As natural gas hydrate forms at low temperature and high pressure (i.e., near critical region), vapor phase fugacity calculation becomes crucial in this region due to the intermolecular interactions. This work introduces the modified form of the Wong-Sandler mixing rule in the Peng-Robinson (PR) and Patel-Teja (PT) equation of state (EoS) models to revamp the fugacity calculation of vapor phase. This mixing rule which is based on the excess Gibbs free energy leads to precisely capture the polar and asymmetric properties of mixture components. The modified Wong-Sandler mixing rule is formulated by representing its correction factors for energy and co-volume parameters in terms of temperature and gas-phase composition. Here, the hydrate phase fugacity is determined by the Chen-Guo model that is coupled with an EoS model for hydrate equilibrium analysis. On the other hand, the liquid phase nonideality is estimated by using the Wilson activity-coefficient model. The proposed modified Wong-Sandler based phase equilibrium models are shown to be better than the existing phase rule based models with the three example natural gas hydrate systems (CH4 + N-2, CH4 + C2H6, CH4 + C2H4) using tetrahydrofuran as a thermodynamic promoter. Validating these models with real time data sets, it is further investigated that the PT based model shows a better performance compared to the PR equation of state. This apart, these two models show their superiority over the existing PT-van der Waals (PT-vdW) model, for which, a new parameter set is proposed for the said three systems for their improved performance.