A nonlinear seepage theory model is developed using nuclear magnetic experiment and fractal theory

The threshold pressure gradient becomes notably evident during water injection in soft, low-permeability coal seams. This phenomenon reduces the pressure hydrodynamic force and limits the effectiveness of dust reduction measures in coal mines through water injection. In this study, several mathematical models were developed to clarify the mechanism behind the threshold pressure gradient and identify the key parameters affecting permeability changes during this process. This model combines the stress sensitivity properties of the fluid boundary layer and coal body with fractal theory. The validity of the mathematical model was confirmed by comparing it with both visual experimental results from nuclear magnetic resonance water injection and other theoretical models. Particularly, the Bingham model effectively predicts the effective permeability of coal. Through the analysis of the influencing factors, it is found that the effective permeability increases with the pressure difference, pore compression coefficient, porosity, and maximum pore radius. Conversely, it decreases as the yield stress, fluid viscosity, tortuosity fractal dimension, and pore size distribution fractal dimension increase. Upon considering the impact of various factors, the pore compression coefficient was identified as having the most significant effect on coal permeability, whereas the yield stress has the greatest influence on the threshold pressure gradient. Collectively, our findings provide a theoretical foundation for enhancing the efficacy of water injection in soft, low-permeability coal seams.