Ind. Eng. Chem. Res. 1997, 36, 5447-5453
5447
GENERAL RESEARCH Oxygen Transfer Modeling of Diffused Aeration Systems Jia-Ming Chern* and Cheng-Fu Yu Department of Chemical Engineering, Tatung Institute of Technology, 40 Chungshan North Road, 3rd Sec., Taipei, Taiwan 10451, Republic of China
A new oxygen mass-transfer model with an analytical solution was used to analyze the unsteadystate reaeration data of diffused aeration systems in order to find the volumetric mass-transfer coefficients that can be used to estimate the emission rate of volatile organic compounds from the same aeration systems. Two series of unsteady-state reaeration tests in 500-L and 4-L tanks were performed to validate the model. The air flow rate was varied from 2.25 × 10-4 to 7.67 × 10-4 normal m3/s in the 500-L tank and from 2.00 × 10-5 to 8.67 × 10-5 normal m3/s in the 4-L tank. The water temperature was varied from 288.5 to 294.1 K in the 500-L tank and from 299.5 to 304.3 K in the 4-L tank. Both the ASCE and the new oxygen mass-transfer models were used to analyze the unsteady-state reaeration data. An empirical equation was used to successfully correlate the volumetric mass-transfer coefficients. Introduction The activated sludge process is an aerobic, biological wastewater treatment method that uses the metabolic reactions of microorganisms to produce an improved effluent quality by removing substances that have a biological oxygen demand (WPCF, 1987). In the activated sludge process, the aeration system represents the most energy-intensive operation in the wastewater treatment process. Therefore, many different types of aeration system designs have been developed over the years in an effort to improve the energy efficiency of aeration. Because the measurement of oxygen transfer rate is the key step for aeration system evaluation and design and the fact that the design parameters obtained from the measurement are strongly affected by the experimental conditions and procedures and even the techniques employed in analyzing the experimental data (Brown and Baillod, 1982), 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. The standard describes in detail the experimental apparatus and methods, procedures, data analysis, and aeration system evaluation criteria (ASCE, 1984; Boyle, 1979, 1985). The oxygen mass-transfer model used in the ASCE standard, although it can statistically fit reaeration data quite well, has little physical significance and therefore cannot be used for scale-up design. It involves several unreasonable assumptions that were critically examined by McWhirter and Hutter (1989). A more fundamentally rigorous oxygen mass-transfer model for diffused aeration systems was developed (McWhirter and Hutter, 1989). The new model recognized that there existed two different mass-transfer zones in diffused aeration systems: the gas bubble zone and the surface reaeration zone. McWhirter and Hutter used a tedious numerical algorithm to solve the new oxygen mass transfer and * To whom correspondence should be addressed. E-mail:
[email protected]. Phone: 01188625925252 ext. 3487. Fax: 01188625861939. S0888-5885(97)00062-6 CCC: $14.00
reanalyzed the unsteady-state reaeration data of a fullscale diffused aeration system (Yunt and Hancuff, 1979). They found that the major part of oxygen mass-transfer occurred in the gas bubble zone and the relative portion of oxygen transfer in the two zones depended on water depth, air flow rate, and type of diffuser used. The new oxygen mass-transfer model was modified to predict the volatile organic compound (VOC) emission rate from diffused aeration systems (Chern and Yu, 1995). This paper presents an analytical solution to the new oxygen mass-transfer model and determines the volumetric mass-transfer coefficients of oxygen in the two masstransfer zones, which can be used in the near future to predict the VOC emission rate. 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:
dCO2 dt
) KLaO2(C*∞,O2 - CO2)
(1)
Assuming that KLaO2 and C*∞,O2 are constant throughout the testing period, eq 1 is integrated to yield the following expression for CO2 as a function of time:
CO2 ) C* ∞,O2 - (C* ∞,O2 - C0) exp(-KLaO2t)
(2)
A nonlinear regression analysis based on the GaussNewton method is recommended by the ASCE (1984) to fit eq 2 to the experimental data using KLaO2, C* ∞,O2, and C0 as three adjustable model parameters. The statistically determined value of KLaO2, is then adjusted to the standard conditions of 1 atm pressure and 20 °C water temperature by the following equation:
KLaT,O2 ) KLa20,O2θT-293.15
(3)
A generally accepted value of the temperature correction factor, θ, is 1.024 (Stenstrom and Gilbert, 1981). © 1997 American Chemical Society
5448 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
New Oxygen Mass-Transfer Model
2
The development of the new oxygen mass-transfer model is based on the following assumptions (McWhirter and Hutter, 1989): (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 with the 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 new model are as follows:
A
∂yO2
∂CG,O2 ) -G
∂t
∂Z
- KLBaB,O2(1 - )A(C* O2 - CO2)
AZS(1 - )
∫0
ZS
dt
KLBaB,O2(C* O2 - CO2)(1 - )A dZ +
C* O2 ) C* 1
yO2(P - Pw) y0(1 - Pw)
K1 )
dZ
(7)
with the following boundary condition: at Z ) 0, yO2 ) y0 ) 21/79 ) 0.2658. In eq 6, the gas pressure is a function of the liquid depth:
P ) P0 + Fg(1 - )(ZS - Z) Combining eqs 6-8 leads to
KLBaB,O2(1 - )A
(11)
G
a ) P0 - Pw + Fg(1 - )ZS
(12)
Fg(1 - ) 2
b)
(13)
Combining eqs 5, 6, and 9 leads to the following analytical solution:
KLBaB,O2A2 + KLSaS,O2C* O2,S
(
A1 )
The key step in developing an analytical solution is to assume that the gas-phase oxygen concentration does not vary with time. This pseudo-steady-state assumption was adopted in the previous models (Matter-Muller et al., 1981; Roberts et al., 1984a,b) and was also justified by McWhirter and Hutter (1989). Accepting the pseudo-steady-state assumption leads to the following ordinary differential equation:
KLBaB,O2(1 - )A (CO2 - C* O2) G
(10)
y0(1 - Pw)G
K2 )
(6)
Analytical Solution to the New Oxygen Mass-Transfer Model
)
KLBaB,O2(1 - )AC* 1
A1 + KLSaS,O2
+
)
KLBaB,O2A2 + KLSaS,O2C* O2,S A1 + KLSaS,O2
e-(A1+KLSaS,O2)t (14)
where
Equation 4 represents the oxygen mass balance in the gas phase, eq 5 the oxygen mass balance in the liquid phase, and eq 6 the equilibrium oxygen concentration in the tank. Note that the symbols used here are slightly different from those used by McWhirter and Hutter. Basically, McWhirter and Hutter solved the above three equations numerically and used KLBaB,O2, KLSaS,O2, and C0 as three adjustable parameters to best fit the unsteady-state reaeration data.
dyO2
1
where
C0 -
KLSaSO2(1 - )(C* O2,S - CO2)AZS (5)
x
1
CO2 ) )
2
( )
K1a2 π exp × K1b 4b
K2CO2
[erf(2ba xK b) + erf[(2ba - Z)xK b]]} (9)
(4) dCO2
{
yO2 ) e-K1(aZ-bZ ) y0 +
(8)
1 2ZS
A2 )
x
) ]{ (
a 2 π a exp K1b ZS erf xK1b + K1b 2b 2b a - ZS xK1b (15) erf 2b
[ (
[(
C* 1
)
) ]}
{1 - exp[-K1ZS(a - bZS)]} (16)
K1ZS(1 - Pw)
It is important to note that the new model seems to contain many parameters; there are actually only three independent parameters, KLBaB,O2, KLSaS,O2, and C0 which can be determined either from nonlinear regression of unsteady-state reaeration data or from the ASCE model parameters by solving the following simultaneous algebraic equations:
KLaO2 ) A1 + KLSaS,O2 C* ∞,O2 )
KLBaB,O2A2 + KLSaS,O2C* O2,S A1 + KLSaS,O2
(17) (18)
It is very interesting to find that eqs 2 and 14 are mathematically indistinguishable; i.e., they are of the same mathematical form. Therefore, the method of statistical analysis of the unsteady-state reaeration data for the ASCE model can be applied to the new model as well. Experimental Section Most of the unsteady-state reaeration tests were primarily conducted in a 500-L aeration tank which measured 0.83 m in diameter and 1.2 m in height. The schematic diagram of the experimental apparatus is shown in Figure 1. A detailed layout of the coarsebubble diffuser used can be found in Yu’s thesis (Yu, 1995). The air system was supplied by a 1 in. diameter
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5449
Figure 1. Schematic diagram of the unsteady-state reaeration test apparatus. Table 1. Summary of Unsteady-State Reaeration Test Conditions aeration tank diffuser type air flow rate, Nm3/s air temperature, K gauge pressure, atm tank diameter, m tank area, m2 tank depth, air off, m tank depth, air on, m liquid volume, m3 barometric pressure, atm water temperature, K
500-L system coarse bubble 2.25 × 10-47.6 × 10-4 287.75-294.15 0.789-1.086 0.83 0.541 0.84 0.845-0.860 0.454 1.000-1.012 288.45-294.05
4-L system fine bubble 2.00 × 10-58.67 × 10-5 300.35-301.65 0.888-1.382 0.11 0.0095 0.369 0.372-0.383 0.00351 1.002-1.007 299.45-304.25
PVC air supply line. The air flow rate was metered by a rotameter whose measurement range was from 0 to 50 NL min-1. Air flow rates, not measured at the standard conditions of 1 atm and 25 °C, were corrected to the standard conditions (Cooper and Alley, 1986). The actual air temperature and pressure were measured by the in-line gauges. The dissolved oxygen (D.O.) level in the test tank was continuously measured by a D.O. meter (Model OXI96B). The detailed experimental test procedure and techniques used were primarily those specified by the ASCE Standard (ASCE, 1984). Results and Discussion The new oxygen transfer model for diffused aeration systems was first applied to analyze the results of a series of unsteady-state reaeration tests in the 500-L tank. Table 1 summarizes the operating conditions used for this series of reaeration tests. The water temperature was varied from 288.5 to 299.5 K, and the air flow rate was varied from 2.25 × 10-4 to 7.67 × 10-4 Nm3/s in the 500-L aeration tank. Next, a jacketed 4-L tank, equipped with a ceramic diffuser, was used to run another series of unsteady-state reaeration tests at higher water temperatures. The operating conditions used for this series of reaeration tests are also shown in Table 1. The reaeration test data for each run were first analyzed using the ASCE standard oxygen transfer model, and the associated parameters KLaO2 and C* ∞,O2 were determined. The volumetric mass-transfer coefficients in the new model, KLBaB,O2 and KLSaS,O2, were then calculated from the ASCE model parameters and the associated test conditions, including the air flow rate, water temperature, water depth, and tank cross-
Figure 2. Unsteady-state reaeration curves at 288.45 K and varying air flow rates in the 500-L tank.
Figure 3. Unsteady-state reaeration curves at 300.25 K and varying air flow rates in the 4-L tank.
sectional area. In the calculation of the volumetric mass-transfer coefficients, the gas holdup, , was calculated from the liquid depth measurements with the air on and off. Figures 2 and 3 show typical plots of the experimental dissolved oxygen concentrations versus time compared to the calculated results of the new mass-transfer model for the 500-L and 4-L tank systems, respectively. The solid curves represent the calculated data, while the dots represent the experimental ones. As would be expected from the good statistical fit of the data, the calculated and experimental data agree to well within the probable experimental error of the dissolved oxygen measurements. The calculation results of the 500-L and 4-L systems are summarized in Tables 2 and 3, respectively. The surface reaeration volumetric mass-transfer coefficient in streams of 1 ft in depth with water velocities varying from 1 to 4 ft/s was found to range from 2.5 × 10-4 to 6.4 × 10-4/s (Churchill et al., 1962; Owens et al., 1964; Thomann and Mueller, 1987). This value is quite comparable to that shown in Table 2. The bubble zone
5450 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 Table 2. Summary of the Volumetric Mass-Transfer Coefficients in the 500-L Tank System new model
ASCE model
run
Q, Nm3/s
Ww, K
KLBaB,O2, s-1
KLSaS,O2, s-1
3 C* ∞,O2, kmol/m
KLaO2, s-1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
2.25 × 10-4 2.25 × 10-4 2.25 × 10-4 2.25 × 10-4 4.00 × 10-4 4.00 × 10-4 4.00 × 10-4 6.08 × 10-4 6.08 × 10-4 6.08 × 10-4 7.67 × 10-4 7.67 × 10-4 7.67 × 10-4 5.00 × 10-4 5.00 × 10-4 6.50 × 10-4
288.45 290.65 291.35 294.05 288.45 291.85 293.65 291.35 291.85 292.25 291.35 291.85 292.95 288.45 291.35 288.45
2.06 × 10-4 2.52 × 10-4 2.84 × 10-4 2.73 × 10-4 2.97 × 10-4 4.21 × 10-4 5.13 × 10-4 5.68 × 10-4 5.46 × 10-4 6.14 × 10-4 6.41 × 10-4 6.62 × 10-4 5.87 × 10-4 4.18 × 10-4 5.20 × 10-4 4.57 × 10-4
2.37 × 10-4 2.65 × 10-4 2.53 × 10-4 2.36 × 10-4 2.92 × 10-4 3.80 × 10-4 3.38 × 10-4 5.24 × 10-4 4.63 × 10-4 4.33 × 10-4 5.79 × 10-4 5.70 × 10-4 6.28 × 10-4 3.96 × 10-4 3.30 × 10-4 4.57 × 10-4
3.40 × 10-4 3.17 × 10-4 3.10 × 10-4 2.83 × 10-4 3.42 × 10-4 3.10 × 10-4 2.94 × 10-4 3.10 × 10-4 3.05 × 10-4 2.99 × 10-4 3.10 × 10-4 3.03 × 10-4 2.94 × 10-4 3.36 × 10-4 3.42 × 10-4 3.06 × 10-4
4.82 × 10-4 4.85 × 10-4 5.20 × 10-4 4.87 × 10-4 6.22 × 10-4 7.82 × 10-4 8.31 × 10-4 1.07 × 10-4 9.84 × 10-4 1.20 × 10-4 1.21 × 10-3 1.21 × 10-3 1.21 × 10-3 8.22 × 10-4 8.43 × 10-4 9.40 × 10-4
Table 3. Summary of the Volumetric Mass-Transfer Coefficients in the 4-L Tank System new model
ASCE model
run
Q, Nm3/s
T w, K
KLBaB,O2, s-1
KLSaS,O2, s-1
3 C* ∞,O2, kmol/m
KLaO2, s-1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
3.33 × 10-5 3.33 × 10-5 3.33 × 10-5 5.00 × 10-5 5.00 × 10-5 2.00 × 10-5 2.00 × 10-5 5.83 × 10-5 5.83 × 10-5 5.83 × 10-5 4.33 × 10-5 4.33 × 10-5 4.33 × 10-5 7.67 × 10-5 6.67 × 10-5 6.67 × 10-5 8.67 × 10-5
300.25 303.05 304.25 299.45 300.25 300.25 304.25 299.45 302.65 304.25 299.45 303.05 304.25 300.25 302.65 303.75 300.25
4.78 × 10-3 5.13 × 10-3 5.36 × 10-3 6.90 × 10-3 6.52 × 10-3 2.94 × 10-3 3.90 × 10-3 7.56 × 10-3 7.38 × 10-3 7.26 × 10-3 6.78 × 10-3 6.68 × 10-3 6.73 × 10-3 7.71 × 10-3 8.23 × 10-3 9.85 × 10-3 8.32 × 10-3
4.46 × 10-3 3.82 × 10-3 4.53 × 10-3 6.01 × 10-3 5.74 × 10-3 2.13 × 10-3 3.79 × 10-3 6.37 × 10-3 6.48 × 10-3 6.35 × 10-3 4.89 × 10-3 4.52 × 10-3 5.36 × 10-3 6.53 × 10-3 6.87 × 10-3 7.28 × 10-3 8.40 × 10-3
2.56 × 10-4 2.42 × 10-4 2.34 × 10-4 2.59 × 10-4 2.61 × 10-4 2.57 × 10-4 2.32 × 10-4 2.58 × 10-4 2.48 × 10-4 2.46 × 10-4 2.54 × 10-4 2.46 × 10-4 2.40 × 10-4 2.51 × 10-4 2.45 × 10-4 2.63 × 10-4 2.59 × 10-4
9.26 × 10-3 8.94 × 10-3 9.88 × 10-3 1.29 × 10-2 1.22 × 10-2 5.04 × 10-3 7.66 × 10-3 1.39 × 10-2 1.38 × 10-2 1.22 × 10-2 1.16 × 10-2 1.12 × 10-2 1.21 × 10-2 1.50 × 10-2 1.47 × 10-2 1.67 × 10-2 1.67 × 10-2
volumetric mass-transfer coefficient to the surface reaeration zone volumetric mass-transfer coefficient ratio ranges from 0.87 to 1.52. McWhirter and Hutter (1989) found that the ratio ranges from 2 to 3 for coarse-bubble diffusers and from 5 to 8 for fine-bubble diffusers. A possible reason for the low ratio found in this study is that the aeration tank used in this study is much shallower than that used by McWhirter and Hutter (0.84 m versus 7.62 m). The effect of the water depth on the volumetric mass-transfer coefficients should be studied in more detail. As is shown in Tables 2 and 3, the volumetric masstransfer coefficients of both mass-transfer zones in the 4-L tank are greater than those in the 500-L tank. The main reason is a more efficient fine-bubble diffuser was used in the 4-L tank. Also shown in Tables 2 and 3 are the variation of the volumetric mass-transfer coefficients with the water temperature and the air flow rate. The following empirical equation was used to correlate all the test results at different water temperatures and air flow rates for a given aeration system.
KLa ) (k1 + k2Qk3)θT-293.15
(19)
where KLa is the volumetric mass-transfer coefficient, Q the feed air flow rate, and k1 to k3 are correlation parameters. Obviously, for Q ) 0, i.e., no air flow, KLBaB,O2 ) 0. This suggests that k1 ) 0 for the bubblezone volumetric mass-transfer coefficient, KLBaB,O2. In general, k1 * 0 for the surface reaeration zone volumetric mass-transfer coefficient, KLSaS,O2, and the ASCE
Table 4. Summary of the Correlation Parameters for the Volumetric Mass-Transfer Coefficients in the 500-L Tank System k1 k2 k3 θ
KLBaB,O2, s-1
KLSaS,O2, s-1
0 2.753 × 10-2 0.673 1.059
1.200 × 5.975 1.385 1.019
10-4
KLaO2, s-1 6.91 × 10-13 0.1076 0.717 1.036
Table 5. Summary of the Correlation Parameters for the Volumetric Mass-Transfer Coefficients in the 4-L Tank System k1 k2 k3 θ
KLBaB,O2, s-1
KLSaS,O2, s-1
KLaO2, s-1
0 1.433 0.619 1.027
2.31 × 10-12 3.73 0.691 1.012
2.29 × 10-11 5.185 0.640 1.010
model volumetric mass-transfer coefficient, KLaO2. This correlation equation for the volumetric mass-transfer coefficient is purely empirical in nature and tries to lump all possible factors such as changes in the masstransfer coefficient, mass-transfer area, viscosity, surface tension, diffusion coefficient, etc., into a simple mathematical form. The best-fit parameters in eq 19 are shown in Tables 4 and 5 for the 500-L and 4-L tank systems, respectively. The volumetric mass-transfer coefficients predicted by eq 19 are shown in Figures 4 and 5. As is shown in Figures 4 and 5, the predicted volumetric mass-transfer coefficients scatter around the diagonal line. This indicates that eq 19 can be used to correlate the
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5451
Figure 4. Comparison of the experimental and predicted volumetric mass-transfer coefficients in the 500-L tank system.
Figure 6. Simulated volumetric mass-transfer coefficients at varying air flow rates and water temperatures in the 500-L tank system.
Figure 5. Comparison of the experimental and predicted volumetric mass-transfer coefficients in the 4-L tank system.
volumetric mass-transfer coefficients at varying water temperatures and air flow rates satisfactorily. Although some studies showed that the volumetric mass-transfer coefficient in the ASCE model decreased with increasing water temperature (Howe, 1977; Chao et al., 1987a,b), most of the literature studies, however, showed that the volumetric mass-transfer coefficient increased with increasing water temperature (Downing and Truesdale, 1955; Elmore and West, 1961; Metzger and Dobbins, 1967; Bewtra et al., 1970; Lakin and Salzman, 1977). The average of all θ values in Tables 4 and 5 is 1.027, which is very close to 1.024, a value recommended by the ASCE standard. The effects of the air flow rate on the volumetric masstransfer coefficients in the 500-L and 4-L tank systems were simulated and shown in Figures 6 and 7, respectively. At a given water temperature, the volumetric mass-transfer coefficients in the bubble zone and the surface reaeration zone both increase with increasing air flow rate. In the bubble zone, oxygen is transferred from the moving bubbles to the stationary bulk liquid. The volumetric mass-transfer coefficient in the bubble
Figure 7. Simulated volumetric mass-transfer coefficients at varying air flow rates and water temperatures in the 4-L tank system.
zone consists of two terms, the mass-transfer coefficient, KLB, and the interfacial mass-transfer area, aB; both terms are affected by the air flow rate. As the air flow rate increases, the mass-transfer coefficients, KLB, increases and so does the mass-transfer area, aB. Due to the similarity of the mass-transfer mechanism in the bubble zone, the effect of the air flow rate on the volumetric mass-transfer coefficient is quite similar in the 500-L and 4-L tank systems, as is shown in Figures
5452 Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997
6 and 7. The volumetric mass-transfer coefficient in the surface reaeration zone also consists of two terms, the mass-transfer coefficient, KLS, and the interfacial masstransfer area, aS. For a highly turbulent surface, e.g., in the 4-L tank system, a lot of water droplets are created by the bubbling action of the air; oxygen is transferred from the atmospheric air to the water droplets. The effect of the air flow rate on the volumetric mass-transfer coefficient in this zone is therefore similar to that in the bubble zone in which oxygen is transferred from the gas bubbles to the bulk water. On the contrary, in the 500-L tank, the tank surface water was slightly aerated only. A small increase of the gas bubble rising velocity results in a significant increase of the mass-transfer area. The effect of the air flow rate on the surface zone volumetric mass-transfer coefficient is therefore more remarkable, as is shown in Figure 6. Although the ASCE model and the new model lead to mathematically indistiguishable forms of the unsteadystate D.O. concentration, these two models are fundamentally different. The ASCE standard uses an oversimplified oxygen mass-transfer model to interpret the unsteady-state reaeration data of all types of aerators, including diffused aeration systems. The model parameters resulting from the reaeration data are strongly dependent on aeration conditions and therefore cannot be used for predicting or assessing the impact of changes in operating conditions. On the contrary, the new oxygen mass-transfer model is more rigorous in nature and can be used for process optimization and scaleup. More applications of the new model will be presented in the future. Conclusions A new oxygen mass-transfer model, with an analytical solution, for diffused aeration systems has been developed for the analysis of unsteady-state reaeration data. Unlike the ASCE model which lumps the overall oxygen mass-transfer into one zone, the new oxygen masstransfer model recognizes two different mass-transfer zones: the bubble dispersion mass-transfer zone and the surface reaeration zone. Like the ASCE model, a more sophisticated yet analytical solution to the new oxygen mass-transfer model is obtained. Although both the ASCE and the new models give mathematically indistinguishable results, the new model provides more insight to the understanding of the oxygen masstransfer process. The new model has been successfully used to analyze two series of unsteady-state reaeration data. The volumetric mass-transfer coefficients in both the bubble zone and the surface reaeration zone increase with increasing water temperature or air flow rate. A simple empirical equation is proposed to account for the effects of the water temperature and the air flow rate and gives satisfactory correlation results. Acknowledgment This work was supported by the National Science Council of Taiwan, Republic of China (Grant No. NSC 82-0113-E-036-080-T). Nomenclature a ) interfacial mass-transfer area per unit volume of liquid in the ASCE model, m2/m3
aB ) interfacial mass-transfer area per unit volume of liquid in the gas bubble mass-transfer zone, m2/m3 aS ) interfacial mass-transfer area per unit volume of liquid in the surface mass-transfer zone, m2/m3 A ) cross-sectional area of the aeration tank, m2 C0 ) initial dissolved oxygen concentration at t ) 0, kmol/ m3 CG,O2 ) gas-phase oxygen concentration in the gas bubble, kmol/m3 CO2 ) dissolved oxygen concentration at time t, kmol/m3 C*1 ) equilibrium dissolved oxygen (D.O.) concentration at 1 atm pressure, kmol/m3 C*LS ) equilibrium D.O. for surface mass-transfer zone, kmol/m3 C*O2 ) equilibrium D.O. in the water at position Z, kmol/ m3 C*∞,O2 ) saturated dissolved oxygen concentration, kmol/ m3 g ) gravity acceleration constant, m/s2 G ) nitrogen molar flow rate, kmol/s k1 ) correlation parameter in eq 27, 1/s k2 ) correlation parameter in eq 27, sk3-1/m3k3 k3 ) correlation parameter in eq 27 KLaO2 ) oxygen volumetric mass-transfer coefficient in the ASCE model, 1/s KLBaB,O2 ) oxygen volumetric mass-transfer coefficient in the gas bubble zone, 1/s KLSaS,O2 ) oxygen volumetric mass-transfer coefficient in the surface mass-transfer zone, 1/s KLa20,O2 ) oxygen volumetric mass-transfer coefficient at 20 °C, 1/s KLaT,O2 ) oxygen volumetric mass-transfer coefficient at T (°C), 1/s P ) gas pressure at the depth ZS - Z, atm P0 ) atmospheric pressure, atm Pw ) water vapor pressure at water temperature T, atm Q ) feed air flow rate, m3/s R ) gas constant, atm m3/kmol K t ) time, s T ) temperature, K yO2 ) 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, m3/m3 F ) water density, kg/m3 θ ) temperature correction factor
Literature Cited ASCE. ASCE Standard Measurement of Oxygen Transfer in Water; ASCE: New York, 1984. Bewtra, J. K.; Nicholas, W. R.; Polkowski, L. B. Effect of Temperature on Oxygen Transfer in Water. Water Res. 1970, 4, 115. Boyle, W. C., Ed. Proceedings: Workshop Toward an Oxygen Transfer Standard. EPA-600/9-78-021; U.S. EPA: Cincinnati, OH, 1979. Boyle, W. C., Ed. Seminar Workshop in Aeration System Design, Testing, Operation and Control; EPA-600/9-85-005; U.S. EPA: Cincinnati, OH, 1985. Brown, L. C.; Baillod, C. R. Modeling and Interpreting Oxygen Transfer Data. J. Environ. Eng. Div. (Am. Soc. Civ. Eng.) 1982, 108, 607. Chao, A. C.; Chanh, D. S.; Smallwood, C., Jr.; Galler, W. S. Influence of Temperature on Oxygen Transfer. J. Environ. Eng. Div. 1987a, 113, 722. Chao, A. C.; Chanh, D. S.; Smallwood, C., Jr.; Galler, W. S. Influence of Temperature on Oxygen TransfersLaboratory Studies. J. Environ. Eng. Div. (Am. Soc. Civ. Eng.) 1987b, 113, 1089.
Ind. Eng. Chem. Res., Vol. 36, No. 12, 1997 5453 Chern, J.-M.; Yu, C.-F. Volatile Organic Compound Emission Rate from Diffused Aeration Systems. 1. Mass Transfer Modeling. Ind. Eng. Chem. Res. 1995, 34, 2634. Churchill, M. A.; Elmore, H. L.; Buckingham, R. A. Prediction of Stream Reaeration Rates. J. Sanit. Eng. Div. Am. Soc. Civ. Eng. 1962, Paper 3199. Cooper, C. D.; Alley, F. C. Air Pollution Control: a Design Approach; Waveland Press: Prospect Heights, IL, 1986. Downing, A. L.; Truesdale, G. A. Some Factors Affecting the Rate of Solution of Oxygen in Water. J. Appl. Chem. 1955, 5, 570. Elmore, H. L.; West, W. F. Effect of Water Temperature on Stream Reaeration. J. Sanit. Eng. Div., Am. Soc. Civ. Eng. 1961, 87, 59. Howe, R. H. L. Proposed Modification of K2-Temperature Relation. J. Environ. Eng. Div. (Am. Soc. Civ. Eng.) 1977, 103, 729. Lakin, M. B.; Salzman, R. N. Surface Aeration Evaluation. J. Water Pollut. Control Fed. 1979, 51, 2419. Matter-Muller, C.; Gujer, W.; Giger, W. Transfer of Volatile Substances from Water to the Atmosphere. Water Res. 1981, 15, 1271. McWhirter, J. R.; Hutter, J. C. Improved Oxygen Mass Transfer Modeling for Diffused/Subsurface Aeration Systems. AIChE J. 1989, 35, 1527. Metzger, I.; Dobbins, W. E. Role of Fluid Properties in Gas Transfer. Environ. Sci. Technol. 1967, 1, 57. Owens, M.; Edwards, R.; Gibbs, J. Some Reaeration Studies in Streams. Int. J. Air Water Pollut. 1964, 8, 469. Roberts, P. V.; Munz, C.; Dandiker, P.; Matter-Muller, C. Volatilization of Organic Pollutants in Wastewater TreatmentsModel Studies. EPA-600/S2-84-047; U.S. EPA: Cincinnati, OH, 1984a.
Roberts, P. V.; Munz, C.; Dandiker, P. Modeling Volatile Organic Solute Removal by Surface and Bubble Aeration. J.-Water Pollut. Control Fed. 1984b, 56, 157. 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. Thomann, R. V.; Mueller, J. A. Principles of Surface Water Quality Modeling and Control; Harper & Row: New York, 1987. WPCF. Activated Sludge, Manual of Practice. Report No. OM-9; Water Pollution Control Federation: Alexandria, VA, 1987. Yu, C.-F. Prediction of Volatile Organic Compounds Emission Rate from Aeration Systems. M.S. Thesis, Tatung Institute of Technology, Taipei, Taiwan, Republic of China, 1995. Yunt, F. W.; Hancuff, T. O. Aeration Equipment Evaluation: Phase IsClean Water Test Results. U.S. EPA Contract No. 1412-150; U.S. EPA: Washington, DC, 1979.
Received for review January 21, 1997 Revised manuscript received May 6, 1997 Accepted August 9, 1997X IE9700627
X Abstract published in Advance ACS Abstracts, October 1, 1997.
