Dispersive diffusion of gases in coals. Part I: Model development

Abstract

The accurate prediction of gas flow in coals in the field or laboratory requires an accurate model of diffusion within the coal. One major determinant of diffusion rates is the pore size distribution within the coal. In this study, CO2 and CH4 sorption kinetic data have been obtained for two coals of similar rank, but different maceral composition. We used this data to develop a model that assumes a distribution of characteristic times for diffusion. The so-called ‘stretched exponential’ model couples a characteristic rate parameter, k∅, with a stretching parameter, β (0<β<1), in the exponent. This model fitted the experimental data significantly better than a two-stage model that treated diffusion as having a single fast and single slow component. The values of β are similar for the two gases in the same coal at the same pressures. This indicates that β is an intrinsic property of the coal sample (e.g. pore structure, distribution, composition), rather than being caused by the coal–gas interaction. β represents a spread in diffusion times, with the spread reducing as β increases. β increased with pressure for vitrinite-rich coal, indicating that the spread decreased at high pressure. The values of β for inertinite-rich coal did not show a clear trend with pressure. The vitrinite-rich coal may contain pores that sorb gas strongly, and saturate at low pressure, compared with the inertinite-rich coal. In agreement with previous findings, the diffusion rate was substantially faster for CO2 than CH4 for the same coal and the inertinite-rich coal had a far faster diffusion rate than the vitrinite-rich coal. However, the ratios of diffusion rates for CO2 and CH4 differed between the two coals. Our results show that analysing sorption data using the stretched exponential fit provides useful information about the nature of sorption and diffusion processes in coal.