Multifractal analysis and evolution rules of micro-fractures in brittle tectonically deformed coals of Yangquan mining area

Micro-fractures act as a bridge between pores and macro-fractures and directly affect the permeability of coal reservoirs. Understanding the micro-fracture heterogeneity and its relationships with deformation can enrich our knowledge on the gas transportation behavior of tectonically deformed coals. The multifractal theory was applied to characterize the variations and heterogeneity of micro-fractures in high-rank brittle tectonically deformed coals. The results indicated that the micro-fractures exhibit multifractal behavior at epsilon = 1-1/16 (epsilon being the size of the boxes considered), and that the obtained generalized dimension spectra D-q-q, multifractal singularity spectrum f(alpha)-alpha, and characteristic parameters, including the capacity dimension D-0, information dimension D-1, correlation dimension D-2, D-1/D-0, the width of multifractal spectrum Delta alpha, and the difference of the fractal dimensions Delta f(alpha), can be applied to accurately describe the differences and variations of the micro-fracture distributions and scales. Moreover, the deformation has a significant influence on the variation and heterogeneity of micro-fracture distributions and scales, as demonstrated by the change rules of the characteristic parameters. The D-1, D-2, and D-1/D-0 increased with the increase of deformation degree, while Delta alpha and Delta f(alpha) decreased. Consequently, the deformation leads to higher density, more uniform distributions, and more dispersed and complex scales in the micro-fractures of brittle tectonically deformed coals, and controls the permeability of coal reservoirs.