School of Engineering :: The University of Jordan :: Multilevel Discrete Modelling of Microbial Cell Cultures using Population Balances

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Multilevel Discrete Modelling of Microbial Cell Cultures using Population Balances

Microbial cell population balance models are used because of culture heterogeneity due to complex intercellular phenomena governed by cell growth, substrate utilization, and product formation. To solve these models, an efficient multilevel system approach based on conservation of cell distribution moments is introduced. This conservation is propagated along the characteristic curves of these hyperbolic conservation laws. This is assured by the careful design of numerical discrete schemes that pass the conserved discrete information from the initial state to its final extracellular state. The discrete model on each layer is derived with a guarantee to satisfy the conservation of cell total number and the mean cell biomass. Many reference solutions based on the Chebyshev-QMOM, the maximum entropy method, and the Lax-Wendroff finite difference scheme are used to validate the developed model. When compared to these methods, the model exhibits extreme accuracy and rapid convergence at a low CPU time cost.​​