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In this study, the phase equilibria of semi-clathrate hydrates of methane (CH4), carbon dioxide (CO2), nitrogen (N2), and hydrogen sulfide (H2S) in an aqueous solution of tetra-n-butyl ammonium bromide (TBAB) were modeled using a correlation based on a two-stage formation mechanism: a quasi-chemical reaction that forms basic semi-clathrate hydrates and adsorption of guest molecules in the linked cavities of the basic semi-clathrate hydrate. The adsorption of guest molecules was described by the Langmuir adsorption theory and the fugacity of the gas phase was calculated by Peng–Robinson (PR) equation of state (EOS). The water activity in the presence of TBAB was calculated using a correlation, dependent on temperature, the TBAB mass fraction, and the nature of the guest molecule. These equations were coupled together and form a correlation which was linked to a genetic algorithm for optimization of tuning parameters. The results showed an excellent agreement between model results and experimental data. In addition, an outlier diagnostic was performed for finding any possible doubtful data and assessing the applicability of the model. The results showed that more than 97 % of the data were reliable and they were in the applicability domain of the model.