SAFT-VR

MCC McCabe, C., Galindo, A., Garcia-Lisbona, M.N., and Jackson, G., Examining the absorption (vapor-liquid equilibria) of short-chain hydrocarbons in low-density polyetltylene with SAFT-VR approach, Ind. Eng. Chem. Res., 40, 3835,2001. 

A form analogous to eq 5.37 was used to predict the ky by Haslem et al. and these values were used with SAFT-VR equation of state to predict the phase boundaries of (CH4 + CgHi8) with surprisingly good results when compared with experimental data using ky = d. For (CF4-I-C4H10) the SAFT-VR with predicted ky was able to correctly predict the phase behaviour. Huynh et 173,174 form proposed in ref 43 to predict binary parameters... 

While the application of the SAFT-VR equation has primarily focused on a square-well potential, recent work has looked at the family o m — n Mie potentials.The SAFT-VR Mie approach of Lafitte et alP when compared to the original SW-based SAFT-VR equation, PC-SAFT (discussed below) and a LJ-based SAFT-VR, was found to provide a more accurate description of both the phase behaviour and derivative properties, such as condensed phase isothermal compressibility and speed-of-sound, of alkanes, alcohols and their mixtures, suggesting that the variable ranged repulsive term is needed to describe derivative properties. 

In related work, a modified SAFT-VR equation for square well potentials termed SAFTl has been proposed in which a truncation term is added to the monomer free energy expansion (eq 8.28) to account for higher-order terms. SAFTl has been successfully used to study both simple fluids such as alkanes,alcohols,polymers,and more recently room temperture as well as ionic liquids. ... 

Figure 8.5 Prediction of the water and methanol dielectric constant as a function of dipole moment fi (lD 3.33564-10 C-m) from the SAFT-VR-I-DE equation of state at room temperature and pressure. and , the theoretical predictions - -----------, the experimental value of the dielectric con-...

In this area a key challenge remains the study of mixed-solvent systems. The preliminary works of Wu and Prausnitz and Patel et on salting out in aqueous solutions are promising, but are also simple cases in which the extreme phase separation and difference in dielectric constant allows the electrolyte to be considered only in one of the two phases this greatly simplifies the treatment of mixture dielectrics. The SAFT-VR-t-DE approach provides another promising route for mixed solvent electrolyte systems, since the dielectric constant is a product of, and not a required input to, the calculations (see for example Figure 8.5). Non-aqueous solvents will also mean that ion pairing will need to... 

Recently the DFT method combined with SAFT equations of state has been used to predict the interfacial properties of real fluids. LDA methods are accurate enough to treat liquid-liquid and liquid-liquid interfaces where the density profiles are usually smooth functions, and have been used in combination with the SAFT-VR approach to predict the surface-tension of real fluids successfully. The intermolecular model parameters required to treat real substances are determined by fitting to experimental vapour-pressure and saturated liquid density data in the usual way (see section 8.5.1) and the resulting model is found to provide accurate predictions of the surface tension. A local DFT treatment has also been combined with the simpler SAFT-HS approach, but in this case only qualitative agreement with experimental surface tension data is found due to the less accurate description of the bulk properties provided by the SAFT-HS equation. Kahl and Winkelman" have followed a perturbation approach similar to the one proposed with the SAFT-VR equation and have coupled a local DFT treatment with a Lennard-Jones based SAFT equation of state. They predict the surface tension of alkanes from methane to decane and of cyclic and aromatic compounds in excellent agreement with experimental data. 

Figure 8.6 Pressure as a function of temperature T for the phase diagram of (C4H10 + CF4). , pure component critical point O, pure component critical part O, vapour pressure of the pure substances , critical points of the mixture —, predictions obtained from SAFT-VR equation with the predicted value of = 0.063 determined from the use of eq 8.56 correctly...

SAFT-VR with kij = predicted an erroneous type of phase behaviour. Reprinted with permission of Fluid Phase Equilibria. 

The key difference between the two approaches lies in the treatment of the chain term, in SAFT-y the SAFT-VR chain term is used through the... 

In both the GC-SAFT-VR and SAFT-y approaches, compared in Figure 8.7, the group parameters are determined by fitting to the experimental vapour pressures and saturated-liquid densities of the smaller members of chosen chemical families i.e. alkanes, branched alkanes, 1-alkenes, alkylbenzenes, ketones, alkyl acetates and methyl esters, among others). The predictive capability of the methods is then tested by assessing the description of the fluid phase behaviour of larger molar mass compounds that were not included in the determination of the group parameters. 

A key additional advantage of both SAFT-y and GC-SAFT-VR is that mixtures can be treated in a fully predictive marmer without the need to propose combining rules and adjustable parameters. In this context both methods have been shown to provide a good description of the pressure and composition of mixtures including binary mixtures of alkanes, alkenes, alkanols, namely (alkanes + alkylbenzenes), (alkane + ketones), (alkane + esters), (alkane + adds), (alkanes + amines) and even cases with highly non-ideal behaviour including liquid-liquid equilibrium (LLE) and polymer systems. ... 

McCabe, C., Gfl-VHegas, A., and Jackson, G., 1999. Gibbs ensemble computer simulation and SAFT-VR theory of non-conformal square-well monomer-dimer mixtures. Chem. Phys. Lett., 303 27. 

Haslam, A.J, von Solms, N., Adjiman, C.S., Galindo, A., Jackson, G., Paricaud, P, Michelsen, M.L., and Kontogeorgis, G.M., 2006. Predicting enhanced absorption of light gases in polyethylene using simph-fied PC-SAFT and SAFT-VR. Fluid Phase Equilib., 243 74. 

Behzadi, B., Patel, B.H., Galindo, A., and Ghotbi, C., 2005. Modeling electrolyte solutions with the SAFT-VR equation using Yukawa potentials and the mean-spherical approximation. Fluid Phase Equilib., 236 241-255. 

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