Characterizing the complexity assembly of pore structure in a coal matrix: principle, methodology, and modeling application

Here we identify the microstructures in a coal matrix as a dual-complexity system consisting of the original and behavioral complexities, where the former includes the scaling types of single- or multi-scale/phase/type characteristics, and the latter determines the scale-invariance properties of self-similarity, self-affinity, and multifractality. Next we clarify the essentials of scale-invariance properties and unify the definition of behavioral complexity. By employing Voronoi diagrams, we develop a dual-porosity coupling algorithm to describe the original complexity, and set up a mathematical framework to characterize the complexity assembly in fractal dual-porosity media. For modeling demonstration, we select some typical coal samples from different reservoirs in China, extract the scale-invariance parameters and establish fractal topography based on mercury intrusion porosimetry (MIP) and N₂ adsorption data. Using experimental tests, mathematical derivation and numerical simulations in combination, we reveal the principle and methodology for the characterization of the complexity assembly in a coal matrix.