Using the density functional theory (DFT) and grand canonical Monte Carlo (GCMC) simulation, the adsorptions of each of an individual gas molecule (CH4, CO2, H2O or N-2) and their mixed gases on heterogeneous surface models of coal (HSMC) have been investigated systematically. The GCMC calculations show that the amount of gases adsorbed increases gradually with the rise of pressures and tends to be gently adsorption equilibrium after high pressure as well as decreases step by step with the coverages from 3.125% to 50% or with moisture range from 0.84 to 23.57 mmol/g at room temperature and pressure up to 10 MPa. In mixed gases, we also found that CO2 preferentially adsorbs at importantly greater loadings than CH4 and N-2, whereas CH4 is more preferentially adsorbed than N-2 on HSMC. The presence of N-2 no significantly effect on CH4 and CO2 adsorption, particularly for CO2. Meanwhile, a trace amount of CH4 and/or CO2 in mixtures is easy to dissolve in H2O or to form CH4 or CO2 clathrates while a large number of N-2 molecules exist in containing moisture systems of HSMC. (C) 2016 Elsevier B.V. All rights reserved.