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A methodology to calibrate and to validate effective solid potentials of heterogeneous porous media from computed tomography scans and laboratory-measured nanoindentation data

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Abstract

Built on the framework of effective interaction potentials using lattice element method, a methodology to calibrate and to validate the elasticity of solid constituents in heterogeneous porous media from experimentally measured nanoindentation moduli and imported scans from advanced imaging techniques is presented. Applied to computed tomography (CT) scans of two organic-rich shales, spatial variations of effective interaction potentials prove instrumental in capturing the effective elastic behavior of highly heterogeneous materials via the first two cumulants of experimentally measured distributions of nanoindentation moduli. After calibration and validation steps while implicitly accounting for mesoscale texture effects via CT scans, Biot poroelastic coefficients are simulated. Analysis of stress percolation suggests contrasting pathways for load transmission, a reflection of microtextural differences in the studied cases. This methodology to calibrate elastic energy content of real materials from advanced imaging techniques and experimental measurements paves the way to study other phenomena such as wave propagation and fracture while providing a platform to fine-tune effective behavior of materials given advancements in additive manufacturing and machine learning algorithms .

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Acknowledgements

This work was funded by X-Shale Hub: the Science and Engineering of Gas Shale, a collaboration between Shell, Schlumberger, and the Massachusetts Institute of Technology, enabled through MIT’s Energy Initiative. Authors would like to acknowledge Vincent Richefeu (Universite Joseph Fourier), Jean-Yves Delenne (Montpellier SupAgro) and Saeid Nezamabadi (Universite de Montpellier) who provided the backbone of the LEM code used for simulations. FR would like to acknowledge the support of the ICoME2 Labex (ANR-11-LABX-0053) and the A\(*\)MIDEX projects (ANR-11-IDEX-0001-02) cofunded by the French program Investissements d Avenir, managed by the French National Reseach Agency (ANR).

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Siavash Monfared, Hadrien Laubie & Franz-Josef Ulm

  2. 〈MSE〉2, UMI 3466 CNRS-MIT Energy Initiative, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Farhang Radjai & Roland Pellenq

  3. LMGC, UMR-5508 CNRS, Universite de Montpellier, 163 Rue Auguste Broussonnet, 34090, Montpellier, France

    Farhang Radjai

  4. Department of Civil, Environmental and Architectural Engineering, Colorado University, Boulder, CO, 80309, USA

    Mija Hubler

  5. CINaM, CNRS, Aix Marseille Universite, Campus de Luminy, 13288, Marseille Cedex 09, France

    Roland Pellenq

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  1. Siavash Monfared
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Correspondence to Siavash Monfared.

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Monfared, S., Laubie, H., Radjai, F. et al. A methodology to calibrate and to validate effective solid potentials of heterogeneous porous media from computed tomography scans and laboratory-measured nanoindentation data. Acta Geotech. 13, 1369–1394 (2018). https://doi.org/10.1007/s11440-018-0687-9

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