Swelling and anomalous diffusion mechanisms of co2 in coal
We propose a theory to explain the diffusion process of CO2 in coal and its relation to matrix swelling. The swelling of coal matrix by the sorption of CO2 is characterized by an anomalous diffusion process. We suggest the application of theories of sorption behavior of polymers for coals. The mechanism of CO2 diffusion in coal can be determined by a variety of experimental techniques. Considering the fact that swelling is proportional to the amount of material that has diffused into the matrix, the dimensionless mass uptake curve can be plotted against time according to the equation Mt/Me≈ktn . If the diffusion exponent n is 0.5 (for planar systems) the diffusion is Fickian. Non-Fickian / anomalous behavior is observed for 0.5<n<1.0, with a limit of Case II transport for n = 1.0. Anomalous and Case II diffusion are indicative of the coupling of diffusional and relaxational mechanisms.
Relaxation is related to the transition of coal from glassy to a rubbery state. Major relaxational mechanisms are indicative of swelling related stresses in coal. The diffusion exponent for a Warndt Luisenthal coal sample has been experimentally determined having values inbetween 0.7 and 0.8. A mathematical model is presented, which can be used to describe the anomalous transport of CO2 in thin coal slabs. Parameters specific to a CO2 - coal system have been determined and simulation results will be presented. The sharp diffusion front which is a characteristic of Case II diffusion is observed and results from a discontinuity in the diffusivity - concentration relationship. This model will be useful in defining anomalous transport behavior of CO2 in the macromolecular network structure of coal.