Impact of matrix swelling area propagation on the evolution of coal permeability under coupled multiple processes

• Transition from local swelling to global swelling is quantified under most complex situations.
• Critical Swelling Area defines the relationship between swelling and permeability.
• Concepts of Swelling Transition and Critical Swelling Area explain experimental observations.

In coal permeability models, it is normally assumed that coal matrix pressure is equalized with the fracture pressure (local equilibrium). In this assumption, coal swells uniformly under constant confining (total) stress conditions commonly used in laboratory measurements. Under these conditions, a uniform swelling will not change the fracture aperture for a matchstick model where only two sets of vertical fractures cut through the whole matrix blocks. However, a uniform swelling changes both the fracture aperture and the spacing (the coal bridge swelling increases the fracture aperture while the matrix swelling changes the spacing only) for a fractured coal model, where fractures do not create a full separation between adjacent matrix blocks but where solid coal bridges are present, is used. Therefore, coal permeability remains unchanged for a matchstick model or increases slightly due to the coal bridge swelling under common laboratory conditions. These conclusions are directly contradictory with most laboratory observations in the literature. This direct contradiction suggests that the local equilibrium condition has not been achieved under common laboratory conditions. If this was the case, the current local equilibrium assumption based approach would be inappropriate for the analysis of laboratory measurements.In our previous studies, we introduced a concept of matrix swelling transition from local to global under stress conditions. In this concept, we recognized the fact that coal permeability evolves as a function of time from the initial equilibrium state (both matrix pressure and fracture pressure are equal to the initial reservoir pressure) to the final equilibrium state (both matrix pressure and fracture pressure are equal to the injection pressure). In this study, we extended this concept to the most complex situations where multiple processes (thermal transport, gas transport and coal deformation) are involved. Based on the concept of matrix swelling transition, we introduced a new concept of Critical Swelling Area that defines the relationship between swelling transition and coal permeability evolution. The combination of swelling transition and Critical Swelling Area concepts can explain why adsorptive types of gas injection reduces coal permeability in the early stage of the injection and may rebound later.