Modeling agglomeration processes in fluid-bed granulation

Many agrochemicals are formulated as water dispersive granules through agglomeration, beginning with a fine powder ( similar to 1 mu m) and ending with granules on the order of 500 mu m. Powders are charged into a granulation system with a liquid binding agent, and granules are subsequently grown to an appropriate size. Granulation in fluid beds is presented using a mass conserving discretized population balance equation. Coalesce kernels governing the rate and extent of granulation are assumed dependent on the Stokes number, which is indirectly linked to important process variables (air and binder flow rate bed charge, bed geometry) such that the physical processes governing particle coalescence and rebound are correlated to process variables. A new coalescence kernel is proposed based on physical insight, simplicity, and deterministic equivalent modeling to account for uncertainty. This kernel is based on a Stokes number method where uncertainty in the Stokes number is characterized by polynomial chaos expansions. The magnitude of the coalescence kernel is proportional to the probability of the distribution of Stokes number exceeding a critical value. This mechanistic/semiempirical approach to fluid-bed agglomeration fosters an environment for process scaleup by eliminating specific equipment and process variable constraints to focus on the underlying mechanisms for proper scale-up procedures. Model predictions using this new kernel are then compared to experimental pilot-plant observations.