Parameter Estimation for a Packed Bed Reactor
Parameter Estimation for a Packed Bed Reactor
Consider the reversible reaction . This reaction involves three chemical species, , , and , and takes place in a packed bed reactor (PBR) with axial mixing.
A+BC
k
f
⇌
k
r
A
B
C
Introduce the dimensionless parameters , = (Péclet number), and =kτ (Damköhler number). Then the governing equations are:
τ=
L
u
P
e
uL
D
D
a
∂
C
A
∂t
1
P
e
2
∂
C
A
∂
2
x
∂
C
A
∂x
D
a
∂
C
B
∂t
1
P
e
2
∂
C
B
∂
2
x
∂
C
B
∂x
D
a
and =-+ r,
∂
C
C
∂t
1
P
e
2
∂
C
C
∂
2
x
∂
C
C
∂x
D
a
where and =/.
r=-
C
A
C
B
C
C
K
e
K
e
k
f
k
r
Initially, the reactor contains only species and such that (x,t=0)=0.6mol/L and (x,t=0)=0.4mol/L. Here we apply the Danckwerts boundary conditions for a closed-closed vessel [1]. The feed to the reactor is also composed of only and such that (x=,t)=0.6mol/ and (x=,t)=0.4mol/L.
A
B
C
A
C
B
A
B
C
A
-
0
L
C
B
-
0
Suppose you have measured experimentally the outlet concentrations of species , , and . To generate such data, select the values of the Péclet and Damköhler numbers as well as the level of white noise that interferes with your experimental measurements.
A
B
C
This Demonstration correlates the given experimental data to the above dispersion model to estimate the Péclet and Damköhler numbers (reported in magenta and gray, respectively). The estimates closely agree with the user-set values of the Péclet and Damköhler numbers, especially when the experimental error is minimal. Finally, both the prediction (solid-colored curves) and the experimental data (colored dots) are plotted. This gives a qualitative feel for the goodness of fit.