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

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