Dynamical modeling of coupled heat and mass transfer process of coalbed methane desorption in porous coal matrix

Abstract

Although it has been well known that heat transfer occurs with coalbed methane desorption in porous coal matrix, little is understood about the coupling interaction between the heat transfer and mass transfer in this process. In this work, considering the endothermic characteristics of gas desorption and the dependence of gas diffusion on temperature, a coupled gas diffusion and heat conduction model with isothermal or adiabatic boundary condition is developed to accurately describe the dynamical process of heat and mass transfer in coal matrix. The heat induced by gas desorption is treated as an unsteady volumetric heat sink and compared with the traditional uncoupled diffusion model. The governing equations are solved by an implicit finite-difference scheme with the method of Gauss-Seidel iterations. The variations of the fraction of gas desorbed, gas concentration and temperature distributions and heat flux as well as their parametric sensitivity analysis are systematically discussed. It is revealed that the heat transfer in coal matrix has significant effects on the behaviors of gas desorption. With the increasing desorption time, the excess temperature under isothermal boundary condition first drops rapidly and then rises slowly, while the excess temperature under adiabatic boundary condition monotonically drops and changes far more than the isothermal condition. Furthermore, the excess gas concentration decreases with the initial temperature, but increases with the activation energy of gas desorption. The differences in gas concentration under different thermal boundary conditions are increasing with time, but decrease with radial distance. Comparing with the coupled model, the uncoupled diffusion model overestimates the fraction of gas adsorbed. Finally, the heat flux through the coal matrix increases rapidly to the peak value and then decreases slowly to zero.