## 4. BASIC PRINCIPLES OF THE DESIGN OF FISH POND AERATORS

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:

_{}

where

_{}

_{}

H = Henry’s constant (P_{a}). (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.

_{}

where

P *=* the pressure of gas mixture (P_{a})

_{}

**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 m^{3}

_{}

where

_{}

_{}

_{} |
_{} |

thus

_{}

The weight fraction _{} can be converted into weight concentration (C_{s}) as follows:

_{} |
(kg . m^{-3)} |

where

C

_{s}= 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 (C_{s}) can be calculated as follows:

_{} |
(kg . m^{-3}) |

_{} |
(g . m^{-3}) |

Table 5 Density of pure water

Temperature°C |
Densitykg/m |
Temperature°C |
Densitykg/m^{3} |

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 H_{2}0 = 9.80665 P_{a}). In the case of a surface aerator, one has to calculate only with the atmospheric pressure. The C_{s} 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”

_{}

_{}

where

z = elevation above sea level (m)

p_{z}=atmospheric pressure at z elevation above sea level (P_{a})

p_{0}= atmospheric pressure at sea level (P_{a})

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

101325 P

_{a}(= 760 torr = 1 atm)

g = acceleration due to gravity (ms^{-2}) its value for practical calculations is: g = 9.81 ms^{-2}

S_{0}= the density of air (sea level, normal atmospheric pressure, 273 K (0° C) temperature)S

_{0}= 1.2928 kg . m^{-3}q

=temperature (K)

R = gas constantits 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:

_{}

where

K

_{L}a = modified mass transfer coefficient (h^{-1})

C_{s}= the equilibrium concentration of dissolved O_{2}(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 C_{0} is as follows:

_{}

The K_{L}a modified mass transfer coefficient is a product of multiplication of the mass transfer coefficient (K_{L}) and the specific area (_{}) as follows:

where

K

_{L}= mass transfer coefficient (m h^{-1})

A = diffusion area (m^{2})

V = volume (m^{3})

K_{L} is dependent on the temperature

_{}

where

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

Generally:

_{}

The organic and inorganic materials in the water have an influence on K_{L}a.

K¢

_{L}a = a K_{L}a

where

K¢

_{L}a = 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 m^{3} 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 = K_{L}a (10°C) . C_{s} (10°C)

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

_{}

where

_{}

When the same aerator is used for the oxygenation of a larger water volume than 1 m^{3} less oxygen can be dissolved. This is why total oxygen intake (O_{t}) is introduced.

O_{t} = V . OC |
(g h^{-1}) |

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

The specific total oxygen intake O_{ts} shows the efficiency of the oxygenation related to the power input.

_{} |
(g h^{-1} kW^{-1}) |

where

P = power input of the aerator (kW)

## 5. DIMENSIONING OF AERATORS

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 d

_{B}= 1 to 5 mm

b) Medium bubbles d_{B}= 5 to 10 mm

c) Coarse bubbles d_{B}= larger than 10 mm

The size of the bubble can be expressed as follows

_{}

where

d

_{B}= bubble diameter (mm)

s = surface tension of the liquid (N m^{-1})

S_{f}= density of the liquid (kg m^{-3})

S_{g}= 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:

d_{B} < 0,15 mm |
V_{B} = 478 500 d_{B}^{2} (ms^{-1}) |

0,15 mm < d_{B}– < 2.10 mm |
V_{B} = 758 d_{B}^{1.25} (ms^{-1}) |

2.10 mm < d_{B} < 7.20 mm |
V_{B} = 0.0164 d_{B}^{0.5} (ms^{-1}) |

d_{B} > 7.20 mm |
V_{B} = 2.24 d_{B}^{0.5} (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 |

where

Q

=air volume (m^{3}h^{-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:

_{}

or

_{}

where

S = density of air (kg m

^{-3})

w = mole fraction of O_{2}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}

and

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 m^{3}h^{-1} and 30 m^{3}h^{-1}

where

Q

=the amount of air flowing through the aerator (the amount of air is calculated for normal conditions, 0°C and 101325 P_{a}) (m^{3}h^{-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

Temperature(°C) |
_{} |

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 m^{3}/h |
|||||

20 pcs. | 0.8 | 135 Hgmm | 2.7 | 9.4 | 0.29 |

512 m^{3}/h |
|||||

20 pcs. | 0.8 | 120 Hgmm | 2.4 | 7.5 | 0.32 |

410 m^{3}/h |
|||||

20 pcs. | 1.2 | 135 Hgmm | 3.0 | 5.9 | 0.51 |

312 m^{3}/h |
|||||

20 pcs. | 1.2 | 120 Hgmm | 1.9 | 4.05 | 0.47 |

228 m^{3}/h |

1 Hgmm = 133.322 P

_{a}= 13.5957 mm H_{2}OSource: KULI: Részjelentés a halastavi vizlevegöztetö berendezések viszgálatáról MÉM Müszaki Intézet, Gödöllö, 1982

## 6. REFERENCES

Abeliovitch, A., 1967, Oxygen regime in Beit-Shean fish ponds related to summer mass fish mortalities: preliminary observations. Bamidgeh, 19(1):3-15

Albrecht, M.L., 1977, Bedeutung des Sauerstoffs un Schädigungen durch Sauerstoffmangel um Kohlensäureübersättigung bei Fischen. Z. Binnenfish. D.D.R., 24(7):207-13

Barthelmes, D., 1975, Elemente der Sauerstoffbilanz in Karpfenteichen ihre Wirkungsweise sowie die Optimierungs Möglichkeiten durch Silberkarpfen. Z. Binnenfish. D.D.R., 22 (II): 325-33. (.12): 355-63

Boyd, C.E., 1973, The chemical oxygen demand of waters and biological materials from ponds. Trans. Fish. Soci., 102(3):606-11

Busch, C.C., J.L. Koon and R. Allison, 1973, Aeration, water quality and catfish production. Pap. Am. Soc. Agric. Eng., (.73-559)

Chavin, W., 1973, Responses of fish to environmental changes. Springfield, Illinois, C.C. Thomas Publishers, 459 p.

Horváth, I., 1975, Levegöztetö rendszerek a szennyviztechnológiában. Budapest, Budapest, Müszaki Egyetem Továbbképzö Intézete

Horváth, I., 1976, A csatornázás és szennyvizkezelés hidraulikája. Budapest, VIZDOK

John, H.,1976, Vegyészmérnökök kézikönyve. Budapest, Müszaki Könyvkiadó

J.P.F. Scientific Corporation, 1971, Engineering methodology for river and stream reservation. Water Pollut. Control Res. Ser., (16080.F.S.N. 10/71)

Juhász, J., 1976, Hidrogeologia. Budapest, Akadémiai Kiadó

Knösche, R.,1971, Möglichkeiten zur Belüftung von Wasser in Fischzuchtbetrieben. Z. Binnenfisch. D.D.R., 18(11):331-40

Knósche, R.,1976, Der Sauerstoffgehalt in Pelletintensivteichen und technische Möglichkeiten zur Verbesserung. Z. Binnenfisch. D.D.R., 23(2):48-56

Knósche, R.,1979 Sauerstoffproduction urn Zehrung in Belüften und unbelüften Pelletintensivteichen. Z. Binnenfisch. D.D.R., 26(6):205-6

Menyhért, J.,1977, Az épületgépészet kézikönyve. Budapest, Müszaki Könyvkiadó

Nikolskii, G.V., 1963, The ecology of fishes. London, Academic Press, 352 p.

Odum, H.,1956, Primary production in flowing water. Limnol. Oceanogr., 1(2):102-17

Oláh, J.,1979, Halak oxigénfogysztása (kézirat). Szarvas, Haltenyésztési Kutató Intézet

Oláh, J., A. Zsigri and A.V. Kintzly,1978, Primary production estimations in fishponds by the mathematical evaluation of daily 0» curves. Aquacult. Hung., 1:3-14

Paulát, M., and P. Hartman, 1974, Overovani a posozovani ucinsosti ruznych typu pritoku a nove aeracui techniky na sadkach. Cesk. Rybn., 2:13-9

Petit, J.,1981, Utilisation de l’oxygène pur en pisciculture. Schr. Bundesforschungsanst. Fisch., Hamb., (16/l7) Vol. 1:429-54

Rappaport, V. and M. Marek, 1975, Results of tests of various aeration systems on the oxygen regime in the Genosar experimental ponds and growth of fish there in 1975. Bamidgeh. 28(3):35-49

Ruttkay, A., 1978, A halastavak anyag és energiaforgalmának vizsgálata. In Halhustermelés Fejlesztése, 5. Szarvas, Haltenyésztési Kutató Intézet

Ruttkay, A., 1978, Ivadék utónevelés polikulturaban. Halászat, Tudományos melléklet, 71:16-7

Sarig, S. and M. Marek, 1973, Results of intensive and semi-intensive fish breeding techniques in Israel in 1971-1973. Bamidgeh, 26(;2):28-50

Schroeder, G.L., 1975, Nighttime material balance for oxygen in fish ponds receiving organic wastes. Bamidgeh, 27(3):65-74

Sowerbutts, B.J. and J.R.M. Forster, Gases exchange and reoxygenation. Schr. Bundesforschungsanst. Fisch. ,Hamb., (16/l7)Vol. 1:199-217

Steeby, J.A., 1976, Effects of compressed air aeration in a heavily-fed farm pond stocked with channel catfish. M.S. Dissertation, Auburn, Alabama

Váradi, L.,1969, Air-0-Lator AF-12 tószellöztetö berendezés üzemi vizsgálata. Halászat, 62(3):72-4

Uhlmann, D. and R. Wegelin, 1967, Oxydationsteiche, Theorice, Betriebverhaltungen. Hinweise für Bau und Betrieb. WTZ – Mitt., Leipzig, 36(3)

Warren, S.E., 1971, Biology and water pollution control. Philadelphia, W.B. Saunders Co., 434 p.

Winberg, G.G., 1961, Novie dannie ob intenzivnoszti obmena u rib. Minsk, Beloruskovo Gosudarstvennovo Universiteta Imena V.I. Lenina, 1(18):157-65

Zsigri, A., J. Oláh and P. Szabó, 1973, Átfolyóvizes, in situ metaboliméter a természetes vizek oxigénfogyasztásának, termelésének, és diffuziójának mérésére. Hidrol. Közlöny, Budapest, 5:216-8