Decisions that determine the input/output structure flowsheet
Vent gaseous reactant, propylene and gaseous feed impurity, propane so that the inert-propane gas does not accumulate in the gas recycle loop.
Remove DIPB and use it as part of the fuel supply. It is more economical to pay for the increased raw material cost (propylene) that was converted to DIPB than to oversize all equipment in that recycle loop.
Recover and recycle excess Benzene
Decision That determine the Recycle Flowsheet
Since both reactions take place at the same temperature and pressure and with a catalyst, only one reactor is required
Use of Excess benzene leads to increased selectivity which can be seen from Selectivity= rate (desired)/Rate (undesired).
Formulation of the Recycle material as a function of the dominant design variables, selectivity, molar ratio of Benzene to Propylene, mole fraction of propyelene in feed and vent.
FG-Molar flow rate of Propylene+Inert impurity (propane)
FFB- Molar flow rate of Fresh Benzene
FB- Molar Flow rate of Benzene
RB- Molar Flow rate of Recycle Benzene
PC, PDIPB, PG- Molar Flow rates of Cumene, DIPB, fuel gas (Vent)
YFP, YPP- Mole fractions of propylene in feed and vent
Selectivity definition I used= Moles of Desired product formed (Cumene)/Moles of Undesired Product (DIPB)
The images below are my attempt to formulating the recycle material balance. To check if I am heading in the right direction, If I were to plug in values for the design variable the resulting numbers should be equal or close to the flow rates in the table as I assumed for instance, that 100% of benzene is recovered and recycled. But I am facing a difficulty, I tried to estimate the equilibrium coversion by setting the mole balance and concentration equation for all the components at the reactor outlet and considered a PFR reactor operating isothermally but I cant proceed from this point.
Another Difficulty I am facing is what composition can I assume for the propylene in the vent and on what basis