An industrial example was given by Dasila et al. I am going to use the dimensions and other parameters from that example.
The bed height is 6.5 m and the diameter is 4.5 m. Dasila modeled this bed as a plug flow for the gas and a CSTR for the catalyst. There was no emulsion phase. To me, it seems unlikely that the solid is well mixed without also some backmixing of the gas. As their model was based on a number of other papers, which I have not read, I don't know the basis for the plug flow assumption. It is well known that the conversion of the limiting reactant, here oxygen, is higher in a plug flow reactor compared to a CSTR of the same volume. Unless there is a tracer study or possibly CFD basis for the plug flow assumption, then I would suspect the kinetics of the combustion were not determined independent of the flow assumption.
Tracer curve example
The following figure shows the tracer curves for a typical example.
Helium tracer was injected into the air supply starting at 20 s. The ramp up and down created a trapezoidal input curve. The exit concentrations from the plug flow and CSTR regions are shown in blue and red. The green curve is the concentration at the exit. It has been delayed due to the freeboard plug flow region. This green curve would be the curve measured in an actual tracer study.
Effect of f
The extreme possibilities of f = 0.01 (CSTR) and f = 0.99 (plug flow) are shown in the next figure. In this example, residence time ratio, alpha, was assumed to be 1.
Intermediate values of f will result in curves that are a blend of these curves, as shown in the first plot.
Effect of alpha
The figure below shows that even a small change in alpha changes the exit curve in a noticeable manner.
Dasila, Prabha K, Indranil Choudhury, Deoki Saraf, Sawaran Chopra, and Ajay Dalai. “Parametric Sensitivity Studies in a Commercial FCC Unit.” Adv. in Chem. Eng. Sci. 2012, no. January (2012): 136–49.