Alterations in the pore morphology of porous materials cause changes to the characteristic hydraulic properties, which are mostly non-linear and inherently difficult to predetermine. Assuming the alterations are known with sufficient accuracy, the relation between the altered pore structure, measured in terms of porosity, and intrinsic permeability may be determined by simulations with enormous computational effort. We focus on microfluidic experiments during the course of which the pore space becomes increasingly occupied with solid precipitate over elapsed process time. To analyze these domains, we present a novel geometry-informed drag formulation which allows for solving pseudo-3D Stokes equations for image-based input data of clogging porous media with accuracy and efficiency. In a pre-processing step, local pore space properties are analyzed and employed to spatially vary the magnitude of the drag term, which reflects the influence of neglected 3D effects. Calibration and validation is achieved through fully 3D Finite Difference Stokes simulations of different benchmark cases. With the proposed formulation we achieve the high accuracy of the pseudo-3D methods as far as permeability is concerned (<30% deviation), but also with respect to local velocities, for a microfluidic domain throughout the clogging process. Noteworthy, the computational cost is being reduced to less than 1%. Combining the efficiency of a Stokes 2D simulation and accuracy of a 3D model the presented approach is rendered an interesting option to investigate remaining open questions, for example on anisotropy of effective hydraulic parameters during the clogging process.

中文翻译：

---

一种新颖的几何信息阻力项公式，用于不同孔径的伪 3D Stokes 仿真


多孔材料孔隙形态的改变会导致特征水力特性的变化，这些特性大多是非线性的，本质上很难预先确定。假设已知这些变化足够准确，那么以孔隙率衡量的改变的孔隙结构与内禀渗透率之间的关系可以通过具有大量计算工作的模拟来确定。我们专注于微流体实验，在此过程中，随着过程的流逝，孔隙空间越来越多地被固体沉淀物占据。为了分析这些域，我们提出了一种新的几何知情阻力公式，该公式允许准确有效地求解基于图像的堵塞多孔介质输入数据的伪 3D 斯托克斯方程。在预处理步骤中，分析了局部孔隙空间属性，并利用这些属性在空间上改变阻力项的大小，这反映了被忽视的 3D 效应的影响。校准和验证是通过对不同基准案例的全 3D 有限差分斯托克斯模拟来实现的。通过提出的公式，我们实现了伪 3D 方法的高精度，就渗透率（<30% 偏差），以及在整个堵塞过程中微流体域的局部速度。值得注意的是，计算成本已降至 1% 以下。结合斯托克斯 2D 仿真的效率和 3D 模型的准确性，所提出的方法成为研究剩余悬而未决问题的有趣选择，例如堵塞过程中有效水力参数的各向异性。