Equilibrium data, accuracy

In Equation (24), a is the estimated standard deviation for each of the measured variables, i.e. pressure, temperature, and liquid-phase and vapor-phase compositions. The values assigned to a determine the relative weighting between the tieline data and the vapor-liquid equilibrium data this weighting determines how well the ternary system is represented. This weighting depends first, on the estimated accuracy of the ternary data, relative to that of the binary vapor-liquid data and second, on how remote the temperature of the binary data is from that of the ternary data and finally, on how important in a design the liquid-liquid equilibria are relative to the vapor-liquid equilibria. Typical values which we use in data reduction are Op = 1 mm Hg, = 0.05°C, = 0.001, and = 0.003... 

For gas-liquid solutions which are only moderately dilute, the equation of Krichevsky and Ilinskaya provides a significant improvement over the equation of Krichevsky and Kasarnovsky. It has been used for the reduction of high-pressure equilibrium data by various investigators, notably by Orentlicher (03), and in slightly modified form by Conolly (C6). For any binary system, its three parameters depend only on temperature. The parameter H (Henry s constant) is by far the most important, and in data reduction, care must be taken to obtain H as accurately as possible, even at the expense of lower accuracy for the remaining parameters. While H must be positive, A and vf may be positive or negative A is called the self-interaction parameter because it takes into account the deviations from infinite-dilution behavior that are caused by the interaction between solute molecules in the solvent matrix. 

Consider the accuracy of the equilibrium data required to calculate the number of equilibrium stages needed for the separation of a mixture of acetone and water by distillation (see Chapter 11, Example 11.2). Several investigators have published vapour-liquid equilibrium data for this system Othmer et al. (1952), York and Holmes (1942), Kojima et al. (1968), Reinders and De Minjer (1947). 

At low reflux ratios the calculated number of stages will be very dependent on the accuracy of the vapour-liquid equilibrium data available. If the data are suspect a higher than normal ratio should be selected to give more confidence in the design. 

A binary mixture is to be separated by distillation into relatively pure products. Where in the distillation column is the vapor-liquid equilibrium data required at the highest accuracy ... 

The equilibrium adsorption characteristics of gas or vapor on a solid resemble in many ways the equilibrium solubility of a gas in a liquid. Adsorption equilibrium data are usually portrayed by isotherms lines of constant temperature on a plot of adsorbate equilibrium partial pressure versus adsorbent loading in mass of adsorbate per mass of adsorbent. Isotherms take many shapes, including concave upward and downward, and S-curves. Equilibrium data for a given adsorbate-adsorbent system cannot generally be extrapolated to other systems with any degree of accuracy. 

The NRTL-SAC model was first published in 2004 [1] and is still being developed by the authors. The parameter tables are likely to change as new equilibrium data and solvents are added to improve its accuracy and functionality. The solvent parameters and binary interaction values used in this example are given in Tables 2 and 13. 

Equilibrium data usually have to be determined by tedious laboratory methods. Proposals have been made which enable the complete diagram to be deduced with reasonable accuracy from a relatively small number of experimental values. Some of these methods are discussed by Robinson and Gilliam) 1 1 and by Thornton and Garner . 

For borane complexes of intermediate strength the order of relative stabilities can also be estimated from equilibrium data as well, obtained in gas phase or in solution.11,23 From the temperature dependence of the equilibrium constant for the dissociation in the gas phase the A% values can be determined with great accuracy.22... 

Existing correlations of phase equilibrium data contain many regressed parameters, they are often semi-empirical, and they may be successful in fitting the data in parts of the phase diagram -even with high accuracy. As far as prediction is concerned, models developed for that purpose attempt to justify theoretically a link between the model parameters and real physical phenomena. However, the distinction between these two methods is often lost, since theoretically based models are forced to fit the data better by the introduction of additional adjustable parameters. 

At high pressures, especially approaching the critical pressure, the accuracy of the vapour-liquid equilibrium data are questionable. Direct measurement is not easy prediction with equations of state is risky [1],... 

The three sets of vapor-liquid equilibrium data appearing on the x-y diagram show some disagreement, so that great accuracy cannot be expected from determination of tray requirements, particularly at the low water concentrations. The upper operating line in the first column is determined by the overall material balance so it passes through point (0.995, 0.995), but the initial point on the operating line is at x = 0.53, which is the composition of the reflux. The construction is shown for 50% vaporized feed. That result and those for other feed conditions are summarized ... 

Gas and Liquid Phases. Equilibrium data (P-V-T) and thermodynamic properties for the single-component systems water (steam) and ammonia are complete and apparently of the best accuracy because of the extensive use of these substances in cyclic systems 14,20). 

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... 

The calculational base consists of equilibrium relations and material and energy balances. Equilibrium data for many binary systems are available as tabulations of v vs. y at constant temperature or pressure or in graphical form as on Figure 13.3. Often they can be extended to other pressures or temperatures or expressed in mathematical form as explained in Section 13.1. Sources of equilibrium data are listed in the references. Graphical calculation of distillation problems often is the most convenient method, but numerical procedures may be needed for highest accuracy. 

Through repetition of the same experiment and subsequent evaluation of the equilibrium data, the accuracy may be increased by averaging the values, if no systematic errors occur. Too high a deviation between equivalent measurements indicates problems in either the data evaluation or the experiment itself. In the latter case, it should be checked if the pumps deliver a constant flow rate and that the temperature is constant in the range of a few tenths of one centigrade. If the eluent consists of a fluid mixture, the influence of slight changes in eluent composition must be taken into account (Section 6.5.7.1). 

The difficulty of reaching general conclusions is most serious, however. Comparisons are possible only between carefully optimized procedures, which may take a significant amount of time, as it requires the acquisition of a large amoimt of accurate thermodynamic data. Band profiles depend so much on the exact features of the isotherms that a high degree of accuracy, first in the measmement and then in the modeling of the equilibrium data, is required. 

The constants may, in fact, be calculated from a single equilibrium data point (vapor-liquid or liquid-liquid if intended for liquid-liquid equilibrium calculations) although the results would be heavily weighted to that point, probably resulting in less accuracy for the remaining range of compositions. 

The constants proposed by Starling for mixtures are presented in Ref. 65. With the advantage of increased accuracy achieved by use of the 11-constant equation proposed by Starling65 came the disadvantage that the constants could no longer be obtained from pure component properties. Experimental equilibrium data, density data, and enthalpy data for mixtures had to be included in the regression procedure for obtaining the constants.2... 

While the Redlich-Kwong equation is said to give volumetric and thermal properties of pure components and of mixtures with good accuracy, the vapor-liquid-equilibrium data predicted by this equation often gives poor results.59 To improve this equation for the prediction of vapor-liqnid-equilibrium data, Soave59 proposed the following modified form of the Redlich-Kwong equation of state... 

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