Mathematical Geosciences

, Volume 50, Issue 5, pp 495–523 | Cite as

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

  • Fatiha Bouchelaghem
Special Issue


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.


Multi-scale transport model Interlamellar and inter-aggregate pores Effective diffusion tensor Finite element simulation Breakthrough curves 


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© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’AlembertSorbonne UniversitesParisFrance

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