Use of the NRTL equation for simultaneous correlation of vapour-liquid equilibria and excess enthalpy

The NRTL model has been used to correlate the data for the aqueous alkanolamine systems of (MEA+H₂O), (DEA+H₂O) and (MDEA+H₂O). The model was successfully applied to correlate simultaneously the excess enthalpy, vapour-liquid equilibria, and low temperature activity coefficients. A large database of data was collected for the investigation and it covers a wide range of composition, temperature and pressures. It was found that the form of the binary interaction parameters used by Posey (1996) with a variable non-randomness parameter gave the best results.     

New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures

Huron, M.-J. and Vidal, J., 1979. New mixing rules in simple equations of state for representing vapour-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilibria, 3: 255-271.Good correlations of vapour-liquid equilibria can be achieved by applying the same two-parameter cubic equation of state to both phases. The results primarily depend on the method used for calculating parameters and, for mixtures, on the mixing rule. True parameters are the covolume b and the energy parameter a/b. For this latter one, deviations from a linear weighting rule are closely connected to the excess free energy at infinite pressure. Thus any mixing rule gives a model for the excess free energy, or any accepted models for this property can be used as mixing rules.From the above, an empirical polynomial mixing rule is used for data smoothing and evaluation, while for practical work a local composition model is used. The mixing rule thus obtained can be reduced to the classical quadratic rule for some easily predicted values of the interaction energies. For highly polar systems, it includes three adjustable parameters. Using literature data, the new mixing rule is applied, in the low and high pressure range, to binary mixtures with one or two polar compounds, giving good data correlation and sometimes avoiding false liquid-liquid immiscibility.     

A low-parametric state equation for calculating the thermodynamic properties of substances in liquid and gaseous state

Using methods and approaches developed by the authors, a new low-parametric state equation for describing the thermal properties of normal substances is obtained that allows us to describe the thermal properties of gases, liquids, and fluids over a range of densities from the ideal gas state to the triple point, except for a critical region, with a high degree of accuracy close to that of an experiment. The caloric properties and speed of sound are calculated for argon, nitrogen, and carbon dioxide without using any caloric data except for the enthalpy of an ideal gas. It is established that the calculated values of enthalpy, heat capacity, the speed of speed of sound, etc., are in good agreement with the experimental (reliably tabulated) data.     

Calculation of vapour-liquid equilibrium of associated systems by an equation of state

A recently proposed equation of state of the van der Waals type is applied to calculate phase equilibria in hydrogen-bonding, non-electrolytic systems. Association is accounted for by treating alcohols, acids, etc., as mixtures of associated species formed by up to 14 monomers. The method involves essentially one weakly temperature-dependent adjustable parameter per binary system.The calculations cover vapour-liquid equilibrium both at low and elevated pressure in binary systems formed by an associating substance and a non-associating compound such as a hydrocarbon or halogenated hydrocarbon. An attempt has been made to include all experimental data available for these systems in the literature. A number of calculations for ternary systems as well as of liquid-liquid equilibria are included, and a limited number of solvated systems are also treated.Owing to its single adjustable parameter, the method may be used to test existing experimental data and to predict such data.     

A semi-empirical equation of state applied to vapor-liquid equilibria calculations

A five-parameter equation of state is proposed to calculate the vapor-liquid equilibria of compounds in binary and multicomponent mixtures. This equation is closely related to a previous equation of state proposed by the author, the main modification being in the entropic term where the parameter m assumes a constant value for all compounds. It is shown that the van der Waals conditions at the critical point and the Morbidelli-Carra' algorithm enable the calculation of three other constants. Rules are given to calculate the remaining constant K which pertains to the enthalpic term. The proposed method only requires knowledge of the critical constants and of the normal boiling temperature as input parameters. A wide application of the new equation to both polar and non-polar binary systems indicates the following: the proposed method is predictive for ideal or nearly ideal mixtures; the correlation of mixtures of hydrocarbons having very different molar volumes can be obtained by optimizing only the binary interaction parameter linked to the enthalpic term; the new equation also correlates well with strongly non-ideal systems which exhibit a miscibility gap; the prediction of multicomponent vapor-liquid equilibria from the binary data alone is also reliable for both polar and non-polar mixtures.     

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

A new approach has been developed for calculating the properties of mixtures based on an equation of state explicit in reduced Helmholtz energy. This approach allows for the representation of the thermodynamic properties over a wide range of fluid states and is based on highly accurate equations of state for the pure components combined at the reduced temperature and density of the mixture. The reducing parameters used for temperature and density depend on composition. For simple mixtures (those that closely follow Raoult's law), a very accurate representation of all thermodynamic properties has been achieved with relatively simple functions. For nonideal mixtures, the reducing functions for density and temperature were modified, and a departure function was added to the equation of state. Generally, the model is able to represent liquid and vapor states with uncertainties of 0.1% in density, 1% in heat capacities and 1% in bubble point pressures if experimental data of comparable uncertainties exist. Two applications of the mixture model concepts were developed independently by the authors in the United States and Germany over the same time period. These applications include the development of individual equations for each binary system and a generalization of the model which is valid for a wide variety of mixtures. The individual approaches are presented with an explanation of the similarities and differences. Although the paper focuses mainly on binary systems, some results for ternary mixtures are also presented.     

A modified clausius equation of state for calculation of multicomponent refrigerant vapor-liquid equilibria

Gow, A.S., 1993. A modified Clausius equation of state for calculation of multicomponent refrigerant vapor-liquid equilibria. Fluid Phase Equilibria, 90: 219-249.

A modified Clausius equation of state with a single temperature dependent energy-volume parameter a(T) in the attractive term was designed to describe the vapor pressure vs. temperature relationship of 39 pure refrigerant fluids including elementary cryogenic materials (e.g. He, Ar, N₂, CO₂, CH₄, etc.), chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), hydrochlorofluorocarbons (HCFCs), fluorocarbons (FCs), and various other simple cryogenic compounds. The equation developed represents the vapor-liquid coexistence dome, and the superheated vapor compressibility factor and enthalpy for pure refrigerants.

The vapor-liquid equilibrium for refrigerant mixtures is calculated using a “phi-phi” method with “one fluid” van der Waals mixing and combining rules for the equation of state parameters a_M(T), b_M and c_M. A single interaction constant k₁₂ is used to describe non-ideal behavior of each binary. The binary interaction constant, which is a strong function of temperature, and the sign of which signifies the type of deviations from Raoult's law, is obtained by correlating experimental bubble point data for isothermal binary refrigerant mixtures. The proposed equation of state generally describes binary P-x,y data more accurately the higher the temperature for a given system. The method presented is extended to predict vapor-liquid equilibria for the R14-R23-R13 ternary system at 198.75 K using binary interaction constants at this temperature for the three binaries involved.     

A generalized method for calculation and prediction of vapour-liquid equilibria at high pressures

A generalized method for prediction of vapour-liquid equilibria in hydrocarbon mixtures containing some nonhydrocarbon gases at high pressures has been developed following the approach of Chao and Seader (1961) and Lee et al. (1973). The method proposed is based on three equations: (1) a generalized equation of state for vapour phase calculations, (2) a generalized expression for the pure liquid fugacity coefficient suggested by Lee et al. (1973), and (3) an activity coefficient expression based on a surface modification of the regular solution model. The equations used contain only one partially generalized binary parameter, which has been evaluated from experimental K-value data. The method proposed has been tested by computing K-values and pressures in binary and multicomponent systems consisting of 13 hydrocarbons and three nonhydrocarbon gases. The results have shown that the proposed method can be applied over a wide range of conditions with a good degree of accuracy, which is comparable with that of more complicated methods.     

A versatile algorithm for calculating vapour—liquid equilibria

A versatile algorithm is proposed for solving vapour—liquid equilibrium problems. It has been prepared so that the search procedure is generally applicable with any analytical equation of state and any kind of data. Special attention is paid to the applicability of the method in critical and high-pressure regions. Derivatives of the quantities describing the state of the system can be obtained for any equilibrium state as soon as equilibrium is determined. Results are reported for computing based on the use of a modified Redlich—Kwong equation of state.     

Modelling of phase equilibria for associating mixtures using an equation of state

In the present work, the group contribution with association equation of state (GCA-EoS) is extended to represent phase equilibria in mixtures containing acids, esters, and ketones, with water, alcohols, and any number of inert components. Association effects are represented by a group-contribution approach. Self- and cross-association between the associating groups present in these mixtures are considered. The GCA-EoS model is compared to the group-contribution method MHV2, which does not take into account explicitly association effects. The results obtained with the GCA-EoS model are, in general, more accurate when compared to the ones achieved by the MHV2 equation with less number of parameters. Model predictions are presented for binary self- and cross-associating mixtures.     

Cubic equation of state for calculation of phase equilibria in association systems

Chemical potential of an associating component is derived from cubic equation of state. It is separated in the rigorous way into effective physical part and excess of chemical contribution. The both parts of the chemical potential are given in form of explicit expressions, which does not need any cumbersome integration or differentiation. The simple expression for association equilibrium is derived. It depends only on repulsive term of EOS. The proposed method is applied for correlating VLE equilibria in binary mixtures and for prediction of pressure in ternary mixtures on basis of the constituent binary VLE data.     

Mean-field lattice gas description of vapour-liquid and supercritical equilibria

Recently we improved the mean-field two-component lattice-gas model introducing interacting surface areas and an empirical entropy of mixing parameter. The treatment in its present form has proven to be well capable of describing almost quantitatively fluid-phase behaviour of non-polar and polar substances of low- and high molar mass and mixtures thereof in large temperature and pressure ranges. The model works particularly well in the critical fluid region which allows adjustment of the parameters to scarce experimental data with expressions for spinodal, critical condition and equation of state.     

A new equation for correlation of vapour-liquid equilibrium data of strongly non-ideal mixtures

A new equation for correlation of the thermodynamic excess functions of mixing, based on considerations of geometrical shape is proposed. Use of this equation for the correlation of heat of mixing data and vapour-liquid equilibrium data is proposed. The possibility of predicting multicomponent vapour-liquid equilibrium from binary data by using the proposed equation is shown. The equation is especially useful for correlating the excess functions of strongly non-ideal systems and for checking thermodynamic consistency of vapour-liquid equilibrium data.     

Vapor-liquid equilibria simulation and an equation of state contribution for dipole-quadrupole interactions

A systematic investigation on vapor-liquid equilibria (VLEs) of dipolar and quadrupolar fluids is carried out by molecular simulation to develop a new Helmholtz energy contribution for equations of state (EOSs). Twelve two-center Lennard-Jones plus point dipole and point quadrupole model fluids (2CLJDQ) are studied for different reduced dipolar moments micro*2=6 or 12, reduced quadrupolar moments Q*2=2 or 4 and reduced elongations L*=0, 0.505, or 1. Temperatures cover a wide range from about 55% to 95% of the critical temperature of each fluid. The NpT+test particle method is used for the calculation of vapor pressure, saturated densities, and saturated enthalpies. Critical data and the acentric factor are obtained from fits to the simulation data. On the basis of this data, an EOS contribution for the dipole-quadrupole cross-interactions of nonspherical molecules is developed. The expression is based on a third-order perturbation theory, and the model constants are adjusted to the present 2CLJDQ simulation results. When applied to mixtures, the model is found to be in excellent agreement with results from simulation and experiment. The new EOS contribution is also compatible with segment-based EOS, such as the various forms of the statistical associating fluid theory EOS.     

A simplified approach to vapor–liquid equilibria calculations with the group-contribution lattice-fluid equation of state

Equations of state that are based on the lattice-statistics approach use Guggenheim's quasi-chemical approximation to describe the non-randomness in the mixture due to the energetic interactions between the molecules. For ternary and higher-component systems the non-randomness expression is complex and requires an iterative calculation procedure. We have shown that the non-randomness parameters play a negligible role in the application of the GCLF-EoS model (based on the Panayiotou–Vera EoS) for predicting vapor–liquid equilibria. Omission of the non-randomness parameters from such calculations can significantly improve the computation efficiency. Binary, ternary, and quaternary vapor–liquid equilibria predictions were made including polystyrene, polyvinyl acetate, polyethylene, and polypropylene in polar and non-polar solvents to test the theory.     

Solid–liquid equilibria based on an equation of state for chain fluids

Solid–liquid equilibria were studied using an equation of state previously developed for fluids containing chain-like molecules. The method was used to correlate solubilities of normal alkanes and aromatic compounds with high molecular mass in hydrocarbon solvents. With one temperature independent parameter for the interaction energy, good agreement can be obtained between calculated results and experimental data for selected systems.     

Prediction of vapour-liquid equilibria for systems containing longer-chain alcohols and alkanes by various group-contribution methods

Comparisons are made of predicted excess free enthalpies provided by the parameters available for the ASOG model of Derr and Deal, the UNIFAC model of Fredenslund et al., and the CRG (chemical-reticular group-contribution) method of Neau and Péneloux. These methods are applied to predict vapour-liquid equilibria for alcohol-alkane systems having carbon numbers up to 16. Overall, the accuracy of prediction increases in the order UNIFAC, ASOG, CRG.     

Calculation and prediction of fluid phase equilibria from an equation of state

Liquids or compressed gases consisting of light molecules show deviations from classical mechanics, which are caused by the discontinuity of energy levels. From the assumption that each molecule is confined to a cell with a size depending on the free volume, a quantum correction is derived which extends any van der Waals type equation of state to quantum gases. The correction is applied to a semiempirical equation of state developed by the author. The extended equation yields reasonable critical compressibility factors and gives a better representation of PVT data than the uncorrected equation. Furthermore high pressure phase equilibria in mixtures containing helium and hydrogen have been calculated. Again the agreement with experimental data is improved; the adjustable binary interaction parameters have values close to the Berthelot-Lorentz rules and are less temperature dependent.