Tracer sorption and macroscopic transport in clay nano-pores: a lattice-Boltzmann study

Document available in extended abstract form only. The Agence Nationale pour la gestion des Dechets Radioactifs (ANDRA) has been entrusted to find a safe solution for disposing of existing and future nuclear wastes. A prototype site has been considered for the waste disposal in a deep underground sedimentary geological formation. It is composed of clay minerals chosen, among other reasons, for their remarkable ability to limit radionuclide transport. Clay minerals are complex charged porous media characterized by heterogeneities at several length scales. They naturally occur as an assembly of few nano-meter-sized particles connected to form 10 to 100 nm interparticle pores containing water and ions. This intrinsically multi-scale structure, that gives the material its remarkable properties, makes the description of sorption and transport phenomena of transported ions particularly challenging. Experimental studies of water and ion transport through clays mostly consist in evaluating macroscopic effective transport coefficients like permeability or conductivity. They showed that the main transport mechanism is an effective diffusion that not only depends on particle charge but also on its chemical nature, or specificity. The goal of assessing the performance of clays as confinement barriers, particularly in the context of the geological disposal of nuclear waste, requires not only quantitative prediction of the retention and transport of species but also an understanding of the microscopic mechanisms underlying them. A successful approach has been to use numerical simulations via the Lattice-Boltzmann method (LB). It consists in making evolve populations describing the fluid at a level which is consistent with time and length-scales involved in transport properties, while still including a microscopic description of the phenomena. The transport of charged ions at the pore scale has recently been included in LB. In this method, the evolution of a tracer population is followed by making their associated moment to propagate between nodes of a lattice with a probability defined by evolution equations. This evolution with time gives access to macroscopic transport properties like the tracer effective diffusion coefficient. For now, however, the evolution equations do not satisfactorily account for sorption effects as they do not capture their chemical-specific nature. This is our goal to overtake this lack. We have introduced the specific adsorption and desorption mechanisms in the description of tracers transport. This has been done for neutral tracers, as a first step, by introducing a new possible event during the moment propagation of particles standing at solid-liquid interfacial nodes: they may adsorb (desorb) with a probability related to the adsorption and desorption rates of the underlying mechanism occurring at the molecular scale. In order to validate the method and to determine its numerical limitations, we have compared the Lattice-Boltzmann results to an analytical solution developed purposely in the simple geometry consisting of two parallel walls. This last solution comes from a stochastic approach of the longitudinal dynamics of a particle assumed to be driven by a Langevin equation accounting for bulk diffusion and for the adsorption-desorption rates defined above. It is finally shown how sorption phenomena affect the macroscopic transport properties of neutral tracers in geometries and regimes compatible with water in clay nano-pores. (authors)