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Response to Comment on “Field-Scale Transport of Nonpolar Organic Solutes in 3-D Heterogeneous Aquifers” SIR: The comment by Ball et. al. (1) provides an opportunity to review some fundamental issues associated with fieldscale modeling of reactive transport processes. In particular, the two issues we wish to address are (a) laboratory analysis and the diffusion model and (b) extrapolation of laboratoryderived coefficients to field-scale applications. It should also be noted that nearly all of the analysis presented in Cushey and Rubin (2) utilized a mass transfer parameter (ω) based on laboratory data from column studies performed by Ptacek and Gilham (3) (identified as scenario 1) whereas the comment by Ball et. al (1) focuses on scenario 2. Laboratory Analysis and the Diffusion Model. In their comment, Ball et. al. (1) refer to a methodology for converting coefficients for a spherical diffusion model to equivalent coefficients for a linear driving force (LDF) model. To put things in perspective, we refer to the excellent paper by Haggerty and Gorelick (4). That paper includes a lucid discussion on the origin of this methodology and its underlying assumptions. Haggerty and Gorelick (4) indicate that in fact there are many methods for converting coefficients. More fundamentally, however, is the statement of the underlying assumptions, and in particular, the statement: “This trial solution is based on knowledge of diffusion into and out of a sphere that is placed within a well-stirred infinite solution.” (ref 4, p 2388). This assumption is obviously never met in real life applicationsssolute concentrations in aqueous and sorbed phases and the distribution of reaction sites are highly variable and can vary by orders of magnitudes on small scales (5-7). This issue has been discussed in great detail in a recent paper by Kapoor and Kitanidis (8). These facts suggest that one should place great caution in converting laboratory models for use in field applications. The assertion by Ball et. al. (1) that there is one conventional methodology should be studied carefully. In fact, Table 3 in Cushey and Rubin (2) clearly shows the wide range of coefficients utilized by various researchers. Extrapolation of Laboratory-Derived Coefficients. The above discussion leads next to the issue of upscaling. As has become clear in the many modeling studies of the Borden site (e.g., refs 2, 3, and 9-12), the inference of parameters in the laboratory is of limited value in the absence of a clear procedure for upscaling. It can be said that this field of research is quite in its infancy. Hydrogeologists encountered similar problems trying to employ laboratory-inferred diffusion coefficients for modeling field-scale dispersion and mixing. These attempts were of limited value, and the difficulties were resolved only after researchers had recognized that it is the field-scale conditions that cannot be
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accounted for in laboratory-scale experiments, which control the response (13, 14). There are plenty of indications suggesting that chemical reaction parameters are highly heterogeneous (e.g., refs 15 and 16) and that this spatial variability can dominate the response of the contaminant plumes (e.g., refs 17-20). We believe that this is a better venue for interpretation of the Borden experiment than the intricacies of the diffusion and LDF model.
Literature Cited (1) Ball, W. P.; Goltz, M. N.; Roberts, P. V.; Valocchi, A. J.; Brusseau, M. L. Environ. Sci. Technol. 1998, 32, 0000-0000. (2) Cushey, M.; Rubin, Y. Environ. Sci. Technol. 1997, 31, 12591268. (3) Ptacek, C. J.; Gillham, R. W. J. Contam. Hydrol. 1992, 10, 119158. (4) Haggerty, R.; Gorelick, S. M. Water Resour. Res. 1995, 31, 23832400. (5) Wood, W. W.; Kraemer, T. F.; Hearn, P. P. Science 1990, 247, 1569-1572. (6) Mackay, D. M.; Ball, W. P.; Durant, M. G. J. Contam. Hydrol. 1986, 1, 119-132. (7) Pedit, J. A.; Miller, C. T. Environ. Sci. Technol. 1994, 28, 20942104. (8) Kapoor, V.; Kitanidis, P. K. Stoch. Hydrol. Hydraul. 1997, 11, 397-422. (9) Goltz, M. N.; Roberts, P. V. J. Contam. Hydrol. 1988, 3, 37-63. (10) Brusseau, M. L. Water Resour. Res. 1992, 28, 2485-2497. (11) Quinodoz, H. A. M.; Valocchi, A. J. Water Resour. Res. 1993, 29, 3227-3240. (12) Burr, D. T.; Sudicky, E. A.; Naff, R. L. Water Resour. Res. 1994 30, 791-815. (13) Gelhar, L. W.; Axness, C. L. Water Resour. Res. 1983, 19, 161180. (14) Dagan, G. J. Fluid Mech. 1984, 145, 151-177. (15) Robin, M. J. L.; Sudicky, E. A.; Gillham, R. W.; Kachanoski, R. G. Water Resour. Res. 1991, 27, 2619-2632. (16) Boekhold, A. E.; Van der Zee, S. E. A. T. M. Soil Sci. Soc. Am. J. 1992, 56, 747-754. (17) Bosma, W. J. P.; Bellin, A.; Van der Zee, S. E. A. T. M.; Rinaldo, A. Water Resour. Res. 1993, 12, 4031-4043. (18) Wise, W. R. Water Resour. Res. 1993, 29, 2983-2992. (19) Chen, W.; Wagenet, R. J. Environ. Sci. Technol. 1995, 29, 27252734. (20) Miralles-Wilhelm, F.; Gelhar, L. W. Water Resour. Res. 1996, 32, 1541-1549.
Mark A. Cushey* Earth Sciences Division Lawrence Berkeley National Laboratory Berkeley, California 94720
Yoram Rubin Department of Civil and Environmental Engineering University of California Berkeley, California 94720 ES982006I
S0013-936X(98)02006-9 CCC: $15.00
1998 American Chemical Society Published on Web 07/22/1998
