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

Abstract

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.

From Spatial-Temporal Multiscale Modeling to Application: Bridging the Valley of Death in Industrial Biotechnology

“…Haringa et al coupled the 9-pool metabolic model of Penicillium chrysogenum with CFD to track the movement trajectory of cells in a large-scale production and evaluate the impact of flow field changes on yield [ 69 ]. Moreover, Haringa et al considered the compartment model and tracked the intracellular response to extracellular changes during production using a stochastic parcel tracking approach [ 70 ]. This greatly reduced the calculation time of the model and effectively improved the computing capacity [ 70 ].…”

“…Moreover, Haringa et al considered the compartment model and tracked the intracellular response to extracellular changes during production using a stochastic parcel tracking approach [ 70 ]. This greatly reduced the calculation time of the model and effectively improved the computing capacity [ 70 ].…”

A Monte‐Carlo approach for the simulation of microbial population dynamics in an heterogeneous scale‐down bioreactor

“…[27][28][29][30] Coupled with black-box kinetic models, substrate gradients of large-scale bioreactors were investigated in previous studies . [31][32][33] The downside of black-box kinetic models is the disregard of the different time scales of cell adaption to the environment, as they assume instant equilibrium between the extracellular and intracellular conditions. The points raised motivates us to investigate the effect of substrate gradients on microbial growth in a bio-reactor system with two distinct zones.…”

“…CFD simulations have been used as a basis for the compartmentalization of the bioreactors 27–30 . Coupled with black‐box kinetic models, substrate gradients of large‐scale bioreactors were investigated in previous studies 31–33 . The downside of black‐box kinetic models is the disregard of the different time scales of cell adaption to the environment, as they assume instant equilibrium between the extracellular and intracellular conditions.…”

“…Also, the intrinsic noise is considered as a reshuffling of cell properties at cell division. Hence, the population heterogeneity at the reactor scale (as shown in Reference 31) as well as the local distributions of cell physiological properties can be accessed. It will be shown that the randomization of cell properties at birth creates cells whose metabolism is not balanced and introduces new time scale in the cell dynamics.…”