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[CACIE]

I am designing an oxidation reactor for cumene with air to produce cumene hydroperoxide. The reactor is operating at 120^oC and 6 bar. I have found kinetics which explain that the reaction is in the slow reaction regime and hence non mass transfer controlling. I have therefore sized my reactor using a plug flow model using simplified kinetics and a Matlab programme.

However after speaking with my lecturer I have to show that the kinetics are the controlling mechanism and I can do this by calculating a reactor volume required for the kinetic model and the volume of reactor required when it is purely mass transfer controlling. The comparison of the two volumes will show that the larger volume is the controlling mechanism.

I have begun calculations for the mass transfer controlling mechanism. I have obtained a volumetric mass transfer coefficient (k_la) and a diffusion rate which are 2.840 m³/s and 1.12758x10^-5 m²/s respectively. However I am unsure how to get a reactor volume required from these values? I have listed a number of the values I have used in calculations below.

V_G = volumetric gas inlet flowrate = 0.1637 m³/s
V_L = volumetric liquid inlet flowrate = 0.004657 m³/s
d_R = column diameter = 2.18 m (which I have chosen)
k_la = 2.840 m³/s
D = Diffusion rate = 1.12758x10^-5 m²/s

Would I need to calculate a diffusion length from this and this would be my reactor length required?