**5.5 Measurement of K _{La} **

Most common method of measuring k_{La}
is to conduct experiments in the bioreactor when cells are absent,
or cell concentration is low so that consumption by cells can be neglected.
The latter condition is present immediately after inoculating the bioreactor.
Consider Eq (5-7) under these conditions:

If we allow steady state to occur, the dissolved oxygen concentration
will reach saturation value, **
**and the concentration-time profile will be flat, as shown in
the diagram.

Fig 5-2 Oxygen Profile During a Transient. The responses will
be exponential, rather than straight lines.

If the oxygen source (air) is replaced by nitrogen, the resulting response
of the system is described by the above equation with the term, **
**set to zero. That is,

The solution to the above is

If one plots the response on a semi-log plot, the slope will equal to the negative of mass transfer coefficient. It is relatively a simple experiment and the data analysis is also easy to do. When other type of transient mass transfer experiments are conducted, the above equations should be suitably modified. For example for the case of nitrogen to air switch, we should suitably modify the solution because the initial condition is now different.