Question

If τ is the average residence time and σ^2 is the standard deviation, then the number of tanks necessary to model a real reactor as N ideal tanks in series is ____

(a) N = \(\frac{\tau^2}{σ^2} \)

(b) N = \(\frac{σ^2}{τ^2} \)

(c) N = σ^2

(d) N = \(\frac{1}{τ^2} \)

The question was posed to me in semester exam.

I need to ask this question from Tanks in Series Model in section Compartment Models, Models for Non Ideal Reactors of Chemical Reaction Engineering

Answer 1

Right option is (a) N = \(\frac{\tau^2}{σ^2} \)

Best explanation: τ^2 = 1 and σ^2 = \(\frac{1}{N}.\) The standard deviation is obtained as, σ^2 = \(\int_0^∞\)(t-τ)^2E(t)dt.