Question

A CMFR is operating at steady state with a second order decay reaction of rate constant k2=0.5 L/mg/d. It is exactly meeting its goal of 99.9% removal efficiency and the allowed maximum effluent concentration of 0.05 mg/L. The volumetric flow rate is 450 m3Id.

a. What is the influent concentration in mg/L?

b. What is the reactor volume in m3? What volume would be required if the removal efficiency goal were 99.0%? c(5). If the CMFR is replaced with a PFR, what reactor volume is needed (in m3)?

Answer 1

a) conversion = 99.9%

X = 0.999

C = 0.05 mg/L

Influent concentration C₀ = 50 mg/L

For CSTR, performance equation is given by

v₀ = 450 m³/d = 450000 L/d

For 2nd order reaction,

-r = kC²

C = C₀(1-X)

For X = 0.999

.: V = 1.7982 x 10¹⁰ L = 1.7982 x 10⁷ m³

For X = 0.99

.: V = 178200000 L = 178200 m³

For PFR, performance equation is given by

On integrating we get

For X = 0.999

.: V = 1.7982 x 10⁷ L = 1.7982 x 10⁴ m³