I've made a lot of changes to the model since the last post.
New mass balances
I have rewritten the mass balances in mass terms instead of molar terms. This allowed a more explicit connection between the flow through a tank and the overall reactor feed rate. Now the flow variables are mass fractions instead of mol/s.
New convergence for Crgc and Trgn
I am currently using the Minerr optimization routine to close the regenerator coke and energy balances simultaneously instead of the one variable at a time approach that I mentioned earlier. This routine appears to be more robust than the Mathcad root routine I was using. The latter was giving me an error in some cases stating that the problem was too large to solve.
Comparison with plant data in Dasila et al.
I adjusted the reactor catalyst decay function to more closely match the plant oil yield data. I also turned off the CO catalytic oxidation reaction to see how it affected the temperature. The results with this new model are shown below.
The yields agree very well with the plant data, but the regenerator temperature is 35 C below the data value. The flue gas composition was not reported for the plant data, but the unreacted oxygen agrees well with Dasila's model results. However, my model has a higher CO/CO2 ratio than the Dasila model. This may explain the difference in temperature because the heat of reaction to CO2 is higher than to CO on a per atom of oxygen basis. There are no plant data for the coke on the regenerated catalyst.
Updated effect of air flow rate
Increasing the air flow rate results in a slight decrease in the regenerator bed temperature. This is a change from the previous results. I think the change to the mass balances with explicit reference to the inlet mass flows allowed the optimization program to find a better solution to all of the equations. There were no errors in the previous formulation, only errors in the optimization results.
The results shown are for a regenerator that has a bubble phase at the lowest air flow rate. For this situation, increasing air rate doesn't add any air to the emulsion phase. If instead the low flow rate were below the onset of a bubble phase, then an increase in air rate would result in bed expansion with the emulsion phase receiving more air (i.e. oxygen). Thus, the increased oxidation rate would increase the bed temperature until the air rate reached the onset of the bubble phase.
The yield responses to the air flow are very small. For this reactor, there appears to be no incentive from a product viewpoint to increase air rate.
The next post will start a top down overview of the model. Following the overview, I will show some methods that allowed me to express the model in vector notation.
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.