To evaluate the variability of multi-phase flow properties of porous media atthe pore scale, it is necessary to acquire a number of representative samplesof the void-solid structure. While modern x-ray computer tomography has made itpossible to extract three-dimensional images of the pore space, assessment ofthe variability in the inherent material properties is often experimentally notfeasible. We present a novel method to reconstruct the solid-void structure ofporous media by applying a generative neural network that allows an implicitdescription of the probability distribution represented by three-dimensionalimage datasets. We show, by using an adversarial learning approach for neuralnetworks, that this method of unsupervised learning is able to generaterepresentative samples of porous media that honor their statistics. Wesuccessfully compare measures of pore morphology, such as the Eulercharacteristic, two-point statistics and directional single-phase permeabilityof synthetic realizations with the calculated properties of a bead pack, Bereasandstone, and Ketton limestone. Results show that GANs can be used toreconstruct high-resolution three-dimensional images of porous media atdifferent scales that are representative of the morphology of the images usedto train the neural network. The fully convolutional nature of the trainedneural network allows the generation of large samples while maintainingcomputational efficiency. Compared to classical stochastic methods of imagereconstruction, the implicit representation of the learned data distributioncan be stored and reused to generate multiple realizations of the porestructure very rapidly.
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