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An equation of state (EOS) of CH4-N2 fluid mixtures in terms of Helmholtz free energy has been developed by using four mixing parameters, which can reproduce the pressure-volume-temperature-composition (PVTx) and vapor-liquid equilibrium (VLE) properties of CH4-N2 fluid mixtures. The average absolute deviation of all the PVTx data available up to 673.15 K and 1380 bar from this EOS is 0.38%. Combining this EOS of CH4-N2 fluid mixtures and the EOS of CH4-CO2 and CO2-N2 fluid mixtures in our previous work, an EOS of CO2-CH4-N2 fluid mixtures has been developed, which is named ZMS EOS. The ZMS EOS can calculate all thermodynamic properties of ternary CO2-CH4-N2 fluid mixtures and the average absolute deviation of the PVTx data from the ZMS EOS is 0.40% for the CO2-CH4-N2 system. The ZMS EOS can be applied to calculate excess enthalpies of CO2-CH4-N2 fluid mixtures, predict the solubility of CO2-CH4-N2 fluid mixtures in brine and water, and quantitatively estimate the impact of the impurities (CH4 and N2) on the CO2 storage capacity in the CO2 capture and storage (CCS) processes. The ZMS EOS can also be applied to calculate the isochores of CO2-CH4-N2 system in the studies of fluid inclusions. All Fortran computer codes and Origin drawing projects in this paper can be obtained freely from the corresponding author. [ABSTRACT FROM AUTHOR]