Conformable advection–diffusion–reaction models for gas migration in coalbed methane reservoirs

In the framework of conformable calculus, two-dimensional conformable advection–diffusion–reaction (CADR) model for time-dependent gas migration in coalbed methane reservoir is developed in this work. The proposed CADR model is addressed via the $\alpha$-order Laplace and Fourier transform methods under different boundary conditions. Furthermore, the numerical inversions of the Laplace solutions derive the coalbed methane concentration profiles of the CADR model. The numerical simulations demonstrate that the CADR model can well depict the anomalous transport processes of coalbed methane migration in coal seams.