Chapter 14, Problem 14.8P

Interpretation Introduction

Interpretation:

The kinetics of a reversible fluid-phase isomerization is described in terms of the bulk concentrations $C_A$ and $C_B$ by the following expression is to be shown.

    $-r_A^{"}=\frac{k_B\left[C_A-\left(1/K\right)C_B\right]}{1/K+k_B/k_A}$

The required weight of a reactor in terms of catalyst when all the other operating variables are constant is to be calculated.

Concept introduction:

The Thoenes-Kramers correlation for mass transfer in a packed bed is given by the expression.

    ${\text{Sh}}^{\text{'}}=\left(1.0\right){\left({\text{R}}_e^{\text{'}}\right)}^{1/2}{\text{S}}_c^{1/3}$

    $k_c=\frac{D_{AB}\left(1-\varphi \right)\text{γ}}{d_p\varphi }{\left[\frac{\rho U{d}_p}{\mu \left(1-\varphi \right)}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\left[\frac{\mu }{{\rho }_{D_{AB}}}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

Also,

    ${\text{R}}_e^{\text{'}}=\frac{{\text{R}}_e}{\left(1-\varphi \right)\text{γ}}$

    ${\text{Sh}}^{\text{'}}=\frac{\text{Sh}\varphi }{\left(1-\varphi \right)\text{γ}}$

Here,

$d_p$ is the diameter of the particle.

$\varphi$ is the void fraction of packed bed.

$\text{γ}$ is the shape factor.

In case of constant fluid properties and particle diameter, the value of $k_c\text{α}{U}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$.