(226g) Renormalization Group Theory Combined with Molecular-Based Equations of State: An Engineering Tool with the Right Physics Inside

Most industrial processes require a detailed knowledge of the thermodynamic properties, including phase behavior and transport properties of their working fluids. Although the preferred method for obtaining these data would be the experimental one, there are several difficulties associated to it, mainly due to the great amount of data required to have a reliable database for multicomponent mixtures over a wide range of thermodynamic conditions. Theoretical approaches can be used as an alternative in this case; however, the intrinsic non-ideal behavior of these mixtures and the limited range of available experimental data pose a challenge to any theoretical method aimed at quantitative predictions of thermodynamic properties for these complex fluids, especially when the process works near the critical region. Due to their classical formulation most equations of state are unable to accurately describe the density (and concentration) fluctuations appearing as the critical region is approached. This problem has been tackled in recent years with great success thanks to the combination of renormalization group theories, such as the phase cell-space approximation, with accurate theoretical based equations of state, including different versions of SAFT.

This contribution will give an overview on how having the right physics with the adequate level of approximations can lead to an accurate tool for engineering purposes. The discussion will be based using the soft-SAFT equation as an example for how an equation can be systematically extended for this purpose.

Soft-SAFT is one of the refined-versions of SAFT, first published with this name by Blas and Vega in 1997 [1]. Soft-SAFT mainly differs from the original SAFT in the reference term, which is a Lennard-Jones fluid (hence the name “soft”), instead of a hard sphere plus a perturbative attractive term. The Lennard-Jones term accounts for both the repulsive and attractive interactions of the monomers forming the chain in a single term, which turns out to be very important in some systems in which the fluid structure greatly affects the thermodynamic behavior (such as water mixtures, for instance). Over the years, the predictive power of soft-SAFT has been proved by accurately describing the behavior of several complex experimental systems, such as the solubility of hydrogen in heavy n-alkanes, the phase equilibria of mixtures of hydrogen chloride with n-alkanes, the solubility of gases in perfluoroalkanes and ionic liquids, refrigerants, polymers, and the mutual solubilities of alkanes and water, among others.

As all SAFT-type equations soft-SAFT is written as a sum of contributions to the total free energy of the system, in which the molecular effects are separated and quantified. A key factor for succeeding in the description of complex fluids is trying to retain the molecular model as simple as possible while keeping the essential physics of the system.  An additional advantage of SAFT is that the underlying theory of the equation allows its systematic extensions in a sound manner. In this sense, different versions of the equation have been recently extended into several directions: (i) the calculation of second-order thermodynamic derivative properties, (ii) the precise characterization of the critical region through a crossover treatment, and (iii) the calculation of interfacial properties by coupling the van der Waals density gradient theory to the soft-SAFT equation.

This work was partially financed by the Spanish Government under projects CTQ2008-05370/PPQ, CTQ2011-23255 and CENIT SOST-CO2 (CEN-2008-1027). Additional support from the Catalan Government through 2009SGR-666 and Carburos Metálicos was also provided.

[1] F.J. Blas, L.F Vega, Mol. Phys., 92 (1997) 135-150