Speed of free convective fingering in porous media

Abstract

[1] 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 ¼ 0.115 for DPF and f ¼ 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.

Effect of diffusing layer thickness on the density-driven natural convection of miscible fluids in porous media: Modeling of mass transport

“…The crosses (×) denote the experimental results for uniform flow (Sahimi 2001), and the lines are results from pore-scale modeling (Bijeljic and Blunt 2007). In a previous study , the correlation function of the onset time with Rayleigh number and the dispersion coefficient was derived for natural convection in porous media Ghesmat et al 2010;Hassanzadeh et al 2009;Hidalgo and Carrera 2009;Xie et al 2011). Because the thickness of the diffusing layer was constant in all experiments carried out in a previous study, the Rayleigh number was defined using the height of the packed bed H as the characteristic length.…”

“…Two main configurations (De Paoli et al 2016;Hewitt et al 2013) were considered in previous studies depending on the boundary condition at the bottom boundary, namely, the so-called "one-sided" cell, in which the Neumann boundary condition (i.e., no concentration gradient) is imposed at the bottom boundary (Pau et al 2010;Neufeld et al 2010;Slim 2014;Xu et al 2006;De Paoli et al 2017), and the so-called "two-sided" cell, in which the Dirichlet boundary condition (i.e., constant concentrations) is imposed at the top and bottom boundaries (Otero et al 2004;Hewitt et al 2012;Wen et al 2013). Based on theoretical analyses (Coskuner and Bentsen 1990;Hassanzadeh 2013, 2015;Rapaka et al 2008) , numerical simulations Ghesmat et al 2010;Hassanzadeh et al 2007;Hewitt et al 2012Hewitt et al , 2013Hidalgo and Carrera 2009;Hidalgo et al 2015;Otero et al 2004;Pau et al 2010;Riaz et al 2006;Shahraeeni et al 2015;Wen et al 2012;Xie et al 2011), and laboratory experiments including the construction of a nonlinear density profile of a mixture of miscible fluids (Backhaus et al 2011;Faisal et al 2015;Huppert and Neufeld 2014;Hidalgo et al 2012;Neufeld et al 2010;Wang et al 2016), mass transport is modeled as a function of Rayleigh number, because the time required for the shift in trapping mechanism scales with mass flux. In the Rayleigh-Taylor model, Rayleigh-Taylor instability (Kolditz et al 1998) occurs on the interface that separates a lighter fluid from a heavier one located above it, and the fluids convectively mix with each other (Manickam and Homsy 1995;…”

Effects of salinity variations on pore water flow in salt marshes

“…Notwithstanding this uncertainty, there is also a question concerning the possibility of flow instability in the form of fingering flow induced by the upward density gradients at the platform. Rapid penetration of fingers would lead to more extensive and faster solute transport [Simmons et al, 2001;Stevens et al, 2009;Woods and Carey, 2007;Xie et al, 2011]. For a marsh system, the effect of unstable fingers may lead to enhanced exchange between the marsh sediment and tidal water.…”

Effect of layered heterogeneity of a porous medium on density-driven natural convection

“…二酸化炭素気泡には界面張力に伴うトラップが働き，多孔質内部にトラップされる Suekane et al, 2008)． さらに， 二酸化炭素は徐々に地下水へと溶解する (Gilfillan et al, 2009;Iglauer, 2011;Lindeberg and Wessel-Berg, 1997;Lindeberg and Bergmo, 2003;Riaz and Cinar, 2014 Ghesmat et al, 2010;Hewitt et al, 2014;Hidalgo and Carrera, 2009;Pau et al, 2010;Xie et al, 2011)や実験 (Backhaus et al, 2011;Huppert et al, 1986;Neufeld et al, 2010) Fig. 2 Evolution of three-dimensional finger structure associated with the Rayleigh-Taylor convection in a porous medium with the layered structure.…”