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# In the last and the most challenging part three mixtures

In the last and the most challenging part, three mixtures were selected to evaluate the reliability of the presented correlation and the CPA model. For Athabasca bitumen, Amani et al. [25] measured the experimental data at very high temperatures compared to the thermal recovery range up to 644 K (near the water critical temperature). Nonetheless, we used the correlation to estimate the cross-association volume parameter for this mixture. With regard to the high experimental error at elevated temperatures [55], evaluated values shown in Fig. 6 and AARD of 6.1% confirms that CPA can precisely estimate water solubility in Athabasca bitumen. Other mixtures that were considered to investigate the model performance include two mixtures of Athabasca bitumen + toluene + water [26]. As different amount of toluene were added to the mixture of Athabasca bitumen + water, the ternary mixtures had different properties. The hydrocarbon mixtures' properties are taken from the literature [25]. Water solubility data for these two mixtures were measured with ∼30% uncertainty from 512 up to 573 K. Water solubility reported in Fig. 7 shows an acceptable and accurate prediction using predicted with correlation. The AARD for the ternary mixtures with the Mw of 127.2 and 171.6 is 8.2% and 11.6%, respectively.
The presented correlation is specifically developed using water solubility in hydrocarbon rich phase experimental data, and one may not expect to obtain precise predictions for the hydrocarbon solubility in aqueous phase with the same parameters. The mutual solubilities of 1-octene and water [12] are illustrated in Fig. 8 to justify the performance of the model against experimental data. As shown, the water solubility data are in good agreement with the experimental data, while the hydrocarbon solubility data are poorly predicted.
According to the results obtained, it 745 is possible to predict the cross-association volume parameter of the CPA model using simple hydrocarbon's properties. In the last part, in order to improve the proposed correlation (equation (11)), all solubility data presented in Table 2 including three Athabasca bitumen mixtures are considered. The correlation for cross-association volume parameter using the entire set of data is:
The average deviation using above correlation for the three Athabasca bitumen mixtures is 7.6%. The computed AARD% using Eq. (13) for each hydrocarbon is very close to one determined by Eq. (11). The results reveal that the proposed correlation of cross association volume parameter follows a reasonable trend which can be applied to a wide range of hydrocarbons. We ignore presenting AARD% using Eq. (13) for hydrocarbons to avoid repetition and confusion as the results are very close to Eq. (11).
The results of two correlations reveal that the generalized correlation can be applied to different mixtures of water + pure hydrocarbons, oil fractions, heavy crudes and bitumen at high temperatures to make an appropriate prediction of water solubility in hydrocarbons. Fig. 9 shows evaluated water solubility using proposed correlation versus experimental water solubility data for all the hydrocarbons presented in this work. The model is able to evaluate water solubility in light hydrocarbons to heavy crudes in a wide temperature range using the generalized correlation.

Conclusions

Introduction
In recent years CO2 has received a significant amount of negative attention due to its status as a greenhouse gas and the fact that the amount of CO2 in the atmosphere continues to rise. This is believed to be largely due to the combustion of fossil fuels. Technologies are thus needed, which can limit the emission of CO2 to the atmosphere. One such potential technology is carbon capture and storage. During this process, transport of CO2 rich mixtures is an important step which requires accurate knowledge of the phase behaviour, as well as other thermodynamic properties, of mixtures containing hydrocarbons, water and other fluids such as alcohols [1].