Page 336 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

338 Chapter 11 Distillation

mixtures, y is related to x using relative volatility a, which is often temperature dependent. The

relationship already presented earlier in Eq. 11.11 is
ax

y ¼
1 þða 1Þx
Substituting the above expression in Eq. 11.44 gives

B x B 1=ða 1Þ 1 x F a=ða 1Þ
(11.45)

¼
F x F 1 x B
Since the distillate becomes progressively less rich in the lighter component, one would be
interested in the mean distillate composition (x Davg ) given by
x F x B
(11.46)
x Davg ¼ x B þ
1 ðB=FÞ
Usually the design inputs are initial charge/Feed (F) and its composition (x F ) and either the
distillate (x Davg ) or the still composition (x B ) at the end. The corresponding outputs are either (x B ) and
B (bottom product composition and amount) or x Davg and D.
Multistage batch distillation of binary system with reflux: The calculation of multistage batch
distillation of binary mixtures is also based on Rayleigh equation with y replaced by the distillate
mole fraction x D
x
Z B
B dx B
(11.47)
F x D x B
ln ¼
x F
The concentration (x D ) of the distillate depends on vapoureliquid equilibrium or a, separation
efficiency of the column (the number of equilibrium stages N or the number of transfer units N TOG ) and
the reflux ratio R.
Mathematically,
(11.48)
x D ¼ fðx B ; a; N; RÞ
The functional form of Eq. 11.48 depends on the operation, i.e., constant reflux ratio, constant
distillate composition or mixed mode. The reboil duty (Q) and the corresponding design rating would
also be different for each mode of operation. The option selected would dictate the number of theo-
retical stages (NorN TOG ) required for separation. The corresponding vapour and liquid traffic also get
fixed. Calculation of height and diameter of the column additionally require details of the internals
(packing, trays, etc.).
(i) Constant reflux ratio operation: The top product purity in this mode decreases as distillation
proceeds (Fig. 11.19A) and x Davg is the targeted distillate product composition. Therefore, initial
x D has to be higher than the targeted x Davg and distillation would continue even after the
instantaneous x D drops below x Davg . Usually the inputs are N, R and x F and the outputs are D,
x Davg and energy requirement for distillation (Q).
In order to evaluate the aforementioned, a distillate composition (x D1 ) is set and an operating line is
drawn followed by the usual determination of the concentration (x B1 ) in the still by stepping off the