An energy-based model of gas-solid transport in a riser

A simple and reliable method to estimate the solid holdup distribution and solid residence time in a gas-solid riser flow is essential to the optimum design and efficient operations of riser reactors. The traditional approach of equating the local solid holdup to the pressure drop in a riser overlooks the effects of solid acceleration and energy dissipation in the acceleration and dense phase transport regions. The energy dissipation in these regions is mainly due to the interfacial friction between interstitial gas and suspended solids, inter-solid collisions, as well as solid-wall fraction. Most momentum-based models fail to account for the energy dissipation of inter-solid collisions, and the models using the simple granular kinetic theory fail to account for the energy dissipation in micro-sliding or rolling from off-center inter-solid collisions. This paper presents an energy-based mechanistic model to analyze the partitions of the axial gradient of pressure by solid acceleration, collision-induced energy dissipation and solid holdup in gas-solid riser flows. Based on this model, more reasonable estimation of axial distributions of solid holdup and resulted solid velocity can be obtained. Our analysis shows that the effect of solid acceleration on the pressure drop can be significant in a range of moderate solid holdup (typically from 3.5% to 12% by solid volume fraction) whereas the effect of energy dissipation becomes important in the dense phase transport region (typically when the solid volume fraction above 5%). The exemplified results indicate that the traditional approach of equating the local solid holdup to the pressure drop overestimates the solid holdup by an error up to 50% in the acceleration and dense phase transport regions in typical gas-solid riser flow applications.