The dual-quadrature method of generalized moments using automatic integration packages

Despite the several advantages of the moment based methods in solving population balances models, the lack of accuracy of their solutions is still a drawback. This work presents a solution to this problem using the DuQMoGeM, a moment based method written in a weighted residual formulation. The proposed methodology consists of using automatic integration packages in the DuQMoGeM to eliminate the integration errors in the evaluation of the moments of the population balance equation. The results show that the source of the errors in the generalized moments is related to the accuracy of the numerical integration of the aggregation and breakage terms. The use of automatic integration packages in the DuQMoGeM allows the error control of the calculated moments. However, for some problems, accurate values of a small set of moments do not guarantee the accurate representation of the number density distribution function due to the finite moment inversion problem.

► DuQMoGeM was extended to multivariate problems. ► Adaptive quadrature packages were used to accurately integrate the PBE moments. ► Three bivariate problems with breakage and aggregation were solved. ► Generalized moments of the distribution functions were accurately calculated.