Environ. Sci. Technol. 1986, 2 0 , 949-952
Gas-Film Coefficients for the Volatilization of Ethylene Dibromide from Water Ronald E. Rathbun” and Doreen Y. Tal Gulf Coast Hydroscience Center, US. Geological Survey, National Space Technology Laboratories, Mississippi 39529
w Gas-film coefficients for the volatilization of ethylene dibromide (EDB) and water were determined in the laboratory as a function of wind speed and temperature. The ratio of the coefficients was independent of wind speed and increased slightly with temperature. Use of this ratio with an environmentally determined gas-film coefficient for the evaporation of water permits determination of the gas-film coefficient for the volatilization of EDB from environmental waters.
Introduction Ethylene dibromide (EDB) has been used as an additive to leaded gasoline and as a soil fumigant ( I ) . It has also been used to control insects in stored grains ( 2 ) . Widespread use has resulted in its detection in the groundwaters of California, Florida, Hawaii, and Georgia (2) and Connecticut (3),in both the surface and groundwaters of New Jersey ( 4 ) ,and in wells used for irrigation in Georgia ( 5 ) . It is a potent carcinogen and produces mutations in animals ( I ) . Therefore, understanding its behavior in the waters of the environment is necessary. EDB is relatively volatile, having a vapor pressure of 1.85 kPa at 298.2 K (6). It is readily lost from water exposed to the atmosphere and can be purged from water with nitrogen gas (3). Therefore, it is expected that volatilization from water will be a significant process in determining the fate of EDB in environmental waters. A review of the literature, however, showed information on the volatilization characteristics of EDB limited to one experiment on the volatilization of pure EDB into still air (7). Volatilization of organics from water is commonly described by the two-film model (8). This model assumes uniformly mixed water and air phases separated by thin films of water and air in which mass transfer is by molecular diffusion. Mass-transfer coefficients for these films are commonly called the liquid-film and gas-film coefficients, respectively. More complete details of this model have been presented previously (9). Analysis of the equations of the two-film model has shown (20-12) that the relative importance of the water and air film resistances for a specific organic depends on Henry’s law constant. For EDB, Henry’s law constant calculated from vapor pressure data (6)and solubility data (13) is 0.0831 kPa.m3/(g.mol) at 298.2 K. This constant is in the range where both film resistances are important (14). However, most of the previous experimental studies (15-19) of volatilization have considered only organics for which the water film resistance is important. The air film resistance and the corresponding gas-film coefficient has received considerably less attention. Therefore, the present study was directed toward the gas-film coefficient for the volatilization of EDB from water. The liquid-film coefficient will also be needed for predicting volatilization from environmental waters. This coefficient will be the subject of another report. Gas-Film Coefficient In general, the gas-film coefficient for an organic in water cannot be measured directly because such measurement
requires determination of the organic partial pressure at the air-water interface, In the limiting case of an organic with a very small Henry’s law constant such that virtually all resistance to volatilization is in the gas film, the gas-film coefficient can be measured directly. However, the volatilization rate for such an organic would be so small that volatilization probably would not be a significant process in fate determination. For organics other than this limiting case, therefore, gas-film coefficients are determined by measuring the volatilization flux of the pure substance. The basis for this procedure is the rationalization (20-22) that, in the volatilization of a pure liquid, there can be no concentration gradient, and thus, there can be no liquidfilm resistance. It is, in general, not feasible to measure the volatilization fluxes of pure organics under environmental conditions. To solve this problem, water is used as a reference substance. Basis of the use of a reference substance is the assumption that the ratio of the organic and water gas-film coefficients is a constant as expressed by k ~ ~ = J/ ~ ~ / k (1)~ where the constant $ is assumed to be independent of mixing conditions in the air phase. These mixing conditions are usually characterized by the wind speed. It is convenient to use water as the reference substance because evaporation is controlled completely by the gas film, and information exists in the literature on the evaporation of water from lakes and reservoirs (23) and from a canal (24). If the gas-film coefficient for water can be estimated for the environmental water, then the gas-film coefficient for the organic can be computed from eq 1and a laboratory-determined value of $. The reference substance concept for the gas-film coefficient as expressed by eq 1 has been used (12, 25, 26), apparently on the basis of the fact that an equation analogous to eq 1 has been verified for the liquid-film coefficient by using oxygen as the reference substance (17-19). However, the constancy of $ with respect to wind speed has apparently not been verified experimentally for gas-film coefficients. This report describes laboratory measurements of the gas-film coefficients of EDB and water as a function of wind speed and temperature. Results were used to test the validity of eq 1.
Experimental Section Volatilization fluxes for the evaporation of EDB and water were determined as a function of wind speed and temperature by using the apparatus and procedure described previously (26). Briefly, the procedure consisted of measuring the rate of change of the weight of liquid in the top chamber of a two-chamber volatilization apparatus. Water at a constant temperature flowed through the bottom chamber to provide temperature control. The liquid in the top chamber was stirred with a magnetic stirrer. The apparatus was placed in a fume hood which provided the minimum wind speed. Higher wind speeds were obtained with a three-speed window fan placed in front of the fume hood. The fan was used in addition to the fume hood. Diameter of the fan blade was 0.51 m. A wind speed between that of the low fan setting and the
Not subject to US. Copyright. Published 1986 by the American Chemical Society
Environ. Sci. Technol., Vol. 20, No. 9, 1986
949
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Flgure 1. Volatilization flux for EDB as a function of reciprocal absolute temperature for wind speeds of 0.344, 0.862, and 1.06 m/s. 300
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Flgure 3. Volatillzation flux for water as a function of reciprocal absolute temperature for wind speeds of 0.343, 0.804, and 1.09 m/s.
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Figure 2. Volatilization flux for EDB as a function of reciprocal absolute temperature for wind speeds of 1.42 and 1.66 m/s.
fume hood by itself was obtained by placing a wire screen across the front of the fan. Wind speeds were measured with a digital eight-vane air meter placed directly behind the volatilization apparatus.
Results and Discussion Volatilization Fluxes. Fluxes, Aw/AAt, were computed from the experimental volatilization rates, A w l At, and the cross-sectional area, A , of the volatilization chamber. Water fluxes were adjusted to dry-air conditions by using relative humidities measured during the experiments, Fluxes as a function of reciprocal absolute temperature are presented in Figures 1and 2 for EDB and in Figures 3 and 4 for water. The lines shown in these figures are linear regression fits of the logarithm of the volatilization flux as a function of reciprocal absolute temperature. The normalized root-mean-square (rms) error of prediction defined previously (26)was used as a measure of the fit. The slopes and intercepts of the regression equations and the rms errors are given in Table I. An analysis of covariance of the slopes showed no significant differences for both EDB and water at the 5% level. It was concluded that wind speed had no significant effect on the slope of the flux-temperature relation. Gas-Film Coefficients. Volatilization fluxes were interpolated at intervals of 5 K between 293.2 and 313.2 K by using the slopes and intercepts from Table I. Extrapolation to 293.2 K was necessary in some cases as shown 950
Environ. Sci. Technoi., Vol. 20, No. 9, 1986
compound
EDB
water
average wind speed, m/s
slope, K
0.344 0.862 1.06 1.42 1.66 0.343 0.804 1.09 1.38 1.66
-4740 -4870 -4740 -4620 -4730 -5280 -5170 -4970 -5040 -5110
intercept x (g/min)/m2 2.44 7.63 6.14 5.28 8.39 5.98 8.53 5.45 8.32 11.2
error, %
1.39 1.28 2.58 1.52 2.34 2.47 1.30 2.05 4.84 4.30
by the dashed lines in Figures 1-4. Gas-film coefficients were computed from an equation derived previously (26). This equation is
where T i s temperature (K), M is molecular weight (g/(g mol)), Aw/AAt is the volatilization flux ((g/min)/m2),AP is the vapor pressure difference driving force (kPa), and the 12.0 constant results from the ideal gas constant and other conversion factors. For EDB, it was assumed that the fume hood removed the EDB as soon as it volatilized so that the partial
Table 11. Ratio $ as a Function of Wind Speed and Temperature $ = kCEDB/kG,,tsr at wind speeds,
temp,
K
293.2 298.2 303.2 308.2 313.2
m/s, of 0.343 0.804 1.09 1.38 0.407 0.415 0.423 0.430 0.436
0.372 0.385 0.398 0.410 0.421
0.394 0.410 0.425 0.439 0.453
0.393 0.405 0.415 0.425 0.435
0.423 0.436 0.448 0.460 0.470
0.398 0.410 0.422 0.433 0.443
f4.74 k4.48 f4.29 k4.27 A4.26
pressure of EDB in the air above the apparatus was negligible with respect to the vapor pressure. Thus, AI' is assumed to be the vapor pressure of EDB at the temperature of the liquid in the volatilization chamber. Vapor pressures for EDB at the appropriate temperatures were computed from a logarithm vapor pressure vs. reciprocal absolute temperature regression of the four data points of Stull (6)at temperatures of 291.8, 305.8, 321.2, and 331.0 K. Other data from the literature (27,28)gave comparable vapor pressures in this temperature range. For water, AI' is the difference between the saturation vapor pressure of the air at the water temperature and the vapor pressure of the air. These pressures were calculated from equations given by Jobson and Sturrock (24) and measurements of the wet-bulb and dry-bulb air temperatures, the barometric pressure, and the average temperature of the water in the volatilization chamber. The average wind speeds for the EDB and water experiments were approximately the same as shown in Table I. Statistical comparisons showed that only the 0.862 and 0.804 m/s values were significantly different at the 5% level. This particular wind speed was for the condition with the screen across the front of the fan. Because the screen was removed several times during the study, this difference probably occurred because the screen was not placed in exactly the same position each time. $ Factor. Values of $ computed from eq 1 are presented in Table I1 as a function of wind speed and temperature. Mean values and the coefficients of variation are also presented for each temperature. Results in Table I1 show no consistent trend of with wind speed. Linear regressions of $ as a function of wind speed were computed for each temperature. The 95% confidence limits of the slope of the $ vs. wind speed regressions for the different temperatures all included zero, showing no dependence of $ on wind speed a t the 5% level of significance. It was concluded, therefore, that $ is independent of wind speed, and the reference substance concept can be used to predict the gas-film coefficient for the volatilization of EDB from streams and rivers. The $ values in Table I1 show a small, consistent increase with temperature for each wind speed. Analysis of eq 1 and 2 shows that the temperature dependence of rC, depends on the relative temperature dependencies of the volatilization flux and the vapor pressure. Temperature dependencies of the fluxes as percentage increase per degree kelvin at 298.2 K were computed from the slopes and intercepts in Table I. Increases of the EDB flux with temperature for the different wind speeds ranged from 5.32%/K to 5.61%/K and averaged 5.46%/K with a coefficient of variation of *1.88%. Increases for water ranged from 5.73%/K to 6.10% /K and averaged 5.90%/K with a coefficient of variation of f2.42%. Temperature dependencies of the vapor pressures were computed from logarithm vapor pressure vs. reciprocal absolute temperature fits of vapor pressure data. Dependencies at 298.2 K were 5.07% /K for EDB and 6.09% /K for water. Com-
+
'
1.66
coeff of mean variation, % value
bining these dependencies with eq 1 results in predicted temperature dependencies of $ ranging from 0.36% /K to 0.71%/K at 298.2 K. These small dependencies apparently caused the increase of $ with temperature shown in Table 11. For most practical applications,the effect of temperature on $ is probably negligible. The overall average of the $ values in Table I1 is 0.421 with a coefficient of variation of f5.58%. If precise values of $ are needed, then $ can be predicted as a function of temperature from $ = 2.15 exp(-495/T) (3) Comparison with Estimated Factors. Two procedures are used to estimate $ factors when experimental values are not available (25). The first is based on the assumption that the gas-film coefficient is inversely proportional to the square root of the molecular weight. For EDB and water, this gives an estimated $ factor of 0.310 which is 24% less than the experimental value of 0.409 at 298.2 K. The second procedure is based on the assumption that the gas-film coefficient is proportional to the moleculardiffusion coefficient raised to some power q. Theoretical values of q include 1.0 for the two-film model (B), 0.5 for the penetration model (29),and a value varying from 0.5 for high mixing conditions to 1.0 for low mixing conditions for the film-penetration model (30). Experimental studies have resulted in values of 0.684 (31) and 0.5 (32). Molecular-diffusion coefficients for EDB and water in air were estimated at 298.2 K by using the ChapmanEnskog equation as modified by Wilke and Lee (33). Results were 0.744 m2/day for EDB and 1.98 m2/day for water. Estimated $ factors were 0.512 for an q exponent of 0.684 and 0.613 for an exponent of 0.5. These values are 25% and 50% larger than the experimental value of 0.409 at 298.2 K. The differences between the experimental and estimated $ factors are relatively large, and additional testing of the two estimation procedures is needed. Differences of this magnitude may be acceptable for qualitative purposes, but more quantitative modeling efforts may require experimental determination of the $ factor or a more accurate prediction procedure. Analysis of the Reference Substance Concept. The reference substance concept assumes that the ratio of the gas-film coefficients for an organic substance and for water are independent of mixing conditions in the air as indicated by the wind speed. The concept also assumes that this ratio measured in the laboratory applies to all environmental conditions, whatever the condition may be. The first assumption was the subject of this paper and was verified for EDB and water. The second assumption cannot at present be verified because gas-film coefficients of organic substances are not directly measurable for streams and rivers. It is because these coefficients are not directly measurable that the reference substance concept is used. The second assumption, however, requires further analysis because of differences in the thermal effects involved in the processes and possible effects on the $ factor. In the laboratory, measurements for both EDB and water were for high flux conditions. In the field, the water flux will most likely be less than in the laboratory, but the EDB flux will be much less relative to the laboratory because only trace concentrations are expected in environmental waters. Therefore, the thermal effects are different in the two situations. These thermal effects include the latent heat of vaporization and other heat transfer processes which control volatilization at the interface. Environ. Scl. Technol., Vol. 20, No. 9, 1986
951
The importance of these thermal effects can be estimated from two sets of data from the literature. The first set consisted of comparison of water temperatures in a laboratory flume study of water evaporation (34). Surface temperatures measured with an infrared radiometer were, as expected, always less than the bulk water temperature measured with thermistors. The largest difference for high evaporation rates was approximately 1.0 K. Temperature dependencies of the gas-film coefficient determined by correlating the experimental coefficients with reciprocal absolute temperature average 0.72%/K for EDB and 0.18%/K for water at 298.2 K. These small temperature dependencies and the small difference between surface and bulk water temperatures under high flux conditions suggests that thermal effects will have little effect on the $ factor. The second set consisted of simultaneous determination of the evaporation rates of water and tritium in a laboratory flume (35). The ratio of the coefficients for water and tritium was relatively constant for wind speeds from 2 to 7 m/s, suggesting that thermal effects did not significantly affect the $ factor when one of the components, tritium, was present in trace amounts. It is concluded that water can be used as a reference substance to estimate the gas-film coefficients for the volatilization of organic substances from streams. Registry No. EDB, 106-93-4; HzO, 7732-18-5.
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Y. “Energy and Mass Transfer through an Air-Water Interface”; Technical Report 134,1971;Department of Civil Engineering, Stanford University; pp 1-175. (35) Lau, Y. L. Tracer Measurement of River Evaporation: Laboratory Study; Fisheries and Environment Canada: Ottawa, 1977; Scientific Series No. 73, pp 1-19. Received for review June 10, 1985. Revised manuscript received December 9, 1985. Accepted May 6, 1986.
