SAFT Equations of State

PCGC-2 software package, 7 448 PC resins, properties of, 10 196t PCR reaction, 12 514 PC-SAFT equation of state, 24 11 PCT Gazette, 18 236 PCT molding resins, 20 60-61. See also Poly(cyclohexanedimethylene-terephthalate) (PCT)... 

Li, X.-S. Englezos, P. (2006). Prediction of Gas Hydrate Formation Conditions in the Presence of Methanol, Glycerol, Ethylene glycol and Triethylene glycol with the SAFT Equation of State. IndEng Chem Res., 45 (6), 2231-2137. 

All six basic types of fluid phase behaviour have been found experimentally. Type I to V can be predicted with simple equations of state like the van der Waals equation, however type VI, which is found in systems in which specific interactions like hydrogen bonding plays a role, is only predicted with more complicated equations of state like the SAFT equation of state [6-8]. In the mean time many more types of fluid phase behaviour have been found computationally [9], but up till now they have not been found in real systems. 

Chen C.-K., Duran M.A., Radosz M., Supercritical Antisolvent Fractionation of Polyethylene Simulated with Multistage Algorithm and SAFT Equation of State Staging Leads to High Selectivity Enhancements for Light Fractions, Ind. Eng. Chem. Res. 1994, 33(2), 306-10... 

The SAFT equation of state was proposed by Radosz, Gubbins, Jackson, and Chapman and is a model derived based on the perturbation theory of Weirtheim. SAFT is a noncubic equation with separate terms for the various effects (dispersion, polar, chain, hydrogen bonding). SAFT has already found extensive application in both polymer and oil industry, where different capabilities of the model have been exploited. In the oil industry, it is used for describing the complex multiphase equilibria of hydrogen bonding multicomponent systems, e.g., water-oil-alcohols (glycols). Several recent reviews of the SAFT equation of state are available, all of which present results for polymer solutions. 

The original SAFT equation of state is given by the equation ... 

The SAFT equation of state typically contains five pure compound parameters, which are estimated from both vapor pressure and liquid density data. These are the molecular size parameter m, the segment size parameter v, the segment energy parameter u°lk, and the two association parameters the association energy e /k and the association volume. ... 

FIGURE 16.8 Cloud-point curves for the poly(ethylene-octene) (Mn = 33000)-hexane system from experiment points and the SAFT equation of state (curves). (From Jog, P.K. et ah, Ind. Eng. Chem. Res., 41(5), 887, 2002. With permission.)... 

Various modifications of the SAFT equation of state have been already proposed over the last several years. These have been presented in recent reviews.It is worth mentioning that in all these SAFT modifications different attractive terms are proposed, i.e., different terms for the of Equation 16.78. The chain and association terms remain unchanged. SAFT is available in existing process simulators by Aspen Tech and Simulation Sciences, and it is nsed by several indnstries (examples of applications have been reported by Exxon Research and Engineering Company and Shell Oil Company). However, in these simulators, only the nonassociating contributions are incorporated. The SAET eqnation of state has been extensively applied to nonpolymeric systems as well, including mixtures of hydrocarbons, water, alcohols, and phenols. A few applications to cross-associating systems, e.g., alcohol-water, have been also reported. 

FIGURE 16.10 Pressure-composition phase diagram for the system polydimethylsiloxane (PDMS) — -pen-tane with the SAFT equation of state. Using PDMS pure-component parameter sets, which reproduce the PDMS densities well, no acceptable reproduction of the binary equilibria is possible. (From Pfohl, O. et al., Fluid Phase Equilibria, submitted, 2001. With permission.)... 

Feng, W. et al.. Calculation of vapor-liquid equilibria of high concentrated polymer solution by a modified SAFT equation of state, presented at the 9th International Conference on Rroperties and Phase Equilibria for Product and Process Design, Kurashiki, Japan, May 20-25, 2001, 2001. 

Jog, P.K., Garcia-Cuellar, A., and Chapman, W.G., Extensions and applications of the SAFT equation of state to solvents, monomers and polymers, Fluid Phase Equilibria, 158-160, 321-326, 1999. 

VRI Vries, TJ. de, Somers, P.J.A., Loos, Th.W. de, Vorstman, M.A.G., and Keuientjes, J.T.F., Phase behavior of poly(ethylene-co-propylene) in ethylene and carbon dioxide Experimental results and modeling with the SAFT equation of state, Ind. Eng. Chem. Res., 39, 4510, 2000. 

STO Stoychev, L, Galy, J., Foumel, B., Lacroix-Desmazes, P., Kleiner, M., and Sadowski, G., Modeling the phase behavior of PEO-PPO-PEO surfactants in carbon dioxide using the PC-SAFT equation of state Application to dry decontamination of solid substrates, J. Chem. Eng. Data, 54, 1551, 2009. 

HAS Hasch, B.M. and McHugh, M.A., Calculating poly(ethylene-co-acryhc acid)-solvent phase behavior with the SAFT equation of state, J. Polym. Sci. Part B Polym. Phys., 33, 715, 1995. 

HOR Horst, M.H. ter, Behme, S., Sadowski, G., and Loos, Th.W. de, The influence of supercritical gases on the phase behavior of polystyrene-cyclohexane and polyethylene-cyclohexane systems experimental results and modeling with the SAFT equation of state, J. Supercrit. Fluids, 23, 181, 2002. 

Avila-Mendez, G.A., Justo-Garci a, D.N., Garcta-Sdnchez, F., Garcta-Ftores, B.E., n.d. Prediction of phase behavior for the system methane-carbon dioxide-hydrogen sulfide-water with the PR and PC-SAFT equations of state. 

The ratio Uo/k or u/k is analogous to the characteristic parameter T in the equations above. There are two additional volume and energy parameters if association is taken into account. In its essence, the SAFT equation of state needs three pure component parameters which have to be fitted to equilibrium data V , Uj/k and r. Fitting of the segment number looks somewhat curious to a polymer scientist, but it is simply a model parameter, like the c-parameter in the equations above, which is also proportional to r. One may note additionally that fitting to specific volume PVT-data leads to a characteristic ratio r/M (which is a specific r-value), as in the equations above, with a specific c-parameter. Several modifications and approximations within the SAFT-framework have been developed in the literature. Banaszak et or Shukla and Chapman extended the concept to copolymers. 

Adidharma and Radosz provides an engineering form for such a copolymer SAFT approach. SAFT has successfully applied to correlate thermodynamic properties and phase behavior of pure liquid polymers and polymer solutions, including gas solubility and supercritical solutions by Radosz and coworkers Sadowski et al. applied SAFT to calculate solvent activities of polycarbonate solutions in various solvents and found that it may be necessary to refit the pure-component characteristic data of the polymer to some VLE-data of one binary polymer solution to calculate correct solvent activities, because otherwise demixing was calculated. GroB and Sadowski developed a Perturbed-Chain SAFT equation of state to improve for the chain behavior within the reference term to get better calculation results for the PVT - and VLE-behavior of polymer systems. McHugh and coworkers applied SAFT extensively to calculate the phase behavior of polymers in supercritical fluids, a comprehensive summary is given in the review by Kirby and McHugh. They also state that characteristic SAFT parameters for polymers from PVT-data lead to... 

Gross, J., Sadowski, G., Perturbed-chain SAFT An equation of state based on a perturbation theory for chain molecules, oA. Eng. Chm. Res. 40 (2001) 1244-1260. Chapman, W.G., Gubbins, K.E., Jackson, G., Radosz, M., New reference equation of state for associating liquids, Ind. Eng. Chem. Res. 29 (1990) 1709-1721. Diamantonis, N.I., Boulougouris, G.C., Mansoor, E., Tsangaris, D.M., Economou, LG. Evaluation of cubic, SAFT, cmd PC-SAFT equations of state for the vapor-liquid equilibrium modeling of CO2 mixtures with other gases, Ind. Eng. Chem. Res. 52 (2013) 3933-3942. 

To describe the measured cloud-points, the SAFT equation of state (eos) has been used. The SAFT eos [6] is based on the perturbation theory (see Chapter 3), and, in spite of the rather complex derivation of the model equations, the basic idea and the application of the model is less complex. The SAFT eos can be written as a sum of Helmholtz energies. The first contribution is the Helmholtz energy of an ideal gas, followed by a correction for a mixture of hard spheres, a correction for chain formation, and a correction for the dispersion and association forces ... 

Banaszak, M., Chen, C. K. and Radosz, M. (1996) Copolymer SAFT equation of state. 1. Thermodynamic perturbation theory extended to heterobonded chains. Macromolecules 29, 6481-6486. 

Towards the Identification of Optimal Solvents for Long Chain Alkanes with the SAFT Equation of State... 

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