Volume-related mass transfer coefficient

The volume-related mass transfer coefficient , also referred to as the k _L a value or volumetric mass transfer coefficient, is a key figure for the transport of a gas from the gas phase into the liquid phase of a reaction system. It is a measure of the efficiency of the gas input and is therefore of great importance for the planning of chemical or biological reactors . When designing the latter, the oxygen input and thus also the k _L a value of oxygen are of central importance.

Physical basics

The k _L a value in a medium

The derivation of the k _L a value is based on the two-film theory of material exchange. For the sake of simplicity, it is assumed that the transport of a gas through the gas / liquid phase interface is the rate-determining step. The following relationship applies:

${\displaystyle {\mathrm {d} C \over \mathrm {d} t}={k_{L}a\cdot (C^{*}-C)}}$

where C is the dissolved gas concentration and C * is the equilibrium concentration at the phase interface or, in other words, the maximum solubility. The equilibrium concentration can be calculated using Henry's law from the partial pressure of the respective gas.

When considering oxygen, the relationship is usually formulated as follows:

${\displaystyle {\mathit {OTR}}=k_{L}a\cdot (c_{\rm {O2}}^{*}-c_{\rm {O2}})}$

wherein OTR the oxygen transport rate (engl. oxygen transfer rate or sometimes also oxygen transmission rate is).

The difference between the two concentrations is the driving force for the mass transport through the phase interface.

The k _L a value is the product of the mass transfer number ( k _L ) of the liquid phase and the volume-related phase interface ( a ). These two variables cannot be determined separately for reactors with bubble gassing, which is why one speaks of the k _L a value.

Relevance of the k _L a value for biotechnological processes

In a biotechnological process , the k _L a value is of great importance because it makes a statement about how well microorganisms can be supplied with gases in a biotechnological plant. When cultivating aerobic microorganisms, it is important to achieve a high k _L a value for oxygen in the bioreactor, while in autotrophically growing microorganisms, for example, the k _L a values ​​for hydrogen and carbon dioxide also play an important role. Possible measures to increase the k _L a value include, for example, an increase in the stirrer speed, a more efficient type of agitation, an increase in the contact surface with the air (e.g. through ventilation with finer air bubbles) or an optimization of the medium. The usefulness of these measures is limited, however, by the higher mechanical stress on the microorganisms.

Determination of the k _L a value

Sulphite method (for oxygen)

To determine the k _L a value, the bioreactor is operated without microorganisms. For this purpose, an approx. 0.8 molar sodium sulfite solution is presented, which also contains copper sulfate as a catalyst . At the beginning, only sodium sulfite Na ₂ SO _{3 is} present, but if the gas is now gassed with air or pure oxygen, sodium sulfite is oxidized to sodium sulfate Na ₂ SO ₄ . First a zero value is determined, then aerated for a defined time and finally the concentration of sodium sulfate is determined. The rate of oxidation is determined as follows:

${\displaystyle {{\mathit {OTR}} \over c_{\rm {O2}}^{*}-0}={k_{L}a}}$

One advantage is good reproducibility and independence from microbiological disturbances. However, it is disadvantageous that an artificial oxidation system is used, which suggests k _L a values ​​that are too high .

Continuous measurements with probes

Using dissolved gas probes (for example an oxygen sensor ), which can directly measure the concentration of a gas dissolved in a liquid, the product k _L a can be calculated for any gas with the aid of the general formula .

The prerequisite is, of course, that a corresponding sensor exists, which is currently not the case with hydrogen, for example.

literature

• Klaus Mutzall: Introduction to fermentation technology. Behr, Hamburg 1993, ISBN 3-86022-103-5 .
• Horst Chmiel (Ed.): Bioprozesstechnik. Introduction to bioprocess engineering. 2nd, revised edition. Elsevier, Spektrum Akademischer Verlag, Munich 2006, ISBN 3-8274-1607-8 .