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Implications of non-equilibrium sorption on the interception–sorption trench remediation strategy
Geoderma 84 Ž1998. 109–120
Implications of non-equilibrium sorption on the interception–sorption trench remediation strategy P.W. Hitchcock ) , D.W. Smith Department of CiÕil Engineering and SurÕeying, UniÕersity of Newcastle, Newcastle, Australia Accepted 23 July 1997
Abstract Design charts, based on solution of the advection–dispersion equation and assuming equilibrium sorption, have been developed to aid in interception–sorption trench design. The interception–sorption trench method is a simple, cost effective, in situ groundwater remediation technique. The procedure involves excavating a trench downflow of a polluted area and backfilling the trench with a sorbent material. The contaminant is transported through the soil along the natural groundwater gradient and over time the contaminant will be sorbed onto the material contained within the trench. The interception–sorption trench system can be used for groundwater remediation in a decontamination strategy or in a pollution-control strategy. The decontamination strategy comprises removing the trench material when all the contaminant is contained within the trench, thereby decontaminating the groundwater system. Alternatively, with the pollution-control strategy, the sorptive material remains in situ and the system is designed to reduce the postsorptive trench contaminant concentration to an environmentally acceptable level. The important implications of considering non-equilibrium sorption on trench design for both the decontamination and pollution-control strategies were studied using a linear hereditary time-dependent sorption model. For the pollution-control strategy, non-equilibrium conditions can result in underestimation of the maximum trench effluent concentration. For the decontamination strategy, non-equilibrium conditions can result in overestimation of the amount of contaminant in the trench at a given time. q 1998 Elsevier Science B.V. All rights reserved. Keywords: contamination; sorption; non-equilibrium; pollution; remediation
1. Introduction The interception–sorption method is a passive Ž non-pumping. in situ groundwater remediation technique based on interception and sorption. With this )
Corresponding author. Fax: q61 Ž49. 216991; E-mail: [email protected]
0016-7061r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 1 6 - 7 0 6 1 Ž 9 7 . 0 0 1 2 3 - 7
110
P.W. Hitchcock, D.W. Smithr Geoderma 84 (1998) 109–120
method, the mechanisms of solute transport through porous media, namely, diffusionrdispersion and advection are relied upon to transport the pollutant through the soil to an interception point where it is sorbed. The interception–sorption method can be implemented by simply constructing a trench, located downgradient of the contamination, and backfilling the trench with a sorbent material. The sorptive properties of many natural and artificial substances have been actively researched. A review of numerous different sorptive materials, namely, fly ash, zeolite, vermiculite, illite, kaolinite, activated alumina, cullite and activated carbon for sludges containing petroleum and metal finishing sludge was conducted by Liskowitz et al. Ž1976. and Chan et al. Ž1978.. Evans et al. Ž 1990. has reviewed various sorptive materials that could be used as part of the liner of an engineered landfill barrier. Arsenic, lead and cadmium are identified as being preferentially sorbed onto zeolites, while organically modified clays are identified as being candidates for the removal of organic contaminants. It is also known that many pesticides and organic chemicals are strongly sorbed onto humic substances. Many ionisable chemicals, both cations and anions, are strongly sorbed onto allophanic clay soils. In addition, both activated carbon and activated alumina are well known as water purifiers. It is noted that while the construction of vertical barriers is common in pollution management practice, the usual purpose of the barrier is to act as a cut-off wall Že.g. Ryan, 1987. , rather than acting as a sorptive ‘sink’ for the contaminant. A review of the use of physical barriers for waste containment is given by Mitchell Ž 1994. . Conceptually, there are at least two essential ways in which the interception– sorption trench system can be employed for groundwater remediation, namely, the decontamination strategy and the pollution-control strategy. The decontamination strategy previously discussed by Smith et al. Ž1993a., comprises removal of the sorptive material when all the contaminant is contained within the trench thereby decontaminating the groundwater system. By contrast, the pollution-control strategy involves the sorptive material remaining in situ with the system designed to reduce the postsorptive trench contaminant concentration to an environmentally acceptable level. To demonstrate how the decontamination strategy can be designed, Smith et al. Ž1993a. presented a series of non-dimensional design charts based on the solution of a one dimensional dispersion–advection equation with predominantly equilibrium. The pollution-control strategy has been discussed by Hitchcock and Smith Ž 1996. who presented design charts based on equilibrium sorption to enable prediction of the trench effluent concentration for various trench width and sorptive properties of the trench material. It is common for the process of contaminant transport through the soil to be slow compared to the time for equilibrium interaction between the sorbate and contaminant. When this occurs, there will be little error introduced in analysis by assuming that the sorption is equilibrium controlled. In practice, this is often
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the case and many problems of practical interest have been solved, to an accuracy sufficient for engineering purposes, using the equilibrium controlled sorption assumption Ž e.g. Quigley and Rowe, 1986.. Low flow rates are generally required to establish local equilibrium at every point along a flow path Ž Lapidus and Admunson, 1952. . The critical velocity below which equilibrium is established is a function of the properties of both the porous medium and the solute ŽPtacek and Gillham, 1992. . Deviations from equilibrium are attributed to a variety of mechanisms including physical nonequilibrium processes Ždue to slow mass transport to and from sorption sites. and chemical–kinetic non-equilibrium Ž due to slow adsorption–desorption processes at sorbent surfaces. ŽPtacek and Gillham, 1992. . There is a considerable amount of evidence, that for some contaminants and soil types, account should be taken of the time dependence of the chemical or physical interaction Že.g. Mansell et al., 1977; Starr et al., 1985; Parker and Valocchi, 1986; Brusseau, 1991; Barone et al., 1992; Kookana et al., 1992a,b. . In particular, when the rate of interaction of the contaminant with the sorbate is of the same order of magnitude as the rate of contaminant transport, it may prove necessary to incorporate the kinetics of the sorption process in the transport model. The most frequently employed kinetic sorption model is a first-order reaction. The rate of forward reaction being proportional to the concentration of contaminant in the bulk solution and the rate of reverse reaction being proportional to the amount of contaminant sorbed ŽTravis and Etnier, 1981.. In this paper, account is taken of reversible time dependent-reactions, both physical and chemical, that can be expressed in the form of a first-order chemical reaction. This description of the adsorption kinetics has been applied to cation and anion exchange reactions Ž Sposito, 1989. , to phosphate sorption ŽMansell et al., 1977. and the sorption of many organic chemicals Ž Ptacek and Gillham, 1992; Brusseau, 1995. including pesticides Ž Travis and Etnier, 1981. . In this paper we investigate the effect that non-equilibrium sorption has on both the decontamination and pollution-control strategies. We found that nonequilibrium conditions in the trench need to be considered in trench design for pollution control. However, for decontamination, non-equilibrium in both the pretrench and tench material should be considered.
2. Methods 2.1. Modelling approach Contaminant transport through soils is usually modelled mathematically by the diffusionrdispersion–advection equation. Various simplifying assumptions are often made regarding the contaminant sorption onto the soil particles,
112
P.W. Hitchcock, D.W. Smithr Geoderma 84 (1998) 109–120
namely, that the contaminant sorption can be approximated as a linear, reversible, equilibrium controlled process Ž Smith et al., 1993a. . Smith et al. Ž1993a. have generalised the equilibrium models developed by Rowe and Booker Ž1985a,b, 1987. to include reversible non-equilibrium controlled sorption, modelled as a linear hereditary sorption process. The results presented in this paper are based on the solution of the integro-differential equation as follows: Ec E2c t nc Ž t . s nci q ynn q nD 2 d t y Ž c i y c 0 e . Ds K d Ž t . Ez Ez 0 t Ec Ž t . y D K Ž t y t . dt . Ž1. Et s d 0 where cŽ t . s solute concentration in the pore fluid at time t, c 0 e s the equilibrium concentration of solute in the pore fluid that would result in the initial mass of adsorbed solute onto the soil skeleton, c i s solute concentration at time t s 0, n s porosity of soil, y s average linear velocity of pore fluid in the z direction, D s effective diffusionrdispersion coefficient of solute, Ds s dry density of the soil, K dŽ t . s a time dependent distribution coefficient, Ži.e. the increment in mass of solute adsorbed onto the soil skeleton per unit increment of concentration per unit mass of soil at time t .. K dŽ t . is taken to be of the form,
H
ž
/
H
)
K d Ž t . s K d`Ž 1 y eytr t . where t ) s the sorption time constant. Eq. Ž1. may be simplified by the introduction of a Laplace transformation and use of the convolution theorem. For a detailed description of the method of solution of this equation in the Laplace transform domain the reader is referred to Rowe and Booker Ž1987.. Once the solution is found in the Laplace transform domain, the solution in the real time domain may be found using a numerical inversion algorithm developed by Talbot Ž 1979. . 2.2. Problem idealisation In this analysis presented in this paper, the pollutant is idealised as initially evenly spread throughout a saturated soil and that the contaminant transport process through both the soil and the sorbent material is approximated by Eq. Ž1. . The interception–sorption strategy is implemented by excavating a trench constructed at the leading edge of the contaminated region and then backfilling with a sorbent material. The processes of dispersionrdiffusion and advection are being relied upon to transport the contaminant through the soil to the sorbent material and so it is desirable that the advective velocity of the groundwater is not reduced by the presence of the sorbent material in the trench. To ensure that advective transport is not changed to any significant extent, the backfill material has a permeability similar to that of the natural soil. We have
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assumed that the natural soil and the trench material have a similar particle size distribution and porosity, and therefore the dispersivity and permeability of the natural soil is taken to be equal to that of the backfill material. The retardation factor Ž R . is often used in contaminant transport analysis and is defined as Ž1 q Ds K drn. ŽFreeze and Cherry, 1979.. In the following analysis, the ratio of the retardation coefficient of the sorbent material Ž R 2 . to the natural soil Ž R 1 . is equal to 100. It is noted that the design charts for the pollution-control strategy presented by Hitchcock and Smith Ž 1996. , cover a broad range of retardation ratios ranging between 10 and 5000. A schematic representation of the problem to be analysed in this paper is shown in Fig. 1a,b. In this analysis, the ratio of trench width Ž L 2 ., to length of initially contaminated soil Ž L1 . is 1r10. In the design charts presented by
Fig. 1. Ža. geometry of interception–sorption problem analysed indicating initial and boundary conditions. Žb. section showing the interception–sorption trench system.
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Hitchcock and Smith Ž1996. L1rL2 ranges from 1r1 to 1r10 000. The ratio of L1 to the length of the uncontaminated, postsorptive trench L 3 , is taken to be equal to one, although it can be shown that reducing L 3 relative to L1 has little effect on the solution. The boundary conditions for the analysis comprise the upstream surface of the contaminated soil, assumed to be impermeable to the contaminant, while the downstream surface of the soil is assumed to be at a constant concentration of zero. The downstream boundary condition does not affect the non-dimensional solutions prior to the contaminant reaching the downstream surface.
3. Results 3.1. Effect of non-equilibrium sorption on the pollution-control strategy The aim of the pollution-control strategy is to reduce the trench effluent concentration to an acceptable level. In this section, we investigate the effect of non-equilibrium sorption by calculating the maximum trench effluent concentration for various degrees of non-equilibria. A useful measure of the degree of non-equilibria in a system is the Damkohler number ŽDN.. The DN is defined as DN y kL21rD, where k is the first order reaction constant and L1 and D are as previously defined. The reaction constant k is equal to 1rt ) with t ) s the sorption time constant ŽSmith et al., 1993b. which can derived from laboratory batch tests. The DN provides a measure of the relative rate of chemicalrphysical interaction of contaminant and sorbate compared to the rate of diffusive transport ŽCussler, 1984.. The amount of non-equilibrium decreases with increasing DN ŽBrusseau, 1991.. At low DN the sorptive capacity of the soil is not significant before the solute is transported through the trench Ž Smith et al., 1993b.. Also referred to in the following sections is the Peclet number Ž PN; defined as PN s y L1rD .. The PN is a measure of the relative importance of advective transport as compared to diffusiverdispersive transport. A high PN Že.g. a free-flowing sandy aquifer. indicates that advection dominates and, therefore, the contact time between the contaminant and the trench material is relatively short compared to that for low PN Ž a low flow clayey aquifer. . The solutions presented in Fig. 2a–c have been calculated for R 2rR1 s 100, L1rL2 s 10 and show non-dimensional concentration profiles Ž crci . at various DNs ranging from 1 to 1000 and PNs ranged from 1 to 100. Various non-equilibrium and equilibrium scenarios were adopted as shown on Table 1. From Fig. 2a–c, it can be seen that as the degree of non-equilibrium sorption increases the maximum trench effluent concentration increases. The magnitude of the increase in concentration varies with PN. At low PN ŽPN s 1–10, Fig.
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Fig. 2. Ža. maximum post-trench concentration for DNs1–1000, PNs1, R 2 r R 1 s100, L1 r L 2 s10 and for various pretrenchrtrench equilibrium conditions. Žb. maximum post-trench concentration for DNs1–1000, PNs10, R 2 r R 1 s100, L1 r L2 s10 and for various pretrench equilibrium conditions. Žc. maximum post-trench concentration for DNs1–1000, PNs100, R 2 r R 1 s 100, L1 r L2 s10 and for various pretrenchrtrench equilibrium conditions.
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Table 1 Non-equilibrium modelled scenarios Scenario
Presorptive trench material
Trench material
A B C
Non-equilibrium Equilibrium Non-equilibrium
Non-equilibrium Non-equilibrium Equilibrium
2b,c., non-equilibria has little effect on maximum trench effluent concentration until DN - 10. At higher PN Ž PN s 100., the effect of non-equilibrium sorption is more pervasive and divergence between the non-equilibrium and equilibrium cases occurs at DN - 100. Fig. 2c ŽPN s 100., shows that the effect of non-equilibrium sorption is greater at high PN. This is because at high PN, the contact time between the sorbate and the contaminant is reduced, thereby reducing the opportunity for maximum sorption to occur. Fig. 2a–c also shows that the magnitude of the trench effluent concentration increase is mainly influenced by non-equilibrium sorption in the trench Žscenarios A and B. rather than the pretrench material Ž scenario C.. This is because most of the concentration reduction occurs in the trench. 3.2. Effect of non-equilibrium sorption on the decontamination strategy The aim of the decontamination strategy is to capture a predetermined amount of the initial contaminant flux in the trench at a particular time. In this section we investigated the effect of non-equilibrium sorption by assessing the maximum trench efficacy at various Damkohler numbers Ž as previously defined. . Here we define efficacy of contaminant removal to be the ratio of the mass of contaminant contained in the trench at a given time to the initial mass of contaminant. The solutions presented in Fig. 3a,b, show the maximum trench efficacy at DNs ranging from 1 to 1000 and for PNs ranging from 1 to 100. Various non-equilibrium and equilibrium scenarios were modelled as discussed in the preceding section Žsee Table 1.. Referring to Fig. 3a,b, the maximum trench efficacy decreases with an increase in the degree of non-equilibria. The magnitude of this effect varies with PN. At high PN Ž PN s 100., where the contact time between the contaminant and the sorbent is low, the differences between the equilibrium and non-equilibrium cases are greatest. For the case presented in Fig. 3a, the trench efficacy is reduced from 100% to between 10 and 55%, depending on the equilibrium scenario considered.
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Fig. 3. Ža. maximum trench efficacy for DNs1–100, PNs1–10, R 2 r R 1 s 200, L1 r L2 s10 and for various pretrenchrtrench equilibrium conditions. Žb. maximum trench efficacy for DNs1–100, PNs100, R 2 r R 1 s 200, L1 r L 2 s10 and for various pretrenchrtrench equilibrium conditions.
At low PN ŽPN s 1, Fig. 3b. , where the contact time between the contaminant and the sorbent is relatively longer, the magnitude of the decrease in maximum trench efficacy is much less than for the PN s 100 case, decreasing from about 80% at equilibrium to 70% for DN s 1. For scenarios A and B Žnon-equilibrium in the trench. the trench efficacy is lower than when non-equilibrium only occurs in the pretrench material Ž scenario C.. However, it is noted that for the decontamination strategy, non-equilibrium in the pretrench-only case does effect the trench efficacy even at lower DN. This is in contrast to the pollution-control strategy analysis where, for the scenario C case, the maximum post-trench concentration was unaffected by non-equilibrium sorption.
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4. Conclusions The analysis presented in this paper has shown that significant error could be introduced into the design of the interception–sorption trench system, if nonequilibrium conditions are ignored. For the pollution-control strategy, non-equilibrium conditions can result in higher trench effluent concentration compared to the equilibrium case and will therefore result in an underestimation of the maximum trench effluent concentration. For the decontamination strategy, non-equilibrium conditions can result in lower trench efficacy compared to the equilibrium case and will therefore result in an overestimation of the amount of contaminant in the trench at a particular time. For either strategy, the pervasiveness of the non-equilibrium effect is more pronounced at high Peclet numbers Ž PN G 100. at low Damkohler numbers ŽDN s 1–10.. It is noted that for the pollution-control strategy, only non-equilibrium conditions in the trench effect the maximum trench effluent concentration and therefore this only needs consideration during trench design. However, for the decontamination strategy, non-equilibrium in both the pretrench and trench material should be considered. It is not practical to present design charts for all non-equilibrium cases. When non-equilibrium conditions are expected, the specific case should be modelled incorporating sorption time constant data derived from batch tests. However, when equilibrium conditions prevail the design charts presented by Hitchcock and Smith Ž1996. and Smith et al. Ž1993a. can be employed.
Acknowledgements The authors acknowledge the financial support of the Australian Research Council when conducting this research.
References Barone, F.S., Rowe, R.K., Quigley, R.M., 1992. A laboratory estimation of diffusion and adsorption coefficients for several volatile organics in a natural clayey soil. J. Contam. Hydrol. 13 Ž2., 123–139. Brusseau, M.L., 1991. Application of a multiprocess non-equilibrium sorption model to solute transport in a stratified porous medium. Water Resour. Res. 27 Ž4., 589–595. Brusseau, M.L., 1995. The effect of nonlinear sorption on transformation of contaminants during transport in porous media. J. Contam. Hydrol. 17 Ž4., 589–595.
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Chan, P., Liskowitz, J., Perna, A.J. 1978. Pilot scale evaluation of design parameters for sorbent treatment of industrial sludge leachates. Land Disposal of Hazardous Wastes. Proceedings of the Fourth Annual Research Symposium. USEPA, EPA-600r9-78-016. Cussler, E.L., 1984. Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge. Evans, J.C., Sambasivam, Y., Zarlinski, S., 1990. Attenuating materials in composite liners. Proceedings Symposium, Waste Containment Systems: Construction Regulation and Performance, Geotechnical Special Publication No. 26, pp. 246–263 Freeze, R.H., Cherry, J.A., 1979. Groundwater. Prentice-Hall, Englewood Cliffs, New Jersey. Hitchcock, P.W., Smith, D.W. 1996. Pollution control strategy employing an interception sorption trench. Canad. Geotech. J., in press. Kookana, R.S., Aylmore, L.A.G., Gerritse, R.G., 1992a. Time dependent sorption of pesticides during transport in soils. Soil Sci. 154 Ž3., 214–225. Kookana, R.S., Gerritse, R.G., Aylmore, L.A.G., 1992b. A method for studying non-equilibrium sorption during transport of pesticides in soil. Soil Sci. 154 Ž5., 344–349. Lapidus, L., Admunson, N.R., 1952. Mathematics of adsorption in beds, VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns. J. Phys. Chem. 56, 984–988. Liskowitz, J.W., Chan, P.C., Trattner, R.B. 1976. Evaluation of selected sorbents for the removal of contaminants in leachate from industrial sludges. Residual management by land disposal. Proceedings of the Hazardous Waste Research Symposium. USEPA, EPA-600r9-76-015. Mansell, R.S., Selim, H.M., Kanchanasut, P., Davidson, J.M., Fiskell, J.G.A., 1977. Experimental and simulated transport of phosphorus through sandy soils. Water Resour. Res. 13 Ž1., 189–194. Mitchell, J.K., 1994. Physical barriers for waste containment. Proceedings of the First International Congress on Environmental Geotechnics. Edmonton, Canada, 11–15 July, 1994, pp. 951–961. Parker, J.C., Valocchi, A.J., 1986. Constraints on the validity of equilibrium and first order kinetic models in structured soils. Water Resour. Res. 22 Ž3., 399–407. Ptacek, C.J., Gillham, R.W., 1992. Laboratory and field measurements of non-equilibrium transport in the Borden aquifer, Ontario, Canada. J. Contam. Hydrol. 10, 119–158. Quigley, R.M., Rowe, R.K., 1986. Leachate migration through a clay below a domestic waste landfill, Sarnia, Ontario. In: Hazardous and Industrial Solid Waste Testing and Disposal, Vol. 6. ASTM Special Publication No. 933, pp. 93–103. Rowe, R.K., Booker, J.R., 1985a. 1-D Pollutant migration in soils of finite depth. J. Geotech. Engin., ASCE 111 ŽGT4., 479–499. Rowe, R.K., Booker, J.R., 1985b. 2-D Pollutant migration in soils of finite depth. Canad. Geotech. J. 22 Ž4., 429–436. Rowe, R.K., Booker, J.R., 1987. An efficient analysis of pollutant migration through soil. In: Hinton, Bettes, Schrefler ŽEds.., Numerical Methods in Transient and Coupled Systems, John Wiley and Sons, pp. 13–42. Ryan, C.R., 1987. Vertical barriers in soil for pollution containment. Proceedings of the Conference Geotechnical Practice for Waste Disposal, 1987, ASCE Geotechnical Special Publication No. 13, pp. 182–204. Smith, D.W., Rowe, R.K., Booker, J.R., 1993a. Decontamination of a polluted aquifer using as interceptionrsorption trench: dispersion–advection analysis with linear hereditary sorption. Comput. Geotech. 15, 163–186. Smith, D.W., Rowe, R.K., Booker, J.R. 1993b. The analysis of pollutant migration through soil with linear hereditary sorption. Int. J. Analyt. Num. Methods Geomechan. Geoenviron. Engin., 1–20.
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Sposito, G., 1989. Soil Chemistry. Oxford University Press. Starr, R.C., Gillham, R.W., Sudicky, E.A., 1985. Experimental investigation of solute transport in a stratified porous media 2 the reactive case. Water Resour. Res. 21 Ž7., 1043–1050. Talbot, A., 1979. The accurate numerical inversion of Laplace transforms. J. Inst. Math. Appl. 23, 97–120. Travis, C.C., Etnier, E.L., 1981. A survey of sorption relationships for reactive solutes in soil. J. Environ. Qual. 10 Ž1., 8–16.
Implications of non-equilibrium sorption on the interception–sorption trench remediation strategy P.W. Hitchcock ) , D.W. Smith Department of CiÕil Engineering and SurÕeying, UniÕersity of Newcastle, Newcastle, Australia Accepted 23 July 1997
Abstract Design charts, based on solution of the advection–dispersion equation and assuming equilibrium sorption, have been developed to aid in interception–sorption trench design. The interception–sorption trench method is a simple, cost effective, in situ groundwater remediation technique. The procedure involves excavating a trench downflow of a polluted area and backfilling the trench with a sorbent material. The contaminant is transported through the soil along the natural groundwater gradient and over time the contaminant will be sorbed onto the material contained within the trench. The interception–sorption trench system can be used for groundwater remediation in a decontamination strategy or in a pollution-control strategy. The decontamination strategy comprises removing the trench material when all the contaminant is contained within the trench, thereby decontaminating the groundwater system. Alternatively, with the pollution-control strategy, the sorptive material remains in situ and the system is designed to reduce the postsorptive trench contaminant concentration to an environmentally acceptable level. The important implications of considering non-equilibrium sorption on trench design for both the decontamination and pollution-control strategies were studied using a linear hereditary time-dependent sorption model. For the pollution-control strategy, non-equilibrium conditions can result in underestimation of the maximum trench effluent concentration. For the decontamination strategy, non-equilibrium conditions can result in overestimation of the amount of contaminant in the trench at a given time. q 1998 Elsevier Science B.V. All rights reserved. Keywords: contamination; sorption; non-equilibrium; pollution; remediation
1. Introduction The interception–sorption method is a passive Ž non-pumping. in situ groundwater remediation technique based on interception and sorption. With this )
Corresponding author. Fax: q61 Ž49. 216991; E-mail: [email protected]
0016-7061r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 0 1 6 - 7 0 6 1 Ž 9 7 . 0 0 1 2 3 - 7
110
P.W. Hitchcock, D.W. Smithr Geoderma 84 (1998) 109–120
method, the mechanisms of solute transport through porous media, namely, diffusionrdispersion and advection are relied upon to transport the pollutant through the soil to an interception point where it is sorbed. The interception–sorption method can be implemented by simply constructing a trench, located downgradient of the contamination, and backfilling the trench with a sorbent material. The sorptive properties of many natural and artificial substances have been actively researched. A review of numerous different sorptive materials, namely, fly ash, zeolite, vermiculite, illite, kaolinite, activated alumina, cullite and activated carbon for sludges containing petroleum and metal finishing sludge was conducted by Liskowitz et al. Ž1976. and Chan et al. Ž1978.. Evans et al. Ž 1990. has reviewed various sorptive materials that could be used as part of the liner of an engineered landfill barrier. Arsenic, lead and cadmium are identified as being preferentially sorbed onto zeolites, while organically modified clays are identified as being candidates for the removal of organic contaminants. It is also known that many pesticides and organic chemicals are strongly sorbed onto humic substances. Many ionisable chemicals, both cations and anions, are strongly sorbed onto allophanic clay soils. In addition, both activated carbon and activated alumina are well known as water purifiers. It is noted that while the construction of vertical barriers is common in pollution management practice, the usual purpose of the barrier is to act as a cut-off wall Že.g. Ryan, 1987. , rather than acting as a sorptive ‘sink’ for the contaminant. A review of the use of physical barriers for waste containment is given by Mitchell Ž 1994. . Conceptually, there are at least two essential ways in which the interception– sorption trench system can be employed for groundwater remediation, namely, the decontamination strategy and the pollution-control strategy. The decontamination strategy previously discussed by Smith et al. Ž1993a., comprises removal of the sorptive material when all the contaminant is contained within the trench thereby decontaminating the groundwater system. By contrast, the pollution-control strategy involves the sorptive material remaining in situ with the system designed to reduce the postsorptive trench contaminant concentration to an environmentally acceptable level. To demonstrate how the decontamination strategy can be designed, Smith et al. Ž1993a. presented a series of non-dimensional design charts based on the solution of a one dimensional dispersion–advection equation with predominantly equilibrium. The pollution-control strategy has been discussed by Hitchcock and Smith Ž 1996. who presented design charts based on equilibrium sorption to enable prediction of the trench effluent concentration for various trench width and sorptive properties of the trench material. It is common for the process of contaminant transport through the soil to be slow compared to the time for equilibrium interaction between the sorbate and contaminant. When this occurs, there will be little error introduced in analysis by assuming that the sorption is equilibrium controlled. In practice, this is often
P.W. Hitchcock, D.W. Smithr Geoderma 84 (1998) 109–120
111
the case and many problems of practical interest have been solved, to an accuracy sufficient for engineering purposes, using the equilibrium controlled sorption assumption Ž e.g. Quigley and Rowe, 1986.. Low flow rates are generally required to establish local equilibrium at every point along a flow path Ž Lapidus and Admunson, 1952. . The critical velocity below which equilibrium is established is a function of the properties of both the porous medium and the solute ŽPtacek and Gillham, 1992. . Deviations from equilibrium are attributed to a variety of mechanisms including physical nonequilibrium processes Ždue to slow mass transport to and from sorption sites. and chemical–kinetic non-equilibrium Ž due to slow adsorption–desorption processes at sorbent surfaces. ŽPtacek and Gillham, 1992. . There is a considerable amount of evidence, that for some contaminants and soil types, account should be taken of the time dependence of the chemical or physical interaction Že.g. Mansell et al., 1977; Starr et al., 1985; Parker and Valocchi, 1986; Brusseau, 1991; Barone et al., 1992; Kookana et al., 1992a,b. . In particular, when the rate of interaction of the contaminant with the sorbate is of the same order of magnitude as the rate of contaminant transport, it may prove necessary to incorporate the kinetics of the sorption process in the transport model. The most frequently employed kinetic sorption model is a first-order reaction. The rate of forward reaction being proportional to the concentration of contaminant in the bulk solution and the rate of reverse reaction being proportional to the amount of contaminant sorbed ŽTravis and Etnier, 1981.. In this paper, account is taken of reversible time dependent-reactions, both physical and chemical, that can be expressed in the form of a first-order chemical reaction. This description of the adsorption kinetics has been applied to cation and anion exchange reactions Ž Sposito, 1989. , to phosphate sorption ŽMansell et al., 1977. and the sorption of many organic chemicals Ž Ptacek and Gillham, 1992; Brusseau, 1995. including pesticides Ž Travis and Etnier, 1981. . In this paper we investigate the effect that non-equilibrium sorption has on both the decontamination and pollution-control strategies. We found that nonequilibrium conditions in the trench need to be considered in trench design for pollution control. However, for decontamination, non-equilibrium in both the pretrench and tench material should be considered.
2. Methods 2.1. Modelling approach Contaminant transport through soils is usually modelled mathematically by the diffusionrdispersion–advection equation. Various simplifying assumptions are often made regarding the contaminant sorption onto the soil particles,
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namely, that the contaminant sorption can be approximated as a linear, reversible, equilibrium controlled process Ž Smith et al., 1993a. . Smith et al. Ž1993a. have generalised the equilibrium models developed by Rowe and Booker Ž1985a,b, 1987. to include reversible non-equilibrium controlled sorption, modelled as a linear hereditary sorption process. The results presented in this paper are based on the solution of the integro-differential equation as follows: Ec E2c t nc Ž t . s nci q ynn q nD 2 d t y Ž c i y c 0 e . Ds K d Ž t . Ez Ez 0 t Ec Ž t . y D K Ž t y t . dt . Ž1. Et s d 0 where cŽ t . s solute concentration in the pore fluid at time t, c 0 e s the equilibrium concentration of solute in the pore fluid that would result in the initial mass of adsorbed solute onto the soil skeleton, c i s solute concentration at time t s 0, n s porosity of soil, y s average linear velocity of pore fluid in the z direction, D s effective diffusionrdispersion coefficient of solute, Ds s dry density of the soil, K dŽ t . s a time dependent distribution coefficient, Ži.e. the increment in mass of solute adsorbed onto the soil skeleton per unit increment of concentration per unit mass of soil at time t .. K dŽ t . is taken to be of the form,
H
ž
/
H
)
K d Ž t . s K d`Ž 1 y eytr t . where t ) s the sorption time constant. Eq. Ž1. may be simplified by the introduction of a Laplace transformation and use of the convolution theorem. For a detailed description of the method of solution of this equation in the Laplace transform domain the reader is referred to Rowe and Booker Ž1987.. Once the solution is found in the Laplace transform domain, the solution in the real time domain may be found using a numerical inversion algorithm developed by Talbot Ž 1979. . 2.2. Problem idealisation In this analysis presented in this paper, the pollutant is idealised as initially evenly spread throughout a saturated soil and that the contaminant transport process through both the soil and the sorbent material is approximated by Eq. Ž1. . The interception–sorption strategy is implemented by excavating a trench constructed at the leading edge of the contaminated region and then backfilling with a sorbent material. The processes of dispersionrdiffusion and advection are being relied upon to transport the contaminant through the soil to the sorbent material and so it is desirable that the advective velocity of the groundwater is not reduced by the presence of the sorbent material in the trench. To ensure that advective transport is not changed to any significant extent, the backfill material has a permeability similar to that of the natural soil. We have
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assumed that the natural soil and the trench material have a similar particle size distribution and porosity, and therefore the dispersivity and permeability of the natural soil is taken to be equal to that of the backfill material. The retardation factor Ž R . is often used in contaminant transport analysis and is defined as Ž1 q Ds K drn. ŽFreeze and Cherry, 1979.. In the following analysis, the ratio of the retardation coefficient of the sorbent material Ž R 2 . to the natural soil Ž R 1 . is equal to 100. It is noted that the design charts for the pollution-control strategy presented by Hitchcock and Smith Ž 1996. , cover a broad range of retardation ratios ranging between 10 and 5000. A schematic representation of the problem to be analysed in this paper is shown in Fig. 1a,b. In this analysis, the ratio of trench width Ž L 2 ., to length of initially contaminated soil Ž L1 . is 1r10. In the design charts presented by
Fig. 1. Ža. geometry of interception–sorption problem analysed indicating initial and boundary conditions. Žb. section showing the interception–sorption trench system.
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Hitchcock and Smith Ž1996. L1rL2 ranges from 1r1 to 1r10 000. The ratio of L1 to the length of the uncontaminated, postsorptive trench L 3 , is taken to be equal to one, although it can be shown that reducing L 3 relative to L1 has little effect on the solution. The boundary conditions for the analysis comprise the upstream surface of the contaminated soil, assumed to be impermeable to the contaminant, while the downstream surface of the soil is assumed to be at a constant concentration of zero. The downstream boundary condition does not affect the non-dimensional solutions prior to the contaminant reaching the downstream surface.
3. Results 3.1. Effect of non-equilibrium sorption on the pollution-control strategy The aim of the pollution-control strategy is to reduce the trench effluent concentration to an acceptable level. In this section, we investigate the effect of non-equilibrium sorption by calculating the maximum trench effluent concentration for various degrees of non-equilibria. A useful measure of the degree of non-equilibria in a system is the Damkohler number ŽDN.. The DN is defined as DN y kL21rD, where k is the first order reaction constant and L1 and D are as previously defined. The reaction constant k is equal to 1rt ) with t ) s the sorption time constant ŽSmith et al., 1993b. which can derived from laboratory batch tests. The DN provides a measure of the relative rate of chemicalrphysical interaction of contaminant and sorbate compared to the rate of diffusive transport ŽCussler, 1984.. The amount of non-equilibrium decreases with increasing DN ŽBrusseau, 1991.. At low DN the sorptive capacity of the soil is not significant before the solute is transported through the trench Ž Smith et al., 1993b.. Also referred to in the following sections is the Peclet number Ž PN; defined as PN s y L1rD .. The PN is a measure of the relative importance of advective transport as compared to diffusiverdispersive transport. A high PN Že.g. a free-flowing sandy aquifer. indicates that advection dominates and, therefore, the contact time between the contaminant and the trench material is relatively short compared to that for low PN Ž a low flow clayey aquifer. . The solutions presented in Fig. 2a–c have been calculated for R 2rR1 s 100, L1rL2 s 10 and show non-dimensional concentration profiles Ž crci . at various DNs ranging from 1 to 1000 and PNs ranged from 1 to 100. Various non-equilibrium and equilibrium scenarios were adopted as shown on Table 1. From Fig. 2a–c, it can be seen that as the degree of non-equilibrium sorption increases the maximum trench effluent concentration increases. The magnitude of the increase in concentration varies with PN. At low PN ŽPN s 1–10, Fig.
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Fig. 2. Ža. maximum post-trench concentration for DNs1–1000, PNs1, R 2 r R 1 s100, L1 r L 2 s10 and for various pretrenchrtrench equilibrium conditions. Žb. maximum post-trench concentration for DNs1–1000, PNs10, R 2 r R 1 s100, L1 r L2 s10 and for various pretrench equilibrium conditions. Žc. maximum post-trench concentration for DNs1–1000, PNs100, R 2 r R 1 s 100, L1 r L2 s10 and for various pretrenchrtrench equilibrium conditions.
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Table 1 Non-equilibrium modelled scenarios Scenario
Presorptive trench material
Trench material
A B C
Non-equilibrium Equilibrium Non-equilibrium
Non-equilibrium Non-equilibrium Equilibrium
2b,c., non-equilibria has little effect on maximum trench effluent concentration until DN - 10. At higher PN Ž PN s 100., the effect of non-equilibrium sorption is more pervasive and divergence between the non-equilibrium and equilibrium cases occurs at DN - 100. Fig. 2c ŽPN s 100., shows that the effect of non-equilibrium sorption is greater at high PN. This is because at high PN, the contact time between the sorbate and the contaminant is reduced, thereby reducing the opportunity for maximum sorption to occur. Fig. 2a–c also shows that the magnitude of the trench effluent concentration increase is mainly influenced by non-equilibrium sorption in the trench Žscenarios A and B. rather than the pretrench material Ž scenario C.. This is because most of the concentration reduction occurs in the trench. 3.2. Effect of non-equilibrium sorption on the decontamination strategy The aim of the decontamination strategy is to capture a predetermined amount of the initial contaminant flux in the trench at a particular time. In this section we investigated the effect of non-equilibrium sorption by assessing the maximum trench efficacy at various Damkohler numbers Ž as previously defined. . Here we define efficacy of contaminant removal to be the ratio of the mass of contaminant contained in the trench at a given time to the initial mass of contaminant. The solutions presented in Fig. 3a,b, show the maximum trench efficacy at DNs ranging from 1 to 1000 and for PNs ranging from 1 to 100. Various non-equilibrium and equilibrium scenarios were modelled as discussed in the preceding section Žsee Table 1.. Referring to Fig. 3a,b, the maximum trench efficacy decreases with an increase in the degree of non-equilibria. The magnitude of this effect varies with PN. At high PN Ž PN s 100., where the contact time between the contaminant and the sorbent is low, the differences between the equilibrium and non-equilibrium cases are greatest. For the case presented in Fig. 3a, the trench efficacy is reduced from 100% to between 10 and 55%, depending on the equilibrium scenario considered.
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Fig. 3. Ža. maximum trench efficacy for DNs1–100, PNs1–10, R 2 r R 1 s 200, L1 r L2 s10 and for various pretrenchrtrench equilibrium conditions. Žb. maximum trench efficacy for DNs1–100, PNs100, R 2 r R 1 s 200, L1 r L 2 s10 and for various pretrenchrtrench equilibrium conditions.
At low PN ŽPN s 1, Fig. 3b. , where the contact time between the contaminant and the sorbent is relatively longer, the magnitude of the decrease in maximum trench efficacy is much less than for the PN s 100 case, decreasing from about 80% at equilibrium to 70% for DN s 1. For scenarios A and B Žnon-equilibrium in the trench. the trench efficacy is lower than when non-equilibrium only occurs in the pretrench material Ž scenario C.. However, it is noted that for the decontamination strategy, non-equilibrium in the pretrench-only case does effect the trench efficacy even at lower DN. This is in contrast to the pollution-control strategy analysis where, for the scenario C case, the maximum post-trench concentration was unaffected by non-equilibrium sorption.
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4. Conclusions The analysis presented in this paper has shown that significant error could be introduced into the design of the interception–sorption trench system, if nonequilibrium conditions are ignored. For the pollution-control strategy, non-equilibrium conditions can result in higher trench effluent concentration compared to the equilibrium case and will therefore result in an underestimation of the maximum trench effluent concentration. For the decontamination strategy, non-equilibrium conditions can result in lower trench efficacy compared to the equilibrium case and will therefore result in an overestimation of the amount of contaminant in the trench at a particular time. For either strategy, the pervasiveness of the non-equilibrium effect is more pronounced at high Peclet numbers Ž PN G 100. at low Damkohler numbers ŽDN s 1–10.. It is noted that for the pollution-control strategy, only non-equilibrium conditions in the trench effect the maximum trench effluent concentration and therefore this only needs consideration during trench design. However, for the decontamination strategy, non-equilibrium in both the pretrench and trench material should be considered. It is not practical to present design charts for all non-equilibrium cases. When non-equilibrium conditions are expected, the specific case should be modelled incorporating sorption time constant data derived from batch tests. However, when equilibrium conditions prevail the design charts presented by Hitchcock and Smith Ž1996. and Smith et al. Ž1993a. can be employed.
Acknowledgements The authors acknowledge the financial support of the Australian Research Council when conducting this research.
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