Estimation and modeling of pressure-dependent gas diffusion coefficient for coal: A fractal theory-based approach

Abstract

Diffusion coefficient is one of the key parameters determining the coalbed methane (CBM) reservoir economic viability for exploitation. Diffusion coefficient of coal matrix controls the long-term late production performance for CBM wells as it determines the gas transport effectiveness from matrix to fracture/cleat system. Pore structure directly relates to the gas adsorption and diffusion behaviors, where micropore provides the most abundant adsorption sites and meso- and macro-pore serve as gas diffusive pathway for gas transport. Gas diffusion in coal matrix is usually affected by both Knudsen diffusion and bulk diffusion. A theoretical pore-structure-based model was proposed to estimate the pressure-dependent diffusion coefficient for fractal porous coals. The proposed model dynamically integrates Knudsen and bulk diffusion influxes to define the overall gas transport process. Uniquely, the tortuosity factor derived from the fractal pore model allowed to quantitatively take the pore morphological complexity to define the diffusion for different coals.Both experimental and modeled results suggested that Knudsen diffusion dominated the gas influx at low pressure range (<2.5 MPa) and bulk diffusion dominated at high pressure range (>6 MPa). For intermediate pressure ranges (2.5–6 MPa), combined diffusion should be considered as a weighted sum of Knudsen and bulk diffusion, and the weighing factors directly depended on the Knudsen number. The proposed model was validated against experimental data, where the developed automated computer program based on the Unipore model can automatically and time-effectively estimate the diffusion coefficients with regressing to the pressure-time experimental data. The theoretical determined diffusion coefficients well predicted the pressure-dependent variations of the experimental measured diffusion coefficient for different coals. This theoretical model is the first-of-its-kind to link the realistic complex pore structure into diffusion coefficient based on the fractal theory. The experimental results and proposed model can be coupled into the commercially available simulator to predict the long-term CBM well production profiles.