On the representation of QMOM as a weighted-residual method—The dual-quadrature method of generalized moments

Quadrature-closed moment-based methods for the solution of the population balance equation were analyzed. The QMOM was shown to be a particular case of a method based on generalized moments (QMoGeM). Then, a weighted-residual method (WRM) based on the generalized moments was derived (WRMoGeM). If it is closed by the Gauss–Christoffel quadrature, the resulting method (QWRMoGeM) was shown to be identical to the QMoGeM, giving the correct representation of QMOM as a WRM.The WRMoGeM formulation was used to derive a new method (DuQMoGeM) that employs two quadrature rules, one for discretizing the particulate system and other to accurately integrate the integrals in the equations for the generalized moments. A Galerkin version of this method was implemented and used to solve several examples with known analytical solutions. The DuQMoGeM solutions for breakage and aggregation problems were shown to be more accurate than the QMOM solutions.

► A quadrature-closed method was developed to solve the population balance equation.
► The method was called DuQMoGeM (dual quadrature method of generalized moments).
► Eleven test cases were solved for problems with growth, breakage and aggregation.
► DuQMoGeM is more accurate than QMOM for breakage and aggregation problems. DuQMoGeM can solve problems where QMOM fails or cannot be used.