Characterization of complexity assembly 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.