Page 284 - Separation process engineering

F = 100 and Eq. (7-33) becomes

Solving for φ between 0.21 and 1.00, we obtain φ = 0.5454. Equation (7-29) is

where

Dx i,dist = F z(FR) i,dist
i
For benzene this is

Dx ben,dist = 100(0.4)(0.998) = 39.92

where the fractional recovery of benzene is the value calculated in Example 7-1 at total reflux. The
other distillate values are
Dx tol,dist = 100(0.3)(0.95) = 28.5 and Dx cum,dist = 100(0.3)(0.05) = 1.5

Summing the three distillate flows, D = 69.92. Equation (7-29) becomes

From a mass balance, L = V − D = 44.48, and (L/D) min = 0.636.
min
min
E. Check. The Case A calculation gives essentially the same result.

F. Generalize. The addition of more components does not make the calculation more difficult as long
as the fractional recoveries can be accurately estimated. The value of φ must be accurately
determined since it can have a major effect on the calculation. Since the separation is easy,
(L/D) min is quite small in this case. (L/D) min will not be as dependent on the exact values of φ as it
is when (L/D) min is large.

7.3 Gilliland Correlation for Number of Stages at Finite Reflux Ratio

A general shortcut method for determining the number of stages required for a multicomponent distillation
at finite reflux ratios would be extremely useful. Unfortunately, such a method has not been developed.
However, Gilliland (1940) noted that he could empirically relate the number of stages N at finite reflux
ratio L/D to the minimum number of stages N min and the minimum reflux ratio (L/D) min . Gilliland did a

series of accurate stage-by-stage calculations and found that he could correlate the function (N−N min )/(N
+ 1) with the function [L/D − (L/D) min ]/(L/D + 1). This correlation as modified by Liddle (1968) is

shown in Figure 7-3. The data points are the results of Gilliland’s stage-by-stage calculations and show
the scatter inherent in this correlation.
Figure 7-3. Gilliland correlation as modified by Liddle (1968); reprinted with permission from
Chemical Engineering, 75(23), 137 (1968), copyright 1968, McGraw-Hill.