Numerical Technique for Solving Population Balances in Precipitation Processes

A simple, accurate and efficient numerical technique for solving the dynamic population balance associated with precipitation/crystallization reactors is presented. The basic approach is to determine the solute concentration dynamics first using the method of moments and an efficient ordinary differential equation solver, and then to solve the dynamic population balance, a partial differential equation having coefficients which depend on the known solute concentration, by standard finite difference techniques. The method is illustrated by simulating the dynamics of MSMPR and semi-batch reactors for BaSO4 precipitation. The technique should be applicable to a wide range of population balance models.