CNN-PFVS: Integrating Neural Network and Finite Volume Models to Accelerate Flow Simulation on Pore Space Images

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.