Verification of Wind-Driven Volatilization Models

Environmental Fluid Mechanics (2006) 6: 1–24 DOI 10.1007/s10652-005-2933-6

© Springer 2006

Verification of Wind-Driven Volatilization Models CARLO GUALTIERI Hydraulic and Environmental Engineering Department “Girolamo Ippolito” University of Napoli “Federico II”, Via Claudio, 21 – 80125, Napoli, Italy Received 11 October 2004; accepted in revised form 6 September 2005 Abstract. Mass-transfer processes of paramount importance, such as reaeration and volatilization, occur at the air–water interface. Particularly, volatilization is intensively studied because it can be a relevant removal process for toxic contaminants from flowing and standing surface waters. The paper provides a comparison among predictive equations available from literature for standing waters for the case of MTBE contamination. Most of the considered equations tend to overestimate the volatilization rate, while three equations offer a good fit with the observed data. Finally, these equations are applied to a larger amount of field data. Key words: air–water interface, environmental fluid mechanics, field verification, gas-transfer, volatilization, wind effect

1. Foreword Mass-transfer processes of paramount importance for environmental quality occur at the air–water interface. In particular, gaseous pollutants may be directly exchanged between air and water in either direction across the air–water interface; in fact, gas fluxes being transferred could be upward to the air or downward to the water depending on the substances involved. Thus, gas exchange is a two-way process involving both gas absorption, i.e. air to water, and volatilization, i.e. water to air, across an air–water interface, for a volatile or semi-volatile chemical. Since these chemicals may be discharged in rivers and lakes, volatilization can significantly affect their fate within those waterbodies. For example, environmentally important compounds of low molecular weight such as benzene, chloroform, methylene chloride, and toluene have been shown to volatilize rapidly from water [1]. Other environmental contaminants of higher molecular weight such as DDT that might not be expected to volatilize also have been recognized to volatilize at appreciable rates. Therefore, estimation of the E-mail: [email protected]

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CARLO GUALTIERI

volatilization rate is a key issue in the application of a modeling framework of contaminant fate. In the present paper, the influence of the liquid concentration boundary layer (CBL) on mass-transfer for 20 environmental contaminants is first assessed. Then, the influence of environmental conditions on masstransfer is investigated. Wind-driven volatilization, that is typical for standing waters, such as lakes, impoundments and wide estuaries, then is considered. The paper proposes a comparison among predictive equations from the literature for a case of MTBE contamination. These equations are, finally, compared to a SF6 set of volatilization field data. 2. State of the Art: Two-CBL Model Volatilization is the movement of volatile chemicals from the bulk water phase of a waterbody across the air–water interface into the air. It is usually expressed as a first-order process, where its rate is directly proportional to the concentration of the chemical undergoing the process. Thus, chemical flux through the air–water interface equals its rate of change over the time t in the bulk water as [2]: −V ·

dCw = KL · A · (Cw − Ce ) dt

(1)

where V is the water volume [L3 ], A is the area of the air–water interface [L2 ], Cw is the water chemical concentration [M·L−3 ], and Ce is the chemical concentration in water in equilibrium with the concentration in the air [M·L−3 ]. Finally, KL is the mass-transfer coefficient for the chemical [L·T−1 ]. Equation (1) can be also written as: −

dCw = Kvol · (Cw − Ce ) dt

(2)

where Kvol is the volumetric volatilization rate constant [T−1 ], given, if h is the mean water depth, by: KL · A KL = (3) V h Usually, the volatile chemical concentration in the air above the waterbody is negligible with respect to the concentration in the water. Consequently, Ce ≈ 0 in (1) and this equation can be integrated to yield: Kvol =

C = C0 · exp (−Kvol · t)

(4)

where C0 is the chemical concentration in the water at t = 0. It can be useful to compute the time required for the concentration to be halved by volatilization t50 . It follows from (4) that:

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

t50 =

0.693 Kvol

3 (5)

The foregoing analysis points out that the key point in any parameterization of the volatilization process is estimation of the constant KL or Kvol . Gas-transfer is classically considered as a process significantly influenced by turbulence on both sides of the air–water interface. In fact, a turbulent flow is a spectrum of eddy sizes, from the integral scale down to the Kolmogorov scale, that approximates the smallest turbulent motions. As the turbulent eddies approach to the air–water interface, this interface tends to damp them as they approach closer than their length scale. Thus, turbulent transport decreases near the free surface and gas must travel by only molecular diffusion. This process gives rise to diffusive or concentration boundary layers (CBL) on both sides of the interface [3]. Within these layers, the fluid is almost stagnant or only intermittently mixed. Outside the CBLs, turbulent motions provide full vertical mixing and the gas profile becomes practically uniform at the bulk concentration. To be transferred, a gas must cross both the CBLs. Since the movement of a gas across the air–water interface depends on the resistance that it encounters crossing the CBLs, the effect of these layers could be envisioned as that of two resistors in series in an electric circuit [4]. Thus, the mass-transfer coefficient can be equated to: 1 1 1 = + KL kl H · kg

(6)

where kl and kg are the liquid and gaseous layer coefficients [L·T−1 ], respectively, and H is the dimensionless Henry’s constant. Inspection of (6) highlights that chemicals with high H are rapidly purged from the water, whereas chemicals with low H tend to stay in solution. Furthermore, as the reciprocals of mass-transfer coefficients are the resistances to mass-transfer, Equation (6) can rewritten in term of resistances as [5]: rL = rl + rg

(7a)

where: rL =

1 KL

rl =

1 kl

rg =

1 . H · kg

(7b)

Also, Equation (6) states that the total resistance to gas transfer depends on each resistance in the water and gaseous CBL. Therefore, depending on the relative magnitudes of H, kg , and kl , the process may be controlled by

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CARLO GUALTIERI

the liquid, the gas, or both layers. Particularly, the influence of liquid CBL can be quantified as: H rl . = rL H + kl /kg

(8)

Thus, calculating the percentage resistance in the liquid film for a certain substance requires the estimation of mass-transfer coefficients kg and kl . Also, knowledge of Henry’s constant H is necessary. For a gas, such as oxygen, cyclohexane, or nitrogen, that has low-solubility in water and high partial pressure in the atmosphere, mass-transfer is controlled by only the diffusive boundary layer on the liquid side. For these gases, it holds that rl /rL ≈ 1 and Equation (6) becomes KL ≈ kl . Notably, this is a significant simplification to the mass-transfer parameterization. However, its application should be carefully assessed. Notably, for these substances the mass-transfer rate KL can be related to the mean thickness of liquid CBL δc-w as: KL =

Dm δc-w

(9)

where Dm is the molecular diffusivity of the gas into water. 3. Assessment of the Influence of Liquid CBL In this section, the values of ratio rl /rL for 20 environmental contaminants have been evaluated. Particularly, the contaminants considered were six different PCBs; four pesticides, aldrin, dieldrin, lindane and toxaphene; two aromatic hydrocarbons, benzene and naphtalene; two alkyl-benzenes, methylbenzene and ethylbenzene; two halogenated alkanes, chloroform and 1,2dichloroethane; and, finally, chlorobenzene, trichloroethylene (TCE), methyl tertiary-butyl ether (MTBE), and mercury. As H data for those chemicals exhibit some spreading, mean values were considered and are listed in Table I referred to a temperature of 25◦ C [6]. Few data are available for mass transfer coefficients kl and kg . In the open ocean a value of 8.3 × 10−3 m/s is commonly used for kg (Rathbun, 1982). Field and laboratory data show that the gas-film coefficient kg is typically in the range from 3.00 × 10−3 to 3.00 × 10−2 m/s, whereas kl lies between is 5.00 × 10−6 to 5.00 × 10−5 m/s [8]. In lakes, kl varies from 1.16 × 10−6 to 1.16 × 10−4 m/s and kg from 1.39 × 10−3 to 1.39 × 10−1 m/s [6]. These values correspond to a range from 0.1 to 10 m/day for kl and from 120 to 12000 m/day for kg . Thus, the ratio kl /kg generally is in the range from 0.001 to 0.01, with the higher values in small lakes due to lower kg because of wind sheltering [6]. Three values were considered for the ratio kl /kg in this paper. They were obtained coupling maximum, minimum, and

5

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

Table I. Values of Henry’s constants H and He . Chemical

Source

M (g/mole) He (Pa×m3 ×mole−1 ) H

Aroclor 1016 Aroclor 1242 Aroclor 1248 Aroclor 1254 Aroclor 1260 Mean PCBs Aldrin Dieldrin Lindane Toxaphene Benzene Naphthalene Methylbenzene Ethylbenzene Chlorobenzene Trichloromethane Trichloroethylene 1,2-Dichloroethane MTBE Mercury

[6] [6] [6] [6] [6] [6] Various Various Various [6] [2] [2] [2] [2] [2] [2] [7] [2] Various Various

257.9 266.5 299.5 328.4 375.7 305.6 364.91 380.91 290.83 430 78.11 128.2 92.14 106.17 112.6 119.4 131.39 99 88.15 200.59

3.35E+01 3.85E+02 3.59E+02 1.46E+02 7.17E+02 2.18E+02 1.67E+00 1.09E+00 3.33E-01 5.72E+03 5.57E+02 5.60E+01 6.38E+02 7.56E+02 3.58E+02 3.91E+02 1.07E+03 1.14E+02 6.43E+01 1.25E+03

1.35E−02 1.55E−01 1.45E−01 5.91E−02 2.89E−01 8.78E−02 6.72E−04 4.38E−04 1.34E−04 2.31E+00 2.24E−01 2.26E−02 2.57E−01 3.05E−01 1.44E−01 1.58E−01 4.34E−01 4.62E−02 2.59E−02 5.03E−01

Table II. Values of mass-transfer coefficients kl , kg and their ratio kl /kg . High

Mean

Low

Liquid-film coefficient kl (m/s) 1.157E−04 1.157E−05 1.157E−06 Gas-film coefficient kg (m/s) 1.389E−01 1.389E−02 1.389E−03 Ratio kl /kg 8.33E−02 8.33E−04 8.33E−06

mean value for kl with the minimum, maximum, and mean value for kg and they are listed in Table II. The percentage resistance to the mass-transfer in the liquid CBL finally was estimated. Results for the ‘mean’ conditions are shown in Figure 1, where the data for some environmentally important gases, such as ammonia, sulfur dioxide, carbon dioxide, nitrogen and oxygen, are also presented. Results show that lindane, dieldrin, and aldrin are controlled by the gaseous CBL, whereas the remaining chemicals are controlled by the liquid CBL. Noticeably, if a lower value of the ratio kl /kg would be applied, the control shifts to the liquid film. Therefore, results in Figure 1, where the

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CARLO GUALTIERI

Resistance in the liquid film - %

100 MTBE

80

Aroclor 1254

60

Chloroform

CO2

O2

Benzene PCBs

TCE

Toxaphene Aroclor 1260

40 Aldrin

20 Lindane

0 1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

1.0E+02

Henry's constant H

Figure 1. Resistance to mass-transfer in the liquid film.

ratio kl /kg is equal to kl /kg = 8.33 × 10−4 , are representative of ‘mean’ conditions where KL ≈ kl applies. 4. Estimation of Mass-Transfer Coefficients: Available Models Several predictive equations have been proposed to estimate mass-transfer coefficients kl and kg [2, 6, 9, 10]. Particularly, in this Section seven predictive equations for kl and three equations for kg from the literature are considered and presented. They were developed for standing waters, such as lakes, impoundments and wide estuaries, where wind is the dominant factor causing volatilization. Notably, as wind speed exceeds 10 m/s, waves breaking and formation of air bubbles produce an increase in mass-transfer [8]. Inspection of the considered equations shows that they have different structure and numerical constants. Furthermore, they exhibit two different approaches. In fact, some equations directly compute those coefficients, whereas others follow the so-called approach of a reference substance [9]. The reference substance approach states that the film mass-transfer coefficients for a solute are directly proportional to the film mass-transfer coefficients for a reference substance and that the proportionality constants are independent of mixing conditions within the water and air phase [2]. Thus, it results that: kl = φ · kl-ref kg = ψ · kg-ref

(10a) (10b)

where kl/g-ref is water/air-film coefficient for the reference substance and φ and ψ are the dimensionless conversion factors. Therefore, this approach requires the vailability of an equation to compute kl/g-ref . Notably,

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VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

oxygen is typically used as the reference substance for the water film since oxygen is overwhelmingly liquid-film controlled due to its high H value and oxygen absorption, i.e. reaeration, is a process widely studied although recent research has demonstrated that predictive equations in the literature commonly applied for streams and rivers are often inaccurate [11, 12]. Also, a proper approach to mass-transfer at the air-water interface can be obtained using dimensional analysis [13]. However, the equation developed by Lunney et al. [14] uses ethyl ether as a reference substance. On the other hand, water is commonly used for the air film because there is no liquidfilm resistance in the evaporation of water and, thus, this process is completely controlled by the air-film resistance [2]. 4.1.

MASS-TRANSFER COEFFICIENT FOR LIQUID FILM

Predictive equations for kl are herein presented and discussed. Notably, they all result in kl = 0 during periods of no wind. However, other factors, such as residual fluid motions and thermal gradients create a low level of turbulence to maintain some degree of chemical transport on the liquid side of the air–water interface also without wind [10]. Consequently, a quadratic relation with a minimum kl for oxygen in nowind conditions has been suggested [8]: 2 kl-O2 = 0.0004 + 0.00004 · Vwind -10 ·

(11)

where kl,O2 is in cm/s and Vwind-10 is wind speed measured at 10 m above the water surface [L·T−1 ], which is measured in m/s. Furthermore, as a result of the foregoing analysis, predictive equations for kl can be subdivided in two groups: GROUP A. This group comprises two equations that directly estimate kl . These equations have a very different rationale and structure. Their main characteristics are shown in Table III. Wanninkhof et al. [15] used sulfur hexafluoride SF6 as a tracer gas in five lakes in North America to derive the following power law equation:
1.64 kl = 0.108 · Vwind -10 ·

Sc 600

−0.50 (12)

Table III. Equations for direct estimation of liquid film coefficient kl . Author

Type

Chemical Vwind-10 range (m/s).

Wanninkhof et al. [15] Empirical – Field data SF6 O’Connor [16] Theoretical –

0–8.0 Smooth surface 0–7.0

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CARLO GUALTIERI

Table IV. Drag coefficient Cd estimation. Cd

Vwind-10 range

8.50E−04 [0.85 + 0.11 · (Vwind-10 − 5)] · 10−3 2.50E−03

0–5.0 5.0–20.0 >20.0

where kl is in m/day, Vwind-10 in m/s, νw is water kinematic viscosity [L2 ·T−1 ] and its ratio to molecular diffusivity of the solute, Dm , is the dimensionless Schmidt number Sc = νw /Dm . This equation should hold if the average Vwind-10 is less than 8 m/s. Notably, mass transfer kl increases as Sc decreases and, thus, Dm increases. O’Connor has developed a theoretically based set of equations to compute mass-transfer for low-solubility gases, where the liquid film controls mass-transfer and, thus, KL ≈ kl applies, as a function of wind speed Vwind-10 [16]. In fact, as wind blows over water, shear is exerted at the air– water interface, which establishes the structure of the boundary layers in both media. Thus, the rate of transfer between air and water is influenced by the dynamic characteristics of these layers. Particularly, if Vwind-10 < 7 m/s, the air–water interface from both air and water sides can be depicted as a smooth surface, where the height of roughness elements due to shear stress is completely encompassed by the thin, viscous boundary sublayer of the fluid, where the momentum transfer is dominated by viscous forces. As a result, within this sublayer, there is a diffusional sublayer where mass transfer is controlled by molecular diffusion and kl is: 

ρa 0.50 κ 1/3 Dm 2/3 kl = · Cd · · · Vwind-10 (13a) νw ρw 0 where Cd is the drag coefficient, ρa and ρw are air and water densities [M·L−3 ], respectively, κ is the Von K`arman constant, and 0 is a numerical coefficient. Notably, the ratio of the densities ρa /ρw can be taken as 0.0012, whereas κ is commonly taken as 0.40, and 0 is in the range from 5 to 7. Finally, the drag coefficient Cd can be expressed as a function of wind speed Vwind-10 as listed in Table IV [10]. If Vwind-10 > 20 m/s, the air–water interface should be considered a rough surface, whose roughness elements are greater than the thickness of CBL, and the gas-transfer process is also influenced by turbulence. Thus, wind flow on the water is fully established and rough and the gas-transfer rate is [16]:
0.50 Dm ρ a ν a  kl = · · · Cd · Vwind-10 (13b) κ · ze ρw νw

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VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

Table V. Estimation equations for φ. Author

Type

Reference substance

Equation for φ

Mills et al. [18]

Theoretical

Oxygen

φ=

MacKay and

Empirical – laboratory

Oxygen

Yeun [17] Rathbun 1 [9] Rathbun 2 [9]

data Empirical Empirical

Oxygen Oxygen

Lunney et al.

Theoretical

Ethyl ether

 M 0.25 O2

M

 D org 0.50 m-O φ = Dm-org2 φ = 2.52 · Vm−0.301 -org −0.232 φ = 1.84 · Morg  0.50 D ether φ = m−Ethyl Dm

[14]

where ze is the equilibrium roughness, that is ze = 0.25 cm, and νa is kinematic viscosity of air. Thus, at higher wind speeds, the gas-transfer rate depends on the square root of wind velocity. Finally, for intermediate wind speeds, a transitional zone could be defined, where the gas-transfer process could be estimated combining (13a) and (13b). This transition zone extends over the range from 7 to 20 m/s. GROUP B. This group comprises five equations that are based on the previously outlined reference substance approach, i.e. Equation (10a). These five equations are listed in Table V. In this approach, the key point is the estimation of the φ coefficient. The parameter φ depends on the ratio between molecular weight M (Mills et al., 1985) or molecular diffusivity Dm [17] of the reference substance and that of the substance being modeled. For molecular weight, the exponent for φ is 0.25. At fluid–fluid interfaces, the exponent for Dm is 0.57 ± 0.15 [18] with a typical value of 0.50 selected by MacKay and Yeun [17] and Lunney et al. [14] (Schwarzenbach et al. [8]). For a completely stagnant interface the exponent could be set equal to 1 ([10]). Notably, as Dm for some environmental contaminants is unknown, this parameter can be derived using correlation equations with oxygen and water values [10]. In the equations proposed by Rathbun [9] φ is related to M or to the molal volume at the normal boiling temperature Vm , in cm3 /gmole. Both correlations proposed by Rathbun were used here to compare their results. Thus, in this case, φ could be a temperature-dependent parameter, whereas for the equation proposed by Mills et al. [18] φ, which is expressed in terms of molecular weight M, is independent from temperature. Moreover, since the molecular diffusivity could be corrected for temperature using water dynamic viscosity µw [M·L−1 ·T−1 ], Dm variations are the same for each substance [10]. Thus, φ for the Lunney et al. [14] and MacKay and Yeun

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Table VI. Equations for liquid film coefficient kl-O2 and kl-ethylether . Author

Type

Banks and Herrera [20] Wanninkhof et al. [15] Gelda et al. [21] Lunney et al. [14]

Empirical Empirical Empirical Empirical

Chemical – – – –

Field Field Field Field

data data data data

Vwind-10 range (m/s).

O2 SF6 0–8.0 0–10.0 O2 Ethyl ether 5.0–16.0

[17] equations also is independent from temperature. Estimation equations for φ are in Table V. The mass-transfer coefficient through the liquid film for the reference substance, i.e. oxygen, kl-ref = kl-O2 must be evaluated to apply (10a). There are some equations that relate kl-O2 with wind speed. They were derived in reaeration studies and they are mostly power laws for wind speed with the exponent ranging from 0.63 to 2 [19]. Only three reaeration equations have been considered in the present study. Their main characteristics are listed in Table VI. In order to characterize the different turbulence regimes that result at the air–water interface as wind velocity increases, Banks and Herrera [20] derived that kl-O2 , in m/day, is: 0.50 2 kl-O2 = 0.728 · Vwind -10 − 0.317 · Vwind-10 + 0.0372 · Vwind-10

(14)

where Vwind-10 is in m/s. This equation has been considered herein because of its particular structure. Moreover, Wanninkhof et al. [15] Equation (12) can also be applied for oxygen mass-transfer. Assuming that the Schmidt number of oxygen in water is for T = 20◦ C Sc≈ 550, Equation (12) yields: 1.64 kl-O2 = 0.1128 · Vwind -10

(15)

where kl-O2 is in m/day and Vwind-10 is in m/s. Furthermore, Gelda et al. [21] using field data of water column dissolved oxygen concentrations in Onondaga Lake over a rather long period of time derived the following empirical equation for kl-O2 : kl-O2 = 0.20 · Vwind-10 2.0 kl-O2 = 0.057 · Vwind -10

if Vwind-10 < 3.5 m/s if Vwind-10 > 3.5 m/s

(16a) (16b)

where kl-O2 is in m/day and Vwind-10 is in m/s. The Gelda et al. [21] equation was developed on a whole-lake system such as the Wanninkhof et al. [15] equation and they provide substantially similar results.

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VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

Table VII. Input data for kl estimation. T (◦ )C

M (g/mole) Vm (cm3 /mole) He (Pa×m3 ×mole−1 ) H

20 Sc

88.15 ρa /ρl

1102.57 0.0012

129.5 κ

41.33 0

0.40

6.50

ν (m2 /s).

0.0170 1.003 × 10−6 Dm-MTBE (m2 /s). 9.12 × 10−10

Finally, in order to apply Lunney et al. [14] equation, the mass-transfer coefficient for ethyl ether in the liquid phase must be estimated as: 2 kl-ethylether = 0.02256 · Vwind -10

(17)

where kl-ethylether is in m/day and Vwind-10 is in m/s. Equation (17) holds when the fetch, i.e. the distance the wind travels over the water’s surface, 1/2 given as Ar / h, where Ar and h are the area and the depth of the water body, is greater than 50, when Ar and h are in km2 and m, respectively. Also, Equation (17) holds for wind speeds between 5 and 16 m/s, whereas if Vwind-10 < 5 m/s, a minimum value of liquid-film coefficient kl = kl-min = 0.48 m/day should be applied [10]. A first comparison of the liquid film coefficients kl resulting from the previously presented predictive equations was done considering MTBE as the volatile chemical. A range of wind speed Vwind-10 from 0 to 7 m/s was considered. The data needed for the calculations are listed in Table VII. The value of He is that reported by Rathbun [2], corrected for temperature. Notably, the value of molecular diffusion for MTBE in water Dm-MTBE was obtained as the arithmetic mean from values reported by Schwarzenbach et al. [8] and those computed using the correlation equations proposed by Rathbun [9]. Then, the mean Schmidt number was computed. The value of the parameters in Equation (13a) are those suggested by O’Connor [16]. To estimate kl with oxygen as the reference substance, the value of kl-O2 was computed using Equation (15). The values of φ coefficient resulting from the considered equations are listed in Table VIII. They are quite different and are primarly in the range from 0.583 to 0.776. Only value from Lunney et al. [14] equation is > 1, since this value refers to ethyl ether as the reference substance. Comparison shows that the predictive models provide a broad range of results. For Vwind-10 = 7 m/s, values of kl lie in the range from 0.77 to 2.11 m/s. The O’Connor [16] and Mills et al. [18] equations provide minimum and maximum values, respectively. Also, the Wanninkhof et al. [15] and MacKay and Yeun [17] equations exhibit identical values through the considered range of wind speed. The Rathbun [9] equations provide lower

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Table VIII. Values of φ conversion factor. Author

φ

Mills et al. [17] MacKay and Yeun [17] Rathbun 1 [9] Rathbun 2 [9] Lunney et al. [14]

0.776 0.712 0.583 0.651 1.033

Table IX. Estimation equations for ψ. Author

Reference substance

Mills et al. [18]

Water vapor

Rathbun [9]

Water vapor

Harbeck [22]

Water vapor

Equation for ψ  M 0.25 H2 O ψ = Morg −0.462 ψ = 4.42  D · Morg  m-H2 O ψ= Dm

results. Finally, the Lunney et al. [14] equation provides up to Vwind-10 = 4.5 m/s values lower than O’Connor [16] and higher values for Vwind-10 greater than 4.5 m/s. Interestingly, the O’Connor [16] equation, that is only theoretical, has a different shape since it is linear, whereas the remaining equations are power laws with exponents between 1.64 and 2. 4.2.

MASS-TRANSFER COEFFICIENT FOR GAS FILM

All predictive equations of the mass-transfer coefficient for the gas film kg apply the reference substance approach, where water is the reference substance. The dimensionless conversion factor ψ depends on the ratio between molecular weight M of water and that of the substance being modeled [18] or it is related to Vm [9]. In this case, ψ is a temperaturedependent parameter. Estimation equations for ψ are listed in Table IX. As for the liquid film coefficient, the mass-transfer coefficient for the reference substance, i.e. water vapor, in the gas phase must be evaluated. Each author in Table IX has his own equation based on empirical field data for this purpose. Mills et al. [18] developed an equation where kg-H2 O is a linear function of wind speed as: kg-H2 O = 168 · Vwind-10

(18)

where kg-H2 O is in m/day and Vwind-10 is in m/s. Rathbun and Tai [1] proposed an equation that also is temperature-dependent: kg-H2 O = 416 + 156 · Vwind-10 · exp [0.00934 · (T − 26.1)]

(19)

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

13

where kg-H2 O is in m/day, Vwind-10 is in m/s, and T is the temperature of the process, in ◦ C. Finally, Lunney et al. [14] suggested an equation where also the area of the air-water interface Ar is present: kg-H2 O = 192.24 · Vwind-10 · A−0.05 r

(20)

where kg-H2 O is in m/day, Vwind-10 is in m/s, and Ar is km2 . Notably, in Equations (18) and (20) the gas phase mass transfer coefficient is valid for wind speeds Vwind-10 > 0, since if Vwind-10 = 0, then also kg-H2 O = 0 and mass transfer should not occur. On the contrary, Equation (19) results in a minimum value of kg-H2 O = kg-H2 O-min = 416 m/day. However, as the wind speed tends toward zero, weak air-side processes, including thermal gradients and water evaporation, maintain the coefficient at some small finite value [10]. Thibodeaux [10] suggested that under quiescent conditions, kg-H2 O should be conservatively approximated to be 1/100 of the gas phase mass transfer coefficient under windy conditions. 5. Verification of Volatilization Models In this section, the considered equations are applied to test their predictive performance using the field data of methyl tertiary-butyl ether (MTBE) volatilization from Lake Perris, that is located in southern California, 20 km southeast of Riverside [23]. It is owned and managed by the California Department of Water Resources (DWR) as a drinking water reservoir [24]. MTBE is an oxygenated compound that has been added to gasoline in the USA. As a result of its use, detections of MTBE in ground water and surface water have increased in some areas of the USA and Europe [25– 28]. The main source of MTBE in Lake Perris is releases from recreational vehicles. Their number is limited to 450 boats on the lake at any one time. Particularly, two-cycle watercrafts have significantly contributed to elevated concentration of MTBE. However, after recreational boating was ceased and, thus, there was no input of MTBE, its concentration decreased. Moreover, as advective losses were negligible since the hydraulic residence time was much longer than the time associated with volatilization, the decay process within the lake could be described as a first-order process using Equation (4). Therefore, field data of MTBE concentration over the decay process can be used to derive Kvol and KL applying Equations (3) and (4). Notably, at the starting time of the field study, the beginning of October 1996, Lake Perris was stratified and, thus, MTBE was confined in the epilimnion since no MTBE mixing below the thermocline was found [23]. MTBE concentrations were measured at 0.4 m below the water surface and it was assumed that wind action and water currents rapidly mix MTBE throughout the depth of the epilimnion, once introduced into the lake from the boats [23].

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CARLO GUALTIERI

2.5 Wanninkhof et al. O'Connor Mills et al. MacKay and Yeun Rathbun 1 Rathbun 2 Lunney et al.

kl - m/dayz

2.0 1.5

Mills et al. Wanninkhof et al.

Rathbun 1

1.0 Lunney et al.

0.5

O'Connor

0.0 0

1

2

4 3 Vwind-10-m/s

5

6

7

Figure 2. Liquid film coefficient kl for MTBE volatilization. 25

8

(a)

(b)

Wind speed V wind-10 - m/s

Water Temperature - ˚C

7 20

15

10

6 5 4 3 2

5 1 0

0 1

2 3 4 5 6 7 8 9 10 11 12 Time - 10 days periods

1

2

3 4 5 6 7 8 9 10 11 12 Time - 10 days periods

Figure 3. (a) Water temperature in Lake Perris starting October 3 (b) Wind speed near Lake Perris starting October 3, 1996.

The samples were collected over a period of 4 months, up to the end of January 1997. Also, wind speed and water temperature in that period exhibits a considerable temporal variability. Figure 3(a,b) shows wind speed Vwind-10 and water temperature Twater values used for the simulations. These data are the mean over 10 days of the daily mean value. Wind speed data are taken from March Air Force Base, 3 km to the northwest and they were downloaded from the NOOA website. Also, air temperature data were downloaded. Water temperature data are taken from McCord and Schladow [24]. Wind speed ranges from 0 to 6.75 m/s with a mean value over the sampling period of 5.14 m/s. Water temperature significantly decreases from October to mid January, when water temperature remains at 11◦ C. Water temperature values were used to estimate water kinematic viscosity ν and oxygen molecular diffusivity Dm-O2 , that are needed to estimate

15

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

Table X. Equations for gas film coefficient kg-H2 O . Author

Type

Chemical

Vwind-10 range (m/s).

Mills et al. [18] Rathbun and Tai [1] Harbeck [22]

Empirical – Field data Empirical – Field data Empirical – Field data

H2 O H2 O H2 O

– – –

Table XI. Hydraulic and environmental conditions for Lake Perris. Parameter

Value

Surface area, Ar (km2 ) Epilimnion depth, h (m) Whole-lake depth (m). Average hydraulic residence time (years).

9.061 8 35 >1

kl-O2 . Also, temperature data were used to correct Henry’s constant H , molecular diffusivity Dm-MTBE , and Schmidt number values for MTBE, that are listed in Table VII and refer to a temperature of T = 20◦ C. The temperature correction equation for H is that reported in Rathbun [2], whereas for molecular diffusivity the correlation with the absolute viscosity µ suggested by Thibodeaux [10] was applied. As previously outlined, molecular diffusivity also is used to compute the correction factor φ for the MacKay and Yeun [17] and Lunney et al. [14] equations and the correction factor ψ for the Harbeck [22] equation. However, since the variation of Dm-MTBE , Dm-O2 , and Dm-ethyl ether with temperature follows the same correlation, only the correction factor φ for the MacKay and Yeun [17] equation, that is not linear, is affected by the temperature. Other hydraulic and environmental conditions for Lake Perris are listed in Table XI. To test the previously presented equations with the field data of CMTBE in Lake Perris the following procedure was applied. Twelve periods of 10 days from the beginning of October 1996 to the end of January 1997 were considered using the water temperature and wind speed shown in Figure 3a and b. First, the liquid film coefficient kl values for MTBE were directly estimated using Equations (12) and (13a). Then, to apply the reference substance approach, the liquid film mass-transfer kl-ref was estimated. For the equations of Mills et al. [18], MacKay and Yeun [13], Rathbun [9] 1 and 2 the reference substance is the oxygen, whose coefficient kl-O2 was computed using Equations (14), (15), (16a), and (16b). These values were converted to MTBE using the respective conversion factors φ as defined in Table V.

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CARLO GUALTIERI

Table XII. Values of ψ conversion factor. Author

ψ

Mills et al. [18] Rathbun 1 [9] Harbeck [22]

0.672 0.558 1.973

The φ values applied are listed in Table VIII. Therefore, there are three values of kl-MTBE for the Mills et al. [18], MacKay and Yeun [17], and Rathbun [9] 1 and 2 equations. One value is obtained from Banks and Herrera [20] equation, another one value is obtained from Wanninkhof et al. Equation [15], i.e. Equation (15), and the last one is obtained from Gelda et al. [21] equation. Finally, the Lunney et al. [14] equation was used with Equation (17) to compute kl-ethyl ether , that was converted to kl for MTBE using conversion factor φ in Table V. Mass-transfer coefficients in the gas phase kg also were estimated. The available equations, i.e. (18), (19), and (20) provide kg-ref , with water vapor as the reference substance. The mean value for kg-H2 O from these three equations was calculated. Then, it was converted using the respective conversion factor ψ as defined in Table IX. The ψ values used are liste in Table XII. Therefore, three values of kg-MTBE were obtained for each considered 10-day period. Then, the arithmetic mean value also was calculated. Finally, to evaluate the relative importance of the liquid and gas films the ratio rl /rL was computed using Equation (9). The values of rl /rL are in the range from 0.82 to 0.96 and from 0.77 to 0.96 if Equations (14) or (15) are used, respectively. In particular, the O’Connor [16] Equation (13a) provides a mean error of about 5% assuming that KL ≈ kl . This result confirms that MTBE mass-transfer is largely controlled by the liquid film. Then, to compute the mass-transfer coefficient KL through Equation (6), the mean value for kg-MTBE was used together with the seven kl-MTBE values previously estimated. Mass-transfer coefficients KL also were set equal to kl . Finally, the corresponding values of Kvol were obtained both for KL coming from Equation (6) and set equal to kl . However, only values from the complete equation for KL , i.e. (6), are shown in the figures herein presented. Figures 4a,b, 5a,b, 6a,b show decay plots of MTBE in Lake Perris if kl-O2 is computed using the Banks and Herrera [20], Wanninkhof et al. [15] and Gelda et al. [21] equations, respectively. The filled circles in these plots represent the MTBE field data collected at 0.4 m below the water surface. Notably, the decay process has been divided into two different phases, i.e. before the turnover, that occurred at day 30, and after the

17

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS 6

(a) O'Connor

20

5

Lunney

4 CMTBE - µg/L

CMTBE - µg/L

(b)

lake mixing

Rathbun 1

lake mixing

10

O'Connor Lunney

3 MacKay

Rathbun 1

2 MacKay Rathbun 2

1

Rathbun 2

Wanninkhof Wanninkhof

0

0 0

10

20 Time - days

30

30

40

60

90

120

Time - days

Figure 4. (a,b) Lake Perris – Banks and Herrera [20].

(a) 5 CMTBE - µg/L

20 O'Connor

CMTBE - µg/L

(b)

lake mixing

Rathbun 1

4 O'Connor

3 Mills

lake mixing

10

2

Lunney Rathbun 1

Wanninkhof

1

Lunney

Wanninkhof Mills

0

0 0

10

20 Time - days

30

40

30

60

90

120

Time - days

Figure 5. (a,b) Lake Perris – Wanninkhof et al. [15].

turnover until day 102. In fact, in late fall, at the beginning of November 1996, corresponding to day 30, the change of climatological conditions, produced whole-lake mixing. Thus, the hydraulic depth to be considered in the decay process increased from 8 m to about 35 m, i.e. whole-lake depth. This change produces a remarkable decrease in Kvol values, as stated by Equation (3), and the volatilization process, that is fast until day 30, slows down. Therefore, Figures 4a, 5a and 6a show the decay process up to day 30, and Figures 4b, 5b and 6b show the process from day 30 to day 102, when the last field data were collected.

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CARLO GUALTIERI 6

(a)

(b)

lake mixing

5

20

4

CMTBE - µg/L

CMTBE - µg/L

O'Connor

Rathbun 1 lake mixing

10

O'Connor

3 Mills

2

Lunney Rathbun 1

Mills

1

Lunney

Wanninkhof

Wanninkhof

0

0 0

10

20

30

40

30

Time - days

60

90

120

Time - days

Figure 6. (a,b) Lake Perris – Gelda et al. [21].

The turnover also gave rise to a different MTBE concentration in the whole-lake equal to about 5.13 µg/L [24]. Interestingly, this value is higher than that at day 27. It should be recalled that field data were measured close to the water surface. This increase probably is due to the MTBE amount that has been previously trapped in the hypolimnion. This value is indicated by the arrow in Figures 4a, 5a, and 6a. In fact, in a stratified lake any compounds in the epilimnion will not mix into the hypolimnion, but will remain confined in the epilimnion. Sampling data over the water depth demonstrated that generally, before the turnover, the MTBE concentration in the epilimnion was higher than that in the hypolimnion [24]. Lake turnover has mixed in the whole-lake up to water surface the MTBE previously trapped in the hypolimnion, which was about almost 80% of lake volume. In Figures 5a,b, 6a and b the plots for the Rathbun [9] 2 equation are absent, whereas they are shown only in Figure 4a and b. Generally, the Rathbun [9] 2 equation provides results that are slightly lower than the Rathbun [9] 1 equation. Plots for the MacKay and Yeun [17] equation are shown only in Figure 4a and b because this equation, if applied with the Wanninkhof et al. [15] and Gelda et al. [21] equations to compute kl-O2 , closely follows the Wanninkhof et al. [15] results. In Figures 5a,b, 6a,b results from Mills et al. Equation [18] are presented. Generally, the Mills et al. [18] Equation provides CMTBE values lower than the MacKay and Yeun [17] equation but quite similar. With regards to the equations that directly compute Kl-MTBE , before the turnover, the Lunney et al. [14] equation, that is independent from the estimation equation for kl-O2 , closely matches the field data of MTBE concentrations, whereas plots for the O’Connor [16] Equation (13a) and

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

19

Wanninkhof et al. [15] equations exhibit slower and faster decays, respectively, than the field data. The results from the remaining two equations, i.e. MacKay and Yeun [17] and Rathbun [9] 1, are significantly affected by the equation used to estimate kl-O2 . Notably, the Banks and Herrera [20] equation provides the highest MTBE concentration results and the Wanninkhof et al. [15] equation the lowest, whereas the Gelda et al. [21] equation gives intermediate values. Therefore, plots in Figure 4a exhibit a slower decay. In particular, the Rathbun [9] 1 equation together with the Banks and Herrera [20] Equation (14) to compute the liquid film coefficient kl-O2 produces results similar to those from the Lunney et al. [14] equation. The MacKay and Yeun [17] equation tends always to underestimate MTBE concentration in the lake. Then, when Equations (15) and (16) are applied to derive kl-O2 , the MacKay and Yeun [17] equation provides results similar to the Wanninkhof et al. [15] Equation (12). Moreover, when it is used together with the Banks and Herrera [20] equation, the MacKay and Yeun [17] equation offers its best prediction. After the turnover, decay plots have been restarted from CMTBE = 5.13µg/L. Generally, volatilization rates are remarkably reduced because hydraulic depth is now 35 m. Only the Lunney et al. [14] equation and the Rathbun [9] 1 equation with the Banks and Herrera equation can capture MTBE concentration at day 55, while the O’Connor [16] Equation (13a) produces a higher value. The Wanninkhof et al. [15] and the MacKay and Yeun [17] equations result in underprediction. Final MTBE concentrations at day 92 and day 102 are equal, as the volatilization process could be ended. However, these concentrations are better reproduced by the following equations combinations, MacKay and Yeun [17] and Banks and Herrera [20], Rathbun [9] 1 and Wanninkhof et al. [15], and Rathbun [9] 1 and Gelda et al. [21]. O’Connor [16] equation, Lunney et al. [14] equation, and Rathbun [9] 1 in combination with the Banks andzz Herrera [20] equation produce overestimation. Wanninkhof et al. [15] equation and MacKay and Yeun [17] equation in combination with the Wanninkhof et al. [15] and the Gelda et al. [21] equations result in underprediction. A quantitative assessment of model predictions has been carried out considering the average relative differences between model results and the field data. Test results are in listed Table XIII. Among the equations that directly compute the volatilization rate, the Lunney et al. [14] equation provides better results than the Wanninkhof et al. [15] and O’Connor [16] equations. Then, the remaining equations, namely Mills et al. [18], MacKay and Yeun [17], Rathbun [9] 1 and 2, generally exhibit better performance if they are applied with the Banks and Herrera [20] equation to compute kl-O2 . In fact, the mean value of the average relative differences for the Banks and Herrera [20] equation is equal

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Table XIII. Average relative differences between predictions and field data. Average relative differences - % Author

Banks and Herrera Wanninkhof et al. Gelda et al. Mean

1. Wanninkhof et al. [15] −48.48 2. O’Connor (13a) [16] 67.59 3. Mills et al. [18] −13.93 4. MacKay and Yeun [17] −4.76 5. Rathbun 1 [9] 23.13 6. Rathbun 2 [9] 7.32 7. Lunney et al. [14] 26.59 Mean value for 3/4/5/6 2.94

−48.48 67.59 −54.22 −48.54 −28.93 −40.28 26.59 −42.99

−48.48 67.59 −51.28 −45.36 −24.73 −36.65 26.59 −39.50

−48.48 67.59 −39.81 −32.89 −10.18 −23.20 26.59 −26.52

to 2.94%, whereas the value for the Wanninkhof et al. [15] and Gelda et al. [21] equations are −42.99% and −39.50%, respectively. The best performance are for the MacKay and Yeun [17] and Rathbun [9] 2 equations with mean errors of −4.76% and 7.32%, respectively, if they are both applied together with Banks and Herrera [20] equation. This could be considered as the first result of the proposed analysis. Furthermore, to assess the overall performance of each equation, the last column in Table XIII shows the mean of its average relative difference. These values could be considered as they would be obtained using a mean equation resulting from the Banks and Herrera [20], Wanninkhof et al. [15], and Gelda et al. [21] equations for kl-O2 . Four equations, i.e. nn. 3/4/5/6 in Table XIII, tend to always underestimate the MTBE concentration. The Rathbun [9] 1 equation gives the best result with a mean of −10.18%. This result, if it is limited to only the investigated case, is interesting because it was obtained over a relatively long time period with variable wind speed and temperature conditions. Results from Lunney et al. [14] equation, which is independent from kl-O2 estimation, also can be considered good because this equation is able to reasonably reproduce the decay process except for the last two field data. Moreover, the last row in Table XIII compares the results of the considered equations using the Banks and Herrera [20], Wanninkhof et al. [15], and Gelda et al. [21] formulas. The Banks and Herrera [20] equation provides better mean results than the other equations in the investigated volatilization case. Finally, it should be noted that the assumption that KL ≈ kl tends to generally decrease MTBE concentrations modeled. However, model performances are not significantly modified.

21

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS 3.5 Mono Lake Crowley Lake Rockland Lake Lake 302N Pyramid Lake Wanninkhof et al. O'Connor - (13a) Rathbun 1 Lunney et al. MacKay and Yeun

KL(600) - m/day

3.0 2.5 2.0

Wanninkhof et al.

Lunney et al.

1.5

Rathbun 1

1.0 O'Connor - (13a)

MacKay and

0.5 0.0 0

1

2

3

4

5

6

7

8

- m/s

Vwind-10

Figure 7. Gas-transfer rate KL (600) vs. wind speed Vwind−10 .

6. Verification of Lunney and Rathbun 1 Equations on Wanninkhof Data The previous analysis shows that Lunney et al. [14] equation, that is independent from the liquid film coefficient for oxygen estimation, and the Rathbun [9] 1 equation, if a mean value of kl-O2 is used, provide the best average fit with the field data. Also, the MacKay and Yeun [17] equation, if applied with the Banks and Herrera [20] formula, provides the lowest difference with field data. The Rathbun [9] 2 equation produces CMTBE values not very far from those from the Rathbun [9] 1 equation, the O’Connor [21] Equation (13a) provides a slower decay, whereas the remaining equations tend to underestimate MTBE values in Lake Perris. Notably, the acceptable fit of Lunney et al. [14] equation is not surprising since this equation was derived from volatilization of ethyl ether from water and MTBE also is an ether. Therefore, in this section these equations, namely the Lunney et al. [14], Rathbun [9] 1, and MacKay and Yeun [17] equations, have also been tested against the field data used by Wanninkhof et al. [15] to derive Equation (12). The O’Connor [21] Equation (13a) also was considered. It should be recalled that Wanninkhof data were obtained using sulfur hexafluoride SF6 as the tracer gas. In total data from 55 cases are available. Also, they are referred to a compound with Sc = 600, that is the CO2 Schmidt number in freshwater for T = 20 ◦ C. Therefore, it holds that:
 600 −0.50 KL (600) = · KL (21) Sc where KL (600) is the gas-transfer rate for Sc = 600 and KL is the true gastransfer rate. This value of Sc was also used to compute the gas-transfer rate KL ≈ kl for the Rathbun [9] 1, Lunney et al. [14], and O’Connor [21] equations. Notably, for the Rathbun [9] 1 equation, the conversion

22

CARLO GUALTIERI

factor φ should be, following the estimation equation in Table V, φ = 0.765, while for the MacKay Yeun [17] equation, the conversion factor is φ = 0.972. Also, both the Rathbun [9] 1 and MacKay and Yeun [17] equations were applied using the Banks and Herrera [20] equation to compute kl-O2 . Results are presented in Figure 7. Analysis of Figure 7 shows that the Lunney et al. [14], MacKay and Yeun [17], O’Connor [21], and Rathbun [9] 1 equations tend to underestimate gas-transfer. Notably, for wind speeds up to 4 m/s, the Lunney et al. [14] equation provides values lower than the other equations, whereas for Vwind > 4 m/s, the Lunney et al. [14] equation gives higher gas-transfer rates. Anyway, the Lunney et al. [14], MacKay and Yeun [17], Rathbun [9] 1, and O’Connor [21] equations do not exhibit a good fit with the volatilization data of SF6 . 7. Concluding Remarks The influence of wind on the volatilization rate of toxics from flowing and standing waters has been investigated by several researchers who have proposed some predictive equations. Since mass-transfer through the air–water interface could be controlled by the liquid, the air, or both sides, the influence of the liquid side for 20 different environmental contaminants have been herein evaluated. This paper has compared seven predictive equations to assess their performance using available field data for MTBE contamination in Lake Perris, CA. Simulations were performed taking into account changing in water temperature and wind speed over an approximately 120 days period of observation. The average value of water temperature and wind speed over 10 days was considered. Two equations could directly compute MTBE volatilization rate, while five require the estimation of the gas-transfer rate for a reference substance, oxygen for four equations and for the Lunney et al. [14] equation only, ethyl ether. Therefore, kl-O2 values due to the wind blowing on the lake surface have been computed using three equations from literature, namely the Banks and Herrera [20], Wanninkhof et al. [15], and Gelda et al. [21] equations. The test performed shows a large spread of results. Most of the considered equations tend to overestimate MTBE decay due to volatilization. Three equations, namely the Lunney et al. [14], MacKay and Yeun [17], and Rathbun [9] 1 equations, should be considered as the best for the investigated case. The average relative difference between their predictions and the field data ranges between 26.59% and −10.18%, respectively. In particular, the MacKay and Yeun [17] equation, if applied with the Banks and Herrera [20] formula to compute the kl-O2 coefficient, provides a relative difference with the field data of −4.76%, which is the lowest obtained.

VERIFICATION OF WIND-DRIVEN VOLATILIZATION MODELS

23

The Lunney et al. [14] equation results are independent from the estimation of the oxygen liquid film coefficient kl-O2 . The Rathbun [9] 1 equation offers the best fit with the field data for a mean kl-O2 obtained from the Banks and Herrera [20], Wanninkhof et al. [15], and Gelda et al. [21] equations. Moreover, the Banks and Herrera [20] equation provides the best mean fit for the four considered equations that require the estimation of kl-O2 . Notably, after days 30, whole-lake mixing due to change in climatological conditions was considered and the overall lake depth was applied in the equations. The influence of the gas-side CBL on gas-transfer could be considered as not very significant on the predictive ability of the models, because MTBE is a liquid-film controlled chemical. Finally, the application of the Lunney et al. 14, MacKay and Yeun [17], and Rathbun [9] 1 equations to the SF6 gas-transfer field data collected by Wanninkhof et al. [15] do not result in a good fit. Therefore, the tested equations are not generally applicable for any chemicals, but they remain case-specific and offer the best prediction for the compound for which they were derived. References 1. Rathbun, R.E. and Tai, D.Y.: 1983, Gas-film coefficient for streams, J. Environ. Eng. Div. ASCE 109(5) 1111–1127. 2. Rathbun, R.E.: 1998, Transport, behavior and fate of volatile organic compounds in streams, U.S. Geological Survey Professional Paper 1589, Washington, DC. 3. Gualtieri, C.: 2002, Modeling mass-transfer of VOCs in open channels. In: 5th International Conference on HydroScience & Engineering (ICHE 2002), Warsaw (Poland), September 18/21, 2002. 4. Lewis, W.K. and Whitman, W.G.: 1924, Principles of gas absorption, Ind. Eng. Chem. 16(12), 1215–1220. 5. Rathbun, R.E. and Tai, D.Y.: 1982, Volatilization of organic compounds from streams, J. Environ. Eng. Div. ASCE 108(5), 973–989. 6. Chapra, S.C.: 1997, Surface Water Quality Modeling. McGraw-Hill, New-York. 7. NIST: 2000, Standard Reference Database Number 69. February 2000. 8. Schwarzenbach, R.P., Gschwend, P.M. and Imboden, D.M.: 1993, Environmental Organic Chemistry, Wiley-Interscience, New York, USA. 9. Rathbun, R.E.: 1990, Prediction of stream volatilization coefficients, J. Environ. Eng. ASCE 116(3), 615–631. 10. Thibodeaux, L.J.: 1996, Environmental Chemodynamics, John Wiley & Sons, Chichester, UK. 11. Melching, C.S. and Flores, H.E.: 1999, Reaeration equations derived from U.S. Geological Survey database, J. Environ. Eng. ASCE 125(5), 407–414. 12. Gualtieri, C. and Gualtieri, P.: 2000, Field verification for a reaeration model in streams. In: 4th International Conference on Hydroscience & Engineering (ICHE2000), Seoul (Korea), September 26/29, 2000. 13. Gualtieri, C., Gualtieri, P. and Pulci Doria, G.: 2002, Dimensional analysis of reaeration rate in streams, J. Environ. Eng. ASCE 128(1), 12–18.

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14. Lunney, P.D., Springer, C. and Thibodeaux, L.J.: 1985, Liquid-phase mass transfer coefficients for surface impoundments, J. Environ. Prog. 4(3), 203–211. 15. Wanninkhof, R., Ledwell, J.R. and Crusius, J.: 1991, Gas transfer velocities on lakes measured with sulfur hexafluoride, In: Proceedings of the 2th International Conference on Gas Transfer at Water Surfaces, Minneapolis, MN. 16. O’Connor, D.J.: 1983, Wind effects on gas-liquid transfer coefficients, J. Environ. Eng. Div., ASCE, 109(3), 731–752. 17. MacKay, D. and Yeun, A.T.K.: 1983, Mass transfer coefficients correlations for volatilization of organic solutes from water, Environ. Sci. Tech. 16(2), 211–233. 18. Mills, W.B. et al.: 1985 Water Quality Assessment: A Screening Procedure for Toxic and Conventional Pollutants, Part I. Tetra Tech, Inc., Environmental Research Laboratory, Office of Research and Development, USEPA, Athens, GA. 19. Bowie, G.L., Mills, W.B., Porcella, D.B., Campbell, C.L., Pagenkopf, J.R., Rupp, G.L., Johnson, K.M., Chan, P.W.H., Gherini, S.A. and Chamberlin, C.E.: 1985, Rates, Constants and Kinetics Formulation in Surface Water Quality Modeling. U.S. EPA, Office of Research and Development, Environmental Research Laboratory, Athens, GA EPA/600/3–85/040. 20. Banks, R.B. and Herrera, F.F.: 1977, Effect of wind and rain on surface reaeration. J. Environ. Eng. ASCE, 103(3), 489–504. 21. Gelda, R.K., Auer, M.T., Effler, S.W., Chapra, S.C. and Storey, M.L.: 1996, Determination of reaeration coefficients: whole-lake approach. J. Environ. Eng. ASCE 122(4), 269–275. 22. Harbeck, E.G. Jr.: 1962, A practical field technique for measuring reservoir evaporation utilizing mass-transfer theory. Geological Survey Professional Paper 272-E, Washington, DC. 23. Stocking, A.J. and Kavanaugh, M.C.: 2000, Modeling volatilization of MTBE from standing surface waters. J. Environ. Eng. ASCE 126(12), 1131–1136. 24. McCord, S.A. and Schladow, G.S.: 1998, Transport and fate modeling of MTBE in lakes and reservoirs, In: Health and Environmental Assessment of MTBE, Department of Civil and Environmental Engineering, University of California at Davis, CA. 25. Pankow, J.F., Rathbun, R.E. and Zogorski, J.S.: 1996, Calculated volatilization rates of fuel oxygenate compounds and other gasoline-related compounds from rivers and streams, Chemosphere 33(5), 921–937. 26. Zogorski, J.S., Morduchowitz, A., Baehr, A.L., Bauman, B.J., Conrad, D.L., Drew, R.T., Korte, N.E., Lapham, W.W., Pankow, J.F. and Washington, E.R.: 1996, Fuel oxygenates and water quality: Current understanding of sources, occurrence in natural waters, environmental behavior, fate, and significance, Washington D.C., Office of Science and Technology Policy. 27. Reuter, J.E., Allen, B.C., Richards, R.C., Pankow, J.F., Goldman, C.R., Scholl, R.L. and Seyfried, J.S.: 1998, Concentrations, sources and fate of the gasoline oxygenate methyl tert-butyl ether (MTBE) in a multiple-use lake, Environ. Sci. Technol. 32(23), 3666–3672. 28. Achten, C., Kolb, A. and Puttmann, W.: 2002, Methyl tert-butyl ether (MTBE) in river and wastewater in Germany, Environ. Sci. Technol. 36(17), 3652–3661.