Why is (for simple reactions) the space time of not back-mixed reactors always 'shorter' as for the back-mixed types ?

Hope, you know the fundamental
characteristics of the CSTR and the TFR !!

• First take the totally back-mixed stationary CSTR. Here drops the inlet concentration immediately down to the outlet concentration, which is identical to the concentration 'everywhere' in the vessel ("enter and drop down at once" - without delay - in german: "rein und runter" ). A low concentration in the reaction volume means a low reaction rate (r proportional to Cⁿ), i.e. the production rate is 'not good'. In the not back-mixed type TFR the concentration drops gradually along the reactor length, the mean concentration level is higher in comparison with the CSTR and therefore the reaction and production rate too.!
  
  
• You can show that alternatively very comprehensive in the 1/r(U) - Plot.
  Your decision:
  --- "I know this possibility, show me the plot and I will compare the area a with a+b"
  or:
  --- "I need some further explanation"

related matter: when a reaction is carried out in a series of a CSTR and a TFR with conversions about 50 to 50 and a high total conversion (e.g. 90%), which reactor should be taken as first one ? series of CSTR and TFR

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