Bioreactor mass transfer: kLa (O2) versus kLa (CO2)

kLa is an emotive term for many in process development.  It evokes a certain mystery for those whose background is not chemical engineering, a 'TLA' they hear over and over again.  Obtaining values for this scale-dependent 'mass transfer' parameter can be a significant undertaking, whether by experiments, empirical correlations or even CFD.  We provide purpose-designed tools to support fitting kLa to experimental data and for estimation using established correlations.  The experimental approach is the subject of this post.

The dominant experimental technique is the dynamic gassing out method, where dissolved gas concentration is followed versus time using a probe in the liquid phase.  A shortcut method allows kLa to be backed out from a semi-log plot; an implicit assumption here is that there is an abundance of gas.  A more rigorous approach that we advocate fits kLa to a model tracking multi-component mass and composition in both the liquid and gas phases.

The shortcut method contributes to confusion about kLa(O2) versus kLa(CO2), two important gases in cell culture.  Dissolved CO2 can be followed using pH probes.  Practitioners sometimes report separate values for kLa(O2) and kLa(CO2), with kLa(CO2) typically lower and insensitive to agitation.

CO2 is much more soluble than O2 and the two mass transfers are usually in opposite directions in a bioreactor: O2 from gas to liquid and CO2 from liquid to gas.  Incoming air bubbles become saturated with CO2 after a relatively short period of contact, whereas they continue to liberate O2 for most or all of their contact time.  That leads to different sensitivities of dissolved O2 and CO2 to agitation and gas flow rate; and therefore different abilities to measure something close to kLa.  A very nice study of the gas phase in bioreactors by Christian Sieblist and colleagues from Roche bears out this trend.

Practitioners report that successful bioreactor operation and adequate control over both O2 and CO2 (and hence pH) depends strongly on agitation in the case of O2 and gas flow rate in the case of CO2.  In fact, it's a spectrum and kLa and gas flow rate may both be somewhat important for both responses and the particular combination of kLa and gas flow (Qgas) determines the sensitivities for both gases.

We made some response surface plots from a series of gassing out simulations to illustrate.  These show the final amount of dissolved gas in solution at the end of each experiment, when kLa and Qgas are varied systematically in a 'virtual DOE'.  The initial liquid contained no O2 and some dissolved CO2 that was stripped during the experiment; the gas feed was air, so that dissolved O2 increased during the experiment.

Dissolved O2 at the end of a set of kLa measurement experiments in which kLa and Qgas were varied. The final O2 concentration is always sensitive to kLa and only sensitive to Qgas at very low gas flow rates. 

Dissolved CO2 at the end of a set of kLa measurement experiments in which kLa and Qgas were varied. The final CO2 concentration depends only on Qgas at low gas flows; and is sensitive to kLa only at relatively high gas flows. 

Transient concentrations of O2 and CO2 at low gas flow respond differently to changes in kLa.  In this illustration kLa has been increased between runs from 7 1/hr (dashed line) to 21 1/hr (solid line). The dissolved oxygen profile responds but the CO2 profile remains unchanged (click to enlarge).  Clearly, kLa(CO2) cannot be inferred from these data.