WOLFRAM|DEMONSTRATIONS PROJECT

Second-Order Reaction with Diffusion in a Liquid Film

​
collocation points
21
rate constant
0.01
liquid phase diffusivity
A in D
B in D
Gas absorption is often enhanced by a chemical reaction. For instance, acid gases (
CO
2
and
H
2
S
) are usually eliminated from natural gas by absorption using ethanolamine (
H
2
NC
2
H
4
OH
) as a basic solvent.
Consider the absorption of species
A
with a solvent
D
containing a species
B
such as a second-order irreversible chemical reaction,
A+BC
, that takes place in a liquid film. Only species
A
is present in the gas phase since
B
has a very low vapor pressure (i.e.,
B
is a high boiling component). Species
A
is not present in the bulk liquid since all of
A
reacts with component
B
in the liquid film.
he steady state material balances within the film are given by
D
AD
2
d
c
A
d
2
x
=k
c
A
c
B
and
D
BD
2
d
c
B
d
2
x
=k
c
A
c
B
, where the binary diffusion approximation for
A
and
B
in
D
has been used. These equations simply state that the rates of diffusion of species
A
and
B
are equal to the rate of the chemical reaction. The concentration of
B
in the bulk liquid is arbitrarily set to 2 while the concentration of
A
at the gas-liquid interface is set to 1.
This Demonstration displays the liquid film concentrations of species
A
and
B
(blue and orange curves, respectively) as a function of position. You can change the values of the diffusivities,
D
AD
and
D
BD
, the reaction rate constant,
k
, as well as the number of Chebyshev collocation points,
N+1
. Excellent agreement is obtained between the numerical solutions given by Chebyshev orthogonal collocation (blue and orange dots) and by NDSolve (blue and orange curves).