What is kLa in bioreactors?

This article is intended for bioreactor users and manufacturers, as well as other interested parties, in order to give an intuitive idea and basic knowledge of kLa. It is an attempt to explain the essence of kLa in a simple and practical way. The aim of the article is to provide additional knowledge about the selection of bioreactors and their working regimes to achieve as best as possible fermentation results.


In aerobic microorganism cultivation processes, it is necessary to supply nutrients and oxygen to the microorganism cells. The oxygen supply to the cells is more problematic because usually, oxygen solubility is significantly lower compared to glucose and other components of the nutrient media. Oxygen is supplied to the cells by air bubbles, which are introduced into the bioreactor through a sparger or through the headspace. These bubbles are dispersed by mixing. The latter is necessary to supply the oxygen to the cells with sufficient intensity. Insufficient oxygen supply is often the reason for not reaching the required biomass concentrations. To ensure sufficient intensity of oxygen supply, the bioreactor must be properly designed and the appropriate mixing and aeration modes must be provided. The kLa parameter is used to characterize the oxygen mass transfer.

General Principle of kLa

Basically the volumetric oxygen mass transfer coefficient – kLa, is the parameter that controls the rate of how oxygen transitions from the gas phase into the liquid phase. kLa shows numerically how efficiently oxygen, which is introduced through a sparger in the vessel, is dissipated and distributed in the medium by the mixer.

The notion of kLa arises from the two-film theory, which postulates, that the mass transfer between two phases takes place through a boundary layer, between those two phases (see Fig.1.).

The rate of diffusion of a component between phases is dependent on the mass transfer coefficient, for liquids this coefficient often is written as ‘kL’. The overall rate of mass transfer between two phases apart from kL is also dependent on the contact area between those two phases, often termed ‘a’. When we combine the two, we get our volumetric oxygen mass transfer coefficient kLa.

Gas-liquid Oxygen Mass Transfer According to the Two-Film Theory

Another important aspect of kLa can be described by using the following equation: dC/dt = kLa ∙ (C * -CL ) = OTR – OUR (1) Where,

C * – the saturated dissolved oxygen concentration;

CL – the current concentration of dissolved oxygen in the media.

This equation shows us, that the rate of oxygen concentration change in the liquid medium is dependent on kLa and the difference between the current (CL) and maximal possible (or sometimes termed equilibrium – C*) oxygen concentrations. Simultaneously, the rate of the oxygen concentration change is equal to the difference between the oxygen transfer rate to the cultivation medium (OTR) and the oxygen uptake rate (OUR). If the OTR is higher than the OUR term, the medium will inevitably get saturated by oxygen until reaching the equilibrium concentration. On the second hand, if we observe a completely different situation, where the OUR term is larger than OTR, the oxygen concentration will fall below a required level, which would be unsuitable for supporting microorganism growth.

Both situations are unfavourable due to the fact that most often a specific organism requires a certain concentration of oxygen to be maintained, too high oxygen concentrations 2 can lead to a completely different fermentation paths, too low oxygen concentrations can lead to biomass growth and/or target product secretion inhibition.

In result, one of the most widely used means of controlling the dissolved oxygen concentration is regulation of the mixing intensity during fermentations (dissolved oxygen concentration also can be controlled by airflow, oxygen enrichment, overpressure, substrate feeding).

kLa evaluation possibilities

kLa evaluation is important for the selection of a bioreactor for a particular cultivation process. The latter is critical for pilot and industrial scale applications because in laboratory scale bioreactors usually it is easier to achieve necessary oxygen transfer rates. Often, based on the cultivation results in a laboratory scale system, pilot and/or industrial scale bioreactors are selected. It is more convenient to start kLa evaluations by using theoretical calculation equations. Although, following factors can limit the applicability of theoretical kLa calculations:

  1. The chemical composition of the applied medium differs in principle;

  2. The applicability of a particular kLa empirical equations depends on the limits of the parameters at which it was developed.

While the applicability of experimental kLa determination methods is narrowed in the following cases:

  1. The existing kLa formulas are not applicable to the selected bioreactors design;

  2. The necessity to evaluate kLa in real fermentation processes.