Direct numerical simulations of flow on micro-computed tomography (micro-CT) images are extensively used in many disciplines of science and engineering. Recently, we have developed a pore-scale finite volume solver (PFVS) to directly solve for flow on micro-CT images and predict permeability of digital cores. The solver assigns a local conductivity to each voxel based on geometrical and topological constraints. The local conductivity term in PFVS is conventionally calculated by an iterative local scanning algorithm, where the number of iterations depends on the size of the largest flow channel. This can increase the computation time of PFVS significantly if the largest flow channel is reasonably large. In this paper, we apply convolutional neural networks (CNN) to predict local conductivity for each voxel, thus bypassing the iterative algorithm while also preserving the mass conservation in the system by still solving for flow using conventional methods. The network is trained to convert segmented binary images of rocks into a numerical map required for flow simulation by the use of paired image-to-image translation using a ResNet-Style architecture. Comparison of the generated and original coefficient maps shows that the average error is within 1% over the 3D pore geometries used in this study. Then, we compare the absolute permeability results obtained from the original PFVS and the CNN-PFVS and the errors are within 20% with the average of 13.8%. Machine learning improves the computation time significantly especially on the images with large domain size and flow channels. On the samples tested, the speedup factor is 10 times using CNN compared to iterative calculations.

中文翻译：

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CNN-PFVS：集成神经网络和有限体积模型以加速孔隙空间图像的流动模拟

微计算机断层扫描 (micro-CT) 图像上的流动直接数值模拟广泛用于科学和工程的许多学科。最近，我们开发了一种孔隙尺度有限体积求解器 (PFVS)，可直接求解显微 CT 图像上的流动并预测数字岩心的渗透率。求解器根据几何和拓扑约束为每个体素分配局部电导率。PFVS 中的局部电导率项通常由迭代局部扫描算法计算，其中迭代次数取决于最大流动通道的大小。如果最大流道相当大，这会显着增加 PFVS 的计算时间。在本文中，我们应用卷积神经网络 (CNN) 来预测每个体素的局部电导率，从而绕过迭代算法，同时通过仍然使用传统方法求解流来保持系统中的质量守恒。该网络经过训练，可以通过使用 ResNet 样式架构的成对图像到图像转换，将岩石的分段二值图像转换为流动模拟所需的数字地图。生成的系数图和原始系数图的比较表明，本研究中使用的 3D 孔隙几何形状的平均误差在 1% 以内。然后，我们将原始 PFVS 和 CNN-PFVS 获得的绝对渗透率结果进行比较，误差在 20% 以内，平均值为 13.8%。机器学习显着提高了计算时间，尤其是在具有大域大小和流通道的图像上。在测试的样品上，