Optimization of Peng-Robinson and Redlich-Kwong-Soave Equations of State parameters for H2 – CH4 mixtures

Hydrogen (H2) is considered a clean energy fuel that can provide a sustainable energy market and overcome intermittent production issues because it can facilitate the storage of large quantities of energy to balance out long periods of poor wind power supply and seasonal fluctuations. A vast expansion of the H2 economy requires a massive storage capacity which is available in geological storages such as deep aquifers, salt caverns and depleted hydrocarbons reservoirs. However, Underground Hydrogen Storage (UHS) is a complex procedure where containment security, pore-scale phenomena, and large-scale storage capacity can be influenced by H2 contamination due to the mixing with cushion gases and reservoir fluids. The literature lacks comprehensive investigations of existing thermodynamic models, i.e. Equations of State (EoSs) in calculating the accurate transport properties of H2-blend mixtures essential to the efficient design of various H2 storage processes. This study analyzes one possible route for improving the accuracy of the prediction of thermodynamic properties: the mathematical optimization of EoSs parameters to fit experimental data. Using recent experimental data from the literature for H2 –CH4 mixtures at different compositions, the Levenberg-Marquardt and the Trust-Region methods were used and compared for the nonlinear fitting of the Redlich – Kwong – Soave (RKS) and Peng – Robinson (PR) cubic equations of state. The values Ωa, Ωb and binary interaction parameters (BIP) were optimized using a Matlab code and the built-in function lsqcurvefit. It was showed that after the regression the two EoSs can predict density and compressibility factor (Z-factor) accurately, since the deviations are in both cases below 1%. The model that better fits the experimental data is RKS one with an average deviation equal to 0.075%. In order to check the influence of the regressed parameters on the prediction of thermodynamic properties, a sensitivity analysis of the three parameters on density and Z-factor was carried out by optimizing Ωa, Ωb and BIP separately. The results showed that, for the H2–CH4 mixtures reported in this study and using the PR and RKS EoSs, the BIP parameter does not influence significantly the accuracy of the properties of interest, and density and Z-factor are mainly influenced by Ωa and Ωb.