A reactor engineer has one PFR that yields X 1 = 0.4. He needs to increase it to

Question

A reactor engineer has one PFR that yields X1 = 0.4. He needs to increase it to X2 = 0.8. He has an availiable a PFR and CSTR to attach in series. Both reactors can achieve the required conversion. Which combination is the most efficient? Calulate the reactor volume of the best combination if you have FA = 1 Kmol/s.

The reactor volume per unit molar molar flow of liming reactant (VR/FA) for PFR and CSTR is given by the following formulas:

PFR: VR/FA = 2 (XF - X1)2 + (XF - X1)/2

CSTR: VR/FA = 3 (XF - X1)2 + (XF - X1 )

Units are m3 s / kmol. XF and X1 are the output and input conversions of the reactor, respectively.

Explanation / Answer

Generally PFR is better when we dont have any reaction rate

so PFR followed PFR is best combination

sub xf = 0.8 and x1 = 0.4

PFR

Vr/Fa = 2 (0.8 -0.4)2 + (0.8 - 0.4)/2 =0.52

for xf = 0.4 and x1 = 0

also we will have same volume 0.52

CSTR

Vr/Fa = 3 (0.8 -0.4)2 + (0.8 - 0.4) =0.88

so volume required for PFR is less when compared to CSTR

hence PFR follwed by PFR is best combination and total volume will be 0.52 + 0.52 = 1.04 m3s/kmol.

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