Stochastic Characterization, Microstructure Reconstruction and Transport Property Prediction for Porous Media
Authors:   , Fu Jinlong 
Published: March 2022

Porous media are ubiquitous in the natural environment and engineering, and typical ex-amples include rocks, soils, and concretes. Their transport properties (i.e. permeability, effective diffusivity, formation resistivity factor and thermal conductivity) usually exhibit strong uncertainty, due to the intricacy, stochasticity and heterogeneity inherent in pore mi-crostructures. Although high-definition visualizations of opaque porous media can be derived from advanced microscopy imaging techniques (such as micro-CT), it remains a critical challenge to effectively link microstructural characteristics to transport properties. This thesis is devoted to improving the understanding of structure-property relationships of porous media, thereby predicting macroscopic transport properties from observable microstructure informatics. The research objective has been achieved through three interrelated modules: stochastic characterization, microstructure reconstruction and predictive model construction.To bridge the gaps between microstructural characteristics and transport properties, quan-titative characterization of porous media in explicit expression is the essential prerequisite, through which the stochastic morphology of complicated microstructures is reduced to a small set of descriptors related to macroscopic transport properties. A comprehensive review of statistical characterization of pore microstructures is presented, where a wide variety of morphological descriptors are collected through an extensive literature survey, to provide microstructural informatics from the global, local, geometrical and topological perspectives. Tortuosity of porous media is one of the key parameters to model transport properties, and it is systematically examined from the viewpoints of concept and evaluation method in this study. The correlations between geometrical and physical tortuosities are further analyzed, based on which phenomenological relations between them are established.With the limited availability of digital microstructures, the inherent stochasticity of porous media can rarely be captured by using a small number of samples. The complete compu-tational dataset should cover the representative samples with all possible configurations. Stochastic reconstruction of 3D pore microstructure is an effective way to provide large num-bers of samples of arbitrary size for analyzing transport properties of porous media. A novel method is presented to statistically characterize and reconstruct heterogeneous microstruc-tures through a deep neural network model, which can generate 3D pore microstructure samples by well preserving statistical equivalence, long-distance connectivity and transport properties. Besides, another new approach is developed to stochastically reconstruct 3D pore microstructures from 2D cross-sectional images through supervised machine learning, which can rapidly produce more realistic and accurate 3D microstructure samples compared with other three classical approaches.The digital microstructure of high-quality provides a high-fidelity framework for pore-scale simulations of fluid flows, permitting one to evaluate transport properties or explore specific physical phenomena. However, the results obtained from low-resolution images of pore microstructures are often compromised with significant errors, known as the resolution effect. The resolution effect on permeability evaluation from the lattice Boltzmann method is quantitatively investigated, and an error correction model is constructed to reduce/eliminate this resolution effect by identifying the primary error causes. The model uses correlated morphological descriptors to quantify the resolution effect and achieve error correction.What’s more, the dependence of permeability on microstructural characteristics of porous media is fundamentally studied through feature selection and machine learning. The mor-phological descriptors significant to permeability are highlighted and selected through the performance-driven feature selection. In essence, the selected morphological descriptors provide a deep and interpretable insight into the underlying microstructure-permeability linkage. The machine learning-based permeability model is thus built by using the optimal subset of morphological descriptors as the feature data, and the prediction model exhibits excellent performances in predictive accuracy and general applicability.