Coupled effective stress and internal stress for modeling coal permeability

Although the effects of gas sorption and pore pressure have been considered in current permeability models, most of these models have been developed from the perspective of either the effective stress (related to pore pressure and gas sorption) or the internal interaction between the matrix and cleat. The coupling effect has rarely been considered. In this study, two internal stresses (i.e., internal compressive and sorption stresses) are proposed to quantitatively represent the internal interactions between the matrix and cleat, which are associated with pore pressure and gas sorption, respectively. Using this, a new permeability model considering the coupling effect of the effective stress and the internal interaction between the matrix and cleat was established. In addition, three sets of permeability and horizontal stress experiments were performed to determine the unknown parameters in the model. Comprehensive analysis of the experimental results revealed that the horizontal stress increases linearly under an increase in pore pressure; meanwhile, a Langmuir-like equation can well describe the behavior related to gas sorption. Subsequently, a model for the effective horizontal stress of a coalbed is established. In addition, a linear equation and another Langmuir-like equation are used to describe the internal compressive and sorption stresses, respectively. Finally, the effects of these terms in the model on the response of the coal permeability are discussed. The results show that, in addition to the effective stress, the internal stresses are extremely important in controlling coal permeability. The new model results match the experimental data excellently.

Automated summary

This study proposes a new permeability model considering the coupling effect of effective stress and internal interaction between matrix and cleat. Experimental results show that horizontal stress increases linearly with increasing pore pressure, and gas sorption behavior can be described by a Langmuir-like equation.