Plane gravity currents in heterogeneous porous media

Gravity currents (GCs) in porous media are strongly influenced by the spatial variability of hydraulic conductivity, yet most modeling efforts assume homogeneous conditions. In this work, we develop and validate a MODFLOW–NWT numerical model capable of simulating Newtonian gravity-current propagation in both homogeneous and heterogeneous porous media. The model is first benchmarked against classical similarity solutions, showing excellent agreement as the current evolves in time. We then investigate the influence of heterogeneity by generating ensembles of Gaussian and non-Gaussian hydraulic-conductivity fields with varying log10 𝐾 variance and for different anisotropy ratios. For each scenario, 100 realizations are simulated to quantify the effects of spatial variability on GC behavior. Results demonstrate that heterogeneity significantly alters the propagation dynamics, causing individual fronts to diverge from the homogeneous prediction and increasing uncertainty over time. On average, both Gaussian and non-Gaussian heterogeneity yield faster front advancement than the homogeneous case. Probability maps reveal widening uncertainty intervals with increasing variance and anisotropy ratio, with Gaussian fields producing more stretched profiles than their non-Gaussian counterparts. Because nonGaussian fields more closely reflect geological facies structures, they provide a more realistic basis for assessing prediction errors. These findings underscore the importance of incorporating geological heterogeneity into GC modeling, particularly for applications such as aquifer remediation and CO2 sequestration.