Relative volatility averaging

The combined Fenske-Underwood-Gillilland method developed by Frank [100] is shown in Figure 8-47. This relates product purity, actual reflux ratio, and relative volatility (average) for the column to the number of equilibrium stages required. Note that this does not consider tray efficiency, as discussed elsewhere. It is perhaps more convenient for designing new columns than reworking existing columns, and should be used only on at acent-key systems. 

Consider an analysis of the same test data, but with an equilibrium curve based on a VLE prediction which gives higher relative volatilities (average of about 2,5) than the experimental data. With the calculated VLE, the McCabe-Thiele diagram (Fig, 7,125) requires only eight theoretical stages. 

Fractionators = (Relative volatiiity of key components) (Viscosity of feed in cenlipoises), Relative volatility and viscosity are taken at average tower conditions between top and bottom. 

Ethylbenzene is separated from mixed xylenes by fractionation using 360 trays and a high reflux ratio. Ethylbenzene is separated from the closest isomer paraxylene whose normal boiling point is only 3.90°F higher. The average relative volatility between ethylbenzene and paraxylene in the fractionation is about 1.06. The fractionator feed is entirely Cg aromatics which are prepared by the extraction of powerformate by the sulfolane process and by fractionation of the aromatic extract. 

Various average values of a for use in these calculations are suggested in the following section on Relative Volatility. ... 

From Fenske s equation, the minimum number of equilibrium stages at total reflux is related to their bottoms (B) and distillate or overhead (D) compositions using the average relative volatility, see Equation 8-29. 

Sm = total number of calculated theoretical trays at total reflux, from Equation 8-30 X]k = xlk = liquid mol fraction of light key Xhk = xhk = liquid mol fraction of heavy key Ik - hk = LK - HK= average relative volatility of column (top to bottom)... 

Wagle [92] presents an estimate method for the average relative volatility of two components, related to the normal boiling points and the latent heats of vaporization of the two components, in the temperature range of their boiling points ... 

The average relative volatility of benzene and toluene can be determined using the following data T b = 353.3 K, Tbt = 383.8 K, Lb = 7,352 kcal/kmole, and = 7,930 kcal/kmole (where the subscripts b and t denote benzene and toluene, respectively). Substituting these values into Equation 8-52 above, we find that ... 

Assume a multicomponent distillation operation has a feed whose component concentration and component relative volatilities (at the average column conditions) are as shown in Table 8-3. The desired recovery of the light key component O in the distillate is to be 94.84%. The recovery of the heavy key component P in the bottoms is to be 95.39%. 

Component C is to be separated from Component D by distillation. A 95% recovery of both key components (LK, HK) is desired. Saturated-liquid feed composition and relative volatilities (at average column conditions) are given in Table 8-5. 

Relative volatilities, Ui, determined at average temperature between bottom and feed of column. Usually the pinch temperature gives just as satisfactory results. 

Nm = minimum number of stages at total reflux, including the reboiler, a, = average relative volatility of the component i with respect to the reference component. 

The average volatilities will be taken as those estimated in Example 11.5. Normally, the volatilities are estimated at the feed bubble point, which gives a rough indication of the average column temperatures. The dew point of the tops and bubble point of the bottoms can be calculated once the component distributions have been estimated, and the calculations repeated with a new estimate of the average relative volatilities, as necessary. 

A quick estimate of the overall column efficiency can be obtained from the correlation given by O Connell (1946), which is shown in Figure 11.13. The overall column efficiency is correlated with the product of the relative volatility of the light key component (relative to the heavy key) and the molar average viscosity of the feed, estimated at the average column temperature. The correlation was based mainly on data obtained with hydrocarbon systems, but includes some values for chlorinated solvents and water-alcohol mixtures. It has been found to give reliable estimates of the overall column efficiency for hydrocarbon systems and can be used to make an approximate estimate of the efficiency for other systems. The method takes no account of the plate design parameters and includes only two physical property variables. 

The Underwood Equation is based on the assumption that the relative volatilities and molar overflow are constant between the pinches. Given that the relative volatilities change throughout the column, which are the most appropriate values to use in the Underwood Equations The relative volatilities could be averaged according to Equations 9.47 or 9.49. However, it is generally better to use the ones based on the feed conditions rather than the average values based on the distillate and bottoms compositions. This is because the location of the pinches is often close to the feed. 

It may be seen that a increases as the temperature falls, so that it is sometimes worthwhile reducing the boiling point by operating at reduced pressure. When Equation 11.16 is used to construct the equilibrium curve, an average value of a must be taken over the whole column. As Frank 13 points out, this is valid if the relative volatilities at the top and bottom of the column differ by less than 15 per cent. If they differ by more than... 

Binary systems of course can be handled by the computer programs devised for multicomponent mixtures that are mentioned later. Constant molal overflow cases are handled by binary computer programs such as the one used in Example 13.4 for the enriching section which employ repeated alternate application of material balance and equilibrium stage-by-stage. Methods also are available that employ closed form equations that can give desired results quickly for the special case of constant or suitable average relative volatility. 

Calculation Methods. An often satisfactory approximation is to take the mixture in the presence of the solvent to be a pseudobinary of the keys on a solvent-free basis, and to employ the McCabe-Thiele or other binary distillation method to find tray and reflux demands. Since the relative volatility varies with concentration of the solvent, different equilibrium curves are used for above and below the feed based on average loads in those zones. Figure 13.25 is of such a construction. 

The viscosity is in cP and E0c is fractional.) The volatility and viscosity are evaluated at the average arithmetic temperature between the column top and bottom temperatures. The relative volatility is between the key components. 

This measure was based upon the ratio of the minimum necessary number of plates, A min (averaged over the reboiler composition) in a column to the actual number of plates in the given column, Nj. Christensen and Jorgensen assumed that the mixture has a constant relative volatility a and the column operates at total reflux using constant distillate composition (x o) strategy (section 3.3.2) and evaluated Nmin using the Fenske equation ... 

Underwood s method (36). This method solves an equation which relates feed composition, thermal condition of the feed, and relative volatility at the average temperature of the column for a factor 6 which lies numerically between the relative volatilities of the keys. This factor is substituted in a second equation which relates minimum reflux to relative volatility and distillate composition. The method assumes constant relative volatility at the mean column temperature and constant molar overflow (Sec. 2.2.2). This method gives reasonable engineering accuracy for systems approaching ideality (28). The Underwood method has traditionally been the most popular for minimum reflux determination, When no distributed key components are present, the method is... 

Varying relative volatilities. When relative volatility varies throughout the column, the average relative volatility is estimated by one of the criteria in Sec. 3.2.1. 

Example 3.7 Solve Example 2.1 using Smoker s method. Assume an average relative volatility of 2.49, solution (a) Rectifying section ... 

As will be discussed later it is not essential that the separation system be operated at the design pressure throughout the distillation. Therefore, the relative volatility was averaged over three pressures in the vicinity of the design point.) The equilibrium vapor-liquid compositions were calculated using this value for relative volatility ... 

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