Homogenization-informed convolutional neural network to predict permeability and dispersion in porous media

Abstract

Understanding the transport properties of fluids through porous media is crucial in a wide range of scientific and engineering applications. Accurately predicting key parameters, such as permeability and effective dispersion, is essential for optimizing these processes. These parameters depend not only on the pore-scale geometry but also on flow conditions, and are traditionally expensive to compute since they are generally determined by solving direct numerical simulations on macroscopic pore-scale domains. Such computational costs limit the effectiveness of data-driven approaches in terms both of predictive accuracy and/or types of geometries that can be accurately handled. This is because the computational cost for training over a broad set of topologies and dynamic conditions is prohibitive. In this work, we propose an approach that combines deep learning with multiscale modeling techniques, and exploits the computational efficiency of homogenization theory for periodic domains to support a data-driven technique. By using only a unit cell for training purposes, we are able to generate a large dataset of porous media images and corresponding permeability and dispersion tensors at a significantly reduced computational cost, while spanning an unprecedented range of the geometric and dynamic parameter space. The dataset is composed of 10,000 images, is designed to include a wide variety of morphological properties and serves as the training set for a Convolutional Neural Network (CNN) that estimates permeability and dispersion tensors from both microstructural images and input flow conditions described by the Péclet number. The CNN can quickly and accurately characterize effective properties (permeability and dispersion coefficients) spanning more than three orders of magnitude for a wide range of pore-scale topologies and flow regimes. These results highlight the potential to enhance porous media characterization and prediction in various fields.