Question

If \(\overline{X_{Ri}}\) is the mean conversion of a reactant of particle size Ri, Rm is the particle of maximum size in the feed and F(Ri) is the fraction of Ri fed to the reactor, then the mean conversion of solids of a particular size ‘i’ leaving a plug flow reactor converting a mixture of particles of varying sizes is ____

(a) \(\overline{X_{(B)Ri}} = ∑_{R(τ)}^{Rm}\)[1- X(B)Ri]\(\frac{F(Ri)}{F} \)

(b) 1-\(\overline{X_{(B)Ri}} = ∑_{R(τ)}^{Rm}\)[ XRi]\(\frac{F(Ri)}{F} \)

(c) 1-\(\overline{X_{(B)Ri}} = ∑_{R(τ)}^{Rm}\)[1-X(B)Ri]  F (Ri)

(d) 1-\(\overline{X_{(B)Ri}} = ∑_{R(τ)}^{Rm}\)[1-X(B)Ri] \(\frac{F(Ri)}{F} \)

The question was posed to me during an online interview.

Enquiry is from Design of Fluid Particle Reactors in portion Fluid-Particle Reactions: Kinetics of Chemical Reaction Engineering

Answer 1

The correct choice is (d) 1-\(\overline{X_{(B)Ri}} = ∑_{R(τ)}^{Rm}\)[1-X(B)Ri] \(\frac{F(Ri)}{F} \)

To elaborate: Mean value for fraction of ‘i’ unconverted is the summation of the product of fraction of the reactant unconverted in the particle size Ri and the fraction of feed in the size Ri.

1-\(\overline{X_{(B)Ri}}\) = ∑(fraction of the reactant unconverted in the particle size Ri × the fraction of feed in the size Ri).