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# To evaluate the new quadrupolar CPA qCPA the pure fluid

To evaluate the new quadrupolar CPA (qCPA) the pure fluid properties of CO2 are predicted both in the critical region and in the compressed liquid region. The model is furthermore applied for the prediction and correlation of binary mixtures with CO2 and n-alkanes, water, alcohols and a few quadrupolar compounds. The model is compared with two other CPA approaches namely non-associating (n.a.) CPA, where CO2 is assumed to be an inert compound, and the case when CO2 is assumed to be self-associating following the 4C association scheme (notation from Huang and Radosz [21]). Tsivintzelis et al. [18] have published similar results with the two CPA approaches for most of the binary mixtures investigated in this work.

Models
The CPA EoS (Kontogeorgis et al. [20]) is an engineering EoS which has been extensively studied in the literature (e.g. [22], [23], [24]). It combines the SRK EoS with the association term from Wertheim’s theory, which is also employed in SAFT [25], [26], [27]. The SRK term accounts for the physical interactions between molecules, while the association term takes hydrogen bonding interactions into account.
In the literature CPA is typically presented as a pressure explicit EoS, however, it is often much more convenient to express an EoS in terms of the residual Helmholtz energy, (A(T, V, n)), since all other residual properties can be obtained as partial derivatives of the state variables T, V and n. The reduced residual Helmholtz free MHY1485 for qCPA can be expressed as the addition of the physical SRK term, Wertheim’s association term and the quadrupolar term:
where R is the ideal gas constant. In the absence of association or quadrupolar interactions Eq. (1) reduces to the SRK EoS.

Results and discussion

Conclusion
In an effort to improve the predictive capabilities of classic thermodynamic models, primarily for mixtures containing CO2, a quadrupolar equation of state contribution, developed from statistical mechanics [5], have been modified and combined with CPA. The resulting qCPA can be used without introducing any other adjustable pure compound parameters or, alternatively, an additional adjustable parameter can be used. The model results were compared with CPA n.a. and CPA 4C.
When the same number of adjustable parameters are used for CPA n.a. and qCPA, a systematic improvement in the correlation of the saturated liquid density and vapor pressure is observed. This is particularly true for the strongly quadrupolar CO2 molecule, but applies to benzene and acetylene as well.
The models were employed to predict various pure compound properties for CO2 including the second virial coefficient, the critical properties and various derivative properties. qCPA and CPA 4C seem to perform slightly better than CPA n.a. in regards to the derivative properties. On the other hand CPA n.a. is slightly more accurate in representing the second virial coefficient and the critical point. The differences between the modelling approaches, however, are generally small. The main reason for deviations in the derivative properties seem to be caused by a deficiency in the second order derivatives.
It was found that qCPA (all approaches) significantly improves the prediction of binary VLE and the correlation of LLE between CO2+n-alkane mixtures. A significantly smaller interaction parameter is needed to correlate the experimental data with qCPA compared to the CPA approaches. When it comes to CO2+associating mixtures very good correlations were obtained with qCPA when solvation was taken into account using the approach suggested by Kleiner and Sadowski [77] and a single small binary interaction parameter. The model was finally applied to two quadrupolar-quadrupolar mixtures, which illustrated that the model seem to have difficulties for quadrupolar mixtures of opposite sign such as CO2+acetylene. Overall explicitly accounting for the quadrupolar forces appears to offer significantly improved predictions, and better (smaller k) correlations, for CO2 containing mixtures compared to the two other CPA approaches.