Gas-solid counter-current downer reactors,in which particles move downward in an upward gas flow,can achieve high solid concentration for high heat and/or mass transfer rates.However,the particles may reverse their direction or even be carried out of the reactor as the gas flow rate increases.This is closely related to flooding in counter-current flows.The energy minimization multiscale (EMMS) model well describes multiscale heterogeneity in gas-solid cocurrent upward flows.It is further developed to simulate gas-solid counter-current downward flows because similar heterogeneity can also be found in downers.The model characterizes well the axial hydrodynamics and predicts an inflexional voidage variation with superficial gas velocity in the fully developed region.This is supported by a simulation based on computational fluid dynamics and the discrete element method.The flooding predicted by the model agrees better with experiment than previous models.