Development of a hybrid sectional quadrature-based moment method for solving population balance equations

Various ad hoc methods have been proposed for solving population balance equations (PBEs). Relatively little discussion has taken place to generalize these discretization approaches. In this paper, a flexible method is presented for the discrete solution of PBEs. The method is a generalization of similar techniques. The approach allows for complete control of the discretization and order of approximation of the solution. A simple error analysis of the method is provided. Simulations were performed for pure random breakage, constant kernel aggregation, additive kernel aggregation, combined random breakage/constant kernel aggregation, and free-molecular Brownian coagulation. The numerical results are compared to exact solutions and simulated results from the literature. It was found that increasing the quadrature order within the sections is a more efficient means to increase accuracy as opposed to finer discretization.