Oxygen Transfer Rate in a Coarse-Bubble Diffused ... - ACS Publications

Nov 6, 2003 - To improve the performance of a diffused aeration system, a series of aeration studies using various diffusers was initiated. At this st...
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Ind. Eng. Chem. Res. 2003, 42, 6653-6660

6653

Oxygen Transfer Rate in a Coarse-Bubble Diffused Aeration System Jia-Ming Chern* and Sheng-Ping Yang Department of Chemical Engineering, Tatung University, 40 Chungshan North Road, 3rd Sec., Taipei, 10452 Taiwan

To improve the performance of a diffused aeration system, a series of aeration studies using various diffusers was initiated. At this stage, 35 unsteady-state reaeration test runs in a 1500-L aeration tank with coarse-bubble diffusers have been performed under varying diffused airflow rates (3.04-8.34 m3/h), water temperatures (17.7-34.7 °C), and water depths (0.6-1.8m). The reaeration data were analyzed by the traditional ASCE model and a two-zone model. The experimental results show that the volumetric mass-transfer coefficients of the ASCE model and of the surface reaeration zone increase with the airflow rate and temperature, but decrease with the water depth. The volumetric mass-transfer coefficient of the gas-bubble zone also increases with the airflow rate and water temperature, but is independent of the water depth. The saturation DO concentrations and the volumetric oxygen transfer rates under varying aeration conditions can be predicted by the two-zone model satisfactorily. Introduction The activated-sludge process is one of the most popular processes used to treat domestic and industrial wastewaters. To produce an improved effluent quality by removing substances that have a biological oxygen demand, the aeration system in the activated-sludge process must supply enough oxygen to maintain the metabolic reactions of the microorganisms and provide sufficient mixing in the aeration tank. In the activatedsludge process, the aeration system represents the most energy-intensive operation unit. Therefore, many different types of aeration systems have been developed over the years in an effort to improve the energy efficiency of aeration. Because the measurement of the oxygen transfer rate is the key step in the evaluation of aeration systems and because the design parameters obtained from this measurement are strongly affected by the experimental conditions and procedures and even the techniques employed in analyzing the experimental data,1 the U.S. Environmental Protection Agency (EPA) and the American Society of Civil Engineers (ASCE) jointly developed a standard for the measurement of the oxygen transfer rate in clean water. This standard describes in detail the experimental apparatus, procedures, data analysis, and aeration system evaluation criteria.2 In the ASCE model, the overall oxygen transfer rate is expressed in terms of a lumped mass-transfer coefficient times an overall concentration difference as the driving force. This type of “one-zone” model has been widely used in the chemical engineering field. The obtained model parameters, KLa and C/∞, depend on the operating conditions, the aerators (surface or diffused), and even the geometry and size of the aeration tanks. Although the oxygen mass-transfer model used in the ASCE standard can statistically fit the reaeration data quite well, it has little physical significance and, therefore, cannot be used for scale-up design. Consequently, in practice, aerator manufacturers use full* To whom correspondence should be addressed. E-mail: [email protected]. Tel.: 886-2-25925252 ext. 2561 ext. 23. Fax: 886-2-25861939.

scale aeration tanks to test the performance of their aerators at conditions close to the “standard” conditions specified by the ASCE. This performance test approach of aeration systems wastes both water and money. A better approach using a more reliable oxygen masstransfer model is highly desirable. A more fundamentally rigorous oxygen mass-transfer model considering the oxygen transfer processes in the gas-bubble zone and surface reaeration zone for diffused aeration systems was formulated and numerically solved in 1989.3 Liao and Lee4 also considered oxygen transfer in the two zones and solved the transient model numerically. In addition, Oliveira and Franca5 used the two-zone model to simulate numerically the oxygen transfer process in an aquaculture aeration system. The analytical solution to the two-zone model was developed to determine the volumetric mass-transfer coefficients of oxygen in the two mass-transfer zones, and the effects of the diffused airflow rate, water temperature, and impurities were investigated in 4- and 500-L tanks.6,7 It was generally believed that the oxygen volumetric mass-transfer coefficient increased with increasing diffused airflow rate and water temperature. However, the relationship between the volumetric mass-transfer coefficient and the water depth remains unknown. This study therefore aims to explore this relationship by performing unsteady-state reaeration tests in a deeper aeration tank operating at varying diffused airflow rates, water temperatures, and diffuser depths. ASCE Standard Oxygen Mass-Transfer Model The ASCE standard uses the following simplified mass-transfer model to analyze the unsteady-state reaeration data in a batch aeration tank

dC ) KLa(C/∞ - C) dt

(1)

Assuming that KLa and C/∞ are constant throughout the testing period, eq 1 can be integrated to yield the following expression for C as a function of time

10.1021/ie030396y CCC: $25.00 © 2003 American Chemical Society Published on Web 11/06/2003

6654 Ind. Eng. Chem. Res., Vol. 42, No. 25, 2003

C ) C/∞ - (C/∞ - C0) exp(-KLat)

(2)

A nonlinear regression analysis based on the GaussNewton method is recommended by the ASCE to fit eq 2 to the experimental data using KLa, C/∞, and C0 as three adjustable model parameters. The statistically determined value of KLa is then adjusted to the standard conditions of 1 atm pressure and 20 °C water temperature by the following equation

KLaT ) KLa20θT-293.15

(3)

A generally accepted value of the temperature correction factor, θ, is 1.024.8 The volumetric oxygen transfer rate (VOTR) at zero DO is calculated by eq 4

VOTR ) KLaC/∞

(4)

Two-Zone Model Any meaningful mathematical model should reflect the actual physical situation of the system being modeled. Before we model the oxygen mass-transfer process in diffused aeration systems, let us consider the simplified physical picture of a cross-sectional view of a diffused air aeration tank, as depicted in Figure 1. The gas (air) is diffused into the liquid near the bottom of the aeration tank and flows upward through the liquid to the surface of the tank. The bubbling motion of the gas creates effective bulk motion and mixing of the liquid in the tank and also a turbulent liquid surface. Two different mass-transfer zones and mechanisms of oxygen mass transfer arise: the gas bubble dispersion mass-transfer zone exists below the turbulent surface, and the turbulent surface mass-transfer zone exists in the shallow region of the liquid surface. Each of these zones must be separately analyzed and properly taken into account in the overall oxygen mass-transfer model. The development of the two-zone model is based on the following assumptions: (1) The gas bubbles flow upward through the liquid in a plug-flow fashion. (2) The bulk liquid is completely mixed, i.e., the dissolved oxygen concentration is uniform throughout the tank at any instant of time. (3) Nitrogen transfer is negligible compared to oxygen transfer. (4) The nitrogen molar flow rate is constant. (5) The oxygen mass-transfer processes are controlled by the liquid-phase resistance. The governing equations of the two-zone model are as follows

Figure 1. Oxygen mass-transfer zones in diffused aeration systems.

phase; and eq 7, the equilibrium oxygen concentration in the tank. Assuming pseudo-steady state in the gas bubbles,9,10 eqs 5-7 can be solved analytically6 to give

C)

(

KLBaBA2 + KLSaSC/LS + A1KLBaB + KLSaS

where

1 A1 ) ZS 2

x

AZS(1 - )

dC ) dt

∫0Z

S

[ (

A2 )

C/1{1 - exp[-K1ZS(a - bZS)] } K1ZS(1 - PW) K1 )

KLBaB(1 - )AC/1

K2 )

y0(1 - PW)G KLBaB(1 - )A G

a ) P0 - PW + Fg(1 - )ZS

(5)

KLBaB(C* - C)(1 - )A dZ + KLSaS(1 - )(C/LS - C)AZS (6)

C* )

C/1

y(P - PW)

y0(1 - PW)

) ]{ ( ) [(

a 2 π a erf xK1b + exp K1b ZS K1b 2b 2b a erf - ZS x K1b (9) 2b

b) ∂y ∂CG ) -G - KLBaB(1 - )A(C* - C) A ∂t ∂Z

)

KLBaBA2 + KLSaSC/LS C0 exp[-(A1KLBaB + A1KLBaB + KLSaS KLSaS)t] (8)

Fg(1 - ) 2

(10)

(11)

(12) (13) (14)

The three model parameters KLBaB, KLSaS, and C0 can be determined either from nonlinear regression of the unsteady-state reaeration data or from the ASCE model parameters by solving the following simultaneous algebriac equations

KLa ) A1KLBaB + KLSaS (7)

Equation 5 represents the oxygen mass balance in the gas phase; eq 6, the oxygen mass balance in the liquid

) ]}

C/∞

KLBaBA2 + KLSaSC/LS ) A1KLBaB + KLSaS

(15) (16)

Using the two-zone model, the volumetric oxygen trans-

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Figure 2. Schematic diagram of the aeration experimental setup. Table 1. Summary of Unsteady-State Reaeration Test Conditions parameter

value

water temperature, °C air temperature, °C air flow rate, Nm3/h tank area, m2 gas holdup, water depth, m barometric pressure, mmHg

17.7-34.7 17.9-34.9 3.04-8.85 0.64 -0.002-0.004 0.6-1.8 756.0-772.0

Table 2. Correlation Parameters for Volumetric Mass-Transfer Coefficients

fer rate (VOTR) at zero DO is calculated by eq 17

VOTR ) KLBaBA2 + KLSaSC/LS

Figure 3. Typical unsteady-state reaeration curves at varying diffused airflow rates.

(17)

Experimental Section The experimental setup is schematically shown in Figure 2. All unsteady-state reaeration tests were conducted in a 1500-L aeration tank that was 0.9 m in diameter and 2.4 m in height. Coarse-bubble diffusers (Feng Chern Co., Taiwan) were installed at the bottom of the tank. The actual air temperature and pressure were measured by in-line gauges. The airflow rates, not measured at the standard conditions of 1 atm and 20 °C, were corrected to the standard conditions.11 In the two-zone model, the gas holdup, , was calculated from the liquid depth measurements with the air on and off.12 Two DO meters (WTW, model OXI96B) were used in the preliminary experiments to measure the DO concentrations at one-half and two0thirds water depths in the tank. At any instant of time, the two DO meter readings differed by less than 0.1 mg/L. Therefore, the middle-depth DO concentration was continuously measured and used for data analysis. The detailed experimental test procedure and techniques used were primarily those specified by the ASCE Standard. Table 1 summarizes the experimental conditions of 35 unsteadystate reaeration test runs. Results and Discussion Figure 3 shows a typical set of unsteady-state reaeration curves, with the symbols representing the experimental data and the curves representing the model predictions. The unsteady-state reaeration test data were first analyzed using the ASCE standard oxygen transfer model, and the associated parameters KLa and C/∞ were determined from nonlinear regression of the data. Then, the volumetric mass-transfer coefficients in

parameter

ASCE KLa

bubble-zone KLBaB

surface-zone KLSaS

k1 k2 k3 θ

0.441 1.006 -0.138 1.030

0.194 1.015 0 1.035

0.226 0.978 -0.488 1.032

the two-zone model, KLBaB and KLSaS, were calculated from the ASCE model parameters and the associated test conditions, including the diffused airflow rate, water temperature, water depth, and tank cross-sectional area. Once the parameters of the two-zone model had been obtained, eq 8 was used to calculate the DO concentrations under various operating conditions. As shown in Figure 3, the two-zone model fits the unsteadystate reaeration data quite well. In terms of correlating the unsteady-state reaeration data, the two-zone model does not provide any improvement compared to the ASCE model, because eq 8 for the two-zone model and eq 2 for the ASCE model are mathematically indistinguishable. The two-zone model parameters obtained from direct nonlinear regression of the reaeration data using eq 8 are the same as those calculated from the ASCE model parameters obtained from nonlinear regression of the reaeration data using eq 2. After all data sets had been analyzed, the following power-law-type equation was applied to correlate the volumetric mass-transfer coefficients

KLa ) k1Qk2ZSk3θT-293.15

(18)

This correlation equation for the volumetric masstransfer coefficient is purely empirical in nature and tries to lump all possible factors such as changes in the mass-transfer coefficient, mass-transfer area, viscosity, surface tension, diffusion coefficient, etc., into a simple mathematical form. Equation 18 is a modified version of an empirical equation that successfully correlated the volumetric mass-transfer coefficients of oxygen in 4- and 500-L aeration tanks.6 The original equation used by Chern and Yu is of the form6

KLa ) (k0 + k1Qk2)θT-293.15

(19)

Because the volumetric mass-transfer coefficient at zero diffused airflow rate is very small, k0 is neglected in eq

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Figure 4. Comparison of the experimental and predicted volumetric mass-transfer coefficients.

Figure 6. Comparison of the experimental and predicted saturation DO concentrations.

Figure 7. Comparison of the experimental and predicted volumetric oxygen transfer rates.

Figure 5. Effect of diffused airflow rate on the volumetric masstransfer coefficients.

18. One additional parameter, k3, is employed in eq 18 to account for the effect of the water depth on the volumetric mass-transfer coefficient. Table 2 shows the best-fit parameters in eq 18, with the diffused airflow rate in units of cubic meters per hour, the water depth in units of meters, and water temperature in units of Kelvin. The volumetric mass-transfer coefficients predicted by eq 18 are shown in Figure 4. As can be seen in this figure, the predicted volumetric mass-transfer coefficients scatter around the diagonal line. This indicates that eq 18 can be used to correlate the volumetric masstransfer coefficients at varying water temperatures, diffused airflow rates, and water depths satisfactorily. As suggested by the k2 values in Table 2 (k2 ≈ 1), the volumetric mass-transfer coefficients in the ASCE and two-zone models are almost proportional to the diffused airflow rate. This result is comparable to that obtained by Ashley et al.,13 who found that the value of KLa at

20 °C increased by 122% when the diffused airflow rate was doubled in a coarse-bubble diffusion system. The volumetric mass-transfer coefficient KLa is the product of the specific interfacial area a and the mass-transfer coefficient KL. The diffused airflow rate influences the former more than the latter; an increase in the diffused airflow rate leads to an increase in the interfacial area. The combined effects result in a linear increase in KLa with respect to the diffused airflow rate. Eckenfelder14 presented a general correlation for the ASCE-model volumetric mass-transfer coefficient in diffused aeration systems. According to Eckenfelder’s correlation, the volumetric mass-transfer coefficient is inversely proportional to one-third of the water depth, which is within the range of k3 values listed in Table 2 (-0.488 > -1/3 > -0.138). The water depth dependency parameter for the ASCE-model KLa obtained in this study is less than that given by Eckenfelder ( -0.138 < -1/3). The water depth dependency parameter for the surface reaeration zone KLSaS obtained in this study is greater than that given by Eckenfelder (-0.488 > -1/ 3). The k3 values in Table 2 (k3 < 0) suggest that the volumetric mass-transfer coefficient in the ASCE model and that in the surface reaeration zone of the two-zone

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Figure 8. Comparison of the experimental and predicted VOTR at varying diffused airflow rates.

model decrease with increasing water depth while the volumetric mass-transfer coefficient in the gas bubble zone is independent of the water depth (k3 ) 0). These trends can be seen more clearly in Figure 5. In Figure 5, the volumetric mass-transfer coefficients at temperatures other than 25 °C are corrected to those at 25 °C using the θ factors listed in Table 2. The model curves shown in Figure 5 are calculated with eq 18 using the parameters listed in Table 2. At the same diffused airflow rate and water temperature, the surface turbulence is more vigorous in a shallow tank. Therefore, the surface-zone volumetric mass-transfer coefficient, KLSaS, strongly increases with decreasing water depth. In the bubble transfer zone, however, the volumetric masstransfer coefficient, KLBaB, is independent of the water depth. The conventional ASCE model does not differentiate the oxygen transfer processes in the two different zones and results in a lumped KLa value that moderately increases with decreasing water depth (k3 < 0). So far, the experimental data demonstrate that the two-zone model and eq 18 can be used to fit the volumetric mass-transfer coefficient data successfully. We can further use the two-zone model to predict the saturation DO concentration and the volumetric oxygen transfer rate (VOTR) at zero DO by eqs 16 and 17, respectively. The C/∞ parameter in the ASCE model is called the equilibrium concentration or the “saturation” concentration as time approaches infinity. It is actually the steady-state DO concentration reached in the aeration tank and not a true equilibrium DO concentration as usually used in a thermodynamic sense. In contrast,

the equilibrium concentrations C/1 and C/LS are true thermodynamics equilibrium DO concentrations with which the saturation concentration can be predicted. Figures 6 and 7 show the comparisons of the predicted and experimental saturation DO concentrations and volumetric oxygen transfer rates, respectively. As is clearly shown in Figures 6 and 7, the two-zone model successfully predicts the saturation DO concentrations and volumetric oxygen transfer rates at varying diffused airflow rates, water temperatures, and depths. Figure 8a-d shows that the VOTR increases proportionally with increasing diffused airflow rate at a given water temperature and depth. For the same airflow rate and water depth, the VOTR is higher at a higher water temperature because the volumetric mass-transfer coefficients are higher at the higher temperature, as shown in Figure 8b. Also, as shown in Figure 8c, the VOTR for ZS ) 1 m is slightly higher than that for ZS ) 1.4 m. For a shallow tank with the same diffused airflow rate, the saturation DO concentration is lower, but the surface reaeration mass-transfer coefficient is higher. The overall VOTR is therefore higher in a shallow tank, as shown in Figure 8c. A similar trend was also noted by Wagner and Po¨pel15 through an extensive literature review of operating data. The effects of water depth and temperature on the saturation DO concentration and volumetric oxygen transfer rate can be seen more clearly through simulation. According to the simulation results shown in Figure 9a, the saturation DO concentration increases linearly with increasing water depth, but it seems to be independent of the diffused airflow rate. The gas-

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Figure 9. Simulation results of the effects of water depth.

bubble-zone volumetric mass-transfer coefficient KLBaB is not affected by the water depth (Figure 9b), whereas the surface-reaeration-zone volumetric mass-transfer coefficient KLSaS decreases with increasing water depth (Figure 9c). The combined results lead to a decrease of the volumetric oxygen transfer rate with respect to increasing water depth, as shown in Figure 9d. Although Figure 9d shows that the volumetric oxygen transfer rate (in milligrams per liter per hour) decreases with increasing water depth, the total oxygen transfer rate (in milligrams per hour) increases with the water depth because the equilibrium DO concentration increases linearly with the water depth. It is important to note that, in deeper aeration tanks with efficient finebubble diffusers, the volumetric oxygen transfer rate can increase with increasing water depth. Because the coarse-bubble diffusers used in this study are not very efficient and the tank water is not deep enough, the oxygen transfer rate in the surface zone represents a significant contribution to the overall oxygen transfer rate in our system (from 35% for ZS )1.8 m to 61% for ZS ) 0.6 m). The first term (bubble-zone fraction) in the right-hand side of eq 17 is an increasing function of water depth, but the second term (surface-zone fraction) is a decreasing function of water depth. If the surfacezone oxygen transfer rate is a minor fraction, the volumetric oxygen transfer rate can increase with increasing water depth. Figure 10a shows that the saturation DO concentration decreases with increasing water temperature, but it is independent of the diffused airflow rate. The equilibrium DO concentration at 1 atm, C/1, used in the two-zone model was found from APHA.16 Parts b and c

of Figure 10 show that the volumetric mass-transfer coefficients in the two zones increase with increasing water temperature. Figure 10d shows that the volumetric oxygen transfer rate slightly increases with increasing water temperature. Vogelaar et al.17 studied the influence of temperature (20-55 °C) on the volumetric oxygen transfer rate in a bubble column and used the ASCE model to analyze their data. They found that the volumetric mass-transfer coefficient increased almost linearly with the diffused airflow rate; this study obtained a similar result (k2 ≈ 1). They also found that the volumetric mass-transfer coefficient increased with temperature whereas the saturation DO concentration decreased with temperature and the volumetric oxygen transfer rate also slightly increased with the temperature. It is important to note that the effect of water temperature on the volumetric oxygen transfer rate, although predictable, is not easy to elucidate. The role of water temperature cannot be easily seen from eq 17. As the water temperature increases, the volumetric mass-transfer coefficients in the two zones both increase, but C/1 and C/LS both decrease. Therefore, the volumetric oxygen transfer rate could increase or decrease with increasing water temperature, depending on the water depth and diffused airflow rate. Conclusion A series of unsteady-state reaeration tests in a 1500-L aeration tank were performed, and the data were analyzed by the ASCE model and the two-zone model. An empirical equation was used to correlate the

Ind. Eng. Chem. Res., Vol. 42, No. 25, 2003 6659

Figure 10. Simulation results of the effects of water temperature.

volumetric mass-transfer coefficients satisfactorily. Using the two-zone model along with the correlation equation for the volumetric mass-transfer coefficients, the saturation DO concentrations and volumetric oxygen transfer rates at varying diffused airflow rates, water temperatures, and depths can be predicted successfully. From the results of this study, high volumetric oxygen transfer rates can be achieved by employing higher diffused airflow rates, or shallow aeration tanks. Acknowledgment The financial support from National Science Council of Taiwan under Grant NSC 90-2214-E-036-002 is gratefully acknowledged. Nomenclature a ) parameter defined in eq 13 (atm) A ) cross-sectional area of the aeration tank (m2) A1 ) parameter defined in eq 9 A2 ) parameter defined in eq 10 (kmol/m3) b ) parameter defined in eq 14 (atm/m) C ) dissolved oxygen concentration at time t (kmol/m3) CG ) gas-phase oxygen concentration in the gas bubble (kmol/m3) C0 ) initial dissolved oxygen concentration (kmol/m3) C/1 ) equilibrium dissolved oxygen concentration at 1 atm pressure (kmol/m3)

C* ) equilibrium DO in the water at position Z (kmol/m3) C/LS ) equilibrium DO in the water at atmospheric pressure (kmol/m3) C/∞ ) saturated dissolved oxygen concentration (kmol/m3) g ) gravitational acceleration constant (m/s2) G nitrogen molar flow rate (kmol/h) ki ) correlation parameters defined in eq 18, i ) 1-3 K1 ) lumped parameter defined in eq 11 K2 ) lumped parameter defined in eq 12 KLa ) volumetric mass-transfer coefficient in the ASCE model (1/h) KLBaB ) bubble-zone volumetric mass-transfer coefficient (1/h) KLSaS ) surface reaeration-zone volumetric mass-transfer coefficient (1/h) P ) gas pressure at the depth ZS - Z (atm) P0 ) atmospheric pressure (atm) PW ) water vapor pressure (atm) Q ) diffused airflow rate (m3/h) R ) gas constant [atm m3/(kmol K)] t ) aeration time (h) T ) water temperature (K) VOTR ) volumetric oxygen transfer rate [kmol of O2/(h m3)] y ) mole ratio of oxygen in the gas bubble (kmol of O2/ kmol of N2) y0 ) feed mole ratio of oxygen in the gas bubble (kmol of O2/kmol of N2) Z ) position above the diffuser (m) ZS ) water depth (m)  ) gas holdup

6660 Ind. Eng. Chem. Res., Vol. 42, No. 25, 2003 F ) water density (kg/m3) θ ) temperature correction factor defined in eqs 3 and 18

Literature Cited (1) Brown, L. C.; Baillod, C. R. Modeling and interpreting oxygen transfer data. J. Envir. Eng. Div., ASCE 1982, 108, 607628. (2) ASCE Standard Measurement of Oxygen Transfer in Clean Water, American Society of Civil Engineers (ASCE): Reston, VA, 1992. (3) McWhirter, J. R.; Hutter, J. C. Improved oxygen mass transfer modeling for diffused/subsurface aeration systems. AIChE J. 1989, 35, 1527-1534. (4) Liao, Y. C.; Lee, D. J. Estimation of oxygen transfer rate in sequencing batch reactor. Water Sci. Technol. 1996, 34, 413-420. (5) Oliveira, M. E. C.; Franca, A. S. Simulation of oxygen mass transfer in aeration systems. Int. Commun. Heat Mass Transfer 1998, 25, 853-862. (6) Chern, J.-M.; Yu, C.-F. Oxygen transfer modeling of diffused aeration systems. Ind. Eng. Chem. Res. 1997, 36, 5447-5453. (7) Chern, J.-M.; Chou, S.-R.; Shang, C.-S. Effects of impurities on oxygen transfer rates in diffused aeration systems. Water Res. 2001, 35, 3041-3048. (8) Stenstrom, M. K.; Gilbert, R. G. Effects of alpha, beta and theta factor upon the design, specification and operation of aeration systems. Water Res. 1981, 15, 643-654. (9) Matter-Muller, C.; Gujer, W.; Giger, W. Transfer of volatile substances from water to the atmosphere. Water Res. 1981, 15, 1271-1279.

(10) Roberts, P. V.; Munz, C.; Dandiker, P. Modeling volatile organic solute removal by surface and bubble aeration. Res. J. Water Pollut. Control Fed. 1984, 56, 157-163. (11) Cooper, C. D.; Alley, F. C. Air Pollution Control: A Design Approach, Waveland Press: Prospect Heights, IL, 1986. (12) Akita, K.; Yoshida, F. Gas Holdup and volumetric mass transfer coefficient in bubble columns. Effects of liquid properties. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 76-80. (13) Ashley, K. I.; Mavinic, D. S.; Hall, K. J. Bench-scale study of oxygen transfer in coarse bubble diffused aeration. Water Res. 1992, 26, 1289-1295. (14) Eckenfelder, W. W. Industrial Water Pollution Control; McGraw-Hill: New York, 1989; Chapter 5, p 118. (15) Wagner, M. R.; Po¨pel, H. J. Oxygen transfer and aeration efficiencysInfluence of diffuser submergence, diffuser density, and blower type. Water Sci. Technol. 1998, 38, 1-6. (16) Standard Methods for the Examination of Water and Wastewater, 19th ed.; American Public Health Association (APHA): Washington, DC, 1995. (17) Vogelaar, J. C.; Klapwijk, T. A.; van Lier, J. B.; Rulkens, W. H. Temperature effects on the oxygen transfer rate between 20 and 55 °C. Water Res. 2000, 34, 1037-1041.

Received for review May 5, 2003 Revised manuscript received September 30, 2003 Accepted October 1, 2003 IE030396Y