The Unsteady-State Nature of Sorption and Diffusion Phenomena in the Micropore Structure of Coal: Part 2—Solution

Abstract

Summary A single-phase, 1D mathematical model, formulated in Part 1 of this study, is used to study unsteady-state micropore sorption in the composite micropore/fracture coalbed-methane-transport problem. The mathematical model is solved numerically by writing the transport equations in finite-difference form and linearizing the residual form of the difference equations with the generalized Newton-Raphson procedure. The numerical model is used to compare methane production rates predicted by unsteady- and quasisteady-state sorption formulations. Results indicate that the two models give different rates during early degasification periods. The high rates predicted by the unsteady-state model, however, generally approached lower quasisteady-state rates within the first few months of simulation. The numerical model is also used to examine the time-dependent response of concentration gradients in the micropores to changes in fracture pressure, to compare diffusion rates predicted by spherical and cylindrical micropore elements, and to construct dimensionless type-curve solutions to the coalbed-methane flow problem.