dots (in place of subscripts) denote averages over those subscripts. Nomenclature
C G S
concentration of a discharged substance standard or goal level for C severity, CIG 01 = allowable expected proportion of exceedances of unit severity = calculated severity of source c = critical level o f 9 for classification of source as ‘‘clean’’ or “dirty” /3 = maximum probability for misclassifying a dirty source CT,V, W, 2 = source and ambient factors in model for =
= =
s
c
X ,Y
= combined (product-quotients of) measured and nonmeasured factors, respectively, in model for C v y = long-term geometric mean of Y uu**, ue2 = temporal and measurement-error variances of a factor CT* = In U go2 = sum of temporal variances o f all (log-transformed) factors u2 = sum of total (temporal and measurement-error) variances of all measured (log-transformed) factors (appropriately weighted in the case of repeated measurements)
ni, k = number of measurements of a factor on ith day, 1
introduced by external tubing and our sampling technique. Further experimental evaluation of the dispersion coefficient was not carried out. Reversibility. Whether a reaction is termed reversible or not depends of course on the time frame under consideration. Over the entire time course of the column experiments, the sorption/desorption reactions can be considered to be reversible; that is, all of the material that was sorbed on the column was subsequently eluted from the column. The material balance can be calculated by evaluating the appropriate integrals under the elution curves (Figure 5B). The material balance also confirms that the organic compounds are removed by sorption and not by biological degradation. The tailing on the elution curve could be a manifestation of sorption-desorption kinetics, the hysteretic nature of the sorption-desorption process, or nonequivalent sites. 1366
Environmental Science & Technology
Kinetics. The effect of sorption kinetics can be observed by comparing elution curves from experiments run at different flow rates. In Figure 5C it is seen that the compounds are retained on the column much less effectively at a higher flow rate (experiment C2), indicating slow sorption kinetics. The similarity of breathrough curves from experiments run a t the same flow velocity (Figure SA) supports the hypothesis that the shift of breakthrough volumes seen in Figure 5C is indeed an effect of flow velocity. Comparison of Figure 5C with Figure 1 shows that the simple first-order kinetic sorption model is insufficient to describe the effect of flow velocity on the elution curve. The observed effect of faster flow velocity is a displacement of the elution curve to a smaller breakthrough volume, whereas the calculated effect of faster flow velocity is a broadening of the elution curve a t approximately the same breakthrough volume. This inconsistency could possibly be resolved by a more detailed kinetic model. Instead of a single value for hf,hb for all sorption sites on the column, it is more general to consider a continuous distribution of hf,kb values for all of the different sorption sites. If the rate-limiting step in sorption reactions is diffusive transport from the bulk of solution to a sorption site, the different hf,hb values would correspond to different diffusion path lengths. T o simplify this kinetics model, one could consider sorption reactions a t a certain fraction of the sorption sites to be a t equilibrium, and reactions a t the other sites to be kinetically controlled. The fractions of sites would depend on flow velocity. Van Genuchten et al. (26) have demonstrated the usefulness of this approach in a study of pesticide transport a t different flow velocities; in their study one fraction of sites was assigned infinitely fast kinetics (equilibrium) and the other fraction infinitely slow kinetics (no sorption). The hybrid kinetidequilibrium adsorption model yielded a more satisfactory qualitative description of the experimental results shown in Figure 5C. Detailed quantitative analysis of the distribution of hf,hb values, and the variation of the distribution with flow velocity, will be carried out with other sorbable solutes for which the chemical analysis is less timeconsuming. However, regardless of the model used to describe experimental results, the basic conclusion remains valid-that even a t the slow flow rates observed for natural groundwater flow, the kinetics of sorption must be considered in planning experiments and interpreting results. Summary and Conclusions A variety of laboratory batch and column experiments have been conducted to elucidate the sorption behavior of nonpolar organic compounds of low to intermediate lipophilicity in a river water-groundwater infiltration system. The results of this study can be summarized as follows. (1) For concentrations typically encountered in natural waters, the sorption of nonpolar organic compounds of low to intermediate lipophilicity by aquifer materials is reversible, and a linear sorption isotherm S = K,C is appropriate to describe sorption equilibrium. (2) For sorbents with organic-carbon content greater than 0.1%, a highly significant correlation was found between the K,'s of the compounds and the organic-carbon contents of the sorbents. These findings indicate a very similar lipophilicity of the organic materials present in these natural sorbents. (3) Small K , values have been found for "organic-poor" sorbents, even for those with a high specific surface area. Therefore, the compounds investigated are quite mobile in such media. (4)For all nonporous sorbents, a highly significant linear correlation was found between the logarithms of the partition coefficients K , of the different compounds and the logarithms of the corresponding octanol/water partition coefficients Kow:
+
log K , = a log Kow b. For a specific sorbent the value of the slope a of the regression line is a measure of the change in the free energy of transfer from the aqueous phase to the sorbent per unit change in the lipophilicity of the solute relative to octanol. (5) For sorbents with organic-carbon contents of greater than 0.1%,the K , value can be estimated for many nonpolar organic compounds from their octanol/water partition coefficients and the organic-carbon content of the sorbent. Predictions within a factor of 2 are possible. (6) Partition-coefficient values determined from column experiments run a t velocities u < 10-3 cm s-l were quite similar to those determined from 18-h equilibrium batch experiments. Column experiments run a t u = 10-2 cm s-1 showed the effect of slow sorption kinetics. Thus, sorption kinetics may have an effect on material transport over the range of flow velocities encountered in aquifers. Acknowledgment
We thank P. Baccini, C. Shaffner, and A. Vagenknecht for experimental assistance. We are indebted to P. Brezonik, R. H. Bromund, W. Giger, H. Hohl, and W. Stumm for reviewing the manuscript. Valuable comments were made by S. G. Wakeham. Literature Cited (1) Sontheimer, H. J . Am. Water Works Assoc. 1950, 72,386. (2) Piet, G. J.; Zoeteman, B. C. J. J. Am. Water Works Assoc. 1950, 72.400. .-,
Office of Water Recycling, California State Water Resources Control Board, Sacramento, CA, 1980; p 93. (7) Boast, C. W. Soil Sci. 1973,115, 224. (8) Lapidus, L.; Amundson, N. R. J . Phys. Chem. 1982,56,984. (9) Ogata, A. “Mathematics of Dispersion with Linear Adsorption Isotherm”, Geological Survey Professional Paper, 411-H; U.S. Government Printing Office: Washington, DC, 1964. (10) Bird, R.; Stewart, W. A.; Lightfood, E. “Transport Phenomena”; Wiley: New York, 1968; p 703. (11) Leo, A,; Hansch, C.; Elkins, D. Chem. Reu. 1971, 71,525. (12) Karickhoff, S. W.; Brown, D. S.; Scott, T. A. Water Res. 1979, 13, 241. (13) Baccini, R., EAWAG, unpublished data. (14) Giger, W.; Schaffner, C.; Wakeham, S. G. Geochim. Cosmochim. Acta 1950,44,119. (15) Hohl, H.; Stumm, W. J . Colloid. Interface Sci. 1976,55,281. (16) Matter, C. Ph.D. Thesis No. 6403, Swiss Federal Institute of Technology, Zurich, Switzerland, 1979 (in German). (17) Grob, K. J.Chromatogr. 1973,84,255. (18) Grob, K.; Zurcher, F. J . Chromatogr. 1976,117,285. (19) Schwarzenbach, R. P.; Molnar-Kubica, E.; Giger, W.; Wakeham, S . G. Enuiron. Sei. Technol. 1979,13, 1367. (20) Westall, J. C.; Schwarzenbach, R. P. In “Laboratory Study for Transport of Volatile Nonpolar Organic Compounds in a Porous Medium”, Technical Report, EAWAG, Duebendorf, Switzerland, 1980. (21) Chiou, C. T.; Peters, L. J.; Freed, V. H. Science 1979, 206, 831. (22) Khan, A.; Hasset, J. J.; Banwart, W. L.; Means, J. C.; Wood, S. G. Soil Sci. 1979,128, 297. (23) . . Rogers. R. D.: McFarlane. J. C.: Cross. A. J. Enuiron. Sci. Technol. i980,14,457. (24) Lambert. S. M. J . A n i . Food Chem. 1968.16.340. (25) Lupta, S:P.; Greenrhorn, R. A. Water Resour. Res. 1974, 10, 839. (26) Van Genuchten. M. T.: Davidson. J. M.: Wierenea. P. J. Soil Sci. SOC.Am. Proc. 1974,38,29. (27) Chiou. C. T.: Freed, V. H.: Schmedolinp, D. W.: Kohnert. R. L. Enuiron. Sci. Technol. 1977,11,475.
-
y
(3) Rao, P. S. C.; Davidson, J. M. In “Environmental Impact of Nonpoint Source Pollution”; Overcash, M. R., Davidson, J. M., Eds.; Ann Arbor Science Publishers: Ann Arbor, MI, 1980; p 23. (4) . , Rao. P. S. C.: Davidson. J. M.: JessuD. R. E.: Selim. H. M. Soil Sci. SOC.Am. J . 1979,43, 22: (5) Roberts, P. V.: McCartv, P. L.: Reinhard. M.: Schreiner. J. J . Water Pollut Control Fed. 1980,52, 161. (6) McCarty,P. L.; Rittmann, B. E.; Reinhard, M. In “Wastewater Reuse for Groundwater Recharge”; Asano, T., Roberts, P. V., Eds.; .I
l
Received for review November 12, 1980. Revised Manuscript Received June4,1981. Accepted June 30,1981. This work was funded by the Swiss National Science Foundation (Nationales Forschungsprogramm“Wasserhaushalt”)and by the Swiss Department of Commerce (Project COST 64b bis).
Desorption Kinetics of Carbon Tetrachloride from Activated Carbon Leonard A. Jonas and Eric B. Sansone* Environmental Control and Research Laboratory, Frederick Cancer Research Center, Frederick, Maryland 21 701
Four partially saturated carbon beds (6,52,69, and 97%) were prepared by varying the exposure time of the beds to CC14 vapor. When the CC14 was desorbed, curves of concentration vs. time were obtained. The experimental data were used to calculate the fractional regeneration of the bed as a function of time. The first-order desorption rate constant for the carbon was calculated from the Wheeler desorption kinetic equation. The log of the desorption rate constant was a linear function of the percentage saturation of the bed, permitting the calculation of the desorption rate constant a t any degree of saturation. This result suggests that a more fundamental relationship between the theoretical equations of adsorption and desorption kinetics exists than had previously been supposed. Activated carbons are usually characterized by the two fundamental properties adsorption capacity ( W e )and adsorption rate constant (k”). These properties, which define the dynamic flow adsorption behavior of a carbon, can be obtained from experimental measurements of vapor breakthrough time ( t b )as a function of carbon weight ( W) and the Wheeler adsorption equation ( I 1. However, carbon-bed filters, although subjected to continuous airflow, are usually exposed 0013-936X/81/0915-1367$01.25/0 @ 1981 American
only intermittently to contaminants, for example, during a leak or an accident. The flow of clean air results in a succession of desorption-adsorption cycles, in which previously adsorbed gas is desorbed only to be readsorbed immediately downstream. It is in this stepwise or wavelike manner (2) that desorption occurs in a carbon bed only partially saturated with adsorbed vapor. I t is important to know the relationship between the desorption characteristics of the carbon and the percentage saturation of the carbon, since it is this relationship and not adsorption alone that determines the protective properties of the carbon for the contaminant vapor. Desorption Kinetics. In contrast to adsorption which takes place spontaneously, desorption requires that work be done on the system. The work is accomplished by mass transport; this involves movement of the adsorbed phase into the streamlines around the sorbent granules, and the adsorbed front “flows” through successive portions of the bed until the bed is penetrated. The kinetics of desorption from a carbon bed saturated with adsorbed vapor was studied by Wheeler ( 3 ) ,who derived the kinetic equation in terms of the time required to regenerate any arbitrarily chosen fraction of the saturated bed. The equation can be shown as
Chemical Society
Volume 15, Number 11, November 1981 1367
