Gas transfer from air diffusers

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40 (2006) 1018– 1026

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Gas transfer from air diffusers Erica L. Schierholza, John S. Gulliverb,, Steven C. Wilhelmsc, Heather E. Hennemand a

Brown and Caldwell, 30 East 7th Street, Suite 2500, St. Paul, MN 55101, USA St. Anthony Falls Laboratory, Department of Civil Engineering, University of Minnesota, Mississippi River at 3rd Avenue, SE, Minneapolis, MN 55414, USA c U.S. Army Corps of Engineers Engineering Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA d U.S. Army Corps of Engineers, Chicago District, 111 N. Canal, Chicago, IL 60606, USA b

ar t ic l e i n f o

A B S T R A C T

Article history:

The bubble and surface volumetric mass transfer coefficients for oxygen, kLab and kLas, are

Received 8 October 2003

separately determined for 179 aeration tests, with diffuser depths ranging from 2.25 to

Received in revised form

32 m, using the DeMoyer et al. [2003. Impact of bubble and free surface oxygen transfer on

17 October 2005

diffused aeration systems. Water Res 37, 1890–1904] mass transfer model. Two empirical

Accepted 20 December 2005

characterization equations are developed for kLab and kLas, correlating the coefficients to air flow, Qa, diffuser depth, hd, cross-sectional area, Acs, and volume, V. The characterization

Keywords:

equations indicate that the bubble transfer coefficient, kLab, increases with increasing gas

Surface transfer

flow rate and depth, and decreases with increasing water volume. For fine bubble diffusers,

Bubble transfer

kLab is approximately six times greater than kLab for coarse bubble diffusers. The surface

Liquid film coefficient

transfer coefficient, kLAs, increases with increasing gas flow rate and diffuser depth. The

Aeration

characterization equations make it possible to predict the gas transfer that will occur

Diffuser

across bubble interfaces and across the free surface with a bubble plume at depths up to

Sparger

32 m and with variable air discharge in deep tanks and reservoirs. & 2006 Elsevier Ltd. All rights reserved.

1.

Introduction

Low dissolved oxygen (DO) levels in water results in anoxia and can contribute to fish kills, odor, and other aesthetic nuisances. Submerged aeration systems are used as water quality enhancement devices in lakes and reservoirs, as well as wastewater treatment facilities, to increase dissolved oxygen levels and promote water circulation. Diffuser systems have been used for many years in hydropower reservoirs to increase the oxygen concentration in the hypolimnion, where water is frequently withdrawn through the hydropower intakes and released downstream. Example reservoirs that employ aeration systems include Richard B. Russell in South Carolina and Georgia, Douglas in Tennessee, Watts Bar in Tennessee, Blue Ridge in Georgia, Shepaug in Connecticut, J. Percy Priest in Tennessee and J. Strom Corresponding author. Tel.: +1 612 625 4080; fax: +1 612 627 4609.

E-mail address: [email protected] (J.S. Gulliver). 0043-1354/$ - see front matter & 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2005.12.033

Thurmond in South Carolina and Georgia. Examples of nonhydropower reservoirs include Normandy in Tennessee, Spring Hollow in Virginia and the Upper San Leandro in California. Environmental issues are also motivating the construction of large wastewater reservoirs. The idea is to provide storage for combined sewage and stormwater during big storms that would otherwise be discharged untreated into area waterways. This is an important problem in Chicago, Illinois. The McCook, Thornton and O’Hare reservoirs make up the Chicagoland Underflow Plan (CUP), an integral part of Chicago’s $3 billion Tunnel and Reservoir Plan (TARP) (U.S. Army Corps of Engineers, 2001). This system of intercepting sewers, dropshafts, tunnels and reservoirs will capture and store combined sewage and stormwater until municipal water reclamation plants can treat it.

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4 0 (200 6) 101 8 – 102 6

Nomenclature

Acs Ab As CO CN CO(init)

cross-sectional tank area surface area of bubbles surface area of water body actual dissolved nitrogen concentration

diffusion coefficient of gas in water diffusion coefficient of oxygen in water diffusion coefficient of nitrogen in water bubble diameter Froude number gravity

A major concern of the CUP reservoirs is odor. Implementation of coarse bubble aeration systems has been proposed to help alleviate the odor. Aeration in these reservoirs presents unique design issues because they will contain variable water quality and variable water depths that could exceed 75 m (Robertson 2000). Low dissolved oxygen concentration in many reservoirs and the release of water through hydroturbines also necessitates the use of an aeration system that may be placed at depths of 100 m or greater. When designing aeration systems at variable depths it is necessary to be able to separately calculate the bubble and surface volumetric mass transfer coefficients kLab and kLas. It is also necessary to conserve mass, and compute the concentration of oxygen and nitrogen inside of the bubbles. The purpose of this paper is to develop correlations between kLab, kLas and aeration/reservoir characteristics such as water volume, V, tank cross-sectional area, Acs, diffuser depth, hd and air flow rate, Qa, so that aeration systems can be properly designed at large depths. Correlations are needed because design guidelines for aeration systems at depths above 7 m do not exist and because tests at these depths are difficult and expensive.

2.

kLas

actual dissolved oxygen concentration

initial dissolved oxygen concentration before deoxygenation CN(init) initial dissolved nitrogen concentration CN(init) percent nitrogen concentration C
O liquid-phase equilibrium oxygen concentration of a bubble C
N liquid-phase equilibrium nitrogen concentration of a bubble CsatðO2 Þ saturation oxygen concentration in water at atmospheric pressure CsatðN2 Þ saturation nitrogen concentration in water at atmospheric pressure CSSðO2 Þ steady-state oxygen concentration CSSðN2 Þ steady-state nitrogen concentration

D DO2 DN2 db Fr g

hd kLs kLab

Analysis model

Numerous disturbed equilibrium aeration tests will be analyzed by an improved mass transfer model (DeMoyer et

kLat L P Pwv Qa Re Sc Sh t U V We y z f b1, b2, a Z s r n

1019

depth to diffuser surface liquid film coefficient volumetric bulk mass transfer coefficient for oxygen at the bubble surface volumetric mass transfer coefficient for oxygen at the water surface bulk volumetric mass transfer coefficient for oxygen characteristic length of turbulence atmospheric pressure water vapor pressure gas flow rate Reynolds number Schmidt number Sherwood number time characteristic velocity, Qa/Acs in this paper volume of water body to diffuser depth Weber number gas-phase oxygen composition distance from the diffuser gas void ratio

b3, b4, b5 adjustable dimensionless coefficients adjustable dimensional coefficient adjustable dimensionless coefficient surface tension liquid density kinematic viscosity

al., 2003) recognizing that there exist two different mass transfer zones in diffused aeration systems, the gas bubble mass transfer zone and the free surface mass transfer zone. Each of the zones must be separately analyzed and properly accounted for in the overall mass transfer model (McWhirter and Hutter, 1989). The two-zone mass-transfer model includes the mass conservation of oxygen, dCO kL ab ¼ dt hd

Z 0

hd

ðC
O  CO Þ dz þ kL as ðCsatðO2 Þ  CO Þ,

(1)

where kLab is the volumetric bulk mass transfer coefficient for oxygen at the bubble surface, kLas is the volumetric mass transfer coefficient for oxygen at the water surface, hd is the depth to the diffuser, z is a variable distance from the diffuser, C
O is the liquid-phase equilibrium oxygen concentration of the bubbles, CO is the actual dissolved oxygen concentration and CsatðO2 Þ is the oxygen saturation concentration, or equilibrium concentration with the atmosphere. The conservation of nitrogen and argon should also be included:
 Z dCN kL ab DN 1=2 hd
¼ ðCN  CN Þ dz dt hd DO 0
1=2 DN þ kL as ðCsatðN2 Þ  CN Þ, DO

ð2Þ

where DN and DO are the diffusion coefficients for nitrogen and oxygen, CN is the dissolved nitrogen concentration, C
N is

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the liquid-phase equilibrium nitrogen concentration of the bubbles, and CsatðN2 Þ is the nitrogen saturation concentration. Argon, being approximately 1% of the atmosphere, is assumed to respond similar to nitrogen, since both are essentially inert gases. Since the volumetric bulk mass transfer coefficients for oxygen are used in Eq. (2), the ratio of diffusion coefficients is also required. The oxygen and nitrogen equilibrium concentrations are given by C
O ¼ CsatðO2 Þ

ðP  Pwv þ rgðhd  zÞÞ y=ð1 þ yÞ , P  Pwv 0:21

(3)

C
N ¼ CsatðN2 Þ

ðP  Pwv þ rgðhd  zÞÞ 1=ð1 þ yÞ , P  Pwv 0:79

(4)

where y is the gas-phase oxygen composition, which is the molar ratio of oxygen to other gases (primarily nitrogen) in the gas phase, P is atmospheric pressure, Pwv is water vapor pressure, r is the density of water and g is the acceleration of gravity. The boundary condition for Eqs. (3) and (4) is that the gas-phase oxygen molar ratio, y, is known when the bubbles are released from the diffuser, or y ¼ 0:266 at z ¼ 0. From a mass balance on the bubbles, the gas-phase oxygen composition as a function of depth is given by
dy Acs 1 ¼  kL ab ðC
 CO Þ dz Q a HN C
N O !
1=2 DN HO C
O
 ðC  C Þ , ð5Þ N N DO ðHN C
N Þ2 where Acs is the cross-sectional surface area of the tank, Qa is the gas flow rate, and H is Henry’s law constant. With Eqs. (3)–(5), the gas-phase oxygen or nitrogen composition, y, and the local equilibrium concentrations, C
O and C
N , can be calculated at all depths and times. The resulting values can then be used in either Eq. (1) or (2), along with the experimental aeration data to obtain the best-fit values for the unknown parameters, kLab and kLas.

3.

Experimental data

3.1.

LACSD tests

Experimental diffused-air reaeration tests were conducted in 1978 and 1979 by the Los Angeles County Sanitation Districts (LACSD) at the LACSD Joint Water Pollution Control Plant under EPA Contract 14-12-150 (Yunt and Hancuff, 1979). The tests were performed in a tank 6.1 m long by 6.1 m wide by 7.6 m deep. Diffuser depths ranged from 2.25 to 7.5 m and airflow rates ranged from 55.6 (standard cubic meter per hour) to 709.2 scmh. The following eight diffusers were tested: Sanitaire fixed orifice coarse bubble diffusers, Envirex fixed orifice coarse bubble diffusers, FMC fixed orifice coarse bubble diffusers, Bauer variable orifice coarse bubble (CB) diffusers, Kenics static tube aerators, Norton fine bubble (FB) ceramic dome diffusers, FMC fine bubble plastic tube diffusers and Pentech jet aerators. The Pentech jet aerators acted similar to fine bubble diffusers in bubble size and the Kenics static tube aerators acted similar to coarse bubble diffusers. Detailed descriptions of the tests can be found in Yunt and Hancuff

(1979). The data used in this analysis and the results of our analysis for kLab and kLas are given in the Appendix.

3.2.

Sanitaire tests

Non-steady-state aeration tests were conducted at a test facility at the Sanitaire-Water Pollution Control Corporation in Milwaukee, Wisconsin. The tests were conducted in a tank 10.5 m wide by 1.8 m long by 7.3 m deep. This tank was used to test the Sanitaire coarse bubble diffuser at diffuser depths between 3.3 and 6.4 m and airflow rates between 91.9 and 516.0 scmh. A variety of diffuser layouts and tank geometries were used. A detailed description of the data collected is described by Schmit and Redmon (1978). These data and the results of our analysis for kLab and kLas are given in the Appendix.

3.3.

2001 WES tests

In July 2001, standardized tank aeration tests were performed at the U.S. Army Corps of Engineers Waterways Experiment Station (WES) in Vicksburg, Mississippi. The experiments were conducted in a large cylindrical tank of 7.6 m diameter by 10.3 m depth. This tank was used to test the Aercor coarse bubble diffuser at diffuser depths of 8.33 m and flow rates between 51.1 and 78.2 scmh. A detailed description of the clean water gas transfer tests can be found in Demoyer et al. (2003). These data and the results of our analysis for kLab and kLas are given in the Appendix.

3.4.

1995 WES tests

From 1995 to 1996, standardized tank aeration tests were also performed at the U.S. Army Corps of Engineers Waterways Experiment Station (WES) in Vicksburg, Mississippi. The experiments performed at WES in 1995–1996 were conducted in the same large cylindrical tank of 7.6 m diameter by 10.3 m depth as the 2001 experiments. This tank was used to test the Aercor coarse bubble diffuser at diffuser depths ranging from 2.8 to 9.1 m. Airflow rates tested were between 22.8 and 100.5 scmh. A detailed description of these gas transfer tests can be found in Demoyer et al. (2001). The tests performed at WES in 2001 and in 1995–1996 were conducted in the same tank, with the same coarse bubble diffuser; however, they were calibrated differently. During the 2001 tests, oxygen saturation values were obtained using air calibration and the percent saturation scale on traditional dissolved oxygen meters (Clark meters). This eliminated the need to compute any oxygen concentration because the Clark meter reading is proportional to percent saturation (Parkhill and Gulliver, 1997). The 1995–1996 tests were calibrated with laboratory Winkler titrations, and it is common for these titrations to give incorrect saturation values due to a bias in the titrant. Because of the greater accuracy of the 2001 tests, b, the oxygen saturation adjustment coefficient, for the 1995–1996 tests was adjusted to 94% so that the 1995–1996 tests would coincide with the 2001 tests. These data and the results of our analysis for kLab and kLas are given in the Appendix.

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Lower Granite Lock tests

118

116 115 % Saturation

Deep-water tests were conducted in the Lower Granite Lock, operated and maintained by the U.S. Army Corps of Engineers (USACE). The Lower Granite Lock and Dam is located on the Snake River in eastern Washington. The lock is 86 ft (26 m) wide by 675 ft (206 m) long with a 105 ft (32 m) lift. Five Aercor coarse bubble diffusers were anchored longitudinally along the bottom of the lock. To insure the diffusers did not move during the filling and emptying of the lock, each diffuser was mounted on a steel I-beam. Three tests were performed at Lower Granite Lock. In each test, the diffuser depth was 32 m. In tests one and two, the airflow rate per diffuser was 39.1 scmh. In test three the airflow rate was 78.2 scmh per diffuser. The tests performed were not typical aeration tests. Due to the volume of the lock, the water was not chemically deoxygenated at the start of each test. Also, due to regulations to protect fish in the Snake River, the total dissolved gas concentration could not exceed 120% during testing. Two air compressors supplied air to the five diffusers. A filter system removed oil residue in the compressed air. The delivery pressure was measured with a certified Bourdon gauge, and a thermistor was placed in the delivery line to monitor the compressed air temperature. A set of Brooks rotameters provided gas flow measurements. The air flow rate at standard temperature (20 1C) and pressure (1 atm) was set to approximately 39 or 78 scmh per diffuser. Total dissolved gas (TDG) concentrations, DO concentrations and temperatures were measured with six air-calibrated Hydrolab MiniSonde 4a multiprobes at various locations from 1 to 20 m depth in the lock. Air calibration was an important aspect of these tests because all measurements were referenced to a local saturation value, and the DO readings relative to this saturation value were needed (Parkhill and Gulliver, 1997). The data for the three tests are provided in Figs. 1–3.

TDG Nitrogen

117

114 113 112 111 110 109

Aeration shut off for 14 hours

108 0

50

100 150 200 250 300 350 400 450 Time (min)

Fig. 2 – Total dissolved gas data and calculated dissolved nitrogen concentration as percent saturation for lock test 2.

121

TDG Nitrogen

120 119 % Saturation

3.5.

1021

4 0 (200 6) 101 8 – 102 6

118 117 116 115 114 113 0

118

100 150 Time (min)

200

250

Fig. 3 – Total dissolved gas data and calculated dissolved nitrogen concentration as percent saturation for lock test 3.

TDG Nitrogen

116

50

% Saturation

114 112 110 108 106 Aeration shut off for 14 hours

104 102 0

200

400

600 800 Time (min)

1000

1200

Fig. 1 – Total dissolved gas data and calculated dissolved nitrogen concentration as percent saturation for lock test 1.

During testing it was believed that the biochemical oxygen demand (BOD) in the water was inhibiting the increase of the oxygen concentration. Because of this unknown sink, nitrogen concentrations were used in place of the oxygen concentrations in the mass transfer model by solving Eq. (2) instead of Eq. (1). The kLab and kLas values were determined by comparing the solution of Eq. (2) to the nitrogen concentrations, which were determined by subtracting the oxygen measurements and water vapor pressures from the TDG measurements. The data used and the results of our analysis for kLab and kLas are given in Table 1. Sensitivity analyses were conducted on both the kLab and kLas estimates from these tests because of the limited data set

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Table 1 – Lower Granite Lock data used and estimated values of kLab and kLas Test no. 1 2 3

Acs (m2)

hd (m)

Qa (scmh)

676 676 676

32 32 32

39.08 39.08 78.16

kLab

20 1C

(h1)

0.0094 0.0083 0.0187

kLas

20 1C

(h1)

0.0298 0.0045 0.0767

0.30 0.25

Test 1 Test 2 Test 3

∆ kLab/kLab

0.20 0.15 0.10 0.05 0.00 0.00

0.05

0.10

0.15 0.20 ∆ kLas/kLas

0.25

0.30

Fig. 4 – Sensitivity of the lock tests to changes in kLas and kLab.

and the relatively small difference in measured concentrations indicated in Figs. 1–3. A sensitivity analysis shows the numerical importance of the kLab and kLas values in obtaining a best-fit curve. The sensitivity of the curve-fit to specific kLab and kLas values can be determined by varying kLas from the best-fit value and examining the change in the best-fit value for kLab. Fig. 4 illustrates the sensitivity of the kLab values for the lock tests when the kLas values are changed up to 30%. For test one, kLab changes by 7.7% when kLas changes by 30%. This means that the curve fit is approximately four times more sensitive to kLab than to kLas. For test two, kLab changes by 1.7% when there is a 30% change in kLas. The curve fit for test two is approximately 17 times more sensitive to kLab than to kLas. For test three, kLab changes by 16.9% when kLas changes by 30%. kLab for test three is almost twice as sensitive to kLas in the curve fit. The curve fits for all three lock tests are more sensitive to kLab than to kLas. The increased sensitivity of kLab in test three may be due to the short length of testing time (200 min) and the small increase in nitrogen concentration (3.5%). Our previous kLab and kLas estimates for the 2001 WES tank tests (DeMoyer et al., 2003) indicated that an accurate determination of the ratio kLas/kLab was dependent upon approaching steady state in the tests. Extrapolating the steady state values of the WES tank tests to the depth of the Lower Granite Lock tests results in a steady state nitrogen concentration of 215% of saturation. Thus, the Lower Granite

Lock tests were not close to steady state and it is unlikely that the kLas computations were accurate. The sensitivity analysis indicated that the kLab determinations were relatively accurate, This can be attributed to two factors: first, if the concentration is close to saturation, the net surface transfer is close to zero, and the slope of the concentration measurements with respect to time is only attributable to bubble transfer. Second, at the large depths of the experiment, with up to three atmospheres of concentration difference across the bubble–water interface, the significance of bubble transfer over surface transfer is enhanced. The slope of the measured data is primarily due to bubble transfer for these deep water experiments.

3.6.

Nitrogen concentrations

The DeMoyer et al. (2003) mass transfer model requires the input of nitrogen concentrations, which can be determined by subtracting oxygen measurements and vapor pressures from TDG measurements. Total dissolved gas concentrations, however, were only measured for the 2001 WES tests and the Lower Granite Lock tests. Therefore, for the LACSD tests, the Sanitaire tests and the 1995 WES tests, the nitrogen concentrations had to be simulated. This was done assuming that the ratio of initial nitrogen concentration to nitrogen saturation was equal to the ratio of initial oxygen concentration to oxygen saturation before deoxygenation:
 CsatðN2 Þ , (6) CNðinitÞ ¼ COðinitÞ CsatðO2 Þ where CN(init) is the initial nitrogen concentration, which can be determined from the known initial oxygen concentration before deoxygenation, CO(init).
 CsatðN2 Þ CSSðN2 Þ ¼ CSSðO2 Þ , (7) CsatðO2 Þ where CSSðN2 Þ and CSSðO2 Þ are the steady-state nitrogen and oxygen concentrations. Finally, using Eq. (8) the nitrogen concentration as a percent, CN(%), can be calculated. 

 CNðinitÞ CSSðN2 Þ  CNðinitÞ CNð%Þ ¼ 100 (8) þ ð1  ekL at t Þ, CsatðN2 Þ CsatðN2 Þ where kLat is the bulk volumetric oxygen transfer coefficient and t is time. CSSðO2 Þ in Eq. (7) and kLat in Eq. (8) were determined by applying the ASCE Standard (1992) non-linear regression to the experimental data of dissolved oxygen concentrations over time. The sensitivity of the results using Eq. (8) was tested by trying different realistic assumptions in the analysis, such as

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keeping the value of CN at CSS throughout the test. The sensitivity of the resulting kLab and kLas values to the choice between realistic assumptions was found to be small.

4.

Data analysis

4.1.

Bubble mass transfer

The mass transfer coefficient for the bubble–water interface can be characterized by modifying a theoretical relationship developed by Azbel (1981) for bubble swarms: kL ab ¼ b1

f ð1  fÞ1=2 D1=2 UZ , db ð1  f5=3 Þ1=4 L1Z nZ1=2

(9)

where f is the gas void ratio, db is bubble diameter, D is diffusivity, U is a characteristic turbulence velocity, L is a characteristic length of turbulence, and n is kinematic viscosity. The original equation developed by Azbel was for bubble swarms where Z ¼ 0:75. Values for Z have ranged from 0.6 to 1 (Akita and Yoshida, 1973; Deckwer et al., 1982; ElTamtamy et al., 1984; Godbole et al., 1984; Hughmark, 1967; Joseph et al., 1984; Nakanoh and Yoshida, 1980; Kawase and Moo-Young, 1986). The gas void ratio for bubble plumes in large water bodies is typically small. Thus, the importance of the second and third f terms in Eq. (9) is considered negligible, and will hereafter be neglected. Then, Eq. (9) becomes: kL ab ¼ b1

f D1=2 UZ . db L1Z nZ1=2

(10)

The following equation for bubble diameter is taken from Hinze (1955):
3=5
2=5 s L , (11) db  r U3 where s is surface tension and r is liquid density. Eq. (11) is for the larger bubble diameters, which will be determined by a balance of shear and surface tension forces as the bubbles try to increase in size due to reducing hydrostatic pressure as they rise. Substituting in Eq. (11) for bubble diameter, and using the diffuser depth, hd for the characteristic length, Eq. (10) becomes: ! r3=5 U3 2=5 D1=2 UZ kL ab ¼ b1 f . (12) s hd h1Z nZ1=2 d

Rearranging and simplifying: !3=5 U2 hd r D1=2 Z Z2 U hd . kL ab ¼ b1 f s nZ1=2

(13)

The gas void ratio can be obtained from the following (Azbel, 1981) correlation: 2Fr  Fr, (14) 1 þ 2Fr pffiffiffiffiffiffiffiffi where Fr ¼ U= ghd is the Froude number. The Froude number is small (1  103 ! 9  107 ) and thus Eq. (14) essentially becomes the Froude number. Substituting in the Froude number, the Weber number, We ¼ U2 hd r=s, the Reynolds number, Re ¼ Uhd =n, the Schmidt fave ¼

1023

number, Sc ¼ n=D, and the Sherwood number, Sh ¼ kL ab h2d =D, Eq. (13) takes the following dimensionless form: Sh ¼ b1 Frb2 We3=5 Sc1=2 ReZ .

(15)

For the velocity we will use, U ¼ Q a =Acs , the superficial gas velocity. Most of the turbulence generated in a diffuser system is due to oscillations of the bubbles, and superficial gas velocity is a convenient means of representing rising bubbles. In addition, this Sherwood number is a bulk average for the water body, so it is necessary to have one term that is also a bulk average on the right-hand side of Eq. (15). The coefficient b2 was added to the Froude number in Eq. (15) because the gas void ratio correlation, Eq. (14), was developed for bubble columns and does not take into account the entrainment that occurs in bubble plumes in lake and reservoir aeration systems. This should have a significant effect upon the gas void ratio.

4.2.

Surface mass transfer

Surface mass transfer depends upon similar parameters as bubble mass transfer, with the exception of the Froude and Weber numbers. Therefore, the results of the analysis of aeration data were fit to the following equation: !b5 Acs , (16) Shs ¼ b3 Sc1=2 Reb4 h2d where Shs is the Sherwood number for surface transfer, kLAs/ (hdD), and As is the surface area of the water body. Using Eqs. (15) and (16), both design parameters, kLab and kLAs, can be quickly determined from knowing V, Acs, hd and Qa.

5.

Results and discussion

Performing a linear regression on Eq. (15), the adjustable coefficients b1, b2 and Z were fit to the kLab results of the twozone mass transfer model. Because there were only three tests at 32 m of depth, each of these was weighted by a factor of five in the regressions. The Reynolds number exponent, Z, was determined to be 1.001, while the Froude number exponent, b2, was determined to be –1.043. These exponents were then set to 1 and –1, respectively, and another regression was performed on the following equation: Sh ¼ b1

We3=5 Sc1=2 Re , Fr

(17)

where b1 was separately determined for the fine bubble and coarse bubble diffusers. For the fine bubble diffusers b1 ¼ 0:165 and for the coarse bubble diffusers b1 ¼ 0:027. This indicates that for fine bubble diffusers, kLab is approximately six times greater than kLab for coarse bubble diffusers under otherwise similar conditions. It should be noted that data for fine bubble diffusers are limited to depths of less than 8 m. Fig. 5 shows the correlation between the dimensionless Sherwood number (kLab) and the dimensionless parameters, Froude number, Fr, Weber number, We, Reynolds number, Re and Schmidt number, Sc. The figure separately identifies the coarse bubble and fine bubble diffusers as well as the deepwater lock tests. The correlation plotted includes depths

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Eq. (16) becomes

β1 We 3/5 Sc1/2 Re / Fr

1.0E+09

1.0E+08

CB FB Lock Tests Upper CI Lower CI

Shs ¼ 49Sc1=2 Re

Acs

!0:72

h2d

(21)

or, !0:28
1=2 kL As D h2d ¼ 49 . n Qa Acs

1.0E+07

1.0E+06

1.0E+05 1.0E+05

1.0E+06

1.0E+07 Sh

1.0E+08

1.0E+09

Fig. 5 – Correlation of the bubble mass transfer coefficients to dimensionless parameters for all tests, separated by coarse bubble and fine bubble diffusers. Included is the 95% confidence interval.

ranging from 2.25 to 32 m. Note how well the large-depth lock tests are predicted with this relationship. The 95% confidence interval shown in Fig. 5 corresponds to +/67% in the value of b1. Rearranging and separating each variable in Eq. (17) we get: 1=10

6=5 hd kL ab ¼ b1 D1=2 g1=2 n1=2 r3=5 s3=5 Q a6=5 Acs

.

(18)

From Eq. (18) it can be seen that kLab increases with increasing airflow rate and depth; however, as the volume of water to be aerated increases, kLab decreases. This seems logical and is comparable with the results from the improved mass transfer model. To more quickly determine kLab for design purposes, Eq. (18) can be simplified into the following form:
1=2
 D Q a 6=5 1=10 kL ab ¼ a hd , (19) n Acs where a includes the previously determined b1 values, g, r at 20 1C and s at 20 1C. The values of r and s do not significantly change from 0 to 30 1C. The results only increase by 3.4% from 0 to 30 1C, so it is felt that the inclusion of r and s into the coefficient a is acceptable. D and n, however, do change more significantly with temperature, and they are therefore not included in a. a was determined from the b1 values, g, r(20 1C) and s(20 1C) to be 30.5 m13/10 h1/5 for the fine bubble system and 5.0 m13/10 h1/5 for the coarse bubble system. Eq. (19) would be difficult to use in reservoirs with a highly variable cross-section, Acs. It can be converted in to an equation for the mass transfer coefficient, kLAb, where Ab is the surface area of the bubbles. This results in
1=2
1=5 kL Ab D Qa 13=10 ¼a hd , (20) n Qa V where Acs ¼ V=hd and V is the volume between the free surface and hd. The best fit of the adjustable coefficients in Eq. (16) gave b4 ¼ 0:996. When that value was set to one, b3 and b5 in Eq. (16) resulted in values of 49.0 and 0.72, respectively. Then

(22)

This indicates that the surface transfer coefficient, kLAs, increases with increasing air flow rate and with diffuser depth, and decreases with increasing cross-sectional area. Fig. 6 illustrates the correlation of Eq. (21) for all experimental test results, and separately identifies each diffuser tested. In general, each individual manufacturer’s diffuser tends to follow the perfect fit line. The exceptions are the Sanitare course bubble diffuser (Sanitare tests), which tends to have a lower Shs, and the Norton fine bubble diffuser, which tends towards a higher Shs, than that predicted. The LACSD tests of the Sanitare course bubble diffuser, however, follows the perfect fit line more closely, likely because the methodology was similar to the other LACSD tests. The importance of Qa on kLs is evident in Eq. (22). It does not include the influence of wind, which can be estimated through equations described by Wanningkof et al. (1991). Eq. (21) proves to be a good correlation in Fig. 6 except for two of the three deep-water lock tests. However, it is felt that the surface mass transfer coefficient, kLas, was not accurately determined for the lock tests. The experimental lock tests must approach a steady-state concentration in order to accurately fit the value of kLas in the mass transfer model. As seen in Figs. 1–3, it is apparent that these tests did not sufficiently approach steady-state. For this reason, there is a great deal of uncertainty in the kLas values determined from the lock tests. A sensitivity analysis has shown that the value of kLas does not substantially impact the value of kLab for these tests. The ratio of kLas to kLab for all data is given in Fig. 7. It can be seen from Fig. 7 that the fine bubble diffusers have a lower ratio of kLas to kLab than the coarse bubble diffusers. This goes along with the above finding that values of kLab for fine bubble diffusers can be six times greater than those for coarse bubble diffusers under similar test conditions. As the Reynolds number gets up to 100,000, however, the value of kLas/kLab seems to tend towards 1 for both course bubble and fine bubble diffusers. The highest Reynolds number of the fine bubble diffusers, however, was 36,000, where the ratio was 0.45.

6.

Application to McCook reservoir

Applying the developed equations to the DeMoyer et al. (2003) model, both a coarse bubble and a fine bubble aeration system for the McCook reservoir in Chicago can be designed. The aeration design needs to maintain aerobic conditions in the reservoir (at least 2 mg/L) that has an area of 395,300 m2 (Robertson, 2000). The 1-in-100-year event in July should cause the McCook reservoir to fill to its maximum of 73 m (Robertson, 2000). A 5-day BOD design range of 30 mg/L when

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4 0 (200 6) 101 8 – 102 6

49.0 Sc1/2 Re (Acs/hd2)0.72

1.0E+08 Aercor CB (2001 WES) Aercor CB (1995 WES) Sanitaire CB (LACSD) Envirex CB (LACSD) FMC CB (LACSD) Bauer CB (LACSD) Kenics CB (LACSD) Norton FB (LACSD) FMC FB (LACSD) Pentech FB (LACSD) Aercor CB (Lock Tests) Sanitaire CB (Sanitaire) Perfect Fit

1.0E+07

1.0E+06

1.0E+05 1.0E+05

1.0E+06

1.0E+07

1.0E+08

Shs Fig. 6 – Correlation of the surface mass transfer coefficients to dimensionless parameters for all diffusers. Included is the 95% confidence interval.

10.00 CB FB

kLas/kLab

1.00

0.10

0.01 100

1000

10000

100000

Re Fig. 7 – Ratio of Reynolds number versus mass transfer coefficients for all tests, separated by coarse bubble and fine bubble diffusers.

full to 80 mg/L when at the lowest depth of 10 m is estimated and a BOD decay rate of 0.25 d1 is assumed. Other design criteria are that the diffusers will be 1 m above the bottom of the reservoir, the maximum air flow rate per coarse bubble diffuser is 100 scmh and the maximum air flow rate per fine bubble diffuser is 20 scmh. Using an iterative procedure between the mass transfer model described by Eqs. (1)–(5) and the transfer coefficient correlations, Eqs. (15) and (21), an aeration system to accommodate the BOD range was designed. The system was first designed using coarse bubble diffusers and the high BOD

of 80 mg/L, assumed to occur at a depth of 10 m. It was determined that a coarse bubble diffuser with an air flow rate of 100 scmh would maintain aerobic conditions for an area of 341 m2 with the above conditions. Based on this, 1160 coarse bubble diffusers supplying a total air flow of 116,000 scmh would be needed for the McCook reservoir. For this case, kL ab ¼ 0:063 h1 and kL as ¼ 0:064 h1 . The air flow of the coarse bubble aeration system was then adjusted for the lower BOD of 30 mg/L that is assumed to occur at a depth of 73 m, with each of the 1160 diffusers maintaining 2 mg/L in a 341 m2 area. An air flow rate of 29 scmh per diffuser (33,640 scmh total) was determined, assuming that the empirical relationships developed herein may be extrapolated to 73 m of depth. For this case, kL ab ¼ 0:018 h1 and kL as ¼ 0:003 h1 . During the high BOD period at 10 m depth, approximately 3.5 times as much air flow is needed to maintain aerobic conditions. A fine bubble aeration system for McCook reservoir was designed using the same procedure. The system was first designed for the high BOD of 80 mg/L and a depth of 10 m. It was determined that a fine bubble diffuser with an air flow rate of 20 scmh would maintain aerobic conditions for an area of 115 m2. From this, 3438 fine bubble diffusers supplying a total air flow of 68,760 scmh would be needed for the reservoir. For this case, kL ab ¼ 0:207 h1 and kL as ¼ 0:044 h1 . The air flow of the fine bubble system was then adjusted for the lower BOD of 30 mg/L and 73 m depth. With each of the 3438 diffusers maintaining 2 mg/L in a 115 m2 area, an air flow rate of 3.8 scmh per diffuser (13,065 scmh total) was determined. For this case, kL ab ¼ 0:034 h1 and kL as ¼ 0:001 h1 . During the high BOD period, approximately 5.3 times as much air flow is needed to maintain aerobic conditions.

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A coarse bubble aeration system for McCook reservoir requires only 1160 diffusers, approximately one-third of the 3438 diffusers needed for a fine bubble aeration system. However, significantly less air flow is needed for the fine bubble diffusers in comparison to the coarse bubble diffusers. At the more common 10 m depth, the air flow required by the fine bubble diffusers was 39% of that required by the coarse bubble diffusers. These considerations and the mixing requirements of the reservoir are a part of the aeration system design.

7.

Conclusions

Previously, there was insufficient data to safely design air diffuser systems for deep reservoirs and tanks. Using the results from 179 experimental tests with diffusers depths ranging from 2.25 to 32 m, two equations characterizing the volumetric mass transfer coefficients for bubble transfer and free-surface transfer, kLab and kLas, have been successfully developed to aid in the design of deep diffused aeration systems. It was determined that the bubble mass transfer coefficient, kLab, for fine bubble aeration systems is six times greater than those for coarse bubble aeration systems. It was also established that kLab increases with increasing depth and air flow rate, and decreases with increasing water volume. The surface mass transfer coefficient, kLAs, increases linearly with increasing gas flow rate and to the 0.28 power with increasing depth. Applying the predictions to the DeMoyer et al. (2003) model, one can more effectively design diffused aeration systems for lakes, reservoirs, and wastewater treatment facilities at a variety of water depths through separate determination of the surface mass transfer coefficient and the bubble mass transfer coefficient.

Acknowledgments The experiments described and data presented, unless otherwise noted, were part of research conducted under authority given by the U.S. Army Corps of Engineers District–Chicago. The authors thank Gary Johnson, U.S. Geological Survey; Andy Waratuke, University of Illinois; and Calvin Buie, U.S. Army Corps of Engineers; for all of their hard work setting up the tests at the Lower Granite Lock and for operating the diffusers.

Appendix A.

Supplementary data

Supplementary data associated with this article can be found in the online version at doi:10.1016/j.watres.2005.12.033.

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