•The dodecahedral-cage deformation effect on hydrate formation was first modeled.•The effects of multiple solutes on hydrate formation were first modeled.•The gas dissolution effect on hydrate formation was discussed.•The saturation effect of TBAB concentration on hydrate formation was found.•The hydrate formation pressure is accurately predicted by this model. The accurate prediction of thermodynamic equilibrium hydrate formation pressure (Peq) is crucial to the industrial application of hydrate-based gas separation. This study evaluated Peq of CH4-CO2 gas mixtures with different TBAB solutions at different temperatures. Unlike previously reported models, the proposed model accounted for the effects of interaction of multiple solutes and the deformation of dodecahedral (D)-cages on Peq, thereby minimizing deviations in predictions. The effects of the interaction of multiple solutes on Peq can be attributed to gas dissolution and the presence of electrolytes. For accurate prediction, the proposed model incorporated the aforementioned effects based on the electrolyte-cubic plus association equation of state and the parameters for interaction among guest molecules in cages Furthermore, the proposed model can quantitatively describe the effects of gas dissolution, the presence of electrolytes and deformation of D-cages on the Peq values for corresponding systems.