Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS

TL;DR

This paper introduces a physics-informed CNN trained on DNS-generated permeability data from micro-CT images, improving accuracy and robustness in predicting permeability of geological samples by incorporating flow-based features.

Contribution

The novel approach combines DNS simulations with a physics-informed CNN that uses flow-based features, overcoming LBM limitations and enhancing permeability prediction accuracy.

Findings

High prediction accuracy across sandstone samples

DNS-based training data improves model robustness

Flow-based features enhance permeability estimation

Abstract

In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations.