Rapid Permeability Upscaling using Convolutional Neural Networks
Mohammad Sayyafzadeh, Dominique R. Guerillot · 2022
Summary Calculating the effective permeability entails considerable computation, even with local upscaling techniques. This study proposes a convolutional neural network architecture that estimates effective permeability. The network’s input is the permeability maps of those layers of the fine-scale model that are intended to be upscaled into a single layer with horizontally coarsened cells. It treats each layer of the fine-scale permeability maps as a channel of a high-resolution image. The output is a 3 -channel lower-resolution image where each channel presents the upscaled permeability map in one major direction. The proposed architecture is simple and robust. It consists of two 2D convolutional hidden layers with small kernels and a 2D MaxPooling layer. The network was tested using two different datasets, (1)- a binary-facie fluvial model and (2)- a continuous Gaussian model. For each dataset, 500 geological realisations were created and upscaled using a pressure-solver with periodic boundary conditions. 50% of the realisations were used for training and the remaining for testing. The network captured the nonlinear behaviour very promisingly with no overfitting signs. The results were not only visually acceptable, but also the mean of the L2 norms was negligible (below 0.05 mD in the first dataset and below 0.01 mD in the second dataset). Two-phase simulation results also verified the accuracy of the estimated permeabilities. The proposed method can reduce the upscaling computation significantly. The training time was considerably less than the computation time needed for upscaling using the pressure-solver method. The proposed method can be a step towards more computationally efficient extended-local and quasi-global permeability upscaling methods.