Rapid Permeability Upscaling of Digital Porous Media via Physics‐Informed Neural Networks

Abstract Subsurface processes are important in solving many of the grand challenges facing our society today, including the sustainable extraction of hydrocarbons, the permanent geological sequestration of carbon dioxide, and the seasonal storage of renewable energy underground. Permeability characterization of underground rocks is the critical first step in understanding and engineering these processes. While recent advances in machine learning methods have enabled fast and efficient permeability prediction of digital rock samples, their practical use remains limited since they can only accommodate subsections of the digital rock samples, which is often not representative of properties at the core‐scale. Here, we derive a novel analytical solution that approximates the effective permeability of a three‐dimensional (3D) digital rock consisting of 2 × 2 × 2 anisotropic cells based on the physical analogy between Darcy’s law and Ohm’s law. We further develop physics‐informed neural network (PINN) models that incorporate the analytical solution and subsequently demonstrate that the PINN equipped with the physics‐informed module achieves excellent accuracy, even when used to upscale previously unseen samples over multiple levels of upscaling. Our work elevates the potential of machine learning models such as 3D convolutional neural network for rapid, end‐to‐end digital rock analysis at the core‐scale. Key Points We derive a novel analytical solution that approximates the permeability of a three‐dimensional (3D) digital rock consisting of 2 × 2 × 2 anisotropic cells We develop physics‐informed neural network (PINN) models that incorporate the analytical solution for accurate permeability upscaling The PINN model, when applied in concert with a 3D convolutional neural network model, achieves rapid, accurate permeability prediction of large digital rock samples