Perturbed-Chain Statistical Associating Fluid Theory

Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT)... 

The ability to model Selexol-based unit operations in Aspen Plus or Aspen HYSYS was recently made possible by the inclusion of the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) physical property model. As in Aspen HYSYS (see Section 6.1.1), a single chemical DEPG be used as a proxy for the mixture. Simple example files for using PC-SAFT with Selexol for one- or two-unit operations are included with the Aspen Plus distributiOTi, and an example for using PC-SAFT in Aspen HYSYS is available for download to subscribers of the Aspen Technology support website. 

Cameretti LF, Sadowski G, Mollerup JM (2005) Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory. Ind Eng Chem Res 44 3355-3362 ibid., 8944... 

Gonzalez et alP modeled the asphaltenes precipitation in live oils with the (Perturbed Chain-Statistical Associating Fluid Theory (PC-SAFT) see Chapter 8 for additional material. It is not an easy task to apply a complicated model such as PC-SAFT to systems consisting of a very large number of chemical... 

Gross, J. and Sadowski, G., 2002. Modehng polymer systems using the perturbed-chain statistical associating fluid theory equation of state. Ind. Eng. Chem. Res., 41 1084. 

Experimental data including the acidic species in the vapor phase within the above concentration range are scarce. Only very few publications of VLE data in that range are available [168, 173]. In contrast, numerous vapor pressure curves are accessible in literature. Chemical equilibrium data for the polycondensation and dissociation reaction in that range (>100 wt%) are so far not published [148]. However, a starting point to describe the vapor-Uquid equilibrium at those high concentratirMis is given by an EOS which is based on the fundamentals of the perturbation theory of Barker [212, 213]. Built on this theory, Sadowski et al. [214] have developed the PC-SAFT (Perturbed Chain Statistical Associated Fluid Theory) equation of state. The PC-SAFT EOS and its derivatives offer the ability to be fuUy predictive in combination with quantum mechanically based estimated parameters [215] and can therefore be used for systems without or with very little experimental data. Nevertheless, a model validation should be undertaken. Cameretti et al. [216] adopted the PC-SAFT EOS for electrolyte systems (ePC-SAFT), but the quality for weak electrolytes as phosphoric... 

PC-SAFT Perturbed-chain statistical associating fluid theory rRESPA Reversible reference systems propagator algorithm SAET Statistical associating fluid theory... 

Karakatsani EK, Economou IG (2006) Perturbed-chain statistical associating fluid theory extended to dipolar and quadrupolar molecular fluids. J Phys Chem B 110 9252-9261... 

The non-cubic equations of state are characterized by the use of a repulsive term that is based on the Camahan-Starling or on the HCB expressions already reported in Table 3. The attractive part is generally based on that derived from the perturbed hard chain theory (PHCT) [49], or from the statistical associating fluid theory SAFT [50, 51]. These approaches were the precursors of many theoretical attractive terms and consequently of different equations of... 

The statistical-associated fluid theory (SAFT) of Chapman et al. [25, 26] is based on the perturbation theory of Wertheim [27]. The model molecule is a chain of hard spheres that is perturbed with a dispersion attractive potential and association potential. The residual Helmholtz energy of the fluid is given by the sum of the Helmholtz energies of the initially free hard spheres bonding the hard spheres to form a chain the dispersion attractive potential and the association potential,... 

For the calculations, different EoS have been used the lattice fluid (LF) model developed by Sanchez and Lacombet , as well as two recently developed equations of state - the statistical-associating-fluid theory (SAFT)f l and the perturbed-hard-spheres-chain (PHSC) theoryt ° . Such models have been considered due to their solid physical background and to their ability to represent the equilibrium properties of pure substances and fluid mixfures. As will be shown, fhey are also able to describe, if not to predict completely, the solubility isotherms of gases and vapors in polymeric phases, by using their original equilibrium version for rubbery mixtures, and their respective extensions to non-equilibrium phases (NELF, NE-SAFT, NE-PHSC) for glassy polymers. 

The best-known model of this kind is the Statistical Associated Fluid Theory (SAFT) model [58-61]. Here, a non-spherical molecule (solvent or polymer) is assumed to be a chain of identical spherical segments. Starting from a reference system of m hard spheres (A ), this model considers three perturbation contributions, which are assumed to effect independently attractive interactions of the (non-bonded) segments (A ), hard-sphere chain formation (A ), and association (A ° ) ... 

The above-mentioned deficiencies of the Flory-Huggins theory can be alleviated, in part, by using the local-composition concept based on Guggenheim s quasichemical theory for the random mixing assumption and replacing lattice theory with an equation-of-state model (Prausnitz et al., 1986). More sophisticated models are available, such as the perturbed hard sphere chain (PHSC) and the statistical associating fluid theory (SAFT) (Caneba and Shi, 2002), but they are too mathematically sophisticated that they are impractical for subsequent computational efforts. 

Vargas, F.M., Gonzalez, D.L., Hirasaki, G.J., and Chapman, W.G., 2009. Modeling asphaltene phase behavior in crude oil systems using the perturbed chain form of the statistical associating fluid theory (PC-SAFT) equation of state. Energy Fuels, 23 1140. 

The decisive advantage of the original Elory-Huggins theory [1] lies in its simplicity and in its ability to reproduce some central features of polymer-containing mixtures qualitatively, in spite of several unrealistic assumptions. The main drawbacks are in the incapacity of this approach to model reality in a quantitative manner and in the lack of theoretical explanations for some well-established experimental observations. Numerous attempts have therefore been made to extend and to modify the Elory-Huggins theory. Some of the more widely used approaches are the different varieties of the lattice fluid and hole theories [2], the mean field lattice gas model [3], the Sanchez-Lacombe theory [4], the cell theory [5], different perturbation theories [6], the statistical-associating-fluid-theory [7] (SAET), the perturbed-hard-sphere chain theory [8], the UNIEAC model [9], and the UNIQUAC [10] model. More comprehensive reviews of the past achievements in this area and of the applicability of the different approaches are presented in the literature [11, 12]. 

Deviations of real molecules from the reference system may occur, e.g., due to attractive interactions (dispersion), formation of hydrogen bonds (association), or the nonspherical shape of the molecules (which can be understood as the formation of chains from spherical segments). These contributions are usually assumed to be independent of each other and are accounted for by different perturbation terms. Depending on the kind of considered perturbation and on the expression used for its description, different models have been developed. One of the first models derived from that idea was the Statistical-Associating-Fluid Theory (SAFT) (Chapman et al. [12, 13] Huang and Radosz [14, 15]). 

Contemporary Approaches. Numerous advanced theories have been formulated in the last decades to reproduce or even predict experimental findings for polymer containing mixtures. Most of them are particularly suitable for the description of some phenomena and special kinds of systems, but all have in common that they have lost the straightforwardness characterizing the Flory-Huggins theory. The following, incomplete collocation states some of the wider used approaches These are the different forms of the lattice fluid and hole theories (38), the mean field lattice gas model (39), the Sanchez-Lacombe theory(40), the cell theory (41), various perturbation theories (42), the statistical-associating-fluid-theory (43) (SAFT), the perturbed-hard-sphere chain theory (44), the... 

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