The Autocatalytic reaction (7 snapshots. scroll down!!)
batch reaction for CB,0 = 0.001 mol/l

batch reaction for CB,0 = 0.1 mol/l

the reaction rate of an autocatalytic reaction

remarks: at conversion U = 0 and U = 1 the function is infinite
The autocatalytic reaction in a CSTR with 50 % conversion

remarks: X0=CA,0 = 1 (mol/l) ;Y0 = CB,0 = 0.001 (mol/l) ; m = k 1 (l/mol sec) ; n = tau = 2 (sec)
If you take several taus from 1 to 16 sec:

You see that (after tau = 2 sec) you need more and more space time for 'a little' more conversion
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Autocatalytic Reaction, searching for an optimal recirculation factor R in a loop reactor (conversion U=99%)

This calculation was carried out with unicalc1. The red curve represents space-time (Y) versus R (X), the minimal space time is 7.5 sec for R=0.19. The other curves represent partial terms of the calculation (for control)
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