Stochastic Reconstruction of 3D Heterogeneous Microstructure Using a Column-Oriented Multiple-Point Statistics Program

Three-dimensional (3D) microstructure reconstruction is a key approach to exploring the relationship between pore characteristics and physical properties. Viewing the training image as a prior model, multiple-point statistics (MPS) focus on reproducing spatial patterns in the simulation grid. However, it is challenging to efficiently generate 3D nonstationary models with varying microstructures. In this work, we propose column-oriented simulation (ColSIM) to achieve the stochastic reconstruction of 3D porous media. A heterogeneous system is understood as a spatially evolving process that consists of frequent transitions of small magnitude and abrupt changes of large magnitude. First, a training image selection step is suggested to find representative microstructures. Our program applies modified Hausdorff distance, t-distributed stochastic neighboring embedding, and spectral clustering to organize two-dimensional (2D) candidate images. The medoid of each group is applied to guide the following programs. Second, we introduce column-oriented searching into MPS. To save simulation time, a subset of conditioning points is checked to find desired instances. Our program suggests an early stopping strategy to address complex microstructures. Third, a contrastive loss term is designed to create 3D models from 2D slice. To automatically calibrate the volume fraction and simplify parameter specification, the computer consistently monitors the difference between the present model and the target. The performance of ColSIM is examined by 3D multiphase material modeling and 3D heterogeneous shale simulation. To achieve quantitative evaluation, we compute various statistical functions and physical descriptors on simulated realizations. The proposed ColSIM exhibits competitive performance in terms of calculation efficiency, microstructure reproduction, and spatial uncertainty.