2634
Ind. Eng. Chem. Res. 1995,34, 2634-2643
Volatile Organic Compound Emission Rate from Diffused Aeration Systems. 1. Mass Transfer Modeling Jia-Ming Chern* and Cheng-Fu Yu Department of Chemical Engineering, Tatung Institute of Technology, 40 Chungshan North Road, 3rd Section, Taipei, Taiwan 10451, R.O.C.
The release of volatile organic compounds (VOCs) from wastewater treatment plants has recently caused great concern. In wastewater treatment plants, many operation units such as equalization and aeration involve oxygen transfer between wastewater and air. While oxygen is transferred from air to wastewater, VOCs are stripped from wastewater to air. Due to increasingly stringent environmental regulations, wastewater treatment operators have to do VOC inventory of their facilities. A mass transfer model for VOCs is therefore called for to assess VOC emission rates from wastewater treatment processes. Almost all existing methods adopt a n oxygen mass transfer model standardized by the American Society of Civil Engineers (ASCE) to evaluate VOC emission rates. A new and more fundamental oxygen mass transfer model for diffused aeration systems was developed to assess the VOC emission rates. The new model provides better insight of the VOC mass transfer process and requires only aeration performance data to predict the VOC emission rates. The results and implications of both models were discussed and compared.
Introduction The activated sludge process is one of the most commonly used biochemical oxidation process for the secondary treatment of municipal and industrial wastewaters. In this process, naturally occurring microorganisms oxidize the toxic organic pollutants in the wastewater into carbon dioxide, water, and new microorganism cell mass. The effective operation of the activated sludge process requires an adequate and continuous supply of dissolved oxygen to support the microbial oxidation processes that occur in the liquid phase. The overall oxygen dissolution process is the primary use of energy in the secondary treatment process and represents a significant capital cost as well (Wesner et al., 1977; Barnhat, 1985). Therefore a great deal of effort has been expended over the past several decades to increase the overall energy transfer efficiency of the oxygen dissolution process to reduce the energy consumption in the secondary treatment process and reduce the capital cost if possible. Many different types of aeration systems have been developed over the years t o improve the energy efficiency of the oxygen transfer process. The types of aeration systems that have been developed can be broadly categorized into three groups: mechanical surface aerators, diffused aeration systems, and subsurface mechanical aerators with some type of gas sparging system. The performance evaluation of different types of aeration systems has been well standardized in recent years and is based upon the rate of oxygen that can be dissolved from air into clean tap water at so-called "standard conditions" of 0 dissolved oxygen level, 20 "C water temperature, and 1 atm pressure (ASCE, 1984). The standard aeration efficiency is then defined as the rate of oxygen transfer under standard conditions divided by the total electrical horsepower input into the aeration system. The determination of the standard oxygen transfer rate cannot be directly measured under the defined
* To whom correspondence should be addressed. E-mail:
[email protected]. FAX: 886-2-5861939.
standard conditions and instead must be calculated from unsteady-state reaeration test data. The experimental techniques and calculation procedures for accomplishing this are well understood and accepted in the industry and referred to as the American Society of Civil Engineers (ASCE) Standard for the Measurement of Oxygen Transfer in Clean Water. The ASCE standard for determination of the oxygen mass transfer performance of aeration systems, however, is based on a grossly oversimplified mass transfer model that is essentially an empirical statistical correlation of the unsteady-state reaeration data. More fundamentally rigorous oxygen mass transfer models were developed by McWhirter and his co-workers (McWhirter and Hutter, 1989; Hutter, 1990; Chern, 1990). Unfortunately, these improved oxygen mass transfer models did not receive great attention in the past few years. This paper will modify the improved oxygen mass transfer model for diffused aeration systems to estimate the emission rates of volatile organic compounds (VOCs) from aerated basins in the activated sludge processes. During the aeration process, oxygen is transferred into wastewater while VOCs are stripped from the wastewater. This process was once viewed as one good method to remove the VOCs from wastewaters and is called air stripping (Okoniewski, 1992). However, the release of VOCs from wastewater treatment plants has recently caused great concern. Due to increasingly stringent environmental regulations, wastewater treatment operators are asked to control the VOC emission from their facilities. To facilitate the VOC inventory assessment, a mass transfer model for VOCs based on the ASCE oxygen mass transfer model parameter is used in integrated computer software such as WATER7, TOXCHEM, PAVE, and BASTE. The mass transfer model for VOCs was first developed by Matter-Muller et al. (1981) and modified by Roberts (1984). The model described the transfer of VOCs to gas bubbles as the bubbles rise through the aeration tank. Because the model used an inadequate parameter that is obtained from the ASCE oxygen mass transfer model to estimate the VOC emission rates, it did not agree with the results of experiments conducted under bubble aeration (Rob-
0888-5885/95/2634-2634~Q9.QQIQ0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2635 erts et al., 1984). This paper presents a new mass transfer model for VOCs based on the improved oxygen mass transfer model for diffused aeration systems developed by McWwhirter and his co-workers and uses the new model to estimate VOC emission rates from diffused aeration systems.
ASCE Oxygen Mass Transfer Model The ASCE standard is based on the unsteady-state reaeration technique wherein the body of clean test water is first deoxygenated using cobalt-catalyzed, sodium sulfite solution and then reaerated back to “saturated or steady-state conditions with accurate experimental measurement of the dissolved oxygen level with time. The reaeration data obtained are then analyzed by the following simplified mass transfer model:
where Co, is the dissolved oxygen concentration at time t , C:,o the steady state saturated dissolved oxygen concenbation, and KLUO, the volumetric mass transfer coefficient for oxygen. If KLuo, and C:,o, are constant throughout the testing period, eq 1 can be readily integrated to yield the following expression for CO,as a function of time:
Co2= Cl,o, - (Cl,02- Co) exp(-KLao$
(2)
where COis the initial dissolved oxygen concentration a t t = 0. A nonlinear regression analysis based on the Gauss-Newton method is recommended by the ASCE t o fit eq 2 t o the experimental data using KLUO,, C:,02,and COas three adjustable model parameters. A set of values for KLUO,,Ct,O,, and COare obtained for each data set for a specific test condition. The statistically determined values of KLUO,are then adjusted to the standard conditions of 1 atm pressure and 20 “C water temperature by the following equation:
-K a
KLU20,0, -
L 0,
0293.15-T
(3)
where 8 is a temperature correction factor and T i s the absolute temperature of water. A generally accepted value of 8 is 1.024 (Stenstrom and Gilbert, 1981).
Estimation of VOC Mass Transfer Coefficients The volumetric mass transfer coefficients for VOCs are usually expressed in terms of that for oxygen as follows (Roberts et al., 1984): (4) where qj is a coefficient of proportionality. Roberts et al. reported that the range of values for J!T+ was from 0.55 to 0.65. The volumetric mass transfer coefficient is actually the product of the overall liquid-phase mass transfer coefficient,KL,and the interfacial area per unit volume of liquid, a. For oxygen and most VOCs that are sparingly soluble in water, the liquid film resistance controls the rate of mass transfer. Thus the overall liquid-phase mass transfer coefficient is essential equal to the individual liquid-film mass transfer coefficient, k ~ that , varies with the molecular diffision coefficient in water. According to the two-film theory (Lewis and Whitman, 19241, the mass transfer coefficient is directly
proportional to the molecular diffusion coefficient, D:
kL a D
(5)
According to the penetration theory (Higbie, 1935) and surface renewal theory (Danckwerts, 1951), the mass transfer coefficient is proportional to the square root of the molecular diffusion coefficient:
kL= According to the film penetration theory (Dobbins, 1956, 19641, the mass transfer coefficient is a complicated function of the molecular diffusion coefficient, the surface renewal rate, r, and the liquid film thickness,
L:
k, = 6coth
(7)
As the surface renewal rate, r, approaches zero, kL approaches DIL and the film penetration theory predicts the same mass transfer coefficient relationship as the two-film theory does. As the surface renewal rate approaches infinity, however, KL approaches (DlL)o.5and the film penetration theory predicts the same mass transfer coefficient relationship as the surface renewal or penetration theory does. There exist many other gas-liquid mass transfer models and theories that are modified versions of the four basic models. A good review is given by Coantic (1980). For engineering application purposes, the mass transfer coefficient can be expressed as a power law of the molecular diffusion coefficient:
k, = kfin
(8)
with the exponent, n, varying between 0.5 and 1 and the constant, ko, depending on specific hydrodynamic conditions. Many different values of n have been reported in the literature, 0.56 (Gilliland and Sherwood, 1934),0.5(Vivian and King, 19641, and 0.985 (Dobbins, 1964a,b) for specific gas-liquid contacting operations. At a given set of operating conditions, the ratio of the VOC volumetric mass transfer coefficient and oxygen volumetric mass transfer coefficient becomes
The ratio of the VOC diffusion coefficient and oxygen diffision coefficient at the same operating conditions can be calculated by the following equation: Dvoc
0.6
(10)
where VO,and Vvoc are the molar volumes of oxygen and the VOC at their normal boiling temperatures, respectively. Equation 10 can be derived from the Wilke-Chang correlation (1955). The molar volume of oxygen a t its normal boiling point is 25.6 cm3/mol(Reid et al., 1987). The molar volume of VOC can be calculated by an additive method (Reid et al., 1987) or by the Tyn and Calus method (Reid et al., 1987): Vvo, = 0.285Vc1.048
(11)
where V, is the critical volume of the VOC. Note that
2636 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 Table 1. Diffusion Coefficient Ratios and Henry's Law Constants of Several VOCE organic compound formula M w VC" DvodDo, 0.43 153.8 275.9 cc4 carbon tetrachloride 0.47 119.4 238.9 CHCl3 chloroform 0.67 50.5 138.9 CH3C1 chloromethane 0.42 165.8 289.6 Czc14 tetrachloroethene 0.45 131.4 256.0 C2HCl3 trichloroethene 0.59 62.5 169.0 C2H3Cl vinyl chloride 0.48 99.0 236.0 CzH4C1z 1,l-dichloroethane 0.49 99.0 225.0 CzH4C12 1,2-dichloroethane 0.53 64.5 199.0 CzHsC1 chloroethane 0.49 113.0 226.0 C3HsCh 1,2-dichloropropane 0.37 147.0 360.0 CsH4C12 o-dichlorobenzene 0.40 112.6 308.0 C&&1 chlorobenzene 0.45 78.1 259.0 benzene CsHs 0.40 92.1 316.0 toluene C7He ethylbenzene CsHio 106.2 374.0 0.36 0.34 CioHs 128.2 413.0 naphthalene 0.28 178.2 554.0 C14H10 anthracene 0.28 178.2 554.0 C14H10 phenanthrene a
(DVOCJDO,)~~~ 0.66 0.69 0.82 0.65 0.67 0.77 0.69 0.70 0.73 0.70 0.61 0.64 0.67 0.63 0.60 0.58 0.53 0.53
H,at 25 "Cb 1.18 1.52 x 1.86 1.10 3.54 x 3.71 2.17 x 4.70 x 7.22 x 1.15 x 6.70 x 1.60 x 2.23 x 2.99 x 3.44 x 4.46 x 1.29 x 1.23 x
lo-' 10-1
10-1 10-1
lo-' 10-1 lo-' lo-' 10-1
lo2
In cm3/mol. Calculated from the data bank of Hwang et al. (1992).
in eq 11,VVOCand V, have units of cm3/mol. Combining eqs 9-11 and substituting the value of Vo, leads t o (12)
As mentioned above, the exponent, n, varies with the hydrodynamic conditions of the systems. For diffused aeration systems with practical operating air flow rates, the mixing condition is rather vigorous. Thus the exponent, n, can be taken as 0.5 rather than 1. Substituting n = 0.5 into eq 12 gives
(13) The critical volumes and the volumetric mass transfer coefficient ratios for several VOCs are listed in Table 1. According to eq 13, once the volumetric mass transfer coefficient of oxygen for a given aeration system is obtained and the critical volume of a VOC is known, the volumetric mass transfer coefficient of the VOC can be readily calculated.
Estimation of VOC Emission Rates by the Conventional Model The state-of-the-art VOC mass transfer model for diffised aeration system was that developed by MatterMuller et al. (1981) and Roberts et al. (1984). The model uses a single volumetric mass transfer coefficient for VOC that is calculated from a proportional coefficient, +, times the oxygen volumetric mass transfer coefficient. According to the model, the degree of saturation of a VOC in the gas bubble is calculated as follows: s d
(
= 1 - exp
(14)
where H,is the Henry's law constant of the VOC, VL the liquid volume in the aeration tank, and QG the diffused air flow rate. In a batch aeration system where no water enters and exits the aeration tank and the gas-phase VOC concentration in the atmospheric air above the aeration tank is zero, the liquid-phase VOC concentration can be calculated by the equation derived by Hsieh et al. (1993):
where CVOC and CVOC,~ are liquid-phase VOC concentrations at time t and to, respectively. The VOC transfer rate can be derived from eq 15 as follows:
dCvoc VOCTR = -VL 7 - Q&$dCVOC
(16)
The dimensionless VOC transfer rate can be defined as VOCTR QGCVOC
(17)
This dimensionless VOC transfer rate is so defined that the emission rates of various VOCs under the same aeration conditions can be compared. In a diffused aeration system where water continuously enters and exits the aeration tank and the gas-phase VOC concentration in the atmospheric air above the aeration tank is zero, the fraction of the VOC removed from the liquid phase is (Eckenfelder, 1989; Metcalf and Eddy, 1991)
where CVOC,~ and CVOC,~ are influent and effluent VOC concentrations, respectively, and QLissthe steady-state liquid flow rate. In eqs 15-18, the gas flow rate, QG, should be evaluated a t the middepth water pressure:
where QGSTD is the standard air flow rate, ZSthe water depth, e the water density, g the gravity acceleration constant, and 6 the gas holdup. New VOC Mass Transfer Model The state-of-the-art estimation of VOC emission rates uses the oxygen volumetric mass transfer coefficient that is obtained from the ASCE mass transfer model, to estimate the VOC volumetric mass transfer coefficient. The assumptions and problems associated with the ASCE model have been discussed by McWhirter and Hutter (1989), and are not repeated here. One key
Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995 2637 Bubble Mass Transfer Zone
Air
Gas out
Surface Mass Transfer Zone
t
--r0yorI
t
\
z=zs
I
’
I Gy L + b Z
0
0 0
0 O 00
0
0
0
o y
0
0
0
0 00 0
0
O
1
t
O
0 ‘
0
E O 0 0
Figure 1. Schematic diagram of two mass transfer zones in a diffused aeration system.
problem is that the ASCE model uses a single mass transfer coefficient and does not differentiate two distinctly different mass transfer mechanisms in diffused aeration systems. Consider a diffused aeration system 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 a turbulent liquid surface. There exist two different mass transfer zones and mechanisms for oxygen and VOC mass transfer in diffused aeration systems (McWhirter and Hutter, 1989; Hutter, 1990; Chern, 1990). The gas bubble dispersion mass transfer zone exits below the turbulent liquid surface and represents the major portion of the overall gas-liquid mass transfer process. The turbulent surface mass transfer zone exists in the shallow region of the liquid surface and represents the minor portion of the overall gas-liquid mass transfer process. Each of these mass transfer zones must be separately analyzed and properly accounted for in the development of an adequate mass transfer model for oxygen and VOCs. The development of the diffused aeration 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 and VOCs concentrations are uniform throughout the tank a t any instant of time. 3. Nitrogen transfer is negligible compared with the oxygen and VOC transfers. 4. The molar gas flow rate is constant. 5. The oxygen and VOC mass transfer processes are controlled by the liquid-phase resistance. Consider the mass balance for a VOC over the control volume as depicted in Figure 2. The governingequation for the VOC mass balance in the gas phase is
Gas in Figure 2. Differential VOC material balance in a diffused aeration system gas bubble mass transfer zone.
the bubble rising time, G the air molar flow rate, KLUVOC the volumetric mass transfer coefficient of the VOC in the gas bubble mass transfer zone, and CGoc the equilibrium dissolved VOC concentration in the water. Since the gas bubble residence time in the aeration tank is very short, one can reasonably assume that the mole fraction of the VOC reaches steady state, i.e., @voJat~ = 0 in eq 20. This pseudo-steady-state assumption was also adopted in the previous models (Matter-Muller et al.,1981; Roberts et al. 1984). Accepting the pseudo-steady-state assumption leads to
The equilibrium dissolved VOC concentration in the water can be calculated by Henry’s law:
(22) In eq 22, the gas pressure is a function of the liquid depth:
+
P = Po @g(l- €)(ZS- 2)
(23)
where PO is the barometric pressure. Combining eqs 21-23 leads to
where
p - p w ?hoc EA--RT at,
(25)
@voc -G az + KLavoc(l - c)A(Cvoc - CiOc>(20) where A is the cross-sectional area of the aeration tank, P the gas pressure at the depth ZS - 2,PW the water vapor pressure a t temperature T, R the gas constant, yvoc the mole fraction of the VOC in the gas bubble, tg
a = Po- P w
+ @g(l- 4 2 s
(27)
2638 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 b=
eg(l - E ) 2
(28)
Note that the liquid-phase VOC concentration Cvoc is independent of the position according to OUT complete mixing assumption. If the entering gas bubbles contain no VOC, Le., at Z = 0, yvoc = 0, one can integrate eq 24 as follows:
fI(
er Z - - 2ab)\r;-l] Kb
(29)
Equation 29 can be used to calculate the mole fraction of VOC in the gas bubbles at any position in the aeration tank. The mole fraction of the VOC in the gas bubbles when the bubbles just exit the aeration tank can be readily calculated by letting Z = ZS. Thus the degree of saturation of the VOC can be calculated as follows:
Estimation of VOC Emission Rates by the New Model Consider a batch aeration tank where no water enters and exits the tank. The mass balance of the VOC in the water is
-Azs(l
- E)
Similarly, to eq 17, the dimensionless VOC emission rate can be defined as
If the partial pressure of the VOC in the atmospheric air above the aeration tank is zero, then Ctoc,s = 0 and eq 36 becomes
Note that this equation is more complicated than eq 1, which is derived from the traditional VOC mass transfer model using the ASCE mass transfer model parameter. Consider a diffused aeration system with continuous water input and output and assume that the aeration tank is completely mixed by the gas bubbling motion. The steady-state mass balance of a VOC is QLcvoc,i - QLCVOC,e + K L ~ V O C ( G-Ocvoc,e)VL C + KLsas(C~oc,s- CvOc,JVL= 0 (38)
dCvoc dt
Combining eqs 34 and 38 leads to cVOC,e
= (Cvoc,i + ~ ~ L ~ ~ + , v o c G o ~ , ~ ) /
where K~sas,vocis the volumetric mass transfer coefficient of the VOC in the surface mass transfer zone and Cboc,sthe equilibrium dissolved VOC concentration at the water surface. Equation 31 can be rewritten as where the hydraulic retention time t is defined as
z = VL/QL where the average equilibrium dissolved VOC concentration is defined as
(40)
The fraction of the VOC removed from the aeration tank is
-
(33)
CVOC,e -
Combining eqs 22, 23, 29, and 33 leads t o
Thus,
Again, if the partial pressure of the VOC in the
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2639 Table 2. Typical Aeration Data and Calculation Results” aeration device Sanitaire coarse-bubble diffusers water temperature 22.6 “C 1 atm atmospheric pressure 437.82 std m3/h diffused air flow rate 7.62 m water depth 37.16 m2 tank cross-sectional area 10.27 h-’ ASCE model Kmo, new model KLUO, 7.10 h-’ 3.65 h-I new model K~saso, corrected ASCE model Kmo, 10.59 h-l corrected new model KLUO, 7.52 h-l corrected new model KLSUSO,3.86 h-l a The same set of data were analyzed by the ASCE and new oxygen mass transfer models. The temperature correction factor used is 1.024.
atmospheric air above the aeration tank is zero, C;,,, is zero and eqs 37 and 41 can be further simplified. It is important to note that the degree of saturation and the emission rate of a VOC in a batch aeration tank and the fractional removal in a continuous tank depend, according t o the new model, upon the VOC properties such as the Henry’s law constant and the diffusion coefficient, and the operating conditions such as water depth, tank cross-sectional area, diffused air flow rate, and water temperature.
Results and Discussion A set of oxygen transfer data from the EPA results of Yunt and Hancuff (1979) will be used as the reference data to demonstrate how to estimate the VOC emission rates using the conventional mass transfer model and the new one developed in this study. The test conditions and regression results are shown in Table 2. In the estimation of VOC emission rates and degree of saturation, the Henry’s law constants for the VOC must be known. Many experimental data and methods to estimate the Henry’s law constant of VOCs are available (Mackay and Shiu, 1981 and 1986; Munz and Roberts, 1987;Ashworth et al., 1988;Yaws et al., 1991). A good review of the estimation methods for VOC Henry’s law constants is provided by Hwang et al. (1992). The calculated degree of saturation and dimensionless emission rates of the selected VOCs in a batch aeration tank are shown in Table 3. As expected, the two mass transfer models for VOCs give different results. The conventional model predicts a higher degree of saturation but a lower emission rate. This is because the conventional model uses a single mass transfer coefficient that is estimated from the ASCE model parameter and does not consider the mass transfer of the VOC at the turbulent water surface. Kyosai and Rittmann (1991) reported that the surface mass transfer of the VOC accounted for 17-60% of the four chlorinated solvents. They also concluded that the conventional mass transfer model underestimated VOC emission rates in diffused aeration systems. The new mass transfer model for VOCs developed in this study recognizes the two different mass transfer contributions from the gas bubble zone and the surface zone and predicts higher emission rates of the VOCs. Since the ASCE oxygen mass transfer model uses a single mass transfer coefficient for the whole aeration tank, it overestimates the true mass transfer coefficient in the gas bubble zone. According to eq 14, the degree of saturation of a VOC increases with an increasing mass transfer coefficient. The conventional model therefore predicts a higher degree of saturation than the new model does.
It is also important to note that, from Table 3, as the Henry’s law constant increases the degree of saturation decreases while the dimensionless emission rates increase. The Henry’s law constant of a VOC, by definition, is an indicator of the VOC solubility in water. A higher value of the Henry’s law constant indicates a lower value of the VOC equilibrium solubility in the liquid phase for the same gas-phase VOC concentration. A lower equilibrium solubility of the VOC in the liquid phase means that the VOC is easier to be stripped from the liquid phase into the gas phase and less likely to reach saturation in the gas phase. The emission rates of VOCs therefore increase with increasing Henry’s law constants and the degree of saturation decreases with increasing Henry’s law constants. In Table 3 the ratios of the VOC mass transfer coefficients to the oxygen mass transfer coefficients are calculated from the ratios of the molecular diffusion coefficients raised to an exponent of 0.5. Although the mass transfer coefficient ratios for all VOCs are not the same, the effect of the ratio is minor compared with the effect of the Henry’s law constant. The values of the volumetric mass transfer coefficient ratio, v , for halogenated aliphatic compounds containing one or two carbon atoms have been reported in the range of 0.50.7 (Eckenfelder, 1989). Hereafter a value of 0.6 for the mass transfer ratio will be used in the following calculations. The effect of the Henry’s law constant on the degree of saturation and the dimensionless emission rate for VOCs in a batch aeration tank as calculated by the two models is clearly shown in Figures 3 and 4, respectively. According to the new mass transfer model for VOCs, the overall emission rate consists of two terms, one from the gas bubble mass transfer zone and the other from the surface reaeration mass transfer zone. The contributions from the two mass transfer zones are shown in Figure 5. As seen from Figure 5, the emission rate from the surface zone for a VOC is independent of the Henry‘s law constant while that from the gas bubble zone increases with increasing Henry’s law constant. According to the new model, the effects of the water depth, i.e., the diffuser depth in the aeration tank, on the degree of saturation and dimensionless emission rates of VOCs in a batch aeration tank are shown in Figures 6 and 7,respectively. As shown in Figure 6, the degree of saturation of the VOC approaches unity for very low Henry’s law constants and approaches zero for very high Henry’s law constants regardless of the water depth. This means the water depth has no effect on the degree of saturation of the VOCs with extreme Henry’s law constants. For most VOCs of concern as shown in Table 1,the water depth indeed has a strong effect on the degree of saturation on the VOCs. The degree of saturation of a VOC is higher in a deeper aeration tank. As shown in Figure 7, the dimensionless emission rates of the VOCs increase with increasing water depth. The actual VOC emission rate expressed in moles per hour should however be evaluated for different water depths according to eq 17. According t o the new model, the effects of the crosssectional area of the aeration tank on the degree of saturation and dimensionless emission rates of VOCs in a batch aeration tank are shown in Figures 8 and 9, respectively. Again the cross-sectional area of the aeration tank has no effect on the degree of saturation of the VOCs with extremely low or high Henry’s law constants, as shown in Figure 8. The dimensionless
2840 Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995 Table 3. Degree of Saturation and Dimensionless Emission Rates of Several VOCs in a Batch Aeration Tank
H,at 25 "C
organic compound carbon tetrachloride chloroform chloromethane tetrachloroethene trichloroethene vinyl chloride 1,l-dichloroethane 1,2-dichloroethane chloroethane 1,2-dichloropropane o-dichlorobenzene chlorobenzene benzene toluene ethylbenzene naphthalene anthracene phenanthrene a
1.18 1.52 x 1.86 1.10 3.54 x 3.71 2.17 x 4.70 x 7.22 x 1.15 x 6.70 x 1.60 x 2.23 x 2.99 x 3.44 x 4.46 x 1.29 x 1.23 x
lo-' 10-1
10-'
lo-' 10-1
lo-'
10-1 lo-' 10-1
lo2
v
sda
0.66 0.69 0.82 0.65 0.67 0.77 0.69 0.70 0.73 0.70 0.61 0.64 0.67 0.63 0.60 0.58 0.53 0.53
0.9947 1.0000 0.9838 0.9960 1.0000 0.8564 1.0000 1.0000 0.9999 1.0000 1.0000 1.oooo 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Sdb 0.7925 0.9389 0.7511 0.8005 0.9036 0.5603 0.9274 1.0000 0.8604 0.9462 0.9519 0.9350 0.9252 0.9093 0.8989 1.0000 1.0000 1.0000
?! 0.8581 0.1110 1.3396 0.8030 0.2589 2.3259 0.1585 0.0344 0.5287 0.0839 0.0491 0.1174 0.1632 0.2186 0.2518 0.0327 0.0095 0.0090
tb 2.6183 1.8681 3.4998 2.5382 2.0067 4.0779 1.9288 1.7462 2.4687 1.8587 1.5861 1.7531 1.8890 1.8534 1.8213 1.4487 1.3258 1.3258
Calculated results of the conventional model. Calculated results of the new model.
Conventional Model 0.5
0.4
0.3 0.2
f
New model
1 .o
0.1
0.0
'
I
' """"
"""'1
.l
.01
'
'
'''''"1
10
1
0.0 100
1000
10000
Hc Figure 3. VOC degree of saturation predicted by two mass transfer models. PO = 1 atm; T =*25 "C; QG = 437.8 m3/h; 2s = 7.62 m; A = 37.16 m2; q = 0.6; Cvoc,s= 0.
.01
.l
10
1
100
1000
10000
Hc Figure 5. VOC transfer rates from two mass transfer zones of the new model. PO = 1 atm; T = 25 "C; QG = 437.8 m3h;2 s = 7.62 m; A = 37.16 m2; v, = 0.6; C;oc,s = 0.
I
6.0 j
u-
0.0
j
.01
0.1 ,
,,
,
I
.1
'
I
, ,,
/,,,
10
, , , , , ,,,,
100
, , , ,, 1000
, , ,,,
0.0
.Ol
10
Hc Figure 4. VOC transfer rates predicted by two mass transfer models. PO = 1 atm; T y 25 "C; QG = 437.8 m3h; 2 s = 7.62 m; A = 37.16 m2; q = 0.6; Cvoc,, = 0.
emission rates of the VOCs increase with increasing cross-sectional area of the aeration tank, as shown in Figure 9. The fractional removal of VOCs in a continuous flow aeration tank with a 6-h hydraulic retention time is predicted by the conventional and new models, and the result is shown in Figure 10. For VOCs with very high Henry's law constants both models predict the same fractional removal. For VOCs with low Henry's law constants the conventional model however underestimates the fractional removal because it neglects the surface mass transfer contribution to the overall VOC emission.
I
' """"
.1
' """"
1
'
"""
I
10
100
1000
'
""
10000
Hc Figure 6. Effect of water depth on the VOC degree of saturation. Ps,= 1 atm; T = 25 "C; QG = 437.8 m3/h; A = 37.16 m2; q = 0.6; C"OC,S
= 0.
According to the new model the effect of the hydraulic retention time on the fractional removal of VOCs is shown in Figure 11. The fractional removal of the VOCs increases with increasing hydraulic retention time as would be expected. All the above simulation results are based on one of the assumptions that the overall mass transfer rate is controlled by the liquid-phase resistance only. The volumetric mass transfer coefficients for VOCs can therefore be estimated from that for oxygen according to eq 13. This assumption is reasonable for oxygen but is not necessarily true for some VOCs. The effect of the
Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995 2641 1
6.0 j
1.o 0.9
0.8 0.7
4.0 5,0!
0.6 0.5 0.4 0.3
0.2 Zs=3.05m
0.1
1
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I
.01
' """"
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I
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100
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10000
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Figure 7. Effect of water depth on the VOC transfer rate. PO = 1 atm; T = 25 "C; QG = 437.8 m3h; A = 37.16 m2; v = 0.6;
Goes = 0.
Figure 10. Fractional removal of VOC in a continuous aeration tank predicted by two ?ass transfer models. PO = 1 atm; T = 25 "C;QG = 437.8 m3h; Cvoc,s = 0; Zs = 7.62 m; A = 37.16 m2; v = 0.6; 5 = 6 h.
0.99
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/-
0.94
0.3
0.93 0.1 0.92 0.91
.01
.1
10
1
1000
100
z=4h
1 1
10000 .Ol
Hc
Figure 8. Effect of aeration tank cross-sectional area on the VOC degree of saturation. PO= 1 atm; T = 25 "C;QG = 437.8 m3h; ZS = 7.62 m; v = 0.6; Cvoc,s = 0.
.1
1
10
100
1000
10000
Hc
Figure 11. Effect of hydraulic retention time on the VOC fractional removal in a continuous aeration tank. PO= 1 atm; T = 25 "C; QG = 437.8 m3h; Zs = 7.62 m; A = 37.16 m2; v = 0.6; cvoc,s = 0.
I
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For oxygen, the overall volumetric mass transfer coefficient, Km, equals the individual liquid-phase volumetric mass transfer coefficient, K L ~ because , K L is much less than KG and H,is not extremely low. The ratio of the overall volumetric mass transfer coefficient for VOC and oxygen becomes
''3°F
10000
Hc
Figure 9. Effect of aeration tank cross-sectional area on the VOC transfer rate. ,Po = 1 atm; T = 25 "C; QG = 437.8 m3h; 2s = 7.62 m; v = 0.6; C, = 0.
gas-phase resistance on the VOC transfer rates can be estimated by using the two-film theory (Lewis and Whitman, 1924). According to the two-film theory, the overall mass transfer resistance is the result of two resistance in series, namely those of the liquid- and gasphase boundary layers,
1 -
KLu
1 KLu
1 +-KGuH,
Rearranging eq 42,we can get eq 43.
(42)
As long as the k&L ratios of VOCs in both mass transfer zones are known, the volumetric mass transfer coefficient of the VOC can be calculated from that of oxygen. Munz and Roberts (1989) reported that, for many VOCs,the KdkL ratio was 100-150 for naturally aerated waters, especially those in which wind-driven turbulence dominated the liquid-side transport. They also reported that this ratio could be as low as 40 for mechanical surface aeration with high specific power input. The kdkL ratio depends on the degree of mixing in the liquid phase and the gas phase. In our new model, the overall VOC mass transfer is the combination of the gas bubble dispersion mass transfer and the turbulent surface mass transfer. The values of K d K L ratios in both zones should be considered separately. In the gas
2642 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 6.0
4.6 4.0
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I
I
(kJkL)B = 160
8.0
2.6
l'O 0.6
i ,001
.01
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10000
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Figure
12. Effect of the value of (K&L)S on the, VOC transfer rate. PO= 1 atm; T = 25 "C;QG = 437.8m3/h; C,, = 0; 2s = 7.62 m; A = 37.16 m2;I+9 = 0.6;(k&L)B = 150. 6.0
1
I
LP
Z.6
2.0 1.6
Conclusions A new mass transfer model has been used for determining VOC emissions in diffused aeration systems. The model takes into consideration that the VOC mass transfer occurs in two separate mass transfer zones instead of lumping the overall VOC transfer in the whole aeration tank as is done in the conventional model. Only the performance data of the aeration system, i.e., the volumetric mass transfer coefficients for oxygen in the two mass transfer zones, are required to estimate the VOC emission rates under the same operating conditions. This new model predicts a higher VOC emission rate and a lower degree of saturation than the conventional model that has been recognized to underestimate VOC emission rates. The effect of the gas-phase resistance on VOC emission rates can be assessed, by this new model, if the mass transfer coefficient ratio of the gas and liquid sides is known. This new model may serve as an auxiliary tool for the existing computer software to estimate the VOC emission rates from diffused aeration systems.
3 (kG'kL)E,l'
(kC/kL)B=
0.6 1.0
namic model should be used to describe the vaporliquid equilibrium relation of those VOCs. As shown in Figure 13, the ( k d k ~ratio ) ~ itself has almost no effect on the dimensionless VOC transfer rate for a constant ( k d k ~ratio ) ~ of 150. The lower dimensionless VOC transfer rate, as compared to that for infinite ( k d k ~ ) is~ caused , ~ , by the lower ( k d k ~ratio )~ (150 versus infinity). We can conclude that the gas-phase resistance has little effect on the VOC transfer rate in the gas bubble mass transfer zone, but it indeed has effect on the VOC transfer rate in the surface reaeration mass transfer zone for the VOCs with low Henry's law constants. Neglecting the gas-phase resistance will lead to an overestimation of VOC emission rates. The actual VOC emission rates may lie somewhere in between the curves that compare the conventional and new models. With experimental data of the ( k d k ~ ratios ) of both mass transfer zones, we can predict the VOC emission rates more accurately using our new mass transfer model.
.001
.01
,;,
:p
10
.I
100
1000
10000
Hc Figure 13. Effect of the value of ( k d k ~on ) ~the, VOC transfer rate. PO= 1 atm; T = 25 "C;QG = 437.8 m3h, C,, = 0;2s = 7.62 m; A = 37.16 m2; 1+9 = 0.6;( k d k ~=) 150. ~
Acknowledgment This work was supported by the National Science Council of Taiwan, Republic of China (Grant No. NSC 82-0113-E-036-080-T).
bubble mass transfer zone, with practical air flow rates, the gas-phase resistance films within the bubbles are very thin because of rapid motion within the bubbles. Nomenclature Thus the value of (kG/k& is large enough to allow us a = interfacial mass transfer area per unit volume of to neglect the gas-phase resistance. However, in the liquid in the gas bubble mass transfer zone, l/m surface mass transfer zone, the value of ( k G / k ~ )varies s as = interfacial mass transfer area per unit volume of with the turbulent state, mainly the wind speed, of the liquid in the surface mass transfer zone, l/m air above the water surface. A = cross-sectional area of the aeration tank, m2 The effects of the (kdkL)s and (k&& ratios on the CO= initial dissolved oxygen concentration at t = 0, kmoll dimensionless VOC transfer rate are shown in Figures m3 12 and 13, respectively. As shown in Figure 12, for Co2 = dissolved oxygen concentration at time t , kmol/m3 VOCs with the Henry's law constant greater than about CVOC= liquid-phase VOC concentrations at time t , kmoll unity, the (kG/kL)s ratio has very little effect on the dimensionless VOC transfer rate for a constant ( k d k ~ ) ~ m3 = average equilibrium dissolved VOC concentration, ratio of 150. For VOCs with lower Henry's law conkmol/" stants, the gas-phase resistance indeed decreases the CVOC,O = liquid-phase VOC concentrations at time to, kmoll overall volumetric mass transfer coefficients of the m3 VOCs, and then decreases the dimensionless VOC CVOC,~ = eMuent VOC concentrations, kmol/" transfer rates. This phenomenon is more remarkable CVOC,~ = influent VOC concentrations, kmollm3 for the VOCs with extremely low Henry's law constants. However, VOCs with extremely low Henry's law conCzTOc = equilibrium dissolved VOC concentration in the water, kmol/m3 stants do not follow Henry's law; another thermody-
Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995 2643 C;oc,s = equilibrium dissolved VOC concentration at the
Dobbins, W. E. Mechanism of Gas Absorption by Turbulent Liquid.
Subscripts
Partition Coefficients of the Polychlorinated Biphenyls. J. Phys. Chem. Ref. Data 1986,15,911. 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. Vivian, J. E.; King, C. J. Diffusivities of Slightly Soluble Gases in Water. AIChE J . 1964,10,221. Wesner, G. M.; et al. Energy Conservation in Municipal Wastewater Treatment; EPA-43019-77-011;US EPA Washington, DC, 1977. Wilke, C. R.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J. 1955,1, 264. Yaws, C.; Yang, H.-C.; Pan, X. Henry's Constants for 362 Organic Compounds in Water. Chem. Eng. 1991,Nov, 179. Yunt, F. W.; Hancuff, T. 0.Aeration Equipment Evaluation: Phase I-Clean Water Test Results; U S . EPA Contract No. 14-12-150, 1979.
In Proceedings of Znternational Conference on Water Pollution; water surface, kmol/" Pergamon Press: New York, 1964. Cl o, = saturated dissolved oxygen concentration, Eckenfelder, Jr., W. W. Industrial Water Pollution Control, 2nd Irmol/" ed.; McGraw-Hill: New York, 1989. D = molecular diffusion coefficient, m2/s Gilliland, E. R.; Sherwood, T. K. Diffusion of Vapors into Air g = gravity acceleration constant, d s 2 Stream. Znd. Eng. Chem. 1934,26,516. G = air molar flow rate, kmoYs Higbie, R. The Rate of Absorption of Pure Gas into a Still Liquid H , = Henry's law constant of the VOC, (km0Vm3in gas)/ during Short Periods of Exposure. Trans. Am. Znst. Chem. Eng. 1935,31,365. (km0I/m3in liquid) Hsieh, C.-C.; Babcock, Jr., R. W.; Stenstrom, M. K. Estimating kG = overall gas-phase mass transfer coefficient, d s Emissions of 20 VOCs. 11: Diffised Aeration. J . Environ. Eng. K L = overall liquid-phase mass transfer coefficient, d s ASCE 1993,119,1099. KLao, = volumetric mass transfer coefficient for oxygen, Hutter, J. C. Improved Analysis and Modeling of the Oxygen Mass 11s Transfer Process in Aeration Systems. Ph.D. Thesis, The KLavoc = volumetric mass transfer coefficient of the VOC, Pennsylvania State University, University Park, 1990. 11s Hwang, Y.-L.; Olson, J. D.; Keller, G. E., 11. Steam Stripping for Kms,voc = volumetric mass transfer coefficient of the VOC Removal of Organic Pollutants from Water. 2. Vapor-Liquid in the surface mass transfer zone, 11s Equilibrium Data. Ind. Eng. Chem. Res. 1992,31,1759. L = liquid film thickness, m Kyosai, S.; Rittmann, B. E. Effect of Water-Surface Desorption P = gas pressure at the depth 2 s - 2, atm on Volatile Compound Removal under Bubble Aeration. Res. PO= atmqspheric pressure, atm J . WPCF 1991,63,887. PW = water vapor pressure at temperature T , atm Lewis, W. K.;Whitman, W. C. Principles of Gas Adsorption. Ind. Eng. Chem. 1924,16,1215. QG = air flow rate, m3/s Mackay, D.; Shiu, W. Y. A Critical Review of Henry's Law QGSTD = standard air flow rate, m3/s Constants for Chemicals of Environmental Interest. J . Phys. QL = liquid flow rate, m3/s Chem. Ref. Data 1981,10,1175. r = surface renewal rate, l/s Matter-Muller, C.; Gujer, W.; Giger, W. Transfer of Volatile R = gas constant, atmm3/(mol-K) Substances from Water to the Atmosphere. Water Res. 1981, s d = degree of saturation of VOC in gas bubble 15,1271. t = time, s McWhirter, J. R.; Hutter, J. C. Improved Oxygen Mass Transfer to = initial time, s Modeling for DiffusedSubsurface Aeration Systems. AIChE J . t b = bubble moving time, s 1989,35,1527. T = temperature, K Metcalf & Eddy, Inc. Wastewater Engineering Treatment, Disposal, V, = critical volume of VOC, m3/km0l and Reuse, 3rd ed.; McGraw-Hill: New York, 1991. VL = liquid volume in aeration tank, m3 Munz, C.; Roberts, P. V. Air-Water Phase Equlibria of Volatile VO, = molar volume of oxygen at normal boiling temperOrganic Solutes. J. AWWA 1987,79,62. ature, m3/kmol Munz, C.; Roberts, P. V. Gas- and Liquid-Phase Mass Transfer Resistances of Organic Compounds During Mechanical Surface VOCTR = VOC transfer rate, kmolls Aeration. Water Res. 1989,23,589. VVOC= molar volume of VOC at normal boiling temperaOkoniewski, B. A. Remove VOCs from Wastewater by Air Stripture, m3/kmol ~ V O C= mole fraction of VOC in gas bubble, k m o l ~ ~ C / k m o l ~ ~ ping. ~ Chem. Eng. Prog. 1992,88,89. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases ZS= water depth, m and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Greek Letters Roberts, P. V.; Munz, C.; Dandiker, P.; Matter-Muller, C. Volatilization of Organic Pollutants in Wastewater Treatment-Model 5 = dimensionless VOC transfer rate studies; U S EPA-600lS2-84-047, 1984a. 7 = fraction of a VOC removed from aeration tank Roberts, P. V.; Munz, C.; Dandiker, P. Modeling Volatile Organic 1/, = ratio of VOC and oxygen mass transfer coefficients Solute Removal by Surface and Bubble Aeration. J . WPCF 8 = temperature correction factor for volumetric mass 1984b,56,157. transfer coefficient Shiu, W. Y.; Mackay, D. A Critical Review ofAqueous Solubilities, E = gas holdup, m3 of air/ m3 of bed Vapor Pressures, Henry's Law Constants, and Octanol-Water
= oxygen VOC = volatile organic compound 0 2
Literature Cited ASCE. ASCE Standard Measurement of Oxygen Transfer in Water; ASCE: New York, 1984. Ashworth, R. A.; Howe, G. B.; Mullins, M. E.; Rogers, T. N. AirWater Partitioning Coefficients of Organics in Dilute Aqueous Solutions. J. Hazard. Mater. 1988,18,25. Barnhart, E. L. An Overview of Oxygen Transfer System. In Proceeding of Seminar Workshop in Aeration System Design, Testing, Operation and Control; Boyle, W. C., Ed.; EPA-6001985-005; US EPA Cincinnati, OH, 1985. Chern, J.-M. Fundamental Analysis and Modeling of the Oxygen Mass Transfer Process in Aeration Systems. Ph.D. Thesis, The Pennsylvania State University, University Park, 1990. Coantic, M. Mass Transfer Across the Ocean-Air Interface: Small Scale Hydrodynamic and Aerodynamic Mechanisms. PCH 1980, 1, 249. Danckwerts, P.V. Significance of Liquid-Film Coefficients in Gas Absorption. Znd. Eng. Chem. 1951,43,1460. Dobbins, W. E. The Nature of the Oxygen Transfer Coefficient in Aeration System. In Biological Treatment of Sewage and Industrial Wastes; McCabe, J . , Eckenfelder, Jr. W. W., Eds.; Reinhold: New York, 1956.
Received for review October 27, 1994 Revised manuscript received May 23, 1995 Accepted J u n e 2, 1995@ IE940623J
Abstract published in Advance ACS Abstracts, July 1, 1995. @
