Wilson correlation

B. Guo, S. Kao, H. McDonald, A. Asanov, L.L. Combs, W.W. Wilson, Correlation of second viral coefficients and solubilities useful in protein crystal growth, J. Cryst. Growth 196 (1999) 424-433. 

This formulation is Raoult s law extended by the inclusion of the activity coefficient and is not much more difficult to use and it has much greater utility and accuracy at moderate pressures than Raoult s law. It is especially useful when correlations are available for liquid phase activity coefficients yj. Correlations for this purpose will be discussed in a later section. In the case of systems acetone-chlorobenzene and acetone and chloroform shown respectively in Figs. 2 and 3, the Wilson correlation equation was used to successfully fit the data. The Wilson correlation would also fit the data of benzene-toluene shown in Fig. 1 however, the fit would be no better than Raoult s law and is not illustrated in the figure. 

This equation is implicit in fly, inasmuch as the saturated volumes are dependent on fly, but the equation can be readily solved, for instance, by the method of repeated substitution. By using the solved value of fly in the eos. Equation (4.162), the vapor pressure calculated by the eos simply reproduces the experimental vapor pressure data. Wilson correlated the fly s that are fitted to vapor pressure data of a number of normal fluids to obtain Equation (4.157), the Wilson eos. Vapor pressure calculated by the Wilson eos is improved over that of the RK eos, but the accuracy still leaves something to be desired. Soave correlated the vapor pressure, fitting fly with Equation (4.164). Even better, the Soave eos is useful for the quantitative calculation of vapor pressure. In addition, the Peng-Robinson and the chain-of-rotators eos s provide quantitative calculations of vapor pressure. 

In order to be able to apply this rule in practice, it must be possible to precalculate both the level under reflux conditions and the initial level. Besides other alternative models the so-called Wilson correlation provides a possibility. This model correlates system specific substance data and the relative free board level a. 

The Xj-values are estimated from the Wilson correlation (Eq. (4.16)) or other suitable correlations. However, if the feed composition z is... 

In Step 1, we can use. ffj-values from the Wilson correlation (see Eq. (4,16)) to proceed with the stability of the original phase and to calculate the composition of the trial second phase. The Wilson correlation may not be appropriate if the trial phase and the original phase are in liquid states. From Eq. (4.16), = 4.564, i co, 0.8709, and... 

S. Wilson, Electron Correlation in Molecules Clarendon, Oxford (1984). 

The activity coefficient (y) based corrector is calculated using any applicable activity correlating equation such as the van Laar (slightly polar) or Wilson (more polar) equations. The average absolute error is 20 percent. 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

Wilson, S. [1984] Electron Correlation in Molecules, Clarendon Press, Oxford. 

Wilson, S. [1987] (ed.), Methods in Computational Chemistry , volume 1, Electron Correlation in Atoms and Molecules, Plenum, New York. 

Noteworthy also is the extensive compilation of early data on layered MX2 given by Wilson and Yoffe [37], who worked out a group-by-group correlation of transmission spectra of the compounds to available electrical and structural data and produced band models in accord with a molecular orbital approach. 

The correlation of phosphate precipitation with decrease of conductivity (Wilson Kent, 1968), increase in pH (Kent Wilson, 1969) and hardness (Wilson et al, 1972) is shown in Figure 6.16. These results demonstrate the relationship between the development of physical properties and the underlying chemical changes, but there are no sharp changes at the gel point. Evidence from infrared spectroscopy (Wilson Mesley, 1968) and electron probe microanalysis (Kent, Fletcher Wilson, 1970 Wilson et al, 1972) indicates that the main reaction product is an amorphous aluminophosphate. Also formed in the matrix were fluorite (CaF ) and sodium acid phosphates. 

P.N. Craig, Comparison of the Hansch and Free-Wilson approaches to structure-activity correlation, In Biological Correlations — The Hansch Approach (R.F. Gould, Ed.). Advances in Chemistry Series, No. 114. American Chemical Society, Washington DC, 1972, pp. 115-129. P.N. Craig, Interdependence between physical parameters and selection of substituent groups for correlation studies. J. Med. Chem., 14 (1971) 680-684. 

A. H. Fitter, T. R. Stickland, M. L. Harvey, and G. W. Wilson, Architectural analysis of plant root systems 1. Architectural correlates of exploitation efficiency. New PItytol. 119 515 (1991). 

Thiessen and Wilson (1987) presented a modified isopiestic apparatus and obtained osmotic coefficient data for KC1 solutions using NaCl as reference solution. The data are given in Table 15.4. Subsequently, they employed Pitzer s method to correlate the data. They obtained the following values for three Pitzer s... 

Blanco et al. have also correlated the results with the van Laar, Wilson, NRTL and UNIQUAC activity coefficient models and found all of them able to describe the observed phase behavior. The value of the parameter ai2 in the NRTL model was set equal to 0.3. The estimated parameters were reported in Table 10 of the above reference. Using the data of Table 15.7 estimate the binary parameters in the Wislon, NRTL and UNIQUAC models. The objective function to be minimized is given by Equation 15.11. 

A number of workers have published correlations based on a step counting approach Taylor (1977), Wilson (1971). These and other correlations are reviewed and compared in the Institution of Chemical Engineers booklet, IChemE (1988). 

ACT = correlation for liquid-phase activity coefficient such as, Wilson, NRTL, UNIQUAC, UNIFAC. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Correlation for nonuniform heat flux. On the basis of Tong s shape factor formulation (1967a), Wilson et al. (1969) developed another set of constants ... 

Combined with Eq. (5-114), they correlated the Wilson et al. s (1969) data of 81 data points as obtained from rod bundles 72 in. (1.83 m) long having 15-in. (0.38-m) grid span with a standard deviation of 11.5%. 

The functional dependence of jD on Reynolds number has been the subject of study by many investigators [e.g., Thodos and his co-workers (77, 78), and Wilson and Geankoplis (79)]. A variety of equations have been proposed as convenient representations of the experimental data. Many of these correlations also employ the bed porosity (eB) as an additional correlating parameter. This porosity is the ratio of the void volume between pellets to the total bed volume. 

The most important aspect of the simulation is that the thermodynamic data of the chemicals be modeled correctly. It is necessary to decide what equation of state to use for the vapor phase (ideal gas, Redlich-Kwong-Soave, Peng-Robinson, etc.) and what model to use for liquid activity coefficients [ideal solutions, solubility parameters, Wilson equation, nonrandom two liquid (NRTL), UNIFAC, etc.]. See Sec. 4, Thermodynamics. It is necessary to consider mixtures of chemicals, and the interaction parameters must be predictable. The best case is to determine them from data, and the next-best case is to use correlations based on the molecular weight, structure, and normal boiling point. To validate the model, the computer results of vapor-liquid equilibria could be checked against experimental data to ensure their validity before the data are used in more complicated computer calculations. 

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