Density-driven free convection in heterogeneous aquifers with connectivity features

Free convection usually happens in variable-density groundwater flow systems, and it favors contaminant transport by enlarging length scales and shortening timescales compared to advection and diffusion/dispersion alone. Previous studies have demonstrated that heterogeneity with multi-variate Gaussian distribution for logarithmic permeabilities (log₁₀k) plays an important role in the onset, growth, and/or decay of instability during the density-driven convective process. Nevertheless, the connectivity features (i.e., connected structures of extremely high/low-k values), which are common in natural aquifers, have received little attention. In this study, the classical problem of transient free convection has been modified and numerically simulated by Monte Carlo approach to investigate the effects of connectivity features in heterogeneity on the unstable convective processes. Results show that free convection is promoted by the connected high-k structures and retarded by the connected low-k structures during mainly the early-stage mass loading. The impacts of connectivity features tend to be amplified by higher variation in log₁₀k distributions, and can be secondarily influenced by correlation lengths and anisotropy. Under the multi-variate Gaussian assumption, the existence of connected high-k structures leads to underestimation of density-driven instability, in which the risk differs based on the statistics of permeability fields, metrics of interest and timeframe. This study highlights the importance of understanding connectivity features in heterogeneous geological media when assessing density-dependent solute transport in groundwater systems.