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.     

Phase behavior of the system hyperbranched polyglycerol + methanol + carbon dioxide

Phase equilibrium data have been measured for the ternary system hyperbranched polyglycerol + methanol + carbon dioxide at temperatures of 313–450 K and pressures up to 13.5 MPa. Phase changes were determined according to a synthetic method using the Cailletet setup. At elevated temperatures the system shows a liquid–liquid–vapor region with lower solution temperatures. Besides the vapor–liquid and liquid–liquid equilibria, the vapor–liquid to vapor–liquid–liquid and vapor–liquid–liquid to liquid–liquid phase boundaries are reported at different polymer molar masses and can serve as test sets for thermodynamic models. A distinct influence of the polymer molar mass on the vapor–liquid equilibrium can be noticed and indicates the existence of structural effects due to the polymer branching. Modeling the systems with the PCP-SAFT equation of state confirms these findings.     

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.     

An analytical perturbed equation of state for hard chain fluids: Application to n-alkanes and n-perfluoroalkanes

A completely analytical equation of state for pure hard chain fluids, derived on the basis of perturbation theory and reported in our previous work, is applied for the calculation of pVT properties and the prediction of vapour–liquid equilibria of n-alkanes and n-perfluoroalkanes. The molecules are treated as a chain formed from freely joined spheres which interact via an extended site-site square-well potential. The molecular parameters of compounds are obtained from the experimental compressibility factor data above the critical temperature. These parameters are capable of relatively satisfactory prediction of the vapour–liquid equilibrium coexistence curves of compounds. Linear relationships have been found between the potential parameters of fluids and their molecular weight, which make it possible to predict the pVT data and vapour–liquid phase equilibria of heavier compounds.     

A new cubic equation of state for prediction of VLE of polymer solutions

A new cubic equation of state (CEOS) is proposed based on temperature–pressure superposition principle. A generic CEOS form, with the Peng–Robinson parameters, is used and a temperature-dependent attractive term a(T)$a(T)$ is developed, allowing an easy calculation of thermodynamic properties and vapor–liquid equilibrium. The new equation is applied to pure polymer and polymer solutions and its results are compared with those of two others equations of state. For polymer solutions, two mixing rules without binary interaction parameters were used. The vapor–liquid equilibrium (VLE) predictions showed good agreement with experimental data as well as pressure–volume–temperature (PVT) behavior of polymer liquids, attesting the appropriate form of the new equation proposed.     

A modification to the Peng–Robinson-fitted equation of state for pure substances

In this work we present two modifications to the Peng–Robinson-Fitted equation of state where pure component parameters are regressed to vapor pressure and saturated liquid density data. The first modification (PR-f-mod) is a method that enhances the equation of state pure component property predictions through simple temperature dependent pure component parameters. In the second modification (PR-f-prop) we propose a temperature dependency for co-volume b in the repulsive parameter of the EoS, and revise the temperature function in the attractive term. The agreement with experimental data for 72 pure substances, including highly polar compounds, is remarkably good. We obtain average absolute deviations in saturated liquid density of less than 1% for all substances studied.     

Linear models for prediction of ibuprofen crystal morphology based on hydrogen bonding propensities

Solvents have a significant impact on the final crystal form of organic solids during solution crystallization. The use of polarity scales such as Hildebrand solubility parameter and dielectric constant for solvent selection often proves too generalized and do not provide enough insights into the solvent–solute intermolecular interactions directly affecting crystal growth and morphology. This paper addresses the challenging task of selecting an appropriate single component solvent property index that most accurately and sufficiently characterizes crystal morphology. Cooling crystallization experiments were carried out in a wide range of solvents using ibuprofen as a model pharmaceutical compound. Subsequently, optical microscope images were used for quantitative characterization of morphology. Linear models that correlate ibuprofen crystal morphology with pure solvent properties were developed. Our results show that, in general, there is a negative linear correlation between crystal aspect ratio (morphology) and a given solvent index. Some correlations revealed significant deviations which were explained with the help of infrared spectroscopic measurements. The “acceptance number” was identified as an index that significantly captures the ibuprofen–solvent hydrogen bonding intermolecular interactions. Predictions, using model based on acceptance number, were found to compare very well with experimentally determined aspect ratio data from the open literature. Finally, based on insights gained from this work, a flowchart which serves as a useful solvent selection guideline for crystallization of ibuprofen is proposed.     

A noncontinuum model of van der Waals interactions for describing the physicochemical properties of pure molecular liquids

A noncontinuum model based on the use of such molecular characteristics as molecular refraction, dipole moment, and molar volume is suggested for quantitatively describing the physicochemical properties (surface tension, enthalpy of vaporization, boiling temperature, viscosity, etc.) of pure molecular liquids. The ratio between the coefficients of correlation equations relating electrostatic and dispersion contributions to all the properties analyzed was found to be invariant.     

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.     

Mixing rules for van-der-Waals type equation of state based on thermodynamic perturbation theory

A concept based on the thermodynamic perturbation theory for a `simple fluid' has been applied to the attractive term of a van-der-Waals type equation of state (EOS) to derive a simple mixing rule for the a parameter. The new mixing rule is a small correction to the original one-fluid approximation to account for the influence of particles of j-type on the correlation function of ii-type in a mixture consisting of particles of i and j types. The importance of the correction has been shown by comparison of the calculated results for binary mixtures of Lennard–Jones fluids with the data obtained by numerical method (Monte-Carlo simulation). The new mixing rules can be considered as a flexible generalization of the conventional mixing rules and can be reduced to the original v-d-W mixing rules by defaulting the extra binary parameters to zero. In this way the binary parameters already available in the literature for many systems can be used without any additional regression work. Extension of the new mixing rules to a multicomponent system do not suffer from `Michelsen–Kistenmacher syndrome' and provide the correct limit for the composition dependence of second virial coefficients. Their applicability has been illustrated by various examples of vapor–liquid and liquid–liquid equilibria using a modified Patel–Teja EOS. The new mixing rules can be applied to any EOS of van-der-Waals type, i.e., EOS containing two terms which reflect the contributions of repulsive and attractive intermolecular forces.     

Estimation of pure component properties. Part 4: Estimation of the saturated liquid viscosity of non-electrolyte organic compounds via group contributions and group interactions

A new group contribution method for the prediction of pure component saturated liquid viscosity has been developed. The method is an extension of the pure component property estimation techniques that we have developed for normal boiling points, critical property data, and vapour pressures. Predictions can be made from simply having knowledge of the molecular structure of the compound. In addition, the structural group definitions for the method are identical to those proposed for estimation of saturated vapour pressures. Structural groups were defined in a standardized form and fragmentation of the molecular structures was performed by an automatic procedure to eliminate any arbitrary assumptions. The new method is based on liquid viscosity data for more than 1600 components. Results of the new method are compared to several other estimation methods published in literature and are found to be significantly better. A relative mean deviation in viscosity of 15.3% was observed for 813 components (12,139 data points). By comparison, the Van Velzen method, the best literature method in our benchmarking exercise produced a relative mean deviation of 92.8% for 670 components (11,115 data points). Estimation results at the normal boiling temperature were also tested against an empirical rule for more than 4000 components. The range of the method is usually from the triple or melting point to a reduced temperature of 0.75–0.8. Larger than average deviations were observed in the case of molecules with higher rotational symmetry, but no specific correction of this effect was included in this method.     

A new development of equation of state for square-well chain-like molecules with variable width 1.1 ≤ λ ≤ 3

A new equation of state (EOS) for square-well chain molecules and their mixtures with variable well-width range (SWCF-VR-EOS) has been developed based on the sticky-point model for chemical association. Two important modifications have been made. Firstly, a new dispersion contribution to the Helmholtz function of monomers due to square-well potential with variable well-width range of 1.1 ≤ λ ≤ 3 was established by combining the second-order perturbation theory and Chiew's PY2 approximation of the integral equation. Secondly, the contribution of chain formation to the Helmholtz function is divided into two parts: One is from the hard sphere, and the other is from the effect of square-well potential described via the nearest-neighbor and next-to-nearest-neighbor residual cavity correlation functions (CCFs). The predicted compressibility factors and vapor–liquid coexistence curves for square-well fluids as well as for their mixtures are in good agreement with simulations. The new EOS has been applied to real non-associating fluids and the corresponding mixtures by adopting one-fluid mixing rule. The pVT and vapor–liquid equilibria (VLE) can be correlated satisfactorily. The model parameters for some homologous compounds are found to be linear with the molar mass indicating that the pVT and VLE of those homologous compounds can be predicted even if no accurate data are available.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

Evaluation of co-volume mixing rules for bitumen liquid density and bubble pressure estimation

The Peng–Robinson cubic equation of state (CEOS) is widely used to predict thermodynamic properties of pure fluids and mixtures. The usual implementation of this CEOS requires critical properties of each pure component and combining rules for mixtures. Determining critical properties for components of heavy asymmetric mixtures such as bitumen is a challenge due to thermolysis at elevated temperatures. Group contribution (GC) methods were applied for the determination of critical properties of molecular representations developed by Sheremata for Athabasca vacuum tower bottoms (VTB). In contrast to other GC methods evaluated, the Marrero–Gani GC method yielded estimated critical properties with realistic, non-negative values, followed more consistent trends with molar mass and yielded normal boiling points consistent with high temperature simulated distillation data. Application of classical mixing rules to a heavy asymmetric mixture such as bitumen yields saturated liquid density and bubble pressure estimates in qualitative agreement with experimental data. However the errors are too large for engineering calculations. In this work, new composite mixing rules for computing co-volumes of asymmetric mixtures are developed and evaluated. For example, composite mixing rules give improved bubble point predictions for the binary mixture ethane + n-tetratetracontane. For VTB and VTB + decane mixtures the new composite mixing rules showed encouraging results in predicting bubble point pressures and liquid phase densities.     

An equation of state for hydrogen fluoride

Using a similar approach as Lencka and Anderko [AIChE J. 39 (1993) 533], we developed an equation of state for hydrogen fluoride (HF), which can correlate the vapor pressure, the saturated liquid and vapor densities of it from the triple point to critical point with good accuracy. We used an equilibrium model to account for hydrogen bonding that assumes the formation of dimer, hexamer, and octamer species as suggested by Schotte [Ind. Eng. Chem. Process Des. Dev. 19 (1980) 432]. The physical and chemical parameters are obtained directly from the regression of pure component properties by applying the critical constraints to the equation of state for hydrogen fluoride. This equation of state together with the Wong–Sandler mixing rule as well as the van der Waals one-fluid mixing rule are used to correlate the phase equilibria of binary hydrogen fluoride mixtures with HCl, HCFC-124, HFC-134a, HFC-152a, HCFC-22, and HFC-32. For these systems, new equation of state with the Wong–Sandler mixing rule gives good results.     

Solubility calculation of pharmaceutical compounds – A priori parameter estimation using quantum-chemistry

Pure-component electrostatic properties for pharmaceutical compounds and intermediates (xanthene, ibuprofen, aspirin, p-hydroxyphenylacetic acid, p-toluic acid and o-anisic acid) were obtained by quantum-chemical methods. Afterwards, these properties were used for the a priori determination of the pure-component parameters for the Perturbed-Chain Polar Statistical-Associating Fluid Theory (PCP-SAFT). These parameters were applied to perform solubility calculations for binary solute–solvent mixtures. In these calculations the only parameter fitted was the binary parameter. The results show a good agreement of the modeled solubility and experimental data for the considered solutes in non-polar and polar solvents. Finally, the application of different combination rules to also predict the binary interaction parameter in the mixture was investigated.