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, 2 Toluene→Benzene+Xylene2T→catalystB+X 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=kda2 and the rate law for low conversions is −rT′=kTPTa with kT = 20 g mol/h·kg-cat·atm and k_d = 1.6 h^–1 at 735 K.
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.
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.
c. Explore the effect of catalyst feed rate on conversion.
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 Ed = 25 kcal/mol?
e. The decay law more closely follows the equation
rd=kdPT2a2
with kd = 0.2 atm–1. Redo parts (b) and (c) for these conditions.