4.1.2 Combination of CFD Approaches with Mechanistic Models
(Euler–Lagrange) to Describe the Large Scale
Computational fluid dynamics has been traditionally used to describe the flow under
defined conditions, as a way of characterizing the heterogeneous conditions in largescale bioreactors. With the increasing computational power it is possible to implement in such CFD approaches cellular reaction kinetics. For the first time this
interaction between the intracellular state of the individual cells of the population
and the turbulent flow field in the bioreactor has been realized by Lapin et al.
[99]. This so-called Euler–Euler approach considers gas, liquid, and biophase as a
continuum and is an answer to the very complex simulation, which is dependent on
the definition and resolution of the reactor into flow cells. Later, the pioneering paper
by Lapin et al. [100] was the first approach to couple a CFD model of a bioreactor
with a Lagrangian approach for the combined solution of flow patterns and cellular
kinetics.
In this Lagrangian–Euler approach the liquid phase is treated as a continuum
(Euler) and the dispersed phase is tracked using Lagrangian representation. While
this modeling approach was first used in gas–liquid simulations, here cells with their
specific metabolic reaction network were described as discrete entities. With these
models, individual cells are monitored with respect to their experience of local
environments in relation to the fluid-dynamic distribution and pathways within the
bioreactor. This kind of structured-segregated approach realizes that the individual
history of a biological entity determines their reaction. With a big computational
power this can be realized also in a three-dimensional turbulent field. This approach
allows one to get an indication of the heterogeneity in the biotic and abiotic phases of
the reactor and it considers the individual history of the cells as important for its final
response. By tracking the pathway of a single particle over time it is possible to
derive lifelines of a big number of cells and thus draw conclusions for regimes,
i.e. conditions which should be represented in scale-down experiments.
In summary, the use of mathematical descriptions of large-scale bioreactors by
the combination of Euler–Lagrangian approaches is very illustrative and has made
major progress during the last years.
However, there are some limitations:
1. Due to calculation expense it is not possible to consider realistic amounts of cells.
Current computational approaches consider approx. 100,000 cells, which is
enough to see and follow the population dynamics. Currently this number of
cells is fixed. However, it would be interesting to consider growth and an increase
in cell number over time.
2. The cellular models and the parameters used in these studies are mostly derived
from continuous experiments (mostly chemostats), i.e. from experimental conditions which do not reflect the large scale. Thus, as discussed above, the reactions
in a real reactor may be totally different. Therefore urgent approaches and
methods which describe how a cellular model can be derived and parameterized
16
P. Neubauer et al.
(Euler–Lagrange) to Describe the Large Scale
Computational fluid dynamics has been traditionally used to describe the flow under
defined conditions, as a way of characterizing the heterogeneous conditions in largescale bioreactors. With the increasing computational power it is possible to implement in such CFD approaches cellular reaction kinetics. For the first time this
interaction between the intracellular state of the individual cells of the population
and the turbulent flow field in the bioreactor has been realized by Lapin et al.
[99]. This so-called Euler–Euler approach considers gas, liquid, and biophase as a
continuum and is an answer to the very complex simulation, which is dependent on
the definition and resolution of the reactor into flow cells. Later, the pioneering paper
by Lapin et al. [100] was the first approach to couple a CFD model of a bioreactor
with a Lagrangian approach for the combined solution of flow patterns and cellular
kinetics.
In this Lagrangian–Euler approach the liquid phase is treated as a continuum
(Euler) and the dispersed phase is tracked using Lagrangian representation. While
this modeling approach was first used in gas–liquid simulations, here cells with their
specific metabolic reaction network were described as discrete entities. With these
models, individual cells are monitored with respect to their experience of local
environments in relation to the fluid-dynamic distribution and pathways within the
bioreactor. This kind of structured-segregated approach realizes that the individual
history of a biological entity determines their reaction. With a big computational
power this can be realized also in a three-dimensional turbulent field. This approach
allows one to get an indication of the heterogeneity in the biotic and abiotic phases of
the reactor and it considers the individual history of the cells as important for its final
response. By tracking the pathway of a single particle over time it is possible to
derive lifelines of a big number of cells and thus draw conclusions for regimes,
i.e. conditions which should be represented in scale-down experiments.
In summary, the use of mathematical descriptions of large-scale bioreactors by
the combination of Euler–Lagrangian approaches is very illustrative and has made
major progress during the last years.
However, there are some limitations:
1. Due to calculation expense it is not possible to consider realistic amounts of cells.
Current computational approaches consider approx. 100,000 cells, which is
enough to see and follow the population dynamics. Currently this number of
cells is fixed. However, it would be interesting to consider growth and an increase
in cell number over time.
2. The cellular models and the parameters used in these studies are mostly derived
from continuous experiments (mostly chemostats), i.e. from experimental conditions which do not reflect the large scale. Thus, as discussed above, the reactions
in a real reactor may be totally different. Therefore urgent approaches and
methods which describe how a cellular model can be derived and parameterized
16
P. Neubauer et al.