Seepage Characteristics and Critical Scale in Gas-Bearing Coal Pores Under Water Injection: A Multifractal Approach

To investigate the flow characteristics of movable water in coal under the influence of micro-nano pore fractures with multiple fractal structures, this study employed nuclear magnetic resonance (NMR) and multifractal theory to analyze gas–water seepage under different injection pressures. Then, the scale threshold for mobile water entering coal pores and fractures was determined by clarifying the relationship among “injection pressure-T2 dynamic multiple fractal parameter seepage resistance-critical pore scale”. The results indicate that coal samples from Yiwu (YW) and Wuxiang (WX) enter the nanoscale pore size range at an injection pressure of 8 MPa, while the coal sample from Malan (ML) enters the nanoscale pore size range at an injection pressure of 9 MPa. During the water injection process, there is a significant linear relationship between the multiple fractal parameters log X(q, ε) and log(ε) of the sample. The generalized fractal dimension D(q) decreases monotonically with increasing q in an inverse S-shape. This decrease occurs in two distinct stages: D(q) decreases rapidly in the low probability interval q < 0; D(q) decreases slowly in the high probability interval q > 0. The multiple fractal singularity spectrum function f(α) has an asymmetric upward parabolic convex function relationship with α, which is divided into a rapidly increasing left branch curve and a slowly decreasing right branch curve with α0 as the boundary. Supporting evidence indicates the feasibility of a methodology for identifying the variation in multiple fractal parameters of gas–water NMR seepage and the critical scale transition conditions. This investigation establishes a methodological foundation for analyzing gas–water transport pathways within porous media materials.