Quantification of multiscale heterogeneity is the key to the simulation of gas-solid two-phase flow. The energy-minimization multiscale (EMMS) model can be used at different scales to describe local and global heterogeneities as well as steady-state fluid dynamics of gas-solid fluidization. However, the same cluster diameter correlation based on energy dissipation was used in all cases, which may give a smaller cluster diameter than single particle diameter at low solids fluxes. In this paper, a description of the solids mass transfer between the dilute and dense phases in heterogeneous gas-solid flow is proposed to replace the correlation of cluster diameter to avoid some problems associated with the empirical calculation of the cluster diameter. This cluster description can facilitate the prediction of the drag coefficient at the scale of numerical cells in computational fluid dynamics (CFD) at extremely low solids fluxes and the radial heterogeneity in large-scale circulating fluidized bed (CFB) risers with downward particle velocities near the wall. It is integrated with two-fluid model (TFM) to simulate the fluid dynamics in an industrial-scale CFB riser accurately, which is also accelerated significantly by using the predicted radial voidage distribution as the initial condition of CFD. (C) 2016 Elsevier B.V. All rights reserved.