Van Der Waals One-fluid Theory Research Articles

Excess properties of Lennard-Jones binary mixtures from computer simulation and theory

Monte Carlo simulation and theory are used to calculate the excess thermodynamic properties of binary mixtures of spherical Lennard-Jones molecules. We study the excess functions of three binary mixtures characterized by the following size and dispersive energy ratios: (1) (σ22/σ11)3 = 2 and ε22/ε11 = 2; (2) (σ22/σ11)3 = 1 and ε22/ε11 = 1/2 and (3) (σ22/σ11)3 = 1/2 and ε22/ε11 = 2. In all cases, the unlike size parameter, σ12, is kept constant and equal to the value given by the Lorentz combining rule (σ12 = (σ11 + σ22)/2). However, different unlike dispersive energy parameter values are considered through the following combining rules: (a) ε12 = (ε11ε22)1/2 (Berthelot rule); (b) ε12 = ε11 (association); and (c) ε12 = ε22 (solvation). The pressure and temperature dependence of the excess volume and excess enthalpy is studied using the NpT Monte Carlo simulation technique for all the systems considered. Additionally, the simplest conformal solution theory is used to check the adequacy of this approach in predicting the excess properties in a wide range of thermodynamic conditions and variety of binary mixtures. In particular, we have applied the van der Waals one-fluid theory to describe Lennard-Jones binary mixtures through the use of the Johnson et al. [1993, Molec. Phys., 78, 591] Helmholtz free energy. Agreement between simulation results and theoretical predictions is excellent in all cases and thermodynamic conditions considered. This work confirms the applicability of the van der Waals one-fluid theory in predicting excess thermodynamic properties of mixtures of spherical molecules. Furthermore, since binary mixtures of spherical Lennard-Jones molecules constitute the reference fluid to be used in perturbation theories for complex fluids, such as the statistical association fluid theory (SAFT), this work shows clearly the applicability of the conformal solution theory within the framework of SAFT for predicting excess functions.

Phase equilibria study of Lennard–Jones mixtures by an analytical equation of state

The recently developed equation of state (EOS) for Lennard–Jones mixtures [Y. Tang, B.C.-Y. Lu, Fluid Phase Equilibria 146 (1998) 73.] is further investigated in this work for describing phase equilibria of these mixtures. The investigation covers vapor–liquid equilibria (VLE), liquid–liquid equilibria (LLE), vapor–liquid–liquid equilibria (VLLE) and vapor–vapor equilibria (VVE) over a wide range of temperatures, pressures and molecular characteristic parameters. Results from the van der Waals one-fluid (VDW1) theory are included for comparison. The newly proposed theory performs very well for VLE and LLE and the performance is better than the VDW1 theory; but both theories yield only qualitative results for VVE. It is also found that one system should exhibit VLLE, which was not noticed in previous investigations. Results from two other perturbation theories are also compared in some cases.

An improved perturbation theory and van der Waals one-fluid theory of binary fluid mixtures Part 2. Phase equilibria

In this paper, we have tested how accurately our improved form of perturbation theory and van der Waals one-fluid theory can predict recent simulation results for vapor/liquid, liquid/liquid and gas/gas equilibria of highly nonideal binary mixtures.In these mixtures, size and energy parameters of the like as well as unlike components differ significantly. Comparisons of theoretical predictions with simulation results for vapor/liquid and liquid/liquid equilibria show a very good performance of perturbation theory in different nonideal conditions. Prediction of gas/gas equilibria of mixtures with large unlike size parameter is only qualitative. Van der Waals one-fluid theory is successful in predicting vapor/liquid equilibria of moderately nonideal mixtures only. It becomes less reliable in describing liquid/liquid and gas/gas equilibria of highly nonideal mixtures.

Excess properties of ternary fluid mixtures from simulation, perturbation theory and van der Waals one-fluid theory: size and energy parameter effects

In this paper, we report isothermal-isobaric molecular dynamics simulation results for total and excess properties of 48 equimolar and 24 nonequimolar ternary mixtures consisting of Lennard-Jones fluids in different nonideal conditions. Energy and size parameters of the components differ appreciably, lying in the range ( 1 ≤ ε BB ε AA ≤ 1.75 , 1 ≤ ε CC ε AA ≤ 2 ) and ( 1 ≤ σ BB σ AA ≤ 1.75 , 1 ≤ σ CC σ AA ≤ 2 ). Unlike energy and size parameters of mixtures are determined using Lorentz-Berthelot combination rule. Mixtures are considered at four different conditions, ( kT ε AA = 1 , Pσ AA 3 ε AA = 0.5 ), ( kT ε AA = 2 , Pσ AA 3 ε AA = 1.2 ), ( kT ε AA = 2 , Pσ AA 3 ε AA = 2.5 ) and ( kT ε AA = 3 , Pσ AA 3 ε AA = 2.5 ). The effects of unlike size and energy interaction parameters on total and excess properties of mixtures deviating from the Lorentz-Berthelot combination rule have also been investigated at two different conditions, ( kT ε AA = 1 , Pσ AA 3 ε AA = 0.5 ) and ( kT ε AA = 2 , Pσ AA 3 ε AA = 2.5 ). These simulation results have been used to test our recently developed first-order perturbation theory and van der Waals one-fluid theory of ternary mixtures. Perturbation theory is based on the hard sphere reference mixture and involves no mixing rules. Van der Waals one-fluid theory is based on an accurate equation of state for the pure fluids. An extensive comparison of theoretical predictions with simulation results show that, in general, perturbation theory is very successful in describing simulation results for ( 1 ≤ ε BB ε AA ≤ 1.75 , 1 ≤ ε CC ε AA ≤ 2 ) and ( 1 ≤ σ BB σ AA ≤ 1.75 ; 1 ≤ σ CC σ AA ≤ 2 ). On the other hand, van der Waals one-fluid theory is reliable in describing total properties in the range 1 ≤ σ CC σ AA ≤ 1.18 and excess properties in the range 1 ≤ σ BB σ AA ≤ 1.25 , for all the energy parameter ratios considered in this paper.

Associating models and mixing rules in equations of state for water/hydrocarbon mixtures

Equations of state (EoS) for associating fluids calculate explicitly the effect of hydrogen bonding by using chemical theory, perturbation theory or quasi-chemical theory. In all cases, the number of hydrogen bonding sites per molecule is an input parameter to the model. Specifically for water, two-, three- or four-site models have been used in the past by different investigators. In this work, the associated-perturbed-anisotropic-chain-theory (APACT) and the statistical-associating-fluid-theory (SAFT) are applied to predict the phase equilibrium of water/hydrocarbon mixtures, with emphasis on liquid-liquid equilibria (LLE). The accuracy of the different models to describe association in water is investigated. Different mixing rules are examined for SAFT. The original mixing rules proposed based on the van der Waals one-fluid theory work well for vapor-liquid equilibria (VLE) predictions, but not for water/hydrocarbon LLE, which are primarily influenced by the large difference in intermolecular interactions between water and hydrocarbon. For water/hydrocarbon mixtures, the one-fluid theory fails to predict reliably the hydrocarbon solubility because the local composition is very different from the bulk composition. A more realistic mixing rule for these systems is proposed that is based on the asymmetric mixing rule introduced originally for the perturbed-hard-chain-theory (PHCT). This mixing rule is used here for SAFT predictions of water/hydrocarbon LLE resulting in an improvement of the hydrocarbon solubility predictions. Nevertheless, the agreement of all the models investigated with the experimental data is, in general, poor. For comparison, calculations with the Redlich-Kwong-Joffe-Zudkevitch (RKJZ) cubic EoS are also reported.

An improved perturbation theory and van der Waals one-fluid theory of binary fluid mixtures: Part 1. Total and excess thermodynamic properties

We have examined the accuracy of a modified first-order perturbation theory of nonideal binary mixtures and van der Waals one-fluid theory, which uses an accurate equation of state for pure fluids. Perturbation theory consists of the first-order perturbation theory of high temperature approximation and the random phase approximation. Inclusion of random phase approximation enhances the applicability of perturbation theory to much wider ranges of temperatures and densities. In this part of the paper, results are reported for pressure, residual chemical potentials at finite concentration and in infinite dilution, total and excess properties of several fluid mixtures under highly nonideal conditions. In these mixtures, size and energy parameters of like as well as unlike components differ significantly. Comparisons of theoretical predictions with accurate simulation results show, in general, a very good performance of the perturbation theory in varying nonideal conditions. Van der Waals one-fluid theory is successful in predicting equation of state, residual chemical potentials at finite concentration and in infinite dilution in moderately nonideal mixtures only. It becomes less reliable in describing residual chemical potentials in infinite dilution in highly nonideal mixtures, and becomes unreliable in predicting excess properties of even moderately nonideal mixtures. In general, the present form of perturbation theory offers a significant improvement over the previous forms based on high temperature approximation, and is essentially more accurate than the van der Waals one-fluid theory.

Thermodynamic properties of ternary fluid mixtures from the improved perturbation theory and van der Waals one-fluid theory—I. Model mixtures

In this paper, we present a first-order hard sphere perturbation theory of nonideal ternary fluid mixtures. Results are reported for total and excess thermodynamic properties of three ternary mixtures, in which size parameters of the mixture components are the same, but energy parameters differ significantly. Comparisons of theoretical predictions with accurate simulation results for mixture density, internal energy, excess Gibbs free energy, excess volume and excess enthalpy show the very good performance of perturbation theory. We have also checked the accuracy of van der Waals one-fluid theory, which uses an accurate equation of state for the pure fluids. Van der Waals one-fluid theory is successful in predicting excess properties of nearly ideal to moderately nonideal mixtures, but becomes less reliable when the mixtures become highly nonideal. In general, perturbation theory is very reliable in predicting thermodynamic properties of ternary mixtures, and is found to be more accurate than van der Waals one-fluid theory.

Thermodynamic properties of ternary fluid mixtures from the improved perturbation theory and van der Waals one-fluid theory—II. Real mixtures

In this paper, a previously developed first-order hard sphere perturbation theory of a ternary fluid mixture (Fotouh and Shukla, 1996, Chem. Engng Sci. 51, 4923–4931) is applied to predict excess properties of a real ternary fluid mixture using a theoretically consistent combination rule. We consider a ternary fluid mixture N 2/Ar/CH 4, for which experimental data for excess properties are available and which can be modeled adequately using the simple Lennard-Jones potential function. Comparisons of theoretical results with experimental data show a very good performance of perturbation theory for different pressures and compositions of the mixture. Also, we checked the accuracy of a recent form of van der Waals one-fluid theory based on the most accurate equation of state for pure Lennard-Jones fluids. Van der Waals one-fluid theory is found to be equally reliable in describing excess properties of such a moderately nonideal mixture.

Excess Thermodynamic Properties of Ternary Fluid Mixtures from Molecular Dynamics Simulation and Van Der Waals One-Fluid Theory

Abstract In this paper, we report isothermal–isobaric molecular dynamics simulation results for total and excess thermodynamic properties of three selected nonideal ternary fluid mixtures, in which particles interact via a Lennard-Jones pair potential. In these mixtures, size parameters of the components are kept to be the same, but energy parameters of the components differ significantly. Simulation results are reported for mixture density, internal energy, excess Gibbs free energy, excess volume and excess enthalpy of equimolar ternary mixtures as a function of temperature and pressure. The excess Gibbs free energy is obtained directly using the coupling parameter charging approach, which avoids the cancellation or magnification of errors in the simulation. These simulation results are used to check the accuracy of a form of the van der Waals one–fluid theory, which uses an accurate equation of state for the pure fluids. Van der Waals one–fluid theory is successful in predicting total and excess properties of these nonideal mixtures within simulation uncertainties.

Phase equilibria in ternary Lennard-Jones systems

Gibbs ensemble Monte Carlo simulations are used to test the ability of the van der Waals one-fluid theory to predict phase equilibria for ternary systems of particles interacting with Lennard-Jones potentials. Simulation results for asymmetric systems are compared to theoretical results for mixtures that obey the Lorentz-Berthelot combining rules. Good agreement is found between theory and simulation far form the plait point. The theory is found to overestimate the plait point, as expected from previous studies of binary systems. Liquid-liquid equilibria in a symmetric ternary system with energy parameters deviating from the geometric mean (Berthelot) rule are also investigated at three different pressures. A three-phase region is found at high pressures. The agreement between theory and simulation is excellent for the symmetric systems studied here.

Exact calculations of fluid-phase equilibria by Monte Carlo simulation in a new statistical ensemble

A recently proposed method, Monte Carlo simulation in the Gibbs ensemble, allows the prediction of phase equilibria from knowledge of the intermolecular forces. A single computer experiment is required per coexistence point for a system with an arbitrary number of components. The new technique has significant advantages relative to free-energy methods that have been used for phase equilibrium calculations is the past. In this work, a variation of the Gibbs method appropriate for calculations in mixtures with large differences in molecular size is developed. The method is applied for the calculation of high-pressure phase equilibria in two mixtures of simple monatomic fluids, the systems argon-krypton and neon-xenon. Pairwise additive potential functions of the Lennard-Jones type are used to describe the intermolecular interactions. Agreement with experimental results is generally good over a wide range of temperatures and pressures, including the fluid-fluid immiscibility region for the neon-xenon system. Results from the Van der Waals one-fluid theory are compared with experimental data and computer simulation predictions. Agreement is excellent for the mixture with small differences in size (argon-krypton), but the theory fails to describe the coexistence curve for the highly asymmetric system neon-xenon.

Excess enthalpies of { xN 2 + (1 − x)CO}(I) at 83.82 K: experiment and theory

The excess molar enthalpies H m E {xN 2 +(1−x)CO}(1) have been determined at 83.82 K using a low-temperature batch calorimeter. The value of H m E (x=0.5) at mixture saturation pressure is (41.2 ± 1.1) J·mol −1 . The results for H m E are in good agreement with the values derived from published phase equilibria. The ability of two theoretical methods to predict the excess enthalpy was tested. The simple van der Waals one-fluid theory gives good results; however. a spherical reference-based perturbation theory is found to give an even better prediction of H m E (within 5.1 per cent at x = 0.5).

Van der waals one-fluid theory : justification and generalisation

We describe an approach to van der Waals one-fluid theory based on thermodynamic consistency and propose a method for generalising it to non-conformal fluids.

MOLECULAR SHAPE FACTORS FOR AMMONIA AND THEIR APPLICATION TO VAPOR-LIQUID EQUILIBRIUM CALCULATIONS

The empirical molecular shape factors for ammonia relative to methane as a reference were correlated for 0.7≤Tr≤, 1.4 and 0<Pr≤30. They could well represent the compressibility factors and the fugacity coefficients of ammonia. On the basis of the corresponding-states principle, the vapor-liquid equilibria of binary systems containing ammonia were predicted by using pseudo-potential parameters, obtained by the van der Waals one-fluid theory coupled with molecular shape factors. Good results were obtained except in high pressure ranges.