For the previous models, I assumed that the amount of catalyst present in the emulsion phase was known. That is not a good assumption. Although we may know how much catalyst inventory is present, that does not mean we know how much is present in the emulsion phase. Much of the catalyst may be below the air inlets and therefore stagnant. Also, the degree of fluidization will change the void fraction and therefore the amount of catalyst in the bed. Thus, I have added the emulsion phase void fraction as another parameter to be determined by the tracer study.
The new parameter was added to Model 2 which is the model most likely to be used for the FCC regenerator application.
I also changed the cross flow parameter from an absolute, dimensional parameter, kgex kg/cu m/s, to a relative, dimensionless parameter, fx. The new parameter is the fraction of the inlet flow to the bubble phase that gets exchanged. This change greatly improved the parameter estimation efficiency and accuracy because it resulted in all of the parameters being scaled to the same order of magnitude.
The addition of the void fraction parameter has slightly degraded the accuracy of the estimation, but the results are still quite satisfactory. A couple of cases are shown below.
A new use for the tracer study
My original purpose for the tracer study was to establish the parameters for modeling an existing reactor using the mixed model method. This new model may also be useful for diagnosing poor performance. For example, low values of the emulsion void fraction may indicate poor fluidization. Also, high values of bypass flow (i.e. high "f") can lead to high flue gas temperatures. The affects of the parameters on reactor performance will be discussed when the model is presented.