[T6022]

Hi everyone! I need help about productivity of ideal reactors. I searched on many books, but i haven't found anything clear.

So I decided to write few notes about this topic, but I need help to figure out if what i think is correct or not. Sorry for any language mistake, and thanks for eventual correction 

REACTION: any kind of reaction with elemental kinetics (power law).


BATCH (or STR):

td=dead time; Pp=productivity in product p; xa= conversion of reactant "a"; na0=initial moles of A; δ= stoichiometric ratio (p/a)

Pp = (δ na0 xa)/(t+td)

Only way to maximize productivity in this case is to write "xa" in function of "t", after that we need to put equal to zero the derivative dPp/dt. At last we get xa and t for the maximum productivity in p.


CONTINUOUS REACTOR (CSTR & PFR)

There are three situations:

1): Volume and volumetric flow rate are known.

In this case we can only calculate the productivity. No optimization are possible.

Pp =  δ Q0 Ca0 xa^e

Where xa^e is final conversion, Q0 the volumetric flow rate and Ca0 is the initial concentration of reagent (A).

2): Only volumetric flow rate is known.

By plotting Pp vs. xa we can see that the graph is a straight line ( Pp =  δ Q0 Ca0 xa^e ) so for reach the maximum productivity we should push the reaction to unitary conversion (xa^e=1).
But this could mean getting enormous reactor (V  inf). In this case we need an economical balance.

3): Only reactor's volume is known.

ra = reaction rate; ra** = average integral value of reaction rate.

for CSTR: Pp = δ V ra(xa^e)

for PFR: Pp = δ V xa^e ra**

for elemental reaction (kinetic described by power law), we can reach the biggest reaction rate only for small value of "xa".
The ONLY way to maximize the productivity is to work with differential reactor. It means that we need to use a volumetric flow rate high enough to obtain very little value of conversion (xa^e ≈ 3-5 %).

Are all the argument that i've done correct? thanks in advance! I hope that this post can also help someone else!