Predicting the high-pressure phase equilibria of water plus n-alkanes using a simplified SAFT theory with transferable intermolecular interaction parameters

The high-pressure phase equilibria of water + n-alkane mixtures are characterized by vapor-liquid critical lines which first exhibit a temperature minimum and then extend to temperatures above the critical point of pure water; this so-called ''gas-gas'' coexistence is a consequence of the large degree of immiscibility of the two components. We use a simplified version of the SAFT equation of state, which is based on the thermodynamic perturbation theory of Wertheim for associating fluids: the original SAFT equation of state treats the molecules as chains of Lennard-Jones segments while the simplified SAFT-HS equation treats molecules as chains of hard-sphere segments with van der Waals interactions. The water molecules are modeled as spherical repulsive cores with four association sites which mediate the hydrogen-bonding interactions. It turns out that a simple relationship for the parameters of the various mixtures can be used with the SAFT-HS treatment. The nonspherical nature of the alkanes is incorporated into the theory by treating the molecules as chains formed from united-atom spherical segments. The parameters for the pure components of the water + n-butane mixture are fitted to the critical points of each component; the strength and range of the hydrogen-bonding interaction between water molecules were obtained in a separate study by fitting to the vapor pressure and saturated liquid density of pure water. The parameters for the unlike interactions are fitted to the minimum of the high-pressure gas-liquid critical line of the water + n-butane mixture. We use a simple relationship between the number of segments in the united-atom chain models of the n-alkanes and the number of carbon atoms to predict the properties of mixtures of water with other n-alkane homologues without the recourse to further fitting. The phase equilibria of the mixtures obtained using this transferable interaction parameter approach are in excellent agreement with the experimental data even though the parameters are fitted to just one mixture. The water + methane system is the exception to this: the pure component parameters have to be refitted to the anomalous critical point of methane, as does the unlike mean-field interaction. We also predict that the type III phase behavior exhibited by water + n-alkane mixtures persists even for very long n-alkane chains, i.e., water + n-eicosane.