Liquid-solid circulating fluidized beds have a number of attractive features suitable for processes where liquid-solid contact is important (Liang et al., 1996;Zhang et al., 2002). Liang et al. (1996) and Zheng et al. (2002) studied the radial profile of the solid fraction in the liquid-solid circulating fluidization regime and found that it is not uniform, unlike the conventional liquid-solid fluidized bed. This non-uniformity can affect reactant concentration distribution, mass transfer and ultimately reactant conversion. Therefore, information on the radial flow structure is crucial to reactor design and process optimization.
Most studies on the radial non-uniformity in a liquid-solid circulating fluidized bed have been experimental except the work by Liang et al. (1996) in which a core-annulus model was proposed. The core-annulus model assumes that there are two homogeneous flow regions (core and annulus) in the radial direction of the bed and uses the differences between them to describe the radial non-uniform flow structure. However, this model cannot provide a detailed radial profile of the solid fraction. Lucas et al. (2001) proposed a method for the prediction of the radial gas profile for a given bubble size distribution in gas-liquid systems. It is based on the equilibrium of the forces acting on a bubble perpendicular to the flow direction. Likewise, in a liquid-solid circulating fluidized bed, lateral forces acting on the particles determine the movement of the particle in the radial direction, and this creates a radial profile for the solid fraction. This work proposes a model to calculate the radial profile of the solid fraction in a liquid-solid circulating fluidized bed based on the balance of the lateral force and the turbulent dispersion force.