Liquid phase activity coefficient Wilson equation

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. 

Table 13-1, based on the binary-system activity-coefficient-eqnation forms given in Table 13-3. Consistent Antoine vapor-pressure constants and liquid molar volumes are listed in Table 13-4. The Wilson equation is particularly useful for systems that are highly nonideal but do not undergo phase splitting, as exemplified by the ethanol-hexane system, whose activity coefficients are snown in Fig. 13-20. For systems such as this, in which activity coefficients in dilute regions may...

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. 

The boiling point of THF at 5 atm (404.2 K) is chosen as the reference temperature. The liquid phase activity coefficients were calculated using the Wilson equation... 

Application of the Wilson equation for evaluation of activity coefficients requires knowledge of the liquid-phase composition. We therefore calculate x, by Eq. (12.27) ... 

The fugacity coefficient is usually obtained by solving an equation of state (e.g., Peng-Robinson Redlich-Kwong). The activity coefficient is obtained from a liquid phase activity model such as Wilson or NRTL (see Walas, 1985). 

The development of equations that successfully predict multicomponent phase equilibrium data from binary data with remarkable accuracy for engineering purposes not only improves the accuracy of tray-to-tray calculations but also lessens the amount of experimentation required to establish the phase equilibrium data. Such equations are the Wilson equation (13), the non-random two-liquid (NRTL) equation (14), and the local effective mole fractions (LEMF) equation (15, 16), a two-parameter version of the basically three-parameter NRTL equation. Larson and Tassios (17) showed that the Wilson and NRTL equations predict accurately ternary activity coefficients from binary data Hankin-son et al. (18) demonstrated that the Wilson equation predicts accurately... 

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. 

The liquid phase is a non-ideal solution, for which liquid activity coefficients can be predicted with good accuracy by the Wilson equation (Equation 1.36). The vapor phase is assumed to behave as an ideal gas at the relatively low pressure of 35 kPa. Under these conditions, the K-values may be calculated by Equation 1.29a. 

Activity coefficients are generally predicted by one of the Wilson, UNIQUAC, NRTL, or van Laar methods. The Wilson and UNIQUAC methods are presented briefly here. Most chemical engineering thermodynamics textbooks have a section on phase equilibria that can provide more detailed descriptions. The Wilson equation [1] is only used with miscible fluids. For highly non-ideal fluids and for systems in which liquid-liquid splitting occurs, the NRTL method is applicable [2], When no experimental data are available, the UNIQUAC method can be used [3,4]. 

Laar Margules Wilson nonrandom, two liquid phases (NRTL), or Renon-Prausnitz and Universal Quasi-Chemical Activity Coefficients (UNIQUAC). All of these equations have two constants except for the NRTL, which has three. 

The use of the Wilson equation for liquid-liquid equihbrium is unusual because the equation cannot predict phase separation. In the present application the equation is not being used to predict immiscibility-the organic and water phase are assumed to be immiscible. The Wilson equation is used instead to correlate activity coefficients in the miscible range for the hydrocarbon-cosolvent and water-cosolvent systems. 

The Wilson equation can be extended to immiscible liquid systems by multiplying the right-hand side of (5-41) by a third binary-pair constant evaluated from experimental data. However, for multicomponent systems of three or more species, the third binary-pair constants must be the same for all constituent binary pairs. Furthermore, as shown by Hiranuma, representation of ternary systems involving only one partially miscible binary pair can be extremely sensitive to the third binary-pair Wilson constant. For these reasons, application of the Wilson equation to liquid-liquid systems has not been widespread. Rather, the success of the Wilson equation for prediction of activity coefficients for miscible liquid systems greatly stimulated further development of the local composition concept in an effort to obtain more universal expressions for liquid-phase activity coefficients. 

In an attempt to place calculations of liquid-phase activity coefficients on a simpler, yet more theoretical basis, Abrams and Prausnitz used statistical mechanics to derive a new expression for excess free energy. Their model, called UNIQUAC (universal qua si-chemical), generalizes a previous analysis by Guggenheim and extends it to mixtures of molecules that differ appreciably in size and shape. As in the Wilson and NRTL equations, local concentrations are used. However, rather than local volume fractions or local mole fractions, UNIQUAC uses the local area fraction 0,j as the primary concentration variable. 

Most of the empirical and semitheoretical equations for liquid-phase activity coefficient listed in Table 5.3 apply to liquid-liquid systems. The Wilson equation is a notable exception. As examples, the van Laar equation will be discussed next, followed briefly by the NRTL, UNIQUAC, and UNIFAC equations. 

The Wilson constants for the ethanol(l)-benzene(2) system at 45°C are Ai2 = 0.124 and A2i= 0.523. Use these constants with the Wilson equation to predict the liquid-phase activity coefficients for this system over the entire range of composition and compare them in a plot like Fig. 5.5 with following experimental results lAust. J. Chem., 7, 264 (1954)]. 

A Fortran programme has been elaborated by Williams and Henley [89] for tlie computation of multicomponent vapour-liquid equilibria. To take into account real behaviours a number of subprogrammes are available which enable fugacities to be calculated by means of the virial equation, the Redlich-Kwong relation or according to Chao-Seader. Activity coefficients may be considered following Wilson, van baar or Hildebrand. The state of the art of precalculating vapour-liquid equilibria in multicomponent mixtures was surveyed by Hala [89a]. Lu and Polak [89b] discussed the special requirements for the calculation of phase equilibria at low temperatures (20 K to room temperature). 

If a liquid phase appears, it will definitely be nonideal, and we adopt the Wilson equation ( 5.6.5) as the model for liquid-phase activity coefficients. Values of the parameters A,y in the Wilson model were taken from McDonald and Floudas [25], who in turn abstracted them from Suzuki et al. [27] the values are given in Table 11.9. We assume the vapor at 1.0133 bar is an ideal gas, so the activities are merely... 

The introductory discussion of models for liquid-phase activity coefficients, presented in Chapter 5, included a description of the Wilson equation, which is appropriate for many nonelectrolyte mixtures that exhibit large deviations from ideality. However, the Wilson model cannot correlate liquid-liquid equilibrium data, and therefore it cannot be used in LLE and VLLE calculations. To overcome this deficiency, Renon and Prausnitz [1] devised the NRTL model for (NonRandom, Two-Liquid). 

Vapor-Liquid Equilibrium Data Collection (Gmehling et al., 1980). In this DECHEMA data bank, which is available both in more than 20 volumes and electronically, the data from a large fraction of the articles can be found easily. In addition, each set of data has been regressed to determine interaction coefficients for the binary pairs to be used to estimate liquid-phase activity coefficients for the NRTL, UNIQUAC, Wilson, etc., equations. This database is also accessible by process simulators. For example, with an appropriate license agreement, data for use in ASPEN PLUS can be retrieved from the DECHEMA database over the Internet. For nonideal mixtures, the extensive compilation of Gmehling (1994) of azeotropic data is very useful. 

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