Deep learning for pore-scale two-phase flow: Modelling drainage in realistic porous media

In order to predict phase distributions within complex pore structures during two-phase capillary-dominated drainage, we select subsamples from computerized tomography (CT) images of rocks and simulated porous media, and develop a pore morphology-based simulator (PMS) to create a diverse dataset of phase distributions. With pixel size, interfacial tension, contact angle, and pressure as input parameters, convolutional neural network (CNN), recurrent neural network (RNN) and vision transformer (ViT) are transformed, trained and evaluated to select the optimal model for predicting phase distribution. It is found that commonly used CNN and RNN have deficiencies in capturing phase connectivity. Subsequently, we develop a higher-dimensional vision transformer (HD-ViT) that drains pores solely based on their size, regardless of their spatial location, with phase connectivity enforced as a post-processing step. This approach enables inference for images of varying sizes and resolutions with inlet-outlet setup at any coordinate directions. We demonstrate that HD-ViT maintains its effectiveness, accuracy and speed advantage on larger sandstone and carbonate images, compared with the microfluidic-based displacement experiment. In the end, we train and validate a 3D version of the model.