Bridge, J. S.: Rivers and floodplains: forms, processes, and sedimentary record, John Wiley & Sons., ISBN 978-1-444-31126-6, 2009.
Carle, S. F., Esser, B. K., and Moran, J. E.: High-resolution simulation of basin-scale nitrate transport considering aquifer system heterogeneity, Geosphere, 2, 195–209, https://doi.org/10.1130/GES00032.1, 2006.
Chen, C., Packman, A. I., Zhang, D., and Gaillard, J. F.: A multi-scale investigation of interfacial transport, pore fluid flow, and fine particle deposition in a sediment bed, Water Resour. Res., 46, https://doi.org/10.1029/2009WR009018, 2010.
Dagan, G.: Solute transport in heterogeneous porous formations, J. Fluid. Mech., 145, 151–177, https://doi.org/10.1017/S0022112084002858, 1984.
Dagan, G.: Flow and Transport in Porous Formations, Springer Science and Business Media, https://doi.org/10.1007/978-3-642-75015-1, 1989.
Dagan, G.: Solute plumes mean velocity in aquifer transport: Impact of injection and detection modes, Adv. Water Resour., 106, 6–10, https://doi.org/10.1016/j.advwatres.2016.09.014, 2017.
Dai, Z., Ritzi Jr, R. W., Huang, C., Rubin, Y. N., and Dominic, D. F.: Transport in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales, J. Hydrol., 294, 68–86, https://doi.org/10.1016/j.jhydrol.2003.10.024, 2004.
Dai, Z., Ritzi Jr., R. W., and Dominic, D. F.: Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies, Water Resour. Res., 41, https://doi.org/10.1029/2004WR003515, 2005.
Dai, Z., Zhan, C., Dong, S., Yin, S., Zhang, X., and Soltanian, M. R.: How does resolution of sedimentary architecture data affect plume dispersion in multiscale and hierarchical systems?, J. Hydrol., 582, 124516, https://doi.org/10.1016/j.jhydrol.2019.124516, 2020.
Dai, Z., Ma, Z., Zhang, X., Chen, J., Ershadnia, R., Luan, X., and Soltanian, M. R.: An integrated experimental design framework for optimizing solute transport monitoring locations in heterogeneous sedimentary media, J. Hydrol., 614, 128541, https://doi.org/10.1016/j.jhydrol.2022.128541, 2022.
de Barros, F. P.: Evaluating the combined effects of source zone mass release rates and aquifer heterogeneity on solute discharge uncertainty, Adv. Water Resour., 117, 140–150, https://doi.org/10.1016/j.advwatres.2018.05.010, 2018.
de Barros, F. P. and Dentz, M.: Pictures of blockscale transport: Effective versus ensemble dispersion and its uncertainty, Adv. Water Resour., 91, 11–22, https://doi.org/10.1016/j.advwatres.2016.03.004, 2016.
Dentz, M., Kinzelbach, H., Attinger, S., and Kinzelbach, W.: Temporal behavior of a solute cloud in a heterogeneous porous medium: 2. Spatially extended injection, Water Resour. Res., 36, 3605–3614, https://doi.org/10.1029/2000WR900211, 2000a.
Dentz, M., Kinzelbach, H., Attinger, S., and Kinzelbach, W.: Temporal behavior of a solute cloud in a heterogeneous porous medium: 1. Point-like injection, Water Resour. Res., 36, 3591–3604, https://doi.org/10.1029/2000WR900162, 2000b.
Dentz, M., Le Borgne, T., Englert, A., and Bijeljic, B.: Mixing, spreading and reaction in heterogeneous media: A brief review, J. Contam. Hydrol., 120, 1–17, https://doi.org/10.1016/j.jconhyd.2010.05.002, 2011.
Dentz, M., Hidalgo, J. J., and Lester, D.: Mixing in porous media: concepts and approaches across scales, Transport. Porous. Med., 146, 5–53, https://doi.org/10.1007/s11242-022-01852-x, 2023.
Ershadnia, R., Hajirezaie, S., Amooie, A., Wallace, C. D., Gershenzon, N. I., Hosseini, S. A., Sturmer, D. M., Ritzi, R. W., and Soltanian, M. R.: CO
2 geological sequestration in multiscale heterogeneous aquifers: Effects of heterogeneity, connectivity, impurity, and hysteresis, Adv. Water Resour., 151, 103895, https://doi.org/10.1016/j.advwatres.2021.103895, 2021.
Faroughi, S. A., Soltanmohammadi, R., Datta, P., Mahjour, S. K., and Faroughi, S.: Physics-informed neural networks with periodic activation functions for solute transport in heterogeneous porous media, Mathematics, 12, 63, https://doi.org/10.3390/math12010063, 2023.
Fiori, A. and Dagan, G.: Concentration fluctuations in aquifer transport: A rigorous first-order solution and applications, J. Contam. Hydrol., 45, 139–163, https://doi.org/10.1016/S0169-7722(00)00123-6, 2000.
Fiori, A., Boso, F., de Barros, F. P., De Bartolo, S., Frampton, A., Severino, G., Suweis, S., and Dagan, G.: An indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity, Water Resour. Res., 46, https://doi.org/10.1029/2009WR008590, 2010.
Fitts, C. R.: Uncertainty in deterministic groundwater transport models due to the assumption of macrodispersive mixing: Evidence from the Cape Cod (Massachusetts, USA) and Borden (Ontario, Canada) tracer tests, J. Contam. Hydrol., 23, 69–84, https://doi.org/10.1016/0169-7722(95)00101-8, 1996.
Freyberg, D. L.: A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers, Water Resour. Res., 22, 2031–2046, https://doi.org/10.1029/WR022i013p02031, 1986.
Garabedian, S. P., LeBlanc, D. R., Gelhar, L. W., and Celia, M. A.: Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts: 2. Analysis of spatial moments for a nonreactive tracer, Water Resour. Res., 27, 911–924. https://doi.org/10.1029/91WR00242, 1991.
Gelhar, L. W., Welty, C., and Rehfeldt, K. R.: A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28, 1955–1974, https://doi.org/10.1029/92WR00607, 1992.
Guo, Z., Fogg, G. E., and Henri, C. V.: Upscaling of regional scale transport under transient conditions: Evaluation of the multirate mass transfer model, Water Resour. Res., 55, 5825–5841, https://doi.org/10.1029/2019WR024953, 2019.
Hansen, S. K. and Berkowitz, B.: Modeling non-Fickian solute transport due to mass transfer and physical heterogeneity on arbitrary groundwater velocity fields, Water Resour. Res., 56, e2019WR026868, https://doi.org/10.1029/2019WR026868, 2020.
Harbaugh, A. W.: MODFLOW-2005, the US Geological Survey modular ground-water model: the ground-water flow process (Vol. 6). Reston, VA, USA: US Department of the Interior, US Geological Survey, https://doi.org/10.3133/tm6A16, 2005.
Henri, C. V., Harter, T., and Diamantopoulos, E.: On the conceptual complexity of non-point source management: impact of spatial variability, Hydrol. Earth. Syst. Sci., 24, 1189–1209, https://doi.org/10.5194/hess-24-1189-2020, 2020.
Jia, S., Dai, Z., Zhou, Z., Ling, H., Yang, Z., Qi, L., Wang A. H., Zhang, X. Y., Thanh H. V., and Soltanian, M. R.: Upscaling dispersivity for conservative solute transport in naturally fractured media, Water Res., 235, 119844, https://doi.org/10.1016/j.watres.2023.119844, 2023.
LaBolle, E. M., Fogg, G. E., and Tompson, A. F.: Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods, Water Resour. Res., 32, 583–593, https://doi.org/10.1029/95WR03528, 1996.
Lee, J., Rolle, M., and Kitanidis, P. K.: Longitudinal dispersion coefficients for numerical modeling of groundwater solute transport in heterogeneous formations, J. Contam. Hydrol., 212, 41–54, https://doi.org/10.1016/j.jconhyd.2017.09.004, 2018.
Lester, D. R., Trefry, M. G., and Metcalfe, G.: Chaotic advection at the pore scale: Mechanisms, upscaling and implications for macroscopic transport, Adv. Water Resour., 97, 175–192, https://doi.org/10.1016/j.advwatres.2016.09.007, 2016.
Ma, Z., Dai, Z., Zhang, X., Zhan, C., Gong, H., Zhu, L.,Wallace C. D., and Soltanian, M. R.: Dispersivity variations of solute transport in heterogeneous sediments: numerical and experimental study, Stoch. Env. Res. Risk. A., 36, 661–677, https://doi.org/10.1007/s00477-021-02040-x, 2022.
Ma, Z., Qi, L., Dai, Z., Yang, Z., Ma, Y., Wang, D., Carroll, K. C., and Soltanian, M. R.: Impact of multiscale heterogeneous sediments and boundary conditions on dispersivity spatial variations, Water Resour. Res., 61, e2024WR039151, https://doi.org/10.1029/2024WR039151, 2025.
Neuman, S. P. and Tartakovsky, D. M.: Perspective on theories of non-Fickian transport in heterogeneous media, Adv. Water Resour., 32, 670–680, https://doi.org/10.1016/j.advwatres.2008.08.005, 2009.
Pauloo, R. A., Fogg, G. E., Guo, Z., and Henri, C. V.: Mean flow direction modulates non-Fickian transport in a heterogeneous alluvial aquifer-aquitard system, Water Resour. Res., 57, e2020WR028655, https://doi.org/10.1029/2020WR028655, 2021.
Proce, C. J., Ritzi, R. W., Dominic, D. F., and Dai, Z.: Modeling multi-scale heterogeneity and aquifer interconnectivity, Groundwater, 42, 658–670, https://doi.org/10.1111/j.1745-6584.2004.tb02720.x, 2004.
Puyguiraud, A., Perez, L. J., Hidalgo, J. J., and Dentz, M.: Effective dispersion coefficients for the upscaling of pore-scale mixing and reaction, Adv. Water Resour., 146, 103782, https://doi.org/10.1016/j.advwatres.2020.103782, 2020.
Ramanathan, R., Ritzi Jr., R. W., and Allen-King, R. M.: Linking hierarchical stratal architecture to plume spreading in a Lagrangian-based transport model: 2. Evaluation using new data from the Borden site, Water Resour. Res., 46, https://doi.org/10.1029/2009WR007810, 2010.
Ren, W., Ershadnia, R., Wallace, C. D., LaBolle, E. M., Dai, Z., de Barros, F. P., and Soltanian, M. R.: Evaluating the effects of multiscale heterogeneous sediments on solute mixing and effective dispersion, Water. Resour. Res., 58, e2021WR031886, https://doi.org/10.1029/2021WR031886, 2022.
Ren, W., Dai, H., Yuan, S., Dai, Z., Ye, M., and Soltanian, M. R.: Global sensitivity study of non-reactive and sorptive solute dispersivity in multi-scale heterogeneous sediments, J. Hydrol., 619, 129274, https://doi.org/10.1016/j.jhydrol.2023.129274, 2023.
Ritzi Jr., R. W. and Allen-King, R. M.: Why did Sudicky [1986] find an exponential-like spatial correlation architecture for hydraulic conductivity at the Borden research site?, Water Resour. Res., 43, https://doi.org/10.1029/2006WR004935, 2007.
Scheibe, T. D. and Freyberg, D. L.: Use of sedimentological information for geometric simulation of natural porous media structure, Water Resour. Res., 31, 325–337, https://doi.org/10.1029/95WR02570, 1995.
Soltanian, M. R. and Ritzi, R. W.: A new method for analysis of variance of the hydraulic and reactive attributes of aquifers as linked to hierarchical and multi-scaled sedimentary architecture, Water Resour. Res., 50, 9766–9776, https://doi.org/10.1002/2014WR015468, 2014.
Soltanian, M. R., Ritzi, R. W., Huang, C. C., and Dai, Z.: Relating reactive solute transport to hierarchical and multi-scale sedimentary architecture in a L agrangian-based transport model: 1. Time-dependent effective retardation factor, Water. Resour. Res., 51, 1586–1600, https://doi.org/10.1002/2014WR016353, 2015a.
Soltanian, M. R., Ritzi, R. W., Huang, C. C., and Dai, Z.: Relating reactive solute transport to hierarchical and multi-scale sedimentary architecture in a L agrangian-based transport model: 2. Particle displacement variance, Water. Resour. Res., 51, 1601–1618, https://doi.org/10.1002/2014WR016354, 2015b.
Soltanian, M. R., Sun, A., and Dai, Z.: Reactive transport in the complex heterogeneous alluvial aquifer of Fortymile Wash, Nevada, Chemosphere, 179, 379–386, https://doi.org/10.1016/j.chemosphere.2017.03.136, 2017.
Soltanian, M. R., Behzadi, F., and de Barros, F. P.: Dilution enhancement in hierarchical and multi-scale heterogeneous sediments, J. Hydrol., 587, 125025, https://doi.org/10.1016/j.jhydrol.2020.125025, 2020.
Sudicky, E. A.: A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resour. Res., 22, 2069–2082, https://doi.org/10.1029/WR022i013p02069, 1986
Tellam, J. H. and Barker, R. D.: Towards prediction of saturated-zone pollutant movement in groundwaters in fractured permeable-matrix aquifers: the case of the UK Permo-Triassic sandstones, Geological Society, London, Special Publications, 263, https://doi.org/10.1144/GSL.SP.2006.263.01.01, 2006.
Vuković, M. and Soro, A.: Determination of hydraulic conductivity of porous media from grain-size composition, 83 pp., ISBN: 9780918334770, 1992.
White, C. D. and Willis, B. J.: A method to estimate length distributions from outcrop data, Math. Geol., 32, 389–419, https://doi.org/10.1023/A:1007510615051, 2000.
Yin, M., Zhang, Y., Ma, R., Tick, G. R., Bianchi, M., Zheng, C., Wei, W., Wei, S., and Liu, X.: Super-diffusion affected by hydrofacies mean length and source geometry in alluvial settings, J. Hydrol., 582, 124515, https://doi.org/10.1016/j.jhydrol.2019.124515, 2020.
Yin, M., Ma, R., Zhang, Y., Lin, J., Guo, Z., and Zheng, C.: Competitive control of multi-scale aquifer heterogeneity on solute transport in an alluvial aquifer, J. Hydrol., 616, 128819, https://doi.org/10.1016/j.jhydrol.2022.128819, 2023.
Zheng, C., Bianchi, M., and Gorelick, S. M.: Lessons learned from 25 years of research at the MADE site, Groundwater, 49, 649–662, https://doi.org/10.1111/j.1745-6584.2010.00753.x, 2011.
Zhou, D., Zhang, Y., Gianni, G., Lichtner, P., and Engelhardt, I.: Numerical modelling of stream–aquifer interaction: Quantifying the impact of transient streambed permeability and aquifer heterogeneity, Hydrol. Process, 32, 2279–2292, https://doi.org/10.1002/hyp.13169, 2018.
Zinn, B. and Harvey, C. F.: When good statistical models of aquifer heterogeneity go bad: A comparison of flow, dispersion, and mass transfer in connected and multivariate Gaussian hydraulic conductivity fields, Water Resour. Res., 39, https://doi.org/10.1029/2001WR001146, 2003.
