Three parameter corresponding

This method utilizes essentially the concept developed by Fitzer in 1955. According to the principle of three-parameter corresponding states, the compressibility factor z, for a fluid of acentric factor w, is obtained by interpolating between the compressibilities Zj and Z2 for the two fluids having acentric factors w, and (p -... 

Pitzer s Corresponding-States Correlation A three-parameter corresponding-states correlation of the type developed by Pitzer, K.S. Thennodynamic.s, 3ded., App. 3, McGraw-HiU, New York, 1995) is described in Sec. 2. It has as its basis an equation for the compressibility factor ... 

Lee, B. I. and Kesler, M. G. (1975) AIChemEJL 21, 510. A generalized thermodynamic correlation based on three-parameter corresponding states. 

Calculated values of the quantities (Hr)°/RTc, (HRy/RTc, (Sr)°/R, an (SRy/R are shown by plots of these quantities vs. Pr for various values of Tr i Figs. 6.6 through 6.13. These plots, together with Eqs. (6.56) and (6.57), alio estimation of the residual enthalpy and entropy on the basis of the three-paramet corresponding-states principle as developed by Pitzer (Sec. 3.6). 

The Lee/Kesler tables are adapted and published by permission from "A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States," by Byungik Lee and Michael G. Kesler, AIChE J.,21,510-527 (1975). The numbers printed in italic type are liquid-phase properties. 

An extensive set of three-parameter corresponding-states correlations has been developed by Pitzer and coworkers [Pitzer, Thermodynamics, 3d ed., App. 3, McGraw-Hill, New York (1995)]. Particularly useful is the one for the second virial coefficient. The... 

Equations of state, such as the Redhch-Kwong (RK) equation, which expresses Z as a function of T, and P, only, yield two-parameter corresponding-states correlations. The SRK equation and the PR equation, in which the acentric factor CO enters through function aiT, Co) as an additional parameter, yield three-parameter corresponding-states correlations. The numerical assignments for parameters , C, 2, and 9 are given in Table 4-2. Expressions are also given for aiT, CO) for the SRK and PR equations. 

The primary key to Soave s early success was the recognition of the need to extend from two-parameter to three-parameter corresponding states. With two parameters, it is possible to fit the critical temperature and critical pressure of any compound, but a general description of the vapor pressure curve is unattainable. 

Three-Parameter, Corresponding-States Conformal Solution Mixing Rules for Mixtures... 

Table 3.2 presents a selection of the most used thermodynamic options for phase equilibrium with suitable enthalpy and entropy methods. The accuracy of both phase equilibrium and enthalpy/entropy computation must be examined when using EOS models. For example, often a cubic EOS underestimates the enthalpy of vaporisation. In this case other methods are more accurate, as those based on three-parameters corresponding states law (Lee-Kesler, Curl-Pitzer, etc.). Mixtures rich in components with particular behaviour, as or CH, need special methods for accurate simulation. When binary interaction parameters for liquid activity models are absent, the UNI FAC predictive method may be employed. It is worth to note that UNIFAC is suitable only for exploratory purposes, but not for final design. When high non-ideal mixtures are involved at higher pressure then the combination of EOS with liquid activity models is recommended (see Chapter 6). 

The computation of the second virial coefficient B can follow different ways. Here we illustrate the use of three-parameter corresponding states law. The following equations can be conveniently represent the behaviour of non-polar molecules ... 

One of the most interesting applications in this class is the method of Lee-Kesler (LK). The compressibility factor is described by three-parameter corresponding states correlation of the form ... 

The first test of the theory was made to the solution spectra of Hoogschagen and Gorter (1948) for Nd 4f and Er 4f . This involved summing over the quantum numbers n and ji, since the sublevel structure becomes blurred to at least some degree when the lanthanides are in solution. A remarkably good fit could be made to the experimental data with just three parameters, corresponding to t = 2, 4 and 6 (Judd 1962). The field soon developed a life of its own and is the subject of the review by Carnall (1979) in the third volume of this Handbook. Axe (1963) examined the fluorescence bands Dq F4 and Di - F3, F4 in europium ethylsulphate and showed that the theory works equally well for the individual transitions of the type Two other bands, Do-> Fi and Di - F2, were... 

For nonassociating molecules, the methods of Tsonopoulos [14] and Hayden and O Connell [15] yield pretty good results for the estimation of the second virial coefficient. The first method works with the three-parameter corresponding-states principle (Section 2.4.4) the second method takes into account several molecular effects. In case of vapor phase association (Section 13.2), the model of Hayden-O Connell is extended by a chemical equilibrium term, whose parameters have to be fitted to experimental data. 

The three-parameter corresponding-state principle is applicable to many substances only for strongly polar or associating substances large deviations between the theoretical and experimental values can occur. 

For the description of thermophysical properties, estimation methods based on the three parameter corresponding states principle mostly employ the critical temperature (Tc), the critical pressure (Pc), and the acentric factor (co) as characteristic... 

Corresponding-states correlations of Z based on this theorem are referred to as two-parameter correlations. They require the use of two reducing parameters, and P. These correlations are nearly exact when used to describe noble gases such as argon, krypton, and xenon. When complex fluids were encountered, a three-parameter corresponding states parameter was found to be needed. An acentric factor, o), can be defined as introduced by Pitzer [11]. The acentric factor for a pure substance is defined with respect to its vapor pressure ... 

An equation of state has been developed by Kosinski and Anderko (2001) for the representation of the phase behavior of high-temperature and supercritical aqueous systems containing salts. They improved the EOS by Anderko and Pitzer (1993a) to enhance the predictive capability of the EOS using the three-parameter corresponding-states principle. The model was successfully apphed to the H2O + NaCl solutions up to 573 K, and correctly predicts the p VTx properties of H2O + KCl solution up to 773 K. This EOS also considerably extended the validity range. The EOS is also applicable to water + nonelectrolyte solutions such as water + methane and water + n-decane systems. 

The third virial coefficients of pure non-polar gases have also been correlated using a three-parameter corresponding-states model by Orbey and Vera. However, in order to obtain a reliable correlation for the third virial coefficients of both polar and non-polar substances it is again necessary to introduce an additional parameter. Liu and Xiang present a correlation of this kind in which the fourth parameter is the critical compression factor Z, their model is " ... 

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