A dual-permeability model for coal under tri-axial boundary conditions

Abstract

Matrix and fracture permeability are important parameters of the dual porosity numerical model for CBM production and ECBM recovery, and thus various dual-permeability models have been developed. However, the deformation mechanisms of coal matrix and fracture under tri-axial boundary conditions have not yet fully considered in these models. In this study, these mechanisms are described from the following two aspects: (1) the newly defined mechanistic compressibility and sorption coefficients have respectively introduced to characterize mechanistic and sorption-induced strains of the matrix system, and both the confining and gas pressure of matrix are considered to quantify the matrix deformation. (2) based on cubic model, the REV deformation, which is derived from the linear dual-porosity constitutive law, and matrix deformation are considered to define the fracture deformation. And then, the new dual-permeability model is formulated with four different expressions to characterize the evolution of matrix and fracture permeability under tri-axial, bi-axial, and uni-axial strain, as well as fully rigid constraints. Furthermore, the model robustness is verified through comparisons with published experimental data, field data. The results show good consistency under both field and laboratory conditions, and our model can cover most of the variation trends of the other models. Finally, The model sensitivity to three newly defined parameters (Cmpc(M) , f , f1) is addressed by application in a finite element model, and show that Under different tri-axial boundary conditions, the mechanistic compressibility Cmpc(M) and the sorption coefficient f have a more significant impact on the matrix permeability km respectively, while the sorption coefficient f1 has a more obvious influence on the fracture permeability kf. Besides, permeability evolution under fully rigid constrained condition is significantly different from that under other boundary conditions and more susceptible to changes in these three parameters.