ARTICLE IN PRESS

Water Research 39 (2005) 13791387 www.elsevier.com/locate/watres

Predicting oxygen transfer of ne bubble diffused aeration systemsmodel issued from dimensional analysis S. Gillota,, S. Capela-Marsala, M. Roustanb, A. Heduitab a Cemagref, Parc de Tourvoie BP 44, 92163 Antony cedex, France LIPE, INSA Toulouse, 135, avenue de Rangueil, 31077 Toulouse cedex 4, France

Received 8 July 2003; received in revised form 17 December 2004; accepted 11 January 2005 Available online 14 March 2005

Abstract The standard oxygenation performances of ne bubble diffused aeration systems in clean water, measured in 12 cylindrical tanks (water depth from 2.4 to 6.1 m), were analysed using dimensional analysis. A relationship was established to estimate the scale-up factor for oxygen transfer, the transfer number N T 1=3 0:24 0:15 0:13 kL a20 n2 Sp Sp D 7:77 105 . NT h UG g S Sa The transfer number, which is written as a function of the oxygen transfer coefcient kL a20 ; the gas supercial velocity U G ; the kinematic viscosity of water n and the acceleration due to gravity g; has the same physical meaning as the specic oxygen transfer efciency. N T only depends on the geometry of the tank/aeration system [the total surface of the perforated membrane Sp ; the surface of the tank S or its diameter D; the total surface of the zones covered by the diffusers (aerated area, Sa ) and the submergence of the diffusers h]. This analysis allowed to better describe the mass transfer in cylindrical tanks. Within the range of the parameters considered, the oxygen transfer coefcient kL a20 is an increasing linear function of the air ow rate. For a given air ow rate and a given tank surface area, kL a20 decreases with the water depth (submergence of the diffusers). For a given water depth, kL a20 increases with the number of diffusers, and, for an equal number of diffusers, with the total area of the zones covered by the diffusers. The latter result evidences the superiority of the total oor coverage over an arrangement whereby the diffusers are placed on separate grids. The specic standard oxygen transfer efciency is independent of the air ow rate and the water depth, the drop in the kL a20 being offset by the increase of the saturation concentration. For a given tank area, the impact of the total surface of the perforated membrane Sp and of the aerated area Sa is the same as on the oxygen transfer coefcient. r 2005 Elsevier Ltd. All rights reserved.Keywords: Aeration; Dimensional analysis; Oxygen transfer; Transfer number; Wastewater treatment

1. Introduction Since the end of the 1980s, aeration tanks have been increasingly equipped with EPDM membrane diffusers. These ne bubble aeration systems have several advantages, which have contributed to their extensive devel-

Corresponding author

E-mail address: sylvie.gillot@cemagref.fr (S. Gillot).

0043-1354/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2005.01.008

ARTICLE IN PRESS1380 S. Gillot et al. / Water Research 39 (2005) 13791387

Nomenclature oxygen concentration at saturation at 20 1C (ML3) D tank diameter (L) Dd diameter of the membrane (L) Df diffusivity (L2 T1) Dnp diameter of the nonperforated zone of a membrane (L) DD diffuser density (dimensionless) DDL local diffuser density (dimensionless) ei exponent (dimensionless) g acceleration due to gravity (LT2) h diffuser submergence (L) H water depth (L) k constant (dimensionless) K constant (dimensionless) kL a oxygen transfer coefcient (T1) kL a20 oxygen transfer coefcient at 20 1C (T1) M O2 mass ow of oxygen in the air stream (MT1) modied transfer number (dimensionless) NT (NT)xk reduced transfer number (dimensionless) C 120

oxygen transfer rate (MT1) air ow rate (L3 T1) surface area of the tank (L2) total surface area of the zones occupied by the diffusers (aerated area) (L2) Sp total surface area of the perforated membrane (L2) Sperf surface area of one perforated membrane (L2) SOTE standard oxygen transfer efciency (dimensionless) SSOTE specic standard oxygen transfer efciency (L1) UG gas velocity (LT1) dimensionless gas load (LT1) U G V tank volume (L3) OTR QG S Sa Greek letters m n r dynamic viscosity of water (ML1 T1) kinematic viscosity of water (L2 T1) density of water (ML3)

opment: high oxygenation performances, adaptability to varying oxygen requirements, and a reduction in the ` production of aerosols (Duchene et al., 2001). The performances of these systems are commonly measured in clean water, before the starting up of the wastewater treatment plant, according to a standardised procedure (ASCE, 1992; NFEN, 2004). Despite these measurements, oxygenation performance prediction, at a project stage, is still relatively inaccurate, as it fails to take into account all the parameters affecting mass transfer (tank geometry, layout of the aeration system, operating conditions). A better forecast of the oxygen transfer would help the optimisation of the installations, in terms of both cost and effectiveness, especially in the case of medium-size facilities where performance checks cannot be systematically carried out. As a substantial number of oxygenation performance measurements of ne bubble aeration systems was available in the Cemagref, the establishment of relationships between the oxygen transfer and the parameters affecting it could be considered using dimensional analysis. This type of analysis has already been applied to characterise the efciency of agitation mobiles and surface aerators (Zlokarnik, 1978; Roustan and Roques, 1979; Rao, 1999). Various relationships characterising the mass transfer of submersed aerators have also been developed (Zlokarnik, 1978; Kulkarni et al., 1987; Dudley, 1995; Hebrard, 1995), most of them in bubble columns, but they are not directly applicable to aeration tanks equipped with ne bubble diffusers as they are not

taking account of important parameters such as the diffuser density and layout. On real sites, Harremoes (1979) proposed using the parameter gQG =L1=3 (QG air ow rate; L tank length) as a characteristic criterion of the aeration system. Zlokarnik (1979), Roustan (1996) and Capela et al. (2001) dened a transfer number (N T kL a=U G n2 =g1=3 ; kLa oxygen transfer coefcient ; UG gas velocity; n kinematic viscosity of the water). This dimensionless group has the same physical meaning as the specic standard oxygen transfer efciency (SSOTE in%/m of submergence). Khudenko and Shpirt (1986) proposed for parallelepipedic tanks a dimensionless relationship which takes account of the width of the aeration zone. Finally, Capela (1999) established two relationships, based on the dimensional analysis of data from 88 clean water tests at 31 sites, enabling the prediction of the oxygen transfer coefcients with an acceptable degree of accuracy (maximum difference of 20% between the calculated kL a and the measured kL a). These relationships, however, were determined for tanks of different geometries (annular, cylindrical, and others) for which it is difcult to establish a single relevant list of parameters. Moreover the arrangement of the diffusers (total oor coverage or grid arrangement) was not taken into consideration. As far as the geometric and hydrodynamic properties of aeration systems are concerned, it would appear that cylindrical tanks (without mechanical mixing) must be dissociated from annular oxidation ditches (equipped with mixers).

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The aim of this work was to establish relationships enabling the prediction of the oxygenation performances (kL a and SSOTE) of ne bubble aeration systems in cylindrical tanks, in order to propose a design tool and to evidence the impact of certain geometric and dynamic parameters on oxygen transfer. This relationship was developed from the dimensional analysis initiated by Capela (1999) on the basis of results from some twenty oxygenation tests performed in clean water on full scale wastewater treatment plants.

formed from the relevant parameters are the following: N T kL a=U G n2 =g1=3 ; the transfer number, similar to the sorption number introduced by Zlokarnik (1978) and used by Capela et al. (2001) Sc m ; the Schmidt number rDf 1=3 mg ; the dimensionless gas load: r

U UG G

2. Material and methods 2.1. Dimensional analysis The design and operating parameters considered as being characteristic of oxygen transfer in cylindrical aeration tanks equipped with ne bubble diffusers are shown in Fig. 1 and explained in Table 1. Other parameters were tested during the analysis (such as the distance between the diffusers), but failed to appear signicant and were therefore omitted in the nal relationship. As kL a is a volume-related intensive quantity, process parameters have been expressed as intensive quantities (Zlokarnik, 1978). Therefore the gas ow was replaced by the supercial gas velocity (U G in m s1, U G QG =S=3600). For a given geometry, kL a is a function of the supercial gas velocity (U G ; m s1), the acceleration due to gravity (g; m s2) and the liquid properties (density of water r; kg m3, dynamic viscosity m; Pa s, coefcient of molecular diffusion Df ; m2 s1). The following expression can therefore be written: kL a f U G ; g; r; m; Df . (1)

The transfer number can therefore be expressed as follows: !e2 1=3 kL a n2 UG e1 NT kSc (2) UG g rn1=3 where k is a constant, ei, is numerical exponents. As different geometrical conditions have been investigated, 4 additional dimensionless numbers were introduced, to give the following expression: NT 1=3 kL a n2 UG g

KSce1

!e2 S p e3 Sp e4 D e5 H e6 , 1=3 h h S Sa rn 3 UG

According to the theory of similarity, from the six variables and the three base dimensions (Mass, Length and Time) contained in their secondary dimensions, it is possible to establish a relationship between three dimensionless groups. For a given geometry, the groups

where Sp is the surface area of the perforated membranes (m2), S is surface area of the tank (m2), Sa is surface area covered by the diffusers (m2), D is diameter of the tank (m), h is diffuser submergence (m), H is water depth (m), K is constant, ei is numerical exponents. The rst two terms of Eq. (3) govern the dynamic similarity of the system. The last four represent the geometric similarity. The objective of the analysis performed was therefore to use the experimental data obtained on real sites to study the dependence of the transfer number to the dimensionless groups, gathered on Table 2. 2.2. Database

S

Df

h kLa QG

H

Sa

Sperf DFig. 1. Relevant design and operating parameters in cylindrical aeration tanks.

The database gathers the results of the clean water tests performed in full scale cylindrical tanks equipped with ne bubble aeration systems. The aim of the tests, performed according to a procedure integrated in the NFEN 12255-15 standard (2004), was to determine the standard oxygen transfer rates of the aeration systems (commissioning tests). To compare the systems, the results of the oxygenation measurements are expressed at standard conditions: (1) zero dissolved oxygen concentration,

ARTICLE IN PRESS1382 S. Gillot et al. / Water Research 39 (2005) 13791387 Table 1 Relevant design and operating parameters in cylindrical aeration tanks Parameter Dependant variable Geometrical variables Oxygen transfer coefcient Surface of the tank Total surface of the perforated membranea Total area of the zones covered by the diffusers (aerated area) Water depth Diffuser submergence Supercial velocity Acceleration due to gravity Dynamic viscosity of water Density of water Diffusivity of air in water Symbol kL a S Sp Sa H h UG g m r Df Dimension T 1 L2 L2 L2 L L LT1 LT2 ML1 T1 ML3 L2 T1 Usual unit h1 m2 m2 m2 m m m s1 m s2 Pa s kg m3 m2 s1

Cinematic variables Properties of the liquid phase

a

For the derivation of one perforated membrane area (Sperf), cf. Appendix.

Table 2 Dimensionless groups Dimensionless group Dimensionless gas load Symbol U G Relation 1=3 mg UG r m rDf 1=3 k L a m2 U G r2 g Sp S Sp Sa D h H h Ratio of forces of viscous diffusion to the forces of molecular diffusion Similar to the specic oxygen transfer efciency Ratio of the total surface of the perforated membranes to the tank area Ratio of the total surface of the perforated membranes to the aerated area Ratio of the tank diameter to the diffuser submergence Ratio of the water to the diffuser submergence Physical meaning

Schmidt number

Sc

Transfer number

NT

Diffuser density

DD

Local diffuser density

DDL

Ratio tank diameter to the diffuser submergence Ratio water depth to the diffuser submergence

(2) water temperature 20 1C, (3) atmospheric pressure 1013 hPa.

quantity of oxygen transferred to the quantity of oxygen injected divided by the diffuser submergence: SSOTE kL a20 C V 120 . 10 hM O2 (4)

The oxygenation performances are reported in terms of: Oxygen transfer coefcient at 20 1C (kL a20 ) Specic standard oxygen transfer efciency per metre (SSOTE in%/m of diffuser submergence), ratio of the

where kL a20 is the oxygen transfer coefcient at 20 1C (h1), C* N20 the oxygen concentration at saturation at 20 1C (mg L1), V the volume of the tank (m3), M O2 the

ARTICLE IN PRESSS. Gillot et al. / Water Research 39 (2005) 13791387 Table 3 Range of the measured parameters and dimensionless numbers Parameter Range D (m) 7.514.7 h (m) 2.25.9 H (m) 2.46.1 V (m3) S (m2) Sp (m2) 3.413.1 U G UG kL a20 SSOTE (Nm3 h1) (h1) (% m1) 9.2167.6 2.210.6 3.213.4 3.75.6 N T 105 Sa (m2) 1383

108757 44170 Sc

D=h Dimensionless DD Sp/S DDL Sp/Sa H=h number Range 0.040.14 0.050.41 1.031.11 1.45.1

3.3 103 0.030.14 4.77.2

mass ow of oxygen in the air stream (kgO2 h1), M O2 0:3 QG, h the diffuser submergence (m). Measurements performed: Twenty one measurements performed on 12 sites, all equipped with disc diffusers, were analysed. Table 3 shows the ranges of the parameters measured and of the dimensionless numbers obtained. Experimental results led to transfer numbers comprised between 4.7 105 and 7.2 105, in the range of the values obtained by Zlokarnik (1978).

8.0 7.5 Calculated NTx105 7.0 6.5 6.0 5.5 5.0 4.5 4.0 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

3. Results and discussion 3.1. Prediction of the transfer number The constant and the coefcients of the dimensionless equation (Eq. (3)) that allow to calculate the transfer number were determined by minimising the sum of the squares of the differences between the measured N T values (from the measured kL a20 ; cf. Table 2, line 3) and the calculated N T values. As the ratio H=h varies only slightly (cf. Table 3), it was integrated into the constant K: The results of the tests being expressed at one temperature (20 1C), the Schmidt number is a constant, also integrated into K: The exponent e2 was very low (o0.05), therefore the corresponding dimensionless group has been omitted in the nal relationship. The dimensionless relationship can therefore be written as follows: 1=3 e3 e4 e5 kL a n2 Sp Sp D NT K0 , (5) UG g h S Sa where K0 constant KSc (H=h) 0:24 0:15 0:13 Sp Sp D . N T 7:77 105 S Sa h

Measured NTx105Fig. 2. Measured vs. calculated transfer numbers N T :

mental values is therefore considered very satisfactory. The differences obtained are due to the empirical nature of the relationship established (not all the affecting parameters are taken into account), to measurement errors (kL a; geometric magnitudes, air ow rate, etc.), and to the quality of the water used for the test (tap water, river water). Eq. (6) is only applicable within the ranges of the dimensionless numbers considered (cf. Table 3). 3.2. Impact of the air ow rate on the transfer number According to Eq. (5), the transfer number is independent of U G and is only a function of the geometric parameters of the aeration tank/aeration system Sp =S; S p =Sa ; D=h: 3.3. Sensitivity of the transfer number to the geometric dimensionless numbers

(6) The sensitivity of oxygen transfer efciency to the diffuser density (DD Sp/S), the local diffuser density (DDL Sp/Sa) and to the diameter of the tank in relation to the diffuser submergence D=h was studied from the dimensionless relationship proposed (Eq. (6)). For each of the three dimensionless numbers xk considered (associated to the powers ek ), the transfer

Fig. 2 shows the experimental transfer numbers as a function of the values calculated from Eq. (6): The regression coefcient r2 is 0.90. The relative difference between the measured and calculated values is on average 3.1%, with a maximum value of 6.4%. The match between the calculated values and the experi-

ARTICLE IN PRESS1384 S. Gillot et al. / Water Research 39 (2005) 13791387

numbers N T have been expressed in the following reduced form: N T xk (7)(NT)DD

1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 DDLFig. 4. Inuence of DDL on the variable N T DDL :Total floor coverage

N T experimental ek xk . Q K in xei i1 i

This variable N T xk expresses the residual impact of the parameter xk on the oxygen transfer when the effect of all the other parameters is hidden. For example, the impact of diffuser density (DD) is studied using the following parameter (NT)DD: N T DD N T experimental 7:8 106 DD0:24 DD0:15 L 0:13 DD D h0:24

3.4. Sensitivity of the transfer number to the diffuser density Fig. 3 shows the transfer number expressed in the reduced form (NT)DD as a function of the diffuser density (DD Sp/S). Within the density range studied (0.040.14), the transfer efciency increases with the percentage of the tank surface area covered by the diffusers, which conrms the bibliographical results (ASCE, 1992; Capela et al., 2001; Mueller et al., 2002).

(NT)D/h

N T experimental 0:13 . D 7:8 106 DD0:15 L h

8

1.30 1.25 1.20 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80 0.0

1.0

2.0

3.0 D/h

4.0

5.0

6.0

Fig. 5. Inuence of D=h on the variable N T D=h :

3.5. Sensitivity of the transfer number to the local diffuser density Fig. 4 shows the impact of local diffuser density (DDL Sp/Sa) on the transfer number expressed in the reduced form (NT)DDL. For an identical diffuser density, the DDL gives an information about the spacing between diffusers. A low DDL value corresponds to a total oor coverage (DDL DD), whereas a high value

evidences a small spacing between diffusers (separated grids of diffusers). For an equivalent diffuser density, an increase in the local diffuser density within the range of 0.050.41 results in a drop in the oxygenation performance. The highest N T values, and therefore the best oxygenation performances, are obtained when the diffusers are arranged in total oor coverage.

3.6. Sensitivity of the transfer number to the ratio D=h The inuence of the ratio D=h; within the range of 1.45.1, is presented in Fig. 5. For a given conguration of the aeration system, the oxygenation capacity is higher when the ratio D=h is higher. It should be noted, however, that the measurements were performed for relatively low diffuser submergence (o6 m). Additional data on higher tank would allow to investigate the effect of high water depth, which have been recognised to lower the oxygenation capacity (Wagner and Popel, 1998; Gillot and Heduit, 2003). In conclusion, as mentioned in the literature, the congurations inducing spiral ows in the water caused by the rising air bubbles (low diffusion area, arrangement of the diffusers in separated grids) have a negative impact on oxygen transfer.

0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.00

(NT)DD

0.02

0.04

0.06

0.08 DD

0.10

0.12

0.14

0.16

Fig. 3. Inuence of DD on the variable (NT)DD.

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3.7. Impact of the characteristic parameters of the tank/ aeration system on oxygen transfer in clean water Eq. (6) can be modied to obtain a relationship between the oxygen transfer coefcient at 20 1C and the characteristic parameters of the tank/aeration system: kL a20 K 00 QG S1e3 e5 =2 Se3 e4 S e4 he5 , p a e5 =2 4 , where : K constante 2 =g1=3 p n00

(9)

K0

kL a20 1:69QG S 1:18 S 0:10 S 0:15 h0:13 . p a

(10)

The specic standard oxygen transfer efciency can be determined using Eq. (4). The value of oxygen concentration at saturation and at 20 1C is deduced from the measurements performed during the aeration tests (Winkler method), presented in Fig. 6. The oxygen concentration at saturation is written as follows: C 8:84 h0:11 . 120 (11)

diffusers, with the total surface area of the zones covered by the diffusers (reduction of the water circulation movements). The specic oxygen transfer efciency per metre of immersion is independent of the air ow rate (Eq. (13)) and of the water depth, the drop in kL a20 being offset by the increase of the oxygen concentration at saturation. For a given tank surface, the impact of the total area of the perforated membrane and of the aerated area is the same as that on the oxygen transfer coefcient. The air ow rate has therefore no noticeable impact on water circulation movements. This observation is in accord with the results of Khudenko and Shpirt (1986) on parallelepidic tanks, but diverges from the results obtained in annular ditches (Deronzier et al., 1996; Gillot et al., 2000) where the increase in the air ow rate has a negative impact on the SSOTE. This discrepancy may be attributed to the presence of much larger gaps between the diffuser grids in the case of ditches, where spiral ows of the water would be affected by the air ow rate. 3.8. Application to the design of an aeration system: the case of a cylindrical aeration tank in an activated sludge wastewater treatment plant of 3000 PE The example presented below is based on a plant of 3000 PE requiring a tank volume of 700 m3. Oxygen transfer rate (OTR) is estimated to be 60 kg h1 in standard conditions (clean water at 20 1C, P 1013 hPa, C 0 mg L1). Eq. (10) is used to calculate the air ow rate required to obtain this hourly input in a cylindrical tank, taking account of the couple tank/aeration system chosen. The various stages of the design can be summarised as follows: (1) Choice of diffuser submergence, h; and calculation of the dissolved oxygen concentration at saturation of the tank (Eq. (11)), to deduce the kL a20 to be obtained (kLa20 OTR/(Cs.V)). (2) Choice of the diffuser density, DD, calculation of the total surface area of the membranes, Sp DD.S, and calculation of the number of diffusers to be installed. (3) Choice of the aerated surface area, S a and calculation of QG (Eq. (10)). (4) Calculation of the specic standard oxygen transfer efciency (Eq. (13)). Application to the plant of 3000 PE: 1. h 4.8 m (H 5.0 m), then C* 10.50 mg L1, N20 S 140 m2 (D 13.35 m) and kLa20 60 1000/ (700 10.50) 8.16 h1 2. DD 0.07, then Sp DD S 9.8 m2

This relationship corresponds to an overpressure of 33% of the diffuser submergence. The equation linking the specic standard oxygen transfer efciency (SSOTE) to the characteristic parameters is therefore written as follows (considering H=h 1:06 on average): SSOTE K 000 Se3 e5=2 S e3 e4 S e4 he5 0:11 , p a (12)

where K000 constante K00 8.84 1.06/0.3/10 3.12 K00 SSOTE 5:27S0:18 S0:1 S0:15 . p a (13)

The oxygen transfer coefcient appears to be an increasing linear function of the air ow rate (Eq. (10)). For a given air ow rate and a given tank surface area, kL a20 drops with the water depth, due to the higher bubble coalescence (Zlokarnik, 1979). The oxygen transfer coefcient increases with the total surface area of the perforated membrane, and, for an equal number of12 11 Cs20. 1013 (mg L-1) 10 9 8 7 6 5 1.0 2.0 3.0 4.0 5.0 6.0 Diffuser submergence (m) 7.0

Fig. 6. Oxygen transfer at saturation vs diffuser submergence.

ARTICLE IN PRESS1386 S. Gillot et al. / Water Research 39 (2005) 13791387 Table 4 Inuence of the aerated surface on the required air ow rate and on the specic standard oxygen transfer efciency Sa (m2) 140 (Total oor coverage) 100 75 50 QG (Nm3 h1) 765 804 840 893 SSOTE (% m1) 5.7 5.4 5.2 4.9

in separate grids. The air ow rate per diffuser, in a cylindrical tank, is clearly not a parameter to be used to predict the oxygen transfer efciency (within the ranges of the parameters in Table 2).

4. Conclusions Until now, prediction of oxygenation performance in aeration tanks was often inaccurate, as the models failed to take into account all the geometric and hydrodynamic parameters affecting the oxygen transfer. Application of dimensional analysis to 21 measurements of oxygen transfer performed in 12 real size cylindrical tanks has made it possible:

6.0 4.0 3.8 5.5 3.6 3.4 5.0 3.2 4.5 3.0 2.8 4.0 2.6 2.4 3.5 2.2 3.0 2.0 150 170 190 210 230 250 270 290 310 330 350 Number of diffusers

QG per diffuser (Nm3.h-1)

SSOTE (%.m-1)

to establish a dimensionless relationship enabling theestimation of the transfer number. It is written as follows: 1=3 k L a n2 NT UG g 0:24 0:15 0:13 Sp D 5 S p 7:77 10 . h S Sa

Fig. 7. Inuence of the diffuser number on the required air ow rate per diffuser (E) and on the SOTEs (&).

to establish a relationship between the oxygen transferBy choosing disc diffusers with a perforated area of 0.04 m2, the number of diffusers to be installed is 245. 3.9. Impact of the aerated area on the required air ow rate Table 4 shows the air ow rates to be injected and the specic standard oxygen transfer efciencies obtained depending on the aerated area (Sa), according to Eq. 10 and 13. This example illustrates the superiority of the total oor coverage in comparison to a grid arrangement. For a given number of diffusers, the oxygenation performance levels obtained are better in the rst case. The air ow rate to be injected to obtain a given hourly input, and therefore the size of the blowers to be installed, increases when the aerated area decreases. 3.10. Impact of the number of diffusers on the SSOTE coefcient kL a20 and the affecting factors: air ow rate (QG), diffuser submergence (h), surface of the tank (S), surface of the diffusers (Sp) and the aerated area (Sa). This relationship is written as follows: kL a20 1:69QG S1:18 S0:10 S0:15 h0:13 . p a The specic Standard Oxygen Transfer Efciency of the aeration system can thus be estimated using the following equation: SSOTE 5:27S0:18 S 0:10 S0:15 . p a The relationships proposed enable, at the project stage, to estimate the oxygenation performance levels of the aeration system considered. Moreover, it has been shown that in a cylindrical tank, and within the ranges of the dimensionless numbers (Table 2):

theFig. 7 shows the air ow rates and the SSOTE obtained as a function of the number of diffusers (Sa S; total oor coverage). The SSOTE shows a slight variation (5.65.9% m1) with the number of diffusers (from 200 [DD 0:06] to 320 [DD 0:09]), whereas the air ow rate per diffuser drops considerably (from 3.9 to 2.3 Nm3 h1). These results have been conrmed for a diffuser arrangement

specic standard oxygen transfer efciency is independent of the water depth, the drop in the kL a20 being offset by the increase of the oxygen concentration at saturation. for a given water depth, the oxygen transfer coefcient increases with the number of diffusers, and, for an equal number of diffusers, with the aerated area. The latter result evidences the superiority of the total oor coverage over an arrangement

ARTICLE IN PRESSS. Gillot et al. / Water Research 39 (2005) 13791387 1387

whereby the diffusers are placed on separate grids. Therefore the congurations which induce spiral ows (arrangement of the diffusers in separate grids, small aerated area) result in relatively low oxygenation performances. the air ow rate has no noticeable impact on the SSOTE, which is mainly determined by the geometry of the system.

Acknowledgements The authors would like to acknowledge the FNDAE (Fonds National pour le Developpement des Adductions deau) for its nancial support. They are also grateful to the persons that have been involved in the oxygenation tests. The constructive comments of Dr Zlokarniks review are nally acknowledged.

Appendix. Determination of the perforated area The total perforated area of the diffusers Sp is calculated as the product of the perforated area of one diffuser (Sperf) per the number of diffusers. The perforated area of one diffuser is a function of the diffuser shape. For a disc, it is calculated as follows: p Sperf D2 D2 , np 4 d where Dd disc diameter m, Dnp diameter of the nonperforated zone m,

Diameter of the non perforated zone

Disc diameter Dd

ReferencesASCE, 1992. ASCE Standard Measurement of Oxygen Transfer in Clean Water. American Society of Civil Engineers, New York. Capela, S., 1999. Inuence des facteurs de conception et des conditions de fonctionnement des stations depuration en

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