Structured mixing model for stirred bioreactors: An extension to the stochastic approach

The potentiality of a stochastic approach is examined in the case of a mixing model for stirred vessels. This model is interesting due to the probabilistic and discrete properties that can be used further to facilitate the implementation of a hydrodynamic model into complex reacting systems, such as those encountered in bioprocesses. Stochastic model performances are compared to well known deterministic compartment mixing models (CM). It appears that parameters coming from CM can be used in the stochastic approach and that they give equivalent results. A methodology is elaborated that simplifies the determination procedure of the adjustable parameters of the stochastic model. The most important parameter to determine is the time step of a simulation performed by the aim of the stochastic model. Indeed, the time step is not explicitly given by the model and a correlation is necessary to translate simulation intervals into real time increments. After an appropriate analysis of several mixing systems (single or multi-agitated), it appears that a simple correlation involving circulation time could be used to perform this translation. The correlation contains an adjustable parameter, which has been quantified for the operating conditions covered in the study. The circulation of micro-organisms was also simulated simply by using the transition matrix coming from the stochastic model, which shows the potentiality of this kind of model in the field of complex reacting systems, such as those encountered in bioprocesses.