When operated at twice the minimum fluidization velocity 86.5% conversion is realized in a fluidized bed reactor which has aof 0.5. It is proposed to increase the pressure from 1 atm. to 4.0 atm. and decrease the temperature from 427°C to 227°C. Assuming the height to diameter ratio is large, what new column height (relative to the old height) will be needed for a column of the same diameter to achieve the same conversion if the reaction is:

(a) Mass Transport limited with very few particles in the bubble phase and very small gas diffusivity.
(b) Reaction limited and the activation energy is 19,870 cal/mole. The volumetric flow rate,₀ (hence superficial velocity) is to be the same in both cases.