Operation of an Absorption Column

​
inlet vapor mole ratio
y
N + 1
(ppm)
100
temperature (°C)
25
pressure (atm)
2.5
solvent flow rate (Mmol/h)
100
mole ratios (ppm):
outlet vapor
y
1
10
inlet liquid
x
0
0.05
(L/V)
min
show diagram with 5 stages
​
In this Demonstration, a trayed absorption column is used to remove an impurity solute (chloroform) from a gas feed by absorbing the impurity in a liquid solvent. The number of trays/stages needed to obtain an outlet solute mole ratio of
y
1
ppm in the gas stream (set with a slider) is calculated. A stage is a plate that contacts the liquid solvent and the gas to promote mass transfer. Use a slider to set the solute mole ratio
x
0
of the liquid feed stream. When a partial stage is calculated, the number of stages is rounded down to the nearest full stage. Use sliders to change the pressure and temperature in the column, the solvent flow rate
L
and the solute mole ratio in the gas feed,
y
N+1
. The slope of the pink operating line,
L/V
, is shown on the column on the right. Checking the "
(L/V)
min
" box shows the minimum slope for the operating line; the desired separation would require an infinite number of stages at a lower slope. The equilibrium line is orange. Check "show diagram with 5 stages" to set conditions that require 5 stages and display the mole ratios entering and leaving each stage. Move your mouse over the pink and orange lines on the
x-y
diagram to see their labels.

Details

A mole balance on the absorption column for the impurity species gives:
x
0
L+
y
N+1
V=
x
N
L+
y
1
V
.
Rearranging this yields the operating line for the absorber:
y
N+1
=
L
V
(
x
N
-
x
0
)+
y
1
,
where
L
is the solvent liquid flow rate (Mmol/h),
V
is the gas molar flow rate (Mmol/h),
x
n
and
y
n
are the mole ratios of the impurity (ppm) in the liquid and gas streams leaving stage n (these streams leaving stage n are in equilibrium),
x
0
is the mole ratio of impurity in the inlet solvent stream,
y
N+1
is the mole ratio of impurity in the feed gas stream,
x
N
is the mole ratio of impurity in the outlet solvent stream, and
y
1
is the mole ratio of impurity in the treated gas stream.
The equilibrium line is calculated using Henry's law:
y
eq
=
H
P
x
N
,
H=
0
H
-
E
R
1
T
-
1
T
0
e
,
where
H
is Henry's constant (atm),
0
H
is Henry's constant at
T
0
=298K
,
P
is pressure (atm),
E
is the activation energy (J/mol),
R
is the ideal gas constant (J/mol K), and
T
is temperature (K).
Stages are counted by locating
y
N+1
on the operating line. The corresponding
x
N
value on the operating line is from the mass balance:
x
N
=
x
0
+
y
N+1
-
y
1
L/V
.
A vertical line is then drawn from (
x
N
,
y
N+1
) to the equilibrium line. These values (
x
N
,
y
N
) are the equilibrium mole fractions leaving stage
N
. Next draw an horizontal line from (
x
N
,
y
N
) to the operating line. From this point (
x
N-1
,
y
N
) on the operating line, a vertical line is drawn to the equilibrium line, and this process is repeated until
x
1
is reached.

References

[1] P.C. Wankat, Separation Process Engineering: Includes Mass Transfer Analysis, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 2012.

External Links

Carbon Dioxide Absorption in Water
McCabe-Thiele Method for Methanol/Water Separation

Permanent Citation

Adam J. Johnston, Rachael L. Baumann, John L. Falconer
​
​"Operation of an Absorption Column"​
​http://demonstrations.wolfram.com/OperationOfAnAbsorptionColumn/​
​Wolfram Demonstrations Project​
​Published: May 2, 2017