Reasonable description of cluster parameters is significant for the development of drag model for heterogeneous gas-solids flows. This study proposed the cluster model for solids concentration in clusters and the cluster size based on theoretical analysis. The profile of cluster parameters with solids concentration had a peak locating between local solids concentration of 0.1 and 0.15

indicating largest heterogeneity there. The cluster model was validated directly by experimental data. Energy minimum multiscale method (EMMS) was improved by introducing the cluster model. The improved drag model agreed well with the experiment-based empirical model. Drag correction factors of both models first decreased and then increased with increasing solids concentration

and tended to unity at extremely small solids concentration close to zero and solids concentration at minimum fluidization. The improved drag model was coupled with the two-fluid model for simulations of gas-solids flows in CFB risers containing Geldart A and B particles. Heterogeneous solids distributions

local slip velocity

local heterogeneity and choking state were predicted and agreed well with experimental results

indicating the reasonability of the cluster and drag models.