A Comparative Study of Numerical Methods for Solving Continuous Population Balance Models for Aggregation Processes

In this paper two discretization methods—Hounslow's fixed discretization method and Ramkrishna's adjustable discretization method—will be applied to population balance models in order to compare their performance under various modelling and simulation scenarios. The methods will be tested using an integrated dynamic modelling and simulation system for analysis of particulate processes in the case of agglomeration in a continuous granulation unit where the fresh feed and the recycle have different particle size distributions. In this comparison we will consider the accuracy of the results, the computational time required and the modelling effort. The results show that Hounslow's method is able to give satisfactory predictions for small to medium particle size ranges but the quality of predictions for large size ranges is poor. The method of Kumar and Ramkrishna is slightly more complex than Hounslow 's method but is able to give good predictions for all particle size ranges. Both methods requires similar computational time when a geometrical grid with a size ratio equal to 2 is used while Kumar and Ramkrishna's technique requires more time to be implemented and solved for finer grids.