Mechanism analysis of the solids holdup variations in downer reactors based on volumetric flux

•Solids volumetric flux (Vs) is used to study the solids holdup in downers.•Vs should be more appropriate to define the high-density operation.•Limit operation conditions in the downer based on Vs are analyzed and defined.•The RSM analysis method based on Vs is applied to analyze solids holdup variation.