**5.3 Bioreactor Oxygen Balance**

Let us now consider the case of oxygen balance within a bioreactor in
which cells are growing and in the process consuming oxygen. There is a
continuous inflow of air at a constant volumetric flow rate. The liquid
broth is agitated by a Rushton agitator (flat blade stirrer ). Le the metabolic
oxygen uptake rate be q_{O2} and cell concentration is X. Let us
examine the reactor system over a sufficiently short period that we can
treat X as a constant. Consider oxygen balance over the liquid phase of
the bioreactor.

O2 transfered from Gas Phase - O_{2} consumed
by Cells = Accumulation

For constant liquid phase volume, the above can be simplified to

The concentration, C_{DO} is readily measured
using an dissolved oxygen electrode. A later segment of the course on Biosensors,
will deal with principle of measurement and construction of DO electrodes.

If oxygen being supplied is in exact balance with the oxygen consumed by the cells, we expect the dissolved oxygen concentration to remain constant; that is, the derivative in Eq(5-7) will vanish. That is,

One useful application of the above is in estimating the maximum cell
concentration a particular bioreactor is capable of supporting in terms
of oxygen supply. See the example below.

Example 5-1.

A bioreactor has an oxygen mass transfer coefficient capability of 400 h

^{-1}. What is the maximum concentration of E. coli that can be grown aerobically in this reactor. Respiration rate of E. coli is 0.35 g O2 (g Cell)^{-1}h^{-1}. Critical oxygen concentration is 0.2 mg/L. Assume oxygen saturation with air to be 6.7 mg/L.

SolutionFrom Eq(5-8), we have

The maximum oxygen concentration driving force that can be expected is

= ( 6.7 - 0.2) = 6.5 mg/L.

Therefore, maximum cell concentration that can be grown at maximum growth rate is