Statistical Associating Fluid Theory SAFT equation of state

Karakatsani EK, Spyriouni T, Economou IG (2005) Extended statistical associating fluid theory (SAFT) equations of state for dipolar fluids. AIChE J 51 2328-2342... 

Bias, F. J. Vega, L. F. (1998b). Prediction of Binary and Ternary Diagrams Using the Statistical Associating Fluid Theory (SAFT) Equation of State. Ind. Eng. Chem. Res. 1998,37,660-674. 

Various equations of state have been developed to treat association in supercritical fluids. Two of the most often used are the statistical association fluid theory (SAFT) (60,61) and the lattice fluid hydrogen bonding model (LFHB) (62). These models include parameters that describe the enthalpy and entropy of association. The most detailed description of association in supercritical water has been obtained using molecular dynamics and Monte Carlo computer simulations (63), but this requires much larger amounts of computer time (64—66). 

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... 

Very many noncubic equations of state have been proposed for polymers. Most of them are rather complicated and a few of them, such as several of the models discussed previously, are based on the GC concept, like the GC-Flory and the GCLF equation of state. Several of these equations of state are reviewed elsewhere, and we will restrict here our presentation to one equation of state that is very promising for polymer systems and has already found widespread acceptance. This is the Statistical Associating Fluid Theory (SAFT). 

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 phase behavior of polymer/SCF mixtures can be described using versions of the lattice fluid (LF) model such as that developed by Sanchez and Lacombe [17]. The LF equation of state is relatively simple, and has been successfully used to describe either polymers dissolved in SCFs, or SCFs dissolved in polymers [18,19], including phenomena such as retrograde vitrification. The statistical associating fluid theory (SAFT) [20] can also describe the phase behavior of polymers dissolved in SCFs. The SAFT model, while somewhat more cumbersome to implement than the LF model, is especially well-suited for polymers with varying backbone architecture, such as branched polymers or copolymers. Both the Sanchez-Lacombe and SAFT models have been incorporated into commercially available modeling software [21]. 

A number of equation of state theories have been used to model phase behavior of polymers in supercritical fluids. For example the lattice-fluid theory of Sanchez and Lacombe[4U 42] includes holes on the lattice in order to model compressibility. The lattice-fluid theory has been applied to model phase behavior of both homopolymers and copolymers in supercritical fluids[32, 38, 43, 44]. The statistical associating fluid theory (SAFT)[43,45-48] and corresponding state models[49] have also been employed to model compressible polymer-solvent mixtures. Figure 1 gives the pressure-concentration phase diagram for poly(dimethyI siloxane) in CO2 modeled with the lattice-fluid equation of state[50]. 

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. 

The last type of equation of state that we will consider is the Statistical Associating-Fluid Theory (SAFT) first proposed by Chapman et and Huang and Radosz, and for which there are now many variants as discussed in Chapter 8. 

However, equations of state, too, will be an essential component of chemical engineering theory and practice for the foreseeable future, and as ever, the balance will need to be struck between rigorous theory and engineering applicability. One equation of state, which seems to have done an admirable job of bridging the gap between molecular theory and engineering application, is statistical associating fluid theory (SAFT) and it is with this equation of state and its spin-offs that the remainder of this discussion is concerned. 

The modeling of the (temperature dependent) densities is described briefly in Sect. 6.1.2, using equations of state (EoS) derived from various modifications of the statistical associated fluid theory (SAFT), the COSMO-RS model, the Sanchez-Lascomb lattice fluid model (SL), or the perturbed hard sphere model (PHS). Each... 

Equations of state offer a number of advantages over activity coefficient models for example, they can be applied to both low and high pressures, for properties other than phase equilibria, and the density is not required as an input parameter. However, often they are more difficult to develop for complex fluids and mixtures than are activity coefficient models. Very many equations of state have been proposed for polymers Section 16.7 discusses the reason. Recent reviews have been presented. " " We will not attempt to cover all the various approaches, but essentially discuss in detail only two of them, which seem promising for polymer solutions and blends the cubic equations of state and the SAFT (Statistical Associating Fluid Theory) method. 

Le Thi, C., Tamouza, S., Passarello, J.P., Tobaly, R, de Hemptinne, J.-C., 2006. Modeling phase equilibrium of H-2-tn-alkane and COj-l-n-alkane binary mixtures using a group contribution statistical association fluid theory equation of state (GC-SAFT-EOS) with a k(ij) group contribution method. Ind. Eng. Chem. Res., 45 6803-6810. 

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. 

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... 

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