A new model for predicting fluid flow through porous materials

What is it about?

Our paper investigates natural convection driven by species concentration gradients within porous media. Traditionally, scientists rely on the Darcy-Oberbeck-Boussinesq (DOB) equations for macroscopic simulations, which assume that if the Darcy number is small, macroscopic diffusion can be safely neglected. We demonstrate that this underlying assumption is incorrect, as macroscopic diffusion is actually of the same order as the buoyancy force and Darcy drag. To solve this, we propose a 'two-length-scale diffusion' (TLSD) model that incorporates a macroscopic diffusion term determined by both the pore scale and the macroscopic length scale, yielding highly accurate mass concentration and velocity data compared to expensive direct numerical simulations (DNS).

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Photo by Reza Amanda on Unsplash

Photo by Reza Amanda on Unsplash

Why is it important?

Natural convection in porous media is a fundamental process underlying critical environmental engineering technologies, including the long-term storage of carbon dioxide in deep saline aquifers, geothermal energy extraction, and large-scale thermal-energy storage. Standard DOB models often fail to capture real-world physics, falsely predicting a linear scaling of the mass transfer rate (Sherwood number) at high Rayleigh numbers. Our TLSD model successfully captures the nonlinear scaling of the Sherwood number at high porosities and accurately reflects how mass transfer increases with decreasing porosity and increasing Schmidt numbers. By providing a computationally efficient macroscopic model that successfully mirrors the physics of pore-resolved DNS, we give engineers a much more reliable tool for designing systems that combat climate change.

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