By
AHMAD ZIAD SULAIMAN
MASSEY UNIVERSITY, NEW ZEALAND
The productivity of aerobic fermentations is often limited by the availability of oxygen in the fermentation broth. Oxygen supply can be enhanced by increasing the rate of oxygen transfer into the liquid from the gas. The volumetric oxygen transfer rate is given as follows:
volumetric oxygen transfer rate = kLaL (C* - CL)
where CL is the concentration of dissolved oxygen in the liquid, C* is the saturation concentration of dissolved oxygen in the absence of consumption and kLaL is the overall volumetric mass transfer coefficient that is used to characterize the mass transfer rate in the reactor or bioreactor. In kLaL, kL is the liquid-film mass transfer coefficient and ‘aL’ is the interfacial area per unit liquid volume. kLaL is generally increased by increasing ‘aL’. Because the surface area of spheres is proportional to the diameter squared, while the volume is proportional to the diameter cubed, ‘aL’, is inversely proportional to the bubble diameter. kLaL itself depends on the operating conditions (i.e., aeration rate, the rheological properties of the fluid, density , surface tension, the system geometry and the intensity of agitation (Cruz et al. 1999).
The aqueous solubility of oxygen is controlled by the partial pressure of oxygen, the temperature and the presence of others solutes in the broth. The solubility of sparingly soluble gases such as oxygen is often modeled by Henry’s law:
[3.1]
where C* = liquid phase saturation concentration of oxygen
PG = the partial pressure of oxygen in the gas in contact with the liquid
H = Henry’s law constant
Many methods are available to determine kLaL in bioreactors system. These have been reviewed by Gogate and Pandit (1999). A common method that is used in the bioreactors is the dynamic gas-in method. This method is based on the following mass balance on oxygen in the liquid phase of a bioreactor :
Schematic of bioreactor setup for kLa measurements
where A is the total gas-liquid interfacial area
A rearrangement of the above gives:
Because 
, the above equation becomes;
where C* = saturation concentration of dissolved oxygen in the broth
CL = actual instantaneous concentration of dissolved oxygen in the
broth
= interfacial area per unit liquid volume
= mass transfer coefficient (length/time)
VL = liquid volume in the reactor
t = time
Equation below applies only when there is no consumption of oxygen in the broth.
Integration of Equation below between the limit t = 0, CL = Co and t = t, CL = CL, gives:
where Co = dissolved oxygen concentration at t=0
A semilog plot of Equation above provides kLaL as the slope. In the event of oxygen consuming reaction occurring in the bioreactor, Equation above needs to be modified as discussed by Lamping et al. (2003).
Dissolved oxygen (DO) probes are widely used to monitor the concentration of dissolved oxygen in bioreactors. Polarographic type DO probe are the most common (Philichi and Stenstrom 1989). Equation above assumes that the oxygen concentration measured is instantaneous. In practice this is not so and a dissolved oxygen probe with a fast response time is required for measurement of CL, otherwise the dynamic method will not give accurate results. Probe response time can be measured by instantly transferring the probe from an oxygen saturated medium to an oxygen free medium (Mueller et al. 1967; Leeuwen 1979; Nakanoh and Yoshida 1980; Linek et al. 1987; Philichi and Stenstrom 1989; Tribe et al. 1995; Badino et al. 2000; Lamping et al. 2003; Carbajal and Tecante 2004; Kumar et al. 2004; Fadavi and Chisti 2005; Boodhoo et al. 2008). The time constant of the probe is the time when the probe response reaches 63.7% of the steady state dissolved oxygen concentration measured by the DO probe. If the time constant is less than 10 s, (1/ kLaL is <>-1), Equation above can be solved to determine the value of kLaL. If the kLaL is larger than 0.1 s-1, or the probe response is longer than 10 s, the following equation needs to be used in calculating the kLaL from the measured dynamic response curves :
where Cp = DO concentration measured by the probe
tm = 1/ kLaL
τp = response time of the DO probe
Equation above was solved for kLaL using Microsoft Excel at various value of t and the results were averaged (Badino et al. 2000; Lamping et al. 2003; Boodhoo et al. 2008).
References :
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Carbajal, R. I. and A. Tecante (2004). "On the applicability of the dynamic pressure step method for kLa determination in strirred Newtonian and non-Newtonian fluids, culture media and fermentation broths." Biochemical Engineering Journal 18: 185-192.
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