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On the Maximum Concentration of Contaminants in Natural Aquifers

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Abstract

We examine the temporal evolution of the maximum concentration of a dissolved inert solute in spatially heterogeneous subsurface flows. The maximum concentration of a given substance is at the basis of most of environmental regulatory practices where maximum tolerable levels of concentration are typically prescribed for a variety of known contaminants. Through the use of the Lagrangian framework, we elaborate over a physically based, semi-analytical model for the maximum concentration. Specifically, we address how the maximum concentration is affected by key geostatistical parameters (i.e., logconductivity variance), local-scale dispersion processes and engineering design variables such as the dimensions of the solute injection zone. The model will help in identifying the major components that determine the maximum concentration, which is important in order to better allocate resources toward site characterization and reduce uncertainty in predictions. The ultimate scope is to provide a theoretical framework that is application-oriented to estimate the maximum concentration in natural aquifers and provide some guidance in applications. It also provides an useful tool for preliminary, screening analysis and testing scenarios. We test the performance of the model against the MADE transport experiment, with reasonably good agreement.

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References

  • Adams, E.E., Gelhar, L.W.: Field study of dispersion in a heterogeneous aquifer: 2. Spatial Moments Anal. Water Resour. Res. 28(12), 3293 (1992)

    Article  Google Scholar 

  • Andricevic, R.: Exposure concentration statistics in the subsurface transport. Adv. Water Resour. 31(4), 714 (2008)

    Article  Google Scholar 

  • Andričević, R., Cvetković, V.: Evaluation of risk from contaminants migrating by groundwater. Water Resour. Res. 32(3), 611 (1996)

    Article  Google Scholar 

  • Attinger, S., Dentz, M., Kinzelbach, W.: Exact transverse macro dispersion coefficients for transport in heterogeneous porous media. Stoch. Environ. Res. Risk Assess. 18(1), 9 (2004)

    Article  Google Scholar 

  • Barlebo, H.C., Hill, M.C., Rosbjerg, D.: Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three-dimensional inverse flow and transport model. Water Resour. Res., 40(4), (2004)

  • Bear, J.: Dynamics of Fluids in Porous Media. Dover Publications, Mineola (1988)

    Google Scholar 

  • Bear, J.: Hydraulics of Groundwater. Dover Publications, Mineola (2007)

    Google Scholar 

  • Bellin, A., Salandin, P., Rinaldo, A.: Simulation of dispersion in heterogeneous porous formations: statistics, first-order theories, convergence of computations. Water Resour. Res. 28(9), 2211 (1992)

    Article  Google Scholar 

  • Bellin, A., Rubin, Y., Rinaldo, A.: Eulerian-Lagrangian approach for modeling of flow and transport in heterogeneous geological formations. Water Resour. Res. 30(11), 2913 (1994)

    Article  Google Scholar 

  • Berkowitz, B., Cortis, A., Dentz, M., Scher, H.: Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys., 44(2), (2006)

  • Berkowitz, B., Klafter, J., Metzler, R., Scher, H.: Physical pictures of transport in heterogeneous media: advection-dispersion, random-walk, and fractional derivative formulations. Water Resour. Res. 38(10), 9 (2002)

    Article  Google Scholar 

  • Boggs, J.M., Young, S.C., Beard, L.M., Gelhar, L.W., Rehfeldt, K.R., Adams, E.E.: Field study of dispersion in a heterogeneous aquifer: 1. Overview Site Descrip. Water Resour. Res. 28(12), 3281 (1992)

    Article  Google Scholar 

  • Bohling, G.C., Liu, G., Dietrich, P., Butler, J.J., Jr.: Reassessing the MADE direct-push hydraulic conductivity data using a revised calibration procedure. Water Resour. Res. 52(11), 8970 (2016)

    Article  Google Scholar 

  • Boso, F., Tartakovsky, D.M.: The method of distributions for dispersive transport in porous media with uncertain hydraulic properties. Water Resour. Res. 52(6), 4700 (2016)

    Article  Google Scholar 

  • Boso, F., Bellin, A., Dumbser, M.: Numerical simulations of solute transport in highly heterogeneous formations: a comparison of alternative numerical schemes. Adv. Water Resour. 52, 178 (2013)

    Article  Google Scholar 

  • Boso, F., de Barros, F.P.J., Fiori, A., Bellin, A.: Performance analysis of statistical spatial measures for contaminant plume characterization toward risk-based decision making. Water Resour. Res. 49(6), 3119 (2013)

    Article  Google Scholar 

  • Carrera, J.: An overview of uncertainties in modelling groundwater solute transport. J. Contamin. Hydrol. 13(1–4), 23 (1993)

    Article  Google Scholar 

  • Ciriello, V., de Barros, F.P.J.: Characterizing the influence of multiple uncertainties on predictions of contaminant discharge in groundwater within a Lagrangian stochastic formulation. Water Resour. Res., p. e2020WR027867

  • Cvetkovic, V., Shapiro, A.M.: Mass arrival of sorptive solute in heterogeneous porous media. Water Resour. Res. 26(9), 2057 (1990)

    Article  Google Scholar 

  • Cvetković, V., Shapiro, A.M., Dagan, G.: A solute flux approach to transport in heterogeneous formations: 2. Uncertain. Anal. Water Resour. Res. 28(5), 1377 (1992)

    Article  Google Scholar 

  • Dagan, G.: Solute transport in heterogeneous porous formations. J. Fluid Mech. 145, 151 (1984)

    Article  Google Scholar 

  • Dagan, G.: Flow and Transport in Porous Formations. Springer-Verlag, Berlin (1989)

    Book  Google Scholar 

  • Dagan, G.: Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations. J. Fluid Mech. 233, 197 (1991)

    Article  Google Scholar 

  • Dagan, G., Cvetkovic, V., Shapiro, A.: A solute flux approach to transport in heterogeneous formations: 1. General Framework Water Resour. Res. 28(5), 1369 (1992)

    Article  Google Scholar 

  • de Barros, F.P.J., Fiori, A., Bellin, A.: A simple closed-form solution for assessing concentration uncertainty. Water Resour. Res. 47(12), (2011)

  • de Barros, F.P.J.: Evaluating the combined effects of source zone mass release rates and aquifer heterogeneity on solute discharge uncertainty. Adv. Water Resour. 117, 140 (2018)

    Article  Google Scholar 

  • de Barros, F.P.J., Fiori, A.: First-order based cumulative distribution function for solute concentration in heterogeneous aquifers: theoretical analysis and implications for human health risk assessment. Water Resour. Res. 50(5), 4018 (2014)

    Article  Google Scholar 

  • de Barros, F.P.J., Ezzedine, S., Rubin, Y.: Impact of hydrogeological data on measures of uncertainty, site characterization and environmental performance metrics. Adv. Water Resour. 36, 51 (2012)

    Article  Google Scholar 

  • de Barros, F.P.J., Fiori, A., Boso, F., Bellin, A.: A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media. J. Contam. Hydrol. 175, 72 (2015)

    Article  Google Scholar 

  • Dentz, M., de Barros, F.P.J.: Mixing-scale dependent dispersion for transport in heterogeneous flows. J. Fluid Mech. 777, (2015)

  • Dentz, M., Tartakovsky, D.M.: Probability density functions for passive scalars dispersed in random velocity fields. Geophys. Res. Lett. 37(24), (2010)

  • Dentz, M., Le Borgne, T., Englert, A., Bijeljic, B.: Mixing, spreading and reaction in heterogeneous media: a brief review. J. Contamin. Hydrol. 120, 1 (2011)

    Article  Google Scholar 

  • Dogan, M., Van Dam, R.L., Liu, G., Meerschaert, M.M., Butler, J.J., Jr., Bohling, G.C., Benson, D.A., Hyndman, D.W.: Predicting flow and transport in highly heterogeneous alluvial aquifers. Geophys. Res. Lett. 41(21), 7560 (2014)

    Article  Google Scholar 

  • Enzenhoefer, R., Nowak, W., Helmig, R.: Probabilistic exposure risk assessment with advective-dispersive well vulnerability criteria. Adv. Water Resour. 36, 121 (2012)

    Article  Google Scholar 

  • Fernàndez-Garcia, D., Sánchez-Vila, X., Guadagnini, A.: Reaction rates and effective parameters in stratified aquifers. Adv. Water Resour. 31(10), 1364 (2008)

    Article  Google Scholar 

  • Fiori, A.: On the influence of pore-scale dispersion in nonergodic transport in heterogeneous formations. Transp. Porous Media 30(1), 57 (1998)

    Article  Google Scholar 

  • Fiori, A.: The Lagrangian concentration approach for determining dilution in aquifer transport: theoretical analysis and comparison with field experiments. Water Resour. Res. 37(12), 3105 (2001)

    Article  Google Scholar 

  • Fiori, A.: Channeling, channel density and mass recovery in aquifer transport, with application to the MADE experiment. Water Resour. Res. 50(12), 9148 (2014)

    Article  Google Scholar 

  • Fiori, A., Dagan, G.: Concentration fluctuations in aquifer transport: a rigorous first-order solution and applications. J. Contam. Hydrol. 45(1), 139 (2000)

    Article  Google Scholar 

  • Fiori, A., Dagan, G.: Transport of a passive scalar in a stratified porous medium. Transp. Porous Media 47(1), 81 (2002)

    Article  Google Scholar 

  • Fiori, A., Berglund, S., Cvetković, V., Dagan, G.: A first-order analysis of solute flux statistics in aquifers: the combined effect of pore-scale dispersion, sampling, and linear sorption kinetics. Water Resour. Res. 38(8), 12 (2002)

    Article  Google Scholar 

  • Fiori, A., Dagan, G., Jankovic, I., Zarlenga, A.: The plume spreading in the MADE transport experiment: Could it be predicted by stochastic models? Water Resour. Res. 49(5), 2497 (2013)

    Article  Google Scholar 

  • Fiori, A., Zarlenga, A., Jankovic, I., Dagan, G.: Solute transport in aquifers: the comeback of the advection dispersion equation and the first order approximation. Adv. Water Resour. 110, 349 (2017)

    Article  Google Scholar 

  • Fiori, A., Zarlenga, A., Bellin, A., Cvetkovic, V., Dagan, G.: Groundwater contaminant transport: prediction under uncertainty, with application to the MADE transport experiment. Front. Environ. Sci. 7, 79 (2019)

    Article  Google Scholar 

  • Gómez-Hernández, J.J., Butler, J.J., Fiori, A., Bolster, D., Cvetkovic, V., Dagan, G., Hyndman, D.: Introduction to special section on Modeling highly heterogeneous aquifers: lessons learned in the last 30 years from the MADE experiments and others. Water Resour. Res. 53(4), 2581 (2017)

    Article  Google Scholar 

  • Harvey, C., Gorelick, S.M.: Rate-limited mass transfer or macrodispersion: Which dominates plume evolution at the macrodispersion experiment (MADE) site? Water Resour. Res. 36(3), 637 (2000)

    Article  Google Scholar 

  • Henri, C.V., Fernàndez-Garcia, D., de Barros, F.P.J.: Assessing the joint impact of DNAPL source-zone behavior and degradation products on the probabilistic characterization of human health risk. Adv. Water Resour. 88, 124 (2016)

    Article  Google Scholar 

  • Hrachowitz, M., Clark, M.P., Opinions, H.E.S.S.: The complementary merits of competing modelling philosophies in hydrology. Hydrol. Earth Syst. Sci. 21(8), 3953 (2017)

    Article  Google Scholar 

  • Jankovic, I., Maghrebi, M., Fiori, A., Dagan, G.: When good statistical models of aquifer heterogeneity go right: the impact of aquifer permeability structures on 3D flow and transport. Adv. Water Resour. 100, 199 (2017)

    Article  Google Scholar 

  • Julian, H.E., Boggs, J.M., Zheng, C., Feehley, C.E.: Numerical simulation of a natural gradient tracer experiment for the natural attenuation study: flow and physical transport. Groundwater 39(4), 534 (2001)

    Article  Google Scholar 

  • Kapoor, V., Kitanidis, P.K.: Concentration fluctuations and dilution in aquifers. Water Resour. Res. 34(5), 1181 (1998)

    Article  Google Scholar 

  • Kelly, E.J., Campbell, K.: Separating variability and uncertainty in environmental risk assessment-making choices. Human Ecol. Risk Assess. 6(1), 1 (2000)

    Article  Google Scholar 

  • Kitanidis, P.K.: Prediction by the method of moments of transport in a heterogeneous formation. J. Hydrol. 102(1–4), 453 (1988)

    Article  Google Scholar 

  • Le Borgne, T., Dentz, M., Villermaux, E.: Stretching, coalescence, and mixing in porous media. Phys. Rev. Lett. 110(20), 204501 (2013)

    Article  Google Scholar 

  • Libera, A., de Barros, F.P.J., Guadagnini, A.: Influence of pumping operational schedule on solute concentrations at a well in randomly heterogeneous aquifers. J. Hydrol. 546, 490 (2017)

    Article  Google Scholar 

  • Libera, A., Henri, C.V., de Barros, F.P.J.: Hydraulic conductivity and porosity heterogeneity controls on environmental performance metrics: implications in probabilistic risk analysis. Adv. Water Resour. 127, 1 (2019)

    Article  Google Scholar 

  • Matheron, G., De Marsily, G.: Is transport in porous media always diffusive? Counterexample Water Resour. Res. 16(5), 901 (1980)

    Article  Google Scholar 

  • Maxwell, R.M., Carle, S.F., Tompson, A.F.: Contamination, risk, and heterogeneity: on the effectiveness of aquifer remediation. Environ. Geol. 54(8), 1771 (2008)

    Article  Google Scholar 

  • Morales-Casique, E., Neuman, S.P., Guadagnini, A.: Non-local and localized analyses of non-reactive solute transport in bounded randomly heterogeneous porous media: theoretical framework. Adv. Water Resour. 29(8), 1238 (2006)

    Article  Google Scholar 

  • Moslehi, M., de Barros, F.P.J.: Uncertainty quantification of environmental performance metrics in heterogeneous aquifers with long-range correlations. J. Contam. Hydrol. 196, 21 (2017)

    Article  Google Scholar 

  • Okkonen, J., Neupauer, R.M.: Capture zone delineation methodology based on the maximum concentration: preventative groundwater well protection areas for heat exchange fluid mixtures. Water Resour. Res. 52(5), 4043 (2016)

    Article  Google Scholar 

  • Oladyshkin, S., de Barros, F.P.J., Nowak, W.: Global sensitivity analysis: a flexible and efficient framework with an example from stochastic hydrogeology. Adv. Water Resour. 37, 10 (2012)

    Article  Google Scholar 

  • Rehfeldt, K.R., Boggs, J.M., Gelhar, L.W.: Field study of dispersion in a heterogeneous aquifer: 3. Geostat. Anal. Hydraul. Conduct. Water Resour. Res. 28(12), 3309 (1992)

    Article  Google Scholar 

  • Rubin, Y.: Applied Stochastic Hydrology. Oxford University Press, Oxford (2003)

    Book  Google Scholar 

  • Rubin, Y., Dagan, G.: Conditional estimation of solute travel time in heterogeneous formations: impact of transmissivity measurements. Water Resour. Res. 28(4), 1033 (1992)

    Article  Google Scholar 

  • Rubin, Y., Cushey, M.A., Bellin, A.: Modeling of transport in groundwater for environmental risk assessment. Stoch. Hydrol. Hydraul. 8(1), 57 (1994)

    Article  Google Scholar 

  • Sahimi, M.: Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches. John Wiley & Sons, London (2011)

    Book  Google Scholar 

  • Sanchez-Vila, X., Guadagnini, A.: Travel time and trajectory moments of conservative solutes in three dimensional heterogeneous porous media under mean uniform flow. Adv. Water Resour. 28(5), 429 (2005)

    Article  Google Scholar 

  • Shvidler, M., Karasaki, K.: Probability density functions for solute transport in random field. Transp. Porous Media 50(3), 243 (2003)

    Article  Google Scholar 

  • Siirila, E.R., Maxwell, R.M.: Evaluating effective reaction rates of kinetically driven solutes in large-scale, statistically anisotropic media: Human health risk implications. Water Resour. Res., 48(4), (2012)

  • Soltanian, M.R., Behzadi, F., de Barros, F.P.J.: Dilution enhancement in hierarchical and multiscale heterogeneous sediments. J. Hydrol. 587, 125025 (2020)

    Article  Google Scholar 

  • Tonina, D., Bellin, A.: Effects of pore-scale dispersion, degree of heterogeneity, sampling size, and source volume on the concentration moments of conservative solutes in heterogeneous formations. Adv. Water Resour. 31(2), 339 (2008)

    Article  Google Scholar 

  • USEPA, Risk assessment guidance for Superfund: Volume III–Part A: Process for conducting probabilistic risk assessment. Tech. Rep. Tech. Rep. EPA 540/R-02/002 (2001)

  • Valocchi, A.J., Bolster, D., Werth, C.J.: Mixing-limited reactions in porous media. Transp. Porous Media 130(1), 157 (2019)

    Article  Google Scholar 

  • Verdonck, F., Van Sprang, P., Vanrolleghem, P.: Uncertainty and precaution in European environmental risk assessment of chemicals. Water Sci. Technol. 52(6), 227 (2005)

    Article  Google Scholar 

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Acknowledgements

FPJdB gratefully acknowledges the financial support by the National Science Foundation under Grant 1654009. AF acknowledges funding from the Italian Ministry of Education, University and Research (MIUR) in the frame of the Departments of Excellence Initiative 2018-2022 granted to the Dept. of Engineering of Roma Tre University.

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  1. Sonny Astani Department of Civil and Environmental Engineering, University of Southern California, Kaprielian Hall, Room 224B, 3620 S. Vermont Avenue, Los Angeles, CA, 90089-2531, USA

    Felipe P. J. de Barros

  2. Department of Engineering, Roma Tre University, Via Vito Volterra, 62, 00146, Rome, Italy

    Aldo Fiori

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  1. Felipe P. J. de Barros
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de Barros, F.P.J., Fiori, A. On the Maximum Concentration of Contaminants in Natural Aquifers. Transp Porous Med 140, 273–290 (2021). https://doi.org/10.1007/s11242-021-01620-3

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