Generation of pore-space images using improved pyramid Wasserstein generative adversarial networks

High-resolution three-dimensional X-ray microscopy can be used to image the pore space of materials. Machine learning algorithms can generate a statistical ensemble of representative images of arbitrary sizes for rock characterization, modeling, and analysis. However, current methods struggle to capture features at different spatial scales observed in many complex rocks which have a wide range of pore size. We use the Improved Pyramid Wasserstein Generative Adversarial Network (IPWGAN) to automatically reproduce multi-scale features in segmented three-dimensional images of porous materials, enabling the reliable generation of large-scale representations of complex porous media. A Laplacian pyramid generator is introduced, which creates pore-space features across a hierarchy of spatial scales. Feature statistics mixing regularization enhances the discriminator’s ability to distinguish between real and generated images by mixing their feature statistics, thereby indirectly enhancing the generator’s ability to capture and reproduce multi-scale pore-space features, leading to increased diversity and realism in the generated images. The method has been tested on five sandstone and carbonate samples. The generated images, which can be of any size – including cm-scale ten-billion-cell images – demonstrate the power of the approach. These images have two-point correlation functions, porosity, permeability, Euler characteristic, curvature, and specific surface area closer to those of the training datasets than existing machine learning techniques. The generated images accurately capture geometric and flow properties, demonstrating a considerable improvement over previously published studies using generative adversarial networks. For instance, the mean relative error in the calculated absolute permeability between the Berea sandstone images generated by IPWGAN and the corresponding real rock images can be reduced by 79%. The work allows representative models of a wide range of porous media to be generated, offering potential benefits in carbon dioxide sequestration, underground hydrogen storage, and enhanced oil recovery.