Chapter 10, Problem 10.19P

With the increasing demand for xylene in the petrochemical industry, the production of xylene from toluene disproportionation has gained attention in recent years [Ind. Eng. Chem. Res., 26, 1854 (1987)]. This reaction,

$\begin{array}{l}2\text{ Toluene}\to \text{Benzene}+\text{Xylene}\\ \text{2T}\stackrel{\text{catalyst}}{\to }\text{B}+\text{X}\end{array}$

was studied over a hydrogen mordenite catalyst that decays with time. As a first approximation, assume that the catalyst follows second-order decay

$r_d=k_d{a}^2$

and the rate law for low conversions is

$-{r^{\prime }}_{\text{T}}=k_{\text{T}}{P}_{\text{T}}a$

with k_T = 20 g mol/h·kg-cat·atm and k_d = 1.6 h⁻¹ at 735 K.

1. (a) Compare the conversion-time curves in a batch reactor containing 5 kg-cat at different initial partial pressures (1 atm, 10 atm, etc.). The reaction volume containing pure toluene initially is 1 dm³ and the temperature is 735 K.
2. (b) What conversion can be achieved in a moving-bed reactor containing 50 kg of catalyst with a catalyst feed rate of 2 kg/h? Toluene is fed at a pressure of 2 atm and a rate of 10 mol/min.
3. (c) Explore the effect of catalyst feed rate on conversion.
4. (d) Suppose that E_T = 25 kcal/mol and E_d = 10 kcal/mol. What would the temperature–time trajectory look like for a CSTR? What if E_T = 10 kcal/mol and E_d = 25 kcal/mol?
5. (e) The decay law more closely follows the equation

$r_d=k_d{P}_{\text{T}}^2{a}^2$

with k_d = 0.2 atm⁻² h⁻¹. Redo parts (b) and (c) for these conditions.