Dynamic modeling of the circulating fluidized bed riser

Abstract

Dynamic modeling is required to understand hydrodynamics of a circulating fluidized bed (CFB) riser as a function of time. The paper develops a dynamic model of the riser from the conservation of solid mass. Solid mass that flows out of the riser requires particle residence time to close the mass balance equation. The mean residence time of solids was derived as the riser length divided by the superficial riser gas velocity normalized by a ratio of solid concentration in the riser outlet to that in the riser itself. For bed materials including high-density polyethylene beads, glass beads, and cork, the percentage of solid concentration in the horizontal crossover pipe connecting the riser exit and the cyclone inlet was found to be 22% of the average concentration of solids in the riser. Upon finding the particle residence time, we calculated the solid flow rate out of the riser and along with the knowledge of solids flowing into the riser column we determined the riser inventory as a function of time. We used the estimated solid inventory to model overall pressure drop across the riser from the conservation of momentum. The momentum equation included the balance of pressure force by the hydrostatic head of solids, and the wall frictions due to gas and solids in a fully developed zone. The prediction of overall riser pressure drop compared well with its measured values at many dynamic conditions. Therefore, our dynamic model is useful for developing advanced control strategy or for improving existing control systems of the CFB plant. The residence time approach is also useful for the design of a transport reactor. The technique also comes handy when setting up the boundary condition for the overall pressure drop in the CFD modeling that can simulate incremental pressures along the riser height.