Page 337 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

11.8 Batch distillation 339

number of stages (N). Subsequently, another distillate composition (x D2 ) and the corresponding
bottom concentration (x B2 ) is determined similarly. The operating lines are parallel (Fig. 11.19A)
R
as the reflux ratio R is constant and the slope is . In this way, the relation between x D and x B is
Rþ1
determined over the operating range and the integral in Eq. 11.47 is solved by evaluating the area
1
under the curve plotted with on the ordinate and the actual bottoms composition (x B ) on the
x D x B
abscissa. The area (A) between x F to x B represents the solution to the integral and gives the value of
B. The moles of distillate obtained is
(11.49)
D ¼ F ð1 B = FÞ¼ F f1 expðAÞg
and the mean distillate concentration (x Davg ) is obtained from the material balance as
(11.50)
x F x B ðB=FÞ
x Davg ¼
1 ðB=FÞ
The amount of vapour (V) generated in the still is
(11.51)
V ¼ D ðR þ 1Þ
Usually the boil-up rate associated with a specific (distillation) system is known from past expe-
rience. In case of a new system, the boils up rate is found by dividing the total vapour load by the time
of distillation for only the production run (step iii in batch operation) and the charging time, heat up
time, cooling time and clean up time are not included.
The heat (Q) required for the separation is related to the other variables as
Q
(11.52)
¼ð1 B = FÞ ðR þ 1Þ
F l F
where l F is the latent heat of vaporisation of the mixture.
(ii) Constant distillate composition operation: In this case the decrease in distillate concentration
(x D ) is avoided by continuously increasing the reflux ratio (R) with time. The relationship
between still concentration (x B ) and the corresponding reflux ratio (R) is determined graphically
on the x-y plot as shown in Fig. 11.19B. x D is located on the 45 degrees line and an initial reflux
ratio (R) and the position of the operating line is specified to satisfy N stages and the
corresponding still concentration (x B ) is noted. In this case, direct integration of Rayleigh’s
equation can be performed to give
x D x F
(11.53)
B ¼ F
x D x B
x F x B
(11.54)
D ¼ F
x D x B
Correspondingly, the energy requirement (Q) which depends on the variable R is
Z B )
x (
Q ðR þ 1Þ
dx B (11.55)
2
¼ðx D x F Þ
F l F
ðx D x B Þ
x F