QgcO20 cO2
after measuring cO2 in the exhaust gas. The change in the dissolved oxygen concentration is very low compared with the respiration rate because of the high Henry coefficient H, which is defined by Henry's law, see Eq. (5.6):
where c is the O2 concentration in the gas and c^2 is the O2 concentration at the border gas/liquid at equilibrium.
In comparison to rO2_z, rCO2,z is more difficult to measure for two reasons:
• The solubility of CO2 in water is much higher than that of O2.
• The soluted CO2L reacts rapidly with water, forming carbonic acid.
4.3 Measurement of O2 Consumption Rate rO2,x and CO2 Production Rate rCO2,x  77 However, the equilibrium constant following from:
k1 sco2,l sh2o s
sco2,l is very low, showing that only ~0.16% of the soluted CO2 is present in the form
H2CO3. Following the concept of Nazaroff and AlvarezCohen (2001), we summarize CO2L and H2CO3 by writing:
or rather as "carbonic acid" concentration, considering Eq. (4.50):
SH2CO3,X = SCO2,L + SH2CO3 = SCO2,L (1 + Ke) (4.52)
Depending on the pH, "carbonic acid" dissociation reactions display the following equilibria:
HCO i H+ + CO2 (4.54) which are strongly influenced by SH+ or pH =  log SH+:
SH2CO3,I
shco3
A fraction Oi of each species S^o^x, shco and sco2 related to the total concentration:
SCX = SH2CO3,X + SHCOj + SCo3 (4.57) can be calculated using Eqs. (4.55) and (4.56). (Note: SH2CO3,x « SCO2):
SH2COj,I
For aH2co3,z = aHCo5 = 0.5 and for aHCo5 = aCO = 0.5, the pH values are called pK and pK2, showing characteristic values (pK = 6.33; pK2 = 10.33).
Equations (4.58) to (4.60) are plotted in Fig. 4.2, presenting some important results:
• At pH < 4.5, all dissolved carbon is in the form of H2CO3Z « CO2.
• At 4.3 < pH < 8.3, H2CO3,z « CO2 and HCO dominates.
• At 8.3 < pH < 12.3, HCO and COf dominate.
• At pH > 12.3, all dissolved carbon is in the form of CO2.
This equilibrium can be influenced by temperature and the concentration of other anions.
Fig. 4.2 Normalized concentrations a of the dissociation products of "carbonic acid" H2CO3X, HCO and COf as a function of pH (Nazaroff and AlvarezCohen 2001); T = 20°C.
PROBLEM 4.1
An industrial wastewater is polluted mostly by polysaccharides (CnH2nOn or for n=1CH2O, respectively). The composition of the bacteria is given by C5H7O2N. The flow rate is 10000 m3 d1, the concentration of the influent is S0 = 2000 mg L1 DOC; and 90% removal should be achieved.
Calculate the amount of nitrogen which must be added.
How much sludge must be treated?
The specific growth rate p is large compared to the decay coefficient kd. In Section 4.2.1, YN/SC = 0.067 mol N (mol DOC)1 and YXC/SC=1/3 mol C (mol DOC)1 was calculated for aerobic degradation of hydrocarbons.
Solution rNV molN 14 g N
YN/sc = — = 0.067 = 0.067 ■ — g N (g C)1 = 0.078
rSCV molDOC 12 g C
rNV = rSCVYN/SC = 18 ■ 0.078 = 1.4 t N d1 nitrogen must be added. molC
mol DOC
rxcV — rscVYXc/sc — 18,000 ■ 0.33 — 5940 kg C d1 50% C per mass MLVSS
rMLVSSV — 2 rXC V; 12 t MLVSS d1 sludge must be treated.
PROBLEM 4.2
In a completely mixed (stirred) tank reactor (CSTR), a wastewater loaded with organics and without inorganic carbon is treated aerobically. For this process, carried out in a steady state, the following data are given:
Wastewater flow rate Qw = 1000 m3 d1
Air flow rate QA = 7500 m3 d1
Reactor volume V = 1000 m3, pH 8
Henry's law is given by
(Nazareff and AlvrezCohen 2001).
For CO2 and 25 °C Hg = 29 atm (mol/L)1 is given. In order to get Henry coefficiet H in its dimensionless form p = RTc must be introduced giving
With R = 8.314 J mol1 K1 = 82.05 ■ 106 m3 atm (mol K)T = 273 + 25 = 298 K
CO2/HCO equilibrium constant K1 — 4.47 ■ 107 mol L1
Calculate the portion of carbon:
produced as CO2 in the air leaving the reactor and produced as CO2, HCO and CO2 in the water leaving the reactor.
Solution
C balance in water: Qw
0 —  (Sco2 + Shco + Sco3) ^vq dissolved in the effluent water
Sco2 can be neglected (pH 8)
Qa cCO2 + rCO2
stripped out produced with air
5H2CO2,X
From (4.61) we obtain with Eqs. (4.62) and (4.63) S __^_
K1 — 4.47 ■ 107 mol L1, MHCO — 61 g mol1 K1 — 4.47 ■ 61 ■ 107 — 272.67 ■ 107 g L1 SH+ — 108 mol L1 — 108 g L1, H — 1.19
9000
9000 2744.6
With Eq. (4.61) the different parts can be calculated
29.36
CO2 trans HCO3 trans CO2 stripped ported with water ported with water with air
In reality two further reactions are of importance, which reduce HC03 concentration:
References
Behrendt, J. 1994, Biologischchemische Behandlung von Prozesswässern der Altlastensanierung sowie von kontaminierten Grundwässern, VDIForschungsberichte, Reihe 15, Umwelttechnik 119.
Heinze, L. 1997, Mikrobiologischer Abbau von 4Nitrophenol, 2,4Dinitrophenol und 2,4Dinitrotoluol in synthetischen Abwässern, VDIForschungsberichte, Reihe 15, Umwelttechnik 167.
Herbert, D. 1958, Some principles of continuous culture, in: Recent Progress in Microbiology, ed. Tunevall, G., Almqvist, Stockholm, p. 381396.
Lax, E. 1967, Taschenbuch für Chemiker und Physiker, SpringerVerlag, Berlin.
Nazaroff, W.W.; AlvarezCohen, L. 2001, Environmental Engineering Science, John Wiley & Sons, New York, 96, 114.
Gas/Liquid Oxygen Transfer and Stripping
Transport by Diffusion
Oxygen is needed for all aerobic biological processes. Usually, it consumption rate depends on oxygen mass transfer1'. If we wish to increase the rate of these processes, we must increase the gas/liquid interfacial area and the rate of the specific mass transfer, which consists of diffusion and convection. The specific mass transport rate of diffusion without convection is given by Fick's law:
D is the diffusion coefficient. If c' is the dissolved oxygen concentration in water, then D = DO2/H2O is the diffusion coefficient of oxygen in water. It can be calculated by using the Einstein equation (Daniels and Alberty 1955) or the NernstEinstein equation (Bird et al. 1962)
where K = 1.380 1023 J K1 (Boltzmann's constant), T is the temperature (K), wO2 is the rate of diffusion of oxygen molecules (mol m h1) and FO2 is the power of resistance of oxygen molecules (J mol m1).
FO2 is obtained from Stokes' law for the motion influenced by high friction forces (ReP1):
where r is the dynamic viscosity of water (g m1 h1) and RO2 is the molecular radius of O2 (m).
Introducing Eq. (5.3) in Eq. (5.2), this follows: KT
1 Only for very low reaction rates is it not dependent on oxygen mass transfer.
Wilke and Chang (Reid et al. 1987) calculated for T = 20°C:
and recommended that the influence of temperature should be taken into account using:
At the gas/liquid boundary, the specific transfer rate of oxygen in water calculated by using Eq. (5.1) is low if only diffusion is involved. This follows not only from the low diffusion coefficient, but also from the low solubility of oxygen in water:
Equation (5.6) is called the Henry absorption equilibrium (Henry's law, see Eq. 4.46) and is valid up to oxygen pressures of nearly p = 10 bar (c = p/RT). H decreases with increasing temperature and concentration of chlorides (Table 5.1).
For 20 °C and deionized water H = 32.6 which means that, for an O2 concentration in air of 298.7 mg L1, only 9.17 mg O2 L1 are dissolved in water. Therefore, oxygen transfer into water by diffusion is a slow process, due to the low diffusion coefficient and the low solubility (Fig. 5.1).
If we want to use oxygen for a chemical or biological process in water, we must: (a) use convection in addition to diffusion and (b) increase the gas/liquid interfacial area.
Furthermore, it may be necessary to use pure oxygen instead of air in some cases, resulting in a higher dissolved oxygen concentration at the boundary c* by a factor of 4.8. But in our further discussion we will only consider the use of air.
air 
water 

Co2 


c*=c0' 
 
c' 

Fig. 5.1 Transport of oxygen from air into water only by diffusion.
Fig. 5.1 Transport of oxygen from air into water only by diffusion.
Table 5.1 Dissolved oxygen concentration in water c' for different temperatures and chloride concentrations; c = 20.9% O2 in air; pair = 760 bar (Chow et al. 1972).
Temperature 

Chloride concentration (mg L 
1) 

(°C) 











0 
5000 
10000 
15 000 
20000 
0 
14.62 
13.79 
12.97 
12.14 
11.32 
1 
14.23 
13.41 
12.61 
11.82 
11.03 
2 
13.84 
13.05 
12.28 
11.52 
10.76 
3 
13.48 
12.72 
11.98 
11.24 
10.50 
4 
13.13 
12.41 
11.69 
10.97 
10.25 
5 
12.80 
12.09 
11.39 
10.70 
10.01 
6 
12.48 
11.79 
11.12 
10.45 
9.78 
7 
12.17 
11.51 
10.85 
10.21 
9.57 
8 
11.87 
11.24 
10.61 
9.98 
9.36 
9 
11.59 
10.97 
10.36 
9.76 
9.17 
10 
11.33 
10.73 
10.13 
9.55 
8.98 
11 
11.08 
10.49 
9.92 
9.35 
8.80 
12 
10.83 
10.28 
9.72 
9.17 
8.62 
13 
10.60 
10.05 
9.52 
8.98 
8.46 
14 
10.37 
9.85 
9.32 
8.80 
8.30 
15 
10.15 
9.65 
9.14 
8.63 
8.14 
16 
9.95 
9.46 
8.96 
8.47 
7.99 
17 
9.74 
9.26 
8.78 
8.30 
7.84 
18 
9.54 
9.07 
8.62 
8.15 
7.70 
19 
9.35 
8.89 
8.45 
8.00 
7.56 
20 
9.17 
8.73 
8.30 
7.86 
7.42 
21 
8.99 
8.57 
8.14 
7.71 
7.28 
22 
8.83 
8.42 
7.99 
7.57 
7.14 
23 
8.68 
8.27 
7.85 
7.43 
7.00 
24 
8.53 
8.12 
7.71 
7.30 
6.87 
25 
8.38 
7.96 
7.56 
7.15 
6.74 
26 
8.22 
7.81 
7.42 
7.02 
6.61 
27 
8.07 
7.67 
7.28 
6.88 
6.49 
28 
7.92 
7.53 
7.14 
6.75 
6.37 
29 
7.77 
7.39 
7.00 
6.62 
6.25 
30 
7.63 
7.25 
6.86 
6.49 
6.13 
There are two possibilities to realize the conditions (a) and (b):
• We can produce small air bubbles, which rise to the surface of the water, causing an oxygen transfer into the water and to the suspended microorganisms.
• We can produce trickling films, which flow downwards at the surface of solids covered by biofilms.
In this chapter we will concentrate only on the transfer of oxygen from bubbles to water by diffusion and convection.
Mass Transfer Coefficients
Definition of Specific Mass Transfer Coefficients
In contrast to Fig. 5.1, where mass is only transferred by molecular motion (diffusion), we now want to augment it with convective motion (Fig. 5.2).
As a result of the high diffusion coefficient of oxygen in air, the concentration of oxygen in air remains locally constant as before. But in the water, the situation has changed completely: in addition to the molecular motion, total liquid mass is now moved by hydrodynamic forces, i.e. pressure, inertia and friction forces in the direct vicinity of a rising air bubble. This convective transport increases the local slope of the concentration at the boundary dc'/dx  x_0 and the specific rate of mass transfer:
But the gradient is not measurable and can be calculated only for low liquid flow rates. In contrast, the concentration difference c*c' can easily be measured (Fig. 5.2):
where k,
and 8 is the thickness of the boundary (see Fig. 5.3).
The proportionality factor kL in Eq. (5.8) depends on the diffusion coefficient D as well as the bubble velocity w, the kinematic viscosity v and the surface tension o,
air 
water 

Co2 


c*=c0' 
* JD+C 

WLt 
k" 
c' 
Fig. 5.2 Transport of oxygen from air into water by diffusion and convection.
Fig. 5.2 Transport of oxygen from air into water by diffusion and convection.
for example. We cannot assume that we are able to measure the total boundary surface area A gas/liquid of all the bubbles:
Applying Eq. (5.9) to the volume of the system V, the specific oxygenation capacity follows:
with kLa as the specific mass transfer coefficient.
kLa and c' are dependent on the temperature. For a temperature of 20 °C and c' = 0, we obtain the maximum specific standardized oxygenation capacity:
(kLa)20 and c*20 are dependent on the concentration of dissolved inorganic and organic substances. Applying the ratio of values effective for wastewater and clean water, we write:
reflecting the mass transfer coefficients for T = 20 °C gives:
(kLa)20 w for wastewater (kLa)200 for clean water and concentrations of dissolved oxygen at the interface:
c20w for wastewater c'20,0 for clean water
Especially in industrial wastewater, different components may be dissolved which may desorb during the absorption of oxygen. Because of their low Henry coefficient H, a transport resistance occurs in both phases, in water and air. This case will be discussed in the next section.
Two Film Theory
Three models have been developed to improve the understanding of gas/liquid mass transfer: the surface renewal model of Higbie (1935) and Danckwerts (1951, 1970); the 'still surface' model of King (1964) and the 'two film' model of Whitman air water air water c
Fig. 5.3 Absorption and desorption of compounds dissolved in water with a low Henry coefficient, H = c/c* = c0/c'0; (a) absorption, (b) desorption.
Fig. 5.3 Absorption and desorption of compounds dissolved in water with a low Henry coefficient, H = c/c* = c0/c'0; (a) absorption, (b) desorption.
(1923). We will limit our discussion to the two film theory. A review of all theories is given by Danckwerts (1970).
Let us look at the mass transfer at the boundary water/air for desorption processes and for the case that two films are formed. The desorption of oxygen into an oxygenfree gas film, e.g. nitrogen, is a simple case which follows nearly directly from Fig. 5.2. But such equilibria, which are characterized by a low Henry coefficient, lead to concentration profiles in both water and air for absorption (Fig. 5.3a) and desorption (Fig. 5.3b).
The rate of desorption must now be calculated using the two film theory. Table 5.2 compiles some compounds with low H.
Note that in Fig. 5.3b the concentration c in the air bubble is much lower than c*, the theoretical equilibrium concentration.
An overall mass transfer rate is given using KLa. If we define the specific overall mass transfer coefficient KLa by writing:
for the specific overall mass transfer rate, we can conclude that this rate is the same as in the liquid film:
which also agrees with the rate in the gas film: kLa(c' c0) = kGa(cocG)
with:
Table 5.2 Solubility and Henry coefficient of different compounds (Nyer 1992, supplemented), Henry's law:
Pcw Kp
RT Cw
Compound 
Maximal solubility 
Henry coefficient 
Henry coefficient 

(Cax, mg L1) 
(Kp, bar) 
(H, ) 
1 Acetone 
1 • 106 
0 
0 
2 Benzene 
1.75 • 103 
230 
0.1690 
3 Bromodichloromethane 
4.4 • 103 
127 
0.0934 
4 Bromoform 
3.01 • 103 
35 
0.0257 
5 Carbon tetrachloride 
7.57 • 102 
1282 
0.943 
6 Chlorobenzene 
4.66 • 102 
145 
0.107 
7 Chloroform 
8.2 • 103 
171 
0.126 
8 2Chlorophenol 
2.9 • 104 
0.93 
0.684 • 103 
9 pDichlorobenzene (1,4) 
7.9 • 101 
104 
0.0765 
10 1,1Dichloroethane 
5.5 • 103 
240 
0.176 
11 1,2Dichloroethane 
8.52 • 103 
51 
0.0375 
12 1,1Dichloroethylene 
2.25 • 103 
1 841 
1.353 
13 cis1,2Dichloroethylene 
3.5 • 103 
160 
0.117 
14 trans1,2Dichloroethylene 
6.3 • 103 
429 
0.315 
15 Ethylbenzene 
1.52 • 102 
359 
0.264 
16 Hexachlorobenzene 
6 • 103 
37.8 
0.0278 
17 Methylene chloride 
2 • 104 
89 
0.0654 
18 Methylethylketone 
2.68 • 105 
1.16 
0.853 • 103 
19 Methyl naphthalene 
2.54 • 101 
3.2 
0.235 • 103 
20 Methyl tertbutylether 
4.8 
196 
0.144 
21 Naphthalene 
3.2 • 101 
20 
0.0147 
22 Pentachlorophenol 
1.4 • 101 
0.15 
0.1100103 
23 Phenol 
9.3 • 104 
0.017 
0.0125 • 103 
24 Tetrachloroethylene 
1.5 • 102 
1035 
0.761 
25 Toluene 
5.35 • 102 
217 
0.160 
26 1,1,1Trichloroethane 
1.5 • 103 
390 
0.287 
27 1,1,2Trichloroethane 
4.5 • 103 
41 
0.030 
28 Trichloroethylene 
1.1 • 103 
544 
0.400 
29 Vinyl chloride 
2.67 • 103 
355 000 
261.0 
30 oXylene 
1.75 • 102 
266 
c'0 follows from Eqs. (5.15) to (5.18). cG is the concentration of the desorbed compound in the air and c* is its equilibrium value at the interface:
kLa kGa
After introducing Eq. (5.19) into Eq. (5.15), we obtain: 1
Ka overall resistance kca H
resistance of the air film
kLa resistance of the water film
Note that:
• This simple equation is only applicable if we use c' c* as the driving concentration difference to define the specific overall transfer coefficient KLa.
• The resistance of the air film increases with decreasing Henry coefficient H, i.e. higher dissolution in water at lower concentration in air.
• The influence of H is increased at low kGa and high kLa.
Looking at Table 5.2 and assuming similar values for kGa and kLa, mass transfer resistance lies nearly completely on the air film side for compounds with low H (2chlorophenol, methyl ethyl ketone, phenol and others) and nearly completely on the water film side for vinyl chloride with its very high H.
Although H = 32.6 (T = 20 °C) for oxygen/water (clean water) is relatively high (Section 5.1) and mass transfer is controlled for normal conditions by the resistance of the water film, we want to use the specific overall mass transfer coefficient KLa as well.
Measurement of Specific Overall Mass Transfer Coefficients KLa
Absorption of Oxygen During Aeration 5.3.1.1 Steady State Method
The absorption of oxygen will first be discussed for a completely stirred tank reactor (CSTR) filled with clean water and equipped with a perforated annular tube below the stirrer (Fig. 5.4).
Sodium sulfite, Na2SO3, is dissolved in the clean water together with a cobalt catalyst. Sulfite ions oxidize immediately, consuming the dissolved oxygen:
5.3 Measurement of Specific Overall Mass Transfer Coefficients KLa 91 
 Fig. 5.4 Installation for measuring the mass transfer coefficient in clean water or wastewater without activated sludge.
Therefore, c' is zero until the dissolved SO is totally oxidized to SO42. If we want to measure in nearly saltfree water after aeration, only a small amount of Na2SO3 should be added  just enough for a few experiments. The exhaust air with a low O2 concentration flows through absorption systems for drying and CO2 removal before entering online oxygen gas analyzers and flow rate measurement devices.
The steady state oxygen balance in the completely mixed gas is:
c where V is the water volume, QG is the gas flow rate and co dissolved oxygen concentration.
QG (cin cout)H
In larger aerated reactors, the O2 gas concentration is often not completely mixed and better results can be obtained if an arithmetic mean value is used for:
This relatively small simplification is only allowed for small decreases in the percent of oxygen volume inside the air bubbles, e.g. from 20.9 to 19.0%. For a greater decrease, a more complicated evaluation is necessary. Better results follow if a logarithmic mean value is used.
5.3.1.2 Nonsteady State Method
Only a low amount of Na2SO3 is added to the water (clean water or wastewater free of activated sludge) using the dissolved O2 for oxidation. After the Na2SO3 is completely oxidized, c' increases. It is measured by one or several O2 electrodes, which are combined with a computer for direct evaluation. For this purpose, the O2 dissolved in the completely mixed water must be balanced:
Considering the initial condition:
t = 0 c' = 0 the solution of Eq. (5.25) gives: , c*  c'
A plot of ln (c* c')/c* versus t must give a straight line, if the assumption of a completely mixed system is to be met. Frequently, a better linear plot is obtained using an arithmetic mean value for c*. Equation (5.26) should go over at least 1.5 decades
5.3.1.3 Dynamic Method in Wastewater Mixed with Activated Sludge
The specific overall mass transfer coefficients KLa can be influenced not only by temperature and pressure (bubble diameter) but also by dissolved and suspended matter, such as minerals and activated sludge (Eqs. 5.12 to 5.14). Therefore, it is necessary to measure (KLa)20w in an activated sludge system which can be treated as a CSTR in continuous flow or in batch operation. We will describe this method for a batch system. After a period of continuous operation (Fig. 5.5, period I) and after an input of a given bacteria mass, the flow of wastewater and air is stopped, without reducing the stirrer speed to maintain the activated sludge in suspension. During period II, the concentration of dissolved oxygen c' is decreased by respira
bacteria input
continuous 1 , 
III 

c'min 
* ' ro2 / (K_a)w 



< At► 
Fig. 5.5 Nonsteady state method for measuring the mass transfer coefficients in wastewater with activated sludge.
Fig. 5.5 Nonsteady state method for measuring the mass transfer coefficients in wastewater with activated sludge.
5.3 Measurement of Specific Overall Mass Transfer Coefficients KLa  93
tion. Period II is finished as soon as cmin;2 mg L—1 is reached. In the region of lower c' values, respiration rate may be limited by oxygen. Now aeration resumes and c' increases up to a constant value (period III).
The balance for dissolved oxygen in period II and the initial condition are: dc'
The balance for period III and the initial condition are: dc'
Equation (5.29) can be solved by the separation of variables. After integration and consideration of the initial condition:
(KLa)w c*  ro2  (KLa)w C can be written, and finally:
■ (KLa)wt c* cmin ) exp [ (KLa)w t] + Tl7~2 (5.30)
For higher values of time t: ro
(KLa)w and (Kl a)w can be calculated.
The experimental curve in period III is described in the best possible way obtaining a more exact value for (KLa)w. By comparing this value (KLa)w to KLa measured in clean water, both at 20°C, aw can be determined (see Eq. 5.12).
Desorption of Volatile Components During Aeration
Dissolved volatile organic components (VOC) can be divided into two groups, according to their Henry coefficient H (see Table 5.2).
For Hp1 (e.g. oxygen/water), overall mass transfer resistance is given by liquid mass transfer:
KLa KGa H kLa
KLa = kLa and usually the desorption capacity for T = 20°C follows from (see Fig. 5.3b):
If the desorbing component has nearly the same diffusion coefficient as oxygen, the same kLa can be used. For molar masses of individual VOCs different from oxygen, it is most effective to use a corrected kLa:
/DVOC\n
DVOC can be measured or calculated using Eq. (5.4). The exponent n is not easily obtainable and depends on the mixing equipment.
For H < 10, the overall mass transfer resistance is normally given by liquid and gas mass transfer rates using the film model (Fig. 5.3 where H < 1). In this case, the desorption capacity at T = 20 °C is:
with:
kGa H
if the diffusion coefficient of the desorbing component is nearly the same as that of oxygen. Otherwise, Eqs. (5.33) and (5.34) must be corrected in a similar way to Eq. (5.32):
DVOC n DVOC
KLa kca kLa
For at least three different components with different Henry coefficients, H/KLa can be measured in the same mixing system at exactly the same conditions (stirrer speed, flow rate). A straight line must go through the date plotted as H/KL a versus H. The resulting value of kLa follows from the slope and ksa from the ordinate intercept.
Only the results of a few studies are available (Libra 1993) to date.
5.4 Oxygen Transfer Rate, Energy Consumption and Efficiency in Largescale Plants  95
Oxygen Transfer Rate, Energy Consumption and Efficiency in Largescale Plants
Surface Aeration
5.4.1.1 Oxygen Transfer Rate
Principally, the same methods are used for measuring overall specific mass transfer coefficients KLa as described before in Section 5.3, but often the following terms are used:
• OTR oxygenation transfer rate (ASCE 1997: Standard guidelines for inprocess oxygen transfer testing).
• OC oxygenation capacity (ATV 1997: Guidelines according to ATV Arbeitsblatt M 209).
We select OTR, which is related to reactor volume V and is calculated from (see Fig. 5.3a):
However, the air flow rate QG as well as the oxygen concentration of the escaping air is normally not measurable. Therefore, the only way to measure KLa is by using data obtained from absorption measurements and the balances for oxygen absorption described in Section 5.3.1.2 (see Eq. (5.27) for period II and Eq. (5.29) for period III).
One problem must be noted: in Section 5.3 the reactors used for laboratory or pilot experiments have a small volume of several liters to 12 m3; and, regardless of the aeration method (volume or surface aeration), a nearly completely mixed gas and liquid phase cannot be guaranteed. Largescale basins of several hundreds to several thousands of cubic meters cannot be completely mixed by surface aerators, such as centrifugal aerators. Therefore KLa as well as c' are different at several points of a "mixed" tank with one or more aerators.
Nevertheless, the only way to obtain information about OTR in largescale basins is to evaluate the measurements with Eq. (5.25) for clean water without sludge or Eqs. (5.27) and (5.29) for wastewater with sludge.
Three measures are necessary to standardize OTR:
• Use a fixed temperature (in Europe T = 20 °C).
• Limit the maximum value for the difference of concentration.
For the standardized oxygen transfer rate we write: SOTR = (KLa)20,0 c*20,0 ( 5.38)
1) Remember: Only for this definition of KL a, it is not influenced by concentration; see Eq. (5.20).
For a measurement in wastewater with or without sludge, we obtain:
Figure 5.6 shows a Simplex aerator. Different values of KLa can be selected via the rotation speed and depth of submersion. Frequently, a transmission makes three speeds possible.
For a Simplex aerator with the dimensions presented in Fig. 5.6, the standardized oxygen transfer rate (SOTR) is plotted versus power consumption P/V (see Fig. 5.7, in the next section).
We will now consider a surface aerator and the power required to achieve a desired oxygen transfer rate. 
 Fig. 5.6 Simplex aerator, number of blades = 24 (Zlokarnik 1979).
5.4.1.2 Power Consumption and Efficiency
The power consumption of a rotating turbine powered by an electric motor is usually given as the total power consumption Pt:
Çm ' Çg where çm is the efficiency of the electric motor and çg is the efficiency of the transmission.
If we compare different kinds of aerators, we must use the effective power:
considering the measurable Pt:
and the values for e.g. Çm = 0.93 and Çg = 0.93, or those obtained from the manufacturer (Zlokarnik 1979).
5.4 Oxygen Transfer Rate, Energy Consumption and Efficiency in Largescale Plants  97 The efficiency of the aerator follows as: OTR
The total efficiency, which cannot be used in comparisons because of different and g, is (see Eq. 5.37):
Pt/V
Pt/V
Et provides information about the total energy needed for the aeration of real wastewater with a given system at the effective conditions.
If we wish to compare this system with others with different temperatures and kinds of wastewater, we must use the standardized oxygen transfer rate OTR20 = SOTR (see Eq. 5.38) and the power P without considering the energy loss from the motor and the transmission:
OTR2
SOTR
and we have to measure in clean water.
Some results for OTR, P/V and E are presented in Fig. 5.7 (Zlokarnik 1979). In spite of the scattering of the measured data, it can be concluded from Fig. 5.7 that for specific powers P/V = 15 kW m3 and a SOTR = 45 kg O2 (m3 h)1 an efficiency of E ; 3 kg O2 (kWh)1 may be attained. However, the total electrical power 
 Fig. 5.7 Standardized oxygen transfer rate, power consumption and efficiency of a Simplex aerator (Schuchardt 2005, data from Zlokarnic 1979).
Pt which must be supplied is higher by the factor 1/rm g = 1.16, resulting in a lower efficiency of at most:
In reality c' = 14 mg L1 and Et is 10 to 40% lower for e.g. 15 °C water temperature (Eq. 5.45 and Table 5.1). We must not forget that these measurements were carried out in a very small test unit of only 100 L. It is not permissible to transfer these results to a larger tank with a larger aerator without further intermediate studies.
The question should be: can we use these results for a largescale plant with the same type of aerator if we take the theory of similarity into account? We will return to this question in Section 5.5.

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