Theoretical stages, estimation

Design data for separation of the particular or similar mixture in a packea column are not available. Design procedures are better estabhshed for tray-type columns than for packed columns. This is particularly so with respect to separation efficiency since tray efficiency can be estimated more accurately than packed height equivalent to a theoretical stage (HETP). 

Mass Transfer As mentioned earlier, spray columns rarely develop more than 1 theoretical stage due to the axial mixing in the column. Nevertheless, it is necesary to determine what column height will give this theoretical stage. It is recommended by Cavers in Lo et al. Handbook of Solvent Extraction p. 323 and p. 327, John Wiley Sons, New York, 1983 that the following equation be used to estimate the overall efficiency coefficient ... 

The Fenske Method gives a quick estimate for the minimum theoretical stages at total reflux. 

After actual theoretical trays are determined (see Actual reflux and theoretical stages) one needs to estimate the actual physical number of trays required in the distillation column. This is usually done by dividing the actual theoretical trays by the overall average fractional tray efficiency. Then a few extra trays are normally added for offload conditions, such as a change in feed composition. 

The gas stream shown in Table 8-10 is fed to an isothermal absorber operating at 90°F and 75 psia. 90% of the n-butane is to be removed by contact with a lean oil stream consisting of 98.7 mol% non-volatile oil and the light components shown in Column 2 of Table 8-10. Estimate the composition of the product streams and the required number of theoretical stages if an inlet rate of 1.8 times the minimum is used. 

Equation 9.60 allows an estimate of the number of theoretical stages the column requires. 

Thus, the error in the prediction of the minimum reflux ratio has little effect on the estimate of the number of theoretical stages for this example. The error in the prediction of the energy consumption is likely to be more serious. 

Example 2 Estimation of overall column efficiency. A continuous fractionation unit has been designed to operate on a liquid feed containing components, A, B, C, and D. Calculations have shown that 20 theoretical stages are necessary in the column, not including the reboiler. On the basis of the following data, estimate the overall column efficiency and the number of actual trays needed in the column by (a) Fig. 16-9, (b) Eq. (4), and (c) Eq. (6) ... 

FIGURE 8.19 Estimate of theoretical stages, or of reflux ratio, for batch distillation. 

Make a rough estimate of the number of theoretical stages required. This step employs the procedures developed in Example 8.1. Use the Fenske-Underwood-Gilliland approach rather than the McCabe-Thiele, because the small boiling-point difference indicates that a large number of stages will be needed. 

Thus, for multicomponent mixtures, the required number of theoretical stages N, is calculated, and the HETP for the key components is estimated from the approximate relationship. 

Minimum and Maximum Solvent-to-Feed Ratios Normally, it is possible to quickly estimate the physical constraints on solvent usage for a standard extraction application in terms of minimum and maximum solvent-to-feed ratios. As discussed above, the minimum theoretical amount of solvent needed to transfer a high fraction of solute i is the amount corresponding to % =. In practice, the minimum practical extraction factor is about 1.3, because at lower values the required number of theoretical stages increases dramatically. This gives a minimum solvent-to-feed ratio for a practical process equal to... 

The simulation result of 7.53 theoretical stages is close to this shortcut estimate, indicating that the simulation is indeed delivering reasonable results. 

The Fenske Method gives a quick estimate for the minimum theoretical stages at total reflux. N 1 Xhk)d( hk/Xlk)b] " ln(aLKHK),vG Nomenclature LK = subscript for light key Nm = minimum theoretical stages at total reflux Xhk = mol fraction of heavy key component Xlk = mol fraction of the light key component otLK/HK = relative volatility of component vs the heavy key component... 

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