“Vapor-liquid” equilibrium measurements and modeling for the cyclohexane + n-hexanoic acid binary system

To simulate cyclohexane to cyclohexanol oxidation reactors, the acquisition and modeling of vapor-liquid equilibria of the key components, under the process conditions, are essential. n-Hexanoic acid is a co-product of the reaction. Vapor-liquid equilibrium data are reported for the cyclohexane + n-hexanoic acid binary system at four temperatures: 413, 423, 464 and 484 K. All measurements have been carried out using an apparatus based on the “static-analytic” method, with two ROLSI™ pneumatic capillary samplers. The generated data are successfully correlated using two equations of state, the Peng-Robinson (PR) and the Perturbed Chain Statistical Association Fluid Theory (PC-SAFT). Both models are capable of representing the experimental data, but the PC-SAFT EoS uses less binary interaction parameters.     

Use of monomer fraction data in the parametrization of association theories

Association theories such as the CPA (cubic-plus-association), NRHB (non-random hydrogen bonding) equations of state and the various variants of SAFT (statistical associating fluid theory) have been extensively applied to phase equilibrium calculations. Such models can also be used for estimating the monomer fraction of hydrogen bonding compounds and their mixtures. Monomer fraction data are obtained from spectroscopic measurements and they are available for a few compounds such as pure water and alcohols as well as for some alcohol–alkane and similar mixtures. These data are useful for an understanding of the capabilities and limitations of association models. The purpose of this work is two-fold: (i) to compare the performance of three models, CPA, NRHB and sPC-SAFT, in predicting the monomer fraction of water, alcohols and mixtures of alcohol-inert compounds and (ii) to investigate whether “improved” model parameters can be obtained if monomer fraction data are included in the parameter estimation together with vapor pressures and liquid densities. The expression “improved” implies parameters which can represent several pure compound properties as well as monomer fraction data for pure compounds and mixtures. The accuracy of experimental monomer fraction data is discussed, as well as the role of monomer fraction data in clarifying which association scheme should be used in these equations of state. The results reveal that the investigated association models (CPA, sPC-SAFT and NRHB) can predict, at least qualitatively correct, monomer fractions of associating compounds and mixtures. Only, small differences are observed between the models. In addition, it has been shown that, using a suitable association scheme, a single set of parameters can describe satisfactorily vapor pressures, liquid densities and monomer fractions of water and alcohols. The 4C scheme is the best choice for water, while for methanol there is small difference between the 2B and 3B association schemes.     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

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.     

Modeling aqueous electrolyte solutions: Part 1. Fully dissociated electrolytes

Liquid densities (pvT), vapor pressures (VLE), and mean ionic activity coefficients (MIAC) at 25 °C of 115 single-salt electrolyte solutions containing univalent up to trivalent ions are modeled with the ePC-SAFT equation of state proposed by Cameretti et al. [L.F. Cameretti, G. Sadowski, J.M. Mollerup, Ind. Eng. Chem. Res. 44 (2005) 3355–3362; ibid., 8944]. For each ion, only two model parameters were adjusted to experimental density and MIAC data. Without using any additional binary parameters, ePC-SAFT is able to reproduce experimental data of the respective salt solutions up to high electrolyte molalities. Moreover, it is even able to describe the reversed MIAC series for alkali hydroxides and fluorides.     

Vapor–liquid equilibrium measurements and modeling of the n-butane + ethanol system from 323 to 423 K

Vapor–liquid equilibrium (VLE) data are presented for the n-butane + ethanol system in the temperature range from 323 to 423 K. Measurements were performed using a “static-analytic” apparatus, equipped with two electromagnetic ROLSI™ capillary samplers, and thermally regulated via an air bath. This work presents vapor compositions which have not been explicitly measured previously. The modeling of the data was performed using two models: the Peng–Robinson equation of state with the Wong and Sandler mixing rule and NRTL excess function (PR/WS/NRTL); and the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state. To assess the effect of dipole–dipole interactions present, a dipolar contribution developed by Jog and Chapman (1999) [20] was tested with the second model. Temperature dependent binary interaction parameters have been adjusted to the new data. The PR/WS/NRTL equation of state shows good correlation with the results, while the PC-SAFT is slightly less accurate.     

Equation of state for aqueous electrolyte systems based on the semirestricted non-primitive mean spherical approximation

The semirestricted non-primitive mean spherical approximation (npmsa) is used in combination with the PC-SAFT equation of state to model completely dissociating aqueous alkali halide systems. The salts are described using ion-specific parameters from tables and correlations. Upon analyzing aqueous electrolyte systems at infinite dilution of the salt it was concluded that for the arithmetic mean ion diameter of anion and cation, the semirestricted npmsa contribution gives no reliable results. Therefore, this parameter is adjusted in this work. The model was applied to aqueous alkali halide systems up to the solubility limit at T = 298.15 K. Mean ionic activity coefficients and osmotic coefficients were correlated with good results. The model was subsequently applied to temperatures up to T = 373.15 K and compared to liquid densities and to system pressures up to the solubility limit of the salts in water. The agreement between experimental data and the proposed equation of state is satisfactory for the liquid densities and excellent in case of the system pressures.     

Vapor pressure measurements in the range 10 Pa to 1 Pa of four pentaerythritol esters: Density and vapor–liquid equilibria modeling of ester lubricants

Vapor pressures of four pure pentaerythritol esters, PE, pentaerythritol tetrapentanoate, pentaerythritol tetraheptanoate, pentaerythritol tetranonanoate and pentaerythritol tetra 2-ethylhexanoate were measured between 334 and 476 K in a recently developed gas saturation apparatus. The experimental vapor pressure values for the four polyolesters range from 5.6 × 10⁻⁵ Pa to 0.94 Pa. These data together with density values were used to determined SAFT and PC-SAFT characteristic parameters. The linearity of molecular parameters for both models with the molecular weight permits to interpolate and extrapolate these parameters for pentaerythritol ester with linear chains. For pentaerythritol esters with ethyl-alkanoic chains, the parameters of SAFT and PC-SAFT have been estimated assuming that the slope of these straight lines is the same for PEs with linear chains that for PE with branched chains. This procedure was used to predict density of commercial POEs, estimating the molecular weight when it is not available from the viscosity at 313.15 K. PC-SAFT gives better performances than SAFT to predict density data for these four compounds at high pressures and for other PEs at atmospheric pressure. Furthermore, characteristic parameters for Soave-Redlich-Kwong and Peng Robinson EoSs were also estimated from the experimental vapor pressures and literature density values.     

Modeling phase equilibria of alkanols with the simplified PC-SAFT equation of state and generalized pure compound parameters

The simplified PC-SAFT equation of state has been applied to liquid–liquid, vapor–liquid and solid–liquid equilibria for mixtures containing 1- or 2-alkanols with alkanes, aromatic hydrocarbons, CO₂ and water. For the alkanols we use generalized pure compound parameters. This means that two of the physical pure compound parameters, m (segment number) and σ (segment diameter), are obtained from linear extrapolations, since m and mσ³, increase linearly with respect to the molar mass, and moreover, the two association parameters (association energy and association volume) were assumed to be constant for all alkanols. Only the dispersion energy is fitted to experimental data. Thus it is possible to estimate parameters for several 1- and 2-alkanols. The final aim is to develop a group contribution approach for PC-SAFT which is suitable for complex compounds, considering that the motivation of this project is to obtain a thermodynamic model which can be used in the development of sophisticated products such as pharmaceuticals, polymers, detergents or food ingredients. One of the severe limitations in applying SAFT-type equations of state to these compounds is that the procedure for obtaining the pure compound parameters is usually based on fitting to saturated vapor pressure and liquid density data over an extended temperature range. However, such data are rarely available for complex compounds. To verify the new pure compound parameters, comparisons to ordinary optimized alkanol parameters, where all five pure compound parameters were fitted to experimental liquid density and vapor pressure data, were made. The results show that the new generalized alkanol parameters from this work perform at least as well as other alkanol parameter sets.