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Two dimensional relaxation of gravitational instability in porous media

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posted on 24.11.2021, 13:30 by Niloy DeNiloy De
Due to its central interest in Carbon Capture and Storage (CCS), gravitational instability has been extensively studied numerically, primarily in (2D) bi-dimensional configuration. Likewise, several experimental studies have been performed in model 2D geometries (HeleShaw cell) where dispersive nature of the medium was overlooked. We propose here a preliminary study that aims at accounting for the pore-scale effects such as mixing and dispersion. We first study the behaviour of a solutal plume generated in a Hele-Shaw cell from an extended source. Doing so, we introduce a new length scale in the system, a first step towards more complex multi-scale geometries. The CO2-concentration is measured by using a pH-sensitive dye and the velocity field is measured by utilizing standard particle image velocimetry (PIV). Concentration and velocity fields are scrutinized over one order of magnitude in Rayleigh number (Ra) and for two different values of the Darcy number (Da). A semi-empirical relationship linking Nusselt to the Darcy and Rayleigh numbers number is proposed. Two regimes, Ra Da < 1 and Ra Da > 1, are observed for which the scaling laws for velocity and concentration are presented. While the concentration field measurements are marred by a large uncertainty due to the logarithmic nature of the pH-concentration relationship, the experimental data obtained from the PIV measurements show a good agreement with the numerical results. We next address more complex (multiscale) 2D porous geometries where pore-scale effects are explicitly taken into account. To do so, we study gravitational instability in bespoke 2D micromodels, the core of which is made from Norland optics 63 or NOA63, a UV curable photo resin which is impermeable to gases. We describe a soft-lithography repeatable protocol suitable for the manufacturing of symmetric regular patterns of cylindrical pillars sandwiched between two vertical plane walls, with pillars radii ranging from R = 200 to 400 µm, and edge-to-edge distances (between pillars) ranging from R to 4R. We present an empirical correlation bridging the permeability of the system with the porosity and specific surface area of the 2D micromodels. The wavenumber of gravitational instability induced by the dissolution of carbon dioxide is found to be larger than the theoretical value obtained for Hele-Shaw cells (of equivalent permeability) possibly due to wavelength locking by the porous pattern. The time profile of the mass flux indicates a clear diffusive regime of dissolution despite the presence of a convective dissolution fingering pattern.


Loughborough University

Univerisity Rennes, France

Aix-Marseille University, France



  • Mechanical, Electrical and Manufacturing Engineering


Loughborough University

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© Niloy De

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A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of the degree of Doctor of Philosophy of Loughborough University.




Francois Nadal

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