WOLFRAM|DEMONSTRATIONS PROJECT

Chromatographic Reactor

​
diffusivity
adsoprtion constants
parameters

A
1.
α
A
0.15
fluid velocity u
8.

B
2.
α
B
0.25
reaction constant k
1.

C
3.
α
C
0.35
species A pulse time τ
2
Chromatographic reactors integrate chemical reaction and separation in one apparatus. This Demonstration analyses the reaction
A
k
⇌
k
B+C
conducted in a chromatograph.
The equations describing the fluid concentration
C
i
of the three species in a fixed-bed chromatography column are:
ϵ
∂
C
i
∂t
+(1-ϵ)
∂
q
i
∂t
=

i
ϵ
2
∂
C
i
∂
2
x
-uϵ
∂
C
i
∂x
±(1-ϵ)r,i=A,B,C
,
where
t
is time,
x
is distance,
ϵ
represents porosity,

i
stands for the effective diffusivity,
r
is the rate of chemical reaction (negative for reactants and positive for products), and the
q
i
are the solid-phase concentrations that are related to the fluid concentrations via adsorption constants
α
i
,
q
i
=
α
i
C
i
.
The reaction rate is
r=k(
α
A
C
A
-
α
B
C
B
α
C
C
C
)
, and the initial and boundary conditions are: ​
C
i
(x,0)=0
,​
C
A
(0,t)

1
t<τ
0
t≥τ
,​
C
B
(0,t)=
C
C
(0,t)=0
, and​
∂
C
i
(∞,t)
∂x
=0
,
i=A,B,C
,where
τ
is the time that species
A
is injected into the chromatograph. Chromatographic separation is based primarily on the difference in adsorptivity
α
i
, as well as the difference in the diffusion coefficient

i
.
You can follow the trajectory of the system by varying adsorptivities, diffusion coefficients, fluid velocity, reaction rate, and the time of injection of reactant
A
.