Buoyancy-driven natural convection in porous media, known as Rayleigh-Darcy convection (RDC), is ubiquitous in geological and engineering systems, where it is induced by natural or anthropogenic temperature and concentration gradients under which higher density fluid lays above lower density fluid. Although medium heterogeneity is widely recognized as a key factor governing subsurface fluid flow, its role in regulating RDC remains poorly understood. Using high-resolution numerical simulations over a broad range of Rayleigh numbers ($Ra$), we show that the interplay between the permeability correlation length ($\mathcal{L}$) and the characteristic flow-structure length fundamentally controls RDC dynamics. In the stable convective-cell regime ($Ra<1300$), $\mathcal{L}$ constrains the horizontal extent of convection cells and therefore modifies transport efficiency. In the transition regime ($1300\le Ra\le 7500$), heterogeneity disrupts the transverse coherence of the boundary layers and suppresses the merging of microplumes into large-scale megaplumes, which significantly amplifies convective instability and enhances transport. In the chaotic regime ($Ra>7500$), heterogeneity with small $\mathcal{L}$ has a negligible effect, whereas that with large $\mathcal{L}$ regulates the boundary-layer thickness through local permeability variations. These results provide a unified physical framework for understanding how heterogeneity regulates buoyancy-driven convection in porous media.

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• Convection
• Convection in porous media
• Flows in porous media
• Geophysical fluid dynamics
• Porous media
• Direct numerical simulations