InterPore2021

Rayleigh-Taylor Instability in 2D and 3D Dispersive Porous Medium

4 Jun 2021, 15:30

15m

Oral Presentation (MS8) Mixing, dispersion and reaction processes across scales in heterogeneous and fractured media MS8

Speaker

Dr Jayabrata Dhar (Univ. Rennes, CNRS, G´eosciences Rennes (UMR6118), 35042 Rennes, France)

Description

CO$_2$ injected in deep saline aquifers for subsurface carbon sequestration is supercritical (sCO$_2$), and thus less dense than the resident brine. The plume of sCO$_2$ to the top of the formation and widens under the cap rock, where it is placed above the brine. Due to its partial solubility in the brine, sCO$_2$ dissolves into it, leading to the formation, at its interface with the brine, of an aqueous mixture which is denser than the brine. A gravitational instability then develops, and the convection that ensues allows dissolved CO$_2$ to be transported deeper into the formation, where it remains trapped by gravity. The convection also puts the sCO$_2$ with CO$_2$-devoid brine, which nurtures the dissolution process. This convective dissolution in essence results from the coupling between dissolution of sCO$_2$ into the aqueous phase, buoyancy-triggered flow of the latter phase, and transport of the dissolved CO$_2$ within it. When modeled at the continuum (i.e., Darcy) scale, the solute transport equation must take into account dispersion. Continuum scale numerical simulation of convective dissolution has attracted much attention ; many of these previous studies have considered simple diffusive transport (i.e., a constant diffusion/dispersion coefficient in the transport equation), and few of them have tackled three-dimensional (3D) geometries. We present a numerical investigation, based on the open source numerical toolbox OpenFOAM associated to a custom-written solver relying on the stream function, of convective dissolution in two-dimensional (2D) and 3D geometries, taking into account dispersive transport through a classic anisotropic dispersion tensor proportional to the local Darcy velocity and featuring two main parameters: (i) the dispersion's strength (as compared to molecular diffusion), and (ii) the ratio of the longitudinal dispersivity to the transverse dispersivity. A systematic study was performed as a function of these two parameters and of the Rayleigh number, which quantities the relative importance of convection-controlled advective transport and dispersive transport. The convective dissolution process is characterized in terms of the onset times of the linear instability and of nonlinear convection, the number density of convective fingers, and the associated flux of dissolved CO$_2$. The onset time of nonlinear convection is found to strongly depend on the Rayleigh number, but not of the intensity of dispersion. However the two parameters characterizing dispersion have a strong influence on the global time scale of CO$_2$ dissolution. We also discuss the differences in convective finger structures between the 2D and 3D geometries, and their consequences on the convective dissolution process.