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The Simple Plug Flow Model

The situation is described in Fig. 5.8: all bubbles rise with the same velocity w, which is not easy to measure. Therefore, the average void velocity is used:

with Ar as the cross-sectional area of the reactor (bubble column). We can balance the gaseous oxygen in the total volume of the bubble column; and it is not necessary to determine the total gas volume, which would be nearly impossible in large open tanks.

Fig. 5.8 Upward plug flow of water and flowing bubbles with corresponding diameters.

This steady-state experiment can be carried out:

• with clean water and Na2SO3, resulting in an oxygen-free liquid system,

• with real wastewater with or without activated sludge.

Let us discuss the first case. For the steady-state oxygen gas balance, we write:

dx L

and considering Henry's law: c = H c*

as well as the boundary condition: x = 0 c = cin

the result for the concentration profile is: c K,a ln — =--= x (5.49)

Cin H w

Frequently, a mean O2 concentration of the bubbles c is calculated using:

cout which is introduced into the integral balance:

Instead of Eq. (5.50), we need to write for the case of a finite dissolved oxygen concentration (c' ( 0):

Equations (5.51) and (5.52) are approximations for two reasons:

• A totally mixed liquid system cannot be passed through by gas bubbles flowing with the same velocity and exhibit a detectable decrease in the oxygen concentration.

• A plug-style flow of bubbles cannot be realized precisely when using a swarm of bubbles.

In wastewater technology, this plug flow model is used only seldom. Instead of an exponential decrease in oxygen concentration inside the bubbles, a linear decrease is considered with an arithmetic mean value:

which is a very rough approximation for larger, actual differences (cin- cout)/cin (Zlokarnik 1979). Now, the oxygen transfer rate (OTR) can be calculated by using either:

5.4 Oxygen Transfer Rate, Energy Consumption and Efficiency in Large-scale Plants 1101 A value of further interest is the oxygen transfer efficiency (OTE):

Using Eq. (5.55), OTE can be obtained simply. We will now describe the mass transfer in more detail.

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