Three-moments conserving sectional techniques for the solution of coagulation and breakage population balances

Abstract

Sectional (zero order) methods constitute a very important class of methods for the solution of the population balance equation offering distinct advantages compared to their competitors, namely, higher order and moment methods. For the last ten years a particular sectional method, the so called fixed pivot technique (Kumar et al, 1996) has been the one most extensively used in the scientific community for the solution of the coagulation and breakage equations because it offers arbitrary grid choice and conservation of two moments of the particle size distribution. More recently, a new method (called cell average technique; Kumar et al, 2006; Kostoglou, 2007) has been developed which gives more accurate results than the fixed point technique. In the present work, the extension of this new method in order to conserve three moments is attempted. A stable algorithm for the solution of the coagulation and breakage equation is developed. The new method allows improved computation of moments of practical interest.