Response of a Reactor with Axial Dispersion to a Pulse Input Tracer (E-Curve)
Response of a Reactor with Axial Dispersion to a Pulse Input Tracer (E-Curve)
A reactor with axial dispersion is governed by the following PDE:
∂
c
A
∂t
∂
c
A
∂z
2
∂
c
A
∂
2
z
c
A
This PDE can be transformed into a system of ODEs by finite differencing the reactor length into equally sized segments of length .
L=1
N
Z
dz=L/
N
Z
The Péclet number is given by =, where is the effective axial diffusivity, the reactor length, and the velocity. This dimensionless number appears naturally and is a measure of convection versus dispersion effects.
P
e
Lu
D
D
L
u
If the reaction rate constant is set to 0 it is possible to get the -curve, by using the pulse inlet concentration, for various values of the Péclet number, . It is observed that there is large dispersion when the number is small, which corresponds to large values of the axial diffusivity.
k
E
P
e
P
e