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PFR and CSTR in Parallel

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An elementary liquid phase reaction (irreversible first order) A à R, takes place in a PFR and the conversion is 96%. If a mixed flow reactor of 10 times as large as the PFR is hooked up in parallel with the existing unit, by what fraction could the production be increased for the same 96% conversion?

Calculations:

Design equation for PFR: (first order reaction)

k t = -ln (1 - X_{A})

Design equation for CSTR: (first order reaction)

k t = X_{A} / (1 - X_{A})

For the 96% conversion in PFR,

k t = -ln (1 - 0.96)

k t = 3.219

i.e.,

k V_{PFR }/ v_{PFR} = 3.219

for the same 96% conversion in CSTR,

k t = 0.96/(1 - 0.96) = 24

The CSTR to be used is of 10 times as large as the PFR. Therefore,

k V_{CSTR }/ v_{CSTR} = 10 k V_{PFR} / v_{CSTR} = 24

i.e., 10 x 3.219 v_{PFR} / v_{CSTR} = 24

v_{PFR} / v_{CSTR} = 0.7456

Total volumetric rate = v_{PFR} + v_{CSTR} = (1 + 1/0.7456) v_{PFR} = 2.341 v_{PFR}

That is the production will increase to 2.341 times of the present production rate.