Model-based scale-up methodology for aerobic fed-batch bioprocesses: application to polyhydroxybutyrate (PHB) production

This work presents a general model-based methodology to scale-up fed-batch bioprocesses. The idea behind this approach is to establish a dynamics hierarchy, based on a model of the process, that allows the designer to determine the proper scale factors as well as at which point of the fed-batch the process should be scaled up. Here, concepts and tools of linear control theory, such as the singular value decomposition of the Hankel matrix, are exploited in the context of process design. The proposed scale-up methodology is first described in a bioprocesses general framework highlighting its main features, key variables and parameters. Then, it is applied to a polyhydroxybutyrate (PHB) fed-batch bioreactor and compared with three empirical criteria, that are traditionally employed to determine the scale factors of these processes, showing the usefulness and distinctive features of this proposal. Moreover, this methodology provides theoretical support to a frequently used empirical rule: scale-up aerobic bioreactors at constant volumetric oxygen transfer coefficient. Finally, similar process dynamic behavior and PHB production set at the laboratory scale are predicted at the new operating scale, while it is also determined that is rarely possible to reproduce similar dynamic behavior of the bioreactor using empirical scale-up criteria.