A hybrid perturbed-chain SAFT density functional theory for representing fluid behavior in nanopores

The perturbed-chain statistical associating fluid theory (PC-SAFT) density functional theory developed in our previous work was extended to the description of inhomogeneous confined behavior in nanopores for mixtures. In the developed model, the modified fundamental measure theory and the weighted density approximation were used to represent the hard-sphere and dispersion free energy functionals, respectively, and the chain free energy functional from interfacial statistical associating fluid theory was used to account for the chain connectivity. The developed model was verified by comparing the model prediction with molecular simulation results, and the agreement reveals the reliability of the proposed model in representing the confined behaviors of chain mixtures in nanopores. The developed model was further used to predict the adsorption of methane-carbon dioxide mixtures on activated carbons, in which the parameters of methane and carbon dioxide were taken from the bulk PC-SAFT and those for solid surface were determined from the fitting to the pure-gas adsorption isotherms measured experimentally. The comparison of the model prediction with the available experimental data of mixed-gas adsorption isotherms shows that the model can reliably reproduce the confined behaviors of physically existing mixtures in nanopores.

Modeling of molecular gas adsorption isotherms on porous materials with hybrid PC-SAFT–DFT

In this work, a general f‐theory viscosity model based on the perturbed‐chain statistical associating fluid theory (PC‐SAFT) equation of state (EoS) has been developed for the description of the viscosity behavior of the normal alkanes family (from methane to n‐octadecane). This general f‐theory model has been shown to provide satisfactory results for the modeling of the viscosity of the normal alkanes as well as carbon dioxide and nitrogen over wide ranges of temperatures and up to 100 MPa. In addition, using simple mixing rules, an evaluation of the model performance has been carried out for several n‐alkane and carbon dioxide + n‐alkane mixtures over wide ranges of temperature and pressure. The chosen mixing rules provide good mixture viscosity prediction, close to or within experimental uncertainty, which is satisfactory for most applications (industrial and research). Further, the combination of the PC‐SAFT EoS with the f‐theory adds one more thermophysical property to the list of properties for which this model already delivers an improved representation, making the application potential for the PC‐SAFT EoS even wider. © 2006 American Institute of Chemical Engineers AIChE J, 2006

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

The density of CO2 + crude oil mixtures is one of the most important parameters influencing CO2 diffusion and migration in oil reservoirs. However, it would be quite time consuming to obtain comprehensive density data for CO2 + alkane mixtures over a wide range of temperatures and pressures via experimental methods, therefore the development of a reliable model for predicting the densities of various CO2 + alkane mixtures with high accuracy is crucial. In this paper, the parameters (m, σ, and ε/k) in the perturbed‐chain statistical associating fluid theory (PC‐SAFT) Equation of State (EoS) were optimized by correlating density data of pure n‐alkanes from heptane to nonadecane (except undecane and hexadecane). For comparison, the G‐S PC‐SAFT and HTHP PC‐SAFT EoS(s) were also employed to fit the densities of these n‐alkanes, and the results demonstrated that the PC‐SAFT EoS with the optimized parameters in this study exhibited superior accuracy. Subsequently, by correlating density data of CO2 + alkane mixtures containing C7–C14 alkanes, the binary interaction parameter kij was optimized. Furthermore, for the first time, correlations between the optimized parameters (m, σ, ε/k, and kij) and alkane carbon number (n) were established. These correlations provided PC‐SAFT EoS with a good universality and scalability for density prediction. Using the parameters calculated from these correlations, the densities of hexadecane and saturated CO2 + alkane mixtures containing C10–C20 alkanes were successfully predicted with relatively high accuracy. This work provides a new way for modeling the thermodynamic properties of CO2 + alkane mixtures. © 2020 Society of Chemical Industry and John Wiley & Sons, Ltd.

Simplified Flory-dimer equation of state for application to non-associating fluids, polymers and their mixtures

A mathematical model for polymerization kinetics and molar mass development in the nitroxide‐mediated polymerization (NMP) of vinyl monomers in supercritical carbon dioxide (scCO2) has been developed. The method of moments is used for molar mass development. The perturbed‐chain statistical associating fluid theory (PC‐SAFT) equation of state is used to estimate the number of stable phases present at equilibrium in the reaction mixture, critical number average chain length at which polymer particles are formed, and monomer concentration in each phase. Pure and binary PC‐SAFT interaction parameters are estimated from liquid–liquid equilibrium (LLE) and liquid–vapour equilibrium (LVE) experimental data at 60 to 129°C. The effect of pressure on monomer conversion and molar mass development in the polymerization of styrene (Sty) using benzoyl peroxide (BPO) and 2,2,6,6‐Tetramethylpiperidinyl‐1‐oxyl (TEMPO) at 120°C and 300–500 bar is studied. It was observed that increasing pressure increases polymerization rate without significantly affecting molar mass development.

To predict the size (m, σ) and energy (ε) parameters of the perturbed‐chain statistical associating fluid theory (PC‐SAFT) based on the conductor‐like screening model for realistic solvents (COSMO‐RS), in this work, the PC‐SAFT model parameters of 304 substances were reviewed and summarized, their COSMO‐RS results linked to the size and energy were predicted, and the relationships between the PC‐SAFT parameters and COSMO‐RS results were obtained in 3 cases (Case 1: relationships based on n‐alkanes, Case 2: category‐specific relationships, Case 3: generic relationships for 138 substances). Case 2 (including Case 1) shows the lowest average absolute relative deviations (AARDs) of 7.63% (m), 3.05% (σ), and 9.05% (ε), while Case 3 provides the prediction capacity with AARDs of 10.00% (m), 4.05% (σ), and 13.21% (ε), which is better than those developed by others. Finally, the new PC‐SAFT parameters were used to predict the densities and vapor pressures of 8 representative substances and compared with the results using the original PC‐SAFT parameters, showing that the parameters in Case 3 can be used to reproduce densities and the parameters in Case 2 (including Case 1) can be used to reproduce both densities and vapor pressures.

The group contribution methodology developed by Elliott and Natarajan has been extended to the statistical associating fluid theory (SAFT) and perturbed-chain statistical associating fluid theory (PC-SAFT) equations of state (EOS). Thermodynamic properties were correlated and predicted for a database of 878 compounds, including associating compounds. Association contributions were treated with Wertheim’s theory. The database covers 19 chemical families including hydrocarbons, cyclic hydrocarbons, aromatic hydrocarbons, alcohols, amines, nitriles, thiols, sulfides, aldehydes, ketones, esters, ethers, halocarbons, and silicones. The present group contribution (GC) method was developed in two stages. Initially, pure component parameters of each EOS were obtained by matching their boiling temperatures at 10 or 760 mmHg and available GC estimates of solubility parameter and liquid density, while applying standard hydrogen-bonding parameters. Then, group contributions were regressed for the shape factor parameters of each EOS. Group contributions are presented for 84 first-order functional groups (FOG). Given the GC shape factors, the same GC estimates of solubility parameter and liquid density can be applied to estimate all EOS parameters on a GC basis. The resulting correlation enables three-parameter corresponding states predictions without any experimental data. A byproduct of the correlation for equation of state parameters is the capability to predict vapor pressure only on the basis of chemical structure. This capability was evaluated by computing the vapor pressures at 10, 100, and 760 mmHg. On the basis of the present work, vapor pressure average absolute percent deviations (P AAD%) were 36% for Elliott−Suresh−Donohue (ESD) EOS, 65% for SAFT, 32% PC-SAFT. For comparison, the first- and second-order groups (FOG and SOG) provided by Tihic et al. (for simplified PC-SAFT) have been applied to ∼650 nonassociating compounds. The resulting P AAD% were 53% for Tihic FOG and 42% for Tihic SOG. An alternative characterization of accuracy is the average absolute deviation (|ΔT|) between experimental and calculated saturated temperature. These were 8, 12, 8, 10, and 9 K for ESD, SAFT, PC-SAFT, Tihic FOG, and Tihic SOG equations, respectively.

The performance of the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) using classical mixing rules, induced-association schemes for mixtures exhibiting cross-association phenomena between two components that do not self-associate, and one regressed temperature-independent binary interaction parameter (kij) per mixture is assessed using a high-quality reference database containing binary-system data for various properties. The binary mixtures that are included in the database are divided into nine categories (Binary Association Codes, BACs) according to their ability to be involved in a hydrogen bond. Grading of the EoS is done by applying an already published procedure with certain modifications that were also published recently. An important feature is the inclusion of a performance indicator, called the “Success Ratio” (SR), that quantifies the percentage of experimental data points which the model can qualitatively reproduce. The original marks of the PC-SAFT EoS when implemented with classical mixing rules, no induced-association scheme, and a kij parameter set equal to zero are recalculated with the modified grading procedure and are directly compared with the new marks obtained in this work. The effect of including induced-association effects in PC-SAFT for mixtures that belong to BAC6, BAC7, and BAC8 (mixtures in which cross-association takes place without both components being self-associating) is also investigated. The effect of regressing cross-association parameters vs regressing kij parameters for mixtures belonging to the BAC6 group (mixtures in which cross-association arises although the two components do not self-associate) is showcased. The final optimized PC-SAFT EoS utilizes classical mixing rules, induced-association effects (using regressed cross-association parameters for some binary systems belonging to BAC6 and a predictive method for BAC7 and BAC8), and one temperature-independent kij parameter per binary mixture (except for binary systems belonging to BAC6 for which cross-association parameters were adjusted). The final average mark of the optimized EoS is 9.3/20.

Asphaltene precipitation modeling with PR and PC-SAFT equations of state based on normal alkanes titration data in a Multisolid approach

Evaluation of SAFT and PC-SAFT models for the description of homo- and co-polymer solution phase equilibria

Accurate thermodynamic models for phase equilibria calculations of carbon dioxide mixtures with other gases are of high importance for the safe and economic design of carbon capture and storage (CCS) technologies. In this work, we assess the capability of Redlich–Kwong (RK), Soave–Redlich–Kwong (SRK), Peng–Robinson (PR) cubic equations of state (EoS), as well as Statistical Associating Fluid Theory (SAFT) and Perturbed-Chain SAFT (PC-SAFT) in modeling vapor–liquid equilibria for binary mixtures of CO2 with CH4, N2, O2, SO2, Ar, and H2S, and for the ternary mixture CO2–N2–O2. Liquid density calculations for some of these mixtures are also performed. Experimental data available are used to assess the accuracy of the models. Two different expressions are used for the calculation of parameter α in PR EoS. PC-SAFT is, on average, more accurate than cubic EoS and SAFT when no binary interaction parameter is used. However, when a binary interaction parameter fitted to the experimental data is used, model correla...

ABSTRACTThe knowledge of solubility of gases and hydrocarbons in polymer has enormous importance in the design and development of reactor, polymer foaming, and membrane separation processes. In this work, the solubility of gases and hydrocarbons in polyethylene was correlated using a thermodynamic model based on perturbed‐chain statistical associating fluid theory (PC‐SAFT). The experimental solubility data of various gases such as ethylene, carbon dioxide, nitrogen, methane, and hydrocarbons of up to chain length of seven in both molten and semicrystalline polyethylene has been reviewed and the suitability of the developed model based on PC‐SAFT was then tested using the available solubility data in literatures for various gases and hydrocarbons. Furthermore, the optimum values of adjustable solvents‐solute binary interaction parameters (Kij) of PC‐SAFT at different temperatures have been estimated by regression of the PC‐SAFT model using experimental solubility isotherms. A suitable correlation of Kij with temperature was then developed using the estimated Kij at different temperatures. The solubility calculated from the developed model using the estimated Kij was then compared to the experimental results and a reasonably good correlation was observed. © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

Accurate vapor-liquid phase equilibria predictions of hydrogen sulfide and carbon dioxide mixtures are critical to the safe and economic design of gas processing and flow assurance technologies. In addition, inaccurate predictions of the vapor-liquid equilibria also can lead to erroneous hydrate phase equilibrium predictions. In this work, different equations of state are used to predict vapor-liquid equilibria for mixtures of hydrogen sulfide and carbon dioxide along with other hydrocarbons and various cross-associating components (including water, methanol, ethanol, monoethylene glycol) as well. The equations of state used in these predictions include the Cubic Plus Association (CPA), the Soave-Redlich-Kwong (SRK), the Peng-Robinson (PR), the Statistical Associating Fluid Theory (SAFT), and the Perturbed-Chain SAFT (PC-SAFT) equations of state. Five parameters of the CPA equation of state were determined for the associating components by simultaneous minimization of absolute errors using experimental saturated liquid densities and vapor pressures. Model accuracies were compared without using binary interaction parameters.