A data-driven surrogate to image-based flow simulations in porous media

Abstract The objective for this work is to develop a data-driven surrogate to high-fidelity numerical flow simulations using digital images of porous media. The proposed model can capture the pixel-scale velocity vectors in a large verity of digital porous media created by random two-dimensional (2D) circle packs. To develop the model, images of the 2D media (binary images of solid grains and void spaces) along with their corresponding velocity vectors at the pixel level computed using lattice Boltzmann simulation runs are used to train and to predict the solutions with a high accuracy in much less computational time. The velocity vector predictions made by the surrogate models are used to compute the permeability tensor for samples that have not been used in the training. The results show high accuracy in the prediction of both velocity vectors and permeability tensors. The proposed methodology harness the enormous amount of generated data from high-fidelity flow simulations to decode the often under-utilized patterns in simulations and to accurately predict solutions to new cases. The developed model can truly capture the physics of the problem and enhance the prediction capabilities of the simulations at a much lower cost. These predictive models, in essence, do not spatially reduce the order of the problem. They, however, possess the same numerical resolutions as their Lattice Boltzmann simulations equivalents do with the great advantage that their solutions can be achieved by a significant reduction in computational costs (speed and memory).