The dense zone (assumed to be the bubbling bed) is modeled according to the modified two-phase theory. Bubble size is calculated as a function of bed height (Darton and LaNauze, 1977), and it is assumed that all bubbles at any cross­section are of uniform size:

or

where A/Nor is the number of orifices per unit of cross-section area of the bed.

The interphase mass transfer between bubbles and emulsion, essential for the gas-solid reactions, is modeled semi-empirically using the specific bubble surface as the exchange area, the concentration gradient, and the mass-transfer coefficient. The mass-transfer coefficient, KBE, based on the bubble-emulsion surface area (Sit and Grace, 1978), is

Umf 4£mfDr Ub

“ = + ПВ

where Umf and emf are, respectively, fluidization velocity and voidage at a minimum fluidizing condition, Dr is the bed diameter, and UB is the rise velocity of a bubble of size dB.

The axial mean voidage in the freeboard is calculated using an exponential decay function.