For the following conditions determine whether a CMFR or a PFR is more efficient in removing a reactive compound from the waste stream under steady-state conditions with a first-order reaction: reactor volume = 280 m3, flow rate = 14 m3 · day-1, and reaction rate coefficient = 0.05 day-1.

The PFR is more efficient in the removal of the reactive compound as it has the higher conversion ratio.

Xₚբᵣ = 0.632

X꜀ₘբᵣ = 0.5

Xₚբᵣ > X꜀ₘբᵣ

Explanation:

From the reaction rate coefficient, it is evident the reaction is a first order reaction

Performance equation for a CMFR for a first order reaction is

kτ = (X) / (1 - X)

k = reaction rate constant = 0.05 / day

τ = Time constant or holding time = V/F₀

V = volume of reactor = 280 m³

F₀ = Flowrate into the reactor = 14 m³/day

X = conversion

k (V/F₀) = (X) / (1 - X)

0.05 * (280/14) = X / (1 - X)

1 = X / (1 - X)

X = 1 - X

2X = 1

X = 1/2 = 0.5

For the PFR

Performance equation for a first order reaction is given by

kτ = In [1 / (1 - X) ]

The parameters are the same as above,

0.05 * (280/14) = In (1 / (1-X)

1 = In (1 / (1-X))

e = 1 / (1 - X)

2.718 = 1 / (1 - X)

1 - X = 1/2.718

1 - X = 0.3679

X = 1 - 0.3679

X = 0.632

The PFR is evidently more efficient in the removal of the reactive compound as it has the higher conversion ratio.