Application of sedimentation model to uniform and segregated fluidized beds

Similarities between fluidization and sedimentation have been recognized for decades, and it is even common practice to estimate the solids holdup in the particulate regions of the fluidization beds using expressions developed for describing rates of particulate sedimentation. The most frequently used expression is that of Richardson and Zaki. This equation has a simple form and predicts for suspensions of uniform particles sedimentation rates that are proportional to the Stokes settling velocities at infinite dilution and proportional to the void fraction raised to an exponent between 2 and 5. The value of the exponent depends upon the Reynold's number for the settling particles. However, recent measurements have shown that this relation does not always give an accurate description of the slip velocities or the solid holdup in particulate fluidized beds. The Richardson and Zaki equation predicts slip velocities between the fluid and the particles that are usually too high; this means that the predicted solids holdup is often lower than those measured experimentally. This paper incorporates concepts of unimodal and bimodal sedimentation to develop a model that accurately predicts bed expansion during particulate fluidization. During bed expansion a particle is considered to be fluidized not by the pure fluid, but by a slurry consisting of the pure fluid and other surrounding particles. The contributions of the other surrounding particles to the additional buoyant and drag forces are accounted for with the use of effective fluid or slurry properties, density and viscosity. As bed expansion proceeds, influences of the surrounding particles decrease; therefore, these effective properties are functions of the changing void fraction of the suspension. Furthermore, the expansion index, which empirically represents the degree to which viscous and inertial forces are present, is traditionally a function of a constant terminal Reynold's number. Because the effective fluid properties are considered to be changing as fluidization proceeds, the degree to which viscous and inertial forces also changes; therefore, the expansion index is written as a function of a local or intermediate Reynold's number. These concepts are further extended to bimodal fluidization in which small or light particles aid in the fluidization of the large or heavy particles. The results indicate that the proposed model more accurately predicts particulate bed expansion for a wider range of systems (gas - liquid, low Reynold’s number - high Reynold's number) than other analytical or empirical models.