The Unsteady-State Nature of Sorption and Diffusion Phenomena in the Micropore Structure of Coal: Part 1 - Theory and Mathematical Formulation

Abstract

Summary A single-phase, 1D mathematical formulation is developed in radial/cylindrical coordinates to examine unsteady-state micropore sorption in a composite micropore/fracture, coalbed-methane transport problem. In the formulation, the micropore transport equation accounts for unsteady-state sorption and diffusion in the primary porosity. Gas entering the fracture network is considered a source term in the fracture-transport equation. The micropore and fracture systems are coupled by equating the gas pressure at the surface of the micropore elements to the pressure in the fracture network. Introduction Coalbed-methane reservoirs are characterized by a dual-porosity nature. Gas molecules stored in the micropore structure by adsorption are subject to desorption from the coal grain surfaces and to diffusional transport to a well-defined, natural fracture network. Laminar flow dominates in the fracture network where methane gas flows simultaneously with formation water. Gas transport in the micropores is generally modeled with quasisteady- or unsteady-state sorption formulations. In the first case, the matrix-to-fracture gas transfer rate is calculated from the average concentration gradient in the matrix elements over a discrete timestep. In contrast, unsteady-state formulations use a nonuniform micropore concentration gradient to determine the matrix transfer rate. Quasisteady-state models offer the advantage of simplified mathematics, which can reduce computer simulation costs. Reservoir Characteristics of Coal Seams. Coal seams are characterized by a natural fracture network commonly referred to as cleat. The cleat system consists of two perpendicular fissures, the more predominant of which is the face cleat. The butt cleat is less continuous and often ends when it intersects the face cleat. Fig. 1 is a highly idealized representation of the physical relationship between the matrix and fracture system.