This work started from the

This work started from the standard version of the CPA model [17] and investigated its known weaknesses: 1) not meeting the defined critical temperature, 2) missing the temperature dependence of pure component saturated liquid densities, 3) using an α function in the cubic term that can provide unreliable results for a few properties in some extreme conditions (as discussed by Le Guennec et al. [36]), and 4) having an incorrect description of the molar volume pressure dependence, which lead to a poor description second derivative properties. For this analysis the n-alkanols will be used as case study, as this family should also allow us to look into the associative parameters for the –OH group, trying to establish some “rules” or tendencies for their change with chain length.
s-CPA model Below we will refer to the published simplified CPA model as s-CPA [17]. CPA models account for physical interactions using a term based on a cubic EoS. In the case of s-CPA this is the SRK EoS [37]. Equation (1) presents the s-CPA in terms of the compressibility factor.Where represents the Gefitinib receptor parameter (), the covolume parameter (), is the density, is a simplified hard-sphere radial distribution function [17], is the mole fraction of component i not bonded to site A and is the mole number of component i. As proposed by Michelsen et al. [38], it is preferable to use a single sum over sites to improve computational efficiency, thus equation (1) can be rewritten as:Where is the mole number of sites of type i. The mixture a and b parameters are obtained from the following mixing rules:where:and k are binary interaction parameters. The alpha function most used with s-CPA is the Soave function [37] which has a quasi-linear dependency with temperature. An alternative alpha function that provides a more flexible temperature dependence is the Mathias-Copeman function [39] which is also one of the most widely applied alpha functions for cubic EoS. This function presents a cubic dependence with temperature: Equation (8) relates to the association strength.where:where, and are the association energy and volume for interactions between sites i and j. The use of a simplified radial distribution function is the difference between the s-CPA and the original version of CPA [8]. This function is given by equation (10)[17], [40]. In this work, as suggested by Oliveira et al. [41] for SAFT, we also looked at adding more pure component properties in the fitting of the CPA parameters that is usually based on the simultaneous fitting of vapour pressures and saturated liquid densities. Cp data was also added, but a weighted procedure was used that remains more heavily weighted towards vapour pressures and liquid densities. We started using values from the literature as first estimates, and used as objective function.where wt is the weight given to a specific property during the optimization process. The weights used had the value of 1 for density and vapour pressure and varied between 0.05 and 0.1 for Cp. For binary mixtures equations (12), (13), (14) were considered to optimize the values of kij. (12 and 13 for VLE and 14 for LLE):where npo is the number of phases to optimize. For systems containing two or more associative compounds a combining rule for the cross-associative parameters is required. In this work we used CR-2 [16], presented as CR-1 in some papers [42]. As proposed by Kontogeorgis et al. [15] this combining rule is adequate for systems containing only alcohols. The associative scheme chosen for alcohols was the 2B [6] scheme. As analysed by Kontogeorgis et al. [42], fitting binary phase equilibria for the studied compounds with the more accurate (and complex) 3B [6] scheme does not improve the results when comparing to the 2B scheme. It is also important to note that for the prediction of pure component properties, the same authors and de Villiers et al. [25] showed that each scheme is usually better at describing different sets of properties.