Abstract
Screening tools such as BioScreen, BioChlor, ATRANS, AT123D-AT, ArcNLET, and Hydroscape are routinely employed to simulate the three-dimensional transport of reactive contaminants in groundwater. These tools estimate contaminant plume concentrations either using exact semi-analytical solutions or the approximate closed-form Domenico analytical solution. Semi-analytical solutions involve numerical integration procedures that can be mathematically challenging and computationally demanding. To overcome this, screening tools often use the approximate closed-form Domenico solution. However, the approximate Domenico solution introduces significant errors under realistic values of longitudinal dispersion, especially at plume locations beyond the advective front. Recently, an improved closed-form approximation to the three-dimensional reactive transport problem was developed using the concept of characteristic residence time. However, this solution was only applicable for a rectangular area source subject to a Dirichlet boundary condition. This severely restricts the use and applicability of the closed-form approximate solution to solve practically relevant simplified groundwater contaminant transport problems. Here, we present a library of six exact semi-analytical solutions for point, line, and area sources (three source geometries) under Dirichlet and Cauchy boundary conditions (two boundary conditions). Additionally, we develop approximate closed-form analytical solutions for all six solutions using the characteristic residence time concept. Our approximate solutions match well with the exact solutions under a wide range of parameter and domain conditions. We extend our analytical solutions to include the effects of linear equilibrium sorption, source decay, and pulse source input. Our analytical solution library facilitates the application of screening tools for a wide range of practically relevant simplified groundwater reactive contaminant transport problems.
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References
Aziz, C. E., Newell, C. J., Gonzales, J. R., Haas, P. E., Clement, T. P., Sun, Y.: BIOCHLOR Natural Attenuation Decision Support System. User’s Manual Version 1.0. US Environmental Protection Agency (2000)
Batu, V., van Genuchten, M.T.: First-and third-type boundary conditions in two-dimensional solute transport modeling. Water Resources Res. 26(2), 339–350 (1990). https://doi.org/10.1029/WR026i002p00339
Bear, J.: Dynamics of Fluids in Porous Media. Dover pubications Inc., New York, USA (1972)
Burnell, D.K., Lester, B.H., Mercer, J.W.: Improvements and corrections to AT123D code. Groundwater 50(6), 943–953 (2012). https://doi.org/10.1111/j.1745-6584.2011.00905.x
Chrysikopoulos, C.V.: Three-dimensional analytical models of contaminant transport from nonaqueous phase liquid pool dissolution in saturated subsurface formations. Water Resources Res. 31(4), 1137–1145 (1995). https://doi.org/10.1029/94WR02780
Cleary, R., Ungs, M.: Analytical Models for Ground-Water Pollution and Hydrology: Princeton university, waterresources program report 78-wr-15, 165 p. Program, Princeton Univ., Princeton, NJ (1978)
Clement, T.P.: Generalized solution to multispecies transport equations coupled with a first-order reaction network. Water Resources Res. 37(1), 157–163 (2001). https://doi.org/10.1029/2000WR900239
Domenico, P.A., Robbins, G.A.: A new method of contaminant plume analysis. Groundwater 23(4), 476–485 (1985). https://doi.org/10.1111/j.1745-6584.1985.tb01497.x
Domenico, P.A.: An analytical model for multidimensional transport of a decaying contaminant species. J. Hydrol. 91(1–2), 49–58 (1987). https://doi.org/10.1016/0022-1694(87)90127-2
Ellsworth, T., Butters, G.: Three-dimensional analytical solutions to the advection-dispersion equation in arbitrary cartesian coordinates. Water Resources Res. 29(9), 3215–3225 (1993). https://doi.org/10.1029/93WR01293
Funk, S.P., Hnatyshin, D., Alessi, D.S.: HYDROSCAPE: a new versatile software program for evaluating contaminant transport in groundwater. SoftwareX 6, 261–266 (2017). https://doi.org/10.1016/j.softx.2017.10.001
Gelhar, L. W., Welty, C., Rehfeldt, K. R. A.: Critical review of data on field-scale dispersion in aquifers’ by L. W. Gelhar, C. Welty, and K. R. Water Resources Res. 29(6), 1867–1869 (1992). https://doi.org/10.1029/92WR00607
Guyonnet, D., Neville, C.: Dimensionless analysis of two analytical solutions for 3-D solute transport in groundwater. J. Contamin. Hydrol. 75(1–2), 141–153 (2004). https://doi.org/10.1016/j.jconhyd.2004.06.004
Karanovic, M., Neville, C.J., Andrews, C.B.: BIOSCREEN-AT: BIOSCREEN with an exact analytical solution. Groundwater 45(2), 242–245 (2007). https://doi.org/10.1111/j.1745-6584.2006.00296.x
Leij, F.J., Skaggs, T.H., van Genuchten, M.T.: Analytical solutions for solute transport in three-dimensional semi-infinite porous media. Water Resources Res. 27(10), 2719–2733 (1991). https://doi.org/10.1029/91WR01912
Leij, F.J., Toride, N., Van Genuchten, M.T.: Analytical solutions for non-equilibrium solute transport in three-dimensional porous media. J. Hydrol. 151(2–4), 193–228 (1993). https://doi.org/10.1016/0022-1694(93)90236-3
Leij, F.J., Priesack, E., Schaap, M.G.: Solute transport modeled with Green‘s functions with application to persistent solute sources. J. Contamin. Hydrol. 41(1–2), 155–173 (2000). https://doi.org/10.1016/S0169-7722(99)00062-5
Martin-Hayden, J.M., Robbins, G.A.: Plume distortion and apparent attenuation due to concentration averaging in monitoring wells. Groundwater 35(2), 339–346 (1997). https://doi.org/10.1111/j.1745-6584.1997.tb00091.x
Neuman, S.P.: Universal scaling of hydraulic conductivities and dispersivities in geologic media. Water Resources Res. 26(8), 1749–1758 (1990). https://doi.org/10.1029/WR026i008p01749
Neville, C.J.: ATRANS: Analytical Solutions for Three-Dimensional Solute Transport from a Patch Source (Version 2). Papadopulos and Associates Inc, S.S (2005)
Newell, C.J., McLeod, R.K., Gonzales, J.R.: BIOSCREEN: Natural Attenuation Decision Support System. User’s Manual Version 1.3. Technical report, United States Environmental Protection Agency (1996)
Ogata, A., Banks, R.B.: A solution of the differential equation of longitudinal dispersion in porous media: fluid movement in earth materials, Technical Report 411 A, US Geological Survey (1961). https://pubs.er.usgs.gov/publication/pp411A
Paladino, O., Moranda, A., Massabò, M., Robbins, G.A.: Analytical solutions of three-dimensional contaminant transport models with exponential source decay. Groundwater 56(1), 96–108 (2018). https://doi.org/10.1111/gwat.12564
Quezada, C.R., Clement, T.P., Lee, K.-K.: Generalized solution to multi-dimensional multi-species transport equations coupled with a first-order reaction network involving distinct retardation factors. Adv. Water Resources 27(5), 507–520 (2004). https://doi.org/10.1016/j.advwatres.2004.02.013
Rios, J.F., Ye, M., Wang, L., Lee, P.Z., Davis, H., Hicks, R.: ArcNLET: a GIS-based software to simulate groundwater nitrate load from septic systems to surface water bodies. Comput. Geosci. 52, 108–116 (2013). https://doi.org/10.1016/j.cageo.2012.10.003
Sagar, B.: Dispersion in three dimensions: approximate analytic solutions. J. Hydraulics Div. 108(1), 47–62 (1982). https://doi.org/10.1061/JYCEAJ.0005809
Sangani, J., Srinivasan, V.: Improved domenico solution for three-dimensional contaminant transport. J. Contam. Hydrol. 243, 103897 (2021). https://doi.org/10.1016/j.jconhyd.2021.103897
Schulze-Makuch, D.: Longitudinal dispersivity data and implications for scaling behavior. Groundwater 43(3), 443–456 (2005). https://doi.org/10.1111/j.1745-6584.2005.0051.x
Shampine, L.: Vectorized adaptive quadrature in MATLAB. J. Comput. Appl. Math. 211(2), 131–140 (2008). https://doi.org/10.1016/j.cam.2006.11.021
Sim, Y., Chrysikopoulos, C.V.: Analytical solutions for solute transport in saturated porous media with semi-infinite or finite thickness. Adv. Water Resources 22(5), 507–519 (1999). https://doi.org/10.1016/S0309-1708(98)00027-X
Srinivasan, V., Clement, T.P.: Analytical solutions for sequentially coupled one-dimensional reactive transport problems - Part I: Mathematical derivations. Adv. Water Resources 31(2), 203–218 (2008). https://doi.org/10.1016/j.advwatres.2007.08.002
Srinivasan, V., Clement, T.P.: Analytical solutions for sequentially coupled one-dimensional reactive transport problems—Part II: special cases, implementation and testing. Adv. Water Resources 31(2), 219–232 (2008). https://doi.org/10.1016/j.advwatres.2007.08.001
Srinivasan, V., Clement, T.P., Lee, K.K.: Domenico solution—Is it valid? Groundwater 45(2), 136–146 (2007). https://doi.org/10.1111/j.1745-6584.2006.00281.x
van Genuchten, M.T.: Analytical solutions of the one-dimensional convective-dispersive solute transport equation. Technical Report 1661, United States Department of Agriculture, Agricultural Research Service (1982)
van Genuchten, M.T.: Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comput. Geosci. 11(2), 129–147 (1985). https://doi.org/10.1016/0098-3004(85)90003-2
van Genuchten, M.T.: Analytical solutions for chemical transport with simultaneous adsorption, zero-order production, and first-order decay. J. Hydrol. 49(3), 213–233 (1981). https://doi.org/10.1016/0022-1694(81)90214-6
Wang, H., Wu, H.: Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media: A library. Front. Environ. Sci. Eng. China 3(1), 112–128 (2009). https://doi.org/10.1007/s11783-008-0067-z
Wang, H., Han, R., Zhao, Y., Lu, W., Zhang, Y.: Stepwise superposition approximation approach for analytical solutions with non-zero initial concentration using existing solutions of zero initial concentration in contaminant transport. J. Environ. Sci. 23(6), 923–930 (2011). https://doi.org/10.1016/s1001-0742(10)60486-x
West, M., Kueper, B.: Natural attenuation of solute plumes in bedded fractured rock. In: Proceedings of the US EPA/NGWA Fractured Rock Conference: State of Science and Measuring Success in Remediation. National Ground Water Association, NGWA Press (2004)
West, M.R., Kueper, B.H., Ungs, M.J.: On the use and error of approximation in the Domenico (1987) solution. Groundwater 45(2), 126–135 (2007). https://doi.org/10.1111/j.1745-6584.2006.00280.x
Wexler, E.J.: Analytical solution for one-, two-, and three-dimensional solute transport in ground-water systems with uniform flow. Technical report, 89–56, USGS (1992). https://doi.org/10.3133/ofr8956
Wilson, J.L., Miller, P.J.: Two-dimensional plume in uniform ground-water flow. J. Hydraulics Div. 104(4), 503–514 (1978). https://doi.org/10.1061/JYCEAJ.0004975
Xu, M., Eckstein, Y.: Use of weighted least-squares method in evaluation of the relationship between dispersivity and field scale. Groundwater 33(6), 905–908 (1995). https://doi.org/10.1111/j.1745-6584.1995.tb00035.x
Yeh, G. T. AT123D: Analytical transient one-, two-, and three-dimensional simulation of waste transport in the aquifer system. Technical report, ORNL-5602 ,Oak Ridge National Lab., TN (USA) (1981). https://doi.org/10.2172/6531241
Acknowledgements
The authors thank the editor and the two anonymous reviewers for their insightful comments and suggestions. This research was partly supported by the Center for Industrial Consultancy and Sponsored Research (ICSR), Indian Institute of Technology Madras, grant numbers: CIE1819847NFIGVENT and CE1920364NFSC008930, and Prime Minister’s Research Fellowship from the Department of Science and Technology, India, grant number SB22230182CEPMRF008930.
Funding
This research was partly supported by the Center for Industrial Consultancy and Sponsored Research (ICSR), Indian Institute of Technology Madras, grant numbers: CIE1819847NFIGVENT and CE1920364NFSC008930, and Prime Minister’s Research Fellowship from the Department of Science and Technology, India, grant number SB22230182CEIITMPMRF008930.
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Sangani, J., Srivastava, A. & Srinivasan, V. Analytical Solutions to Three-Dimensional Reactive Contaminant Transport Problems Involving Point, Line, and Area Sources. Transp Porous Med 144, 641–667 (2022). https://doi.org/10.1007/s11242-022-01828-x
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DOI: https://doi.org/10.1007/s11242-022-01828-x