Determination of Volumetric Mass Transfer Coefficient in a Stirred, Sparged Bioreactor

Eric Jackson

Writer’s comment: ECH 161L was the closest thing to the real world that I have experienced in all of my classes at UC Davis. The details and parameters of the experiments we did were obtained mostly from the literature, rather than from a handout given to us by the professor. That was a first — I actually had to think about the experiment and plan it beforehand. It was also something of a first when I was able to use my experiments in ECH 161L as the basis for a class report — written report — in Engineering Writing (English 102).
- Eric Jackson

Instructor’s comment: Engineering students tend to pay more attention to scientific accuracy than to writing style. And appropriately so; no one wants bridges to fall down because of some engineering miscalculation. But I try to get students to see that writing style does matter. I use the documents leading up to the reactor failure at Three Mile Island to show that how engineers say something (for example, how they organize a document) affects people’s understanding as much as the facts that the engineers might present. I also encourage students to consider what they like to see when they are reading technical documents and to use some of those techniques in their own papers.
     Eric’s report is an excellent example of such an effective scientific style: it is clear, concise, specific, and well-organized. I also like the way that he establishes his research questions in the introduction and concludes by directly stating his answers; readers won’t have any difficulty determining why his work is important and what he learned from it.
- John Stenzel, English Department


     The oxygen transfer rate from a gas to a broth in aerobic fermentation is an important parameter in the design and operation of bioreactors. Aerobic organisms need oxygen for growth, product formation, and cell maintenance. Thus, adequate transfer of oxygen from a gas to the fermentation broth must be maintained. The volumetric mass transfer coefficient, kLa, indicates the rate of oxygen used for fermentation, taking into account all oxygen-consuming variables in the bioreactor. kLa values are used in scaling up from laboratory scale to pilot scale or production scale bioreactors. The determination of the kLa value for a fermentation is important in order to maintain adequate transfer of oxygen in a bioreactor, for laboratory scale use or when scaling up to a larger process.2
     Transfer of oxygen from a gas phase to a liquid phase is complicated by presence of cells, product formation, ionic species, and antifoaming agents. These can alter bubble size and liquid film resistance, which affect oxygen solubility.4 Resulting kLa values are different from those predicted from correlations for oxygen absorption into water. Therefore, it is important to have a reliable method for measuring kLa in fermentation systems.2
     This experiment examines the relative effects of agitation rate and air sparging rate on kLa in distilled water. In addition, the effects of agitation rate on kLa are examined in a fermentation media. The results from the variation of agitation rate in the distilled water and the fermentation media are compared to see how a realistic media affects kLa.


     There are several models which can be used to determine kLa. All models used to evaluate kLa assume ideal mixing of the two phases in the reactor and a negligible resistance of the gas phase to oxygen transfer across the interface.2 This experiment uses the dynamic gassing out method, which gives the following oxygen mass transfer model:

dCL = kLa(C* – CL) (1)

where CL is the dissolved oxygen concentration and C* is the saturated dissolved oxygen concentration in the solution.2,3,4 Figure 1 shows a schematic of the oxygen mass transfer process:

Figure 1. Oxygen Mass Transfer Process
     This model also neglects the response time of the oxygen electrode because the time constant of the electrode is less than the time it takes to saturate the solution. A plot of ln(C* – CL) versus time yields a line with a slope equal to –kLa.4

Experimental Methods



     A 5L bioreactor (New Brunswick Scientific, BioFlo 3000 Model) was used in this experiment. This reactor is equipped with built-in automatic feedback controllers for temperature, agitation, and dissolved oxygen. The agitation system is comprised of a marine propeller stirrer and a radially conveying flat-blade disk stirrer. The disk stirrer is located 6.5 in. from the head plate (3.5 in. above the sparger) and has a diameter of 3.0 in. There are six blades, each with a width of 0.0625 in., a height of 0.625 in., and a length of 0.75 in. The marine propeller is 9.625 in. from the head plate (0.25 in. from the sparger) and has a diameter of 2.25 in. There are three blades, each with a width of 0.125 in.

Dissolved Oxygen (DO) Probe

     A Type T DO Probe (12mm Diameter, Teflon Membrane) was used in this experiment. The time constant given in the specifications is 90s for 98% concentration. During calibration, the probe was found to have a time constant of 99s for 100%.

Figure 2. Experimental Setup (

     The time constant inherent in the DO probe was determined by quickly moving the probe from a nitrogen-sparged liquid to an oxygen-sparged liquid, and observing the response time for the probe to record saturation. To check for hysteresis of the probe, the response time was observed when the probe was placed back into the nitrogen-sparged liquid. There was some hysteresis observed, but this was neglected as all measurements are from a nitrogen-sparged solution to an oxygen-sparged solution.
     The dynamic gassing out method was used to measure the change in dissolved oxygen. The solution was sparged with nitrogen, then sparged with oxygen at the same flow rate and agitation rate. The change in dissolved oxygen was measured until the solution became saturated.2,4
     In order to observe the relative effects of aeration rate in distilled water on kLa, agitation rate was held constant at 500 rpm while aeration rate was varied at 0.5, 1.0, 3.0, 4.0, and 6.0 L/min. To see the effects of agitation rate, aeration rate was held constant at 3.0 L/min while agitation rate was examined at 50, 100, 500, 700, and 1000 rpm.
     To determine the effects of fermentation media on kLa, distilled water in the bioreactor was replaced with McCoy’s 5A Medium (Sigma, M-6523), and only agitation was varied. The same values were used as with distilled water so that they could be compared. A different batch of McCoy’s 5A Medium was used for 500 and 700 rpm, due to contamination of the medium.


     Values for kLa were found by plotting ln(C* – CL) versus time. The slope of the graph is equal to –kLa. In general, kLa increases with an increase in aeration rate or agitation rate. This increase is demonstrated in Figure 3, as kLa varies from 0.02 s–1 to 0.12 s–1 with different aeration rates. Figure 3 also shows that 3 L/min was a good aeration rate to be held constant for variation of agitation rate.

Figure 3. kLa Versus Aeration Rate for Distilled Water
     An increase in kLa is also seen in Figure 4 in the range of 50 to 1000 rpm. Figure 4 also shows a larger range of values for kLa than that seen in Figure 3. Agitation rates vary from about 0.2s–1 to 0.2s–1. Around 500 rpm is a good median value to be held constant for variation of aeration rate.

Figure 4. kLa Versus Agitation Rate for Distilled Water
     Figure 5 shows values for kLa versus agitation rate for the fermentation media. The range of kLa values looks more like that for variation of aeration of distilled water than that for agitation rate. It is also interesting to note that while the general trend is to increase, the kLa value at 700 rpm is greater than the kLa value at 1000 rpm.

Figure 5. kLa Versus Agitation Rate for Fermentation Media
     Table 1 puts the data from Figure 4 and Figure 5 into tabular form so that the kLa values from the two different solutions can be compared.

Table 1. Comparable Values of kLa for Distilled Water and
Fermentation Media (aeration held constant at 3.0 L/min)


Agitation Rate
(rpm ± 1 rpm)
Distilled Water
kLa (1/s ± 3.9%)
Fermentation Media
kLa (1/s ± 3.9%)
50 0.018 0.016
20 00.029 0.029
500 0.053 0.096
700 0.171 0.142
1000 0.213 0.122


     In general, the kLa values for distilled water are greater than the kLa values for the fermentation media. They also show a greater range of kLa values. Table 2 shows the data from three runs of 100 rpm and 3.0 L/min. The results in this table are meant to show the reproducibility of the method and model used in this experiment.

Table 2. Reproducibility Data



Agitation Rate (rpm ± 1 rpm) kLa (1/s ± 3.9%)
1000 0.212
1000 0.222
1000 0.206
Standard Deviation



     In general, values of kLa increased as aeration rates or agitation rates increased. This is consistent with what is found in the literature.1,3 Values found by Atkinson are very similar for both variation of agitation rate (500, 700, and 1000 rpm data available for comparison) and of aeration rate (0.5 and 1.0 L/min available for comparison).1 These comparable results show that the dynamic gassing out method and mass transfer model used give the correct trends and are reliable.
     Values of kLa in Table 2 were calculated for testing the precision of the method and the model used in this experiment. A standard deviation of 3.9% was found from these values. This gives the kLa values in this experiment an error of ±3.9% (acceptable for this experiment).
     The kLa is found in order to determine the rate of oxygen flow needed for fermentation. It takes into account all oxygen-consuming variables in the fermentation, including aerobic organisms. Data from Figure 5 seem to indicate the presence of anaerobic organisms. The values for 50, 200, and 1000 rpm result from a fermentation media that was made hours before the experiment was actually performed. The values for 500 and 700 rpm result from a fermentation media that was made just before the experiment took place. The first batch of fermentation media provided ideal conditions for the growth of aerobic organisms over the several hours before it was used. The relative kLa is low, superficially indicating that it took more time to transfer oxygen. In actuality, the values are lower probably because of the consumption of oxygen by aerobic organisms. This consumed oxygen is part of the overall oxygen delivered, but it is not measured. Therefore a lower kLa results. The contamination of the first batch of fermentation media was probably due to anaerobic organisms.
     The effect of a fermentation media on kLa is seen by the lower values of kLa for the media than those for water. The more viscous solution does not take up oxygen as well as water. Another explanation could be that there are oxygen-consuming variables in the media.


     In general, kLa values increase as agitation rates and aeration rates are increased. Values for kLa are also influenced by factors like fermentation media and the oxygen consumption of aerobic organisms. In aerobic fermentation, it is important to provide adequate transfer of oxygen for the growth, product formation, and cell maintenance of aerobic organisms. kLa calculations must take this oxygen use by aerobic organisms into account, or the values will appear lower than they really are. It is key to have a reliable method and model to use to determine kLa so that this oxygen is provided. The dynamic gassing out method/model is reliable and accurate for this process.


a interfacial gas liquid surface area per unit reactor volume (L2/L3)
CL dissolved oxygen concentration (mol/L)
C* saturated dissolved oxygen concentration in the solution (mol/L)
kL mass transfer coefficient (1/t)
kL avolumetric mass transfer coefficient (s–1)


1. Atkinson, B. 1991. Biochemical Engineering and Biotechnology Handbook,2nd Edition, Stockton Press, New York, NY, Chapter 12.

2. Gauthier, T., Thibault, J. and LeDuy, A. 1991. Measuring kLa with Randomly Pulsed Dynamic Method, Biotechnology and Bioengineering,37: 889-893.

3. Linek, V., Vacek, V. and Benes, P. 1987. A Critical Review and Experimental Verification of the Correct Use of the Dynamic Method for the Determination of Oxygen Transfer in Aerated Agitated Vessels to Water, Electrolyte Solutions and Viscous Liquids, Chemical Engineering Journal,34:11-34.

4. Schuler, M.L. and Kargi, F. 1992, Bioprocess Engineering: Basic Concepts,Prentice Hall, Englewood Cliffs, NJ, pp. 277-281.