Comparison between the Classes Method and the Quadrature Method of Moments for Multiphase Systems

Investigation of multiphase systems generally requires the solution of the population balance equation; bubble columns, crystallisation and precipitation reactors are some examples of important industrial applications. As mixing also plays an important role in determining phase interactions, often the population balance has to be included in a Computational Fluid Dynamics (CFD) code. This can be accomplished only if the source term is provided in an adequate way. Several methods have been proposed; one of the most popular is the Discretised Population Balance (DPB) which presents the disadvantage of requiring an elevate number of scalars to be solved, leading to high computation times. A promising alternative is the Quadrature Method of Moment (QMOM) in which the population balance is written in terms of the transport equation of the moments of the number density function, and all the integrals involving this function are solved through an ad-hoc quadrature approximation. The method has been validated and extended to breakage in previous works, while in this work its performance is compared with those of a DPB approach. The comparison is made in terms of accuracy of prediction, computational time and simplicity of implementation in a CFD code. 1 Corresponding author: [email protected]; current affiliation: Dept. of Chem. Eng., Iowa State University, 3131 Sweeney Hall, Ames (IA) 50011-2230, USA