In the LinkedIn discussion that I mentioned in Part I of this series, there were suggestions that downward flow regions might be important. Those comments may have been in regard to the FCC riser, not the fluidized bed regenerator. However, I have built a model and estimation program that can test for the down-flow possibility.
I have assumed that the down-flow region is in plug flow with axial dispersion. This region was modeled using tanks in series. This region contains both gas and solids. The gas is assumed to come from the emulsion phase (CSTR) at the top of the dense phase. The outlet of the down-flow region re-enters the CSTR at the bottom of the bed.
This change to the model adds an additional flow branch, volume, and dispersion region. Thus, three new parameters are required. I chose f2 (the ratio of gas leaving the CSTR that goes to the down-flow phase), Vdf, the gas volume in the new region, and the number of tanks (10) as the three parameters.
Once again, the estimation program obtained all parameters exactly.
Is Model 4 a general starting point?
Model 4 can be used to determine whether or not a down-flow region exists. I simulated a case with f2=0 (i.e. no down-flow) and the estimation program again obtained all four parameters correctly, showing that there was no down-flow.
Note that I have not included cross flow in this model. That addition would make the model even more general. However, it also might not work well.
Likelihood of down-flow
I've watched several videos of CFD simulations of fluidized beds on the web and I don't see any indication that down-flow is important. The down-flow that is present is part of the circulation in the CSTR phase because it is chaotic rather than being a fixed zone. I think Model 2 with cross-flow should be adequate for most applications.
A disadvantage of Model 4
The extra equations for the down-flow tanks increase the computation time for an integration. Also, the extra parameters increase the estimation time. Estimations required about 30 minutes.