Bacteria in wastewater treatment process are assumed only to be able to utilize very small and simply built molecules for growth. The process can be described using the following expression:



r_V,XB is the vol. biological growth rate
m_max is the max specific growth rate
f(s) describes growth kinetics
X_B is the concentration of the biomass

The substrate consumption corresponding to the biological growth can be found from

Y_max is the maximum yield constant

Monod Kinetics are frequently used, and hence the substrate consumption for growth attains the following description:

It should be noted that the expression applies in a situation where only the substrate, S, is the limiting factor for growth.

Hydrolysis

The hydrolysis process converts larger molecules into small, directly degradable molecules. The process is normally slow compared to the growth process. Hence, in terms of rate of reaction, this is often the limiting step in biological wastewater processes.

The process is often described as a simple first order process with respect the hydrolizable materials (i.e. suspended solids X_S):

A similar expression for the hydrolysis of dissolved organic matter is:

k_his just as hyrdolysis constant and is not the same for the two equations above

The variation of the hydrolysis constant for heterotropic bacteria under different conditions is listed below.

Decay

Living bacteria have a certain death rate which is essential to the conversions of substances in treatment plants. When the organism dies, the amount of substance does not change. Rather, it means that slowly degradable material is added to the system. This material is hydrolyzed and subsequently causes new growth.

Decay is described as a first order process with respect to to the biomass, X_B

b is the constant for decay

References