Vapor-liquid equilibrium binary interaction parameter

Traditionally, the binary interaction parameters such as the ka, kb, k, ki in the Trebble-Bishnoi EoS have been estimated from the regression of binary vapor-liquid equilibrium (VLE) data. It is assumed that a set of N experiments have been performed and that at each of these experiments, four state variables were measured. These variables are the temperature (T), pressure (P), liquid (x) and vapor (y) phase mole fractions of one of the components. The measurements of these variables are related to the "true" but unknown values of the state variables by the equations given next... 

Data at two temperatures were obtained from Zeck and Knapp (1986) for the nitrogen-ethane system. The implicit LS estimates of the binary interaction parameters are ka=0, kb=0, kc=0 and kd=0.0460. The standard deviation of kd was found to be equai to 0.0040. The vapor liquid phase equilibrium was computed and the fit was found to be excellent (Englezos et al. 1993). Subsequently, implicit ML calculations were performed and a parameter value of kd=0.0493 with a standard deviation equal to 0.0070 was computed. Figure 14.2 shows the experimental phase diagram as well as the calculated one using the implicit ML parameter estimate. 

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 distillation calculation is to be performed on a multicomponent mixture. The vapor-liquid equilibrium for this mixture is likely to exhibit significant departures from ideality, but a complete set of binary interaction parameters is not available. What factors would you consider in assessing whether the missing interaction parameters are likely to have an important effect on the calculations ... 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

Initial values of the binary interaction parameters were obtained from vapor-liquid equilibrium data for ternary mixtures (9). These interaction parameters were then adjusted to minimize the difference between calculated and measured phase compositions for the three-phase equilibria measured at 50 C. 

A modified local composition (LC) expression is suggested, which accounts for the recent finding that the LC in an ideal binary mixture should be equal to the bulk composition only when the molar volumes of the two pure components are equal. However, the expressions available in the literature for the LCs in binary mixtures do not satisfy this requirement. Some LCs are examined including the popular LC-based NRTL model, to show how the above inconsistency can be eliminated. Further, the emphasis is on the modified NRTL model. The newly derived activity coefficient expressions have three adjustable parameters as the NRTL equations do, but contain, in addition, the ratio of the molar volumes of the pure components, a quantity that is usually available. The correlation capability of the modified activity coefficients was compared to the traditional NRTL equations for 42 vapor—liquid equilibrium data sets from two different kinds of binary mixtures (i) highly nonideal alcohol/water mixtures (33 sets), and (ii) mixtures formed of weakly interacting components, such as benzene, hexafiuorobenzene, toluene, and cyclohexane (9 sets). The new equations provided better performances in correlating the vapor pressure than the NRTL for 36 data sets, less well for 4 data sets, and equal performances for 2 data sets. Similar modifications can be applied to any phase equilibrium model based on the LC concept. 

The gas phase of the system will mainly consist of H20(g), NHj(g), and C02(g). In order to perform vapor-liquid equilibrium calculations with an activity coefficient model at pressures higher than ambient pressure, the activity coefficient model can be combined with an equation of state for the gases. Usually, there is no need for binary interaction parameters in the equation of state as gas phase fiigacities are only slightly dependent on these binary interaction parameters. For the equilibrium between ammonia in the liquid phase and ammonia in the vapor phase. Equation (13) gives ... 

In using simulation software, it is important to keep in mind that the quality of the results is highly dependent upon the quahty of the liquid-liquid equilibrium (LLE) model programmed into the simulation. In most cases, an experimentally vmidated model will be needed because UNIFAC and other estimation methods are not sufficiently accurate. It also is important to recognize, as mentioned in earlier discussions, that binary interaction parameters determined by regression of vapor-liquid equilibrium (VLE) data cannot be rehed upon to accurately model the LLE behavior for the same system. On the other hand, a set of binary interaction parameters that model LLE behavior properly often will provide a reasonable VLE fit for the same system—because pure-component vapor pressures often dominate the calculation of VLE. 

Once the interaction energies were obtained, they were used to calculate the parameters in the UNIQUAC and Wilson models given by Eq. (24). To test the validity of the method, low-pressure vapor-liquid equilibrium (VLE) predictions were made for several binary aqueous systems. The calculations were done using the usual method assuming an ideal vapor phase (Sandler, 1999). Figures 7 and 8 show the low-pressure VLE diagrams for the binary aqueous mixtures of ethanol and acetone [see Sum and Sandler (1999a,b) for results for additional systems and values of the... 

Here a new parameter jiry, known as the binary interaction parameter, has been introduced to result in more accurate mixture equation-of-state calculations. This parameter is found by fitting the equation of state to mixture data (usually vapor-liquid equilibrium data, as discussed in Chapter 10). Values of the binary interaction parameter k - that have been reported for a number of binary mixtures appear in Table 9.4-1. Equations 9.4-8 and 9.4-9 are referred to as the van der Waals one-fluid mixing rules. The term one-fluid derives from the fact that the mixture is being described by the same equation of state as the pure fluids, but with concentration-dependent parameters. 

Consequently, by a regression analysis of very large quantities of activity coefficient (or, as we will see in Sec. 10.2, actually vapor-liquid equilibrium) data, the binary parameters Onm Omn for many group-group interactions can be determined. These parameters can then be used to predict the activity coefficients in mixtures (binary or multicomponent) for which no experimental data are available. 

Using the proposed procedure in conjunction with literature values for the density (11) and vapor pressure (12) of solid carbon dioxide, the solid-formation conditions have been determined for a number of mixtures containing carbon dioxide as the solid-forming component. The binary interaction parameters used in Equation 14 were the same as those used previously for two-phase vapor-liquid equilibrium systems (6). The value for methane-carbon dioxide was 0.110 and that for ethane-carbon dioxide was 0.130. Excellent agreement has been obtained between the calculated results and the experimental data found in the literature. As shown in Figure 2, the predicted SLV locus for the methane-carbon... 

The unlike pair interaction parameter is determined using binary vapor-liquid equilibrium data as described by Zudkevitch and Joffe (2). The systems used in this study are given in Table I. The interaction... 

When accurate experimental data are available for a binary pair at several different temperatures under vapor-liquid and/or liquid-liquid conditions, plots of the best values for UNIQUAC binary interaction parameters appear to be smooth linear functions of temperature. Often, variations are small over moderate ranges of temperature as shown in Fig. 5.10 for ethanol-n-octane under vapor-liquid equilibrium conditions. 

Values for critical temperature, pressure, and acentric factor for all five components participating in the system are given in Table 9.2. Values for the binary interaction parameters used in Equation 9.28c are given in Table 9.3. Note that the values found in Table 9.3 were obtained from different sources. Where the interaction parameters are unknown, the k, values are zero for the purposes of demonstration. More accurate predictions may be obtained by fitting the relevant vapor-liquid equilibrium data, if available. 

The gas-lattice model considers liquids to be a mixture of randomly distributed occupied and vacant sites. P and T can change the concentration of holes, but not their size. A molecule may occupy m sites. Binary liquid mixtures are treated as ternary systems of two liquids (subscripts 1 and 2 ) with holes (subscript 0 ). The derived equations were used to describe file vapor-Uquid equilibrium of n-alkanes they also predicted well the phase behavior of -alkanes/PE systems. The gas-lattice model gives the non-combinatorial Helmotz free energy of mixing expressed in terms of composition and binary interaction parameters, quantified through interaction energies per unit contact area (Kleintjens 1983 Nies et aL 1983) ... 

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