Environ. Sci. Technol. 1992, 26, 836-837
(18) Johnston, A. E.; Goulding, K. W. T.; Poulton, P. R. Soil Use Manag. 1986,2, 3-10. (19) Jones, K. C.; Johnston, A. E. Environ. Pollut. 1989, 57, 199-216. (20) Adriano, D. C. Trace Elements in the Terrestrial Environment; Springer Verlag: Berlin, 1985. (21) Sanders, G.; Jones, K. C.; Hamilton-Taylor, J.; Dorr, H. submitted for publication in Environ. Toxicol. Chem. (22) Boutron, C. F.; Gorlach, U.; Candelone, J.-P.; Bolshov, M. A.; Delmas, R. J. Nature 1991, 353, 153-156. (23) Hutton, M. Sei. Total Environ. 1983, 29, 29-47. (24) W.H.O. Tech. Rep. Ser. 1972, No. 505. (25) Ministry of Agriculture Fisheries and Food. Survey of Cadmium in Food; Food Surveillance Paper No. 12; HMSO: London, 1983.
(26) Hutton, M. Evaluation of the Relationships Between Cadmium Exposure and Indicators of Kidney Function. Technical Report No. 29; Monitoring and Assessment Research Centre, University of London, 1983. (27) Ellis, K. J.; Yuen, K.; Yasumura, S.; Cohn, S. H. Environ. Res. 1984, 33, 216-226. (28) McGrath, S. P. In Pollutant Transport and Fate in Ecosystems; Coughtrey, P. J., Martin, M. H., Unsworth, M. H., Eds.; Blackwell: Oxford, U.K., 1987; pp 301-317. (29) Sauerbeck, D. Plant Res. Dev. 1984, 19, 24-34.
Received for review October 22, 1991. Revised manuscript received December 19,1991. Accepted December 26,1991. K.C.J. is grateful to the Agricultural and Food Research Council for financial support.
CORRESPONDENCE Comment on "Human Exposure to Volatile Organic Compounds in Household Tap Water: The Indoor Inhalation Pathway "
on the species being transferred. By analogy with early theoretical work on heat transfer in a laminar boundary layer, Nu can be shown to vary with the 1 / 3 power of Sc ( 4 ) . McKone uses this theoretical relationship in order to describe the dependence of the mass-transfer coefficient on the diffusivity of the transferring species, or
SIR In a research paper (1) that appeared in this journal, McKone provided an assessment of the impact on indoor air quality of the release of volatile organic compounds (VOCs) from household water. Due to a lack of mass-transfer data, a relationship was derived which adjusts the measured transfer efficiency for radon to that for VOCs such as 1,2-dibromo-3-chloropropane (DBCP) using the Henry's law constant and liquid and gas diffusivities. Subsequent publications have repeated the derivation (2) and used the result to test hypotheses concerning mass transfer in showers (3). Although the relationship was only intended to be approximate, there is an error in the derivation which casts doubt on its reliability, especially when applied to compounds of low volatility. McKone's derivation is first briefly reviewed. The overall mass-transfer coefficient K (m/s) at the air-water interface reflects the resistance through both the liquid and gas phases
NuL a ScL1l3
(4)
NuG
(5)
om
\-I
where KL and KG are the liquid-phase and gas-phase mass-transfer coefficients (m/s), respectively, R is the gas constant (0.0624Torr m3/mol.K), T i s absolute temperature (K), and H is the Henry's law constant (Torr m3/mol). The liquid- and gas-phase mass-transfer coefficients may be expressed in terms of the Nusselt number, or KL = DLNuL/LL (2) KG = DGNuG/LG
(3)
where DL and DG are the diffusion coefficients (m2/s)of the compound, NUL and NuG are Nusselt numbers, and LL and L G are characteristic lengths (m) in water and air, respectively. Dimensional analysis of convective mass transfer suggests that the Nusselt number is a function of the Reynolds number (Re) and the Schmidt number (Sc) ( 4 ) . Of these two dimensionless groups, only Sc depends 636 Environ. Sci. Technol., Voi. 26, No. 4, 1992
a
ScGli3
where ScL = vL/DL and SCG= vG/DG are the Schmidt numbers in water and air, respectively, vL is the viscosity of water (9.82X lo-' mz/s at 20 "C), and vG is the viscosity of air (1.56 X loy5mz/s at 20 "C). McKone then combines eqs 2-5 and finds KL = O . ~ ( D L ~ / ~ / D G ~ / ~ ) K G (6) which he substitutes into eq 1 to obtain (7)
where /3 is presented as a dimensionless constant that depends upon the physical situation, but is independent of the species under consideration (1). From dimensional considerations, it is apparent that the constant P given in eq 7 cannot be dimensionless. Of greater concern, however, is eq 6, which must include a constant of proportionality, a, or KL = ~ u ( D L ~ ~ ~ / D G ~ ~ ~ ) O . ~(8) KG The proportionality constant a will be carried through to eq 7 resulting instead in
(9) where a = ALG/BLLand p* = AvG1i3/LL.A and B are the constants of proportionality in eqs 4 and 5,respectively, and are related to the Reynolds number of the appropriate phase. The constant p* has the correct dimensions and depends only on the hydrodynamic conditions. Equation 9 has the same form as eq 7 , except for the dimensionless a which appears in the term relating to the gas-phase resistance. Therefore, unless a has a value of unity,
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McKone’s model will not account adequately for gas-phase resistance. A recent study on contaminant volatilization in showers (5) has shown that the ratio KG/KL is typically about 17 and using this value together with eq 8 gives a value for and a of approximately 70 if DL and DG are taken as m2/s, respectively. McKone ( I ) used eq 7 to calculate the ratio K(DBCP)/K(Rn) as 0.59, which is significantly higher than the value of 0.14 obtained using eq 9 and the appropriate values of DL, DG,and H. This result means that the transfer of DBCP in a shower was most likely overpredicted by more than a factor of 4 because McKone assumes that the transfer efficiency is directly proportional to the overall mass-transfer coefficient. Data are lacking with which to reliably estimate how inaccurate eq 7 is when applied to mass transfer during other water uses in, for example, baths, washing machines, and dishwashers. Finally, it should be noted that ref 1 contains an additional error: the Henry’s law constant for ethylene dibromide (EDB) is 0.73 Torr m3/mol at 20 “C (6) or about 1000 times smaller than the value given in Table I11 of ref 1. Registry No. DBCP, 96-12-8; EDB, 106-93-4.
Literature Cited (1) McKone, T. E. Environ. Sei. Technol. 1987,21,1194-1201. (2) McKone, T. E.; Knezovich, J. Presented at the 82nd Annual Meeting of the Air & Waste Management Association, Anaheim, CA, 1989; Paper 89-80.6. (3) McKone, T. E.; Knezovich, J. J.Air Waste Manage. Assoc. 1991,40, 282-286. (4) Welty, J. R.; Wicks, C. E.; Wilson, R. E. Fundamentals of Momentum, Heat, and Mass Transfer, 3rd ed.; John Wiley and Sons: New York, 1984. (5) Little, J. C. Applying the Two-Resistance Theory to Contaminant Volatilization in Showers. Submitted for publication in Environ. Sei. Technol. (6) Selleck, R. E.; Pearson, F. H.; Diyamandoglu, V.; Ungun, Z. G. Application of Air Stripping Technology for the Removal of DBCP Residues in Community and Industrial Water Supplies. SEEHRL Report No. 83-2; Sanitary Engineering and Environmental Health Research Laboratory, University of California, Berkeley, CA, 1983.
John C. Little Indoor Environment Program Lawrence Berkeley Laboratory Berkeley, California 94720
SIR: In his letter addressing my 1987 paper (I),Little raises three issues regarding the derivation of the model and the data used to illustrate the use of the model. These issues are (1)that the parameter P, which is referred to in my paper as dimensionless, does have dimensions; (2) that an added factor, CY,is needed in the model to increase its reliability for estimating transfer efficiencies for compounds with a low Henry’s law constant; and (3) that the Henry’s law constant reported in my paper for EDB is in error. The second point deals with a potential limitation, and although Little has correctly stated the nature of the limitation, I am not convinced that Little has correctly stated how to eliminate this limitation. Furthermore, it is important to recognize that this limitation does not significantly alter the exposure estimates presented in the 1987 paper. My concerns with his suggestions are presented below. The first and third issues are correct and require only a short response on my part. With regard to the 0013-936X/92/0926-0837$03.00/0
factor, my only response is that I should have referred to as “a constant with units of (m.s)-’i3 that results from the introduction of dimensionless mass-transfer coefficients, depends on the physical situation, and is independent of the species under consideration” instead of “a dimensionless constant that depends on ...”. With regard to the Henry’s law constant for ethylene dibromide (EDB), as noted in the 1987 paper, this value was derived from vapor pressure and solubility data reported by Verschueren (2). My check of this reference reveals that I did correctly report what is given by Verschueren. Unfortunately, there is an apparent error in the reported value of EDB solubility by Verschueren, who reported the solubility of EDB as 4.3 mg/L at 30 “C. This is much lower than the value reported in other respected and readily available references; Stephen and Stephen (3) reported the mutual solubility of EDB and water as 11.6 g of EDB/kg of solution and Horvath (4)reported the solubility of EDB in water as 4.3 g of EDB/L of water. The vapor pressure of EDB reported by Verschueren is consistent with the value given by Stull (5). On the second point regarding the derivation of the two-resistance mass scaling, Little suggests there is an error in my derivation and that an added factor, a,is needed to account for differences the water- and air-side scaling of mass transfer with the Schmidt (Sc) number. As he suggests, an additional parameter could be added to increase the generality of the model and improve its ability to fit low Henry’s law value compounds. Nevertheless, given the scientific evidence available in 1987, selecting a value other than unity could have created the potential for underestimating the transfer efficiency and for this reason I intentionally left this ratio at unity. The model in my 1987 paper was intended to provide a first-order estimate of transfer from water to indoor air. It should be noted that the key finding of this model was that transfer efficiency would not scale with Henry’s law constant for highly volatile compounds as had been suggested in an EPA report (6). Given what Little has presented in his letter, it is difficult to comment on the validity of his observation that the recommended CY factor has a value of 70. In addition, I am concerned by the implications of statements in his letter regarding how his estimates of CY comes about. For example, he states that the constants of proportionality relating the mass-transfer Nusselt (Nu) numbers to the Sc numbers should be related to Reynolds (Re) numbers. In my 1987 paper ( I ) , I avoided the use of either Reynolds number or Grashoff number scaling. The Reynolds number is the ratio of the inertia to viscous forces and applies to forced convection heat or mass transfer; the Grashof (Gr) number is the ratio of buoyancy to viscous forces and applies to natural convection heat and mass transfer. Many problems arise when we try using these dimensionless numbers relating to hydrodynamic forces for scaling mass transfers in showers. I am not convinced that there is yet sufficient data to determine the appropriate form of the hydrodynamic scaling in showers or baths. The primary problem is that, unlike the Sc number which relates only to chemical properties, these numbers, Gr and Re, depend on such factors as the diameter of the shower droplets, the distance from the shower nozzle to the shower floor, the distance between the shower nozzle and the point at which the shower stream interacts with the wall, etc. Another major problem is that, in a shower, there are at least four physical configurations for two-resistance mass transfer that must be considered: (1)falling drops, (2) the film of water that forms on the wall of the shower, (3) the
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