Stochastic parcel tracking in an Euler–Lagrange compartment model for fast simulation of fermentation processes

The compartment model (CM) is a well-known approach for computationally affordable, spatially resolved hydrodynamic modeling of unit operations. Recent implementations use flow profiles based on Computational Fluid Dynamics (CFD) simulations, and several authors included microbial kinetics to simulate gradients in bioreactors. However, these studies relied on black-box kinetics that do not account for intracellular changes and cell population dynamics in response to heterogeneous environments. In this paper, we report the implementation of a Lagrangian reaction model, where the microbial phase is tracked as a set of biomass-parcels, each linked with an intracellular composition vector and a structured reaction model describing their intracellular response to extracellular variations. A stochastic parcel tracking approach is adopted, in contrast to the resolved trajectories used in CFD implementations. A penicillin production process is used as a case study. We show good performance of the model compared with full CFD simulations, both regarding the extracellular gradients and intracellular pool response, using the mixing time as a matching criterion and taking into account that the mixing time is sensitive to the number of compartments. The sensitivity of the model output towards some of the inputs is explored. The coarsest representative CM requires a few minutes to solve 80 h of flow time, compared with approximately 2 weeks for a full Euler–Lagrange CFD simulation of the same case. This alleviates one of the major bottlenecks for the application of such CFD simulations towards the analysis and optimization of industrial fermentation processes.