Parameter Estimation for a Packed Bed Reactor

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Consider the reversible reaction . This reaction involves three chemical species, , , and , and takes place in a packed bed reactor (PBR) with axial mixing.


Introduce the dimensionless parameters , (Péclet number), and (Damköhler number). Then the governing equations are:



and ,

where and .

Initially, the reactor contains only species and such that and . 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 and .

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.

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.


Contributed by: Housam Binous, Farrukh Shehzad, Mohammad Mozahar Hossain, Abdullah A. Shaikh, and Ahmed Bellagi(January 2016)
(King Fahd University of Petroleum and Minerals, KSA; ENIM, University of Monastir, Tunisia)
Open content licensed under CC BY-NC-SA




[1] H. S. Fogler, Elements of Chemical Reaction Engineering, 3rd ed., Upper Saddle River, NJ: Prentice Hall, 1999.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.