The gas-phase isomerization A → B is to be carried out in a flow reactor. Experiments were carried out at a volumetric flow rate of υ₀ = 2 dm³/min in a reactor that had the following RTD E(t) = 10 e^10t min^–1 where t is in minutes.
a. When the volumetric flow rate was 2 dm³/min, the conversion was 9.1%. What is the reactor volume?
b. When the volumetric flow rate was 0.2 dm³/min, the conversion was 50%. When the volumetric flow rate was 0.02 dm³/min, the conversion was 91%. Assuming the mixing patterns don’t change as the flow rate changes, what will the conversion be when the volumetric flow rate is 10 dm³/min?
c. This reaction is now to be carried out in a 1-dm³ plug-flow reactor where volumetric flow rate has been changed to 1 dm³/min. What will be the conversion?
d. It is proposed to carry out the reaction in a 10-m-diameter pipe where the flow is highly turbulent (Re = 106). There are significant dispersion effects. The superficial gas velocity is 1 m/s. If the pipe is 6 m long, what conversion can be expected? If you were unable to determine the reaction order and the specific reaction-rate constant in part (b), assume k = 1 min–1 and carry out the calculation!