Form Fig. 14-3 the relation between xD, xl, and the slope of the operating line, dO/dV, can be obtained and Eq. (14-4) integrated to give the vapor requirement.
The use of these methods will be illustrated by the following example.
Batch Fractionation of a Binary Mixture. An equimolal mixture of A and B is to be fractionated in a batch column equivalent to three theoretical plates plus a Still. The still will operate at atmospheric pressure, with a total condenser, and the holdup in the column and condenser is negligible. The company desires to obtain an overhead A product containing 95 mol per cent A, and two methods of operation have been suggested: (1) Operate the column at a constant reflux ratio (O/D) equal to 5.0 and continue the distillation until the average composition of the distillate is 95 per cent A; (2) Operate the column at a variable reflux ratio to give a distillate of constant composition. Using data and notes given below, calculate: 1. For Method 1,
а. The mol per cent of the original charge to the still that can be obtained as the 95 per cent distillate.
б. The mols of vapor per 100 mols of original charge to obtain the distillate of Part a.
2. For Method 2, the mol per cent of the original charge to the still that can be obtained as the 95 per cent distillate, using a total vapor-to-charge ratio equal to that of Part 1, b.
Assume <*ab is constant at 2.5.
Solution. By trial and error the relations between xt and xd could be determined analytically by Eq. (7-62) because the relative volatility is constant and the usual simplifying assumptions apply. However a y,x diagram is probably simpler and will be employed. The mol fractions of component A will be used in the calculations.
The equilibrium curve was calculated from the relative volatility and is given in Fig. 14-4.
Method 1. The slope of the operating line « O/V « % « 0.833. The relation between any and the corresponding xd is found by taking four steps from zd on the operating line. The case for xd 0.94 is shown in Fig. 14-4 and gives xl « 0.41. The values for other cases are given in Table 14-1.
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