Original Statistical Associating Fluid Theory Research Articles

Prediction of the critical properties of n-alkanes and their mixtures with two versions of SAFT equation of state

Two versions of statistical associating fluid theory (SAFT) equation of state (EoS), namely modified SAFT-BACK and original SAFT, were used to calculate the critical temperatures and pressures of 10 n-alkanes (from $$c_{1}$$ to $$c_{10}$$ ). The obtained results were compared with the available experimental data to assess the predictive power of these EoSs in the critical region. The absolute average percentage deviation (AAD %) of the results obtained from the modified SAFT-BACK model indicated that this EoS had a good performance in the prediction of the critical points of the n-alkanes, but the deviation resulting from the original SAFT EoS reflected the limitations of the latter EoS in representing the critical region. Moreover, the critical temperatures for binary mixtures of n-alkane were calculated using both the original SAFT and the modified SAFT-BACK models and the results were compared with the data predicted by the correlation relations. The modified SAFT-BACK model showed a very good performance, while the original SAFT model did not yield an appropriate prediction of the critical temperatures of n-alkane binary mixtures.

Modeling solubilities of subcritical and supercritical fluids in polymers with cubic and non-cubic equations of state

The original statistical associating fluid theory (CK-SAFT), Perturbed-Chain SAFT (PC-SAFT), Sanchez–Lacombe (SL) and Sako–Wu–Prausnitz (SWP) equations of state (EoS) are used to model the solubilities of subcritical and supercritical fluids such as N 2, C 2H 4, C 4H 10, iso-C 4H 10, CO 2 in molten, thermally softened or semicrystalline polymers. Classical van der Waals one-fluid mixing rule with only one adjustable binary parameter is used for all the models. Modeling results are compared with the experimental data for 21 binaries including 78 systems published in open literature. Good agreement can be obtained with the PC-SAFT and SL EoS where the polymers are molten or thermally softened. Moreover, SL EoS gives a reasonable representation of the sorption data for semicrystalline polymers but the results are less satisfactory when compared with amorphous polymer systems. The performance of the CK-SAFT is least satisfactory in most case. Furthermore, SWP EoS provides an encouraging results although it is only a simple cubic equation of state.

Generalized SAFT-DFT/DMT Model for the Thermodynamic, Interfacial, and Transport Properties of Associating Fluids: Application for n-Alkanols

We have developed a “global” crossover (GC) statistical associating fluid theory (SAFT) equation of state (EOS) for associating fluids that incorporates nonanalytic scaling laws in the critical region and in the limit of low densities, ρ → 0, is transformed into the ideal-gas equation EOS. Unlike the crossover SAFT EOS developed earlier, the new GC SAFT EOS contains a so-called kernel term and reproduces the asymptotic scaling behavior of the isochoric heat capacity in the one- and two-phase regions. In addition, we develop on the basis of the density functional theory (DFT) a GC SAFT-DFT model for the surface tension. In the second step, using the GC SAFT EOS and the decoupled-mode theory (DMT), we have developed a generalized GC SAFT-DMT model for transport coefficients that reproduces the singular behavior of the thermal conductivity of pure fluids in the critical region. Unlike the DMT model based on the asymptotic crossover EOS, the GC SAFT-DMT model is valid in the entire fluid state region at T ≥ Tb (where Tb is the binodal temperature), and at ρ → 0 reproduces the dilute gas contributions for the transport coefficients. A comparison was made with experimental data for methanol, ethanol, and higher n-alkanols. For n-alkanols, the GC SAFT-DFT/DMT model contains the same number of the adjustable parameters as the original classical SAFT EOS but reproduces with high accuracy the PVT, VLE, isochoric, and isobaric specific heats, surface tension, and thermal conductivity data close to and far from the critical point.

Application to binary mixtures of a group contribution SAFT EOS (GC-SAFT)

Many authors have shown the ability of the statistical associating fluid theory (SAFT) equations of state (EOS) to model hydrocarbon systems. The parameter estimation in the absence of data strongly limits the use of these equations. As an answer to this problem, a group contribution (GC) method for pure compound parameters was proposed in a previous work [S. Tamouza, J.-P. Passarello, P. Tobaly, J.-C. de Hemptinne, Fluid Phase Equilib. 222–223 (2004) 67–76].In this paper, vapor liquid equilibria (VLE) of several binary mixtures are compared with experimental data, using the GC pure compounds parameters, and without any binary interaction parameter. The calculations have been performed with two versions of the SAFT equations (original SAFT and SAFT-VR). The mixtures that have been investigated are both non-associative (containing n-alkanes) and associative (containing 1-alcohols).The results show that the group contribution (GC) method provides pure compound parameters that allow a satisfactory prediction of the binary mixtures. In several cases, the GC parameters yield even better results for binary mixtures than those adjusted directly on the pure compounds (specific parameters). This rather unexpected observation may be due to the fact that these parameters take more information into account than the specific ones.

Interfacial properties of polystyrene in contact with carbon dioxide

The Cahn–Hilliard theory was combined with equations of state (the original statistical associating fluid theory, the perturbed-chain statistical associating fluid theory or the Sanchez–Lacombe lattice theory) in order to describe both the solubility of carbon dioxide in polystyrene and the interfacial properties between the liquid mixture and the pure gas phase. The comparison between the predicted interfacial tensions and the experimental data from the literature is discussed.

Group contribution method with SAFT EOS applied to vapor liquid equilibria of various hydrocarbon series

A new group contribution method is proposed using the statistical associating fluid theory (SAFT) equation of state (EOS), in order to describe the thermodynamic properties of hydrocarbon series. The method is developed for vapor–liquid equilibrium (VLE) calculations for a large number of hydrocarbons, with the use of several group parameters. SAFT models are chosen for the physical meaning of their parameters. These can be related to the molecular structure. Two versions of the SAFT EOS are used in this work: the original SAFT equation of state, proposed by Chapman et al. [Ind. Eng. Chem. Res. 29 (1990) 1709] and SAFT variable range (SAFT-VR) equation of state, proposed by Gil-Villegas et al. [J. Chem. Phys. 106 (1997) 4168]. The present group contribution method consists in calculating the equation of state parameters (dispersion energy ε, segment diameter σ, chain length m and square-well range parameter λ for SAFT-VR) using group contribution rules. In this paper, we have treated pure compounds of five hydrocarbon families: n-alkanes, alkyl-benzenes, alkyl-cyclohexanes, α-olefins and 1-alkanols. The results obtained are compared with those of the usual approach (fitting the molecular parameters of each compound on its own properties) and seem to be nearly equivalent. The results of the present method are comparable with those of other predictive approaches.

Statistical Associating Fluid Theory. 2. Estimation of Parameters To Predict Lube-Ranged Isoparaffin Properties

Building on part 1, we present a method by which statistical associating fluid theory (SAFT) parameters can be generated for any isoparaffin structure. The SAFT parameters that characterize a pure component are linked to functional relationships based on a number of easily computed topological indices. Simple relationships for the effective number of segments, m, and segment volume, v 00 , are formalized based on observed trends in regressed parameters in the previous work. We also employ a simulated annealing procedure to develop an accurate equation for u 0 /k, the segment interaction energy. The robustness of the parameter estimation method is demonstrated by comparing the quality of the equation of state predictions to the performance of the original SAFT parameter set determined in part 1. Perhaps most importantly, this approach opens the door for quantitative structure-property relationship studies, with particular emphasis on how branching affects specific properties. This is demonstrated by examining the influence of branching on the normal boiling point for a variety of lube-ranged isoparaffins.

Molecular-Based Equations of State for Associating Fluids: A Review of SAFT and Related Approaches

We present a review of recent advances in the statistical associating fluid theory (SAFT). In contrast to the “chemical theory”, in which nonideality is explained in terms of chemical reactions between the species, SAFT and similar approaches relate nonideality to the intermolecular forces involved. Such physical theories can be tested against molecular simulations, and improvements to the theory can be made where needed. We describe the original SAFT approach and more recent modifications to it. Emphasis is placed on pointing out that SAFT is a general method and not a unique equation of state. Applications to a wide variety of fluids and mixtures are reviewed, including aqueous mixtures and electrolytes, liquid−liquid immiscible systems, amphiphilic systems, liquid crystals, polymers, petroleum fluids, and high-pressure phase equilibria.

Equation of State for Nonpolar, Polar, Chain, and Associating Fluids Based on the Dipolar Yukawa Potential

An equation of state (EOS) based on Yukawa and dipolar Yukawa potentials is presented. It is extended to chainlike and associating fluids in the framework of statistical associating fluid theory (SAFT). The EOS is applied to 42 pure real fluids (including nonpolar, polar, and associating fluids) and has a good description of saturated pressures and coexistence curves for these fluids, except very near to the critical point. The parameters for each fluid are regressed from experimental data. Some comparisons among this work, the original SAFT, and the Lennard-Jones (LJ)-based SAFT are carried out. The performance for real polar fluids is also compared between the dipolar Yukawa fluids (DYF) and the Stockmayer fluids (STMF).

Simplified crossover SAFT equation of state for pure fluids and fluid mixtures

A simplified modification of the crossover statistical associating fluid theory (SAFT) EOS is used to describe thermodynamic properties of pure fluids and binary mixtures over a wide range of parameters of state including the nearest vicinity of the critical point. For pure fluids, the simplified crossover (SCR) SAFT model contains only three adjustable parameters but allows an accurate prediction of the critical parameters of pure fluids and yields a better representation of the thermodynamic properties of pure fluids than the original SAFT equation of state. For binary mixtures, simple mixing rules with only one adjustable parameter are used. A comparison is made with experimental data for pure refrigerants R12, R22, R32, R125, R134a, R143a, and mixtures R22+R12, R32+R134a and R125+R32 in the one- and two-phase regions. The SCR SAFT EOS reproduces the saturated pressure data with an average absolute deviation (AAD) of about 1.1% and the saturated liquid densities with an AAD of about 0.9%. In the one-phase region, the SCR SAFT equation represents the experimental values of pressure with an AAD of about 2.2% in the range of temperatures and density bounded by T≥Tc and ρ≤2ρc.

The use of statistical associating fluid theory to improve the BACK equation of state: I. Pure fluids

In this paper, statistical associating fluid theory (SAFT) equation of state (EOS) is incorporated into the Boublı́k–Alder–Chen–Kreglewski (BACK) EOS. The adjustable parameters for 16 pure non-associating fluids are compiled from references and those for 25 pure non-associating fluids are regressed with VLE data in this work. A new equation of state called SAFT-BACK equation is proposed by combining the hard convex body term and dispersion term of BACK equation with the associating term of SAFT equation so that it can describe phase equilibrium behavior for pure associating fluids. In this model, an associating molecule is treated as a convex body with associating sites on it. The adjustable parameters for 13 pure associating fluids are regressed. When compared to the original SAFT, the SAFT-BACK EOS can give more accurate description in the near critical region.

Crossover SAFT Equation of State: Application for Normal Alkanes

In this paper we develop a crossover modification of the statistical associating fluid theory (SAFT) equation of state for macromolecular chain fluids which incorporates the scaling laws asymptotically close to the critical point and is transformed into the original classical SAFT equation of state far away from the critical point. A comparison is made with experimental data for pure methane, ethane, n-hexane, n-decane, and n-eicosane in the one- and two-phase regions. We also present comparisons with experimental single-phase data for n-triacontane and n-tetracontane. We show that, over a wide range of states, the crossover SAFT model yields a much better representation of the thermodynamic properties of pure fluids than the original SAFT equation of state. The crossover SAFT equation of state reproduces the saturated pressure data in the entire temperature range from the triple point to the critical temperature with an average absolute deviation (AAD) of about 3.8%, the saturated liquid densities with a...

Critical behavior and partial miscibility phenomena in binary mixtures of hydrocarbons by the statistical associating fluid theory

Predictions of critical lines and partial miscibility of binary mixtures of hydrocarbons have been made by using a modified version of the statistical associating fluid theory (SAFT). The so-called soft-SAFT equation of state uses the Lennard-Jones potential for the reference fluid, instead of the hard-sphere potential of the original SAFT, accounting explicitly for the repulsive and dispersive forces in the reference term. The mixture behavior is predicted once an adequate set of molecular parameters (segment size, dispersive energy, and chain length) of the pure fluid is available. We use two sets of such parameters. The first set is obtained by fitting to the experimental saturated liquid density and by equating the chemical potential in the liquid and vapor phases for a range of temperatures and pressures. The second set is obtained from the previous one, by rescaling the segment size and dispersive energy to the experimental critical temperature and pressure. Results obtained from the theory with these parameters are compared to experimental results of hydrocarbon binary mixtures. The first set gives only qualitative agreement with experimental critical lines, although the general trend is correctly predicted. The agreement is excellent, however, when soft-SAFT is used with the rescaled molecular parameters, showing the ability of SAFT to quantitatively predict the behavior of mixtures. The equation is also able to predict transitions from complete to partial miscibility in binary mixtures containing methane.

Using Molecular Orbital Calculations To Describe the Phase Behavior of Cross-associating Mixtures

In previous studies, we have used molecular orbital calculations to determine the thermodynamic changes of dimerization for a number of pure and cross-associated species. We have shown that by using these results in a physical equation of state, the statistical associating fluid theory (SAFT), we are able to accurately model the phase behavior of pure self-associating compounds and binary mixtures of a self-associating compound and a nonassociating compound with a reduction in the number of adjustable parameters. In this study, we consider the phase behavior of binary mixtures in which cross-associated species may occur. To determine the equation of state parameters describing cross association, we introduce a mixing rule based on the results of the molecular orbital calculations. We show that using information derived from the quantum-mechanical calculations results in correlations of mixture vapor-liquid equilibrium data with fewer adjustable parameters and no loss of accuracy, indeed frequently with improved accuracy, compared to the original SAFT model.

2. Use of BACK To Modify SAFT in Order To Enable Density and Phase Equilibrium Calculations Connected to Gas-Extraction Processes

Statistical associating fluid theory (SAFT) has been extended to mixtures at temperatures slightly above the critical temperature of one of the compounds as often encountered in gas-extraction processes. The proposed extension is based on the contact values of the average correlation function for a pair in a mixture of hard convex bodies of different types by Boublik and allows a mixture of convex bodies described by the BACK equation of state with associating and nonassociating sphere chains from original SAFT. The supercritical solvent is modeled as a convex body, allowing an accurate description in the near-critical region, while all other compounds are modeled as sphere chains, utilizing the benefits of original SAFT. The proposed extension can be added to any existing SAFT software, quickly. Additionally, different two-parameter mixing rules are proposed that are defined on a segment basis instead of on a molecular or system basis like in original SAFT, promising a higher predictive capability for systems with chemically similar compounds. The SAFT equation extended this way has been used to correlate experimentally determined high-pressure phase equilibria from the gas-extraction processes of 40 systems, where original SAFT fails to give correct qualitative results, because the supercritical solvent's critical temperature is overpredicted.

Using Molecular Orbital Calculations To Describe the Phase Behavior of Hydrogen-Bonding Fluids

The authors have used Hartree-Fock theory and density functional theory to compute the enthalpy and entropy changes of dimerization for water, methanol, and the family of carboxylic acids. These results are used in a physical equation of state, the statistical associating fluid theory (SAFT), in order to model the phase behavior of these hydrogen-bonding compounds. A procedure has been developed to relate the calculated enthalpy and entropy changes to the association parameters in SAFT using only low-pressure data, as well as to relate molar volumes from molecular orbital calculations to the segment size and chain length parameters in SAFT. By doing so, the SAFT model is reduced to a three-parameter equation of state for associating fluids. The modified equation of state is shown to be as accurate as the original SAFT model for correlating pure-component vapor-liquid equilibrium data with fewer adjustable parameters.