Activity coefficient vapor-liquid equilibrium

C vapor-liquid equilibrium-activity coefficient, measured range 20-50°C, Cooling et al. 1992)... 

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. 

The analogy between equations derived from the fundamental residual- and excess-propeily relations is apparent. Whereas the fundamental lesidanl-pL-opeRy relation derives its usefulness from its direct relation to equations of state, the ci cc.s.s-property formulation is useful because V, and y are all experimentally accessible. Activity coefficients are found from vapor/liquid equilibrium data, and and values come from mixing experiments. 

Gmehhng and Onken (Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt, Germany, 1979) have reported a large collection of vapor-liqnid equilibrium data along with correlations of the resulting activity coefficients. This can be used to predict liqnid-hqnid equilibrium partition ratios as shown in Example 1. 

Gmehhng and Onken (op. cit.) give the activity coefficient of acetone in water at infinite dilution as 6.74 at 25 C, depending on which set of vapor-liquid equilibrium data is correlated. From Eqs. (15-1) and (15-7) the partition ratio at infinite dilution of solute can he calculated as follows ... 

Several activity coefficient models are available for industrial use. They are presented extensively in the thermodynamics literature (Prausnitz et al., 1986). Here we will give the equations for the activity coefficients of each component in a binary mixture. These equations can be used to regress binary parameters from binary experimental vapor-liquid equilibrium data. 

Experimental values for the activity coefficients for components 1 and 2 are obtained from the vapor-liquid equilibrium data. During an experiment, the following information is obtained Pressure (P), temperature (T), liquid phase mole fraction (x, and x2=l-X ) and vapor phase mole fraction (yi and y2=l—yi). 

Table 15.7 Vapor-Liquid Equilibrium Data and Activity Coefficients for...

This expression provides the basis for vapor-liquid equilibrium calculations on the basis of liquid-phase activity coefficient models. In Equation 4.27, thermodynamic models are required for cf>y (from an equation of state) and y, from a liquid-phase activity coefficient model. Some examples will be given later. At moderate pressures, the vapor phase becomes ideal, as discussed previously, and fj = 1. For... 

VAPOR-LIQUID EQUILIBRIUM BASED ON ACTIVITY COEFFICIENT MODELS... 

These models are semiempirical and are based on the concept that intermolecular forces will cause nonrandom arrangement of molecules in the mixture. The models account for the arrangement of molecules of different sizes and the preferred orientation of molecules. In each case, the models are fitted to experimental binary vapor-liquid equilibrium data. This gives binary interaction parameters that can be used to predict multicomponent vapor-liquid equilibrium. In the case of the UNIQUAC equation, if experimentally determined vapor-liquid equilibrium data are not available, the Universal Quasi-chemical Functional Group Activity Coefficients (UNIFAC) method can be used to estimate UNIQUAC parameters from the molecular structures of the components in the mixture3. 

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. 

Although the methods developed here can be used to predict liquid-liquid equilibrium, the predictions will only be as good as the coefficients used in the activity coefficient model. Such predictions can be critical when designing liquid-liquid separation systems. When predicting liquid-liquid equilibrium, it is always better to use coefficients correlated from liquid-liquid equilibrium data, rather than coefficients based on the correlation of vapor-liquid equilibrium data. Equally well, when predicting vapor-liquid equilibrium, it is always better to use coefficients correlated to vapor-liquid equilibrium data, rather than coefficients based on the correlation of liquid-liquid equilibrium data. Also, when calculating liquid-liquid equilibrium with multicomponent systems, it is better to use multicomponent experimental data, rather than binary data. 

Prediction of liquid-liquid equilibrium also requires an activity coefficient model. The choice of models of liquid-liquid equilibrium is more restricted than that for vapor-liquid equilibrium, and predictions are particularly sensitive to the model parameters used. 

Chapter 17 - Vapor-liquid equilibrium (VLE) data are important for designing and modeling of process equipments. Since it is not always possible to carry out experiments at all possible temperatures and pressures, generally thermodynamic models based on equations on state are used for estimation of VLE. In this paper, an alternate tool, i.e. the artificial neural network technique has been applied for estimation of VLE for the binary systems viz. tert-butanol+2-ethyl-l-hexanol and n-butanol+2-ethyl-l-hexanol. The temperature range in which these models are valid is 353.2-458.2K at atmospheric pressure. The average absolute deviation for the temperature output was in range 2-3.3% and for the activity coefficient was less than 0.009%. The results were then compared with experimental data. 

Two New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte Systems... 

A wide variety of data for mean ionic activity coefficients, osmotic coefficients, vapor pressure depression, and vapor-liquid equilibrium of binary and ternary electrolyte systems have been correlated successfully by the local composition model. Some results are shown in Table 1 to Table 10 and Figure 3 to Figure 7. In each case, the chemical equilibrium between the species has been ignored. That is, complete dissociation of strong electrolytes has been assumed. This assumption is not required by the local composition model but has been made here in order to simplify the systems treated. 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Figure 7 shows the predicted vapor-phase mole fractions of HC1 at 25°C as a function of the liquid-phase molality of HC1 for a constant NaCl molality of 3. Also included are predicted vapor-phase mole fractions of HC1 when the interaction parameter A23 is taken as zero. There are unfortunately no experimental vapor-liquid equilibrium data available for the HC1-NaCl-FLO system however, considering the excellent description of the liquid-phase activity coefficients and the low total pressures, it is expected that predicted mole fractions would be within 2-3% of the experimental values. 

Calculate the temperatures and vapor compositions from the vapor-liquid equilibrium data, using the subroutine BUfiPT. Raoult s law is used in the example, but nonideality can be included by adding activity coefficient equations. Newton-Raphson convergence is used. 

A procedure is presented for correlating the effect of non-volatile salts on the vapor-liquid equilibrium properties of binary solvents. The procedure is based on estimating the influence of salt concentration on the infinite dilution activity coefficients of both components in a pseudo-binary solution. The procedure is tested on experimental data for five different salts in methanol-water solutions. With this technique and Wilson parameters determined from the infinite dilution activity coefficients, precise estimates of bubble point temperatures and vapor phase compositions may be obtained over a range of salt and solvent compositions. 

Measurements of binary vapor-liquid equilibria can be expressed in terms of activity coefficients, and then correlated by the Wilson or other suitable equation. Data on all possible pairs of components can be combined to represent the vapor-liquid behavior of the complete mixture. For exploratory purposes, several rapid experimental techniques are applicable. For example, differential ebulliometry can obtain data for several systems in one laboratory day, from which infinite dilution activity coefficients can be calculated and then used to evaluate the parameters of correlating equations. Chromatography also is a well-developed rapid technique for vapor-liquid equilibrium measurement of extractive distillation systems. The low-boiling solvent is deposited on an inert carrier to serve as the adsorbent. The mathematics is known from which the relative volatility of a pair of substances can be calculated from the effluent trace of the elutriated stream. Some of the literature of these two techniques is cited by Walas (1985, pp. 216-217). 

Henry s lxm> Constant Henry s law for dilute concentrations of contaminants in water is often appropriate for modeling vapor—liquid equilibrium (VLE) behavior (47). At very low concentrations, a chemical s Henry s constant is equal to the product of its activity coefficient and vapor pressure (3,10,48). Activity coefficient models can provide estimated values of infinite dilution activity coefficients for calculating Henry s constants as a function of... 

The same reference (standard) state, f is chosen for the two phases, so that it cancels on both sides of equation 39. The products stffi and y" are referred to as activities. Because equation 39 holds for each component of a liquid—liquid system, it is possible to predict liquid—liquid phase splitting when the activity coefficients of the individual components in a multicomponent system are known. These values can come from vapor—liquid equilibrium experiments or from prediction methods developed for phase-equilibrium problems (4,5,10). Some binary systems can be modeled satisfactorily in this manner, but only rough estimations appear to be possible for multicomponent systems because activity coefficient models are not yet sufficiendy developed in this area. 

Nitric acid is a strong electrolyte. Therefore, the solubilities of nitrogen oxides in water given in Ref. 191 and based on Henry s law are utilized and further corrected by using the method of van Krevelen and Hofhjzer (77) for electrolyte solutions. The chemical equilibrium is calculated in terms of liquid-phase activities. The local composition model of Engels (192), based on the UNIQUAC model, is used for the calculation of vapor pressures and activity coefficients of water and nitric acid. Multicomponent diffusion coefficients in the liquid phase are corrected for the nonideality, as suggested in Ref. 57. 

The usefulness of these equations derives from the fact that y, values are experimentally accessible through vapor/liquid equilibrium (VLE) data, as explained in the following section. Once established, values of the activity coefficients are used in the calculation of phase compositions for systems in vapor/liquid equilibrium, as discussed in Chap. 12. 

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