PC-SAFT

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.  

In contrast to the other popular versions of the SAFT equation, the PC-SAFT approach considers a hard-chain, rather than a hard-sphere, as the reference system for the application of standard high-temperature perturbation theory to obtain the dispersion contribution. Thus the Helmholtz 

In the original presentation of PC-SAFT parameters were correlated against vapour pressure and saturated liquid density data for 78 non-associating pure fluids and shown to work well in the description of mixture systems. Subsequently the equation has been successfully applied to the study of a wide range of industrially important fluids from simple binary mixtures involving hydro-carbons to associating fluids, pharmaceuticals, and asphaltenes, and, in particular, polymer systems.  

Comparisons between the different versions of SAFT are difficult in that many factors contribute to the observed agreement or disagreement with experimental data. For example, the type of thermodynamic data and the range of thermodynamic conditions used in the parameter optimization procedure must be consistent for a direct comparison and unfortunately such information is not always clearly described in the literature. A true comparison between the different versions of SAFT is therefore only meaningful if a 

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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)... 

One of the versions of SAFT, the so-called PC-SAFT developed by the group of Professor Sad-owski, - has been extensively applied to high-pressure polymer systems. 

FIGURE 16.11 LLE of polypropylene (PP)-propane at three temperatures in a pressure-weight fraction plot. (PP M =290 kg/mol, MJM, = AA). Comparison of experimental cloud points to PC-SAFT calculations (k y = 0.0242). The polymer was modeled using three pseudo-components. (From Tumakaka, F. et al., Fluid Phase Equilibria, 541, 194—197, 2002. With permission.)... 

FIGURE 16.12 Cloud-point curve of polypropylene (PP)-n-pentane-C02 for various COj contents. Initial polymer weight fraction Wpp= 0.03 (before the addition of COj). Comparison of experimental cloud points to PC-SAFT calculations (PP-n-pentane 0.0137, PP-CO2 0.177, -pentane-C02 kij= 0.143). (From... 

BEC Becker, F., Buback, M., Latz, H., Sadowski, G., and Tumakaka, F., Cloud-point curves of ethylene-(meth)acrylate copolymers in fluid ethene up to high pressures and temperatures Experimental study and PC-SAFT modeling. Fluid Phase Equil, 215, 263, 2004. 

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. 

In addition to the simulation of the catalyst, we also performed thermodynamic modeling studies on the reactants and products in order to investigate physical properties during the catalytic reaction. The solubility of hydrogen in benzene and benzene/cyclohexane mixtures was calculated with PC-SAFT at the temperature range 250-523 K. T-P Flash calculations were performed at constant pressure 10, 20 and 50 bar. The results are illustrated in Fig. 2. The composition of the liquid phase in these T-P Flash calculations is not kept constant, therefore the mole fraction of cyclohexane shown in Fig. 2 (0.36 (top) and 0.96 (bottom)) is approximate. 

F. 2 Results of PC-SAFT for hydrogen solubility (mole fraetion) in benzene (dashed lines) and... 

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. 

Keywords Carbon Dioxide, Molecular Dynamics, Monte Carlo Simulation, PC-SAFT, Thermodynamic Properties, Transport Properties... 

This study describes the accuracy of PC-SAFT for the prediction of phase equilibria and density for C02-N2-Ar-02 and C02-N2-Ar-02-S02 and provides a brief comparison with Peng-Robinson (PR) EoS [9] with the Peneloux correction. Furthermore, MD simulations were employed for the calculation of self- diffusion coefficients of CO2 in H2O and H2O in CO2. Recently proposed force-fields for H2O and CO2 were tested over a wide range of temperatures (283.15 K < J < 523.15 K) at a pressure of 20 MPa. 

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

A well-rounded EoS should be able to accurately predict thermodynamic properties over a wide range of temperatures and pressure in each of the snbcritical, critical and supercritical regions. In this work, PC-SAFT is used for the prediction of thermodynamic properties. PC-SAFT is based on perturbation theory and is formnlated in terms of the residnal Helmholtz free energy, A. In the perturbation theory, A is modeled as the sirm of contributions from different intermolecular interactions over a reference fluid. In this respect. Gross and Sadowski [10] proposed the following expression which is an improvement over the original SAFT [11] ... 

For non-associating fluids, PC-SAFT requires three parameters (i) the number of segments in the chain (m), (ii) the soft core volnme (v ) and (iii) the soft core segment diameter (a) [12]. 

As expected, PC-SAFT performs better than PR EoS for both systems. A comparison between the predictions by PC-SAFT and PR and experimental data measured by Creton et al. [6] is seen in Figure 1. Furthermore, Table 3 shows the average absolute deviation for PR and PC-SAFT predictions for all three systems. The molecular simulation data for the C02-N2-Ar-02-S02 mixture lie far from the critical point so the density is more accurately predicted by both PC-SAFT and PR EoS resulting in a lower %AAD. These results show that PC-SAFT follows the trend of experimental data more closely and with higher accuracy than PR. The use of the optimized binary interaction parameters further improves the prediction of density by both PR and PC-SAFT. 

Figure 1. Predictions of (Left) densities for the mixture C02-Ar-N2-02 and (Right) VLB for C02-Ar using ( ) PR EoS and (—) PC-SAFT eompared to experimental data (points) [6],...

Table 3. Average absolute difference for the prediction of density using PC-SAFT and PR EoS for both pure CO2 and the mixture.

Comparing the results of the mixtures to that of pure CO2 indicates that PC-SAFT predicts a lower density mixture when, hghter gases such as Ar, N2 and O2 are added. These predictions are supported by experimental data published by Mazzoccoli and Arato for binary mixtures [23], Furthermore, the addition of SO2 to the quaternary mixture increases the density. 

In this work, representative calculations for the physical properties of CO2 systems using MD simulations and EoS were presented. In all cases, the agreement with experimental data was relatively good. For the case of EoS calculations, both EoS closely captured the qualitative density trends however, PC-SAFT did so more accurately. For transport properties such as diffusion coefficient, MD simulations are the preferred computational... 

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. 

Fig. 2.6 I mpact of the copolymer composition on the solubility in supercritical ethylene. Arrows indicate an increasing amount of the acrylate comonomer(s) in the polymer backbone. Symbols are experimental data. Lines are modeling results with the PC-SAFT...

Lines are modeling results using the PC-SAFT model [27]. 

The recently proposed Perturbed-Chain SAFT (PC-SAFT) model [75, 76] adopts the opposite idea here, a perturbation theory of second order is applied to the reference system of hard chains instead of hard spheres to develop a dispersion term for chain-Hke molecules ... 

Fig. 2.9 Comparison of phase equilibrium calculations using SAFT (dashed lines) and PC-SAFT (solid lines) [76]. (a) Vapor-liquid phase equilibrium of polyethylene-toluene at T=393 K. Filled symbols are experimental data for polymer molecular weight...

The PC-SAFT model was successfully applied to describe a whole variety of polymer solubilities in liquids as well as in supercritical solvents [18, 27, 76-78,... 

Thus, Fig. 2.3 a gives an example of the ability of PC-SAFT to predict the molecular-weight dependence of polymer-solubility data. Although the binary parameter... 

Fig. 2.10 Solubility of poly(vinyl acetate) (PVA Mv,= 125 kg/mol) and poly(methyl acrylate) (PMA M =31 kg/mol) in supercritical carbon dioxide. Symbols are experimental data (Rindfleisch et at 1996). Lines are modeling results using the PC-SAFT model [79].

Chain SAFT (PC-SAFT) (Gross and Sadowski 2001), and Cubic Plus Association (CPA) (Kontogeorgis et al. 1996), which have beat reviewed by Kontogeorgis and Folas (Kontogeoigis et al. 2006a,b) and by Polishuk and Mulero (2011), were examined. 

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