Speed of free convective fingering in porous media

Previous studies have examined free convection and the development of fingers in variable-density groundwater environments, but the penetration rates of fingering processes (i.e., fingering speeds) have not been systematically investigated. Unlike common groundwater processes driven by advection and whose flow rates may be computed using Darcy's law, fingering speeds are far less intuitive. In this study, fingering speeds are analyzed in a natural convection system using two measurable diagnostics: deepest plume front (DPF, providing upper bounds on plume speeds) and vertical center of solute mass (COM, providing global speeds). The permeability, porosity, and dispersion (longitudinal and transverse dispersivities) were varied using a perturbation-based stochastic approach to investigate their effects on fingering speeds. Modeling results show that the characteristic convective velocity, commonly used to represent theoretical fingering speeds, needs to incorporate effective porosity in a similar fashion to hydraulically driven average linear velocity and needs to be further adjusted by multiplying by a corrective factor f for predicting various fingering behaviors (approximately f = 0.115 for DPF and f = 0.034 for COM) in this study. A stochastic analysis demonstrates small variability in the time-varying speed of both DPF and COM between model realizations. This indicates that reproducing fingering speeds is likely to be achieved and that one single realization can adequately produce f for the characteristic convective velocity. This study also identifies that f for speeds of DPF is most likely to be constrained by (0.115, 1.000), which is extremely useful in the design of laboratory and field experimentation.