A simple non-classical equation of state for fluids and fluid mixtures

A method for improving the behavior of classical equations of state (EOS) in the critical region, originally proposed by Fox [J.R. Fox, Fluid Phase Equilibria 14 (1983) 45–53], has been modified in this work for the Patel–Teja (PT) EOS [N.C. Patel, A.S. Teja, Chem. Eng. Sci. 37, 463–473]. The application of the new equation (NPT) for predicting PVT and vapor pressure behavior of pure substances, as well as vapor–liquid equilibrium behavior of binary mixtures, is demonstrated. The NPT equation is simple to use and requires the same input information as the original PT equation. However, it reproduces the correct PVT behavior in the critical region. Limitations of both the PT and NPT equations in calculating the isochoric heat capacity are discussed.     

Application of the crossover lattice equation of state for fluid mixtures

In previous work, we developed the crossover lattice equation of state (xLF EOS) for pure fluids and the xLF EOS yielded the saturated vapour pressure and the density values with a much better accuracy than the classical LF EOS over a wide range. In this work, we extended xLF EOS to fluid mixtures. Classical composition-dependent mixing rules with only adjustable two binary interaction parameters same as the LF EOS are used. A comparison is made upon experimental data for fluids mixtures in the one- and two-phase regions. The xLF EOS shows more improved representations than the LF EOS, especially in the critical region.     

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.     

Modeling and simulation of equation of state for nonadditive hard disk mixtures

We present exact results for mixtures of nonadditive hard disks and use some of them to derive a consistent model for the equation of state. We also performed molecular dynamics simulation for hard disks over a wide range of size ratios. Comparison of the model to the data shows that the model is accurate for all densities in the case of additive and slightly nonadditive (nonadditivity parameter within ±0.1) mixtures. For large nonadditivity, the model is accurate for low to moderate densities only, and starts to deteriorate at high densities.     

Helmholtz energy,extended corresponding states and local composition model for fluid mixtures

We present a model for the calculation of mixture properties. This model is based on the mixture residual Helmholtz energy given by the sum of two terms: one is the residual Helmholtz energy calculated by an extended corresponding states (ECS) model while the other is a correction term. The ECS model is based on methane as the reference fluid and shape factors that carry out the scaling of properties between the fluid of interest and the reference fluid. These shape factors are given by correlations in terms of reduced temperature and density. The application to mixtures is carried out with the one-fluid van der Waals mixture model. The correction term is temperature- and density-dependent as is given by a local composition mixing rule. Local compositions were calculated from a coordination number model based on lattice gas theory. With respect to binary-mixture properties, densities were calculated with an average absolute deviation (AAD) of 0.12%; speeds of sound were calculated with an AAD of 0.16% and bubble pressures were calculated with an AAD of 1.77%. Also, natural gas densities were calculated with AAD of 0.03% and natural gas speeds of sound were calculated with AAD of 0.049%. All these results are very satisfactory when compared with those obtained by modern mixture models.     

A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres

We introduce an expansion of the equation of state for additive hard-sphere mixtures in powers of the total packing fraction with coefficients which depend on a set of weighted densities used in scaled particle theory and fundamental measure theory. We demand that the mixture equation of state recovers the quasiexact Carnahan-Starling [J. Chem. Phys. 51, 635 (1969)] result in the case of a one-component fluid and show from thermodynamic considerations and consistency with an exact scaled particle relation that the first and second orders of the expansion lead unambiguously to the Boublik-Mansoori-Carnahan-Starling-Leland [J. Chem. Phys. 53, 471 (1970); J. Chem. Phys. 54, 1523 (1971)] equation and the extended Carnahan-Starling equation introduced by Santos et al. [Mol. Phys. 96, 1 (1999)]. In the third order of the expansion, our approach allows us to define a new equation of state for hard-sphere mixtures which we find to be more accurate than the former equations when compared to available computer simulation data for binary and ternary mixtures. Using the new mixture equation of state, we calculate expressions for the surface tension and excess adsorption of the one-component fluid at a planar hard wall and compare its predictions to available simulation data.     

A corresponding states principle-based equation for the surface tension of Alkenes

This study presents a new formula for the surface tension prediction of alkenes. As a first step, an analysis of the available data of the experimental surface tension data for alkenes was performed. The experimental data were collected, after a careful literature survey, for the following pure fluids: propene, 1-hexene, 1-heptene, 1-octene, 1-decene, 1-tetradecene, and 1-pentadecene. Then, the experimental data were regressed with the most reliable semi-empirical correlating methods based on the corresponding state theory existing in the literature. As a final step, an analysis of the available data of the experimental surface tension data for alkenes was performed starting from the two recently proposed equations for the prediction of the surface tension of refrigerants based on the corresponding states principle. To minimize the deviation between the predicted data and the experimental data and to find the optimal equation coefficients for experimental data regression, a (μ + λ)-evolution strategy was adopted. The analysis showed that the equation that gave the best results for the prediction of the surface tension of alkenes was the one with a very limited number of parameters. The finally proposed equation is very simple and gives a noticeable improvement with respect to the existing equations. It is based on the corresponding state principle, containing the acentric factor, the critical temperature, and pressure.     

Extended corresponding states model for fluids and fluid mixtures: II. Application to mixtures and natural gas systems

We report an extended corresponding states model optimised for accurate prediction of the thermodynamic properties and vapour–liquid equilibria of natural gases and similar mixtures. The corresponding states model uses methane as the reference fluid and employs shape factors for pure components that were reported recently [Fluid Phase Equilib. 204 (2002) 15]. The van der Waals one-fluid model is used for mixtures and, in this paper, we report two alternative temperature- and density-dependent correlations of the binary interaction parameters. Model ECSmixS1 was optimised for 19 binary systems in the wide domain 90≤T (K)≤670 with p (MPa)≤510 and is suitable for the prediction of both liquid- and gas-phase thermodynamic properties and for the solution of vapour–liquid equilibrium problems. Model ECSmixS2 was specialised for increased accuracy in the natural gas ‘custody transfer’ interval 270≤T (K)≤330 with p (MPa)≤12 and is intended for gas-phase thermodynamic properties only. For mixtures of the major components of natural gas, we obtain with Model ECSmixS1 an overall average absolute deviation (AAD) of 0.12% in calculated densities, an AAD of 0.16% in calculated speeds of sound and an AAD of 1.8% in bubble pressure. With Model ECSmixS2, we obtained improved AADs of 0.03% in density and 0.03% in speed of sound. These results compare very favourably with other commonly used mixture models. The present model may be systematically improved or extended by introducing new or improved correlations of the binary parameters.     

A quartic hard chain equation of state for normal fluids

A new empirical equation of state is proposed which is applicable to mixtures of chain-like molecules. The equation is based on a simple model which uses an approximate chain theory and an approximation of the Carnahan—Starling equation. The results for pure component properties of normal fluids are comparable to the common cubic equations of state. For mixtures of chain-like molecules, the new equation is as good or better than the Peng—Robinson equation.     

Application of hard convex body and hard sphere equations of state to the critical properties of binary mixtures

The critical properties of hydrocarbon mixtures, perfluorocarbon + hydrocarbon, perfluoromethylcyclohexane + siloxane, acetone + hydrocarbon and polydimethyl siloxane mixtures have been calculated from an equation of state for hard convex bodies and from Guggenheim's equation of state for hard spheres. In general, the results of both equations agree well with experimental data.It appears, however, that taking shape factors into account (by using the hard convex body equation) does not lead to a significant improvement in the agreement between theory and experiment for the critical properties.     

Quantum mechanical law of corresponding states from ISM equation of state: compressed liquids

In this paper, we explore the theory of the equation of state from the view point of Ihm–Song–Mason (ISM) equation of state, which has been derived on the basis of statistical mechanical perturbation theory, and is characterized by three temperature dependent parameters, α, b, B₂, and a free parameter Γ. This equation is applied well to non-polar fluids in subcritical and supercritical regions and to molten alkali metals. We present results that show Γ varies slightly with temperature. Among the nobles group, Γ values are quite the same and are correlated except He, which deviates so much even no moderate correlation is seen. In the alkali metals group, Γ values are roughly the same for K, Rb, and Cs but are different for Li and Na. We have previously shown that Γ conforms to B₂, the second virial coefficient, and thus to the nature of the particular fluid system. These observations plus the discussion on quantum mechanical law of corresponding states suggest that the ISM equation of state stands as an analytical equation of state which explicitly incorporates quantum effects by the parameter Γ. Then, we suggest a law of corresponding states as p*=p*(v*, T*, Γ) where, asterisks stand for reduced pressure, volume, and temperature, respectively.     

Integral equation theory for symmetric nonadditive hard sphere mixtures

An integral equation theory is presented for the pair correlation functions and phase behavior of symmetric nonadditive hard sphere mixtures with hard sphere diameters given by sigma(A)(A)() = sigma(BB) = lambdad and sigma(AB) = d. This mixture exhibits a fluid-fluid phase separation into an A-rich phase and a B-rich phase at high densities. The theory incorporates, into the closure approximation, all terms that can be calculated exactly in the density expansion of the direct correlation functions. We find that the closure approximation developed in this work is accurate for the structure and phase behavior over the entire range of lambda, when compared to computer simulations, and is significantly more accurate than the previous theories.     

The principle of corresponding states for liquid normal and branched alkanes

Prigogine's principle of corresponding states for chain-molecule liquids was tested by the determination of the characteristic volumes, temperatures, and pressures of then-alkanes from hexane through dodecane and of branched hexanes, heptanes, and octanes, using the method of Patterson and Bardin. The characteristic parameterV ^* is shown to be influenced by steric hindrance in the molecule. The quantitiesV ^* andT ^* appeared to be slightly dependent on temperature;P ^* is independent of chain length in homologous series of normal and branched alkanes.     

On the corresponding states law of the Yukawa fluid

We have analyzed the currently available simulation results as well as performed some additional Monte Carlo simulation for the hard-core attractive Yukawa fluid in order to study its corresponding state behavior. We show that the values of reduced surface tension map onto the master curve and a universal equation of state can be obtained in the wide range of the attractive Yukawa tail length after a certain rescaling of the number density. Some comparisons with other nonconformal potentials are presented and discussed.     

A crossover lattice fluid equation of state for pure fluids

A lattice fluid model is one of the most versatile, molecular-based engineering equations of state (EOS) but, in common with all analytic equations of state, the lattice fluid (LF) EOS exhibits classical behaviour in the critical region rather than the non-analytical, singular behaviour seen in real fluids. In this research, we use the LF EOS and develop a crossover lattice fluid (xLF) equation of state near to and far from the critical region which incorporates the scaling laws valid asymptotically close to the critical point while reducing to the original classical LF EOS far from the critical point. We show that, over a wide range of states, the xLF EOS yields the saturated vapour pressure data and the density data with much better accuracy than the classical LF EOS.     

Generalized principle of corresponding states and the scale invariant mean-field approach

In this paper we apply the relations between the critical points of the Lennard-Jones fluids and lattice gas model found in [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)] to other short-ranged potentials like Buckingham and the Mie-potentials. The estimates for the corresponding critical point loci correlate quite satisfactory with the available numerical data for these potentials. The explanation for the correlation between the value of the second virial coefficient at the critical temperature and the particle volume found in [G. A. Vliegenthart and H. N. W. Lekkerkerker, J. Chem. Phys. 112, 5364 (2000)] is proposed. The connection of the stability of the liquid phase with the short range character of the potentials is discussed on the basis of the global isomorphism approach.     

Equations of state of mixtures of hard dumbbells

Two ways to predict pVT behavior of hard-dumbbell mixtures in the fluid region are proposed. These are adaptations of the hard convex body equation devised by Boublik and an extension of the first Barker-Henderson perturbation theory. Calculated compressibility factors show good agreement with the ideal mixing assumption and yield a useful equation of state.     

On the equation of state of hard chain molecules

The chain-of-rotators (COR) equation of state developed by Chien, Greenkorn, and Chao makes an assumption on the hard chain partition function based on results for monomers and dimers, i.e., spheres and dumbbells. Here this assumption is checked for trimers by comparison with the results of Boubik's hard convex body equation. It turns out that the COR assumption is, in general, a good approximation. Its quality depends somewhat on the bond length and the bond angle which it does not consider. The agreement is especially good for angles somewhat less than 90°.     

Application of an improved simplified perturbed hard chain theory equation of state for pure compounds and binary asymmetric mixtures

The simplified perturbed hard chain theory equation of state is modified using recently developed repulsive and attractive terms. Both terms meet the low density and close-packed density boundary conditions and are in reasonable agreement with molecular simulation data. The modified equation of state accurately predicts pure component properties including saturated vapor volume, liquid density, vapor pressure and enthalpy of vaporization. Compared with the original equation, the modified one predicts physical properties more accurately. However, the improvement of predicting enthalpy of vaporization is marginal. The two equations are tested for predicting the phase behavior of binary asymmetric mixtures. It is shown that the difference in predicting the phase behavior is not appreciable.