Mathematical analysis of a seeded, nonnucleating continuous zeolite crystallizer

Recently, a new operational scheme for a zeolite crystallizer was reported which facilitated the experimental investigation of high silica ZSM-5 crystal growth and could be used for nucleation studies. The unique feature of the operation was that seed crystals were placed in an appropriate solution in a gently stirred tank vessel, and fresh clear reagent solution was pumped into the vessel on a continuous basis, with the same volumetric flow rate of fluid being removed on a continuous basis. The effluent stream contained a representative sample of the crystals in the vessel, and, therefore, the crystal concentration in the vessel itself decreased with time. A mathematical model of the system was presented by the authors. A more comprehensive mathematical model of the system is presented which accounts for the kinetic and operational steps in that crystallizer operation. The moment transforms of the population balance equation with constant system volume and size-independent crystal growth rate formed the basis of the model. It is shown that an approximate quasi-steady-state form of the model is informative, and yet flawed, whereas the complete transient model fits the experimental data reported previously. It also is shown that the change of the average crystal size with time represents the crystal growth rate at the instantaneous solution concentration, even when the data are not linear with respect to time.