Application of the perturbed chain SAFT equation of state to complex polymer systems using simplified mixing rules

A simplified perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state is applied to polymer systems that include a variety of non-associating (esters, cyclic hydrocarbons), polar (ketones) as well as associating (amines, alcohols) solvents. The solvent pure-component parameters that are not available in the literature are estimated by correlating vapor-pressure and liquid-density data. The performance of the simplified PC-SAFT is compared to the original PC-SAFT equation of state for polymer systems of varying complexity. It is shown that the applied simplification is not at the expense of the accuracy of equation of state, while the computational time and complexity are significantly reduced, especially for associating systems. With no binary interaction parameter, simplified PC-SAFT is successfully able to predict vapor–liquid equilibria of polymers with non-associating solvents. In the case of associating solvents, a small binary interaction parameter k_ij is usually needed for the satisfactory correlation of the experimental data.     

Modeling CO2 solubility in Aqueous Methyldiethanolamine Solutions by Perturbed Chain-SAFT Equation of State

CO₂ capture by aqueous alkanolamines treating is one of the prevalent methods to reduce carbon dioxide emissions and to help environmental problems. For realizing more the thermodynamics of the CO₂–MDEA–H₂O, the PC-SAFT equation of state was used to simulate the absorption of carbon dioxide by MDEA (methyldiethanolamine). A correlation for temperature-dependent binary interaction parameter were calculated by excess enthalpy data for aqueous MDEA at low temperatures (lower than 350 K), and then this binary interaction parameter used to predict phase equilibria of ternary aqueous mixtures of MDEA with carbon dioxide. Smith–Missen algorithm and PC-SAFT EOS have been used to determine concentration of species in chemical equilibrium and physical equilibrium, respectively. In addition, for determining parameter sets of MDEA, vapor pressure and saturated liquid density data were used and different and probable association schemes were considered in parameter estimations. Results show 4(2:2, 0:0) association scheme for MDEA and 4(2:2) association scheme for water have better agreement with binary and ternary VLE experimental data.     

High-pressure fluid phase equilibria: Experimental methods and systems investigated (1994–1999)

As a continuation of an earlier review, a compilation of systems for which high-pressure phase equilibrium data have been published between 1994 and 1999 is given. Vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), vapor–liquid–liquid equilibria (VLLE), solid–liquid equilibria, solid–vapor equilibria, solid–vapor–liquid equilibria, critical points, the solubility of high-boiling substances in supercritical fluids and the solubility of gases in liquids (GLE) are included. For the systems investigated, the reference, the temperature and pressure range of the data, and the experimental method used for the measurements is given in 39 tables. Most of experimental data in the literature has been given for binary systems. Of the 824 binary systems, 350 have carbon dioxide as one of the components. Information on 135 pure components, 337 ternary systems and 120 multicomponent systems is given. Experimental methods for the investigation of high-pressure phase equilibria are classified and described.     

Extension of polar GC-SAFT to systems containing some oxygenated compounds: Application to ethers, aldehydes and ketones

The GC-SAFT equation of state proposed by Tamouza et al. (2004) [51], extended to polar molecular fluids NguyenHuynh et al. (2008) [32], is here applied to model vapor-liquid phase equilibria of various binary mixtures containing at least one oxygenated compound belonging to ethers, ketones or aldehydes chemical families.These systems are modeled using a polar version of the three different versions of SAFT-EOS (original, VR-SAFT and PC-SAFT) in a predictive manner: binary interaction parameters k_ij and l_ij are all set to zero.In the case of alcohol + ether, +ketone, +aldehyde systems, a cross-association interaction between an oxygenated compound (non self-associating compound) and an alcohol is necessary to model/predict accurately the mixture VLE. The corresponding association parameters are assumed to be equal to the self-association parameters of pure 1-alkanols.The above-cited systems have been treated in a comprehensive manner. The general agreement between polar GC-SAFT and experimental data is good (within 4-5% deviation on pressure), similar to the one obtained on previously investigated systems using GC-SAFT.     

Predicting vapor–liquid equilibria of fatty systems

In the present work, a group contribution method is proposed for the estimation of the vapor pressure of fatty compounds. For the major components involved in the vegetable oil industry, such as fatty acids, esters and alcohols, triacylglycerols (TAGs) and partial acylglycerols, the optimized parameters are reported. The method is shown to be accurate when it is used together with the UNIFAC model for estimating vapor–liquid equilibria (VLE) of binary and multicomponent fatty mixtures comprised in industrial processes such as stripping of hexane, deodorization and physical refining. The results achieved show that the group contribution approach is a valuable tool for the design of distillation and stripping units since it permits to take into account all the complexity of the mixtures involved. This is particularly important for the evaluation of the loss of distillative neutral oil that occurs during the processing of edible oils.The combination of the vapor pressure model suggested in the present work with the UNIFAC equation gives results similar to those already reported in the literature for fatty acid mixtures and oil–hexane mixtures. However, it is a better tool for predicting vapor–liquid equilibria of a large range of fatty systems, also involving unsaturated compounds, fatty esters and acylglycerols, not contemplated by other methodologies. The approach suggested in this work generates more realistic results concerning vapor–liquid equilibria of systems encountered in the edible oil industry.     

Thermodynamic modeling of hydrogen sulfide solubility in ionic liquids using modified SAFT-VR and PC-SAFT equations of state

Equations of state based on the statistical associating fluid theory for potentials of variable range (SAFT-VR) and the perturbed chain statistical associating fluid theory (PC-SAFT) have been used to model the PVT behavior of ionic liquids and the solubility of H₂S in six imidazolium-based ionic liquids. The studied systems included [bmim][PF6], [hmim][PF6], [bmim][BF4], [hmim][BF4], [bmim][NTF2] and [hmim][NTF2] at various temperatures and pressures.For pure components, parameters of the models have been obtained by fitting the models to experimental data on liquid densities; the average relative deviation between the calculated and experimental densities for ionic liquids is less than 2.42% in the PC-SAFT model and 5.44% in the SAFT-VR approach, the latter which incorporates the square-well potential for short-range interactions. In both models an additional term has been added to account for dipole-dipole interactions between solute molecules resulting from the permanent charges on the chain molecules of the solvents. The model parameters have also been correlated as functions of the molecular weight of the solvents. For binary mixtures of ionic liquids and H₂S, the association interactions between H₂S molecules and between the ionic liquids and H₂S molecules have also been taken into account in both approaches, using binary interaction coefficients. The results show an average deviation of less than 5% in the calculation of the mole fraction of H₂S in the ionic liquids. The effect of inclusion of the polar term has been studied for binary systems in both models.     

Thermodynamics of 1-alkanol+linear alkanoate mixtures

1-Alkanol?+?linear alkanoate mixtures have been investigated in the framework of the DISQUAC model. The interaction parameters for the OH/COO contacts are reported. The quasichemical parameters are independent of the mixture compounds. The dispersive parameters change with the molecular structure of the components. The same behaviour is observed for the OH/CO (carbonyl) and OH/OCOO (carbonate) contacts. DISQUAC represents well the molar excess Gibbs energies, coordinates of azeotropes and molar excess enthalpies. Using binary parameters only, DISQUAC improves meaningfully predictions on this property from the UNIFAC model for 1-alkanol?+?linear alkanoate?+?hydrocarbon systems. In contrast, the Nitta–Chao and the DISQUAC models yield similar results for the thermodynamic properties of the binary and ternary mixtures considered. 1-Alkanol?+?linear alkanoate mixtures are characterized by strong dipolar interactions between like molecules. In 1-alkanol?+?CH₃COO(CH₂) _{u ?1}CH₃ systems, dipole–dipole interactions between ester molecules are more important for u?≤?7. For u?≥?8, the more important contribution to the excess molar enthalpy comes from the disruption of the alkanol–alkanol interactions. For systems containing a polar compound such as alkanone, alkanoate or linear organic carbonate, dipolar interactions increase in the order: alkanone?<?alkanoate?<?carbonate.     

Prediction of ternary vapor–liquid equilibria for 33 systems by molecular simulation

A set of molecular models for 78 pure substances from prior work is taken as a basis for systematically studying vapor–liquid equilibria (VLE) of ternary systems. All 33 ternary mixtures of these 78 components for which experimental VLE data are available are studied by molecular simulation. The mixture models are based on the modified Lorentz–Berthelot combining rule that contains one binary interaction parameter which was adjusted to a single experimental binary vapor pressure of each binary subsystem in prior work. No adjustment to ternary data is carried out. The predictions from the molecular models of the 33 ternary mixtures are compared to the available experimental data. In almost all cases, the molecular models give excellent predictions of the ternary mixture properties.     

On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols

Nagata, I., 1985. On the thermodynamics of alcohol solutions. Phase equilibria of binary and ternary mixtures containing any number of alcohols. Fluid Phase Equilibria, 19: 153–174.Binary vapor—liquid and liquid—liquid equilibrium data for alcohol solutions includin one or two alcohols are correlated with the UNIQUAC associated solution theory (Nagata and Kawamura). The theory uses pure liquid association constants determined by the method of Brandani and a single value of the enthalpy of the hydrogen bond equal to ?23.2 kJ mol ^?1 for pure alcohols. For alcohol-active nonassociating component mixtures and alcohol—alcohol mixtures the theory involves additional solvation constants. The theory is extended to contain ternary mixtures with any number of alcohols. Ternary predictions of vapor—liquid and liquid—liquid equilibria are performed using only binary parameters. Good agreement is obtained between calculated and experimental results for many representative mixtures.     

Molecular models for 267 binary mixtures validated by vapor–liquid equilibria: A systematic approach

By assessing a large number of binary systems, it is shown that molecular modeling is a reliable and robust route to vapor–liquid equilibria (VLE) of mixtures. A set of simple molecular models for 78 pure substances from prior work is taken to systematically describe all 267 binary mixtures of these components for which relevant experimental VLE data is available. The mixture models are based on the modified Lorentz–Berthelot combining rule. Per binary system, one state independent binary interaction parameter in the energy term is adjusted to a single experimental vapor pressure. The unlike energy parameter is altered usually by less than 5% from the Berthelot rule. The mixture models are validated regarding the vapor pressure at other state points and also regarding the dew point composition, which is a fully predictive property in this work. In almost all cases, the molecular models give excellent predictions of the mixture properties.     

Calculation of high pressure vapour—liquid equilibria for systems containing polar substances with the use of an augmented van der Waals equation of state

An augmented van der Waals equation of state based on a perturbation theory has been applied to the calculation of high pressure vapour—liquid equilibria for systems containing polar substances. The equation of state comprises four terms, which imply the contributions from repulsion, symmetric, non-polar asymmetric, and polar asymmetric interactions. The characteristic parameters of each pure substance have been determined by three methods with the use of vapour pressures and saturated liquid densities. Mixing models for the terms of the repulsion, symmetric, and non-polar asymmetric interactions are the same as used previously. Two types of mixing models based on a three-fluid model and/or a one-fluid model are developed for the polar asymmetric term. The polar asymmetric term has a large effect on the prediction of the vapour—liquid equilibrium. With the introduction of a binary interaction parameter, the equation is found to be useful in correlating the vapour—liquid equilibria for a system containing a polar substance except near a critical region.     

Modeling the phase equilibria of hydrogen sulfide and carbon dioxide in mixture with hydrocarbons and water using the PCP-SAFT equation of state

The perturbed-chain polar statistical associating fluid theory (PCP-SAFT) equation of state is applied to correlate phase equilibria for mixtures of hydrogen sulfide (H₂S) and carbon dioxide (CO₂) with alkanes, with aromatics, and with water over wide temperature and pressure ranges. The binary mixtures of H₂S–methane and CO₂–methane are studied in detail including vapor–liquid, liquid–liquid and fluid–solid phase equilibria. Very satisfying results were obtained for the binary mixtures as well as for the ternary mixture of H₂S–CO₂–methane using the (constant) interaction parameters of the binary pairs.     

Vapor–liquid equilibria predictions of hydrogen–hydrocarbon mixtures with the Huron–Vidal mixing rule

An excess Gibbs-equation of state (G^E-EoS) framework based on the Huron–Vidal mixing rule, has been applied to study vapor–liquid equilibria (VLE) of hydrogen–hydrocarbon mixtures. The mixing rule couples the Peng–Robinson–Stryjek–Vera (PRSV) EoS with a local composition solution model. The solution model is based on one-fluid theory treatment and assigns a single energy parameter to each binary pair. This energy parameter relates to the preference of the molecules for like to unlike interactions. The allocation of a system's number of interactions to the individual species in a binary mixture, incorporates the use of size parameters which gain significance only in the liquid phase. In a two parameter form, the framework has been used for the simultaneous data reduction of a large number of binary and several ternary hydrogen–hydrocarbon mixtures. These systems were taken over an extended range of pressures and temperatures. Results from the data reduction are reported in both tabular and graphical forms. Correlations for the model parameters have been identified with the acentric factor of the hydrocarbon in hydrogen–hydrocarbon binary mixtures. In a fully predictive mode, the model has shown to describe well VLE of binary hydrogen–linear alkane systems. Comparisons of these results with calculations from the Peng–Robinson (PR) EoS and the classical mixing rule (vdW) are included.     

Vapor liquid equilibrium modeling of alkane systems with Equations of State: “Simplicity versus complexity”

Two types of Equations of State (EoS), which are characterized here as “simple” and “complex” EoS, are evaluated in this study. The “simple” type involves two versions of the Peng–Robinson (PR) EoS: the traditional one that utilizes the experimental critical properties and the acentric factor and the other, referred to as PR-fitted (PR-f), where these parameters are determined by fitting pure compound vapor pressure and saturated liquid volume data. As “complex” EoS in this study are characterized the EoS derived from statistical mechanics considerations and involve the Sanchez–Lacombe (SL) EoS and two versions of the Statistical Associating Fluid Theory (SAFT) EoS, the original and the Perturbed-Chain SAFT (PC-SAFT).

The evaluation of these two types of EoS is carried out with respect to their performance in the prediction and correlation of vapor liquid equilibria in binary and multicomponent mixtures of methane or ethane with alkanes of various degree of asymmetry. It is concluded that for this kind of systems complexity offers no significant advantages over simplicity. Furthermore, the results obtained with the PR-f EoS, especially those for multicomponent systems that are encountered in practice, even with the use of zero binary interaction parameters, indicate that this EoS may become a powerful tool for reservoir fluid phase equilibria modeling.     

用二元交互作用函数预测高压下多组分体系的气液平衡

用和体系的状态有关且满足不变性条件的二元交互作用函数,结合F函数修改的立方状态--方程FRKS方程,预测高压下多组分体系的气液平衡.选择15个三元体系及其组分二元系来检验方法的可行性,这些体系覆盖了从简单的接近理想溶液行为的体系到高度非理想体系.计算结果表明,该方法不仅能相当精确地关联各种类型二元系的气液平衡,而且能在仅用组分二元系参数的条件下较准确地预测所考察的所有三元体系的气液平衡     

Thermodynamics of liquid mixtures containing a very strongly polar compound: Part 6. DISQUAC characterization of N,N-dialkylamides

Systems of N,N di(n-alkylamides) (hereafter, N,N-dialkylamides) with alkane, benzene, toluene, 1-alkanol or 1-alkyne have been investigated in the framework of the DISQUAC model. The corresponding interaction parameters are reported. They change regularly with the molecular structure of the mixture components. This variation is similar to those encountered when treating other systems in terms of DISQUAC. The model describes consistently a whole set of thermodynamic properties: liquid–liquid equilibria (LLE), vapor–liquid equilibria (VLE), solid–liquid equilibria (SLE), molar excess Gibbs energies (G^E), molar excess enthalpies (H^E), molar excess heat capacities at constant pressure (C_P^E), partial molar excess properties at infinite dilution, enthalpies and heat capacities. The model also provides good results for the Kirkwood–Buff integrals and for the linear coefficients of preferential solvation. For ternary systems, DISQUAC predictions on VLE and H^E, obtained using binary parameters only, are in good agreement with the experimental data. A short comparison between DISQUAC and Dortmund UNIFAC results is shown. DISQUAC improves UNIFAC results on H^E and C_P^E, magnitudes which strongly depend on the molecular structure. The investigated mixtures behave similarly to those characterized by thermodynamic properties which arise from dipolar interactions. Association/solvation effects do not play, as a whole, an important role in the studied systems. This may explain that the ERAS model fails when representing the thermodynamic properties of dimethylformamide + 1-alkanol mixtures.     

Prediction and experimental verification of the salt effect on the vapour–liquid equilibrium of water–ethanol–2-propanol mixture

Experimental vapour–liquid equilibria of water–ethanol–2-propanol saturated with NaNO₃, NaCl, KCl and containing 0.05 mol CH₃COOK/mol total solvent compared well with those predicted by Tan–Wilson and Tan–non-random two liquid (NRTL) models for multicomponent solvent–solute mixture using a set of solvent–solvent interaction parameters obtained from the regression of the vapour–liquid equilibrium of the solvent mixture without the dissolved solute and a set of solute–solvent interaction parameters calculated from the bubble points of the individual solvent components saturated or containing the same molar ratio of solute/total solvents as the mixture. The results also showed that a solvent component i is salted-in or out of the liquid phase relatively more than solvent component j would depend on whether A_sj/A_si (Tan–Wilson model) or exp(τ_is−τ_js) (Tan–NRTL model) is less or greater than 1. This is consistent with earlier publications on the effect of dissolved solutes (electrolytes and non-electrolytes) on the binary solvents mixtures. These findings confirmed that Tan–Wilson and Tan–NRTL models for multicomponent solvent–solute system can provide an accurate and rapid screening of electrolytes and non-electrolytes for their suitability in facilitating solvent separation by salt distillation of ternary solvent mixtures simply by determining the relative ratios of the solute–solvent interaction parameters from the respective bubble points of the solvent components containing the dissolved solute. The results also suggest that this may also be extended to other multicomponent solvent mixtures.     

Revision of UNIFAC group interaction parameters of group contribution models to improve prediction results of vapor–liquid equilibria for solvent–polymer systems

The objective of this work was to improve the accuracy of group contribution models for prediction of solvent activities in polymer solutions by revising UNIFAC group interaction parameters using a wide range of vapor–liquid equilibrium (VLE) data of solvent–polymer systems. The group contribution models considered in this work were UNIFAC-FV, Entropic-FV, GK-FV and UNIFAC-ZM models. A total of 142 systems that consisted of 16 polymers and 36 solvents containing a large variety of solvent–polymer systems ranging from non-polar to polar substances were considered to optimize 46 pairs of group interaction parameters. Data considered were split up into systems containing alkane and cycloalkane, aromatic, and polar solvents. For athermal systems, the UNIFAC-FV model gave the best results. Therefore, the model was used in optimizing the group parameters. Revised group interaction parameters were found to improve the reliability of VLE predictions in solvent–polymer systems. A significant improvement of prediction results was achieved by UNIFAC-FV model from 20.0 to 10.8% absolute average deviation (AAD) in solvent activities for systems containing polar solvents and from 16.7 to 10.9% AAD for all systems. The prediction results of GK-FV and UNIFAC-ZM models were also improved.     

Towards predictive association theories

Association equations of state like SAFT, CPA and NRHB have been previously applied to many complex mixtures. In this work we focus on two of these models, the CPA and the NRHB equations of state and the emphasis is on the analysis of their predictive capabilities for a wide range of applications. We use the term predictive in two situations: (i) with no use of binary interaction parameters, and (ii) multicomponent calculations using binary interaction parameters based solely on binary data. It is shown that the CPA equation of state can satisfactorily predict CO₂-water-glycols-alkanes VLE and water-MEG-aliphatic hydrocarbons LLE using interaction parameters obtained from the binary data alone. Moreover, it is demonstrated that the NRHB equation of state is a versatile tool which can be employed equally well to mixtures with pharmaceuticals and solvents, including mixed solvents, as well as phase equilibria in mixtures containing glycols. The importance of considering the solvation of CO₂-water (in CPA) when the model is applied to multicomponent mixtures as well as of the multiple associations in heavy glycol-water mixtures (in NRHB) is investigated.