Abstract
Groundwater is a vital resource for human and environmental needs, and the periodic contamination poses a significant threat to groundwater resources. In this regard, to ensure its quality, the study of solute transport has gained significant attention in recent times. But accurate modeling is required to analyze the actual transport pattern of solute species. The present study focuses on multispecies solute transport through heterogeneous porous media, and a numerical approach to the decomposition method has been proposed. The governing equations of multispecies solute transport have been solved quantitatively using the implicit finite difference approach. An increasing exponential time-dependent dispersion describes the heterogeneity of porous media, and this dispersivity function has been further used to analyze the effect of time-dependent dispersion. The developed numerical model has been validated with the analytical solution, and this model evades the critical limitation of heterogeneity where the macrodispersion effect has been neglected. The study encompasses that the solute transport involves a series of first-order decay reactions, and migration of radionuclides and nitrification chain have been taken to carry out the analysis. Different decay rate constants have been used for the analysis to incorporate real field problems, and the results revealed that with the increase in decay rate constant, tailing is noticed in the solute concentration. Furthermore, the spatial moment analysis has been carried out on all species concentrations using these dispersivity functions, and the sensitivity analysis has been made using various breakthrough curves. The results of this analysis indicate that the variance and mean travel distance are susceptible to changes in dispersivity as a function of time and the transport pattern of its transformed species might not be the same. Thus, this study highlights the importance of considering the heterogeneities in the subsurface environment and can also inform the selection of monitoring strategies and remediation techniques for the contaminated sites, mainly where multiple species are involved in a chain reaction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- \({C}_{i}\) :
-
Solute concentration of ith species [ML−3]
- \(D\) :
-
Hydrodynamic dispersion coefficient [L2T−1]
- \({D}_{\mathrm{inf}}\) :
-
Macrodispersion coefficient at the field scale [L2T−1]
- \({D}_{0}\) :
-
Sum of molecular diffusion and microdispersion [L2T−1]
- \(i\) :
-
Species index [ −]
- \({K}_{d,i}\) :
-
Distribution coefficient [L3/M]
- \(l\) :
-
Correlation length of hydraulic conductivity field or integral scale [L]
- \(L\) :
-
Domain length [L]
- \(M\) :
-
Zeroth spatial moment of solute concentration
- \(n\) :
-
Porosity of the porous media [ −]
- N :
-
Number of species [ −]
- \(R\) :
-
Retardation factor [ −]
- \(V\) :
-
Pore water velocity [LT−1]
- \({X}_{1}\) :
-
First spatial moment of solute concentration
- \({X}_{11}\) :
-
Second spatial moment of solute concentration
- \(Y\) :
-
Stoichiometric yield coefficient [ −]
- \(\alpha\) :
-
Dispersivity [L]
- \(\beta\) :
-
Rate of increase of dispersivity with time [T−1]
- \({\lambda }_{i}\) :
-
First-order reaction rates of ith species [T−1]
- \(\rho\) :
-
Bulk density of the porous medium [M/L3]
- \({\sigma }_{f}^{2}\) :
-
Variance of log hydraulic conductivity [–
References
Anshuman A, Eldho TI (2020) Meshfree radial point collocation-based coupled flow and transport model for simulation of multispecies linked first order reactions. J Contam Hydrol 229:103582. https://doi.org/10.1016/j.jconhyd.2019.103582
Aral MM, Liao B (1996) Analytical solutions for two-dimensional transport equation with time-dependent dispersion coefficients. J Hydrol Eng 1(1):20–32. https://doi.org/10.1061/(ASCE)1084-0699(1996)1:1(20)
Bear J (1972) Dynamics of fluids in porous media. Dover publications. Inc., New York
Bear J (1979) Hydraulics of groundwater. McGraw-Hill, New York
Chaudhary M, Singh MK (2020) Study of multispecies convection-dispersion transport equation with variable parameters. J Hydrol 591:125562. https://doi.org/10.1016/j.jhydrol.2020.125562
Chen JS, Ni CF, Liang CP (2008) Analytical power series solutions to the two-dimensional advection–dispersion equation with distance-dependent dispersivities. Hydrol Process: Int J 22(24):4670–4678. https://doi.org/10.1002/hyp.7067
Chen JS, Ho YC, Liang CP, Wang SW, Liu CW (2019) Semi-analytical model for coupled multispecies advective-dispersive transport subject to rate-limited sorption. J Hydrol 579:124164. https://doi.org/10.1016/j.jhydrol.2019.124164
Chen JS, Liu CW, Hsu HT, Liao CM (2003) A Laplace transform power series solution for solute transport in a convergent flow field with scale-dependent dispersion. Water Resour Res 39:1229. https://doi.org/10.1029/2003WR002299
Clement TP (2001) Generalized solution to multispecies transport equations coupled with a first-order reaction network. Water Resour Res 37:157–163. https://doi.org/10.1029/2000WR900239
Gao G, Zhan H, Feng S et al (2010) A new mobile-immobile model for reactive solute transport with scale dependent dispersion. Water Resour Res 46:8533. https://doi.org/10.1029/2009WR008707
Gelhar LW, Axness CL (1983) Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour Res 19(1):161–180. https://doi.org/10.1029/WR019i001p00161
Higashi K, Pigford TH (1980) Analytical models for migration of radionuclides in geologic sorbing media. J Nucl Sci Technol 17(9):700–709. https://doi.org/10.3327/jnst.17.700
Huang G, Huang Q, Zhan H (2006) Evidence of one-dimensional scale-dependent fractional advection–dispersion. J Contam Hydrol 85(1–2):53–71. https://doi.org/10.1016/j.jconhyd.2005.12.007
Hunt B (1998) Contaminant source solutions with scale-dependent dispersivities. J Hydrol Eng 3(4):268–275. https://doi.org/10.1061/(ASCE)1084-0699(1998)3:4(268)
Huo JX, Song HZ, Wu ZW (2014) Multi-component reactive transport in heterogeneous media and its decoupling solution. J Contam Hydrol 166:11–22. https://doi.org/10.1016/j.jconhyd.2014.07.009
Matheron G, De Marsily G (1980) Is transport in porous media always diffusive? A counterexample. Water Resour Res 16(5):901–917. https://doi.org/10.1029/WR016i005p00901
Ostad-Ali-Askari K, Shayan M (2021) Subsurface drain spacing in the unsteady conditions by HYDRUS-3D and artificial neural networks. Arab J Geosci 14:1–14. https://doi.org/10.1007/s12517-021-08336-0
Ostad-Ali-Askari K, Shayannejad M, Ghorbanizadeh-Kharazi H (2017) Artificial neural network for modeling nitrate pollution of groundwater in marginal area of Zayandeh-rood River, Isfahan, Iran. KSCE J Civ Eng 21:134–140. https://doi.org/10.1007/s12205-016-0572-8
Paswan A, Sharma PK (2023) Two-dimensional modeling of colloid-facilitated contaminant transport in groundwater flow systems with stagnant zones. Water Resour Res 59(2):e2022WR033130. https://doi.org/10.1029/2022WR033130
Pathania T, Eldho TI, Bottacin-Busolin A (2020) Coupled simulation of groundwater flow and multispecies reactive transport in an unconfined aquifer using the element-free Galerkin method. Eng Anal Boundary Elem 121:31–49. https://doi.org/10.1016/j.enganabound.2020.08.019
Quezada CR, Clement TP, Lee KK (2004) Generalized solution to multi-dimensional multispecies transport equations coupled with a first-order reaction network involving distinct retardation factors. Adv Water Resour 27(5):507–520. https://doi.org/10.1016/j.advwatres.2004.02.013
Sharma PK, Srivastava R (2012) Concentration profiles and spatial moments for reactive transport through porous media. J Hazard Toxic Radioact Waste 16(2):125–133. https://doi.org/10.1061/(ASCE)HZ.2153-5515.0000112
Sharma PK, Ojha CSP, Swami D, Joshi N, Shukla SK (2015) Semi-analytical solutions of multiprocessing non-equilibrium transport equations with linear and exponential distance-dependent dispersivity. Water Resour Manage 29:5255–5273. https://doi.org/10.1007/s11269-015-1116-6
Shayannejad M, Ghobadi M, Ostad-Ali-Askari K (2022) Modeling of surface flow and infiltration during surface irrigation advance based on numerical solution of Saint-Venant equations using Preissmann’s scheme. Pure Appl Geophys 179(3):1103–1113. https://doi.org/10.1007/s00024-022-02962-9
Slodička M, Balážová A (2010) Decomposition method for solving multispecies reactive transport problems coupled with first-order kinetics applicable to a chain with identical reaction rates. J Comput Appl Math 234(4):1069–1077. https://doi.org/10.1016/j.cam.2009.04.021
Srivastava R, Sharma PK, Brusseau ML (2002) Spatial moments for reactive transport in heterogeneous porous media. J Hydrol Eng 7(4):336–341. https://doi.org/10.1061/(ASCE)1084-0699(2002)7:4(336)
Suk H (2016) Generalized semi-analytical solutions to multispecies transport equation coupled with sequential first-order reaction network with spatially or temporally variable transport and decay coefficients. Adv Water Resour 94:412–423. https://doi.org/10.1016/j.advwatres.2016.06.004
Sullivan TP, Gao Y, Reimann T (2019) Nitrate transport in a karst aquifer: numerical model development and source evaluation. J Hydrol 573:432–448. https://doi.org/10.1016/j.jhydrol.2019.03.078
Sun Y, Clement TP (1999) A decomposition method for solving coupled multispecies reactive transport problems. Transp Porous Media 37:327–346. https://doi.org/10.1023/A:1006507514019
Sun Y, Petersen JN, Clement TP, Skeen RS (1999) Development of analytical solutions for multispecies transport with serial and parallel reactions. Water Resour Res 35(1):185–190. https://doi.org/10.1029/1998WR900003
Sun Y, Petersen JN, Clement TP (1999) Analytical solutions for multiple species reactive transport in multiple dimensions. J Contam Hydrol 35(4):429–440. https://doi.org/10.1016/S0169-7722(98)00105-3
Tompson AF (1993) Numerical simulation of chemical migration in physically and chemically heterogeneous porous media. Water Resour Res 29(11):3709–3726. https://doi.org/10.1029/93WR01526
Van Genuchten MT (1982) Analytical solutions of the one-dimensional convective-dispersive solute transport equation. US Department of Agriculture, Agricultural Research Service No. 1661
Van Genuchten MT (1985) Convective-dispersive transport of solutes involved in sequential first-order decay reactions. Comput Geosci 11(2):129–147. https://doi.org/10.1016/0098-3004(85)90003-2
Yates SR (1990) An analytical solution for one-dimensional transport in heterogeneous porous media. Water Resour Res 26(10):2331–2338. https://doi.org/10.1029/WR026i010p02331
Yates SR (1992) An analytical solution for one-dimensional transport in porous media with an exponential dispersion function. Water Resour Res 28(8):2149–2154. https://doi.org/10.1029/92WR01006
Yu C, Zhou M, Ma J, Cai X, Fang D (2019) Application of the homotopy analysis method to multispecies reactive transport equations with general initial conditions. Hydrogeol J 27(5):1779–1790. https://doi.org/10.1007/s10040-019-01948-7
Zhang WS, Zhao YX, Xu YH, Wang YG, Peng H, Xu GH (2012) 2-D numerical simulation of radionuclide transport in the lower Yangtze River. J Hydrodyn 24(5):702–710. https://doi.org/10.1016/S1001-6058(11)60294-1
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Additional information
Responsible Editor: Broder J. Merkel
Key points of the research
1. A numerical solution is obtained for multispecies transport through heterogeneous porous media.
2. An exponential time-dependent dispersivity is considered to represent the heterogeneity of porous media.
3. Spatial moment analysis depicts the behavior of spreading of multispecies solute transport process in a comprehensive manner.
4. The variance and mean travel distance are susceptible to changes in dispersivity as a function of time, and the role of macrodispersion is significant in the migration of multispecies solute.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Gupta, K.R., Sharma, P.K. Study on multispecies solute transport through heterogeneous porous media. Arab J Geosci 16, 452 (2023). https://doi.org/10.1007/s12517-023-11580-1
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12517-023-11580-1