Mechanistic Modelling for Risk-Based Monitoring of Lactic Acid Bacteria Cultivations

There is increasing interest in process analytical technology (PAT) tools for on-line monitoring and control of bioprocesses. When modelling large-scale production processes, microbial processes, heterogeneous process conditions, and process uncertainties have to be considered. Heterogeneous process conditions arise because of insufficient mixing at a large scale, and they often have an impact on microbial activity and product yield as the cells have to adapt to changing process conditions when circulating through the bioreactor.

Over the past years, computational fluid dynamics (CFD) and compartment models have been applied to account for fluid dynamics in bioreactors. They have been coupled with biokinetic models, and employed to study substrate and oxygen gradients. The focus of this work was on pH gradients in lactic acid bacteria cultivations as the pH is a critical process parameter for these cultivations.

Process uncertainties are considered with a Monte Carlo simulation allowing risk-based decision making. An aerotolerant Streptococcus thermophilus batch cultivation was utilized as a case study, where the cells are the target product as they are used inthe dairy industry as starter cultures, e.g., for yogurt and cheese production.

In this work, a mechanistic model was developed to describe the microbial cultivation, and it was applied together with a CFD and compartment model to account for mixing in the bioreactor. The model was applied to gain deeper process understanding, to test new process conditions, and as a soft sensor for risk-based monitoring of the cultivation.The kinetic model consisted of a biokinetic model and chemical model.The biokinetic model described biomass growth, lactose (substrate) consumption, and lactic acid production (as a by-product) among others.

The chemical model was utilized to predict pH. A comprehensive parameter estimation was performed using lab-scale data in order to assess the identifiability, sensitivity, and uncertainty of model parameters. The model was comprehensively validated with independent batch and continuous cultivations exhibiting arelative mean error of less than 10 % for the biomass concentration.The formation of pH gradients was investigated in a 700-L bioreactor.

A one-phase CFD model and compartment model were developed and validated with tracer-pulse experiments to evaluate mixing time. A mixing time of 48 s was measured while the CFD and compartment models predicted 46 and 52 s at 240 rpm, respectively. The kinetic model was then coupled withboth the CFD and compartment model, and a cultivation was simulated withboth models.

Besides an accurate prediction of the biokinetic state variables, both models predicted the pH gradients qualitatively with a deviation of lessthan 0.15 pH units. However, the CFD simulation took 4 days on 20 CPU cores, while the compartment model was solved within 2 s on an ordinary computer.The compartment model was integrated in a probabilistic soft sensor for the monitoring of lactic acid bacteria cultivations.

The soft sensor used the limited on-line measurements, namely the balance read out of the base (ammonia) addition and pH, to update the model parameters that were used as an input to the dynamic model. A Monte Carlo simulation of the model was performed to account for uncertainties in model parameters, initial process conditions, and on-line measurements.

The soft sensor was validated with historical lab-scale and pilot-scale experiments. If the soft sensor was applied on-line during the production, it would equip plant operators with a tool to assess pH gradients on-line and to take risk-based actions. The probability of not achieving the target biomass yield was predicted based on the probabilistic model predictions.

In the investigated cultivation, the risk was to lose 3.5 % of total production capacity. The operators could react accordingly, for example, by increasing the stirrer speed to reduce the pH gradient and achieve the desired production capacity.