Skip to main content
SpringerLink
Log in

Multicomponent competitive monovalent cation exchange in hierarchical porous media with multimodal reactive mineral facies

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

This paper presents a stochastic model for multicomponent competitive monovalent cation exchange in hierarchical porous media. Reactive transport in porous media is highly sensitive to heterogeneities in physical and chemical properties, such as hydraulic conductivity (K), and cation exchange capacity (CEC). We use a conceptual model for multimodal reactive mineral facies and develop a Eulerian-based stochastic theory to analyze the transport of multiple cations in heterogeneous media with a hierarchical organization of reactive minerals. Numerical examples investigate the retardation factors and dispersivities in a chemical system made of three monovalent cations (Na+, K+, and Cs+). The results demonstrate how heterogeneity influences the transport of competitive monovalent cations, and highlight the importance of correlations between K and CEC. Further sensitivity analyses are presented investigating how the dispersion and retardation of each cation are affected by the means, variances, and integral scales of K and CEC. The volume fraction of organic matter is shown to be another important parameter. The Eulerian stochastic framework presented in this work clarifies the importance of each system parameters on the migration of cation plumes in formations with hierarchical organization of facies types. Our stochastic approach could be used as an alternative to numerical simulations for 3D reactive transport in hierarchical porous media, which become prohibitively expensive for the multicomponent applications considered in this work.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Allen-King RM, Divine DP, Robin MJL, Alldredge JR, Gaylord DR (2006) Spatial distributions of perchloroethylene reactive transport parameters in the Borden Aquifer. Water Resour Res 42:W01413. doi:10.1029/2005WR003977

    Article  Google Scholar 

  • Appelo CAJ (1994) Some calculations on multicomponent transport with cation-exchange in aquifers. Ground Water 32:968–975

    Article  CAS  Google Scholar 

  • Appelo CAJ (1996) Multicomponent ion exchange and chromatography in natural systems. Rev Mineral Geochem 34(1):193–227

    CAS  Google Scholar 

  • Appelo CAJ, Postma D (1993) Geochemistry, groundwater and pollution. Balkema, Rotterdam, p 536

  • Appelo CAJ, Postma D (2004) Geochemistry, groundwater and pollution. CRC Press, Boca Raton

    Google Scholar 

  • Attinger S, Dentz M, Kinzelbach W (2004) Exact transverse macro dispersion coefficients for transport in heterogeneous porous media. Stoch Environ Res Risk Assess 18(1):9–15

    Article  Google Scholar 

  • Bellin A, Rinaldo A (1995) Analytical solutions for transport of linearly adsorbing solutes in heterogeneous formations. Water Resour Res 31:1505–1511

    Article  Google Scholar 

  • Bellin A, Rinaldo A, Bosma WJP, van derZee SEATM, Rubin Y (1993) Linearequilibrium adsorbing solute transport in physically and chemically heterogeneous porous formations: 1. Analytical solutions. Water Resour Res 29(12):4019–4030. doi:10.1029/93WR02303

    Article  CAS  Google Scholar 

  • Bellin A, Lawrence AE, Rubin Y (2004) Models of sub-grid variability in numerical simulations of solute transport in heterogeneous porous formations: three-dimensional flow and effect of pore-scale dispersion. Stoch Environ Res Risk Assess 18(1):31–38

    Article  Google Scholar 

  • Bolster D, Dentz M (2012) Anomalous dispersion in chemically heterogeneous media induced by long-range disorder correlation. J Fluid Mech 695(2012):366–389

    Article  Google Scholar 

  • Bridge JS (2006) Fluvial facies models: Recent developments. In: Posamentier HW, Walker RG (eds) Facies models revisited, vol 84. SEPM Spec. Publ., Soc. for Sediment. Geol. (SEPM), Tulsa, Okla, pp 85–170

  • Brusseau ML, Srivastava R (1997) Nonideal transport of reactive solutes in heterogeneous porous media: 2. Quantitative analysis of the Borden natural-gradient field experiment. J Contamin Hydrol 28(2):115–155

    Article  CAS  Google Scholar 

  • Burr DT, Sudicky EA, Naff RL (1994) Nonreactive and reactive solute transport in three-dimensional heterogeneous porous media: mean displacement, plume spreading, and uncertainty. Water Resour Res 30(3):791–815

    Article  CAS  Google Scholar 

  • Cassel DK, Wendroth O, Nielsen DR (2000) Assessing spatial variability in an agricultural experiment station field: opportunities arising from spatial dependence. Agron J 95:706–714

    Article  Google Scholar 

  • Cheng T, Barnett MO, Roden EE, Zhuang J (2007) Reactive transport of uranium (VI) and phosphate in a goethite-coated sand column: an experimental study. Chemosphere 68(7):1218–1223

    Article  CAS  Google Scholar 

  • Dagan G (1984) Solute transport in heterogenous porous formations. J Fluid Mech 145:151–177

    Article  Google Scholar 

  • Dagan G (1989) Flow and transport in porous formations. Springer, Berlin

    Book  Google Scholar 

  • Dai Z, Samper J (2004) Inverse problem of multicomponent reactive chemical transport in porous media: formulation and applications. Water Res Res. doi:10.1029/2004WR003248

    Google Scholar 

  • Dai Z, Ritzi RW, Huang C, Rubin Y, Dominic DF (2004) Transport in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales. J Hydrol 294(1):68–86

    Article  Google Scholar 

  • Dai Z, Ritzi RW, Dominic DF (2005) Improving permeability semivariograms with transition probability models of hierarchical sedimentary architecture derived from outcrop analog studies. Water Resour Res 41:W07032. doi:10.1029/2004WR003515

    Article  Google Scholar 

  • Dai Z, Wolfsberg AV, Lu Z, Reimus P (2007) Upscaling matrix diffusion coefficients for heterogeneous fractured rocks. Geophys Res Lett 34:L07408. doi:10.1029/2007GL029332

    Google Scholar 

  • Dai Z, Wolfsberg A, Lu Z, Deng H (2009) Scale dependence of sorption coefficients for contaminant transport in saturated fractured rock. Geophys Res Lett 36:L01403. doi:10.1029/2008GL036516

    Article  Google Scholar 

  • Davis JA, Yabusaki SB, Steefel CI, Zachara JM, Curtis GP, Redden GD, Criscenti LJ, Honey BD (2004) Assessing conceptual models for subsurface reactive transport of inorganic contaminants. Trans Am Geophys Union EOS 85(44):449–455

    Article  Google Scholar 

  • de Barros FPJ, Fiori A, Boso F, Bellin A (2015) A theoretical framework for modeling dilution enhancement of non-reactive solutes in heterogeneous porous media. J Contam Hydrol 175–176:72–83. doi:10.1016/j.jconhyd.2015.01.004

  • Deng H, Dai Z, Wolfsberg A, Lu Z, Ye M, Reimus P (2010) Upscaling of reactive mass transport in fractured rocks with multimodal reactive mineral facies. Water Resour Res 46:W06501. doi:10.1029/2009WR008363

    Article  Google Scholar 

  • Deng H, Dai Z, Wolfsberg AV, Ye M, Stauffer PH, Lu Z, Kwicklis E (2013) Upscaling retardation factor in hierarchical porous media with multimodal reactive mineral facies. Chemosphere 91(3):248–257

    Article  CAS  Google Scholar 

  • Dentz M, Bolster D (2010) Distribution-versus correlation-induced anomalous transport in quenched random velocity fields. Phys Rev Lett 105(24):244301

    Article  Google Scholar 

  • Dentz M, Castro A (2009) Effective transport dynamics in porous media withvheterogeneous retardation properties. Geophys Res Lett 36:L03403

    Article  Google Scholar 

  • Dentz M, Bolster D, le Borgne T (2009) Concentration statistics for transport in a random medium. Phys Rev E 80:010101

    Article  Google Scholar 

  • Dentz M, Le Borgne T, Englert A, Bijeljic B (2011) Mixing, spreading and reaction in heterogeneous media: a brief review. J Contam Hydrol 120:1–17

    Article  Google Scholar 

  • Fernández-Garcia D, Illangasekare TH, Rajaram H (2005) Differences in the scale dependence of dispersivity and retardation factors estimated from forced-gradient and uniform flow tracer tests in three-dimensional physically and chemically heteroge- neous porous media. Water Resour Res 41:W03012. doi:10.1029/2004WR003125

    Google Scholar 

  • Fiori A, Dagan G (2002) Transport of a passive scalar in a strati fied porous medium. Transp Porous Media 47:81–98

    Article  CAS  Google Scholar 

  • Gelhar LW (1993) Stochastic subsurface hydrology. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Gelhar LW, Axness CL (1983) Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour Res 19(1):161–180

    Article  Google Scholar 

  • Griffioen J (1993) Multicomponent cation exchange including alkalinization/acidification following flow through sandy sediment. Water Resour Res 29:3005–3019

    Article  CAS  Google Scholar 

  • Jacques D, Mouvet C, Mohanty B, Vereecken H, Feyen J (1999) Spatial variability of atrazine sorption parameters and other soil properties in a podzoluvisol. J Contam Hydrol 36:31–52. doi:10.1016/S0169-7722(98)00141-7

    Article  CAS  Google Scholar 

  • Jin YC, Ye SL (1999) Analytical solution for monovalentdivalent ion exchange transport in groundwater. Can Geotech J 36:1197–1201. doi:10.1139/cgj-36-6-1197

    Article  Google Scholar 

  • Johnston HM, Gillham RM, Cherry, JA (1985) Distribution coefficients for strontium and cesium in overburden at a storage area for low-level radioactive waste. Can Geotech J 22:6–16

    Article  CAS  Google Scholar 

  • Koltermann CE, Gorelick SM (1996) Heterogeneity in sedimentary deposits: a review of structure-imitating, process- imitating, and descriptive approaches. Water Resour Res 32:2617–2658

    Article  CAS  Google Scholar 

  • Kuzyakova IF, Romanenkov VA, Kuzyakova YV (2001) Application of geostatistics in processing the results of soil and agrochemical studies. Eurasian Soil Sci 34(11):1219–1228

    Google Scholar 

  • Langmuir D (1997) Aqueous environmental geochemistry. Prentice Hall, Upper Saddle River

    Google Scholar 

  • Lichtner PC, Yabusaki S, Pruess K, Steefel CI (2004) Role of competitive cation exchange on chro- matographic displacement of cesium in the vadose zone beneath the Hanford S/SX tank farm. Vadose Zone J 3:203–219

    Article  CAS  Google Scholar 

  • Lumley JL, Panofsky HA (1964) The structure of atmospheric turbulence. Wiley, New York

    Google Scholar 

  • Mackay DM, Freyberg DL, Roberts Paul V, Cherry JA (1986) A natural gradient experiment on solute transport in a sand aquifer: 1. Approach and overview of plume movement. Water Resour Res 22:2017–2029

    Article  CAS  Google Scholar 

  • Maghrebi M, Jankovic I, Fiori A, Dagan G (2013) Effective retardation factor for transport of reactive solutes in highly heterogeneous porous formations. Water Resour Res 49(12):8600–8604

    Article  Google Scholar 

  • Matschonat G, Vogt R (1996) Equilibrium solution composition and exchange properties of disturbed and undisturbed soil samples from an acid forest soil. Plant Soil 183(2):171–179. doi:10.1007/BF00011432

    Article  CAS  Google Scholar 

  • Miralles-Wilhelm F (1993). Stochastic analysis of sorption and biodegradation in three-dimensionally heterogeneous aquifers, Ph.D. thesis, Massachusetts Institute of Technology

  • Miralles-Wilhelm F, Gelhar LW (1996) Stochastic analysis of sorption macrokinetics in heterogeneous aquifers. Water Resour Res 32(6):1541–1549. doi:10.1029/96WR00791

    Article  Google Scholar 

  • Moslehi M, de Barros FP, Ebrahimi F, Sahimi M (2016) Upscaling of solute transport in disordered porous media by wavelet transformations. Adv Water Resour 96:180–189

    Article  Google Scholar 

  • Priestley MB (1981) Spectral analysis and time series. Academic Press, San Diego

    Google Scholar 

  • Pucci AA, Szabo Z, Owens JP (1997) Variations in pore-water quality, mineralogy, and sedimentary texture of clay-silts in the lower Miocene Kirkwood Formation, Atlantic City, New Jersey. In: Miller KG, Aubry MP, Browning JV et al. (eds) Proceedings of the ocean drilling program, scientific results, vol. 150X. Ocean Drilling Program, College Station, Texas, pp. 317–341

  • Rajaram H (1997) Time and scale-dependent effective retardation factors in heterogeneous aquifers. Adv Water Resour 20(4):217–230

    Article  Google Scholar 

  • Ramanathan R, Ritzi RW, Allen-King RM (2010) 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:W01510. doi:10.1029/2009WR0O07810

    Google Scholar 

  • Ritzi RW, Soltanian, MR (2015) What have we learned from deterministic geostatistics at highly resolved field sites, as relevant to mass transport processes in sedimentary aquifers? J Hydrol 531:31–39

    Article  Google Scholar 

  • Ritzi RW Jr, Huang L, Ramanathan R, Allen-King RM (2013) Horizontal spatial correlation of hydraulic and reactive transport parameters as related to hierarchical sedimentary architecture at the Borden research site. Water Resour Res 49:1901–1913. doi:10.1002/wrcr.20165

    Article  Google Scholar 

  • Riva M, Guadagnini A, Sanchez-Vila X (2009) Effect of sorption heterogeneity on moments of solute residence time in convergent flows. Math Geosci. doi:10.1007/s11004-009-9240-6

    Google Scholar 

  • Rubin Y (2003) Applied stochastic hydrogeology. Oxford Univ. Press, New York

    Google Scholar 

  • Samper J, Yang C (2006) Stochastic analysis of transport and multicomponent competitive monovalent cation exchange in aquifers. Geosphere 2(2):102–112

    Article  Google Scholar 

  • Samper J, Yang C (2007) A semi-analytical solution for linearized multicomponent cation exchange reactive transport in groundwater. Transp Porous Media 69(1):67–88

    Article  Google Scholar 

  • Samper J, Yang C, Montenegro L (2003) User’s manual of CORE2D Version 4: a code for groundwater flow and reactive solute transport. Universidad de La Corun˜a, La Corun˜a, p 105

  • Samper J, Dai Z, Molinero J, Garcia-Gutierrez M, Missana T, Mingarro M (2006) Interpretation of solute transport experiments in compacted Ca-bentonites using inverse modeling. Phys Chem Earth 31(10):640–648

    Article  Google Scholar 

  • Sanchez-Vila X, Bolster D (2009) An analytical approach to transient homovalent cation exchange problems. J Hydrol 378(3):281–289

    Article  CAS  Google Scholar 

  • Soltanian MR, Ritzi RW (2014) A new method for analysis of variance of the hydraulic and reactive attributes of aquifers as linked to hierarchical and multiscaled sedimentary architecture. Water Resour Res 50:9766–9776. doi:10.1002/2014WR015468

    Article  Google Scholar 

  • Soltanian MR, Ritzi RW, Dai Z, Huang CC, Dominic D (2015a) Transport of kinetically sorbing solutes in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales. Stoch Environ Res Risk Assess 29(3):709–726. doi:10.1007/s00477-014-0922-3

    Article  Google Scholar 

  • Soltanian MR, Ritzi RW, Huang CC, Dai Z (2015b) Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 1. Time-dependent effective retardation factor. Water Resour Res. doi:10.1002/2014WR016353

    Google Scholar 

  • Soltanian MR, Ritzi RW, Huang CC, Dai Z (2015c) Relating reactive solute transport to hierarchical and multiscale sedimentary architecture inva Lagrangian-based transport model: 2. Particle displacement variance. Water Resour Res. doi:10.1002/014WR016354

    Google Scholar 

  • Soltanian MR, Ritzi RW, Dai Z, Huang CC (2015d) Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 1. Time-dependent effective retardation factor. Water Resour Res. doi:10.1002/2014WR016353

    Google Scholar 

  • Soltanian MR, Ritzi RW, Dai Z, Huang CC (2015e) Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: the Lagrangian approach. Chemosphere 122:235–244. doi:10.1016/j.chemosphere.2014.11.064

    Article  CAS  Google Scholar 

  • Soltanian MR, Ritzi R, Huang CC, Dai Z, Deng H (2015f) A note on upscaling retardation factor in hierarchical porous media with multimodal reactive mineral facies. Transp Porous Media 108(2):355–366

    Article  Google Scholar 

  • Sun AY, Ritzi RW, Sims DW (2008) Characterization and modeling of spatial variability in a complex alluvial aquifer: implications on solute transport. Water Resour Res. doi:10.1029/2007WR006119

    Google Scholar 

  • Valocchi AJ, Roberts PV, Parks GA, Street RL (1981a) Simulation of the transport of ion-exchanging solutes using laboratory-determined chemical parameter values. Ground Water 19:600–607

    Article  CAS  Google Scholar 

  • Valocchi AJ, Street RL, Roberts PV (1981b) Transport of ion-exchanging solutes in groundwater: chromatographic theory and field simulation. Water Resour Res 17:1517–1527

    Article  CAS  Google Scholar 

  • Venkatraman A, Hesse MA, Lake LW, Johns RT (2014) Analytical solutions for flow in porous media with multicomponent cation exchange reactions. Water Resour Res 50:5831–5847. doi:10.1002/2013WR015091

    Article  CAS  Google Scholar 

  • Wirth ST (2001) Regional-scale analysis of soil microbial biomass and soil basal CO2-respiration in northeastern Germany. In: Stott RH, Mohtar GC, Steinhardt E (eds) Sustaining the global farm—selected papers from the 10th international soil conservation organization meeting, 24–29 May 1999, West Lafayette, Indiana: West Lafeyette, Indiana, International Soil Conservation Organization in cooperation with the U.S. Department of Agrirculture and Purdue University, pp 486–493. http://topsoil.nserl.purdue.edu/nserlweb/isco99/pdf/isco99pdf.htm

  • Xu T, Samper J, Ayora C, Manzano M, Custodio E (1999) Modeling of non-isothermal multicomponent reactive transport in field scale porous media flow system. J Hydrol 214:144–164

    Article  CAS  Google Scholar 

  • Yang C, Samper J (2009) Numerical evaluation of multicomponent cation exchange reactive transport in physically and geochemically heterogeneous porous media. Comput Geosci 13(3):391–404

    Article  Google Scholar 

  • Zavarin M, Carle SF, Maxwell RM (2004) Upscaling radionuclide retardation-linking the surface complexation and ion exchange mechanistic approach to a linear Kd approach, UCRL-TR-204713, Lawrence Livermore National Laboratory, Livermore, California

  • Zhu L, Dai Z, Gong H, Gable C, Teatini P (2016) Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans. Stoch Environ Res Risk Assess 30(3):1005–1016

    Article  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge the time and expertise given by two anonymous reviewers and the associate editor. Their constructive comments and suggestions helped us to improve the article.

Author information

Authors and Affiliations

  1. School of Earth Sciences, The Ohio State University, Columbus, OH, 43210, USA

    Mohamad Reza Soltanian, Mohammad Amin Amooie & Joachim Moortgat

  2. EES-16, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Mailstop T003, Los Alamos, NM, 87545, USA

    Zhenxue Dai

  3. Bureau of Economic Geology, The University of Texas at AustinUniversity Station, Box X, Austin, TX, 78713-8924, USA

    Changbing Yang

Authors
  1. Mohamad Reza Soltanian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenxue Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Changbing Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Amin Amooie
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Joachim Moortgat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamad Reza Soltanian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Soltanian, M.R., Dai, Z., Yang, C. et al. Multicomponent competitive monovalent cation exchange in hierarchical porous media with multimodal reactive mineral facies. Stoch Environ Res Risk Assess 32, 295–310 (2018). https://doi.org/10.1007/s00477-017-1379-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-017-1379-y

Keywords

Search

Navigation