Michel et al calculated the mutual solubilities of water
Michel et al.  calculated the mutual solubilities of water and hydrocarbons by a cubic equation of state. They asserted that conventional mixing rules can not satisfactorily describe the hydrogen bonding compounds. Kabadi and Danner  applied a modified form of Soave-Redlich-Kwong equation of state to model water + hydrocarbon mixtures. They proposed an asymmetric mixing rule to overcome difficulties associated with predicting hydrocarbon-rich and water-rich liquid data. Landra and Satyro  predicted mutual solubility experimental data for different mixtures of water and hydrocarbon using Peng-Robinson EoS. They could correlate the data using temperature dependent binary interaction coefficients and Huron-Vidal mixing rule. Possani et al.  extended the F-SAC (Functional-Segment Activity) model in order to represent infinite dilution activity coefficient and LLE data for hydrogen bonding systems. They considered solutions of water with alkanes, cycloalkanes, alkenes, cycloalkenes and aromatics. Their model diverges from experimental measurements for C13+ hydrocarbons. Developing advanced association models, which account for the hydrogen-bonded fluids like SAFT (Statistical Association Fluid Theory) and CPA (Cubic Plus Association) equations of state (EoS), resulted in a huge modification in the modeling of association mixtures such as water containing systems. Karakatsani et al.  used the truncated PC-SAFT (PC-SAFT with a polar term) to describe mutual solubility of water + hydrocarbon mixtures. They compared the model with PC-SAFT and concluded that the model would improve by considering the polar interactions. Vega et al.  applied the soft-SAFT EoS to model the mutual solubilities of water-hydrocarbon binary mixtures. They concluded that the soft-SAFT has a better performance in comparison with the original SAFT. The SAFT approach and parameterization are complicated, and it 5,8,11-Eicosatriynoic Acid has been observed that the CPA-EoS along with its simplicity, has better performance for water + hydrocarbon mixtures in comparison with the original SAFT , , . CPA-EoS was originally proposed by Kontogeorgis et al.  and has been successfully applied to various polar mixtures containing alcohols, water and hydrocarbons , , , , . The CPA has also shown satisfactory results for complex polar hydrocarbon mixtures containing asphaltene , , . Yan et al.  used CPA-EoS to model the mutual solubility between light hydrocarbons (methane to n-butane) and water. They extended the model to ill-defined C7+ fractions. Oliveira et al.  applied CPA EoS to describe the water + hydrocarbon equilibria by temperature independent binary interaction coefficients (kij). In the case of aromatics, which cross associate with water, one additional adjustable parameter was required to consider solvation. Zirrahi et al.  evaluated water solubility in some heavy hydrocarbons at high temperatures. They classified nine studied hydrocarbons in to two different categories: petroleum fractions and heavy crudes. They represented individual binary interaction coefficient correlations (in the term of Mw and SG) for each category, which were limited to a specific range of Mw and SG. By comparing the results of different thermodynamic association models in the literature, CPA seems to have an accurate performance to describe hydrocarbon mixtures containing water , , , . Although CPA-EoS has been used previously to calculate water solubility in a limited number of hydrocarbons, we proposed a general approach to evaluate water solubility in ill-defined hydrocarbon mixtures. Heavy reservoir fluids such as heavy crudes and bitumen usually remain ill-defined constituents due to practical limitations to determine their molecular structures and critical properties. In cephalization paper, the emphasis is given to ill-defined hydrocarbons with the minimum available characterization data such as Mw and SG that are readily measurable with high accuracy. In comparison to the earlier works, this modeling approach has become less complex by fixing the cross association volume parameter as the only adjusting parameter of the model, while binary interaction coefficients are neglected. In present work, CPA is applied to predict water solubility in different hydrocarbons for a broad range of Mw between 78 and 678 kg/kmol at elevated temperatures. Water solubility data in a variety of pure hydrocarbons at high temperatures were collected from the critically evaluated literature , , , , , , , . To the best of authors' knowledge, there is no experimental data on solubility of bitumens in water-rich phase in the open literature due to the measurement difficulties and very low solubility of heavy hydrocarbons in aqueous phase. Consequently, in this study the main emphasis was given to the water solubility in hydrocarbon rich phase due to its great interest in different processes in petroleum industry.