Renormalization-Group Corrections to a Perturbed-Chain Statistical Associating Fluid Theory for Pure Fluids Near to and Far from the Critical Region

Abstract

A perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state has been extended to include a crossover correction, based on White's work with renormalization-group (RG) theory, that accounts for the contributions of long-wavelength density fluctuations in the critical region. In the critical region, the improved crossover equation of state provides the correct nonclassical critical exponents. Away from the critical region, the crossover equation reduces to the original PC-SAFT equation, therefore maintaining the accuracy of PC-SAFT in this region. No modifications to the original PC-SAFT molecular parameters are necessary, therefore allowing for an accurate description of thermodynamic properties from the triple point to the critical point. Excellent agreement with vapor-liquid equilibrium experimental data for the n-alkane family is obtained inside and outside the critical region, and all critical constants T c , P c , and F c are calculated within their respective experimental errors. The extrapolative abilities of the RG parameters are demonstrated for higher molecular weight chains. Finally, the present results are contrasted with results from other groups using alternative interpretations of White's theory.

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

“…In usual implementations of the RG relations in SAFT approaches 53,54,[59][60][61] , equations (26) and (27) are expressed asf…”

“…However, in these other works 48,49,[51][52][53][54][59][60][61] , the cutoff length L has a slightly different meaning: it instead separates the classic (mean-field) part of the free energy and the non-classic (critical)…”

“…Defining the volume as V n = (λ n ) 3 leads to the expression of K n used by Prausnitz et al 48,49,51,52 and later contributions 53,54,[59][60][61] , where…”

“…Following work carried out by previous authors 44,48,49,[51][52][53][54]59,61,[63][64][65] the integral in equation (29) is evaluated by numerical integration using the trapezoid rule method and equal size steps. Our standard method was set to use a 1000-point grid in density for the integration.…”

“…This boundary is chosen to ensure liquid-like conditions and is also based on the region of validity of the current parametrization for the radial distribution function used in SAFT-VR 18 . In practice, however, in most cases the calculation can be performed up to values of ρ half the maximum density given by a face-centered cubic (fcc) structure (η 0.74) as done in other works 59,61 .…”