The SAFT-LJ equation of state (EOS) improved by our previous study, which introduces a multi-polar term to explicitly account for the contribution of multi-polar interactions (including the dipole dipole, dipole quadrupole and quadrupole quadrupole interactions), is applied to the H2O-N-2 and H2O-H-2 systems. N-2 and H-2 are modeled as chain molecules with evenly distributing quadrupole moments. The van der Waals one-fluid mixing rule was used to calculate parameters for mixtures and two binary parameters for the interactions of H2O-N-2 and H2O-H-2 pairs were evaluated from mutual solubility data of binary water gas systems. Comparison with the experimental data shows that this molecular-based EOS can well represent vapor liquid equilibria of H2O-N-2 and H2O-H-2 systems over a wide P-T range (273-623 K and 0-1000 bar). In addition, the effect of the dipole moment of H2O and quadrupole moments of N-2, H-2 and CO2 on VLE of the CO2-N-2, H2O-N-2 and H2O-H-2 systems was checked. It was found that the SAFT-LJ model without any polar term gives good prediction (without any binary parameters) for vapor compositions of the CO2-N-2, H2O-N-2 and H2O-H-2 systems except in the critical region and taking account of the contribution of multi-polar interactions does not improve the prediction of this EOS any more. However, taking account of multi-polar interactions indeed significantly improves the prediction of this EOS for compositions of liquid phase. We argue that it is the reason why this EOS can quantitatively represent VLE of highly non-ideal water gas systems. Comparison of calculations of this EOS with experimental VLE data of the ternary CO2-N-2-H2O system confirms the prediction capability of this EOS for thermodynamic properties of multi-component systems. (C) 2015 Elsevier B.V. All rights reserved.