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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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pool of water that forms on the floor of the shower, and (4) the film of water that is on the skin of the individual taking the shower. For mass transfer from failing droplets, Ranz and Marshall (7, 8) have shown that the Nusselt number scales with Sc and Re as Nu = 2 + 0.6Re1/2Sc1/3 (1) On the basis of mass-transfer theory (9),for free convection from the floor of the shower, we would expect a Nu correlation of the form Nu = 0.12(GrS~)l/~ (2) and for convective mass transfer from surfaces such as walls and skin, we might expect a Nusselt correlation of the form Nu = 0.332Re1/2Sc1/3 (3) The only common feature among these mass-transfer relationships is the dependence on the Sc number. Andelman, who originally measured chemical stripping of a volatile compound in showers ( I O ) , has measured a transfer efficiency of 60% for TCE at 30 "C in a full-scale shower with a water flow rate of 10 L/min. This compares well to 62% transfer measured by McKone and Knezovich (11)under similar conditions. In addition, Andelman and his colleagues have measured roughly 65% as the peak transfer efficiency of DBCP in showers with a water flow rate of 10 L/min and a temperature of 42-46 "C, and they have measured an average transfer efficiency of 20% over the duration of a 14-min shower with a water flow rate of 5 L/min and a water temperature of 42 "C (12-14). Finally, it should be noted that it is not correct to imply that an overestimation of peak transfer efficiency will result in a proportional over estimation of shower-air concentration and exposure. The relative transfer efficiencies listed in Table I11 of my 1987 paper ( I ) were the initial value (or peak value) for use when the air concentration in the shower stall is 0. For DBCP, I adjusted the transfer rate to account for increased resistance resulting from the buildup of DBCP in shower-stall air. This is discussed on pages 1198-1199 of the 1987 paper and reflected in results in Table IV ( I ) . Thus, the average ratio of DBCP stripping efficiency to radon stripping efficiency that I used over the duration of a 10-min shower is 0.35. This is not significantly larger than the value 0.14 that Little indicates it should come down to when a is 70. In addition, it is close to the value 0.29 that is implied for this ratio from the work of Giardino and Andelman (14). As has been shown by McKone and Bogen (15),such variations in exposure parameters are expected, given the data available, and are not major contributors to the overall variance in the results of predictions made by risk assessments. Registry No. EDB, 106-93-4; DBCP, 96-12-8.
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Literature Cited (1) McKone, T. E. Enuiron. Sci. Technol. 1987,21,1194-1201. (2) Verschueren, K. Handbook o f Environmental Data on
Organic Chemicals, 2nd ed.; Van Nostrand Reinhold New York, 1983; p 635. (3) Stephen, H.; Stephen, T. Solubilities of Inorganic and Organic Compounds, Volume 1, Binary Systems Part 1; The MacMillan Co.: New York, 1963; p 371. (4) Horvath, A. L. Halogenated Hydrocarbons, SolubilityMiscibility with Water; Marcel Dekker, Inc.: New York, 1982; pp 491, 686. ( 5 ) Stull, D. R. Ind. Eng. Chem. 1947, 39, 517-550. (6) Cothern, C. R.; Coniglio, W. A.; Marcus, W. L. Techniques for t h e Assessment of t h e Carcinogenic Risk to t h e US. Population Due to Exposure for Selected Volatile Organic Compounds f r o m Drinking Water Via Ingestion, Inhalation, and Dermal Routes; Report No. PB84-213941; U.S. Environmental Protection Agency, Office of Drinking Water, U.S. Government Printing Office: Washington, DC, 1984; p 120. (7) Ranz, W. E.; Marshall, W. R. Chem. Eng. Prog. 1952, 48, 141-146. (8) Ranz, W. E.; Marshall, W. R. Chem. Eng. Prog. 1952, 48, 173-180. (9) Eckert, E. R. G.; Drake, R. M. Analysis of Heat and Mass Transfer;Hemisphere Publishing Corp.: Washington, DC, 1987. (10) Andelman, J. B. Sci. Total Environ. 1985, 47, 443-460. (11) McKone, T. E.; Knezovich, J. P. J. Air Waste Manag. ASSOC. 1991, 41, 282-286. (12) Wilkes, C. R.; Small, M. J.; Andelman, J. B. The MAVRIQ Model for Indoor Exposures to VOCs from Contaminated Water Supplies. Presented a t the International Society of Exposure Analysis Meeting, Measuring Understanding and Predicting Exposures in the 21st Century, November 18-21, 1991, Atlanta, GA. (13) Giardino, N. J.; Andelman, J. B. Modelling Emission of Volatile Organic Chemicals from Shower Spray Droplets. Presented at the International Society of Exposure Analysis Meeting, Measuring Understanding and Predicting Exposures in the 21st Century, November 18-21,1991, Atlanta, GA. (14) Giardino, N. J.; Andelman, J. B., personal communication regarding unpublished results, Graduate School of Public Health, University of Pittsburgh, 1991. (15) McKone, T. E.; Bogen, K. T. Environ. Sci. Technol. 1991, 25,1674-1681.
Thomas E. McKone Lawrence Livermore National Laboratory University of California P.O. BOX 5507,L-453 Livermore, California 94550
This work was performed under the auspices o f the U S . Department of Energy through Lawrence Livermore National Laboratory under Contract W-7405-Eng-48 with funding provided by the State of CaliforniaDepartment of Toxic Substances Control.
