Retention Time Distribution

To understand and mathematically describe the activated sludge process in continuous operation, information is needed regarding the degree of mixing inside the reactor. Is the reactor completely mixed? Are there short-circuit flows or regions of eddy currents? What is the dispersion coefficient in a selected type of reactor? Such questions can be answered by measurement and mathematical analysis of retention time distributions (Pippel 1978).

Measurement of the distribution is realized by adding tracers at the influent of the investigated system. In principle, any substance can be used as a tracer, as long as it dissolves completely, does not react with other components and does not change state by desorption, adsorption, precipitation or crystallization. In reality, only a few substances are applicable which are cheap enough, can be measured continuously and are not toxic. Frequently, salts, dyes and other substances not found in wastewater are used which can be measured at very low concentrations. Fig. 6.8 Explanation for measurement of retention time distribution.

(a) Step input and distribution of retention times F(t) as response.

(b) Impulse input and density distribution of retention time E(t) = dF/dt as response.

Fig. 6.8 Explanation for measurement of retention time distribution.

(a) Step input and distribution of retention times F(t) as response.

(b) Impulse input and density distribution of retention time E(t) = dF/dt as response.

The tracer is added at point 1 (Fig. 6.8) as a step signal or as an impulse signal. At point 2, the signal is deformed in a characteristic way. This response to a step signal is called distribution of retention time and is defined as:

co with:

The response to an impulse signal ci(T) is called density distribution of retention time and is defined as:

c0 is here a theoretical concentration, which follows from the mass of the tracer and the volume of the apparatus.

But there is a simple relationship between F and E: dF (t)

The density distribution results from measurements (Fig. 6.8b) and from the distribution by differentiating the dimensionless time.

In the next section we will model some idealized systems and calculate F (t).

140 | 6 Aerobic Wastewater Treatment in Activated Sludge Systems 6.3.2