Steady-state modeling of axial heterogeneity in CFB risers based on one-dimensional EMMS model

• Cluster number density is an indicator to the axial heterogeneity in CFB risers.
• Cluster number density is defined by local and global stability conditions.
• One-dimensional EMMS model enables reproducing the S-shaped profile in CFB risers.

Axial heterogeneity in circulating fluidized bed (CFB) risers is very important to the design of fluidized bed reactors, which is, however, still unable to be described in theory. Based on a successful description of local hydrodynamics in gas–solid flow, the Energy-Minimization Multi-Scale (EMMS) theory further relates axial hydrodynamics with local and global stability conditions in the system, providing a theoretical way to account for the axial heterogeneity in CFB risers. This research reveals that the interaction between particle clusters and the dilute phase as well as the surrounding dense phase has a significant effect on their dynamical evolution. Similar to cluster diameter in the EMMS theory, number density of particle clusters serving as a comprehensive indicator to the heterogeneity in gas–solid flow is constrained by both local and global stability conditions in the system. With the above cognition, a one-dimensional EMMS model is developed to perform steady-state modeling of the axial heterogeneity in CFB risers. The model successfully reproduces a complete transition zone and the parametric effects on it at the choking condition. The S-shaped axial voidage profile calculated by the one-dimensional EMMS model is in good agreement with the experimental results in gas–solid fast fluidization. This research is not only the first step toward implementing the three-scale computation in virtual process engineering (VPE), but also of referential significance to industrial chemical process development.