Apparent Permeability Model for Hydraulically Fractured Coal Seams: Integrating Damage Heterogeneity, Adsorption Swelling, and Klinkenberg Effects

Hydraulic fracturing serves as a critical bridge between the safe and efficient development of unconventional resources and the supply of cleaner energy. Elucidating the complex migration pathways of gases within the stimulated reservoir is essential for ensuring operational safety and reducing carbon emissions. Hydraulic fracturing in coal reservoirs creates zones of varying damage, leading to nonuniform permeability and stress sensitivity during coalbed methane (CBM) extraction. To investigate permeability characteristics across damage gradients, this study establishes an apparent permeability model for coal that integrates effective stress, damage variables, adsorption-induced swelling, and the Klinkenberg effect, based on the dynamic porosity evolution of damaged coal. Coal samples from the No. 15 seam of Sihe Mine were prepared with increasing damage intensities: raw coal (RCS), microfractured coal (MFCS), and penetrated fracture coal (PFCS). Permeability tests conducted on these samples enabled analysis of the dynamic evolution of damage variables across initial damage states and their interplay with other factors. Results demonstrate that higher damage correlates with greater permeability, yielding a radial permeability gradient from hydraulic fracturing boreholes: permeability and its variability are highest near the borehole, accompanied by elevated damage, lower Klinkenberg coefficients, and smaller internal swelling coefficient of matrix (ISCM). Conversely, distal regions exhibit opposite trends. Permeability in both near- and far-bore regions shows low sensitivity to effective stress. Multiple factors collectively govern coal damage and permeability; sensitivity analysis via the model reveals that coal with low maximum adsorption strain, high Langmuir pressure, large ISCM, and low bulk modulus experiences higher damage, enhancing CBM extraction efficiency. During extraction, effective stress and adsorption-induced swelling exhibit a competitive relationship: high pore pressure favors effective stress dominance, while low pressure shifts control to adsorption swelling. The coal samples with greater initial damage were more affected by effective stress than by adsorption-induced swelling (at 5.5 MPa pore pressure), and the contribution ratios increased successively with the increase in damage degree: 1.54, 1.27, and 0.86. Analysis suggests that improved proppant delivery to distal fracture regions can optimize overall seepage. The developed permeability model effectively characterizes postfracturing coal seam permeability behavior under multifactor influences, providing a basis for CBM production prediction.