Anyhow what we did was set up a basic spreadsheet to do material balances around the reactor. Since we know the rate of cumene production we needed we could easily determine the other concentrations by converting everything into molar flow rates. We chose in this system that fraction conversion of propylene to be around 95% (a number we made up it just feels good to say 95%). We also chose to feed benzene in excess a 4:1 ratio. In order to get a good grasp on our mass balance spreadsheet we neglected the 2nd reaction first in order to make sure we understood those fundamental concepts of reaction mass balances.
From the balances we were able to determine the required amount of benzene and propylene that needed to be fed into the reactor as well as the resulting flow rates out of the reactor and the reactor volume.
This was also done for 5:1 ratio of benzene to propylene. As well as incorporating both reactions to solve for the reactor size. These are just preliminary calculations that will be used in Aspen Plus to see whether when in the ballpark or way off base.
The reactor volumes for those approaches were around 8-9 cubic meters. Then involving the 2nd reaction the results were as follows:

With a volume of around 10 I'm somewhat confident we're doing the right approach. It isn't too small or too large (as big as a football field) then now its on to simulation the fun part...
Ran into a few simple mathematical mistakes due to the ti-89. Ti-89 was solving for the integral in the wrong manner returning numbers that were completely off. Solving the integral by hand even though time consuming as well as using other programs such as polymath and math.com helped confirm these results. Checking and rechecking numbers is one of the most annoying things about this design project.
~RSD
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