Rigorous upscaling techniques offer accurate and computationally-efficient strategies for modeling the behaviors of multi-physical, multiscale phenomena in geological porous media. However, such techniques often rely on a variety of methodological assumptions that prohibit their rigorous application to practical systems (e.g., systems involving heterogeneous porous media, system-scale boundary conditions, and fine-scale dynamics that are not diffusion-dominant). In this work, we aim to formulate an upscaling methodology with few methodological assumptions to provide high levels of model generality and foster the utilization of rigorously-derived upscaled models in practice. In particular, we introduce the (MoFA), a novel upscaling methodology for rigorously modeling heterogeneous porous media and system-scale boundary conditions. We detail MoFA’s implementation for the advective–diffusive transport of a single species and compare the methodology with classic numerical techniques, as well as other rigorous upscaling techniques, to highlight MoFA’s unique combination of and . We then validate the derived model while demonstrating its benefits in three numerical experiments. The results suggest that (1.) the applicability and error guarantees of MoFA models do not directly depend on system geometry, (2.) a model’s applicability and error guarantees can be can arbitrarily expanded and reduced, respectively, with further computational expense, and (3.) with MoFA provides an efficient strategy for generating accurate pore-scale solutions from upscaled results. Ultimately, the results evidence that upscaled models can be rigorously derived for heterogeneous porous media systems and resolved in a fraction of the time it takes to perform the equivalent pore-scale simulations.

中文翻译：

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有限平均法：非均质多孔介质的严格升级方法


严格的放大技术为地质多孔介质中多物理、多尺度现象的行为建模提供了准确且计算高效的策略。然而，此类技术通常依赖于各种方法论假设，这些假设阻碍了它们在实际系统中的严格应用（例如，涉及非均匀多孔介质、系统尺度边界条件和非扩散主导的精细尺度动力学的系统）。在这项工作中，我们的目标是制定一种几乎没有方法论假设的升级方法，以提供高水平的模型通用性，并促进在实践中使用严格推导的升级模型。我们特别介绍了（MoFA），这是一种新颖的升级方法，用于严格建模异质多孔介质和系统规模边界条件。我们详细介绍了 MoFA 对单个物种的平流扩散传输的实施，并将该方法与经典数值技术以及其他严格的升级技术进行比较，以突出 MoFA 的独特组合。然后，我们验证导出的模型，同时在三个数值实验中展示其优点。结果表明：(1.) MoFA 模型的适用性和误差保证并不直接依赖于系统几何形状，(2.) 模型的适用性和误差保证可以分别任意扩展和减少，但需要进一步的计算费用，以及(3.) 与 MoFA 一起提供了一种有效的策略，可以根据放大的结果生成准确的孔隙尺度解决方案。最终，结果证明，可以为非均质多孔介质系统严格推导放大模型，并在执行等效孔隙尺度模拟所需时间的一小部分内解决。