One area of intense scientific interest for the study of sandstones, carbonates, and shale at the pore scale is the use of limited image and petrophysical data to generate multiple realizations of a rock’s pore structure. Such images aid efforts to quantify uncertainty in petrophysical properties, including porosity–permeability transforms. We develop and evaluate a deep learning-based method to synthesize porous media volumes using a so-called generative flow model trained on x-ray microscope images of rock texture and pore structure. These models are optimized on a log-likelihood objective and they synthesize large and realistic three-dimensional images. We demonstrate the rapid generation of sandstone image volumes that display realism as gauged by quantitative comparison of topological features using Minkowski functionals of porosity, specific surface area, and the Euler–Poincaré characteristic (i.e., pore connectivity). We also evaluate the single-phase permeability using Navier–Stokes and lattice Boltzmann methods and show that transport properties of the generated samples match measured trends.

在孔隙尺度上研究砂岩、碳酸盐和页岩的一个具有强烈科学兴趣的领域是使用有限的图像和岩石物理数据来生成岩石孔隙结构的多种实现。这些图像有助于量化岩石物理特性的不确定性，包括孔隙度-渗透率变换。我们开发并评估了一种基于深度学习的方法，使用在岩石纹理和孔隙结构的 X 射线显微镜图像上训练的所谓生成流动模型来合成多孔介质体积。这些模型在对数似然目标上进行了优化，它们合成了大而逼真的 3D 图像。我们展示了砂岩图像体积的快速生成，这些图像体积通过使用孔隙度的 Minkowski 泛函对拓扑特征进行定量比较来衡量，显示出真实感，比表面积和欧拉-庞加莱特性（即孔隙连通性）。我们还使用 Navier-Stokes 和格子 Boltzmann 方法评估单相渗透率，并表明生成的样品的传输特性与测量趋势相匹配。