A deep learning approach to predicting permeability of porous media

Abstract

In this work, a data-driven surrogate to high-fidelity numerical simulations is developed to replace the numerical simulations of porous media., This model can accurately predict flow fields for new sets of simulation runs by learning the communications among grid cells in the numerical domain. Because of the many possible random arrangements of particles and their orientation to each other, generalization of permeability with high accuracy is not trivial — nor is it practical using conventional means. Furthermore, building a comprehensive database for different grain/pore arrangements is impossible because of the cost of running numerical simulations to generate the database that represents all possible arrangements. The objective is to predict grid-level flow fields in porous media as a priori to determine the permeability of porous media. This work is a continuation of our previous research. The rationale is that once the detailed grid-level dynamics can be accurately predicted using a data-driven approach, for any configuration/topology of the porous media, the detailed dynamics could be predicted without any need for new expensive new numerical simulation runs. In this work, we improved previous work by accurately predicting permeability of the porous media, irrespective of the grain density, pore/grain shape, with a significant reduction in computational time as opposed to previous work, which was limited to a unique grain shape/size. The surrogate model is developed by employing a deep learning technique using high-fidelity numerical simulations for two-dimensional porous media consisting of circular grains, generated by varying the number and size of the circular solid grains. The robustness of the developed model is then tested for numerous variations of porous media – generated by changing the number and size of the solid grain angularity and elongation – which have not been used for developing the model. The deep convolutional neural network employed in this work combines deep U-Net and ResNet structures to capture context and enable precise localization while avoiding issues in training caused by vanishing gradients.