Phase Equilibria Of Mixtures Research Articles

Low pressure vapor–liquid equilibrium in ethanol + congener mixtures using the Wong–Sandler mixing rule

Phase equilibrium in binary ethanol mixtures found in alcoholic beverage production has been analyzed using a cubic equation of state (EoS) and suitable mixing and combining rules. The main objective of the study is the accurate modeling of the congener concentration in the vapor phase (substances different from ethanol), considered to be an important enological parameter in the alcohol industry. The Peng–Robinson (PR) equation of state has been used and the Wong–Sandler (WS) mixing rules, that include a model for the excess Gibbs free energy, have been incorporated into the equation of state constants. In the Wong–Sandler mixing rules the van Laar (VL) model for the excess Gibbs energy has been used. This combination of equations of state, mixing rules and combining rules are commonly applied to high pressure phase equilibrium and have not yet been treated in a systematic way to complex low pressure ethanol mixtures as done in this work. Nine binary ethanol + congener mixtures have been considered for analysis. Comparison with available literature data is done and the accuracy of the calculations is discussed, concluding that the model used is accurate enough for engineering applications.

Fluid phase stability and equilibrium calculations in binary mixtures: Part I: Theoretical development for non-azeotropic mixtures

A framework is proposed for the solution of fluid phase equilibrium ( P– T flash) for binary mixtures described by equations of state of general form. The framework is based on decomposing the phase equilibrium problem into sub-problems with more convenient and tractable mathematical and numerical properties. Systematic procedures are used to identify the mapping of the problem in the density and composition space, referred to as the density–composition pattern, at specified temperature and pressure. A series of stability tests is then carried out to explore the existence or non-existence of phases. Once the existence of a phase has been determined, the limits of stability and physical bounds on the problem are used to define the search area for that phase in the density–composition pattern. Finally, all available information from this detailed analysis is used for the solution of phase equilibrium between the phases identified in order to find the stable state at the specified conditions. The features of the proposed approach are exposed in detail through an algorithm for the fluid phase equilibria of the augmented van der Waals equation of state applied to non-azeotropic mixtures.

Phase equilibria for mixtures containing nonionic surfactant systems: Modeling and experiments

Surfactants are important materials with numerous applications in the cosmetic, pharmaceutical, and food industries due to inter-associating and intra-associating bond. We present a lattice fluid equation-of-state that combines the quasi-chemical nonrandom lattice fluid model with Veytsman statistics for (intra + inter) molecular association to calculate phase behavior for mixtures containing nonionic surfactants. We also measured binary (vapor + liquid) equilibrium data for {2-butoxyethanol (C 4E 1) + n-hexane} and {2-butoxyethanol (C 4E 1) + n-heptane} systems at temperatures ranging from (303.15 to 323.15) K. A static apparatus was used in this study. The presented equation-of-state correlated well with the measured and published data for mixtures containing nonionic surfactant systems.

Bioethanol Production Optimization: A Thermodynamic Analysis

In this work, the phase equilibrium of binary mixtures for bioethanol production by continuous extractive process was studied. The process is composed of four interlinked units: fermentor, centrifuge, cell treatment unit, and flash vessel (ethanol-congener separation unit). A proposal for modeling the vapor-liquid equilibrium in binary mixtures found in the flash vessel has been considered. This approach uses the Predictive Soave-Redlich-Kwong equation of state, with original and modified molecular parameters. The congeners considered were acetic acid, acetaldehyde, furfural, methanol, and 1-pentanol. The results show that the introduction of new molecular parameters r and q in the UNIFAC model gives more accurate predictions for the concentration of the congener in the gas phase for binary and ternary systems.

Phase equilibrium of liquid mixtures: Experimental and modeled data using statistical associating fluid theory for potential of variable range approach

A study of the phase equilibrium (experimental and modeled) of mixtures formed by a cyclic ether and haloalkanes has been derived. Experimental data for the isothermal vapor liquid equilibrium of mixtures formed by tetrahydrofuran and tetrahydropyran and isomeric chlorobutanes at temperatures of 298.15, 313.15, and 328.15 K are presented. Experimental results have been discussed in terms of both molecular characteristics of pure compounds and potential intermolecular interaction between them using thermodynamic information of the mixtures obtained earlier. The statistical associating fluid theory for potential of variable range (SAFT-VR) approach together with standard combining rules without adjustable parameters has been used to model the phase equilibrium. Good agreement between experiment and the prediction is found with such a model. Mean absolute deviations for pressures are of the order of 1 kPa, while less than 0.013 mole fraction for vapor phase compositions. In order to improve the results obtained, a new modeling has been carried out by introducing a unique transferable parameter k(ij), which modifies the strength of the dispersion interaction between unlike components in the mixtures, and is valid for all the studied mixtures being not temperature or pressure dependent. This parameter together with the SAFT-VR approach provides a description of the vapor-liquid equilibrium of the mixtures that is in excellent agreement with the experimental data for most cases. The absolute deviations are of the order of 0.005 mole fraction for vapor phase compositions and less than 0.3 kPa for pressure, excepting for mixtures containing 2-chloro-2-methylpropane which deviations for pressure are larger. Results obtained in this work in the modeling of the phase equilibrium with the SAFT-VR equation of state have been compared to the ones obtained in a previous study when the approach was used to model similar mixtures with clear differences in the thermodynamic behavior. We show how the SAFT-VR approach is capable of differentiating the molecular features of a relatively wide set of different mixtures.

Thermodynamic modeling of the stability and melting properties of sodium borates relevant to black liquor combustion and gasification

Abstract The use of borates as an autocausticizing agent in kraft recovery boilers of pulp mills is an interesting concept for decreasing the lime consumption at pulp mills. The main autocausticizing reaction is between NaBO2and Na2CO3 forming Na3BO3 and CO2 at high temperatures in a liquid phase in the recovery boiler. The thermodynamic and phase equilibrium data of the Na2CO3 – NaBO2 – Na3BO3 system were evaluated and optimized. The liquid phase was modeled with the modified quasichemical model. The thermodynamic database obtained can be used to calculate the phase equilibrium and thermodynamic properties of multicomponent sodium salt mixtures of importance for the borate autocausticizing concept. The thermodynamic database is a part of an extensive thermodynamic database for alkali salt mixtures of importance for black liquor combustion in the pulp and paper industry.

Revision and summary of the group contribution equation of state parameter table: Application to edible oil constituents

The Group Contribution Equation of State (GC-EoS) was developed by Skjold–Jorgensen in 1984 for predicting phase equilibria of non-polar and polar mixtures. Since the model development, the GC-EoS group parameter table has been revised and extended, and the predictive capability of the model has been widely spread. Furthermore, the model has been successfully applied in the phase equilibria modeling of separation processes, particularly those related with supercritical fluids, and has also been used as a predictive tool for process simulation and optimization. This work is a comprehensive review of the present status of the GC-EoS parameter table, including revisions and extensions carried out by different authors since the model development until present. For a better understanding, available parameters are reported and organized in adequate tables. Additionally, the parameters for the carboxylic acid (COOH) group, which allow the modeling of an important family of compounds, i.e. carboxylic acids, are included in the present work. The application of the model to represent phase equilibria in mixtures of carbon dioxide and the main constituents of edible oils and derived products, demonstrate the capability of the model to be used in supercritical fluid oil-process simulation and optimization.

Modeling of phase equilibrium of binary mixtures composed by polystyrene and chlorofluorocarbons, hydrochlorofluorocarbons, hydrofluorocarbons and supercritical fluids using cubic and non-cubic equations of state

The understanding of the polymer + solvent interactions is of fundamental importance in the development of new products and processes in several important industrial sectors, such as special paints, cosmetics, packing, manufacture of polymeric membranes, etc. Although the nature of these physical interactions is well known, the thermodynamic modeling of polymer + solvent systems in industrial applications presents difficulties, mainly due to the necessity to characterize not only the polymeric phase, in terms of properties that are easily measurable, but also the interaction of the polymer with the other components of low molar mass, through conveniently chosen parameters. In this work, the perturbed chain-statistical associating fluid theory (PC-SAFT) and Sanchez–Lacombe (SL) equations of state (EoS) are used in order to model the gas solubilities of binary systems composed by polystyrene and chlorofluorocarbons, hydrochlorofluorocarbons hydrofluorocarbons and supercritical fluids, which experimental data were obtained from the literature. The results were compared with those obtained by the traditional Peng–Robinson (PR) EoS. In each thermodynamic model, a one fluid-type van der Waals (vDW) mixing rule with conventional combination rules and a temperature-dependent binary interaction parameter were used. Solubilities correlated by the PC-SAFT EoS are in good agreement with the experimental data when compared with those obtained with the SL and PR EoS.

Phase Equilibrium of Binary Mixtures of Cyclic Ethers + Chlorobutane Isomers: Experimental Measurements and SAFT-VR Modeling

The phase equilibria (experimental and modeled) of eight binary mixtures each formed by a cyclic ether (1,3-dioxolane or 1,4-dioxane) and a chlorobutane isomer (1-chlorobutane, 2-chlorobutane, 1-chloro-2-methylpropane, or 2-chloro-2-methylpropane) are presented. New experimental vapor-liquid equilibrium data at isothermal conditions (298.15, 313.15, and 328.15 K) has been obtained, and the statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to model the mixtures. The results are discussed in terms of both the molecular characteristics of the pure compounds and the unlike intermolecular interactions present in the mixtures. The SAFT-VR approach is first used together with standard combining rules without adjustable parameters in order to predict the phase behavior at isothermal conditions. Good agreement between experiment and the prediction is found with such a model. Mean absolute deviations for pressures lie between 1 and 3 kPa, while for vapor phase compositions are less than 0.03 in mole fraction. However, a better agreement, can be obtained by introducing one adjustable parameter kij, which modifies the strength of the dispersion interaction between unlike components in the mixtures. This parameter is adjusted so as to model the phase equilibrium of the whole family of mixtures studied here at isothermal and isobaric conditions. We find that a unique unlike parameter kij is valid for all the studied mixtures and it is not temperature or pressure dependent. This unique transferable parameter together with the SAFT-VR approach provide a description of the vapor-liquid equilibrium of the mixtures that is in excellent agreement with the experimental data. In this case, the absolute deviations are of the order of 0.001 in mole fraction for vapor-phase compositions and less than 1 kPa for pressure.

Modeling vapor–liquid equilibria of ethanol + 1,1,1,2,3,3,3-heptafluoropropane binary mixtures using PC-SAFT

One objective of the Third Industrial Fluid-Properties Simulation Challenge was the extrapolation of mixture phase equilibrium information obtained from one isotherm to other temperatures. In this work, we present modeling results for the vapor–liquid equilibrium of the ethanol/1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) mixture obtained with the PC-SAFT equation of state. The required pure-component parameters were determined by fitting pure-component vapor pressures and liquid density data. To get a quantitative description of the mixture, a temperature-independent binary interaction parameter was adjusted to experimental bubble-point data at 283.17 K. Using these parameters, bubble-point pressures at T = 343.13 K were predicted for different concentrations.

A multi-fluid nonrandom associating lattice fluid model

A lattice fluid theory valid from pure fluids to multi-component mixtures of molecules having any number of associating donor and acceptor groups formulated. Under the fundamental assumption that the intermolecular forces are divided into physical and chemical forces, the Veytsman statistics for associating contribution was combined with the multi-fluid nonrandom lattice fluid (MLF) equation of state developed recently by the present authors. The physical contribution is characterized by temperature independent molecular parameters representing close packed volumes of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a binary mixture. The chemical part is represented by internal energy and entropy of associating system. The resulting multi-fluid nonrandom associating lattice fluid (MALF) equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibrium of mixtures. The results for alkane–alcohol and alcohol–alcohol mixtures were found satisfactory for most systems when compared with the MLF and the statistical associating fluid theory (SAFT) model.

Influence of high pressure on solubility of ionic liquids: experimental data and correlation

The solid–liquid phase equilibrium (SLE) in binary mixtures that contain a room-temperature ionic liquid, IL, and an organic solvent: {1-ethyl-3-methylimidazolium tosylate, [EMIM][TOS] (1) + cyclohexane, or benzene (2)} and {1,3-dimethylimidazolium methylsulfate, [MMIM][CH3SO4] (1) + hexan-1-ol (2)} have been measured under very high pressures up to about 900 MPa at the temperature range from T = 328 to 363 K. The termostatted apparatus for the measurements of transition pressures from the liquid to the solid state was used. The pressure–temperature–composition relation of the high pressure solid–liquid phase equilibria polynomial based on the Yang model was satisfactorily used. The freezing and melting temperatures at a constant composition increase monotonously with pressure. The high pressure experimental results obtained at isothermal conditions (p–x) were interpolated to well known T–x diagrams. Additionally, the SLE of binary systems {[EMIM][TOS] (1) + cyclohexane, or benzene (2)} at normal pressure have been measured by a dynamic method from 270 K to the melting point of the IL. Experimental solubility results are compared with values calculated by means of the non-random, two-liquid equation (NRTL) utilizing parameters derived from SLE and liquid–liquid equilibria (LLE) results. The experimental results at high pressures were compared for every system to these at normal pressure. The paper includes thermophysical basic characterization of pure ionic liquids obtained via differential scanning calorimetry (DSC), temperatures and enthalpies of melting. The influence of the interaction between the IL and solvent on the solubility at 0.1 MPa and high pressure up to 900 MPa was discussed.

A quasi-chemical nonrandom lattice fluid model for phase equilibria of associating systems

The contribution from Veytsman statistics for associating is combined with the quasi-chemical nonrandom lattice fluid (QLF) equation of state developed by the present authors. The physical contribution is characterized by temperature independent molecular parameters, representing close packed volume of a mer, segment numbers and energy parameters of a pure fluid, and a binary interaction parameter for a mixture. The chemical part is represented by the internal energy and entropy of the associating system. The resulting quasi-chemical nonrandom associating lattice fluid equation of state was applied to describe thermodynamic properties of pure fluids and phase equilibria of mixtures. The absolute chemical potentials which are derived from the canonical partition function are presented by using the fundament thermodynamic relations to consistently calculate phase equilibrium properties. The results for alkane–alkanol and alcohol–alkanol mixtures were found satisfactory for most systems when compared with the quasi-chemical nonrandom lattice fluid model and the statistical associating fluid theory model.

Liquid−Liquid Equilibrium in Mixtures of the Ionic Liquid 1-n-Butyl-3-methylimidazolium Hexafluorophosphate and an Alkanol

The liquid−liquid phase equilibrium of mixtures of the room temperature ionic liquid 1-n-butyl-3-methylimidazolium hexafluorophosphate, [bmim][PF6], and three single alkanols (ethanol, 1-propanol, and 1-butanol) was investigated over the entire composition range at ambient pressure. The experiments were conducted from 262 K to the vicinity of the critical solution temperature of the binary mixture (at maximum 362 K) by two different methods, namely, synthetic cloud-point measurements and analytical UV spectroscopy. The cloud-point method was mainly applied for the [bmim][PF6]-rich liquid, whereas UV spectroscopy was used to determine the very small concentrations of [bmim][PF6] in the alkanols, since under these conditions the cloud-point method is no longer applicable. All three systems show an upper critical solution temperature. With increasing chain length of the alcohol, that temperature rises and simultaneously the biphasic region becomes larger. Inspired by recent publications, the liquid−liquid equilibrium of these three binary systems was predicted by applying the COSMO-RS method. Calculations resulted in predictions of a miscibility gap, but the calculated miscibility gap strongly differs from the experimental results. A far better representation of the experimental data was accomplished via a UNIQUAC-based correlation.

Incipient hydrate phase equilibrium for gas mixtures containing hydrogen, carbon dioxide and propane

Incipient hydrate, aqueous liquid, vapor equilibrium conditions of hydrates formed from mixtures containing carbon dioxide and hydrogen or carbon dioxide, hydrogen and propane were determined. The gas phase concentrations at equilibrium were also measured. The presence of carbon dioxide lowers the hydrate formation pressure substantially compared to that for pure hydrogen. Addition of propane as a third substance reduces the pressure even further. An analysis of the pressure–temperature conditions based on the Clapeyron equation was also carried out to infer the structures formed. In both cases it is believed that hydrogen participates in the hydrate phase.

New developments in differential ebulliometry: Experimental and theoretical

A new ebulliometer has been developed in which superheat is discharged from the vapour–liquid mixture issuing from the Cottrell pump before it impinges on an otherwise vacuum-insulated temperature sensor. The convoluted chamber through which the mixture passes should also assist the attainment of phase equilibrium in binary mixtures. Measurements for several solvents showed unusually broad plateau regions with slopes much smaller than those reported by other researchers. Vapour pressures for several solvents were in close agreement with literature values. For the measurement of limiting activity coefficients, a new experimentally very simple procedure was developed for finding the difficult-to-determine evaporation ratio, ϕ, based on the steady-state macroscopic energy balance. Results are presented for two pure solvents, viz. ethylacetate and cyclohexane. Exact equations, based on material balances and equilibrium relationships involving ϕ then permit calculation of limiting activity coefficients. Measured temperature-composition data are presented for the ethylacetate (1)–toluene (2) and hexane (1)–ethylacetate (2) systems and the ebulliometer characterization procedure is illustrated for three binary systems. Exact differential equations for the temperature and pressure derivatives with respect to composition, and incorporating the full Gibbs-Duhem equation, are derived. These can be used to find the very useful temperature–pressure derivative (∂ T/∂ p) x 1 at any composition and also form the basis for a new thermodynamic consistency test.

( p, Vm, T) and phase equilibrium measurements for a natural gas-like mixture using an automated isochoric apparatus

We have developed an automatic apparatus for measuring phase equilibrium and ( p, V m, T) properties of gas mixtures in our laboratory. Based upon the isochoric method, the apparatus can operate at temperatures ranging from 100 K to 500 K at pressures up to 35 MPa, and yield absolute results in fully automated operation. Temperature measurements are accurate to 0.01 K and pressure measurements are accurate to 0.002 MPa. The isochoric method utilizes pressure versus temperature measurements along an isomole (near isochore) and detects phase boundaries by locating the change in the slope of the isomoles. We also have developed a strategy that allows us, when using the above isochoric method together with a second apparatus capable of isothermal density measurements, to collect derived densities that are competitive in accuracy with those of the densimeter, but with a procedure and design that is easy to automate. We present data on a natural gas-like mixture. The experimental data indicate that prediction of the dew point curve with current equations of state is unreliable.

An equation of state contribution for polar components: Polarizable dipoles

AbstractThe renormalized perturbation theory for polarizable polar fluids of Wertheim is applied in combination with a dipole contribution for non‐spherical molecules to account for the non‐additive induction interactions due to the polarization of molecules. A comparison to simulation data of pure polarizable dipolar fluids and mixtures reveals a good to excellent agreement between the renormalized perturbation theory and the simulations. The model framework is applied with the Perturbed‐Chain SAFT equation of state to model phase equilibria of mixtures containing strongly polar components. The considered values of dipole moments and of average molecular polarizabilities stem from independent sources, and there is thus no additional adjustable parameter introduced along with the polar contributions to the equation of state. It is confirmed that accounting for dipolar interactions not only reduces the value of the binary interaction parameter, but in many cases significantly improves the description of pure‐component and mixture phase equilibria. Accounting for molecular polarizability and the dipole induction effects only leads to slightly improved results compared to the case where a permanent dipole moment is considered in the calculations. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Correlations for binary phase equilibria in high-pressure carbon dioxide

The high-pressure phase equilibrium in binary mixtures of carbon dioxide and various liquids such as benzene, toluene, m-xylene, chlorobenzene, 1,2-dichlorobenzene, low molecular weight alcohols, amides and a solid, hexachlorobenzene, was modeled using the Peng–Robinson equation of state with quadratic mixing rules. Though the technique of modeling is not new, the key conclusion of the study is that the two adjustable parameters, k ij and l ij , vary linearly with the addition of functional groups. In addition, the adjustable parameters are found to be nearly independent of temperature and the same values of k ij and l ij can be used for a range of temperatures for the systems considered in the present study.

An equation‐of‐state contribution for polar components: Dipolar molecules

AbstractAccounting for dipolar interactions in a physically based equation of state (EOS) can substantially improve the modeling of phase equilibria of real mixtures. An EOS contribution for dipolar interactions of nonspherical molecules is developed based on a third‐order perturbation theory. Molecular simulation data for vapor–liquid equilibria of the two‐center Lennard–Jones (2CLJ) plus pointdipole fluid is used to determine model constants of the EOS. The resulting model is compared to simulation data of pure dipolar nonspherical molecules and their mixtures and an excellent agreement is found. The proposed dipole term is applied to real substances with the perturbed‐chain statistical associating fluid theory (PC‐SAFT) EOS and it is confirmed that accounting for dipolar interactions not only reduces the binary interaction parameter, but also improves the description of pure component and mixture phase equilibria. Literature values for the dipole moment can thereby be used and no further dipole‐related pure component parameter has to be adjusted. This constitutes an advantage over earlier approaches, where dipole‐related parameters were fitted to pure component data or to mixture data. © 2005 American Institute of Chemical Engineers AIChE J, 2006