Determination of mutual solubility between n-alkanes/n-alkylbenzenes and water by using Peng-Robinson equation of state with modified alpha functions and generalized BIP correlations

It is too specific to a given pair (i.e., solubility data must be re-tuned for a new pair, while it is difficult to achieve generalization) for the widely used models, e.g., Henry's law, cubic-plus-association equation of state (CPA EOS), statistical associating fluid theory (SAFT), and specific solubility equations, to predict mutual solubility for hydrocarbon-water pairs, while other constraints such as increased computational expenses and requirement of molecular structures limit their extensive applications. In this study, a generalized methodology has been developed to predict the mutual solubility for n-alkanes (i.e., C3-C20)/n-alkylbenzenes (i.e., C6-C12)-water pairs by using the Peng-Robinson equation of state (PR EOS). A comprehensive database has firstly been developed with the experimentally measured solubility data in a temperature range of 273.2-479.5 K. In addition to the two newly modified alpha functions respectively for hydrocarbons and water, the binary interaction parameters (BIPs) for both aqueous phase and liquid hydrocarbon phase are tuned to match the experimental solubilities. The tuned BIPs are then regressed as functions of reduced temperatures and carbon numbers of hydrocarbons for both aqueous phase and liquid hydrocarbon phase, respectively. The BIP correlations developed in this work can be used to accurately reproduce the experimental measurements with significant improvements over the existing models except for propane-water pair and n-butane-water pair. Also, such newly developed models have been further validated with the experimentally measured heat of solution, solubility minimum temperature, and heat capacity of solution, while sensitivity analysis has been performed to examine the effects of different parameters on the predicted mutual solubility.