Selection of convection cells during convective instabilities in heterogeneous porous media: Application to heat flux determination and solute transport in geothermal structures

The existence of free convection in geological structures, which has become a matter of course in recent decades, is currently attracting renewed interest in geothermal energy for heat production and solute transport (Lithium). The rolls, and more generally the convection cells, that may develop, localize the thermal anomaly, drive the transport of heat and solutes, and control the characteristic time of thermal recharge. This process is due to an instability known as Rayleigh-Bénard in pure fluids, or Horton-Rogers-Lapwood in porous media. Its existence is characterized by the Rayleigh number Ra = αΔTgL3/νκ in pure fluid, where α denotes the coefficient of thermal expansion, L the characteristic length of the medium across which the temperature difference ΔT is applied, ν the kinematic viscosity of the fluid and κ the thermal diffusivity. For instability to occur, Ra must exceed a critical threshold.

Past works have all focused on determining the critical Ra by adapting the physics to the specific case of the porous medium, most often considering a homogeneous medium. In the unstable case, these approaches say little about the selection of unstable modes that will develop in the form of convection cells, likely to considerably increase local heat flow and solute transport in the medium. Using an approach combining theoretical analysis and simulation, the PhD candidate will study the coupling between the heterogeneity of the porous medium and hydrodynamic instability, in the presence of heterogeneities in permeability and/or in the local thermal diffusion coefficient. The effective transport coefficients obtained on a large scale will be characterized, as well as the important flow localization effects induced by the instability, likely to be of great importance for the setting up of geochemical transformations.

Keywords: Geothermal energy, Lithium, quantitative geosciences, physics, hydrodynamic instabilities, coupling, applied mathematics, programming, numerical simulation

• Academic supervisor    Dr Benoît NŒTINGER, IFPEN, ORCID: 0000-0002-4002-351X
• Doctoral School    ED398 GRNE, Sorbonne Université Nom, Université
• IFPEN supervisor    Dr Frederic DOUARCHE, ORCID: 0000-0001-5943-6405
• PhD location    IFPEN, Rueil-Malmaison, France  
• Duration and start date    3 years, starting in the fourth quarter 2024 (November 4)
• Employer    IFPEN
• Academic requirements    University Master degree in Physics, Applied mathematics, Quantitative geosciences     
• Language requirements    English level B2 (CEFR)

To apply, please send your cover letter and CV to the IFPEN supervisor indicated below.