Finite‐element methods for steady‐state population balance equations

A finite‐element algorithm is developed to solve the population balance equation that governs steady‐state behavior of well‐mixed particulate systems. Collocation and Galerkin methods are used to solve several test problems in which aggregation, breakage, nucleation and growth (and combinations of these phenomena) occur. It is shown that the Galerkin method must be used in growth problems to obtain a well‐conditioned system. In all the cases investigated, density distributions and their moments are accurately predicted by the method. In a direct comparison with the discretized population balance (DPB) of Litster et al. (1995) the finite‐element method proves capable of predictions that are typically two orders of magnitude more accurate than those of the DPB. These results were obtained using smaller systems of equations and with considerably less computational power.