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Laar Activity Coefficients

Figure 6.2.2. Excess enthalpy for the benzene and cyclohexane system at 293 K (dots) and at 393 K (triangles), Tlie lines denote correlations at 293 K and predictions at 393 K using various models. The solid line reflects predictions using the 2PVDW model, the dotted line represents the predictions using the van Laar activity coefficient mode , the short dashed lines signify predictions using the HVOS model, and the long dashed line denotes predictions made with the WS model. Data are from the DECHEMA Chemistry Series (Gmehling and Onken 1977, Vol. 3, Pt. 2, p. 992). Figure 6.2.2. Excess enthalpy for the benzene and cyclohexane system at 293 K (dots) and at 393 K (triangles), Tlie lines denote correlations at 293 K and predictions at 393 K using various models. The solid line reflects predictions using the 2PVDW model, the dotted line represents the predictions using the van Laar activity coefficient mode , the short dashed lines signify predictions using the HVOS model, and the long dashed line denotes predictions made with the WS model. Data are from the DECHEMA Chemistry Series (Gmehling and Onken 1977, Vol. 3, Pt. 2, p. 992).
These equations, along with the van Laar activity coefficient equations, can be solved for the compositions and the amounts of each liquid phase. [Pg.115]

The van Laar activity coefficient model will be used. From Eqs. 10.2-19, we have... [Pg.543]

Using the van Laar activity coefficient model as in Illustration 11.2-2 and the liquid-phase compositions found there, and assuming the vapor phase is ideal, we have the bubble point pressure of liquid phase I as... [Pg.626]

The van Laar activity coefficients that are consistent with this model are... [Pg.817]

TABLE 29-1 Parameters of the van Laar Activity Coefficient Model... [Pg.817]

Based on the van Laar activity coefficient parameters in Table 29-1. [Pg.820]

Van Laar activity coefficient equations. The van Laar activity coefficient model is based on the assumption that — 0 and = 0. Therefore,. In other words, the model allows for heat of mixing but does not allow for volume change on mixing. Van Laar used the van der Waals EOS to calculate and then Eq. (1.144) can be used to obtain the activity coefficients. The predicted activity coefficients for a binary system are... [Pg.30]

A,B Three-suffix Margules or van Laar activity coefficient model parameters... [Pg.710]

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. [Pg.99]

This, the Wilson model, is more complex than the Van Laar model, but it does retain the two-parameter feature. The terminal activity coefficients are related to the parameters ... [Pg.158]

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. [Pg.415]

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. [Pg.539]

It is desirable to use activity coefficients which satisfy Eq. (48) rather than Eqs. (45) or (46) because all well-known mixture models (e.g., Van Laar,... [Pg.159]

From the dilated van Laar model, Chueh obtains two-parameter expressions for the activity coefficients. They are ... [Pg.177]

It is easily possible to introduce refinements into the dilated van Laar model which would further increase its accuracy for correlating activity coefficient data. However, such refinements unavoidably introduce additional adjustable parameters. Since typical experimental results of high-pressure vapor-liquid equilibria at any one temperature seldom justify more than two adjustable parameters (in addition to Henry s constant), it is probably not useful for engineering purposes to refine Chueh s model further, at least not for nonpolar or slightly polar systems. [Pg.178]

While the dilated van Laar model gives a reliable representation of constant-pressure activity coefficients for nonpolar systems, the good agreement between calculated and experimental high-pressure phase behavior shown in Fig. 14 is primarily a result of good representation of the partial molar volumes, as discussed in Section IV. The essential part of any thermodynamic description of high-pressure vapor-liquid equilibria must depend,... [Pg.178]

For the estimation of activity coefficients the Van Laar equation is used. [Pg.611]

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. [Pg.282]

For systems that are only partially miscible in the liquid state, the activity coefficient in the homogeneous region can be calculated from experimental values of the mutual solubility limits. The methods used are described by Reid et al. (1987), Treybal (1963), Brian (1965) and Null (1970). Treybal (1963) has shown that the Van-Laar equation should be used for predicting activity coefficients from mutual solubility limits. [Pg.347]

The Margules and van Laar equations apply only at constant temperature and pressure, as they were derived from equation 11.21, which also has this restriction. The effect of pressure upon y values and the constants and 2i is usually negligible, especially at pressures far removed from the critical. Correlation procedures for activity coefficients have been developed by Balzhiser et al.(ll Frendenslund et alSls>, Praunsitz et alS19>, Reid et al. 2 ) van Ness and Abbott(21) and Walas 22 and actual experimental data may be obtained from the PPDS system of the National Engineering Laboratory, UK1-23). When the liquid and vapour compositions are the same, that is xA = ya, point xg in... [Pg.554]

The activity coefficients were assumed to satisfy van Laar equations of the form... [Pg.67]

A popular model to describe the activity coefficients is the van Laar equation... [Pg.215]

To illustrate the system behavior, the ternary mixture 1 = iso-propanol, 2 = water, and 3 = air is considered here. In order to obtain an algebraic solution, both the dif-fusivities of iso-propanol in air and iso-propanol in water vapor were assumed to be approximately the same, which is not far from reality. The liquid phase mass transfer resistance was negligibly small, as will be shown below. The phase equilibrium constants K/,c and Kjrs were calculated with activity coefficients from van Laar s equation. Water vapor diffuses 2.7-fold faster in the inert gas air than iso-propanol. The ratio of the respective mass transfer coefficients kj3 equals the ratio of the respective diffusivities to the power of 2/3rd according to standard convective mass transfer equations Sh =J Re, Sc). [Pg.112]

From the isothermal vapor-liquid equilibrium data for the ethanol(l)/toluene(2) system given in Table 1.11, calculate (a) vapor composition, assuming that the liquid phase and the vapor phase obey Raoult s and Dalton s laws, respectively, (b) the values of the infinite-dilution activity coefficients, Y and y2°°, (c) Van Laar parameters using data at the azeotropic point as well as from the infinite-dilution activity coefficients, and (d) Wilson parameters using data at the azeotropic point as well as from the infinite-dilution activity coefficients. [Pg.47]

In these equations, y, and y2 are activity coefficients of components 1 and 2, respectively, GE is Gibbs molar excess free energy, A, 2 and A2j, are Van Laar parameters, G, 2 and G2j, are Wilson parameters, that is,... [Pg.48]

Related Calculations. These calculations show how to use vapor-liquid equilibrium data to obtain parameters for activity-coefficient correlations such as those of Van Laar and Wilson. (Use of liquid-liquid equilibrium data for the same purpose is shown in Example 1.20.) If the system forms an azeotrope, the parameters can be obtained from a single measurement of the azeotropic pressure and the composition of the constant boiling mixture. If the activity coefficients at infinite dilution are available, the two parameters for the Van Laar equation are given directly, and the two in the case of the Wilson equation can be solved for as shown in the example. [Pg.50]

Related Calculations. The constants for the binary Margules and Van Laar models for predicting activity coefficients (see Related Calculations under Example 3.4) are simply the natural logarithms of the infinite-dilution activity coefficients A t2 = I n y(XJ and /12,1 = I n y2XJ. [Pg.115]

For this system, / " may be assumed to be the same as the vapor pressure (for a discussion of the grounds for this assumption, see Example 3.6). Activity coefficients can be calculated using the Wilson, Margules, or Van Laar equations (see Example 3.4). [Pg.118]

The Modified van Laar equations (I) have been used to calculate the liquid phase activity coefficients. Coefficients at three temperatures are given in Table III. These are used by the computer to calculate activity coefficients at any composition and temperature in the distillation column. [Pg.12]

So that an azeotrope with acetone does not form, the alcohol used must have a high enough boiling point. This requirement is reliably established only if vapor-liquid equilibrium data for at least two, preferably three, of the members of the series with acetone are known. The Pierotti-Deal-Derr method (4) (discussed later) or the Tassios-Van Winkle method (5) can be used in this case. In the latter method a log-log plot of y°i vs. P°i should yield a straight line. Figure 1 presents results for n-alco-hols and benzene from the isobaric (760 mm Hg) data of Wehe and Coates (6). Reliable infinite dilution activity coefficients are established for the other n-alcohols from data for at least two, and preferably three, of them. These y° values are used with equations like those of Van Laar or Wilson (7) to generate activity coefficients at intermediate compositions and to check for an existing azeotrope or a difficult separation (x-y curve close to the 45° line). [Pg.57]

From Equations 1 and 2, the phase equilibria depend upon knowing the pure component vapor pressures P 0, liquid phase activity coefficients ji and imperfection-pressure coefficients ft. The computer program which has been developed uses any of four different vapor pressure equations for providing Pi°. It uses the modified van Laar Equations (5) to give liquid phase activity coefficients and a Modified van der Waals Equation of State (4,6) to give imperfection-pressure coefficients ft. [Pg.75]

Either isothermal or isobaric vapor—liquid equilibria or both are calculated with a subprogram called VLE. For SOLTER and VLE, Modified van Laar coefficients for two or three temperatures give the data by which liquid phase activity coefficients are calculated for both... [Pg.76]

The results obtained in the solution of a sample problem are summarized here to illustrate the application of the method. An extractive distillation problem from Oliver (6) was used in which methylcyclo-hexane is separated from toluene by adding phenol. The column contains 11 stages (including the reboiler and condenser) and has a feed of 0.4 moles/unit time of methylcyclohexane and 0.6 moles/unit time of toluene to the fourth stage from the reboiler and 4.848 moles/unit time of phenol to the fourth stage from the condenser. We used the same physical property correlations as Oliver. The activity coefficients were obtained from a multicomponent form of the Van Laar Equation (7). [Pg.141]


See other pages where Laar Activity Coefficients is mentioned: [Pg.176]    [Pg.97]    [Pg.176]    [Pg.97]    [Pg.1294]    [Pg.190]    [Pg.45]    [Pg.49]    [Pg.110]    [Pg.111]    [Pg.118]    [Pg.11]    [Pg.68]    [Pg.1117]   


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