Part I: Dynamic evolution of the particle size distribution in particulate processes undergoing combined particle growth and aggregation

Abstract

The present study provides a comprehensive investigation on the numerical problems arising in the solution of dynamic population balance equations (PBEs) for particulate processes undergoing simultaneous particle growth and aggregation. The general PBE was numerically solved in both the continuous and its equivalent discrete form using the orthogonal collocation on finite elements (OCFE) and the discretized PBE method (DPBE), respectively. A detailed investigation on the effect of different particle growth rate functions on the calculated PSD was carried out over a wide range of variation of dimensionless aggregation and growth times. The performance (i.e., accuracy and stability) of the employed numerical methods was assessed by a direct comparison of predicted PSDs or/and their respective moments to available analytical solutions. It was found that the OCFE method was in general more accurate than the discretized PBE method but was susceptible to numerical instabilities. On the other hand, for growth dominated systems, the discretized PBE method was very robust but suffered from poor accuracy. For both methods, discretization of the volume domain was found to affect significantly the performance of the numerical solution. The optimal discretization of the volume domain was closely related with the satisfactory resolution of the time-varying PSD. Finally, it was shown that, in specific cases, further improvement of the numerical results could be obtained with the addition of an artificial diffusion term or the use of a moment-weighting method to correct the calculated PSD.