Mixing and spreading of gravity currents in heterogeneous porous media

TL;DR

This study uses high-fidelity simulations to explore how heterogeneity in porous media affects gravity current mixing, spreading, and dissolution, revealing complex interactions between permeability patterns and flow dynamics.

Contribution

It provides new insights into the impact of heterogeneity, anisotropy, and density stratification on gravity current behavior in porous media through detailed numerical analysis.

Findings

Heterogeneity increases flow speed proportionally to Rayleigh number.

Unstable stratification accelerates convection onset, affecting dissolution.

Permeability variance enhances dissolution, with effects depending on flow conditions.

Abstract

We analyze the mixing, migration and spreading of a gravity current in a heterogeneous porous medium using high-fidelity numerical simulations. Heterogeneity is represented by log-normal permeability fields of varying correlation lengths and variance. Stable and unstable density stratification scenarios are considered through linear and non-monotonic density laws, respectively. Heterogeneity reduces dissolution and increases the speed of the gravity current proportionally to the Rayleigh number. In the unstable case, heterogeneity accelerates the onset of convection. Convection-driven dissolution slows down the gravity current and counteracts the dispersive effect of heterogeneity resulting in a narrower interface and higher dissolution than in the stable case. Permeability anisotropy reduces dissolution because of the barrier effect of low permeability regions, except when blobs of buoyant fluid are trapped in low permeability structures and rapidly dissolve. The variance of the log-permeability field enhances dissolution. However, the homogeneous case outperforms heterogeneous cases except when Rayleigh number is small. This suggest an interaction between the size of the instabilities, the correlation length of the permeability field and the dispersive and barrier effects of the permeability field that controls dissolution efficiency.