Solubility of carbon dioxide in water: some useful results for hydrate nucleation

In this paper, the solubility of carbon dioxide (CO$_{2}$) in water along the isobar of 400 bar is determined by computer simulations using the well-known TIP4P/Ice force field for water and TraPPE model for CO$_{2}$. In particular, the solubility of CO$_{2}$ in water when in contact with the CO$_{2}$ liquid phase, and the solubility of CO$_{2}$ in water when in contact with the hydrate have been determined. The solubility of CO$_{2}$ in a liquid-liquid system decreases as temperature increases. The solubility of CO$_{2}$ in a hydrate-liquid system increases with temperature. The two curves intersect at a certain temperature that determines the dissociation temperature of the hydrate at 400 bar ($T_{3}$). We compare the predictions with the $T_{3}$ obtained using the direct coexistence technique in a previous work. The results of both methods agree and we suggest 290(2)K as the value of $T_{3}$ for this system using the same cutoff distance for dispersive interactions. We also propose a novel and alternative route to evaluate the change in chemical potential for the formation of hydrate along the isobar. The new approach is based on the use of the solubility curve of CO$_{2}$ when the aqueous solution is in contact with the hydrate phase. It considers rigorously the non-ideality of the aqueous solution of CO$_{2}$, providing reliable values for driving force for nucleation of hydrates in good agreement with other thermodynamic routes used. It is shown that the driving force for hydrate nucleation at 400 bar is larger for the methane hydrate than for the carbon dioxide hydrate when compared at the same supercooling. We have also analyzed and discussed the effect of the cutoff distance of the dispersive interactions and the occupancy of CO$_{2}$ on the driving force for nucleation of the hydrate.