1995-oxygen mass-transfer fundamentals of surface aerators

2644 Ind. Eng. Chem. Res. 1995,34, 2644-2654

Oxygen Mass Transfer Fundamentals of Surface Aerators

John R. McWhirter,” Jia-Ming ChernJ and Joseph C. Huttefi Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802

The current state-of-the-art oxygen mass transfer analysis for surface aerators is essentially limited to the first-order, exponential model employed in the ASCE Standard for the Measure- ment of Oxygen Transfer in Clean Water. This simple model has been used for several decades to characterize the oxygen mass transfer performance of surface aerators as well as many other types of aerators. This study develops a more fundamentally rigorous oxygen mass transfer model for surface aerators which provides a more physically realistic description of the actual oxygen transfer mechanisms. This new oxygen mass transfer model separates the oxygen transfer process into a liquid spray mass transfer zone and a surface reaeration mass transfer zone. The model independently analyzes the oxygen transfer process within these two distinctively separate zones and provides the methodology and techniques for quantitatively determining the oxygen transfer rate within each of these important, but fundamentally different, oxygen mass transfer zones.

Background and Introduction The use of surface aerators as oxygen transfer devices

in biological wastewater treatment systems has been commonplace for at least several decades. Surface aerators are a popular choice of aeration system because of their inherent simplicity and reliability and their competitive rate of oxygen transfer per unit of power input under actual mixed-liquor aeration conditions. In spite of their widespread use, however, little progress seems to have been made in developing a basic under- standing of the oxygen transfer mechanisms and result- ing performance characteristics of surface aerators.

The oxygen mass transfer model which has been commonly employed for many years in the analysis of surface aerators using the standard unsteady state reaeration test is as follows:

If CL* and kLa are assumed to be constants for any given set of operating conditions, then eq 1 can be integrated to yield the following very familiar expression:

c,* - c, c,* - c, In = -k,at

There appear, however, to be primarily two techniques which are currently being used in the industry for the evaluation of surface aerators using eq 2.

The ASCE Standard Method for the Measurement of Oxygen Transfer in Clean Water (ASCE Standard, 1984) uses eq 2 in the following form

(3)

where C,* has been substituted for CL* and is defined as the “saturation” or “steady state” dissolved oxygen (DO) level for the bulk liquid at the particular test

C, = C,* - (C,* - C,) exp(-k,at)

’ Present address: Department of Chemical Engineering,

‘ Present address: Argonne National Laboratory, Argonne, Tatung Institute of Technology, Taipei, Taiwan.

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0888-5885/95/2634-26~4~Q9.QQ/Q

conditions in m a . The ASCE Standard procedure then uses a nonlinear regression analysis of the experimental CL versus time data to obtain the best statistical fit of the experimental data to eq 3 (Chapra and Canale, 1989). In this way, the values of k ~ a , C,*, and CO are determined purely from a statistical analysis of the data to give the best possible fit to eq 3. As a consequence, the ASCE Standard produces a strictly empirical set of correlation parameters as defined by eq 3.

The other interpretation of eq 2 which has been used for many years and is still apparently in widespread use for surface aerators is to fix the value of CL* at the surface conditions of the test (barometric pressure of the air and bulk liquid temperature) and to determine the value of km from a best fit, straight line semilogarithmic plot of ln(CL* - CL) versus time. The slope of such a straight line, semilogarithmic plot of ln(CL* - CL) versus time is equal to - k ~ a .

The pros and cons of the above two interpretations of the simple model equation (eq 1) have been argued at length in the literature over the past several decades or more, but both techniques still appear to be in widespread use. The purpose of this paper is not to become embroiled in this controversy but rather to develop a new and improved model for oxygen transfer with surface aerators which is a more meaningful and physically realistic description of the actual oxygen mass transfer mechanisms which occur with surface aerators.

Inherent Assumptions Embodied in the Simplified Model for Oxygen Mass Transfer

The use of eqs 1-3 to characterize the oxygen mass transfer performance of surface aeration systems implies a number of simplifying assumptions which re- quire critical examination relative to the actual mass transfer process involved. The primary assumptions inherently embodied in eqs 1-3 are as follows: (a) The bulk test liquid under aeration is completely mixed (of a uniform DO concentration throughout) at all times. (b) All oxygen mass transfer to the entire test tank liquid occurs at a liquid phase DO concentration driving force of (CL* - CL) or (C,* - CL) throughout the test period. (c) A single and constant value of CL* or C,* is adequately representative of the equilibrium DO concentration for liquid phase oxygen mass transfer for the

0 1995 American Chemical Society

Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2646 Liquid Spray Zone SurfaceReacrationZcnc entire aeration system. (d) A single value of kLu is a

meaningful representation of the total oxygen transfer process. (e) The oxygen transfer process is predomi- nately liquid phase mass transfer controlled, and the gas phase resistance to transfer can be ignored. (f) Other test condition environmental factors such as the temperature and humidity of the atmospheric air do not affect the oxygen mass transfer process and can be ignored. (g) The mass transfer of all gaseous components other than oxygen (including nitrogen and water vapor) have a negligible impact on the oxygen mass transfer process.

The assumption of a liquid phase mass transfer controlled process is entirely appropriate since oxygen is a very sparingly soluble gas in water and, hence, essentially all of the resistance to mass transfer resides in the liquid phase. The gas-liquid mass transfer of all sparingly soluble gases in water is predominantly liquid phase mass transfer controlled (Treybal, 1980).

The complete mixing or uniform DO assumption for the bulk test tank liquid under aeration requires particularly careful consideration for surface aerators. This assumption implies that a relatively high rate of liquid flow and mixing exists within the bulk liquid phase relative to the overall rate of oxygen mass transfer which essentially all occurs at or near the liquid surface with surface aerators. The complete mixing assumption is much more easily realized with diffused- air aeration systems where the oxygen transfer occurs throughout the bulk liquid phase and therefore makes the mixing task much easier. This assumption is more closely approximated as the bulk liquid DO level increases and the rate of oxygen mass transfer decreases during the unsteady state reaeration test. Multiple point sampling in the bulk test tank liquid does show some degree of DO variation in most surface aerator tests, but the complete mixing assumption is still routinely applied, essentially of necessity. Significant DO level gradients in the immediate vicinity of the surface zone could be a problem worthy of further investigation with surface aeration systems in particular (McWhirter, 1965).

The most important and serious limitations involved in eqs 1-3, however, are the implicit assumptions that all of the oxygen mass transfer occurs a t a liquid phase driving force of (CL* - CL) or (C,* - CL) and that a single and constant value of CL* or C,* is representative of the equilibrium DO concentration for the entire oxygen mass transfer process. Other authors have also pondered the impact of these assumptions (Brown and Baillard, 1982; McWhirter and Hutter, 1989) for various types of aeration systems. Unfortunately, these assumptions are not realistic for any type of aeration system including surface aeration systems and result in a considerable oversimplification of the actual oxygen mass transfer process. These assumptions also imply that a single mass transfer coefficient, k ~ u , is adequate to describe the overall oxygen transfer process, and as will be seen, this is clearly not the case. As a result of these simplifying assumptions, eqs 1-3 become little more than strictly empirical correlations of the oxygen transfer process.

The assumption that the other test condition environmental factors such as the temperature and humidity of the atmospheric air do not affect the oxygen transfer process must also be re-examined in the case of surface aerators. Surface aerators involve the simultaneous transfer of heat and water vapor to or from the

t Bulk Liquid

Figure 1. Schematic diagram of surface aerator mass transfer zones.

atmospheric air a t a rate which is dependent upon the temperature difference between the air and bulk liquid and the relative humidity of the air. As a consequence the air temperature and relative humidity can be important environmental factors influencing the overall oxygen transfer process for surface aerators. The effect of these factors and their impact will be discussed in more depth later.

The transfer of gaseous components other than water vapor will have a negligible impact on the oxygen transfer process for surface aerators as it does for most other types of aeration systems when using atmospheric air as the source of oxygen. Operation of surface aerators with high-purity oxygen gas in enclosed aeration tanks, however, requires consideration of the rates of nitrogen, carbon dioxide, and argon transfer as well as oxygen transfer (McWhirter, 1978; Stenstrom, et al., 1989).

Development of a New Oxygen Mass Transfer Model for Surface Aerators

Improved oxygen mass transfer modeling for surface aeration systems must first of all recognize that there are two fundamentally different mechanisms of oxygen transfer involved with surface aerators. Those two distinctly different mechanisms or zones of oxygen mass transfer are created by all generic types of mechanical surface aerators. These two mass transfer zones are: (1) the liquid spray mass transfer zone created in the immediate air space surrounding the periphery of the surface aeration impeller and (2) the bulk liquid surface reaeration mass transfer zone.

These two mass transfer zones involve basically different gas-liquid contacting mechanisms for oxygen transfer and are schematically identified in simplified form in Figure 1. Each of these mass transfer zones must be separately analyzed relative to the governing relationships for the rate of oxygen transfer within each zone. The existence of the liquid spray mass transfer zone has been previously identified in the literature (Eckenfelder and Ford, 1967) but little was done to characterize or quantify its importance.

2646 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995

L m i d Spray Trajeztory

+ BukLiguid CL

Figure 2. Detailed schematic diagram of a surface aerator liquid spray mass transfer zone.

Liquid Spray Mass Transfer Zone

The visual appearance of the operation of a surface aerator is predominantly determined by the liquid spray zone at the periphery of the surface aeration impeller. The high-speed rotation of the surface aerator impeller at the free liquid surface physically accelerates and propels or sprays a relatively large volumetric flow rate of liquid into the air and disperses this liquid into “droplets” or “liquid globules” in the atmospheric air. These liquid droplets or globules are also propelled through the air at a relatively high velocity. In a nominal 74.57 kW surface aerator, these liquid droplets or globules are propelled into the air to a height of up to several feet above the liquid surface and are also propelled outward to a distance of about 4.88 m beyond the periphery of the aerator impeller before the droplets re-impinge on the surface of the liquid and re-enter the bulk liquid in the aeration tank. In this liquid spray mass transfer zone, the atmospheric air is the continuous phase and the sprayed liquid droplets are the dispersed or discontinuous phase in the interphase mass transfer process.

The liquid spray mass transfer zone can be reasonably characterized and modeled as a single-stage gas-liquid contacting zone wherein the liquid is dispersed into a virtually infinite, continuous gas phase of constant atmospheric air composition. The liquid spray which flows through this contacting zone travels in essentially true plug-flow fashion as the liquid droplets traverse their flight path from the tip of the aerator impeller t o the point of re-impingement on the tank liquid surface. The liquid spray zone can then be modeled as a single- stage completely mixed gas phase of constant atmospheric air composition with plug flow of dispersed liquid droplets or globules through the constant composition gas phase. This model of the liquid spray mass transfer zone is schematically shown in simplified form in more detail in Figure 2.

For the liquid droplets traversing through the liquid spray zone we can write the following unsteady state oxygen mass balance equation:

(4)

Equation 4 assumes that the individual liquid droplets or globules are well mixed and of a uniform bulk liquid DO level at any time, tf, during their flight through the atmospheric air. Equation 4 also assumes that there is no back mixing of the droplets or globules as they traverse their flight path through the air which, of course, should be a very good assumption. If the values Of v d , ,$lad, and c d * are all assumed to be constant, then eq 4 can be integrated as follows:

The DO level of the liquid droplets at the inlet to the spray zone at any instant of time is equal to the completely-mixed, bulk liquid DO level in the tank at that time, CL. The DO level of the spray droplets at the exit of the liquid spray mass transfer zone is equal to Cd’, which is the average DO level of the droplets or globules just before they re-impinge on the liquid surface of the tank and re-enter the bulk liquid phase. Solving eq 5 for c d ’ we obtain

It should be noted that eqs 4 and 6 are very similar in form to eqs 1-3. The definition of the parameters in eqs 4-6, however, is very specific to the liquid spray mass transfer zone, and these equations represent a very meaningful description of the actual oxygen mass transfer process in this important, specific mass transfer zone of surface aerators. In contrast, eqs 1-3 are not basic or meaningfully defined mass transfer rate equations and do not represent a realistic description of the overall oxygen mass transfer process for surface aerators. From eq 6 it is seen that c d ’ exponentially approaches the value of c d * as the quantity (klad t ’ f ld) increases. Thus, as t’f or k l a d increases or v d decreases, the value of c d ’ approaches c d * . The fractional approach of c d ’ to c d * can then be defined as the “Mur- phree” contacting efficiency of the liquid spray mass transfer zone as is commonly done in many types of gas-liquid mass transfer operations (King, 1980). Re- arrangement of eq 5 gives the following expression for the fractional approach to equilibrium of the droplets in the liquid spray mass transfer zone.

The value of E m d in eq 7 can vary between the limits of 0.0 and 1.0 with a value of 1.0 representing the theoretical upper limit of complete equilibrium of the droplets with the atmospheric air at an average DO level equal to c d * . This would correspond to the value of the term in parentheses in the exponent in eq 7 being very large which means the gas-liquid contacting is very efficient.

The value of c d * in eqs 4-7 also requires careful analysis and consideration. One’s initial reaction might be to assume that c d * should be evaluated at the bulk liquid temperature in the aeration tank. Upon further reflection, however, it must be remembered that a

Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2647

complex simultaneous heat and mass transfer process involving mass transfer of both water vapor and oxygen and heat transfer is occurring between the sprayed liquid droplets or globules and the atmospheric air in the liquid spray mass transfer zone. For the more general case in which the air temperature is different than the temperature of the bulk liquid in the tank, and also that in which the humidity of the air is less than saturation, there is a rapid rate of heat transfer and water vapor evaporation to or from the spray droplets to the atmospheric air in addition to the transfer of oxygen to the spray droplets. The heat transfer coefficient between the droplet surfaces and the atmospheric air will also be quite large because of the high relative velocity of the droplets through the virtually infinite sink of atmospheric air of constant temperature, humidity, and oxygen composition. Under these conditions it is reasoned that the outer surface of the droplets will immediately become equal to the wet-bulb temperature of the atmospheric air. If, for example, the droplets were to remain in the air for a long enough period of time (about 15-30 s) the entire temperature of the droplet would come to the wet-bulb temperature of the air. This phenomenon is the underlying basis of wet- bulb thermometry. Because of the extremely short duration of the flight time of the droplets, however (about 1 s), the bulk average temperature of the droplets will not normally change significantly. The liquid within the individual droplets is also in rapid motion due to the high velocity with which they are propelled through the air. The liquid surface of the droplets is also rapidly changing, but the outer surface layer of the droplets will almost instantaneously become equal to and remain at the wet-bulb temperature of the air. Thus, it is the wet-bulb temperature of the atmospheric air which should be used to determine the value of c d * for oxygen transfer into the spray droplets.

Therefore, depending upon the environmental conditions of the atmospheric air, namely its temperature relative to the bulk liquid temperature and its relative humidity, the atmospheric air conditions can have a significant impact on the value of C d * and hence the rate of oxygen transfer to the droplets in the liquid spray mass transfer zone. It is felt that eqs 4-7 provide as discussed above the necessary theoretical framework for the proper evaluation and prediction of the impact of the atmospheric air conditions on the oxygen transfer performance of surface aerators.

The basis for evaluating c d * at the wet-bulb temperature of the atmospheric air is primarily the above qualitative, theoretical arguments as far as the present paper is concerned. A comprehensive experimental and quantitative theoretical program has recently been concluded, however, which unequivocally establishes the wet-bulb temperature of the atmospheric air as the correct basis for the value of c d * in the liquid spray mass transfer zone (Chern, 1990). This work is beyond the scope of this paper, however, and will be presented in detail in a subsequent paper.

The value O f E m d as defined by eq 7 will also be a constant for any given surface aerator under a constant set of operating conditions. The quantity of liquid sprayed through the liquid spray mass transfer zone along with the degree of droplet dispersion and therefore the values of k l a d , t’f, and v d will all be constants for a fxed set of operating conditions. The values of these parameters and the value of E m d will, of course, also change as the operating conditions of the aerator are altered.

Table 1. Spray Zone Droplet Murphree Contacting Efficiency Data for Conventional Design, 74.57 kW Surface Aerator

Test Run 1

10 11 12 13 14

4.4 5.0 5.9 5.6 6.4 6.5 7.2 7.3 7.9 8.0 8.0 8.1 8.3 8.4

0.4 9.049 1.0 9.049 1.9 9.049 2.7 9.049 3.6 9.049 4.4 9.049 4.9 9.049 5.4 9.049 5.8 9.049 6.7 9.049 6.9 9.049 7.2 9.049 7.4 9.049 7.7 9.049

best fit value of E,

0.46 0.50 0.56 0.46 0.51 0.45 0.55 0.52 0.65 0.55 0.49 0.49 0.55 0.52

d = 0.503

The experimental measurement of E m d for a given surface aerator under a specific set of operating conditions can be accomplished by physically sampling the average liquid spray droplet DO level, Cd’, just before the droplets re-impinge upon the liquid surface, along with the usual measurement of the bulk liquid DO level, CL, during an unsteady state reaeration test. The spray droplet samples, Cd‘, can be collected in an open top container having a liquid volume of about l-L which is attached to a long rigid pole. The c d ’ samples are collected by manually placing the open top container directly into the spray umbrella just prior to its impingement on the liquid surface. The spray sample liquid can then be transferred into a standard biological oxygen demand (BOD) bottle through a small diameter piece of tygon tubing attached through the bottom of the spray sample container. The spray sample liquid is then carefully transferred by gravity into a standard BOD bottle so as to not aerate the liquid during the transfer process. The DO level, Cd’, can then be determined by the usual Winkler titration procedures (Standard Methods for the Examination of Water and Wastewater, 1985) or by use of a calibrated DO meter.

Thus knowing experimental values of Cd’ and CL at the same time during the unsteady state reaeration test period and calculating the value of C d * from the known wet-bulb temperature of the atmospheric air provides all of the information necessary to calculate experimental values O f E m d for any given surface aerator operating conditions. This has been done for a nominal 74.57 kW commercial scale surface aerator the results of which are tabulated in Tables 1 and 2 and plotted in Figures 3 and 4, respectively. Two duplicate tests were performed under the exact same operating conditions to determine the general reproducibility of this experimental measurement.

The spray zone droplet Murphree contacting efficiency data can also be conveniently correlated by rearranging eq 7 for the definition of the droplet Murphree efficiency as follows:

Equation 8 shows that a plot of c d ’ versus CL should be a straight line with a slope of (1 - E m d ) and an intercept of E&&*. The data from Tables 1 and 2 are replotted according to eq 8 in Figures 5 and 6. These figures show that a good linear correlation is achieved in both cases with the least-squares best fit of the data


Table 2. Spray Zone Droplet Murphree Contacting Efficiency Data for Conventional Design, 74.57 kW Surface Aerator

Test Run 2

time ( m i d cd' (mg/L) CL(mg/L) cd* (mg/L) Emd

0 4.3 0.4 9.049 0.45 1 4.0 1.2 9.049 0.36 2 5.1 2.4 9.049 0.41 3 5.6 2.8 9.049 0.45 4 6.4 3.3 9.049 0.54 5 6.2 4.2 9.049 0.41 6 6.9 4.8 9.049 0.49 7 7.0 5.4 9.049 0.44 8 7.4 5.8 9.049 0.49 10 7.9 6.7 9.049 0.51 11 7.8 7.0 9.049 0.39 12 8.3 7.2 9.049 0.60 13 8.3 7.4 9.049 0.55 14 8.4 7.7 9.049 0.52

best fit value of E m d = 0.439

IO F , d

1.

' I

2 t / 0 0 2 4 6 8 IO 12 14 16 18 20

Time, min Figure 3. Liquid spray mass transfer zone droplet Murphree contacting efficiency data for run 1.

O f ' ' ' . ' ' ' . ' . ' . ' . ' . ' ' 1 0 1 4 6 8 I O 17 14 16 18 20

Time, min

Figure 4. Liquid spray mass transfer zone droplet Murphree contacting efficiency data for run 2.

yielding a value of E m d equal to 0.503 for test run 1 and 0.439 for test run 2. The correlation coefficients for the linear least-squares regression lines shown in Figures 5 and 6 are 0.968 and 0.962, respectively. The 95% confidence limits on E m d for the two test runs reveal that the value of E m d lies between 0.405 and 0.530. A n average value for E m d of 0.471 for the two test runs should therefore be a good estimate.

0

4 0 2 4 6 a

CL, mg/L

Figure 5. Linear regression correlation plot of cd' vs CL for run

8 3

0 2 4 6

c , mglL Figure 6. Linear regression correlation plot of cd' vs CL for run 2.

Once the value of E,d is known, the overall oxygen transfer rate in the liquid spray mass transfer zone can be calculated as follows:

The value of Q must also be separately determined; this will be addressed in a later section of the paper below. Equation 9 thus totally defines the rate of oxygen transfer in the liquid spray mass transfer zone of a surface aerator once the values of Q and E m d are determined. The value of c d * as discussed is the equilibrium DO level at the wet-bulb temperature of the atmospheric air.

Surface Reaeration Mass Transfer Zone The surface reaeration mass transfer zone of a surface

aerator, as schematically shown in Figure 1, exists primarily outside the spray umbrella trajectory of the liquid spray mass transfer zone. The mechanism of oxygen transfer in this zone is entirely different from that in the liquid spray zone and is predominantly characterized by oxygen transfer to a highly turbulent liquid surface exposed to the atmospheric air. As the spray zone liquid impinges on the liquid surface of the tank substantial air bubble entrainment into the surface is accomplished and a "white-water" effect is produced at the periphery of the liquid spray impingement on the


be either higher or lower than CLS* depending on the specific circumstances.

Overall Oxygen Transfer Rate The overall oxygen transfer rate with surface aerators

can now be determined by summing the oxygen transfer rate from the two separate mass transfer zones discussed above. The overall oxygen transfer rate to the completely mixed bulk liquid phase in the aeration tank will then be equal to the following:

surface of the tank liquid. There is also a relatively high velocity, turbulent liquid flow across the entire surface of the aeration tank in which the oxygen transfer mechanism would be expected to be somewhat similar to that which occurs in a shallow, turbulent flowing stream. This zone also includes the oxygen transfer to the highly turbulent liquid surface beneath or under the spray umbrella. The surface reaeration mass transfer zone thus includes all oxygen transfer to the surface liquid due to bubble entrainment and contact of the highly turbulent liquid surface with the atmospheric air. The oxygen transfer rate to the turbulent liquid surface reaeration mass transfer zone can then be simply described by the following mass transfer rate expression.

(10)

As noted the value of the equilibrium DO level for oxygen transfer into the surface reaeration zone, CLS*, is determined from the atmospheric air DO equilibrium level at the temperature of the bulk liquid in the tank. This is in contrast to the atmospheric air equilibrium DO level in the liquid spray mass transfer zone which is determined at the wet-bulb temperature of the atmospheric air as discussed above. This basic difference in the value of CLS* is because of the high degree of mixing and surface renewal of the bulk liquid at the surface of the tank and the relatively low heat transfer rate to be expected between the turbulent liquid surface and the atmospheric air. The heat transfer coefficient for the high-speed liquid droplets traveling through the atmospheric air in the liquid spray mass transfer zone would be far greater than the heat transfer Coefficient between the atmospheric air and the surface of the liquid in the aeration tank.

The values of c d " and CLS* can therefore be quite different depending on the temperature of the air and the temperature of the bulk liquid and the relative humidity of the atmospheric air. Cd* and CLS* will only be the same if the temperature of the air and the water are equal and the air is saturated with water vapor at this temperature. These conditions will rarely occur, however, in real practice except for enclosed or covered aeration tanks such as are employed in high-purity oxygen activated sludge systems or indoor aeration test tanks.

Some examples of the range of difference that can be encountered between cd* and CLS* are illustrated by the following situations. Wintertime operation of an open surface aerated activated sludge aeration tank might typically involve conditions where the bulk liquid temperature under aeration is at 10 "C (50 OF), the atmospheric air temperature is at 4.4 "C (40 O F ) and the relative humidity is at 48%. Under these circumstances the wet-bulb temperature of the atmospheric air is 0.8 "C (33.5 OF). These conditions correspond to values of cd* of 14.3 mgL and CLS* of 11.3 mg/L at a barometric pressure of 760 m d g . Summertime operation of a surface aerator on the other hand might typically involve conditions where the bulk liquid temperature under aeration is at 23.9 "C (75 O F ) , the air temperature is a t 35.6 "C (96 OF), and the relative humidity is at 70%. This corresponds to a wet-bulb temperature of the atmospheric air of 30.6 "C (87 OF). This results in values O f cd* of 7.5 m& and CLS* of 8.4 m& at a barometric pressure of 760 mmHg. Thus, the relative values of cd* and CLS* can vary significantly under different environmental conditions and cd* may

OTRs, = kL&s(CLs* - CL) The first term on the right-hand side of eq 11

represents the oxygen transfer rate from the liquid spray mass transfer zone, and the second term is the oxygen transfer rate from the surface reaeration mass transfer zone. Equation 11 can be rearranged as follows:

The term (QEmdNL) in eq 12 is equivalent to an effective overall oxygen mass transfer coefficient for the liquid spray zone and, of course, has units of reciprocal hours just as the surface reaeration mass transfer coefficient, kLsas. The fundamental character and mechanism of these two effective mass transfer coefficients, however, is quite different as discussed above.

Interestingly eq 12 can be readily integrated by separation of variables as follows:

(% + kLsas) C, (13)

Integration of eq 13 then yields

* + BCLs*)) exp(-(A + B)t) (14) ('O - ("""A + B

where A = Q E m d N L and B = kLsas. It should be noticed that eq 14 is of the exact same

exponential mathematical form as the ASCE Standard model, eq 3. Comparing eqs 3 and 14 it is readily seen that

Thus, the empirically or statistically defined value of C,* in the ASCE model is a specific weighted average value of the true or actual equilibrium DO levels for oxygen transfer in the spray zone, Cd* , and the surface reaeration zone, CLS*, as shown in eq 15. The apparent or effective overall oxygen mass transfer coefficient as defined by eq 1 in the ASCE Standard model is in reality the sum of the "effective" mass transfer coefficients for


the liquid spray zone and the surface reaeration mass transfer zone as shown in eq 16.

The only unknowns in eq 14 are A, B, and CO. At first glance it might seem that a simple non-linear regression analysis of the experimental CL versus time data could be performed to statistically define the best values for A, B, and CO. Unfortunately, this cannot be done in this case, because either term on the right-hand side of eq 12 can be used to force a reasonably good statistical fit of the experimental data. Thus, a purely statistical analysis of the data does not provide a meaningful delineation of the relative magnitude of the performance parameters, QEmdNL and kLsas, in eq 12. Therefore a separate and independent method of determining the value of Q, the volumetric flow rate of liquid propelled by the surface aerator impeller through the liquid spray mass transfer zone, must be developed. Fortunately, the value of Q can be separately and independently determined from an analysis of the spray umbrella trajectory kinematics in the liquid spray zone and the overall power input to the surface aerator.

Kinematic Analysis of the Liquid Spray Zone Umbrella of Surface Aerators

A fundamentally realistic and completely rigorous analysis of the fluid mechanics of surface aerators would be extremely difficult to develop and would probably be of questionable value. Nevertheless, as shown above, we need to develop a convenient and effective way of relating Q, the volumetric flow rate of liquid propelled by the surface aerator through the liquid spray zone, to the overall aerator design parameters such as the impeller diameter, the rotational speed, and the total horsepower input. Direct experimental measurement of Q would be extremely difficult and expensive to accomplish at best. Therefore, we need a method of a priori calculating Q from consideration of basic physical principles applied to surface aerators.

This can be accomplished by consideration of the overall conservation of energy applied to a surface aerator and the measured overall power input to the aerator. Conceptually a surface aerator can be envi- sioned as impeller blades rotating in the free liquid surface of a relatively large body of water wherein the aerator impeller blades accelerate a flow rate of liquid, Q, from a relatively low velocity a t the inlet to the impeller blades up to a relatively high velocity at the discharge from the tip of the aerator impeller blades. The flow rate of liquid Q is then discharged or propelled into the atmospheric air at a relatively high total discharge velocity, VT, from the tip of the aerator impeller blades. If we assume negligible fluid friction losses for the liquid flow across the aerator impeller blades and also that essentially all of the aerator shaft power input goes into accelerating the flow rate of liquid spray, Q, up to the discharge velocity, VT, then we can write the following equation relating the volumetric liquid flow rate discharged through the aerator liquid spray zone to the total shaft power input to the aerator impeller.

Kws = 8.8519 X (&@vT)’ (17)

Equation 17 basically assumes that the aerator impeller is 100% efficient in converting the mechanical energy input of the aerator impeller into the kinetic energy of the liquid sprayed or discharged by the impeller into the atmospheric air. The efficiency of a surface aerator

f c Y.

I

Figure 7. Simplified schematic diagram of a typical liquid spray umbrella trajectory from a conventional surface aerator.

in this sense should be expected to be much higher than that of a centrifugal pump, for example, because of the totally open and free flow operation of the surface aerator impeller blades which should result in much lower fluid frictional losses. The 100% efficiency assumption in this calculation is certainly an approxima- tion but appears to give very reasonable and useful results. Subject to the limitations of the above assumptions, eq 17 then relates Q and VT to the total shaft power input to the aerator impeller. The problem then becomes one of determining the value of VT as a function of the operating parameters and design of the aerator impeller.

Determination of Surface Aerator Discharge Velocity, VT

Fortunately, the value of VT can be calculated from measurements of the flight trajectory of the liquid spray umbrella discharged from the surface aerator blades. The liquid propelled from the tip of the aerator turbine blades will be subject to the same kinematic laws of physics as any free falling projectile. The size of the aerator droplets or globules is also such that atmospheric air frictional losses or impact on the flight trajectory of the liquid can be readily ignored. The problem is then one of determining the total discharge velocity of the liquid propelled from the tip of the aerator turbine blades from measurements of the liquid umbrella spray trajectory from the aerator.

Figure 7 shows a simplified schematic diagram (front cross-sectional view) of a typical liquid spray umbrella trajectory from a conventional surface aerator blade. The surface aerator blade typically extends vertically through the static liquid surface of the water, and liquid is propelled or discharged into the air all along the outer blade edge extending vertically above the water surface. Because water is propelled along the entire blade edge extending out of the water, the discharged liquid is spread into a band or umbrella of liquid spray. That part of the liquid spray discharged by the impeller blade just a t the liquid surface travels the shortest distance from the blade and achieves the lowest vertical height above the liquid surface. In contrast that part of the spray discharged at the top outer edge of the aerator blade will achieve the highest vertical height above the liquid surface and travel the farthest distance from the edge of the aerator blade before re-impinging on the tank liquid surface. Thus, the spray umbrella has a ‘%and” of heights and distances through which the spray liquid is propelled. This, of course, is readily apparent from visual observation of the operation of any particular type of surface aerator.

In spite of the “band or “range” of trajectories within the liquid umbrella spray pattern as discussed above, however, the total discharge velocity of the liquid spray leaving the impeller blade should be reasonably independent of the vertical height at which the spray leaves


YI I

v4 V'

Figure 8. Front cross-sectional view of a surface aerator liquid spray umbrella trajectory.

the outer edge of the impeller blade. In other words, the average spray discharge velocity should be reasonably constant from the impeller blade regardless of the vertical position of discharge along the blade tip. If this assumption is made, then the easiest way to determine the average total discharge velocity of the sprayed liquid is to measure the maximum vertical height of the spray umbrella above the static liquid surface and the maximum radial distance of discharge of the spray umbrella from the outer edge of the impeller blade. These distances are identified as Y, and R m , respectively, in Figure 7. It should also be noticed in Figure 7 that H is the vertical height of the top of the aerator impeller blade out of the surface of the water at static conditions.

Physical measurement of the value of Ym, the maximum vertical height that the spray umbrella trajectory reaches, and R,, the maximum radial distance that the spray umbrella trajectory travels from the outer edge of the aerator impeller blades, can be readily accomplished. It is important to note, however, that the values of Y, and R, are the maximum values and not the "average" values for the spray umbrella as a whole. This makes the values of Y, and R, somewhat easier to experimentally measure.

Figure 8 shows a larger scale overview cross-sectional schematic diagram of a surface aerator spray umbrella trajectory with all of the pertinent spray umbrella dimensions in relation to the radius of the surface aerator impeller itself, R. Figure 8, however, is not intended to be an exact scale drawing but rather a simplified schematic diagram. It is also interesting to note that experimental values of Ym and R, as identified in Figure 8 have been previously reported in the literature for different kinds of surface aerators, but no particular significance or use was identified for these data (Albertsson et al., 1978).

The total spray liquid discharge velocity, VT, from the aerator impeller blades can be broken down into its component velocity vectors as follows:

v,2 = v," + v,2 + voy2 (18)

The vertical velocity vector component of the spray liquid is specifically identified as the initial vertical velocity component since the vertical velocity component of the spray discharge rapidly changes with time due to the acceleration of gravity. In contrast, the values of V, and VR will be reasonably constant. The initial vertical component of the velocity vector a t discharge from the aerator blade can be calculated by the following equation from measurement of the maximum vertical height of the liquid spray umbrella trajectory as shown in Figures 7 and 8.

Straight BladeTip Design VB

V.3

Curved Swept-Back Bladelip Design

Figure 9, Projection of umbrella spray liquid velocities in the horizontal plane.

The time of flight of the spray droplets through the atmospheric air is also readily calculated from Ym as follows:

tf = p y + * E Determination of the horizontal velocity vector com-

ponents in the plane of the water surface, V, and VR, requires a somewhat more complex analysis which also depends on the exact design configuration of the aerator impeller blade tip (Chern, 1990). A detailed analysis of these relationships is beyond the scope of the current paper but will be presented in detail in a subsequent paper. Figure 9 shows the horizontal velocity vector components for both a straight blade tip design and a curved, swept-back blade tip design. In the case of the straight blade tip design configuration, the following relationships apply.

VR=E[- l +",l -(e)) v t ' 2 112 ] (22) t;

For the curved, swept-back blade tip design shown in Figure 9, the following somewhat more cumbersome relationships apply.

v,2 = vO: + v," + vB2 - 2v$,vB sin e (23)

R cos 8 + VB = V, sin 8 - - t/

Once the individual velocity vector components have been determined as shown above, the total discharge velocity, VT , can be calculated from eqs 18 or 23 as appropriate followed by calculation of Q from eq 17.


Table 3. Summary of Full-Scale Surface Aerator Test Conditions and Performance Data Using the New Mass Transfer Model

test conditions and performance parameters test run 1 test run 2

tank area (m2) tank depth (m) liquid volume (L) aerator radius (cm) aerator blade curvature angle, 0 (deg) aerator rotational speed (rpm) aerator power input (kW) bulk liquid temperature ("C) air wet bulb temperature ("C) barometric pressure (cmHg)

C " spray trajectory radius, R, (m) maximum height of spray trajectory, Y m (m) E m d (dimensionless)

Q (LW

c d *

LS

VT ( d S )

Now that the values of both Q and E m d are known for the liquid spray mass transfer zone, the value of A or QEmdNL in eq 14 is also known, and a nonlinear regression analysis of the CL versus time data can be performed to obtain the "best fit" values of B or ( K L S U S ) and CO in eq 14. Thus definitive values of k ~ s u s and CO can be determined from the statistical correlation with all of the other model parameters (Q, E m d , Cd*, and CLS*) being determined from independent experimental measurements and calculations and basic equilibrium considerations.

Analysis of Full-scale Surface Aerator Performance Using the New Oxygen Mass Transfer Model

The new surface aerator oxygen mass transfer model was first applied to the analysis of two replicate test runs of a conventional design, 74.6 kW surface aerator operating in a large indoor test basin. The detailed experimental test procedures and techniques used were essentially those specified by the ASCE Standard Method (ASCE Standard, 1984; Boyle, 1979) using the normal unsteady state reaeration testing procedure. A total of five bulk liquid DO sample points were employed of which two were pumped liquid samples that were titrated using the standard Winkler procedures (Stan- dard Methods, 1985) and three were determined from in situ DO probes. One set of liquid spray samples was collected for each test run to obtain the values of Cd' from which the spray zone Murphree contacting efficiency determinations were made as shown in Tables 1 and 2 and Figures 3-6. A summary of the overall test conditions and the key performance parameters determined from the new oxygen mass transfer model are provided in Table 3.

The maximum height of the aerator liquid spray umbrella trajectory of 0.61 m (Ym) along with the spray umbrella trajectory radius of 4.88 m (R,) corresponds to a total discharge velocity of 6.92 d s for the curved, swept-back aerator blade tip configuration tested where the value of 8 was 20". The value of H for this aerator test was 7.62 cm.

This results in a calculated value of Q of 191 500 Umin for the shaft power input of 76.3 kW. The particular surface aerator tested was also fitted with a 2.13 m diameter draft tube in which an average upward velocity of 0.91 d s was measured during these test runs. This average velocity was independently measured using both a Teledyne-Gurley velocity meter and

15.24 m x 18.29 m 7.68 7.68

15.24m x 18.29 m

2 139 000 127 20 48 76.66 19.0 20.0 75.64 9.05 9.23 4.88 0.61 0.503 6.92 11 500 000

2 139 000 127 20 48 76.66 19.4 20.0 75.64 9.05 9.16 4.88 0.61 0.439 6.92 11 500 000

Table 4. ASCE Standard Model Parameters for Full-scale Surface Aerator Test Runs (Determined from Tank Average CL versus Time Data)

best fit estimate standard deviation (%)

parameter r u n 1 run2 r u n 1 run 2

CO (mgiL) 0.148 0.347 67.8 30.9 C,* (mgiL) 9.73 10.15 3.6 4.5 kLa (h-l) 6.71 6.05 7.3 8.8 SOTR ((kg 02)/h) 140.5 132.04 SAE ((kg 02)KkW h)) 1.83 1.72

a Marsh-McBirney velocity probe. Both velocity meters were located at a distance of two-thirds of the radius from the wall of the draft tube which would be expected to be fairly representative of the average velocity for turbulent flow within the draft tube. This velocity corresponds to an average flow rate up the draft tube of 196 000 Umin which is in quite good agreement with the overall calculated value of Q determined from the liquid spray umbrella trajectory and aerator power measurements.

It should also be noted in Table 3 that the values of c d " and CLS* are quite close. This is a direct consequence of the specific atmospheric air conditions that existed within the indoor test tank facility. In such a facility the temperature of the air is usually quite close to that of the water and the air also has a high relative humidity due to the indoor operation of the aerator. Under these unique circumstances, cd* and CLS* will be essentially equal; this will not usually be the case for normal outdoor operation of surface aerators.

The bulk liquid DO level versus time data for the two test runs were analyzed using both the ASCE model and the new oxygen mass transfer model to determine the overall SOTR and SAE performance levels for the aerator. The values of CO, C,*, and k ~ a for the ASCE Standard model are given in Table 4 along with the standard deviation for these values. It must be noted, however, that these results were calculated from the tank average values of CL versus time data as opposed to the recommended ASCE procedure of determining an SOTR value for each sample point and averaging them. The SOTR values determined from both procedures, however, are very close for these tests.

The values of k ~ s a s and CO for the new mass transfer model are summarized in Table 5 along with their corresponding standard deviations. As shown, there is a comparable if not better fit of the data with the new mass transfer model than with the ASCE Standard model even though the new model is far more rigorous


within the liquid spray mass transfer zone. This would be the case for the standard conditions as defined above for the new model with the air temperature being equal to the bulk liquid temperature and the air being at 100% relative humidity. If the wet-bulb temperature of the air, however, is significantly different than the bulk liquid temperature, then the DO level driving force for oxygen transfer will be different within the two mass transfer zones which may either further increase or decrease the relative oxygen transfer rates between the two mass transfer zones.

The primary utility and strength of the new oxygen mass transfer model will be its ability to more accurately assess the impact of changes in the air environmental conditions on the performance of surface aerators and to effectively translate unsteady state reaeration test results into performance under realistic process design conditions. A more thorough under- standing of the basic performance parameters for surface aerators (Q, E m d , and k ~ s a s ) should also provide improved insight into the scale-up and optimization of surface aerator performance and design.

Table 5. New Oxygen Mass Transfer Model Parameters for Full-scale Surface Aerator Test Runs (Determined from Tank Average CL versus Time Data)

best tit estimate standard deviation (%)

parameter r u n l run2 r u n l run 2 CO (mg/L) 0.052 0.202 186.0 57.0 k ~ s a s W1) 4.84 4.95 2.93 3.43 QEmd/VL (h-') 2.79 2.51 SOTR ((kg O&h) 146.0 143.6 SAE ((kg Oz)/(kW h)) 1.90 1.87

and stringently defined and has one less correlation parameter or degree of freedom. The difference in the values of the various parameters for the two models, of course, has no physical significance since the models themselves are so fundamentally different in nature. It is interesting to note, however, that the values of Cm* for the ASCE Standard model are significantly different in comparison to the values of cd* and CLS* in the new model which are determined from basic gas-liquid equilibrium considerations. The value of c,* versus cd* and CLS* would probably have been closer, however, if more experimental CL versus time data had been taken closer to the equilibrium DO level for the case of the ASCE model. The need for this additional experimental data close to the saturation value of Cm* is not nearly as crucial with the new mass transfer model, however, since cd* and CLS* are not correlation parameters but rather are calculated from basic equilibrium considerations.

Calculation of the SOTR and SAE values using the new mass transfer model requires the additional speci- fication of standard conditions for the atmospheric air temperature and relatively humidity in addition to the usual standard conditions of a bulk liquid water temperature of 20 "C and a barometric pressure of 1.0 atm. The SOTR and SAE values in Table 5 were calculated on the basis of an atmospheric air temperature of 20 "C and 100% relative humidity. As stated above, this corresponds to the special case of cd* being equal to CLS*, which of course, will not normally be the case.

Comparison of the SOTR and SAE values in Tables 4 and 5 shows that the ASCE model and the new oxygen mass transfer model give essentially the same values as would be expected. This is due to the fact that both models use the same CL versus time data and both models give a good statistical fit of the experimental data as discussed previously. This is where the similar- ity between the two models, however, ends. The new mass transfer model provides considerably more insight into the actual oxygen mass transfer process and key performance parameters of the aerator (Q, E m d , and k ~ s a s ) . The new model also has the capability to accurately predict the impact of changes in the atmospheric air environmental conditions on the performance of surface aerators, which cannot be done at all by the existing simplified models.

The data in Table 5 for the new oxygen mass transfer model also quantitatively reveal for the first time ever the relative rates of oxygen transfer within the liquid spray mass transfer zone and the surface reaeration mass transfer zone for a surface aerator. As shown in Table 5, the values for kLsas are 73%-97% percent higher than the values of QEmdNL. This means that with a comparable liquid phase DO level driving force for oxygen transfer within each mass transfer zone, about 63%-66% of the overall oxygen transfer will occur within the surface reaeration mass transfer zone and about 34%-37% of the overall oxygen transfer will occur

Conclusions A new and more fundamentally rigorous oxygen mass

transfer model for the evaluation and design of surface aerators has been developed and demonstrated using full-scale surface aerator test results. The new model analyzes the oxygen transfer performance of surface aerators in terms of separate liquid spray and surface reaeration mass transfer zones. The new model also provides the necessary theoretical framework for improved evaluation and prediction of the impact of the atmospheric air temperature and humidity on the oxygen transfer performance of surface aerators. The new oxygen mass transfer model should also provide new insights into the oxygen transfer characteristics, scale-up, and optimization of surface aerator design.

Acknowledgment This research work was performed as part of a larger

project under a Ben Franklin Partnership Program Research and Development Challenge Grant of the Commonwealth of Pennsylvania. The project cospon- sors were Philadelphia Mixers Corporation and Lotepro Corporation, whose financial support and cooperation are gratefully acknowledged along with those of the Advanced Technology Center of Central and Northern Pennsylvania at Penn State.

Nomenclature A = constant defined in eq 14 (lh) B = constant defined in eq 14 (lh) cd = average liquid DO level of a droplet or globule at any

time, tf, during time of flight through the liquid spray mass transfer zone ( m a )

c d ' = average DO level of the spray liquid immediately prior to re-entry into the bulk tank liquid (mg/L)

c d * = equilibrium DO level at the surface of a spray droplet or liquid globule in the liquid spray mass transfer zone (mg/L)

CL = bulk tank test liquid DO level (mg/L) CL* = equilibrium DO level for oxygen transfer to the bulk

liquid at test conditions (mg/L) CLS* = equilibrium DO level for surface reaeration zone;

surface liquid DO level in equilibrium with atmospheric air at the bulk liquid temperature (mg/L)


CO = initial dissolved oxygen levels (mg/L) C,* = “saturation” or “steady state” DO level for the bulk

test tank liquid at the particular test conditions ( m a ) E,d = spray droplet Murphree contacting efficiency of the

liquid spray mass transfer zone, dimensionless g = acceleration of gravity ( d s 2 ) H = vertical height of top of aerator blade above the static

liquid surface (m) k ~ a = apparent or effective overall volumetric liquid phase

oxygen mass transfer coefficient (lh) klad = individual droplet or globule overall liquid phase

mass transfer coefficient (Us) kL&s = surface reaeration zone mass transfer coefficient (L/h)

k ~ s a s = the surface reaeration zone volumetric mass transfer coefficient (lh)

KWs = total aerator shaft power input (kW) N = rotational speed (reds) OTR~F = oxygen transfer rate in the surface reaeration

mass transfer zone (mgh) OTRsp = oxygen transfer rate in the liquid spray mass zone

(mg/h) Q = the volumetric flow rate of liquid sprayed through the

liquid spray mass transfer zone (L/h) R = radius of the surface aerator impeller (m) R, = the maximum radial distance that the liquid spray

umbrella travels from the outer edge of the aerator impeller blades (m)

R , = R + R , (m) SAE = standard aeration efficiency ((kg Oe)/(kW h)) SOTR = standard oxygen transfer rate at standard condi-

t = time (h) t f = time during flight of droplet or globule through liquid

t f = time immediately prior to liquid spray re-entry into

VB = velocity vector component along blade tip direction

vd = volume of liquid droplet or globule (L) VL = volume of the liquid in the aeration tank (L) V, = initial vertical velocity vector component from aerator

blade tip ( d s ) VR = radial velocity vector component from the aerator

blade tip ( d s ) VT = total discharge velocity of liquid propelled from the

tips of the surface aerator blades ( d s ) V, = velocity vector component tangential to the aerator

blade tip at right angles to the radial direction ( d s ) V’ = velocity defined by eq 21) ( d s ) V, = maximum vertical height of the spray umbrella

tions of 20 “C and 1 atm (kg O h )

spray mass transfer zone (s)

bulk tank liquid (s)

as shown in Figure 9 ( d s )

trajectory above the static liquid surface (m)

Q = density of water (g/cm3) 8 = blade tip angle of curvature to the radial direction as

shown in Figure 9 (deg)

Literature Cited Albertsson, J. G.; Grunert, W. E.; Scaccia, C.; Oxygenation

Equipment and Reactor Design for UNOX Systems. In The Use of High Purity Oxygen in The Activated Sludge Process; McWhirt- er, J. R., Ed.; CRC Press: Boca Raton, FL, 1978; Vol. 2, Chapter 1.

ASCE Standard. Measurement of Oxygen Transfer In Water; American: New York, July, 1984.

Boyle, W. C., Ed. Proceedings: Workshop Journal on Oxygen Transfer Standard, EPA 600/9-78-021; Municipal Environmen- tal Research Laboratory: Cincinnati, OH, USEPA, 1979; Vol. 41.

Brown, L. C.; Baillad, C. R. Modeling and Interpreting Oxygen Transfer Data. J . Environ. Eng. Diu. (Am. Soc. Civ. Eng.) 1982, 108, 607-618.

Chapra, S. C.; Canale, R. P. Numerical Methods for Engineers; McGraw-Hill: New York, 1989; pp 358-361.

Chern, J. M Fundamental Analysis of the Oxygen Mass Transfer Performance of Surface Aerators. Ph.D. Dissertation, The Pennsylvania State University, 1990.

Eckenfelder, W. W.; Ford, D. L. Engineering Aspects of Surface Aeration Design. Purdue Industrial Waste Conference Proceed- ings, 1967.

King, C. J. Separation Processes; McGraw-Hill Book, Co.: London, 1980; Chapter 3, pp 131-134.

McWhirter, J. R. Fundamental Aspects of Surface Aerator Per- formance and Design. Purdue Industrial Waste Conference Proceedings, 1965; pp 75-92.

McWhirter, J. R. Oxygenation System Mass Transfer Design Considerations. In The Use of High Purity Oxygen in The Activated Sludge Process; McWhirter, J. R., Ed.; CRC Press: Boca Raton, FL, 1978; Vol. 1, Chapter 9.

McWhirter, J. R.; Hutter, J . C. Improved Oxygen Mass Transfer Modeling for DiffusedSubsurface Aeration Systems. AIChE J .

Standard Methods for the Examinations of Water and Wastewater; American Public Health Association: Washington, DC, 1985; pp 413-426.

Stenstrom, M. K.; Kido, W.; Shanks, R. F.: Mulkenin, M. Estimat- ing Oxygen Transfer Capacity of a Full-Scale Pure Oxygen Activated Sludge Plant. WPCF J . 1989, 61 (2), 208-220.

Treybal, R. E. Mass Transfer Operations, 3rd ed.; McGraw-Hill: 1980; New York, Chapter 5, pp 104-111.

Received for review November 10, 1994 Revised manuscript received February 22, 1995

Accepted March 13, 1995*

I39406557

1989,35 (91, 1527-1534.

* Abstract published in Advance ACS Abstracts, July 1, 1995.

1995-oxygen mass-transfer fundamentals of surface aerators

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