Effects of Time-Dependent Adsorption and Creep Deformation on Permeability Evolution of Coal

The role of coalbed methane (CBM) in the global energy transition is becoming increasingly significant. Accurately predicting changes in coal permeability plays a crucial role in the extraction of coalbed methane. The adsorption strain induced by gas adsorption is one of the significant factors controlling permeability. This paper considers the influence of time effects on adsorption deformation and establishes an adsorption deformation evaluation model that comprehensively accounts for the effects of time and temperature, using adsorption kinetics theory as a bridge. In addition, the Betti-Maxwell law is modified to incorporate the influence of adsorption strain, and an internal swelling coefficient is introduced to quantify the effect of gas adsorption on the fracture bulk modulus. Building on this foundation, the dynamic impact of combined thermal and mechanical effects on permeability changes is explored. The influences of time and adsorption are integrated into the creep equation, constructing a creep permeability model that considers the time-dependent effects of adsorption strain. The applicability of the model is validated using publicly available permeability test data. The results indicate that over time, coal permeability generally exhibits a declining trend. During the process of increasing temperature, permeability also shows a decreasing trend, primarily due to the increase in thermal stress within the coal body as temperature rises. Simultaneously, the presence of external stress restricts coal expansion, leading to pore reduction, hindering coalbed methane migration, and reducing permeability. Furthermore, the internal swelling coefficient and its evolution under different temperature, stress, and time conditions are discussed to further understand the mechanism of adsorption strain's impact on coal permeability. The research findings provide valuable contributions to understanding the variation patterns of permeability during coalbed methane extraction in complex geologic environments.