Investigation of multifractal features in coal pore-fracture network evolution induced by cyclic cryogenic liquid nitrogen shock

To investigate the influence of cyclic liquid nitrogen cold-shock on coal pore-fracture evolution, specimens underwent cold-shock treatments at varying cycles (5, 10, 15, 20). Large-scale nuclear magnetic resonance (NMR) analysis provided T₂ spectra and imaging of treated samples. Multifractal theory was applied to quantify heterogeneous evolution in T₂ distributions and NMR image intensity with increasing cycles. Spearman correlation analysis established relationships between cycle number and multifractal parameter variations, revealing structural heterogeneity progression. Results indicate cyclic liquid nitrogen exposure induces nonlinear, saturation-characteristic alterations to coal pore-fracture networks. During initial cycles (5–10), porosity increased sharply from 1.76% to 2.05%. Subsequent cycles (10–20) promoted cumulative damage propagation wherein micropores coalesced into macroscale fractures, reducing porosity increment to 2.05%–2.13%. NMR imaging reveals the characteristics of non-uniform distribution of pores and fissures in coal. Under the action of cyclic cold shock, the new pores and fissures mainly expand along the original pores, and the pore development area is more prone to connectivity damage, forming a local banded high permeability channel, which enhances the pore connectivity of coal samples. The non-uniform evolution characteristics of pores and fissures in coal under the action of cyclic cold shock are revealed by the combination of T₂ spectrum and multi-fractal results of nuclear magnetic resonance imaging. With the increase of the number of cycles, the homogeneity of pore size distribution in coal increases but the homogeneity of pore space distribution decreases. The T₂ spectrum multifractal mainly focuses on the quantitative characterization of the pore size and number in the sample, and the nuclear magnetic resonance imaging multifractal focuses on the non-uniform quantitative characterization of the pore space. The fitting relationship between the change of multifractal parameters and the number of cycles is constructed, and the nonlinear saturation characteristics of the damage effect of cyclic cold shock on the pore and fracture of coal body are intuitively revealed. This integrated multifractal approach reveals dynamic heterogeneity in coal pore-fracture systems, providing data-driven support for optimizing field parameters in liquid nitrogen fracturing operations.