Abstract
Transverse dispersion has been studied in the literature less than longitudinal dispersion, especially in porous media with fine and very fine sand. In this research, an experimental and numerical procedure is introduced to accurately determine dispersivity coefficients. Accordingly, three-dimensional tracer experiments (transient and steady state) are conducted in a relatively large sandbox (158 cm × 160 cm in plane and height of 70 cm), filled with a fine sand soil (D50 = 0.17 mm). The effects of different hydraulic heads and several injection concentrations are considered in the experiments. The transverse and longitudinal dispersivity are determined accurately by fitting numerical simulations to the steady-state and transient sandbox experiments, respectively. According to the results, the transverse dispersivity ranges between 0.0025 and 0.06 cm, while the longitudinal dispersivity varies from 0.15 to 0.75 cm. In addition, the ratio of transverse dispersivity to longitudinal dispersivity varies between 0.017 and 0.1, based on hydraulic gradients and solute concentrations. It was observed that the transverse and longitudinal dispersivity coefficients increase as the hydraulic gradient rises. Finally, the sensitivity analysis results show that the simulated depth–concentration curves at the steady-state condition remain approximately constant with the reasonable variations in the longitudinal dispersivity coefficient, the hydraulic conductivity, and the porosity.
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Abbreviations
- α L :
-
Longitudinal dispersivity coefficient
- α T :
-
Transverse dispersivity in both horizontal and vertical directions
- α HT :
-
Horizontal transverse dispersivity
- α VT :
-
Vertical transverse dispersivity
- k :
-
Hydraulic conductivity
- n :
-
Porosity
- EC:
-
Electric conductivity
- L :
-
Length of aquifer
- W :
-
Width of aquifer
- h u :
-
Upstream hydraulic head
- hd :
-
Downstream hydraulic head
- Q :
-
Discharge rate
- ρ b :
-
Bulk density
- C, C 0 :
-
Solute concentration, initial solute concentration
- k d :
-
Adsorption coefficient
- D m :
-
Molecular diffusion
- D i :
-
Dispersion in direction i
- V i :
-
Apparent velocity in direction i
- ρ , ρ 0 :
-
Saline and freshwater density
- t :
-
Time
- D :
-
Dispersion coefficient
- G s :
-
Specific gravity
- C exp :
-
Saline concentration in column test
- C ana :
-
Saline concentration from analytical solution in column test
- N :
-
Number of data for error calculation
References
Ahmed AT (2017) Experimental and numerical study for seawater intrusion remediation in heterogeneous coastal aquifer. J Environ Manage 198:221–232
Atlabachew A, Shu L, Wu P, Zhang Y, Xu Y (2018) Numerical modeling of solute transport in a sand tank physical model under varying hydraulic gradient and hydrological stresses. Hydrogeol J 26:2089–2113
Ballarini E, Bauer S, Eberhardt C, Beyer C (2012) Evaluation of transverse dispersion effects in tank experiments by numerical modeling: parameter estimation, sensitivity analysis and revision of experimental design. J contam hydrol 134:22–36
Benekos ID, Cirpka OA, Kitanidis PK (2006) Experimental determination of transverse dispersivity in a helix and a cochlea. Water Resour Res 42:W07406
Burnett R, Frind E (1987) Simulation of contaminant transport in three dimensions: 2 dimensionality effects. Water Resour Res 23:695–705
Citarella D, Cupola F, Tanda MG, Zanini A (2015) Evaluation of dispersivity coefficients by means of a laboratory image analysis. J Contam Hydrol 172:10–23
Clement TP, Kim YC, Gautam TR, Lee KK (2004) Experimental and numerical investigation of DNAPL dissolution processes in a laboratory aquifer model. Groundw Monit Remediat 24:88–96
Danquigny C, Ackerer P, Carlier J (2004) Laboratory tracer tests on three-dimensional reconstructed heterogeneous porous media. J Hydrol 294:196–212
Delgado J (2007) Longitudinal and transverse dispersion in porous media. Chem Eng Res Des 85:1245–1252
Dewaide L, Bonniver I, Rochez G, Hallet V (2016) Solute transport in heterogeneous karst systems: dimensioning and estimation of the transport parameters via multi-sampling tracer-tests modelling using the OTIS (One-dimensional Transport with Inflow and Storage) program. J hydrol 534:567–578
Guo W, Langevin CD (2002) User's guide to SEAWAT; a computer program for simulation of three-dimensional variable-density ground-water flow, No. 06-A7
Harbaugh AW, Banta ER, Hill MC, McDonald MG (2000) MODFLOW-2000, the U.S. geological survey modular ground-water model-user guide to modularization concepts and the ground-water flow process. Open-file Rep U S Geol Surv 92:134
Hekmatzadeh A, Karimi-Jashani A, Talebbeydokhti N, Kløve B (2012) Modeling of nitrate removal for ion exchange resin in batch and fixed bed experiments. Desalination 284:22–31
Hekmatzadeh AA, Adel A, Zarei F, Haghighi AT (2019) Probabilistic simulation of advection-reaction-dispersion equation using random lattice Boltzmann method. Int J Heat Mass Transf 144:118647
Inoue M, Šimůnek J, Shiozawa S, Hopmans JW (2000) Simultaneous estimation of soil hydraulic and solute transport parameters from transient infiltration experiments. Adv Water Resour 23:677–688
International Organization for Standardization (2004) Geotechnical investigation and testing: identification and classification of soil. Identification and description. International Organization for Standardization
Jakovovic D, Post VE, Werner AD, Männicke O, Hutson JL, Simmons CT (2012) Tracer adsorption in sand-tank experiments of saltwater up-coning. J Hydrol 414:476–481
Kim J, Park Y, Harmon TC (2005) Real-time model parameter estimation for analyzing transport in porous media. Groundwr Monit Remediat 25:78–86
Klotz D, Seiler K-P, Moser H, Neumaier F (1980) Dispersivity and velocity relationship from laboratory and field experiments. J Hydrol 45:169–184
Knorr B, Xie Y, Stumpp C, Maloszewski P, Simmons CT (2016) Representativeness of 2D models to simulate 3D unstable variable density flow in porous media. J hydrol 542:541–551
Koeniger P, Leibundgut C, Link T, Marshall JD (2010) Stable isotopes applied as water tracers in column and field studies. Org Geochem 41:31–40
Konikow LF (2011) The secret to successful solute-transport modeling. Groundwater 49:144–159
Langevin CD, Thorne Jr DT, Dausman AM, Sukop MC, Guo W (2008) SEAWAT version 4: a computer program for simulation of multi-species solute and heat transport. Geological Survey (US), No. 6-A22
Li Q, Zhang H, Guo S, Fu K, Liao L, Xu Y, Cheng S (2020) Groundwater pollution source apportionment using principal component analysis in a multiple land-use area in Southwestern China. Environ Sci Pollut Res 27:9000–9011
Longpré-Girard M, Martel R, Robert T, Lefebvre R, Lauzon J-M (2016) 2D sandbox experiments of surfactant foams for mobility control and enhanced LNAPL recovery in layered soils. J contam hydrol 193:63–73
Maina FH, Ackerer P, Younes A, Guadagnini A, Berkowitz B (2018) Benchmarking numerical codes for tracer transport with the aid of laboratory-scale experiments in 2D heterogeneous porous media. J contam hydrol 212:55–64
Mastrocicco M, Colombani N, Antonellini M (2012) Freshwater–seawater mixing experiments in sand columns. J hydrol 448:112–118
Ogata A, Banks R (1961) A solution of the differential equation of longitudinal dispersion in porous media: fluid movement in earth materials. US Government Printing Office
Ojuri O, Ola S (2010) Estimation of contaminant transport parameters for a tropical sand in a sand tank model. Int J Environ Sci Technol 7:385–394
Oswald S, Kinzelbach W (2004) Three-dimensional physical benchmark experiments to test variable-density flow models. J Hydrol 290:22–42
Parker J, Kool J, Van Genuchten MT (1985) Determining soil hydraulic properties from one-step outflow experiments by parameter estimation: II. experimental studies 1. Soil Sci Soc Am J 49:1354–1359
Patil S, Chore H (2014) Contaminant transport through porous media: an overview of experimental and numerical studies. Adv Environ Res 3:45–69
Qian J, Wu Y, Zhang Y, Liu Y, Lu Y, Yu Z (2015) Evaluating differences in transport behavior of sodium chloride and Brilliant Blue FCF in sand columns. Transp Porous Media 109:765–779
Selvaraju N, Pushpavanam S (2009) Adsorption characteristics on sand and brick beds. Chem Eng J 147:130–138
Sharma P, Sawant V, Shukla SK, Khan Z (2014) Experimental and numerical simulation of contaminant transport through layered soil. Int J Geotech Eng 8:345–351
Shi L, Cui L, Park N, Huyakorn PS (2011) Applicability of a sharp-interface model for estimating steady-state salinity at pumping wells: validation against sand tank experiments. J Cont Hydrol 124:35–42
Swami D, Sharma P, Ojha C (2013) Experimental investigation of solute transport in stratified porous media ISH. J Hydraul Eng 19:145–153
Werner AD, Jakovovic D, Simmons CT (2009) Experimental observations of saltwater up-coning. J Hydrol 373:230–241
Xu T, Ye Y, Zhang Y, Xie Y (2019) Recent advances in experimental studies of steady-state dilution and reactive mixing in saturated porous media. Water 11:3
Zech A et al (2019) A critical analysis of transverse dispersivity field data. Groundwater 57:632–639
Zhan H, Wen Z, Huang G, Sun D (2009) Analytical solution of two-dimensional solute transport in an aquifer–aquitard system. J Contam Hydrol 107:162–174
Zheng C (2010) MT3DMS v5. 3 supplemental user’s guide department of geological sciences. University of Alabama, Tuscaloosa
Zheng C, Wang PP (1999) MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion, and chemical reactions of contaminants in groundwater systems; documentation and user’s guide
Zoia A, Latrille C, Beccantini A, Cartadale A (2009) Spatial and temporal features of density-dependent contaminant transport: Experimental investigation and numerical modeling. J Contam Hydrol 109:14–26
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The authors would like to thank Shiraz University of Technology.
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Ahmadizadeh, A., Hekmatzadeh, A.A., Tabatabaie Shourijeh , P. et al. Modeling Contaminant Transport in Fine Sands: Three-Dimensional Sandbox Experiments and Numerical Simulation. Iran J Sci Technol Trans Civ Eng 46, 2377–2392 (2022). https://doi.org/10.1007/s40996-021-00661-4
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DOI: https://doi.org/10.1007/s40996-021-00661-4