Until now, all systems discussed here have been either completely mixed (Sections 5.3.1.1 to 5.3.1.3, 5.3.2 and 5.4.2.3) or plug flow systems (Section 5.3.1.4). There fore, models could be used and kLa or KLa could be applied. However, in large-scale tanks, the description of oxygen transfer using the concept of Eq. (5.8) is frequently not allowed because of the different locally structured air/water flows. This is demonstrated by Fig. 5.9 (Mueller et al. 2002).
Porous ceramic tubes are installed in such a way as to promote a secondary water circulation which sucks down a portion of the bubbles rising in the vicinity. But even for a system with a locally constant configuration of diffusers (Fig. 5.10), the oxygen transfer rate may change considerably over time because of the change in load over the course of 24 h and also with location, especially in longitudinal tanks (Schuchardt et al. 2002). We will come back to this point in Section 5.4.2.7.
KLa can be calculated from Eq. (5.54b):
and, after introducing c = Hc*, we obtain:
OTE was developed in Section 5.4.2.3, resulting in Eq. (5.68); and OTR can be obtained by using Eq. (5.72).
Considering the influence of temperature on c* at point x by introducing:
with 9 = 1.024 (Stenstrom and Gilbert 1981) and the influence of the hydrostatic pressure on c* at point x = h (h = height of the water column): ^ ^^ (1+ ) ("6)
we write the standardized oxygen transfer rate for deep tanks:21
With Eq. (5.77), the influence of aeration, height of the water column and temperature can be considered.
This SOTR value is valid for measurements in clean water. In wastewater, especially with activated sludge, a lower SOTR value is to be expected, resulting in (Stenstrom and Redman 1996):
SOTR
2) 10.32 m is the height of a water column causing a pressure of 1 bar. c20x = p/HP means that c20 increases linearly with x.
a-Values are dependent upon diffuser configuration, air flow rate, wastewater composition, local position x and temperature T.
We must keep the following simplifications in mind:
• Instead of using the logarithmic concentration difference (5.54a), which followed from the plug flow model, the approximation Ac' = cT -c ' was applied.
• KLa was assumed to be constant, however there are several influences on both a and Kl (lower pressure, diffusing CO2 into the bubble, coalescence of bubbles and increasing velocity).
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