Effects of Pore-scale on the Macroscopic Properties of Natural Convection in Porous Media

TL;DR

This study uses direct numerical simulations to reveal that pore-scale properties significantly influence the macroscopic natural convection behavior in porous media, challenging traditional Darcy-based models.

Contribution

It demonstrates that pore size and porosity affect convection scaling laws, providing a more accurate understanding of flow in porous media beyond Darcy equations.

Findings

Boundary layer thickness depends on pore size.

Sherwood number scales nonlinearly with Rayleigh number.

Porosity influences Sherwood number at high Rayleigh numbers.

Abstract

Natural convection in porous media is a fundamental process for the long-term storage of CO2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy-Oberbeck-Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number (Ra) for high values of Ra (Ra>>1,300). Here, we perform Direct Numerical Simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto- plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.