Use of Method of Characteristics to Solve Population Balance Equations for a Continuous Perfectly Mixed Granulator

BERTIN, DIEGO ESTEBAN; BUCALÁ, VERÓNICA; PIÑA, JULIANA

Berlín, Alemania

Congreso; 4th International Conference on Population Balance Modeling; 2010

The population balance equation (PBE) is the formal tool, based on conservation laws, to calculate the particles distributions (PDs)1,2. In granulation processes, the internal coordinate is normally related to particle size. Nevertheless, PDs with respect to other properties (e.g., temperature, porosity, moisture content, etc.) may be of importance. Although there are analytical solutions for some special cases of the population balance, in general numerical methods are required to obtain the PDs. The PBE should be solved easily and its solution should be accurate and low computation time consuming. The Method of Characteristics (MOC) is based on the Lagrangian approach, i.e. on the description of each particle along its path within the system. Regarding the PBE, MOC allows lumping the accumulation and convective flow terms within the material derivative. By applying MOC, the PBE (partial differential equation) becomes a system of ordinary differential equations along the characteristic curves. In the present work MOC is used to solve the PBE for a melt granulation process in a continuous fluidized bed. Assuming that coating is the only mechanism responsible for the particle size change, the steady and unsteady-state PBE considering one (particle size) or two (particle size and temperature) internal coordinates is solved.   In the continuous fluidized granulator, small particles (called seeds) are constantly incorporated to the bed while a melt is sprayed into the unit. The fluidization air facilitates the solidification of the tiny atomized drops deposited onto the solid particles, leading to the growing phenomenon known as accretion. Besides the particle size, the temperature is selected as an additional internal coordinate. In fact, if the temperature of any particle surpasses the maximum allowable, bed quenching may take place.