Abstract This paper presents a numerical approach for the simulation of fluid flow through porous media by proposing a theoretical and numerical meso-to-macro multiscale framework, which combines the advantages of the lattice Boltzmann method (LBM) with the continuum Theory of Porous Media (TPM) to efficiently and accurately model fluid transport in heterogeneous porous media. In particular, LBM presents an alternative to experiments by studying the flow from a mesoscopic perspective, which in turn, allows the derivation of the material parameters needed for simulating the flow in the macroscopic TPM model. In this work, a meso-macro hierarchic upscaling scheme is applied to investigate the deformation-dependent intrinsic permeability properties and the Darcy/non-Darcy fluid flow regime. Concerning the mesoscale, the intrinsic permeability of the porous domain is computed by means of the LBM model at the first stage. Subsequently, deformation of the medium takes place in furtherance of determining the relation of the aforementioned deformation dependency. Thereupon, these findings are input into the TPM model in order to compute the primary unknown variables, where special focus is laid on the stability challenges in the compaction and near compaction states. With respect to the criteria of non-Darcy fluid flow, the conditions of its onset, i.e. the induced pressure gradient and mean fluid flow velocity, are computed as well using the LBM solver and conveyed afterwards to the macroscopic TPM model. Herein, the non-Darcy intrinsic permeability has been investigated in the TPM approach based on the Forchheimer equation. Simulations done on a synthetic porous micro-structure show that the combined framework proved to stand well between the two approaches.

中文翻译：

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可变形、非均质多孔介质中达西和非达西流体流动的放大 LBM-TPM 模拟方法

摘要 本文结合了格子玻尔兹曼方法 (LBM) 和多孔介质连续介质理论的优点，提出了一种理论和数值的细观到宏观多尺度框架，提出了一种模拟流体通过多孔介质流动的数值方法。 TPM) 以高效准确地模拟非均质多孔介质中的流体传输。特别是，LBM 通过从细观角度研究流动，提供了一种替代实验的方法，这反过来又允许推导在宏观 TPM 模型中模拟流动所需的材料参数。在这项工作中，应用细观宏观分层放大方案来研究变形相关的固有渗透率特性和达西/非达西流体流动状态。关于中尺度，多孔域的固有渗透率在第一阶段通过 LBM 模型计算。随后，介质发生变形以进一步确定上述变形依赖性的关系。因此，这些发现被输入到 TPM 模型中，以计算主要的未知变量，其中特别关注压实和接近压实状态下的稳定性挑战。关于非达西流体流动的标准，其起始条件，即诱导压力梯度和平均流体流速，也使用 LBM 求解器计算，然后传送到宏观 TPM 模型。在此，基于 Forchheimer 方程在 TPM 方法中研究了非达西固有渗透率。