Consider the Problem from Monday’s Lecture:

A plug-flow reactor packed with catalyst, otherwise known as a Packed-Bed Reactor (PFR), within which there is the following elementary reaction taking place:

A + B à C

The reactor is isothermal, and pressure drop within the reactor is described by the Ergun Equation.

We draw a stoichiometric table for this reaction, as follows:

Species	Initial	D	Final
A	F_AO	-F_AOX_A	F_AO(1-X_A)
B	F_BO=Q_B*F_AO	-F_AOX_A	F_AO(Q_B-X_A)
C	F_CO=Q_C*F_AO	+F_AOX_A	F_AO(Q_C+X_A)
total	F_AO(1+Q_B+Q_C)	-F_AOX_A	F_AO(1+Q_B+Q_C-F_AOX_A)

The volumetric flowrate can thus be described in terms of conversion, temperature, pressure and feed compositions as follows:

, where and

substituting into the PBR design equation,

The Ergun equation gives us the second relationship for pressure vs. W, as follows:

We can re-write this in terms of Fogler’s text, such that

And can be solved numerically using MATLAB’s ode45 routine. Download the following two files into your matlab directory:

supp_3.m, which is the main program, and

supp_3_eqns.m, which contains expressions for the two differential equations.

To run the Matlab codes, first start matlab, then (making sure that BOTH files are in the matlab directory), type “supp_3” to run the main code.

The results are shown below, for the case of (solid lines) Ergun-Type Pressure Drop and (dashed-lines) Isobaric Operation.

Feel free to edit the programs to change parameters and study the effects of inlet pressure, ergun coefficient, composition upon reactor performance. Be warned, however – inappropriate selection of ergun coefficient and corresponding packed bed length will result in choking the gas flow through the bed (P à 0), and results obtained after this point will be useless.