiary oil recovery are a few examples. Kozeny–Carman (K–C) models are one of the most frequently used to understand, for instance, the relation between porosity, permeability, and other small-scale parameters. However, they have limitations, such as the inability to capture the correct dependence of permeability on porosity, the imperfect handling of the linear and nonlinear effects yielded by its fundamental quantities, and the insufficiency of geometrical parameters to predict the permeability correctly. In this paper, we cope with the problem of determining shape factors for generic geometries that represent sundry porous media configurations. Specifically, we propose a method that embeds the Poiseuille number into the classical K–C equation and returns a substitute shape factor term for its original counterpart. To the best of our knowledge, the existing formulations are unable to obtain shape factors for pores whose geometry is beyond the regular ones. We apply a Galerkin-based integral (GBI) method that determines shape factors for generic cross sections of pore channels. The approach is tested on straight capillaries with arbitrary cross sections subject to steady single-phase flow under the laminar regime. We show that shape factors for basic geometries known from experimental results are replicable exactly. Besides, we provide shape factors with precision up to 4 digits for a class of geometries of interest. As a way to demonstrate the applicability of the GBI approach, we report a case study that determines shape factors for 19 generic individual pore sections of a laboratory experiment involving flow rate measurements in an industrial arrangement of a water-agar packed bed. Porosity, flow behavior, and velocity distributions determined numerically achieve a narrow agreement with experimental values. The findings of this study provide parameters that can help to design new devices or mechanisms that depend on arbitrary pore shapes, as well as to characterize fluid flows in heterogeneous porous media.

多孔介质的表征对于孔形状影响性能提升的工程项目至关重要。膜过滤器，运动服面料和三次采油就是其中的几个例子。例如，Kozeny-Carman（K-C）模型是最常用于理解孔隙度，渗透率和其他小尺度参数之间关系的模型之一。但是，它们具有局限性，例如无法捕获渗透率对孔隙度的正确依赖性，由其基本量产生的线性和非线性效应的处理不完善，以及无法正确预测渗透率的几何参数不足。在本文中，我们解决了确定代表各种多孔介质构造的通用几何形状的形状因子的问题。具体来说，我们提出了一种方法，该方法将Poiseuille数嵌入经典的K–C方程中，并为其原始对应项返回一个替代形状因子项。据我们所知，现有配方无法获得几何形状超出常规形状的孔的形状因子。我们应用基于Galerkin的积分（GBI）方法来确定孔通道的通用横截面的形状因子。该方法在具有任意横截面的直毛细管上进行测试，该直管在层流状态下经受稳定的单相流动。我们表明，从实验结果得知的基本几何形状的形状因子是可精确复制的。此外，对于一类感兴趣的几何形状，我们提供精度高达4位的形状因数。为了证明GBI方法的适用性，我们报告了一个案例研究，该案例确定了涉及水琼脂填充床工业布置中的流量测量的实验室实验的19个通用单个孔部分的形状因子。数值确定的孔隙率，流动行为和速度分布与实验值实现了狭窄的一致性。这项研究的发现提供了可以帮助设计依赖于任意孔形状的新装置或机制的参数，并有助于表征非均质多孔介质中的流体流动。