Phase behavior and type of non-ideality in n-alkanes mixtures predicted from equations of state: The role of a third parameter

QUINZIO, MARTINA JULIETA; RODRIGUEZ-REARTES, SABRINA BELÉN; CISMONDI-DUARTE, MARTIN

FLUID PHASE EQUILIBRIA

ELSEVIER SCIENCE BV

Año: 2024 vol. 577

0378-3812

In a recent work from our group [1], three different equations of state (EoS) were compared in predictive mode for the computation of activity coefficients in nearly athermal mixtures, using null kij’s as it is typically used in any of those models for alkane mixtures, at least when the first lighter compounds of the series are not involved. The chosen equations of state represented three different classes: the Peng-Robinson (PR) [2] for two-parameter cubic EoS, the Generalized Redlich-Kwong-Peng-Robinson (RKPR) [3] as a three-parameter cubic EoS and the PC-SAFT [4] as a representative of the SAFT family of three-parameter EoS when applied to non-associating systems. It was shown that, contrary to what was believed by an important part of the thermodynamic community, the cubic nature of PR is not the reason for the incorrect trend of positive deviations from ideality observed for the predicted γinf, since the RKPR with the same repulsive term does not suffer from this limitation. The results indicated that when using either the PC-SAFT EoS or the RKPR EoS with a recent parameterization for n-alkanes [5], both models qualitatively predict appropriate behaviors, being in general RKPR predictions closer to reported experimental data.In a later communication, Jaubert and Privat [6] proposed to go deeper in a discussion or debate around the following main issues:-The possible implications of different pure compound parameters in equations of state, beyond the repulsive and the attractive ones, and a comparison between cubic and SAFT type models.-The role of the kij parameter and whether it is appropriate or not to use zero values as default in nearly athermal systems like mixtures of alkanes.-The question of whether two-parameter EoS’s, like SRK or PR, are able to represent the behavior of asymmetric mixtures of alkanes.In particular, Jaubert and Privat proposed a correlation of temperature-dependent (negative) kij values for alkane-alkane binary interactions, to be used with the PR EoS, showing how quantitative errors in the prediction of infinite dilution activity coefficients of n-C6 in heavier alkanes were significantly reduced and claiming that “with such negative kij values, CEoS like SRK or PR can represent asymmetric athermal systems very accurately.”We found a good part of their discussion and of the conclusions quite interesting, sharing the viewpoint of the authors in several aspects. Moreover, we consider their contribution could help to clarify different issues, especially for many potential readers who are users of equations of state or have interest in them, but who do not have a deep experience working with EoS’s and sometimes fall in wrong beliefs or simplifications. For example, the importance of kij parameters is sometimes underestimated, and their zero values can even be associated with ideal solution behavior. Therefore, we consider their Fig. 1 (and also Fig. 2) as a valuable didactic contribution in order to clarify these issues. Also, the analysis to show the central role that the combination rule plays in PC-SAFT for predicting negative deviations with null kij’s is quite interesting.Nevertheless, we cannot share the opinion that asymmetric hydrocarbon mixtures can be accurately represented with SRK or PR just by using appropriate kij values and that a third parameter is not necessary. On the contrary, our results show quantitative and qualitative differences in favor of RKPR in comparison to PR with negative kij’s for these mixtures. Therefore, the goal of this communication is to continue this interesting scientific debate proposed by Jaubert and Privat after our previous work, going deeper in the analysis of some aspects, presenting more results that reinforce our original message on the necessity of a third parameter, not only in SAFT models but also in cubic ones in a similar way.Another point they proposed to debate is how to count the number of parameters in order to categorize or label equations of state as two-, three-, four-parameter, etc. They propose to count every parameter or constant that can be fitted or requires some physical property for its estimation, including constants that define the temperature dependence of the attractive parameter through an alpha function. Instead, we follow a different approach, counting all parameters that have a role in the density dependence of the model, including the attractive, the repulsive and –if any- those structural parameters having an impact on the critical compressibility factor. In this approach, the δ1 parameter of RKPR (or “c” in Schmidt and Wenzel [7] or Patel and Teja [8], etc…) is considered a “third parameter” as it is m in SAFT-type models [4,9]. Although this is more, in our opinion, a terminology issue and in the end a matter of taste among different approaches, each one having its own valid grounds, we thought this was also a good opportunity to keep the issue in the debate, in order to better expose our arguments. Indeed, we will dedicate the next section to this matter of counting the number of parameters, before going to the main section, focused on what can be achieved with each different approach to overcome the observed limitations of classic cubic EoS’s like SRK or PR with null BIPs and what actually happens in terms of excess properties.