# With High Initial Concentration of Bacteria

Monod published the first kinetic studies on the limitation of bacterial growth by substrate concentration. For these experiments he used an aerobic batch reactor, glucose as substrate, and a culture of Escherichia coli (Monod 1942, 1950). His inspiration came from Michaelis-Menten kinetics (see Section 3.2.1.4), which are only valid for a system consisting of one substrate and one enzyme. Although the biodegradation of one substrate by a pure culture of bacteria and, of course, by a mixed culture is a more complicated process, the standard form of the growth kinetics of bacteria shows the same mathematical structure if the growth is not limited by the concentration of dissolved oxygen:

and:

where v is the specific growth rate (d-1), vmax is the maximal specific growth rate (d-1), S is the substrate concentration (g L-1), KS is the saturation coefficient (g L-1), rx is the growth rate (g L-1 d-1 MLSS) and X is the concentration of bacteria (g L-1 MLSS).

Monod's first experiments were carried out in batch reactors. He described his measurements of S and X with respect to time by using the bacterial balance:

dX S

and the substrate balance:

where the substrate consumption rate is:

S vo

and YX/S is the true yield coefficient.

The initial conditions of Eqs. (6.3) and (6.4) are:

The simplest solution can be obtained for a relatively high X0 and a relatively low S0, resulting in a nearly constant X = X0. Only Eq. (6.4) must be solved, which is performed by the separation of variables:

with:

YX/S

The results of an experiment can be tested as a function of S = f(t) and the coefficients KS and rS,max can be determined by transformation of Eq. (6.7) into:

In order to confirm that the results of the batch experiment correspond with the model used to develop Eq. (6.4), we should plot, e.g.:

ln So/S t versus

and the points should form a straight line with a positive slope rSmax/KS and a negative ordinate intercept -1/KS.

For substrate and oxygen limitation, Eq. (6.1) must be expanded: S c'

The region where oxygen limitation is significant can be estimated using K' = 0.2 mg L-1 O2 at T = 20 °C (Putnaerglis 1987). For SP KS the point of limitation may be given as u = 0.9 pmax (90% of maximal growth rate):

For c'6 1.8 mg L-1 we do not expect O2 limitation (T = 20 °C, domestic sewage, no influences of mass transfer at the surface or inside of flocs formed by bacteria).

With KS = 50-120; 85 mg L-1 BOD5 at T = 20°C (Sundstrom and Klei 1979), the region of substrate limitation can be estimated roughly to be:

If both concentrations S and c' decrease to low values during a batch process, the kinetic evaluation is complicated. Therefore, kinetics should be studied considering only under substrate limitation or oxygen limitation. But if we want to study oxygen limitation during a batch process without aeration, the substrate concentration (BOD5, COD, DOC) decreases only about a few milligrams per liter if c' decreases from 8 mg L-1 to 0 mg L-1. This kind of batch experiment can be carried out even for low S values.

If we avoid substrate limitation c'

can be tested.

122 | 6 Aerobic Wastewater Treatment in Activated Sludge Systems For X; const, the oxygen balance is:

dc Fmax C

and a corresponding solution to Eq. (6.9) is obtained which can be linearized as shown before.