Tracer Response in a Packed Bed Reactor

Consider an isothermal packed bed reactor (PBR) of length . Assume that a tracer pulse enters at , with . For a closed-closed vessel, the Danckwerts boundary conditions apply: and . Initially, . The turbulent flow of the fluid in the pipe is characterized by the velocity .
The tracer profile in this PBR is governed by the following partial differential equation:
, , and ,
where is a dispersion coefficient (expressed in ) that takes into account longitudinal mixing in the pipe.
Introduce the dimensionless variables and parameters: , , , , and (Péclet number).
The dimensionless governing equation becomes:
This Demonstration plots the tracer response curve. The experimental and theoretical [1, 2] values of the variance are reported. The two values agree closely. We also compute the skewness of the curve. This parameter is positive, indicating that the tracer distribution is skewed to the right.


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The theoretical value of the variance was first derived by van der Laan [2] in 1958:
[1] O. Levenspiel, Chemical Reaction Engineering, New York: John Wiley & Sons, 1999.
[2] E. T. van der Laan, Chemical Engineering Science, 7(3), 1958 pp. 187–191. doi:10.1016/0009-2509(58)80025-1.
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