Solids motion in the annulus of a spouted bed can be considered as a quasi-static deforming flow similar to that in a silo. Several simplified granular-flow models by Sullivan et al. including kinematic

potential and plastic theory

are investigated in this paper. The model of solids circulation by Morgan et al is combined with the above granular models to predict solids axial velocity in annulus. The finite element method is adopted and the complicated spout-annulus shape geometry is especially considered. Simulated results are compared with experimental data from He et al. It indicates that kinematic theory agrees well with experiments. The regressed kinematic constant B for annulus flow is greatly larger than that for silo flow. Potential theory obtains similar result with kinematic theory

but is incomplete in its physical significance. Plastic theory gives unrealistically oscillatory solution because of the over simplification of stress field. Finally

the Euler equations coupling the momentum transfer of solids with the frictional stress field are proposed for future study.