A model for competitive displacement of adsorbed methane by CO2 injection is presented. A key feature of the model is the use of a bidisperse pore-diffusion model that accounts for both macro- and micropore diffusion in the coal matrix. The model was applied to analyse the performance of a laboratory core flush test and an excellent match to the test date was achieved. The results of history matching indicate that the overall sorption rate is controlled by the micropore diffusion. Furthermore, a variable apparent micropore diffusivity, which is dependent on the total sorbate concentration in the coal sample, is required to yield a close match to the test data.