Ontwikkeling van hybride modellen in (Bio)Chemische Heterogene Populatiesystemen

Many processes within the chemical and biochemical industry are characterized by complex phenomena that originate from various mechanism. A property shared by many of these processes, is the presence of a two-phase system, where one of the phases corresponds with (often solid) dispersed entities or particles, and the other phase is a continuous fluid phase. The dispersed particles often interact with the surrounding continuous medium, or with each other. For example, in pharmaceutical crystallization, solid crystals form from dissolved solutes in a liquid. Or, dispersed unicellular life forms can perform certain functions, such as molecule production in fermentation, or removal of harmful components in wastewater. Collectively, these systems are called heterogeneous population systems, where individual entities (e.g., a single cell or crystal) are slightly different from each other, but still share many common properties. Such heterogeneous population systems can be mathematically described as a Population Balance Model (PBM). This deterministic framework describes the time-dependent evolution of the heterogeneous population using a partial differential equation in combination with ordinary differential equations. The PBM provides a generalized structure that can be adapted to various heterogeneous population systems. However, the PBM contains certain terms that need to be identified in order to resolve the system dynamics for practical applications. This dissertation explores and develops different methods to identify these unknown terms. Two approaches are distinguished: the knowledge-driven identification, using expert information from literature, and data-driven identification, relying on experimental observations. In both cases, the approach is merged with the PBM theory, constituting a hybrid model. As a first practical example, the collection and processing of data from flow cytometry is considered, which is used to characterize and quantify heterogeneity in the system at a high-throughput rate. For this purpose, a procedure is developed, which utilizes a physical model of light scattering aiming to relate light scattering properties with cell diameter. This is applied to estimate size distribution within an algae culture from experimental data. A novel framework combining PBM with Flux Balance Analysis (FBA) is proposed. The latter is an approach that describes cellular behavior from its metabolic network, relying on expert knowledge available in online databases. The novel approach is first tested against a small-scale Escherichia coli network as validation. The method is then extended to a genome-scale metabolic model of green algae species Chlamydomonas reinhardtii. The novel method is validated and verified based on the small-scale model, which demonstrates potential use cases. In addition, the method can be formulated for the genome-scale C. reinhardtii model. With respect to a parameter estimation in this model, some shortcomings are observed. These mainly originate from numerical artifacts in the model solution, and from a lack of the right type of experimental data. Some potential improvements/solutions towards this are discussed. A second system identification method relies on data-driven approaches to infer kinetic rates in the PBM. This utilizes Gaussian Process Regression (GPR) in combination with the PBM. Two variants of this method are tested. The first utilizes the experimental algae data, in combination with the PBM equations. These are adapted within the GPR framework, in order to infer the cell division rate using the experimental dataset. The second variant relies on a transformation of the PBM into a reduced moments-based model. The reduced model is combined with GPR to infer growth and nucleation kinetics in a crystallization system. This is represented via a simulated continuous crystallization model. The influence of measurement noise is evaluated, and indicates that the GPR is able to quantify this uncertainty in its description of kinetic rates. In both variants, the inferred kinetics are successfully used to simulate the heterogeneous population system. The dissertation aims to generalize different approaches for system identification in a PBM. The focus lies on methodological development while using specific case studies for demonstration. The developed system identification tools provide opportunities for the use of the PBM to simulate, design, measure, and control physical heterogeneous population systems.