English is currently available.
Biological & Biosystems Engineering DISCUSSION
In my 5 L stirred bioreactor the dissolved oxygen reading falls steadily during the run and ends up near zero a few hours after inoculation, after which growth becomes linear instead of exponential. The literature keeps referring to kLa as the quantity that describes this.
What does kLa represent, how is it used to calculate the oxygen supply, and what are the practical ways to measure and increase it?
Oxygen is poorly soluble in water: in equilibrium with air at atmospheric pressure the saturation concentration C* is only about 7 to 8 mg/L at 25 to 35 °C, and lower in media with dissolved salts. A dense culture can consume that in well under a minute, so oxygen has to be transferred continuously from the gas bubbles.
The oxygen transfer rate is OTR = kLa × (C* - C), where C is the dissolved concentration in the liquid. kLa is the volumetric mass transfer coefficient: kL, the liquid-film coefficient, times a, the bubble surface area per unit liquid volume. They are hard to separate, so they are treated as one number with units of per hour or per second.
A worked balance. Suppose kLa = 100 per hour, C* = 7 mg/L and you want to keep C at 20 percent of saturation, 1.4 mg/L. OTR = 100 × (7 - 1.4) = 560 mg of oxygen per litre per hour. The culture's demand is OUR = q × X, specific uptake rate times biomass concentration. If the cells use 0.25 g of oxygen per gram of dry cells per hour, supply equals demand at X = 0.56 / 0.25 = 2.2 g/L.
Beyond that density the dissolved oxygen falls towards zero, the driving force reaches its maximum, and the cells can only grow as fast as oxygen arrives. That is the linear growth you see.
To measure kLa in your vessel, the dynamic gassing-out method is the usual choice. In cell-free medium, strip the oxygen with nitrogen, switch to air at the agitation and flow of interest, and record dissolved oxygen as it rises. Then ln((C* - C) / (C* - C0)) = -kLa × t, so the slope of that logarithm against time is -kLa.
The probe's own response time must be much shorter than 1 / kLa or the result is too low. At a kLa of 100 per hour, 1 / kLa is 36 s, and a probe with a response time of tens of seconds already distorts the curve.
There are two sides to the equation and both can be raised. kLa goes up with stirrer speed, which breaks bubbles and increases area, and with air flow rate, within the limit where the impeller floods. Antifoam tends to lower it. The driving force goes up if C* is raised: increasing the head pressure or enriching the inlet gas with oxygen raises the oxygen partial pressure and C* in proportion.
A common control scheme is a cascade: hold the dissolved oxygen setpoint by raising stirrer speed first, then air flow, then oxygen enrichment. Oxygen-enriched gas needs compatible, clean fittings and the supplier's safety guidance.
The other way to avoid limitation is to lower the demand rather than raise the supply. In a fed-batch process the growth rate is restricted by feeding the carbon source slowly, which keeps the oxygen uptake rate below what the reactor can transfer. Lowering the temperature reduces the uptake rate as well and raises oxygen solubility slightly.
Bear in mind that kLa measured in water or clean medium is an upper estimate. Viscous broths, filamentous organisms and surface-active components change it considerably, and it does not stay constant when you scale up to a different vessel geometry.
Back to Biological & Biosystems Engineering community
