A Stochastic Approach for Generating 3D Digital Sandstone Models with Consistent Pore Networks and Grayscale Variability

Abstract Digital rocks are valuable tools for characterizing porous media and play a key role in advancing our understanding of subsurface processes. This work introduces a stochastic modeling framework for generating synthetic 3D pore networks and digital sandstone samples that reproduce key statistical and geometric patterns observed in micro-CT data, including pore connectivity and grayscale heterogeneity. The underlying stochastic model enables systematic computational experiments to investigate how network connectivity, porosity, and material heterogeneity influence pore-scale behavior and transport properties. The method employs thresholded Gaussian random fields (GRFs) to model pore networks, while the grayscale variation representing material heterogeneity is modeled using random fields statistically parameterized from imaging data and the corresponding grayscale distribution. A double-thresholding approach is proposed that distinguishes pores and clay-like transitional material, enhancing microstructural expressiveness. GRF parameters, such as correlation length, variance, and regularity of the synthetic realizations, are tuned to match sandstone features. An additional contribution is the incorporation of a morphological filtering step that further refines the structures and controls fine-scale connectivity. The fidelity of the synthetic models is validated using Minkowski functionals and distribution-based metrics, benchmarking against a high-resolution 10003-voxel Berea sandstone sample from micro-CT. The GRF sampling is computationally efficient, making it feasible for generating synthetic datasets that support studies on larger representative volumes. The generated synthetic sandstones show encouraging agreement with structural, geometric, and material characteristics observed in the real sample. This systematic and extensible framework, with interpretable parameters, enables generation of a wide range of pore structures and heterogeneities, supporting sensitivity analysis, uncertainty quantification, and pore-scale flow simulations. It opens new avenues for extending digital rock modeling to non-homogeneous formations, including adaptations that account for heavy mineral inclusions and other lithologies.