Characterization factor is another variable suggested in the
Characterization factor is another variable suggested in the presented correlation. Specific gravity (SG) and normal boiling point of hydrocarbons are needed to calculate Watson characterization factor , : The boiling point of bitumen cannot be precisely measured, because bitumens contain extremely heavy fractions. For instance, 50 wt% of Athabasca bitumen possesses a nominal boiling point exceeding 797 K . These fractions are not distillable even under vacuum pressures, because the boiling point of heavy fractions (bitumen vacuumed bottoms) is much higher than their thermal cracking temperature (T > 613 K) , . As an example, the estimated average boiling points of the considered heavy crudes according to the Soreide model  are ∼ 700 K which are beyond cracking temperature. The average boiling points for fuel oil, heavy crudes and bitumen including Huntington Beach, Coalinga, Peace River and Cat Canyon were predicted using Soreide model  suggested for heavy oil fractions. Also, the average boiling points for two ternary mixtures (Athabasca + toluene + water) and oil fractions including naphta, kerosene and lubricating oil were reported by Amani et al.  and Griswold and Kasch  respectively. Watson characterization factor remains almost constant for hydrocarbons of similar chemical structure. Paraffinic hydrocarbons exhibit values greater than 12.5; while lower values reveal more naphthenic or aromatic content of crude oil . As seen in Eq. (11), cross-association volume parameter is proportional to the characterization factor with a negative sign which means that as decreases, increases. In the other word, for more naphthenic and aromatic hydrocarbons, the association volume between water and these hydrocarbons becomes larger, which is an expected behavior. The predicted results revealed that the correlation can propose a proper prediction of cross-association volume parameter in comparison with optimized cross-association volume parameter, as presented in Fig. 2. Using this palmitic acid correlation, one can readily predict the phase behavior of water + hydrocarbon mixtures at elevated temperatures. Water solubility in some pure hydrocarbons is also studied in this work. The average deviation between experimental data and predicted values for these light mixtures is less than 16%. Adjusted cross-association volume parameters for water + pure hydrocarbon mixtures are reported in Table 3. As the number of pure hydrocarbons is high, only six of them are selected to be illustrated in Fig. 3. The experimental data of water solubility in benzene , cyclohexane , m-xylene , ethylbenzene , tetralin and 1-ethylnaphthalene  are shown in Fig. 3 for clarification. In addition, evaluated cross-association volume parameters and the absolute average relative deviations (AARD) between experimental data and calculated water solubility are presented in Table 3. As shown in Fig. 3, calculated water solubility has a good accuracy by considering polar interactions and solvation between hydrocarbons and water using the evaluated from generalized correlation. In the next step, water solubility experimental data in oil fractions at high temperatures, obtained from the literature, are studied. Calculated water solubility using optimized and correlated cross-association volume parameter for lubricating oil, naphta, kerosene  and fuel oil  are represented in Fig. 4. As shown in this figure, water solubility in these oil fractions is well described in the entire range of temperature. AARD between water solubility experimental and evaluated values for each crude fraction is presented in Table 3. Compared with the two former cases (pure hydrocarbons and oil fractions), predicting water solubility in heavy crudes and bitumens is more challenging due to the complexity of their properties and high asphaltene content of these mixtures. In the case of heavy oils/bitumens + water binary mixtures, water solubility experimental data in Coalinga, Cat Canyon, Huntington Beach and Peace River bitumens  were investigated. Mw and SG of these crudes were measured by Ref. . For these heavy crudes, Tb cannot be identified with precision and Tb was estimated using Soreide model . Predicted values using adjusted and predicted are exhibited in Fig. 5. As before, the correlated cross-association volume parameter seems enough to properly predict the fluid phase behavior. Fig. 5 confirms that CPA can make an acceptable prediction of water solubility in heavy oils and bitumens in a wide range of temperatures suitable for thermal recovery applications.