Modelling of fully-coupled CO2 diffusion and adsorption-induced coal matrix swelling

Multiple CO2 diffusion mechanisms coexist in the coal matrix in certain pore pressure ranges and the subsequent CO2 adsorption induced-matrix swelling alters the hydro-mechanical properties of the seam. We investigate the CO2 diffusion/adsorption-induced swelling behaviour of the coal matrix, through a fully-coupled gas flow - adsorption - coal deformation model. Besides the constant diffusion coefficient-based approach, the multiple diffusion mechanisms including slip flow and Knudsen diffusion are further modelled with a theoretically-extended diffusion approach. The two models are validated with the CO2 adsorption and volumetric swelling data to confirm the models' reliability on simulating the CO2 diffusion/adsorption-induced swelling behaviour and to guarantee their time-dependent solving performance. The spatial and temporal analysis demonstrates that a larger fraction of matrix swelling occurs well before the coal matrix reaches its pressure equilibrium, confirming the fact that adsorption induced-swelling starts immediately with the coal-CO2 interaction. The sensitivity analysis concludes that although the maximum adsorbed amount of CO2 at the pressure equilibrium increases with the increasing applied CO2 boundary pressure, the increment is not particularly linear, but gradually reaching a plateau at higher applied boundary pressures. The CO2 adsorption and the coal matrix swelling are highly sensitive to the Langmuir sorption constant and to the Langmuir volumetric strain constant, respectively, thus should be precisely determined for a given coal type - to accurately model the adsorption-swelling process. The extended diffusion approach reveals that the total flow conductance through the matrix increases moderately with the increasing pore pressure but changes substantially with the pore radius. The slip flow increases exponentially with the pore pressure at large pore sizes (i.e. r(t) >= 50 nm), in which almost 100% of contribution is provided by the slip flow mechanism at pore pressures greater than 1 MPa. In contrast, at very low pore pressures (i.e. p < 0.5 MPa), the Knudsen diffusion contributes almost 100% to the total flow conductance, irrespective of the pore size. With the decreasing pore size, the contribution from Knudsen diffusion starts to increase, confirming that the Knudsen diffusion mechanism becomes predominant at relatively smaller pore channels, even at larger pore pressure conditions.