Sequestration of CO2 and H2S into deep unminable coal seams is an attractive option to reduce their emission into atmosphere and at the same time displace preadsorbed CH4 which is a clean energy resource. High coal seam permeability is required for efficient and practical sequestration of CO2 and H2S and recovery of CH4. However, adsorption of CO2 and H2S into coals induces strong swelling of the coal matrix (volumetric strain) and thus reduces significantly coal permeability by narrowing and even closing fracture apertures. Our experimental data on three western Canadian coals show that the adsorption‐induced volumetric strain is approximately linearly proportional to the volume of adsorbed gas, and for the same gas, different coals have very similar volumetric strain coefficient. Impacts of adsorption‐induced swelling on stress and permeability around wellbores were analytically investigated using our developed stress and permeability models. Our model results indicate that adsorption‐induced volumetric strain has significant controls on stress and permeability of producing and sequestrating coal seams and consequently the potential of acid gas sequestration. Coal seams may undergo >10 times enhancement of permeability around CH4‐producing wellbores due to a reduction in effective stress as a result of coal shrinking caused by methane desorption accompanying a reduction in reservoir pressure. Injection of H2S and CO2 on the other hand results in strong sorption‐induced swelling and a marked increase in effective stress which in turn leads to a reduction of coal seam permeability of up to several orders of magnitude. Injection of mixtures of N2 and CO2 such as found in flue gas results in weaker swelling, the amount of which varies with gas composition, and provides the greatest opportunity of sequestering CO2 and secondary recovery of CH4 for most coals. Because of the marked swelling of coal in the presence of H2S, even minor amounts of H2S result in a marked reduction in permeability, and hence sequestration of H2S in deep coals will be likely impractical. Furthermore, high stresses resulting from sorption of acid gases will potentially cause the coal to yield, fracture or slip, and produce fine particles, which further affect permeability and thus methane production and acid gas sequestration.