Volatile Organic Compound Emission Rates from Mechanical Surface

Jul 3, 1999 - A new mass-transfer model has been developed to predict the VOC emission rates from batch and continuous aeration tanks with mechanical ...
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Ind. Eng. Chem. Res. 1999, 38, 3176-3185

Volatile Organic Compound Emission Rates from Mechanical Surface Aerators: Mass-Transfer Modeling Jia-Ming Chern* and Shun-Ren Chou Department of Chemical Engineering, Tatung Institute of Technology, 40 Chungshan North Road, 3rd Section, Taipei, Taiwan 10451

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, volatile organic compounds (VOCs) are stripped from wastewater to air. Because of increasingly stringent environmental regulations, wastewater treatment operators have to do VOC inventory of their facilities. A new mass-transfer model has been developed to predict the VOC emission rates from batch and continuous aeration tanks with mechanical surface aerators. 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 ASCE-based model. The predictive capabilities of the two-zone and the ASCEbased models were examined by calculating the emission rates of 10 priority pollutants from aeration tanks. The effects of the hydraulic retention time, the Henry’s law constant, gas-phase resistance, and the water and air environmental conditions on the VOC emission rates were predicted by the two models. Introduction The emission of volatile organic compounds (VOCs) from municipal and industrial wastewater treatment facilities has been identified as one of major air pollution sources and caused great concern. In wastewater treatment facilities, VOCs emit from wastewater collection systems as well as many treatment units.1-7 Most VOC emission problems occur in the aeration basins where oxygen is transferred into wastewater by aeration devices such as mechanical surface aerators and diffused aeration systems. This aeration process was once viewed as one good method to remove the VOCs from wastewaters.8 Because of increasingly stringent environmental regulations, wastewater treatment operators are asked to estimate the VOC emission rates from their facilities and control the emission problems. To facilitate the VOC inventory assessment, VOC mass-transfer models for surface aerators9-12 and diffused aeration systems9-11 based on the American Society of Civil Engineers (ASCE) oxygen mass-transfer model13 were employed in integrated VOC fate models such as BASTE,4 Fate,14 TOXCHEM, and PAVE.15,16 A two-zone VOC mass-transfer model for diffused aeration systems was developed by Chern and Yu17 to predict the VOC emission rates and was calibrated by experimental measurement of the unsteady-state dissolved VOC concentrations in batch aeration tests.18 Unlike the ASCE-based model for diffused aeration systems that expressed VOC mass transfer in terms of one lumped volumetric mass-transfer coefficient, the two-zone model recognized that VOC mass transfer occurred in the gas bubble zone as well as in the surface reaeration zone and used two volumetric mass-transfer coefficients to evaluate the VOC mass-transfer rates. In the ASCEbased VOC mass-transfer model for surface aerators, a * To whom correspondence should be addressed. E-mail: [email protected]. Tel: 011-886-2-25925252 Ext. 3487. Fax: 011-886-2-25861939.

single lumped volumetric mass-transfer coefficient was also used although two different mass-transfer mechanisms were identified.6 In surface aeration systems, oxygen mass transfer occurs in the liquid spray zone as well as in the surface reaeration zone.19 Based on the two-zone oxygen transfer model for surface aerators, this paper develops new mass-transfer models for estimating the VOC emission rates from surface aerators in batch and continuous aeration tanks under varying environmental conditions. ASCE-Based VOC Mass-Transfer Model The currently used VOC mass-transfer model for mechanical surface aerators is based on the ASCE oxygen mass-transfer model6,9-12,20,21 that uses the twofilm theory22 and the oxygen volumetric mass-transfer coefficient to estimate the VOC volumetric masstransfer coefficient:

KLavoc ) KLaO2

( )( Dvoc DO2

n

1+

kL kGHc

)

-1

(1)

where Dvoc and DO2 are the molecular diffusion coefficient of the VOC and oxygen, respectively, Hc is the Henry’s law constant of the VOC, and kL and kG are the individual liquid- and gas-phase mass-transfer coefficients of the VOC, respectively. In eq 1, the exponent, n, ranges between 0.5 and 1, depending upon the hydrodynamic conditions of the aeration systems. For a very turbulently aerated surface, n approaches 0.5; for a quiescent surface, n approaches 1. The oxygen volumetric mass-transfer coefficient of a given mechanical surface aerator is determined from the unsteadystate reaeration test data.13 Once the VOC volumetric mass-transfer coefficient is known, the VOC emission rate from the aeration tank is calculated by the following equation:

10.1021/ie990073v CCC: $18.00 © 1999 American Chemical Society Published on Web 07/03/1999

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3177

(

VOCER ) kLavocVL Cvoc -

)

CG Hc

(2)

where VL is the liquid volume in the aeration tank, Cvoc the dissolved VOC concentration in the tank, and CG the VOC concentration in the atmospheric air. Equation 2 can be used to calculate the VOC emission rates from mechanical surface aeration systems. The generally accepted mechanisms of VOC removal include stripping and volatilization due to aeration, sorption onto biosolids, and degradation due to biochemical reactions. In a batch aeration tank with initial dissolved VOC concentration Cvoco, the VOC mass balance equation is as follows.

(

)

CG dCvoc - rbio - rads ) -KLavoc Cvoc dt Hc

(3)

where rbio and rads are the VOC disappearance rates due to bioreactions and biosorption in the tank, respectively. Neglecting the bioreaction and biosorption mechanisms for the VOC removal and assuming that the gas-phase VOC concentration is constant, the unsteady-state VOC concentration is solved as

Cvoc )

(

)

CG CG + Cvoco exp(-KLavoct) Hc Hc

(4)

According to eq 4, the liquid-phase VOC concentration decreases exponentially with the aeration time and the ultimate concentration equals CG/Hc. The instantaneous VOC emission rate from the batch aeration tank can be calculated from eqs 2 and 4:

(

)

(5)

The normalized VOC emission rate from the batch aeration tank can be defined as

(

)

CG VOCER ) KLavoc 1 exp(-KLavoct) VLCvoco HcCvoco (6)

where VLCvoco is the initial amount of the VOC in the aeration tank. The dimensionless cumulative amount of VOC emission can be calculated from the mass balance:

ξ)

VL(Cvoco - Cvoco) ) VLCvoco

(

1-

Cvoc )

Cvocf τKLavocCG/Hc + 1 + τKLavoc 1 + τKLavoc

(9)

where the hydraulic retention time of the aeration tank, τ, equals VL/QL. The dimensionless VOC emission rate for the continuous-flow tank is then calculated by the following equation:

ζ)

(

)

τKLavoc CG VOCER ) 1QLCvocf 1 + τKLavoc HcCvocf

(10)

Development of a Two-Zone VOC Mass-Transfer Model To develop an improved VOC mass-transfer model for surface aeration systems, one must first recognize that there are two different mechanisms of VOC mass transfer in an aeration tank equipped with a mechanical surface aerator, as shown in Figure 1. Obviously VOCs emit from the aerated water surface during aeration, as is considered in the ASCE-based VOC mass-transfer model. VOCs also emit from the sprayed water droplets, but this facet is totally neglected by the ASCE-based model. These two mass-transfer mechanisms are fundamentally different and should be analyzed separately. VOC Emission from a Liquid Spray Zone

)

CG [1 - exp(-KLavoct)] (7) HcCvoco

For completely mixed aeration tanks with continuous influent and effluent flows, the VOC mass balance is as follows.

VL

mechanisms for the VOC removal and assuming steady state, the effluent VOC concentration can be solved as

where QLCvocf is the VOC loading to the aeration tank.

CG exp(-KLavoct) VOCER ) KLavocVL Cvoco Hc

$≡

Figure 1. Schematic diagram of an aeration tank with a mechanical surface aerator.

(

)

CG dCvoc ) QL(Cvocf - Cvoc) - KLavocVL Cvoc dt Hc rbioVL - radsVL (8)

where QL is the volumetric wastewater flow rate and Cvocf is the dissolved VOC concentration in the feed stream. Neglecting the bioreaction and biosorption

During aeration, the rotation of the surface aerator impeller propels or sprays a large amount of liquid into the atmospheric air and disperses the liquid into droplets. The liquid droplets travel through the atmospheric air and return to the liquid surface. During the droplet flight period, the dissolved VOC in the droplets is oversaturated and will transfer into the atmospheric air. The unsteady-state mass balance of the VOC in a single droplet is as follows.

dCd ) -Kdad voc(Cd - Cd*) dtf

(11)

where Cd is the dissolved VOC concentration in the droplet, tf is the droplet flight time, Kdadvoc is the

3178 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999

volumetric mass-transfer coefficient of the VOC in the liquid spray zone, and Cd* is the saturation VOC concentration in the droplet, which can be expressed in terms of the vapor-phase concentration by Henry’s law:

Cd* ) CG/Hcd

Cd′ - Cd* ) exp(-Kdadvoctf′) Cvoc - Cd*

(13)

The fractional approach of Cd′ to Cd* can be defined as the VOC “Murphree” efficiency in the liquid spray zone as is commonly done in many types of gas-liquid mass transfer operations:23

Cvoc - Cd′ Emdvoc ) ) 1 - exp(-Kdadvoctf′) (14) Cvoc - Cd* The Murphree efficiency in the liquid spray zone for oxygen Emd, a constant for a surface aerator under a given set of operating conditions, is calculated by the following equation:

Emd ) 1 - exp(-Kdadtf′)

(15)

where Kdad is the volumetric mass-transfer coefficient of oxygen in the liquid spray zone. The Murphree efficiency in the liquid spray zone for oxygen can be obtained from a linear plot of the experimental data.19 In the liquid spray zone, the volumetric mass-transfer coefficient of the VOC can also be expressed in terms of that of oxygen by the two-film theory:

( )( nd

1+

)

kL kGHcd

-1

(16)

Combining eqs 14-16 leads to

Emdvoc ) 1 - (1 - Emd)(Dvoc/DO2)

nd(1+(k /k H ))-1 L G cd

(17)

In the surface reaeration zone, the VOC emits from the turbulent liquid surface to the atmospheric air with the emission rate estimated by the following equation:

)

CG VOCERs ) KLSasvocVL Cvoc Hcs

(18)

where KLSasvoc is the volumetric mass-transfer coefficient of the VOC in the surface reaeration zone and Hcs is the Henry’s law constant of the VOC evaluated at the bulk liquid temperature. The volumetric mass-

ns

1+

)

kL kGHcs

-1

(19)

It is important to note that the exponents nd and ns in eqs 16 and 19 are not necessarily the same; they are two constants dependent upon the hydrodynamic conditions in the two mass-transfer zones. Similarly, the individual mass-transfer ratios kL/kG in eqs 16 and 19 are not necessarily the same; they depend on the relative magnitude of the gas- and liquid-phase resistance in the two mass-transfer zones. VOC Emission from a Batch Aeration Tank When Figure 1 is referred to and the VOC removal by biochemical reactions and adsorption is neglected, the unsteady-state VOC mass balance in a batch aeration tank is as follows:

VL

(

)

CG dCvoc ) QdCd′ - QdCvoc - KLSasvocVL Cvoc dt Hcs

(20) where Qd is the volumetric flow rate of the liquid sprayed through the liquid spray mass-transfer zone. In the right-hand side of eq 20, the first term represents the mass flow rate of the VOC returning to the tank, the second term represents the mass flow rate of the VOC leaving the tank, and the third term represents the VOC emission rate from the surface reaeration zone. Combining eqs 12, 14, and 20 leads to

(

)

CG dCvoc QdEmdvoc Cvoc )dt VL Hcd

(

KLSasvoc Cvoc -

)

CG (21) Hcs

The right-hand side of eq 21 contains two terms: the first term is the VOC emission rate from the liquid spray zone and the second term that from the surface reaeration zone. Equation 21 can be integrated to obtain the unsteady-state VOC concentration in the aeration tank:

Cvoc )

VOC Emission from the Surface Reaeration Zone

(

( )(

KLSasvoc Dvoc ) KLSas DO2

(12)

In eq 12, the Henry’s law constant for the droplet Hcd should be evaluated at the droplet average temperature, which is the arithmetic average of the droplet skin temperature and the bulk liquid temperature in the aeration tank.19 The initial condition of eq 11 is as follows: at tf ) 0, Cd ) Cvoc, the dissolved VOC concentration in the bulk liquid of the aeration tank. At the total droplet flight time tf′, Cd ) Cd′, the VOC concentration in the droplet when it re-enters the liquid surface of the aeration tank. With these two conditions, eq 11 can be integrated as follows:

Dvoc Kdadvoc ) Kdad DO2

transfer coefficient of the VOC in the surface reaeration zone can also be related to that of oxygen by the twofilm theory:

(

)

CG B A + + A + B Hcd Hcs CG A B Cvoco + A + B Hcd Hcs

[

(

)]

exp[-(A + B)t] (22)

where Cvoco is the initial VOC concentration in the tank, A ) QdEmdvoc/VL, and B ) KLSasvoc. According to the two-zone model, the liquid-phase VOC concentration also decreases exponentially with the aeration time. Similar to eq 6, the normalized VOC emission rates from the liquid spray zone and the surface reaeration zone can be calculated by the following equations:

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3179

{ [ { [

$d ) A

BCG(1/Hcs - 1/Hcd)

1-

$s ) B

(A + B)Cvoco CG(A/Hcd - B/Hcs)

]

(A + B)Cvoco

ACG(1/Hcd - 1/Hcs)

1-

equation:24

+

}

exp[-(A + B)t]

(23)

f°T HT ) H298.15 f°298.15

(24)

where HT and H298.15 are the VOC Henry’s law constants at T and 298.15 K, respectively, and f°T and f°298.15 are the VOC fugacities at T and 298.15 K, respectively. The VOC fugacity f can be estimated from the following correlation:

+

(A + B)Cvoco CG(A/Hcd + B/Hcs)

]

(A + B)Cvoco

}

exp[-(A + B)t]

The total normalized VOC emission rate from the batch aeration tank is therefore the sum of the above two rates. Similar to eq 7, the dimensionless cumulative amount of VOC emission can be calculated by the following equation:

[

ξ) 1-

)]

(

CG

A B + {1 Cvoco(A + B) Hcs Hcd exp[-(A + B)t]} (25)

VOC Emission from a Continuous-Flow Tank with Surface Aeration For completely mixed aeration tanks with continuous influent and effluent flows, the VOC mass balance without biochemical reactions and adsorption is as follows.

(

)

QdEmdvoc CG dCvoc QL ) (Cvocf - Cvoc) Cvoc dt VL VL Hcd CG (26) KLSasvoc Cvoc Hcs

(

)

τCG

(

)

B A + + Cvoc ) 1 + τ(A + B) 1 + τ(A + B) Hcd Hcs

(27)

The dimensionless VOC emission rate is the sum of the dimensionless VOC emission rates from the two masstransfer zones that are calculated by the following equations, respectively:

[

)]

(

CG τBCG 1 τA 1 1+ ζd ) HcdCvocf Cvocf Hcs Hcd 1 + τ(A + B)

ζs )

(28)

[

(

)]

CG τACG 1 τB 1 1+ HcsCvocf Cvocf Hcd Hcs 1 + τ(A + B)

(29) Assessment of Physical Properties In eqs 1, 16, and 19, the diffusion coefficient ratio can be estimated by the following equation:17

Dvoc 14.86 ) DO2 V 0.6288

ln f° ) A + B/T + D ln T + ETm

(30)

c

where Vc is the critical volume of the VOC. The effect of the water temperature on the Henry’s law constant can be estimated by the following

(32)

where A, B, D, E, and m are correlation parameters that can be found in the AIChE DIPPR (Design Institute for Physical Property Data) databank.25 The effect of the water temperature on the oxygen volumetric mass-transfer coefficient is conventionally estimated by the following equation:

KLaO2T ) KLaO2RθT-TR

(33)

where KLaO2T and KLaO2R are the oxygen volumetric mass-transfer coefficients at the water temperature T and the reference temperature TR, respectively. A generally accepted value of the temperature correction factor θ is 1.024.26 Equation 41 can be directly used to calculate the oxygen volumetric mass-transfer coefficient in the ASCE-based model and that of the surface reaeration zone in the two-zone model. The oxygen Murphree efficiency at a droplet temperature other than the reference temperature can be calculated by the following equation:

EmdT ) 1 - (1 - EmdR)θ

T-TR

Therefore, the steady-state effluent VOC concentration can be calculated by the following equation:

Cvocf

(31)

(34)

Equation 34 can be easily derived from eqs 15 and 33. In summary, with the temperature corrections for the volumetric mass-transfer coefficients and the Henry’s law constant, the VOC emission rates can be calculated by the ASCE-based model (eqs 6 and 10) and the twozone model (eqs 23,24 and 28, and 29). Effect of Henry’s Law Constant The set of unsteady-state reaeration data using a fullscale mechanical surface aerator19 was used to determine the oxygen volumetric mass-transfer coefficients of the ASCE-based and two-zone models. The test conditions and performance parameters are summarized in Table 1. The Henry’s law constants at 25 °C, temperature correction parameters, and critical volumes for 10 priority pollutants are listed in Table 2. The initial normalized VOC emission rates from a batch aeration tank and the dimensionless VOC emission rates from a continuous aeration tank are calculated by eqs 6, 23, and 24, and the results are shown in Table 3. As is shown in Table 3, the initial normalized VOC emission rates from a batch aeration tank increase with increasing Henry’s law constant while the dimensionless VOC emission rates from a continuous aeration tank seem to be independent of the Henry’s law constant. The VOC emission rates predicted by the ASCEbased model are lower than those predicted by the twozone model mainly because of its neglect of the VOC emission from the sprayed droplets.

3180 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999

liquid spray zone exponent nd should depend on the droplet flight time, droplet diameter, diffusivity of VOC, liquid viscosity, and flow conditions inside the drops. However, because of this complex interrelationship that is not easily modeled, the value of 0.5 is adopted in the two-zone model. In the surface reaeration zone, the liquid surface is highly turbulent within the “spray umbrella” radius but is relatively quiescent outside and far away from the umbrella radius; the exponent ns for the surface reaeration zone is therefore between 0.5 and 1.0. The following equation is proposed to calculate the exponent ns for the surface reaeration zone:

Table 1. Full-Scale Surface Aerator Test Conditions and Performance Data test conditions and performance parameter

value

unit

tank cross-sectional area tank depth liquid volume aerator radius aerator blade curvature angle aerator rotational speed bulk liquid temperature air wet-bulb temperature barometric pressure equilibrium DO level at the surface of spray droplets equilibrium DO level at the surface of bulk liquid spray trajectory radius maximum height of the spray trajectory murphree efficiency of oxygen volumetric flow rate of the spray liquid oxygen volumetric mass-transfer coefficient in the ASCE model A ) QdEmdvoc/VL in the two-zone model B ) KLSasvoc in the two-zone model fraction of oxygen transfer rate in the liquid spray zone fraction of oxygen transfer rate in the surface reaeration zone

278.74 7.68 2139000 127 20 48 19 20 75.64 9.05

m2 m L cm deg rpm °C °C cmHg mg/L

9.23

mg/L

4.88 0.61 0.503 11500000 6.71

m m L/h h-1

2.79 4.84 36

h-1 h-1 %

64

%

()

ns ) 1 - 0.5

( )

Au πRu2 ) 1 - 0.5 At At

(35)

where Au is the area covered by the spray umbrella and At the total tank area. Using eq 35 and the data in Table 1, spray trajectory radius ) 4.88 m, tank cross-sectional area ) 278.74 m2, and the exponent ns is found to be 0.87. This value is very close to 0.9 that was found in a 3600-gal aeration tank.27 Comparison of ASCE-Based and Two-Zone Model

In the above calculations, the exponent nd for the liquid spray zone and ns for the surface reaeration zone equal 0.5 and 0.9, respectively,27 while n for the ASCEbased model equals 0.6.4,28 Different n values in the ASCE-based model were used to predict the VOC emission rates from surface aerators. For example, Roberts and Da¨ndiker12 used n ) 0.66, and Hsieh et al.21 and Melcer et al.16 used n ) 0.5. In the liquid spray zone, the mass-transfer process is appropriately described by the surface renewal or penetration model because the droplets fly at very high speed; the exponent nd for the liquid spray zone is therefore close to 0.5. In fact, the

The normalized emission rates of o-dichlorobenzene (Hc ) 0.045 at 19 °C) from a batch aeration system are calculated by eq 6 and eqs 23 and 24 for the ASCE-based model and the two-zone model, respectively. As is shown in Figure 2, the normalized emission rate of the VOC predicted by the two-zone model is slightly greater than that predicted by the ASCE-based model for an aeration time of less than 24 min; after 24 min the ASCE-based model predicted a slightly higher emission rate. Also shown in Figure 2 is that the VOC emission rates from

Table 2. Henry’s Law Constants at 25 °C, Temperature Correction Parameters, and the Critical Volumes for 10 Priority Pollutants VOC

Hc25a

Ab

Bb

Db

Eb

mb

Vcc

1,2-dichloroethane o-dichlorobenzene chloroform benzene toluene trichloroethene tetrachloroethene carbontetrachloride chloromethane vinylchloride

0.047 0.067 0.150 0.223 0.277 0.392 0.723 1.316 1.860 3.709

116.39 82.095 146.43 83.918 80.877 59.403 58.764 78.441 64.697 91.432

-7323 -8108 -7792 -6518 -6902 -5472 -6191 -6128 -4048 -5142

-15.37 -8.99 -20.61 -9.345 -8.776 -5.828 -5.331 -8.577 -6.807 -10.98

1.679 × 10-2 5.082 × 103 2.458 × 102 7.118 × 106 5.803 × 106 4.510 × 103 2.127 × 106 6.847 × 106 1.037 × 105 1.432 × 105

1 1 1 2 2 1 2 2 2 2

225 360 239 259 316 256 290 276 239 169

a H 24 c25 is dimensionless; data were calculated from Hwang et al. cm3/mol; data were taken from Reid et al.29

b

A, B, D, E, and m data are taken from Hwang et al.24

c

Vc in

Table 3. Calculated VOC Emission Rates from Batch and Continuous Aeration Tank for 10 Priority Pollutants ASCE-based modela

two-zone modelb

VOC

Hc at 19 °C

$0 (h-1)

ζ

Hcd at 19.5 °C

Hcs at 19 °C

$0 (h-1)

ζ

1,2-dichloroethane o-dichlorobenzene chloroform benzene toluene trichloroethene tetrachloroethene carbontetrachloride chloromethane vinylchloride

0.035 0.045 0.115 0.168 0.202 0.295 0.522 1.003 1.558 3.093

2.80 2.54 3.66 3.72 3.51 3.92 3.84 3.99 4.24 4.86

0.957 0.953 0.967 0.967 0.966 0.969 0.968 0.970 0.971 0.975

0.036 0.046 0.118 0.172 0.207 0.302 0.537 1.026 1.582 3.141

0.035 0.045 0.115 0.168 0.202 0.295 0.522 1.003 1.558 3.093

3.08 2.72 3.91 3.95 3.69 4.14 4.03 4.18 4.47 5.20

0.961 0.956 0.969 0.969 0.967 0.971 0.970 0.971 0.973 0.977

a

n ) 0.6, CG ) 0, kG/kL ) 50, τ ) 8 h. b nd ) 0.5, ns ) 0.9, CG ) 0, kG/kL ) 50, τ ) 8 h.

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3181

Figure 2. Predicted normalized o-dichlorobenzene emission rates from a batch aeration tank: kG/kL ) 50, Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Figure 3. Predicted dimensionless cumulative o-dichlorobenzene emission from a batch aeration tank: kG/kL ) 50, Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Figure 4. Predicted dimensionless o-dichlorobenzene emission rates from a continuous aeration tank: kG/kL ) 50, Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Figure 5. Effect of gas-liquid mass-transfer coefficient ratio on the normalized o-dichlorobenzene emission rates from a batch aeration tank: Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Effect of Gas-Film Mass-Transfer Resistance the two mass-transfer zones are almost the same (50% in each zone) although the liquid spray zone only contributes 36% of the total oxygen transfer rate.19 This suggests that the mechanical surface aerator used is not optimally designed or operated because it delivers only 36% oxygen but emits 50% of the VOC in the liquid spray zone. A lower rotational speed should be tried in order to reduce the VOC emission from the sprayed liquid droplets while keeping the overall oxygen transfer rate at an acceptable level. Overall, the two-zone model predicts a slightly higher dimensionless cumulative VOC emission than the ASCE-based model, as is shown in Figure 3. The dimensionless emission rates of odichlorobenzene from a continuous aeration system are calculated by eq 10 and eqs 28 and 29 for the ASCEbased model and the two-zone model, respectively, and the results are shown in Figure 4. As is shown in Figure 4, the two-zone model predicts a slightly higher VOC emission rate than the ASCE-based model and the VOC emission rates from the two mass-transfer zones are again almost the same.

According to the two-film theory, the gas-phase masstransfer resistance plays an important role in controlling the VOC emission rate. If the gas-liquid masstransfer coefficient ratio, kG/kL, in eqs 1, 16, and 19 approaches infinity, the gas-phase resistance is negligible and the overall VOC emission rate is controlled by the liquid-phase resistance only. Different kG/kL values were used to predict the VOC emission rates with the ASCE-based model; Barton1 used 150, Munz and Roberts20 used 40-150, Hsieh et al.21 used 38-110, Melcer et al.16 used 40, and Parker et al.6 used 16-24. The effects of the gas-liquid mass-transfer coefficient ratio, kG/kL, on the normalized emission rate of odichlorobenzene (Hc ) 0.045 at 19 °C) from a batch aeration tank and on the dimensionless emission rate of o-dichlorobenzene from a continuous aeration tank are calculated by the two-zone model, and the results are shown in Figures 5 and 6, respectively. Similar results for chloromethane (Hc ) 1.56 at 19 °C) are shown in Figures 7 and 8. The Henry’s law constant of a VOC is an indicator of the VOC solubility in water that

3182 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999

Figure 6. Effect of gas-liquid mass-transfer coefficient ratio on the dimensionless o-dichlorobenzene emission rate from a continuous aeration tank: Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Figure 8. Effect of gas-liquid mass-transfer coefficient ratio on the dimensionless chloromethane emission rate from a continuous aeration tank: Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Figure 7. Effect of gas-liquid mass-transfer coefficient ratio on the normalized chloromethane emission rates from a batch aeration tank: Tw ) 19 °C, Td ) 19.5 °C, and CG/Cvoco ) 0.

Figure 9. Effect of air temperature on the initial normalized o-dichlorobenzene emission rates from a batch aeration tank: kG/ kL ) 50, Tw ) 20 °C, RH ) 50%, and CG/Cvoco ) 0.

decreases with increasing Henry’s law constant. A lower water solubility of the VOC means that the VOC is more easily stripped from the liquid phase into the gas phase, and therefore the effect of the gas-phase resistance on the VOC mass transfer is negligible, as is shown in Figures 7 and 8. However, for a VOC with a lower Henry’s law constant, the effect of the gas-phase resistance on the VOC mass transfer is significant. A higher gas-phase resistance with lower kG/kL value will reduce the VOC emission rate, as is shown in Figures 5 and 6.

rates. From the above results we know that the liquid spray zone plays an important role in the total VOC emission rate. The volumetric mass-transfer coefficient in the liquid spray zone depends on the droplet water temperature, that is, the arithmetic average of the bulk liquid temperature and the wet-bulb temperature. The wet-bulb temperature can be directly read from the psychometric chart for a given air temperature and relative humidity (RH). The effects of the air temperature on the initial normalized emission rate of odichlorobenzene from a batch aeration tank and on the dimensionless emission rate from a continuous aeration tank with τ ) 8 h, kG/kL ) 50, Tw ) 20 °C, RH ) 50%, and CG/Cvoco ) 0 are shown in Figures 9 and 10, respectively. As is clearly shown in Figures 9 and 10, the VOC emission rates predicted by the ASCE-based model are insensitive to the change of the air temperature while those predicted by the two-zone model seem to linearly increase with increasing air temperature. It has long been recognized that the VOC emission problems are more severe in hot weather even if the water temperature is kept constant. This phenomenon is hard

Effect of Air and Water Environments If the bulk liquid temperature in the aeration tank is constant, the traditional ASCE-based model predicts the same VOC emission rates for different air temperatures. This suggests that the ASCE-based model cannot predict the effect of the air temperature on the VOC emission rates. On the contrary, the two-zone model developed in this study has the capability of assessing the impact of the air temperature on the VOC emission

Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999 3183

Figure 10. Effect of air temperature on the dimensionless o-dichlorobenzene emission rates from a continuous aeration tank: τ ) 8 h, kG/kL ) 50, Tw ) 20 °C, RH ) 50%, and CG/Cvoco ) 0.

Figure 12. Effect of the relative humidity on the dimensionless o-dichlorobenzene emission rate from a continuous aeration tank: τ ) 8 h, kG/kL ) 50, Tw ) 20 °C, Tair ) 25 °C, and CG/Cvoco ) 0.

Figure 11. Effect of the relative humidity on the initial normalized o-dichlorobenzene Emission rates from a batch aeration tank: kG/kL ) 50, Tw ) 20 °C, Tair ) 25 °C, and CG/Cvoco ) 0.

Figure 13. Effect of the water temperature on the initial normalized o-dichlorobenzene emission rates from a batch aeration tank: kG/kL ) 50, RH ) 70%, Tair ) 25 °C, and CG/Cvoco ) 0.

to be quantified by the ASCE-based model but can be easily predicted by the two-zone model. The effects of the relative humidity on the initial normalized emission rate of o-dichlorobenzene from a batch aeration tank and on the dimensionless emission rate from a continuous aeration tank with τ ) 8 h, kG/ kL ) 50, Tw ) 20 °C, Tair ) 25 °C, and CG/Cvoco ) 0 are shown in Figures 11 and 12, respectively. Again the ASCE-based model is not able to predict the impact of the relative humidity on the VOC emission rate. As is shown in Figures 11 and 12, the VOC emission rates increase with increasing relative humidity at constant water and air temperatures. At low relative humidities, the VOC emission rates seem to increase linearly with the relative humidity, but at very high humidities, the VOC emission rates approach constant. The effects of the water temperature on the initial normalized emission rate of o-dichlorobenzene from a batch aeration tank and on the dimensionless emission rate from a continuous aeration tank with τ ) 8 h, kG/ kL ) 50, RH ) 70%, Tair ) 25 °C, and CG/Cvoco ) 0 are

shown in Figures 13 and 14, respectively. It is interesting to find that the VOC emission rates predicted by the two-zone model are higher than those predicted by the ASCE-based model for water temperature lower than 26 °C. For water temperature higher than 26 °C, the two-zone model predicts lower VOC emission rates than the ASCE-based model. Conclusions A new mass-transfer model has been developed to predict the VOC emission rates from batch and continuous aeration tanks with mechanical surface aerators. 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 ASCE-based model. The gas-phase mass-transfer resistance is significant for VOCs with low Henry’s law constants. Compared with the ASCE-based VOC masstransfer model, the two-zone model can be used to assess

3184 Ind. Eng. Chem. Res., Vol. 38, No. 8, 1999

Figure 14. Effect of water temperature on the dimensionless o-dichlorobenzene emission rates from a continuous aeration tank: τ ) 8 h, kG/kL ) 50, RH ) 70%, Tair ) 25 °C, and CG/Cvoco ) 0.

the impacts of air environmental conditions, the air temperature, and the relative humidity, on the VOC emission rates from surface aeration systems: (1) For constant water temperature and air humidity, the VOC emission rates from batch aeration tanks and continuous-flow tanks increase linearly with increasing air temperature. The increase is more remarkable for VOCs with lower Henry’s law constants. (2) For constant water and air temperatures, the VOC emission rates from batch aeration tanks and continuous-flow tanks increase with increasing relative humidity, especially for VOCs with lower Henry’s law constants. The new two-zone model also gives more insight to design and operate better mechanical surface aerators that can manipulate the relative magnitude of the oxygen and VOC mass-transfer rates in the two zones to deliver more oxygen and emit less VOCs: (1) If the air temperature is greater than the water temperature, the impeller rotational speed should be lower to minimize the VOC emission from the sprayed droplets. (2) If the air temperature is less than the water temperature, the impeller rotational speed should be higher to maximize the oxygen transfer rate. The correlation between the oxygen/VOC mass transfer in the two mass-transfer zones should be established in the future for designing and operating mechanical surface aerators more effectively. Acknowledgment This work was supported by the National Science Council of Taiwan, Republic of China (Grant NSC 872214-E-036-002). Nomenclature At ) cross-sectional area of the aeration tank, m2 Au ) area covered by the spray umbrella, m2 Cd ) dissolved VOC concentration in the droplet, kmol/m3 Cd* ) saturation dissolved VOC concentration in the droplet, kmol/m3 CG ) VOC concentration in the air, kmol/m3

Cvoc ) dissolved VOC concentration in the bulk liquid, kmol/m3 Cvoco ) initial VOC concentration in the batch aeration tank, kmol/m3 Cvocf ) feed VOC concentration in the continuous aeration tank, kmol/m3 DO2 ) molecular diffusion coefficient of oxygen, m2/s Dvoc ) molecular diffusion coefficient of VOC, m2/s Emd ) Murphree efficiency of oxygen Emdvoc ) Murphree efficiency of VOC Hc ) Henry’s law constant of VOC, (kmol/m3 in gas)/(kmol/ m3 in liquid) Hcd ) Henry’s law constant of VOC at Td, (kmol/m3 in gas)/ (kmol/m3 in liquid) Hcs ) Henry’s law constant of VOC at Tw, (kmol/m3 in gas)/ (kmol/m3 in liquid) kG ) individual gas-phase mass-transfer coefficient, m/s kL ) individual liquid-phase mass-transfer coefficient, m/s Kdad ) volumetric mass-transfer coefficient of oxygen in the liquid spray zone, 1/s Kdadvoc ) volumetric mass-transfer coefficient of VOC in the liquid spray zone, 1/s KLaO2 ) volumetric mass-transfer coefficient of oxygen in the ASCE-based model, 1/s KLavoc ) volumetric mass-transfer coefficient of VOC in the ASCE-based model, 1/s KLSas ) volumetric mass-transfer coefficient of oxygen in the surface reaeration zone, 1/s KLSasvoc ) volumetric mass-transfer coefficient of VOC in the surface reaeration zone, 1/s n ) exponent in eq 1 nd ) exponent in eq 18 ns ) exponent in eq 21 Qd ) droplet flow rate in the liquid spray mass-transfer zone, m3/s QL ) liquid flow rate in the continuous aeration tank, m3/s t ) batch aeration time, s tf ) droplet flight time, s tf′ ) total droplet flight time, s Tw ) bulk liquid temperature, K Td ) average droplet liquid temperature, K Vc ) critical volume of VOC, m3/kmol VL ) liquid volume in the aeration tank, m3 VOCER ) VOC emission rate, kmol/s θ ) temperature correction factor for the volumetric masstransfer coefficient τ ) hydraulic retention time in the continuous aeration tank, s $ ) normalized VOC emission rate from the batch aeration tank, 1/s ξ ) dimensionless cumulative amount of VOC emission from the batch aeration tank ζ ) dimensionless VOC emission rate from the continuous aeration tank

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Received for review January 29, 1999 Revised manuscript received May 7, 1999 Accepted May 20, 1999 IE990073V