Carbon dioxide injection in coal seams is known to improve the methane production of the coal seam, while ensuring a safe and long-term carbon sequestration. This improvement is due to the preferential adsorption of CO(2) in coal with respect to CH(4): an injection of CO(2) thus results in a desorption of CH(4). However, this preferential adsorption is also known to cause a differential swelling of coal, which results in a significant decrease in the reservoir permeability during the injection process. Recent studies have shown that adsorption in coal micropores (few angströms in size) is the main cause of the swelling. In this work, we focus on the competitive adsorption behavior of CO(2) and CH(4) in micropores. We perform molecular simulations of adsorption with a realistic atomistic model for coal. The competitive adsorption is studied at various temperatures and pressures representative of those in geological reservoirs. With the help of a poromechanical model, we then quantify the subsequent differential swelling induced by the computed adsorption behaviors. The differential swelling is almost insensitive to the geological temperatures and pressures considered here and is proportional to the CO(2) mole fraction in the coal.