Comparison of numerical solution strategies for population balance model of continuous cone mill

Population balance models are routinely used for modeling particulate processes involving breakage, agglomeration, crystallisation, etc. In this study, a comparison between three different numerical solution strategies for breakage population balance models is presented. Results are obtained for the fixed pivot technique, moving pivot technique and the cell average technique. These techniques are first compared for models whose solutions are analytically available. The comparison shows that fixed pivot lacks the accuracy of both moving pivot and cell average at coarser grids. At finer grids, all the three solution strategies give similar errors. With increasing grid fineness, all the three methods converge to a grid independent solution. Moving pivot is computationally the most expensive methods, followed by the cell average and fixed pivot. These methods are then applied to a conical screen mill modelled by a continuous population balance equation. For all the discretizations considered, cell average computes a higher median particle size value than the fixed pivot and moving pivot.status: Published onlin