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Estimating Relative Volatility from Batch Distillation Data

​
relative volatility
3
noise
0.
still
distillate
General
:
12.
8.9727×
-30
10
is too small to represent as a normalized machine number; precision may be lost.
Consider an equimolar binary mixture with a constant relative volatility
α
. An initial quantity
M(t=0)=1000moles
of this mixture is fed into the still of a simple batch distillation apparatus.
Assume that the batch distillation is conducted at a constant boil-up rate
V=10mol/min
(i.e. the selected heating policy of the experiment). Thus the overall molar balance gives
M
t
=-V
, where
M(t)
is the still's molar holdup. The experiment stops when the still runs dry at
t=99.99
minutes, when
M(t)=0
.
The liquid composition
x
in the still is related to the distillate composition
y
by
y=
αx
1+(α-1)x
[1, 2].
A component molar balance is given by the equation
M
x
t
=V(x-y)
, with
x(t=0)=0.5
.
Suppose you run a batch distillation experiment and gather the data indicated by the red dots in the plot. To generate such data, fix the value of the relative volatility and the level of the random noise. This Demonstration uses the governing equations to estimate the relative volatility (shown on the plot in magenta) using your "experimental" data. The quality of the theoretical predictions (shown by the blue curve) is given by the root-mean-square deviation or rmsd (reported in
%
and in black on the plot).
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