When gas is passed upward through a bed of solid particles, above a certain velocity the drag force balances the particles' weight and the bed fluidises: the solid begins to behave like a liquid.
The threshold velocity (the minimum fluidisation velocity) is found by equating the bed pressure drop to the particle weight; Ergun's correlation is the classical source for that pressure drop [1].
Bubbles: both the solution and the problem
Above the minimum fluidisation velocity the excess gas passes through the bed as bubbles.
The benefit: rising bubbles mix the solids. That is why fluidised beds give excellent heat distribution and operate almost isothermally.
The harm: the gas inside a bubble passes through the bed with almost no contact with the solids — a bypass route. Reaction or heat transfer efficiency can therefore fall below expectation.
The design is concerned with controlling bubble size: too small and the mixing is weak, too large and the bypass is excessive.
Other regimes
As the velocity rises the bed passes through channelling, slugging and finally pneumatic transport. Each regime has a different modelling approach; choosing a model without knowing which regime you are in is meaningless.
Modelling
Because the solids volume fraction is high, tracking particles individually is impractical; the two phases have to be solved as interpenetrating continua. See the multiphase note.
The result depends strongly on the interphase drag and particle-particle collision closures. That is an uncertainty item and should be reported.
The problem is also inherently transient: bubbles form, coalesce and burst. A steady solution cannot see the bubbles at all and shows the bed as homogeneous. See the steady versus transient note.
References
- Ergun, S. (1952). Fluid flow through packed columns. Chemical Engineering Progress, 48(2), 89–94.
- Morsi, S. A. & Alexander, A. J. (1972). An investigation of particle trajectories in two-phase flow systems. Journal of Fluid Mechanics, 55(2), 193–208. DOI: 10.1017/S0022112072001806