Application of high performance computation methods ...

Application of high performance computation methods to the study of transfers in complex 3D porous media L. Orgogozoa, R. Martina, C. Noiriela, F. Golfierb, R. Guibertc, G. Debenestc, M. Quintardc,d a GET

(Géosciences Environnement Toulouse), Observatoire Midi-Pyrénées, Université Paul Sabatier, University of Toulouse, 14 avenue Edouard Belin, 31400 Toulouse, France b

Géo-Ressources, UMR 7359 CNRS/UL/CREGU, ENSG, 2 rue du doyen Marcel Roubault, TSA 7060, 54518 Vandoeuvre-Lès-Nancy, France

c University

of Toulouse, INPT, UPS, IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France d CNRS,

IMFT, F-31400 Toulouse, France

Context : study of the reactive transport in porous media (biodegradation, precipitation/dissolution …) – estimation of effective transport parameters, interpretation of laboratory experiments (i) Bioremediation methods are operative techniques used to mitigate groundwater pollution by organic pollutants. Large scale models of contaminant transport which take into account the complexity of transport phenomena at the pore-scale are needed (e.g., Sturmann et al., J Contam Hydro 1995).

Problematic

Our approach : use of massively parallel computation techniques to calculate velocity fields in complex 3D pore geometry with acceptable computation times Flow in the pore space of a porous medium (permeability of the biofilm is neglected) : low Reynolds number, Stokes equation in the fluid phase.

(ii) A key point in the development of such large scale models is the evaluation of effective transport parameters (dispersion, reaction rate, …) at the scale of interest by taking into account the presence of biofilm within the pore space. Among others, volume averaging method has been used to reach such a goal (e.g.,

−∇ + µ∆v = −∇−pρ+ ∆

Orgogozo et al., Adv Water Resour 2010, Davit et al., Adv Water Resour 2010, Wood et al., IJEWM 2011).

(i) Numerical resolution with an Uzawa algorithm (periodic BC at the domain frontier and no slip conditions at the internal fluid-solid and fluid biofilm interfaces).

(iii) The acquisition of real porous media 3D structures is now possible in laboratory experiments (e.g., Iltis et al., Water Resour Res 2011, Davit et al., J Microsc-Oxford 2011).

(ii) Discretization : finite volumes.

(iv) The use of volume averaging method in real cases requires to be able to compute velocity field in porous media hosting biofilm phases, with potentially complex 3D structures (e.g., Golfier et al., Adv Water Resour 2009). There is a need to compute accurate velocity fields in such realistic 3D porous medium structures to interpret laboratory experiment and thus going further in our understanding of the relations between small scale phenomena and large scale effective parameters in bioremediation processes.

(iii) Linear systems inversions : SOR algorithm. Golfier et al., Adv Water Resour 2009 : (a) Experimental column with a 250 µm diameter bead pack containing S. onidensis – (b) Unit cell constructed from MRI measurements. Isosurfaces for the solid (red) and biofilm (blue) phases are illustrated.

Davit et al., J Microsc-Oxford 2011 : 3D surface reconstruction of a biofilm (soft blue-green) growing on a polyamid bead (dark) – X-ray tomography with BaSO4 as contrast agent.

(iv) MPI parallelization with domain decomposition in the principal direction of flow. Validation : code to code comparison with OpenFOAM 2.2 : less than 2% of differences on computed permeabilities with both approaches

Application to a 3D realistic porous medium obtained from MRI (geometry based on the one considered in Golfier et al., Adv Water Resour 2009)

L=1,25.10-3 m

Fluid phase

Solid phase

Biofilm phase

Goal : compute a velocity field Study of convergence : Criteria : mean velocity magnitude Error : less than 15% of relative difference wih the mesh dependency – free and precision dependency – free solution Needed mesh : 640*640*640 (~260 millions) cells Computed permeability : 2.10-13 m2

x z y

A view of the field of velocity component in the principal direction of flow (z)

Study of 3D geometry of porous media obtained by X-ray tomography (calcite precipitation experiments in porous media, data from Noiriel et al., CHEM GEOL 2012) Goal : samples = REV ? Permeabilities ? Study of convergence : Before After precipitation precipitation

Criteria : mean velocity magnitude Error : less than 5% of relative difference wih the mesh dependency – free and precision dependency – free solution Needed mesh : 250*250*250 (~16 millions) cells

25x25x25 Before precipitation experiment 50x50x50 Subsampling

250 cells = 4,46 mm

100x100x100

150x150x150 Total sample

After precipitation experiment

= −

200x200x200

The samples are acceptable REV of the considered porous media

Perspectives : parallelization of upscaling codes for transport itself and application to dedicated laboratory biofilm growth and biodegradation experiments