Application of a Crossover Equation of State to Describe Phase Equilibrium and Critical Properties of n-Alkanes and Methane/n-Alkane Mixtures

Abstract

Crossover equations of state (EOSs) are models that incorporate density fluctuations into mean-field thermodynamic models, changing their behavior close to the critical point. In this way, they are capable of describing the analytical behavior of fluids far from the critical region and the asymptotic one near the critical point. Although several crossover EOSs have been developed in the last decades their use in modeling industrial processes is rather limited. In this work, we use the crossover Soave–Redlich–Kwong (CSRK) to describe phase equilibrium and critical properties of pure n-alkanes and methane/n-alkane binary mixtures and compare the results to two other modeling approaches of the SRK EOS. In the case of the pure fluids, CSRK gives an accurate overall description of the phase equilibrium and critical properties; nevertheless, a minor increase in the deviation of the saturation pressure and other properties is observed when compared to that of the mean-field model. For the binary mixtures, an improvement in the description of the critical volumes is seen, while, for the other properties, similar results are obtained.

Comparison of Two Types of Crossover Soave–Redlich–Kwong Equations of State for Derivative Properties of n-Alkanes

“…In other words, the first term on the right-hand side of Eq. (1) is not equivalent to the hard-sphere model [27]. Therefore, the authors used experimental data to fit RG calculations, concluding that the attractive part of the free energy ( ) corresponds to approximately:…”

Comparison of two crossover procedures for describing thermodynamic behavior of normal alkanes from singular critical to regular classical regions

“…The main difference is that the critical temperatures and pressures are overestimated to improve the description of the phase densities far away from the critical region [32]. This procedure was also done for other cubic crossover EoS [32,35,40] and requires the modification of the experimental acentric factors for the correct representation of the vapor pressures of the pure fluids. In fact, the comparison of Tables 1 and 2 shows that , in the crossover model, are smaller than the experimental values, and, in the case of methane, it becomes negative.…”

“…in which is the attractive part of the pair potential. Following other works [32,35], the attractive contribution of the free energy density, i.e. − , was approximated by the expression:…”

“…(12) to (18) is the iteration number. In this work, five iterations were considered enough to correct the analytical behavior of the system in the critical region, as explained in previous work [35].…”

“…It is based on Wilson's [21] phase-space cell approximation method, as a way to effectively to introduce the critical density fluctuations into a classical EoS. White's procedure was extended by Prausnitz and coworkers [22,23] and it has also been applied to several cubic [32,35,40], as well as non-cubic EoS [30-34, 42, 43]. In this procedure, a recursive set of mathematical expressions is used to modify the free energy of fluids near the critical point.…”