Coal permeability behaviors and non-uniform deformations under various boundary conditions: Part 2-modelling study

This article is the second part of the series: modelling study. Physical properties of the coal fractures are not equal to those of coal bulk, which lead to non-uniform deformation between coal bulk and fractures in response to gas adsorption and pressure change. In this study, we defined three kinds of non-uniform deformation indexes: adsorptive non-uniform deformation index (ANDI), mechanistic non-uniform deformation index (MNDI), and comprehensive non-uniform deformation index (CNDI) to quantify the degrees of the non-uniform deformations between coal bulk and fractures, and we established a new multi-physical field coupling model based on these non-uniform deformation indexes. The theoretical solutions of the new permeability model agree well with the experimental solutions. The non-uniform deformation is contributed by the gas adsorption and mechanical ac-tion, and closely related to the type of boundary conditions. The ratio of the coal bulk modulus to the fracture modulus and the Langmuir pressure constant of matrix controls the MNDI and ANDI, respectively. In addition, in order to explain the fact that part of the theoretical solution of permeability is inconsistent with the experimental solution under constant effective stress condition, we proposed the concept of modified effective stress, which is obtained by adding an additional effective stress based on the traditional effective stress. The additional effective stress reflects the contribution of other factors to effective stress except confining pressure and pore pressure, such as gas adsorption, temperature change, biological decomposition etc. The modified effective stress is the only variable in the new permeability model. The definitions of the additional effective stress and modified effective stress solve the problem that the theoretical solution of permeability is inconsistent with the experi-mental solution.