4.1 Equilibrium Concentration of Oxygen in Water
4.2 Mass Transfer Processes of Aerators

4.1 Equilibrium Concentration of Oxygen in Water

The equilibrium concentration is the maximum concentration of oxygen which can be dissolved in the water relative to the concentration of oxygen in the gas under the prevailing conditions of temperature and pressure. In fish pond conditions the gas means the atmospheric air, although pure oxygen also gets into the fish pond water by the oxygen production of phytoplankton and other water plants. In some intensive fish farming systems pure oxygen is applied in order to meet the oxygen requirement of the fish.

The equilibrium concentration in gas-liquid systems is expressed by Henry’s law as follows:


H = Henry’s constant (Pa). (Henry’s constant depends on the temperature).

The partial pressure of one component of a gas mixture is proportional to the volume fraction of that component.


P = the pressure of gas mixture (Pa)

Figure 13. a) Counterflow column

Figure 13. b) Gas recycling

Figure 13. c) Enclosed Operation

Figure 13. d)Venturi oxygenator

Figure 13. e) U tube oxygenator

Figure 13.f) Complex system

21 percent of the atmospheric air is oxygen thus the volume fraction is:

The oxygen concentration expressed in mole fraction can be converted into weight fraction as follows:1/

1/ In the following equations the notations k-1 and m-1 are used to denote per kg or per m3



The weight fraction can be converted into weight concentration (Cs) as follows:

(kg . m-3)


Cs = weight concentration of oxygen at saturation (kg . m-3)

The density depends on temperature as shown in Table 5.

Based on the equations given above, the weight concentration of oxygen at saturation (Cs) can be calculated as follows:

(kg . m-3)
(g . m-3)

Table 5 Density of pure water

0 999.87 16 998.97
1 999.93 17 998.80
2 999.97 18 998.62
3 999.99 19 998.43
4 1 000.00 20 998.23
5 999.99 21 998.02
6 999.97 22 997.80
7 999.93 23 997.57
8 999.88 24 997.33
9 999.81 25 997.07
10 999.73 26 996.81
11 999.63 27 996.54
12 999.52 28 996.26
13 999.40 29 995.97
14 999.27 30 995.68
15 999.13

When calculating the pressure (p), the atmospheric pressure and the water head have to be taken into account (1 mm H20 = 9.80665 Pa). In the case of a surface aerator, one has to calculate only with the atmospheric pressure. The Cs values at normal atmospheric pressure are shown in Figure 1.

In those places where the elevation is different from sea level, the atmospheric pressure can be calculated with the “barometric level formula” as follows:

using the “gas law”


z = elevation above sea level (m)
pz = atmospheric pressure at z elevation above sea level (Pa)
p0 = atmospheric pressure at sea level (Pa)

The normal atmospheric pressure at 45° north at sea level and at 273 K (0°C) temperature is:

101325 Pa (= 760 torr = 1 atm)
g = acceleration due to gravity (ms-2) its value for practical calculations is: g = 9.81 ms-2
S0 = the density of air (sea level, normal atmospheric pressure, 273 K (0° C) temperature)

S0 = 1.2928 kg . m-3

q = temperature (K)
R = gas constant

its value for air is:
R = 287.041 s . kg-1 K-1

The changing of the local atmospheric pressure usually is + 10 percent.

4.2 Mass Transfer Processes of Aerators

The amount of oxygen that can be dissolved in the water by an aerator during a time unit can be expressed as follows:


KLa = modified mass transfer coefficient (h-1)
Cs = the equilibrium concentration of dissolved O2 (g m-3)
C = the dissolved oxygen concentration in the water (g m-3)
t = time (h)

The solution of the differential equation when the initial condition is C0 is as follows:

The KLa modified mass transfer coefficient is a product of multiplication of the mass transfer coefficient (KL) and the specific area () as follows:


KL = mass transfer coefficient (m h-1)
A = diffusion area (m2)
V = volume (m3)

KL is dependent on the temperature


q = temperature (°C)
b = constant with a value between 1.016 and 1.047
In sewage treatment with bubbling aeration usually b = 1.02 is used during the calculations


The organic and inorganic materials in the water have an influence on KLa.

K¢ La = a KLa


K¢ La = the modified mass transfer rate of an impure water
a = constant, its value lies between 0.7 and 0.9 when the water is biologically treated and 0.5 when the water is mechanically treated.

The Oxygenation Capacity (OC) expresses how many grams of oxygen can be dissolved in 1 m3 of water during one hour by the aerator investigated, at normal atmospheric pressure when the water temperature is 10°C and its initial dissolved oxygen content is zero.

The relation between the Oxygenation Capacity and modified mass transfer rate is shown as follows:

OC = KLa (10°C) . Cs (10°C)

The value of OC at different temperature and atmospheric pressure can be computed with the equation:


When the same aerator is used for the oxygenation of a larger water volume than 1 m3 less oxygen can be dissolved. This is why total oxygen intake (Ot) is introduced.

Ot = V . OC (g h-1)

The value of Ot is related to 10 or 20°C temperature, normal atmosphere pressure and C = 0 initial dissolved oxygen concentration.

The specific total oxygen intake Ots shows the efficiency of the oxygenation related to the power input.

(g h-1 kW-1)


P = power input of the aerator (kW)


5.1 Bubble Aeration
5.2 Examples for Dimensioning Fine Bubble Aerators
5.3 Aeration with Ejectors
5.4 Aeration with Paddle Wheels

5.1 Bubble Aeration

The air intake type aerators can be classified according to the size of bubbles produced as follows:

a) Fine bubbles dB = 1 to 5 mm
b) Medium bubbles dB = 5 to 10 mm
c) Coarse bubbles dB = larger than 10 mm

The size of the bubble can be expressed as follows


dB = bubble diameter (mm)
s = surface tension of the liquid (N m-1)
Sf = density of the liquid (kg m-3)
Sg = density of the gas (kg m-3)

When fine and medium size bubbles are produced, the diameter of the bubbles is larger than the size of the hole through which the air enters into the water . When a large bubble is produced its diameter is smaller than the hole size.

The elevation velocity of the bubbles in ease of different bubble size is shown as follows:

dB < 0,15 mm VB = 478 500 dB2 (ms-1)
0,15 mm < dB– < 2.10 mm VB = 758 dB1.25 (ms-1)
2.10 mm < dB < 7.20 mm VB = 0.0164 dB0.5 (ms-1)
dB > 7.20 mm VB = 2.24 dB0.5 (ms-1)

In bubble aeration the following ratio is used as a reference to the efficiency of oxygen dissolving:

The value of this ratio in different systems is as follows:

a) fine bubble aeration: 9-10 percent
b) medium bubble aeration: 5 – 6 percent
c) coarse bubble aeration: 3.5- 5 percent


Q = air volume (m3h-1)
S = density of air (kgm-3)
OCV = (g h-1)

The manufacturers of different aerators use characteristic curves that can be expressed as follows:



S = density of air (kg m-3)
w = mole fraction of O2 in air (kg kg-1)

Generally the air volume (Q) is related to normal atmospheric air. In this case:

S = 1.293 kg m-3


S . w = 1.293 . 0.232 = 0.3 kg m-3

The equations above are related to a given water depth. The different parameters can be converted from one water depth to another using the formula:

Table 7 shows the result of a test during which a bubble aerator (2.3 mm long 25 mm diameter perforated plastic pipe with 1.5 mm diameter holes in two lines with a distance of 20 mm between holes) was utilized in a tank with a surface area of 7.5 × 17.5 m.

5.2 Examples for Dimensioning Fine Bubble Aerators

The scheme of the NOKIA fine bubble aerator is shown in Figure 14. The air intake part of these aerators is made of porous polyethylene material, in pipe (HKP 600) or in disc (HKL 210) form.

They can be dimensioned using the curves given in Figures 15 and 16.

The Flygt 763 type fine bubble aerator is shown in Figure 17. The equation below shows how much oxygen can be dissolved from 1 m air when the temperature of the water is 10°C, its initial oxygen content is zero and when the aerator is placed 1 m below the water surface:

if the value of Q lies between 6 m3h-1 and 30 m3h-1


Q = the amount of air flowing through the aerator (the amount of air is calculated for normal conditions, 0°C and 101325 Pa) (m3h-1)

The relation between the air flow and the required pressure is shown in Figure 17.

5.3 Aeration with Ejectors

The cross-section of an ejector for fish pond aeration (Flygt type 4803, 4804) is shown in Figure 18. The primary water flow (1) passes through a Venturi inlet (2) where its velocity increases while its pressure decreases. The low pressure suction chamber (3) is connected to the atmospheric air by a pipe (4) through which air enters the chamber. In the mixing pipe (5) the air and the primary water are mixed together. As the air-water mixture passes through the ejector its velocity decreases in the diffusor pipe while its pressure rises to the pressure at the end of the pipe in the outside water. As an example, graphs are given in Figure 18 that can be used for the dimensioning of Flygt type 4803 and 4804 ejectors.

Table 6 The value of as a function of temperature

9 1 019
10 1 000
11 0.982
12 0.964
13 0.946
14 0.928
15 0.911
16 0.895
17 0.878
18 0.861
19 0.845
20 0.830
21 0.815
22 0.799
23 0.784
24 0.770

Figure 14. HKP 600 aerator

Figure 15. Oxygen absorption capacity of an HKP 600 tube aerator

Figure 15. Oxygen absorption capacity of an HKL 210 disc aerator

Figure 16. Pressure loss

Figure 17

Figure 18. Flygt ejector 4803, 4804

5.4 Aeration with Paddle Wheels

The basic technical data of two paddle wheel type aerators are given below. These aerators were tested in a concrete tank with 7.5 × 17.5 m surface area. The aerator has a horizontal shaft with two paddle wheels on each end. The shaft is driven by an electric motor and chain. The device is mounted on floats.

Dimensions Type “A” Type “B”
Width 3 550 mm 1 635 mm
Length 2 060 mm 1 720 mm
Diameter of paddle wheel 1 000 mm 650 mm
Kidth of the paddles 250 mm 180 mm
Number of paddles 8 9
Capacity of electric motor 2,2 kW 2,2 kW

The values of the oxygen intake are shown in Table 7,

Table 7 Oxygen intake of paddle wheel type and perforated pipe type aerators

Aerator Water depth (m) Working parameters Average oxygen intake (kg/h) Power input (kW) Specific oxygen intake (kg/kWh)
Paddle wheel 1.2 n = 115 l/min 1.8 1.98 0.91
Type “A” h = 65 nnn
1.2 n = 90 l/min 1.5 1.6 0.94
0.8 h = 90 mm 2.2 1.56 1.41
Paddle wheel 1.2 n = 126 l/min 2.5 2.56 0.98
Type “B” 0.8 h = 210 mm 3.1 2.56 1.21
Perforated PVC pipe
15 pcs. 0.8 160 Hgmm 3.0 13.1 0.23
587 m3/h
20 pcs. 0.8 135 Hgmm 2.7 9.4 0.29
512 m3/h
20 pcs. 0.8 120 Hgmm 2.4 7.5 0.32
410 m3/h
20 pcs. 1.2 135 Hgmm 3.0 5.9 0.51
312 m3/h
20 pcs. 1.2 120 Hgmm 1.9 4.05 0.47
228 m3/h

1 Hgmm = 133.322 Pa = 13.5957 mm H2OSource: KULI: Részjelentés a halastavi vizlevegöztetö berendezések viszgálatáról MÉM Müszaki Intézet, Gödöllö, 1982


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