A first order irrrecersible cracking reaction: A -> B is performed in a fixed be

Question

A first order irrrecersible cracking reaction: A -> B is performed in a fixed bed reactor on a catalyst paricale radius of 0.15 cm. Pure A enters the reactor at a superficial velocity of 2 m/s, at temperature of 2000 C and pressure of 1 atm. Under these conditions, the reaction is severly affected by internal diffusion effects. Calculate the length of the bed necessary to achieve 60 % conversion.

- The intrinsic reaction rate constant by performing experiments with very small particle size of the same catalyst is 0.0003 m^3/g cat S

- Effective dissusivity: 1.5 x 10^-8 m^2/s

- Catalyst density: 2 gm/cm^3

Explanation / Answer

Answer:

for a 1st order cracking reaction occurring in a fixed bed with the spherical catalyst

given conversion for the bed = 60%

ln Co/Ca = k'''t = k''' *V/ velocity of a

the volume of the reactor = 3405 m3

the effective length of the reactor may be calculated

v= area of the particles *L

= 19 m

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