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Modeling Underground Hydrogen (H2) Storage (UHS) and Underground Carbon dioxide (CO2) Storage (UCS) in depleted oil and gas reservoirs requires compositional simulation. Cubic Equation of State (EOS) models for the reservoir fluids have the edge over other models like GERG 2008 and PC SAFT. Soave-Redlich-Kwong (SRK) EOS, a reliable choice of EOS, needs reliable Binary Interaction Parameters (BIPs) for its efficient and reliable application to UHS and UCS modeling. Existing correlations for estimating BIPs for SRK EOS may not be suitable for binaries having long-chain n-alkanes. This exhaustive work presents optimized BIPs and correlations for components relevant to UHS and UCS storages in depleted oil and gas reservoirs. The optimization process uses large amounts of data (3241 P-x data for binary mixtures, 35 critical points data for multicomponent mixtures) and a two-step process. Optimized BIP values are presented in terms of correlations as functions of temperature (T) and carbon number (CN) of the n-alkanes. A comparative analysis shows that the developed correlations are more reliable for compositional phase behavior than Chueh and Prausnitz (1967) and Oellrich et al. (1981) BIP-correlations commonly used in commercial simulators. The BIPs developed for CO2, N2, and n-alkanes mixture have fitting accuracy of 1.3% and 1.9% in terms of Average Absolute Relative Deviations (AARDs) for critical temperature and critical pressure, respectively, for 35 natural gas mixtures with SRK EOS. The correlations proposed are more reliable estimates for developing an EOS model for UHS and UCS in depleted oil and gas reservoirs.