# Estimation Of The Volumetric Oxygen Transfer Coefficient Biology Essay

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The aerobic bioprocesses are usually carried out under optimized conditions such as temperature, pH, pressure, mixing, concentrations of biomass, nutrients and dissolved oxygen. In these processes, oxygen is an importance substrate that is used by the aerobic microorganisms for growth, maintenance and production. Moreover, the deficiency of oxygen affects the process performance. Therefore, it is important to deliver sufficient oxygen from a gas stream to the fermentation broth by estimation of the oxygen transfer rate (OTR) which can be described by the volumetric oxygen transfer coefficient (kLa). The aim of this seminar is to present the estimation of kLa by the dynamic method and the method to develop kLa correlation.

kLa is the proportionality constant to determine the magnitude of the OTR. kLa is influenced by many factors such as operational conditions (agitation speed and aeration rate), physical properties of gas and liquid, geometrical parameters of the reactor and the presence of biomass. As shown in Figure 1 is an illustrated view of the factors affecting OTR and kLa at different levels in a bioprocess. Moreover, kLa is importance for design the reactor for example the distance between two impellers. kLa is used for operate and control the fermentation process such as the adjustment of agitation speed or aeration rate to obtain the desire kLa. Finally, kLa is used as the parameter for scale up to the large scale.

Figure 1 Relationship between OTR, volumetric oxygen transfer coefficient and hydrodynamic parameters in bioreactors at several levels

Source: Garcia-Ochoa and Gomez (2009)

## 2. Experimental determination of the volumetric oxygen transfer coefficient (kLa)

The determination of kLa in reactors is essential for prove the aeration efficiency in the reactors and to investigate the effects of the operating conditions on dissolved oxygen. There are many methods that have been developed to determine the kLa in the reactors such as sulfite oxidation method, gas balancing method and dynamic method.

Dynamic method is the method to determine the kLa base on the mass balance of the dissolved oxygen in the well-mixed liquid phase as shown in equation (1) and (2)

(1)

(2)

is the accumulation rate of oxygen in the liquid phase, represents the oxygen transfer rate from the gas to the liquid phase which is the equilibrium saturation concentration of dissolved oxygen, is the concentration of dissolved oxygen, is the specific oxygen consumption rate and is the biomass concentration. So, the product is the oxygen uptake rate (or OUR).

The methods to measuring the kLa in a microbial bioprocess can be classified into the absence of microorganisms or with dead cells and in the presence of biomass that consumes oxygen at the time of measurement.

2.1 The methods to kLa measuring of without biological consumption of oxygen or gassing-out method (=0)

In the absence of biomass, the oxygen uptake rate by microorganisms is zero (OUR=0). Therefore, equation (2) can be simplified to equation (3)

(3)

The steps of experiments consist of absorption and desorption of oxygen from liquid medium. The desorption of dissolved oxygen is started by means of bubbling nitrogen gas to eliminate oxygen in medium until the oxygen concentration is equal to zero. Subsequently, the liquid is contacted again with air. The oxygen concentration grows up with time as shown in Figure 2

Figure 2 Schematic description of the dynamic technique desorption-absorption of oxygen for inert condition measurements

Source: Garcia-Ochoa and Gomez (2009)

So, the kLa is determined by integration of equation (3) into equation (4) as follow:

(4)

In this case, kLa can be obtained as the slope of a plot of versus time as illustrated in Figure 3

Slope= kLa

Figure 3 A plot of versus time to determine the kLa value in absence of biomass

2.2 The methods to kLa measuring of with biological consumption of oxygen (≠ 0)

In the presence of biomass, the oxygen transfer rate and oxygen uptake rate occur together. Thus, the mass balance of dissolved oxygen is equal to equation (2). In desorption step or the gas supply to the reactor is turned off (OTR=0), the dissolved oxygen concentration will reduce at a rate of oxygen consumption by the respiration of microorganism (Figure 4). Under these step equation (2) can be simplified to equation (5)

(5)

Thus, or OUR can be get as the slope of a plot of versus time. Moreover, the specific oxygen consumption () is easy to calculate using the measured of value.

During the aeration step, the gas is flowed again. The oxygen is absorbed into the broth medium. Both oxygen transfer and oxygen consumption occur together. The equation (2) is rearranged into equation (6) as follow

(6)

For a known biomass concentration () and . kLa is the slope of a plot of versus and the y-intercept of this plot obtains the value of the equilibrium saturation concentration of dissolved oxygen () in the broth.

Figure 4 Schematic description of the direct measuring of OTR in bioprocess by the classical dynamic technique.

Source: Garcia-Ochoa and Gomez (2009)

Figure 5 A plot of versus to determine the kLa value in presence of biomass

## 3. Empirical correlation of kLa values in stirred tank reactor

In stirred tank reactor and the impeller is the main gas dispersing tool and agitation speed and design of impeller have an effect on mass transfer in reactor. Garcia-Ochoa and Gomez (2009) reviewed the empirical correlations for the volumetric oxygen transfer coefficient which depend on geometrical parameters and correlated with the combination of agitation speed (N), superficial gas velocity (VS) and liquid effective viscosity (μa) as shown in the following equation (7)

(7)

where the constant C is the geometrical parameters of the vessel and the impeller employed. The average power input per volume (P/V) is the effect of agitation speed (N) and a, b and c are the values to show a variation range in the different correlations of different authors:

0.3 ≤ a ≤ 0.7; 0.4 ≤ b ≤ 1; -0.4 ≤ c ≤ -0.7

The exponents of different correlations were reviewed by Garcia-Ochoa and Gomez (2009) shown in Table 1

Table 1 Exponent values in equation (7) for stirred tank bioreactors

Moreover, there are some of the dimensionless correlations in the literature for Newtonian and non-Newtonian fluids as shown in Table 2 and 3, respectively.

Table 2 Dimensionless correlations for prediction of kLa in Newtonian fluids in stirred tanks

Table 3 Dimensionless correlations for prediction of kLa in non-Newtonian fluids in stirred tanks

4. A correlation of kLa affecting with agitation and aeration (Aguiar Jr. et al. (2002))

Besides, the empirical correlations which have been developed for estimation of kLa in stirred tank reactor as described above. The simplex correlation for prediction kLa was developed by Aguiar Jr. et al. (2002) using gassing-out method to determine of kLa. The steps to develop this correlation was established as follow

1. The experiments for determine of kLa was conducted in a New Brunswick BioFlow III fermentor with aeration, agitation, temperature, pH and dissolved oxygen control. The studies were carried out at temperature 30 -C in a 2.5 l capacity culture vessel with 2.2 l culture medium at agitation speed 100-900 rpm and air flow at 0.1-4.0 l/min. The dissolved oxygen was measured by Ingold polarographic electrode and kLa was determined using the gassing-out method (absence of biomass).

2. The kLa values were calculated from the dissolved oxygen dynamic balance in absence of biomass (OUR=0) as equation (8)

(8)

where is the equilibrium saturation concentration of dissolved oxygen and is the concentration of dissolved oxygen.

Integration of this equation (8) obtaining equation (9)

(9)

The kLa is slope of this straight line between versus time. The various values obtained in the aeration rate at 0.10 to 4 l/min and agitation speed ranging from 100-900 rpm were used to develop a kLa correlation. In Figure 6 showed the kLa determinations for different agitation speeds at an aeration rate of 1 l/min.

Figure 6 Typical curves for kLa determinations at various agitation speed at aeration rate 1.0 l/min

3. Afterward, the kLa values were plotted at different agitation speeds (N) in different aeration rate (Q)

Figure 7 kLa with different agitation speeds (N) in different air flows (Q)

From this Figure 7, the results showed the kLa values increase when increasing the agitation speed and aeration rate.

4. Figure 8 showed the final correlation after plot (the slope of a plot of kLa versus agitation speed (N)) with aeration rate (Q) obtaining the correlation: = 0.0461 ln (Q) + 0.1165

Figure 8 kLa/N - air flow-final correlation

## CONCLUSIONS

1. A correlation for prediction of kLa which was developed by Aguiar Jr. et al. (2002) was related kLa with agitation speed and aeration rate. The correlation was used for monitor and controller the fermentation to obtaining the desire kLa by varying agitation speed or aeration rate.

2. This correlation was used as the original model for further developing the correlation of kLa which influencing from agitation speed, aeration rate and biomass concentration.

## LITERATURE CITED

Aguiar Jr., W.B., L.F.F. Faria, M.A.P.G. Couto, O.Q.F. Araujo and N. Pereira Jr. 2002. Growth model and prediction of oxygen transfer rate for xylitol production from d- xylose by C. guilliermondii. Biochem. Eng. J. 12: 49-59.

Garcia-Ochoa, F. and E. Gomez. 2009. Bioreactor scale-up and oxygen transfer rate in microbial processes: an overview. Biotechnol. Adv. 27: 153-176.

Lopez, J.L.C., E.M.R. Porcel, I.O. Alberola, M.M.B. Martin, J.A.S. Perez, J.M.F. Sevilla, and Y. Chisti. 2006. Simultaneous determination of oxygen consumption rate and volumetric oxygen transfer coefficient in pneumatically agitated bioreactors. Ind. Eng. Chem. Res. 45: 1167- 1171.

Suresh, S., V.C. Srivastava and I.M. Misha. 2009. Techniques for oxygen transfer measurement in bioreactors: a review. J. Chem. Technol. Biotechnol. 84: 1091-1103.