Page 347 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

11.9 Design illustration e batch distillation 349

Solution 1C: Batch distillation with constant distillate composition
The problem is attempted considering batch distillation with stages and constant distillate
composition. Three theoretical contacting stages in the tower (packed bed) and one stage for the
reboiler still are considered.
The constant composition of distillate is considered to be same as in case of 1B, i.e., x D ¼ 0:572 .
This is not much away from the equilibrium vapour composition with feed (x F ¼ 0.25, y ¼ 0:45).
Four ideal stages were considered in 1B when the initial distillate concentration started from 0.8
and gradually fell; in this case only three stages are considered.
The x-y diagram for McCabeeThiele construction is drawn for a ¼ 2.45. The initial operating
line is constructed by trial and error with total three ideal stages starting from x B ¼ 0:25 and
going up to x D ¼ 0:572 by construction of three stages as shown in Fig. 11.19B. From the y-intercept
x D ¼ 0.336) of the line the corresponding reflux ratio required is calculated as 0.7016. As
( ¼ Rþ1
distillation proceeds, reflux ratio needs to be appropriately increased to keep x D ¼ 0:572, and x B
decreases from 0.25. Therefore, several operating lines passing through (0.572, 0.572) are drawn and
from the y-intercept their reflux ratio in each case is found out. x B is found in each case by constructing
three stages on the operating line from (x D ; x D ). Only the initial and another operating line is shown in
Fig. 11.19B that has y-intercept ¼ 0.151, and x B ¼ 0.16 read out from the graph. R ¼ 2.8 based on the
intercept value. This is also considered to be the ending operating condition as the constant reflux ratio
set for the previous case was also 2.8.
x
Z F
dx B x D x F 0:572 0:25
¼ ln ¼ ln
Calculation of B=F: lnðB = FÞ¼
x D x B 0:572 0:16
ðx D x B Þ
x B
ðB=FÞ¼ 0:78
% recovery of toluene ¼ 0:78 0:16=0:25 100 ¼ 50
The reboiler total heat load may be found from the expression
Q Z x B R þ 1
dx B
2
¼ðx D x F Þ
Fl avg
x F ðx D x F Þ
Observation on the results of this specific problem
(1) Single-stage batch distillation is most inefficient with about 53% toluene recovery of just
acceptable purity of 40% toluene in distillate. This would require minimum investment cost.
(2) Batch distillation with constant distillate composition (w57% purity) is next best as it can be
sold at a higher price. However, in this case the recovery is also low w50%. The distillation may
be continued to further recover toluene but the incremental effect on yield increase would be
lesser and lesser. The investment is more than single stage as two stages of contact in the column
need to be provided.
(3) Batch distillation with constant reflux ratio (w57% distillate purity) produces the same quality
of product that can be sold at a higher price. However, in this case the recovery is much higher
w83%.