A Theoretical Investigation of Coal Fracture Evolution with Hydrostatic Pressure and its Validation by CT

The stress-induced evolution of coal fractures significantly affects permeability and, consequently, gas extraction efficiency. This study introduces a novel coal fracture evolution model based on assumptions of fracture morphology and log-normal distribution of fracture aspect ratio. This model offers a theoretical framework for understanding the fracture closure process, ultimately depicting fracture evolution as a combined result of elastic compression and closure. It predicts the decay curve of fracture porosity under hydrostatic pressure loading. We conducted uniaxial compression experiments for determining the mechanical parameters of the model and in situ CT experiments with confining pressure ranging from 0 to 25 MPa for validating the model. The findings indicate the following: (1) Initially, the decline in fracture porosity with stress is predominantly due to elastic compression, followed by a rapid transition to closure. (2) Sensitivity analysis reveals that an increase in two physical quantities—the cube root of the product of the peak aspect ratio and the square of the mean aspect ratio (x_c) and the bulk modulus of the coal matrix (K_m)—results in a decrease in the rate of fracture porosity decay with stress. (3) Tectonic action has a dual effect of augmenting x_c and diminishing K_m. We define the magnification of x_c and the divisor of K_m under a common term—scaling factor. When the scaling factor of x_c is less than that of K_m, the tectonic action promotes the decay of porosity with stress. Conversely, when the scaling factor of x_c is greater than that of K_m, the effect is reversed.