CFD-based modeling of dissolved

oxygen in microbioreactors

Hilde Larssona, Krist V. Gernaeya, Anne Ladegaard Skovb and Ulrich Krühnea,

aPROCESS - Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Building 229, DK-2800

Kgs. Lyngby, Denmark bDPC - Department of Chemical and Biochemical Engineering, Technical University of Denmark, Søltofts Plads, Build-

ing 229, DK-2800 Kgs. Lyngby, Denmark. Email: hila@kt.dtu.dk

AIM OF THE PROJECT

The focus of this project is to improve the productivity and reliability of microbioreac-

tors used for fermentation processes through process modeling and reactor optimiza-

tion. The internal shapes of the reactors and the mixing methods applied in them will be

optimized using computational fluid dynamics (CFD) and topology optimization, ini-

tially focusing on oxygen transfer improvement.

BACKGROUND

Studying fermentation processes in microbioreactors offers several advantages com-

pared to the use of shake flasks and microtiter plates for purposes such as strain screen-

ing and process optimization. Process parameters such as dissolved oxygen, pH, tem-

perature and optical density can for instance be measured on-line and due to the small

volumes, normally less than 1 ml, little laboratory space and chemicals are required.

Knowing the transient concentrations of oxygen and other chemical substances in a mi-

crobioreactor is very important in order to be able to interpret experimental results cor-

rectly. For example, the amount of dissolved oxygen available to a cell has an enor-

mous impact on its growth and productivity.

The most common way to describe oxygen transfer in bioreactors is via the oxygen

transfer coefficient, kLa, which describes the dynamic relationship between the oxygen

concentration (C) and the oxygen saturation concentration level (C* ) in a volume ac-

cording to the following:

A disadvantage with using this equation is that perfect mixing in the liquid phase is as-

sumed and this could possibly be of extra concern in small reactors, where low Reyn-

olds numbers makes the mass transport less effective in the absence of sufficient turbu-

lence.

Modeling oxygen transfer in a way which takes advantage of both diffusion and con-

vection could therefore be a more suitable method for microbioreactors without sparg-

ing, especially those with a sealed semipermeable oxygenation membrane and no head-

space.

*

L

dCk a C C

dt

METHOD

The 2D reactor shown in Figure 1 was implemented in ANSYS CFX-14.0 and the con-

centration of a tracer representing oxygen was set to 1 at the membrane. The reactor

was set to contain water and the diffusivity of oxygen/tracer in the water domain was

set to 2×10-9 m2/s. Three different reactor designs were evaluated, see Figure 2.

Transient simulations were performed starting from a steady state solution with respect

to the fluid velocities where the bottom walls of the reactors were moving in the posi-

tive x-direction with velocities of 0, 1 and 100 mm/s. Simulations were then performed

where the concentrations of oxygen in the water domain were recorded over time, start-

ing with an initialization of no oxygen in the domain.

RESULTS AND DISCUSSION

The distributions of oxygen in Reactor A with the wall velocities 0, 1 and 100 mm/s at

four different time steps can be seen in Figure 3. It can clearly be seen that the intensity

of mixing applied in the reactor has got a significant effect on the transport of oxygen

into the fluid.

The average fractions of oxygen in the water domains over time are plotted in Figure 4

for five different simulations. It can be seen that the choice of wall velocity has got a

large impact on the reactors oxygen uptake rate and also that the different reactor de-

signs have an impact. This difference is due to different flow patterns within the reac-

tor, which is in turn dependent on the internal shape of the reactors and the mixing

method/wall velocity applied.

The difference between the flow patterns in reactor A, B and C can be seen in Figure 5.

Knowing from Figure 4 that oxygen transfer was most efficient in reactor B, this could

be explained by the vortex developed in reactor B between the cavity and the right

wall. Both reactor A and C lack such large secondary vortex which is probably the ex-

planation behind their lower oxygen transfer capabilities.

Calculated data of average oxygen concentrations at selected time points could be a

very suitable objective function for future optimizations, where both different reactor

shapes and mixing methods can be taken into account and optimized with respect to ox-

ygen transfer characteristics.

FUTURE WORK AND PERSPECTIVE

The reactor designs presented here will be replaced with actual miniaturized reactor de-

signs which will result in simulation results which are more comparable to experi-

mental data. The flow will also be in 3D which will increase the design options and the

definition of the tracer will be re-defined to a molar concentration so that a literature

value of its in water saturated concentration can be used.

Shape or topology optimization methods will also be implemented in order to improve

the reactor design aiming at faster oxygen transfer into the reactors. Theoretically im-

proved reactors will then be fabricated and evaluated in the lab with on-line dissolved

oxygen measurements in order to seek experimental validation for the theoretical mod-

els. Parts of the experimental work could possibly be performed in cooperation with the

research group of Torsten Mayr at TU Graz, focusing on optical sensors in miniaturized

devices.

Figure 1.

Figure 3. Fraction of oxygen in reactor A at different

wall velocities and times

Figure 4. Plot of average oxygen concentration in the

reactors over time

Figure 5. Velocity

vectors for reactor

A, B and C

respectively with

the bottom wall

moving 100 mm/s

Figure 2. Reactor A, B and C

ACKNOWLEDGEMENTS: This PhD project is

founded by Novo Nordisk Foundation