An efficient approximate moment method for multi-dimensional population balance models – Application to virus replication in multi-cellular systems. (16th March 2017) - Dürr, Robert; Müller, Thomas; Duvigneau, Stefanie; Kienle, Achim
Abstract: Many particulate processes in process and bioprocess engineering can be described with multi-dimensional population balances. Approximate moment methods are frequently used for their solution. In the present paper a new approach is presented, which is particular efficient when the number of internal coordinates is high. It combines the direct quadrature method of moments with monomial cubatures. With the new method the computational effort increases only polynomially, in the simplest case even only linearly with the number of internal coordinates, compared to an exponential increase for the well known Gausssian cubatures. The technique is evaluated for a five dimensional benchmark problem describing virus replication in continuous cell cultures. Furthermore, the algorithm is applied to analyze influenza virus replication in genetically modified cell lines. Highlights×: Approximate moment method to solve multidimensional population balance equations. Combination of the DQMOM with a sophisticated choice of weights and abscissas. Evaluation of the proposed technique for a five dimensional population balance model. Moments are accurately approximated while keeping the numerical effort moderate. Application to influenza A virus replication in mammalian cell cultures. Model based investigation of effects of genetic modifications on process.