- Model-based: use of mathematical models, in our case restricted to mechanistic "grey box" models based on physical laws (e.g. balances of mass, momentum, energy,...)
- Analysis: The focus here is to use mathematical models and methodologies as tools to better understand system or process behaviour. This can be done by confronting hypotheses, translated into mathematical equations, with experimental observations. The goal is to develop new or extended mathematical models.
- Optimisation: The focus here is to use mathematical models and methodologies as tools to optimise the behaviour of a system or process. This alludes that a mathematical model is available that is able to describe the system behaviour.
- (bio)processes: The abovedescribed can be applied to basically any physical system. The current fields of application are environmental biotechnology, industrial biotechnology, food biotechnology and pharmaceutical systems.
Applying a variety of modelling frameworks to a variety of systemsThe complexity of a model structure to be used for modelling a certain process is mainly driven by the goal of the modelling exercise. In order to optimise complex systems, new drivers allow or force us in many cases to improve the understanding of these systems: increased availability of good quality experimental data (new and improved techniques), increased requirements of models (decreased model output uncertainty, new output requirements like energy and C-footprint) and increased computational power. The above, in its turn, forces us to use more complex modelling frameworks (see figure).
- Kinetic models: these models are typically based on simple mass balances and assume perfect mixing (CSTR) in order to restrict the problem to (sets of) ordinary differential equation(s) (ODEs) as these are easier to solve numerically. Examples are the Activated Sludge Models (ASMs) used in wastewater modelling, chemical reaction kinetics, drying processes, ...
- Computational Fluid Dynamics (CFD): When spatial heterogeneity is important with respect to the process performance (e.g. dead zones, recirculation), one needs to use partial differential equations (PDEs) that have space as independent variable (next to time). CFD is specifically designed for this purpose and consists of conservation equations of mass and momentum in both space and time.
- Population Balance Modelling (PBM): Some properties of a population of individuals can be distributed (e.g. particle size). PBMs are specifically designed to model dynamics of distributions. These dynamics can be governed by continuous processes (e.g. growth, drying) or discrete processes (e.g. particle aggregation, particle breakage)
BIOMATH is active in all of the above frameworks applying them to several systems. All the above frameworks are powerful in their own respect, but open even wider perspectives when combined:
- CFD-PBM: This is a widely booming field of research as the processes governing the PBM are typically connected to the hydrodynamic behaviour (e.g. shear driving flocculation) or the heat transport (e.g. drying processes) in the system. Vice versa, the state of a population of particles can also influence hydrodynamics (e.g. settling process, membrane filtration, rheological behaviour). This combined framework is powerful and can be applied to ample systems.
- CFD-kinetic: This combination of modelling frameworks has been used frequently in the field of chemical engineering, but to a much lesser degree for bioprocesses. However, substrate availability is of crucial importance for the latter. Currently, simple workarounds are used (e.g. tanks-in-series models). Their limitations force research into better alternatives.
- PBM-kinetic: This combination has been studied quite a bit in the field of fermentation technology. It allows to model the impact of lumped "average" kinetics versus distributed kinetics.
BIOMATH is active in all of the above applied to different systems. The combination of frameworks has the downside of being computationaly expensive. This can be tackled by using efficient solution methods and using the currently available computational power.
Methodology development for balancing modelsWhen combining different models to improve the description of a certain system or to decrease their uncertainty, these are often just "combined" whatsoever. The reason is often that these model were developed separately and often in different platforms. The main focus has, hence, been on coupling models allowing them to communicate. However, combining models has much more repercussions: data requirement for calibration, different parameter sensitivity, different uncertainty behaviour,... Sometimes, very complex models are combined with oversimplified models resulting in erroneous model calibrations and useless models. Finding the right balance of models requires the development of certain concepts that help to address these issues. A couple of these methodology-based efforts are ongoing at BIOMATH.
BIOMATH servicesThe research unit assists in the development of mathematical models by interpreting experimental results and combining this with in-depth knowledge of the processes by the domain experts.
Furthermore, expertise with regard to the following methodologies can be consulted (contact Prof. Nopens):
- Model development and calibration/validation
- Model-based process optimisation
- Sensitivity Analysis (local and global)
- Uncertainty Analysis
- Optimal Experimental Design (OED)
Last update: 03 january 2011, email@example.com