Determining the Solids Mass Flow Rate in a Gas–Solids Riser Using an Integral Momentum Balance

Abstract

Determining the solids mass flow rate (W s ) in a gas−solids riser often entails closing a one-dimensional, two-fluid model by relating the total wall friction (F w ) and the drag coefficient (C d ) to riser conditions. However, this requires relating these two parameters to several riser variables making it difficult to apply these relations generally. In this work, closure is obtained using a model for the conservation of linear momentum in the acceleration (entrance region) of a riser. The model relates the total forces imposed on the control volume to the change in linear momentum of the solids. Additional expressions are obtained from the model which provide a means for defining the boundary condition at the entrance to the control volume. The resulting model provides a means of determining the solids mass flow rate (W s ) from three readily measured and physically relevant riser operating parameters: the dynamic pressure drop across the acceleration section (ΔP a ), the normalized dynamic pressure gradient at the end of the acceleration section (P a ′(1)), and the superficial gas velocity (U) in a riser. The agreement between measured and model values ranges from very good to excellent with the average absolute deviation being <5% of the measured values.