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Multi-scale Study of Pollutant Transport and Uptake in Compacted Bentonite

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Abstract

In a previous work, a multiscale model was developed in order to investigate the impact of cation exchange and surface complexation on the hydraulic conductivity of compacted bentonite. Simulation of lead nitrate percolation tests has displayed the strong connection between hydraulic conductivity increase and textural and structural evolutions at different scales. The present developments deal with the modeling of pollutant transport by advection, molecular diffusion within the interlayer and inter-aggregate voids, and pollutant fixation on the smectite layers’ surface. The evolution of the nanometer and micrometer porous spaces is described by relying on a structural investigation of the solid phase conducted at both scales. The multiscale impact of ionic exchange by heavy metal on macroscopic pollutant transport is expressed through upscaling at the different scales of organization within the compacted bentonite. The anisotropy of the mesoscopic diffusion tensor increases with compaction and is well reproduced by using a random distribution of elongated clay platelets in the computations. The macroscopic diffusion tensor computed with elongated and flat ellipsoidal macropores is quasi-isotropic and agrees fairly well with experimental data. Confrontation with experimental breakthrough curves highlights the importance of a realistic description of texture evolution at both the nanometer (progressive interlamellar space reduction) and micrometer (aggregate splitting and inter-aggregate pores development) levels, in order to express the variations of hydraulic conductivity and surface complexation. The computed macroscopic diffusivity is not affected by the microstructure evolution, while pollutant transport appears to take place mainly by advection coupled with pollutant uptake.

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References

  • Appelo CAJ, Vinsot A, Mettler S, Wechner S (2008) Obtaining the porewater composition of a clay rock by modeling the in- and out-diffusion of anions and cations from an in-situ experiment. J Contam Hydrol 101:67–76

    Article  Google Scholar 

  • Baeyens B, Bradbury MH (1997) A mechanistic description of Ni and Zn sorption on Na-montmorillonite. Part I: titration and sorption measurements. J Contam Hydrol 27:199–222

    Article  Google Scholar 

  • Baeyens B, Bradbury MH (1997) A mechanistic description of Ni and Zn sorption on Na-montmorillonite. Part II: modelling. J Contam Hydrol 27:223–248

    Article  Google Scholar 

  • Baltean D (1999) Etude de la dispersion d’un contaminant passif dans les milieux multiporeux. Doctoral dissertation, University Pierre and Marie Curie, Paris, France

  • Baltean D, Lévy T, Balint S (2003) Diffusion-convection in a porous medium with impervious inclusions at low flow rates. Transp Porous Media 51:19–39

    Article  Google Scholar 

  • Bear J, Bachmat Y (1998) Introduction to modeling of transport phenomena in porous media. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Bouchelaghem F (2014) Multi-scale modelling of diffusive transport in compacted bentonite. In: Mathematics and engineering in marine and earth problems, Aveiro, Portugal, 22–25 July 2014, pp 28–33

  • Bouchelaghem F, Jozja N (2009a) Multi-scale study of permeability evolution of a bentonite clay owing to pollutant transport. Part I: model derivation. Eng Geol 108:119–132

    Article  Google Scholar 

  • Bouchelaghem F, Jozja N (2009b) Multi-scale study of permeability evolution of a bentonite clay owing to pollutant transport. Part II: application to an Mg-bentonite. Eng Geol 108:286–294

    Article  Google Scholar 

  • Bourg IC, Sposito G, Bourg ACM (2006) Tracer diffusion in compacted, water-saturated bentonite. Clays Clay Miner 54(3):363–374

    Article  Google Scholar 

  • Bourg IC, Sposito G, Bourg ACM (2008) Modeling the diffusion of \(\text{ Na }^{+}\) in compacted water-saturated Na-bentonite as a function of pore water ionic strength. Appl Geochem 23:3635–3641

    Article  Google Scholar 

  • Boving TB, Grathwohl P (2001) Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. J Contam Hydrol 53:85–100

    Article  Google Scholar 

  • Brigatti MF, Corradini F, Franchini GC, Mazzoni S, Medici L, Poppi L (1995) Interaction between montmorillonite and pollutants from industrial waste-waters: exchange of \(\text{ Zn }^{2+}\) and \(\text{ Pb }^{2+}\) from aqueous solutions. Appl Clay Sci 9:383–395

    Article  Google Scholar 

  • Chang HC (1983) Effective diffusion and conduction in two-phase media: a unified approach. AIChE J 29(5):846–853

    Article  Google Scholar 

  • Choi JW, Oscarson DW (1996) Diffusive transport through compacted Na- and Ca-bentonite. J Contam Hydrol 22:189–202

    Article  Google Scholar 

  • Comsol Multiphysics 3.5a (2009) Modeling guide, Comsol AB, Stockholm, Sweden

  • Eriksen TE, Jansson M, Molera M (1999) Sorption effects on cation diffusion in compacted bentonite. Eng Geol 54:231–236

    Article  Google Scholar 

  • Glaus MA, Baeyens B, Bradbury MH, Jakob A, Van Loon LR, Yaroshchuk A (2007) Diffusion of \(^{22}\text{ Na }\) and \(^{85}\text{ Sr }\) in montmorillonite: evidence of interlayer diffusion being the dominant pathway at high compaction. Environ Sci Technol 41:478–485

    Article  Google Scholar 

  • Ichikawa Y, Kawamura K, Nakano M, Kitayama K, Kawamura H (1999) Unified molecular dynamics and homogenization analysis for bentonite behavior: current results and future possibilities. Eng Geol 54:21–32

    Article  Google Scholar 

  • Ichikawa Y, Kawamura K, Fujii N, Kitayama K (2004) Microstructure and micro/macro-diffusion behavior of tritium in bentonite. Appl Clay Sci 26:75–90

    Article  Google Scholar 

  • Jozja N (2003) Etude de matériaux argileux albanais. Caractérisation multi-échelle d’une bentonite magnésienne. Doctoral dissertation, University of Orleans. http://tel.archives-ouvertes.fr/tel-00003740/en/

  • Jozja N, Baillif P, Touray JC, Pons CH, Muller F, Burgevin C (2003) Impacts multi-échelle d’un échange (Mg, Ca)-Pb et ses conséquences sur l’augmentation de la perméabilité d’une bentonite. C R Geosci 335:729–736

    Article  Google Scholar 

  • Jozja N, Baillif P, Touray JC, Muller F, Clinard C (2006) Incidence of lead uptake on the microstructure of a (Mg, Ca)-bearing bentonite (Prrenjas, Albania). Eur J Miner 18(3):361–368

    Article  Google Scholar 

  • Kemper WD, Maasland DEL, Porter L (1964) Mobility of water adjacent to mineral surfaces. Soil Sci Soc Am Proc 28:164–167

    Article  Google Scholar 

  • Kozaki T, Fujishima A, Sato S, Ohashi H (1998) Self-diffusion of sodium ions in compacted montmorillonite. Nucl Technol 121:63–69

    Article  Google Scholar 

  • Kozaki T, Inada K, Sato S, Ohashi H (2001) Diffusion mechanism of chloride ions in sodium montmorillonite. J Contam Hydrol 47:159–170

    Article  Google Scholar 

  • Kozaki T, Fujishima A, Saito N, Sato S, Ohashi H (2005) Effects of dry density and exchangeable cations on the diffusion process of sodium ions in compacted montmorillonite. Eng Geol 81:246–254

    Article  Google Scholar 

  • Kraepiel AML, Keller K, Morel FMM (1999) A model for metal adsorption on montmorillonite. J Colloid Interface Sci 210:43–54

    Article  Google Scholar 

  • Madsen FT (1998) Clay mineralogical investigations related to nuclear waste disposal. Clay Miner 33:109–129

    Article  Google Scholar 

  • Molera M, Eriksen T (2002) Diffusion of \(^{22}\text{ Na }^{+}\), \(^{85}\text{ Sr }^{2+}\), \(^{134}\text{ Cs }^{+}\) and \(^{57}\text{ Co }^{2+}\) in bentonite clay compacted to different densities: experiments and modeling. Radiochim Acta 90:753–760

    Article  Google Scholar 

  • Muurinen A, Olin M, Uusheimo K (1990) Diffusion of sodium and copper in compacted sodium bentonite at room temperature. In: Proceedings thirteen symposium on scientific basis for nuclear waste management. Materials Research Society, Pittsburgh, pp 641–647

  • Ochs M, Lothenbach B, Wanner H, Sato H, Yui M (2001) An integrated sorption–diffusion model for the calculation of consistent distribution and diffusion coefficients in compacted bentonite. J Contam Hydrol 47:283–296

    Article  Google Scholar 

  • Pusch R (1996) Microstructural modelling of smectitic buffers and backfills. SKB progress report U-96-28

  • Pusch R (1999) Microstructural evolution of buffers. Eng Geol 54:33–41

    Article  Google Scholar 

  • Sanchez-Palencia E (1980) Non-homogenous media and vibration theory. Lecture notes in physics, vol 127. Springer, Berlin

    Google Scholar 

  • Sato H (2005) Effects of the orientation of smectite particles and ionic strength on diffusion and activation enthalpies of \(\text{ I }^{-}\) and \(\text{ C }_{\text{ s }}^{+}\) ions in compacted smectite. Appl Clay Sci 29:267–281

    Article  Google Scholar 

  • Sato H, Suzuki S (2003) Fundamental study on the effect of an orientation of clay particles on diffusion pathway in compacted bentonite. Appl Clay Sci 23:51–60

    Article  Google Scholar 

  • Smith D, Pivonka P, Jungnickel C, Fityus S (2004) Theoretical analysis of anion exclusion and diffusive transport through platy-clay soils. Transp Porous Media 57:251–277

    Article  Google Scholar 

  • Souli H, Fleureau JM, Trabelsi Ayadi M, Besnard M (2008) Physicochemical analysis of permeability changes in the presence of zinc. Geoderma 145:1–7

    Article  Google Scholar 

  • Suzuki S, Sato H, Ishidera T, Fujii N (2004) Study on anisotropy of effective diffusion coefficient and activation energy for deuterated water in compacted sodium bentonite. J Contam Hydrol 68:23–37

    Article  Google Scholar 

  • Viraraghavan T, Kapoor A (1994) Adsorption of mercury from wastewater by bentonite. Appl Clay Sci 9:31–49

    Article  Google Scholar 

Download references

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  1. UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Universites, 75005, Paris, France

    Fatiha Bouchelaghem

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Correspondence to Fatiha Bouchelaghem.

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Bouchelaghem, F. Multi-scale Study of Pollutant Transport and Uptake in Compacted Bentonite. Math Geosci 50, 495–523 (2018). https://doi.org/10.1007/s11004-017-9724-8

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