Population balance whether be applied to a semi batch- feed, catalyst- or not? How intro-duction of random sampling at different locations and at different time as well as sudden leakage be capacitated?
In - out + generation - consumption = accumulation
So you should have a well mixed reactor so the place where you sample shouldn't matter too much and it is just a good way to make sure your temperature is going to be uniform (for reaction rates and such). If you have a leak just add that to your design equation above and you should be good to go. They have good examples of this sort of thing in Bird Stewart and Lightfoot.
During leakage process is stopped & current status of result is considered final & computation of reaction is done by order of reaction equation. Practically shifting the reaction in another reactor safely the whole mass & continue by filling incidnet report.Such reaction at commercial level taken after proper prevention & risk assesssment approach having failour mode effect analysis including quality by design.
Description is possible. However, you must take into account a random change in the concentration field and a random change in volume of reaction mixture (random dosing and random outflow).It can not be done without stochastic equations. Regards,