WOLFRAM|DEMONSTRATIONS PROJECT

Reactive Distillation Computations Including Heat Effects

โ€‹
option
composition profile 1
composition profile 2
liquid flow rate
vapor flow rate
Damkรถhler number Da
5
reflux ratio
5
ฮป
-0.2
reboil ratio
10.
10.5
11.
11.5
12.
Consider a ternary mixture of components
A
,
B
, and
C
with relative volatilities
ฮฑ
13
=5
and
ฮฑ
23
=3
. This mixture is subject to an exothermic equilibrium-limited chemical reaction
A+Bโ‡ŒC
with reaction rate
r=k
x
A
x
B
-
x
C
K
eq
, where the equilibrium constant
K
eq
=2.0
.
The mixture is fed into a reactive distillation column with 14 total plates. The feed stage location is stage number 5, the reactive stages are from stage 2 to stage 7, and the feed composition is equimolar in
A
and
B
(i.e., the feed is composed of 40 mole%
A
, 40 mole%
B
, and 20 mole%
C
). The feed flow rate is chosen as 100 kmol/hr.
Heat effects are included in the computation through the use of the negative dimensionless ratio,
ฮป=
ฮ”
H
r
ฮ”
H
v
,
where
ฮ”
H
r
and
ฮ”
H
v
are the negative heat of reaction and the heat of vaporization, respectively (both expressed in kJ/kmol). One recovers the no-heat effects case by setting
ฮป=0
.
This Demonstration shows two profiles: (1) the composition versus plate number for components
A
,
B
, and
C
(in red, blue, and green, respectively), with the reactive zone shown in light blue, and (2) a ternary diagram where the composition of
A
versus the composition of
B
is in mole%. In the second profile, the feed composition is shown by a magenta dot and the reactive stages (stages 2 to 7) are displayed in blue. The Demonstration also gives the nonconstant vapor and liquid flow rates in all stages. These flow rates obey the following relations, which are derived from global material and energy balances:
V
m+1
+
L
m-1
-
L
m
-
V
m
+
ฮฝ
T
Hr=0
where
ฮฝ
T
=-1
,
(
V
m-
V
m+1
)ฮ”
H
v
+ฮ”
H
r
Hr=0
.
You can set the values of the Damkรถhler number,
Da=
H/F
1/k
, the reflux ratio, and the reboil ratio, where
H
is the plate molar hold-up,
F
is the feed flow rate, and
k
the reaction rate constant. When
Da=0
, one recovers the case where no reaction is taking place. If
Da
is very large, the simulation represents a situation close to reaction equilibrium (i.e.,
r=0
). The Damkรถhler number is the ratio of the characteristic residence time to the characteristic reaction time.
One snapshot shows a case where the reflux ratio is very high, a situation close to the total reflux operation. For such a situation, the bottom is almost pure
C
and the distillate contains very little
C
. The distillation flow is very small and the distillate stream can be recycled if desired. Thus, for this specific operation, one can produce
C
, if this is the desired reaction product, and convert both reactants
A
and
B
with a single piece of equipment.