Reconciling asymmetry observations in the permeability tensor of digital rocks with symmetry expectations

Lesueur, M.J.B.P.; Guével, Alexandre; Poulet, Thomas

doi:10.1016/j.advwatres.2022.104334

Reconciling asymmetry observations in the permeability tensor of digital rocks with symmetry expectations

Title

Reconciling asymmetry observations in the permeability tensor of digital rocks with symmetry expectations

Author

Lesueur, M.J.B.P. (TU Delft Applied Mechanics; University of Western Australia)
Guével, Alexandre (Duke University)
Poulet, Thomas (CSIRO Mineral Resources)

Date

2022

Abstract

Modelling anisotropic flow in rocks requires their full permeability tensor. While theories derived from the upscaling of Stokes flow to Darcy's law may justify the tensor symmetry, homogenisations from micro-scale rock samples often return a non-zero level of asymmetry. Since most studies dismiss these controversial observations as numerical errors, this contribution looks more closely at the physical possibility of such behaviour. Asymmetry of the permeability tensor, which induces a rotatory flow, is manifested at the micro-scale by tortuous streamlines. Conversely, when considering a larger scale – above the Representative Elementary Volume for permeability – these tortuous paths do not statistically affect the flow direction any longer. At this point, the homogenisation of Stokes flow to Darcy's law reaches its domain of validity. We show that the asymmetry in the permeability tensor vanishes for this scale separation, regardless of the choice of boundary conditions unlike previously thought, if the boundary layer effect is disregarded.

Subject

Asymmetry
MicroCT-scan
Permeability tensor
Upscaling

To reference this document use:

http://resolver.tudelft.nl/uuid:b2c7f773-ddd5-46be-910f-2fe708240530

DOI

https://doi.org/10.1016/j.advwatres.2022.104334

ISSN

0309-1708

Source

Advances in Water Resources, 170

Part of collection

Institutional Repository