Understanding flow of non-Newtonian fluids in porous media is critical to successful operation of several important processes, including polymer flooding, filtration, and food processing. In some cases, such as when a non-Newtonian fluid can be represented by the power-law model, simulation of its flow in a porous medium is a straightforward extension of that of Newtonian fluids. In other cases, such as flow of Bingham fluids, there is a minimum external threshold pressure below which there would be no macroscopic flow in the porous medium. Computing the threshold pressure is a difficult problem, however. We present a new algorithm for determining the threshold pressure for flow of a Bingham fluid through a porous medium, modeled by a pore-network (PN) model. The algorithm, the ant colony optimization (ACO), is described in detail and together with the PN model is used to determine the minimum pressure for flow of Bingham fluids in a heterogeneous porous medium, the Mt. Simon sandstone, whose PN and morphological properties were extracted from the sandstone’s image. To assess the accuracy and computational efficiency of the ACO algorithm, we also carry out the same computations with two previous methods, namely invasion percolation with memory (IPM) and the path of minimum pressure (PMP) algorithms. The IPM does not guarantee identification of the optimal flow path with the minimum threshold pressure, while the PMP algorithm provides an approximate, albeit accurate, solution of the problem. We also compare the computational complexity of the three methods. For large PNs, both the IPM and PMP are much less efficient than the ACO algorithm. Finally, we study the effect of the morphology of the pore space on the minimum threshold pressure.

中文翻译：

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确定最佳路径并计算宾汉流体通过非均质多孔介质流动的阈值压力

了解非牛顿流体在多孔介质中的流动对于几个重要过程的成功运行至关重要，包括聚合物驱、过滤和食品加工。在某些情况下，例如当非牛顿流体可以用幂律模型表示时，其在多孔介质中的流动模拟是牛顿流体流动的直接扩展。在其他情况下，例如宾汉流体的流动，有一个最小外部阈值压力，低于该压力在多孔介质中将没有宏观流动。然而，计算阈值压力是一个难题。我们提出了一种新算法，用于确定宾汉流体通过多孔介质流动的阈值压力，由孔隙网络 (PN) 模型建模。算法，蚁群优化（ACO），详细描述并与 PN 模型一起用于确定宾汉流体在非均质多孔介质 Mt. 中流动的最小压力。Simon 砂岩，其 PN 和形态特性是从砂岩图像中提取的。为了评估 ACO 算法的准确性和计算效率，我们还使用之前的两种方法进行了相同的计算，即内存入侵渗透 (IPM) 和最小压力路径 (PMP) 算法。IPM 不保证识别具有最小阈值压力的最佳流动路径，而 PMP 算法提供了近似但准确的问题解决方案。我们还比较了三种方法的计算复杂度。对于大型 PN，IPM 和 PMP 的效率都远低于 ACO 算法。最后，