Three-dimensional structure of natural convection in a porous medium: Effect of dispersion on finger structure

Wang, Lei; Nakanishi, Yuji; Hyodo, Akimitsu; Suekane, Tetsuya

doi:10.1016/j.ijggc.2016.08.018

Cited by 59 publications

(91 citation statements)

References 43 publications

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“…Also, Figures 2e and 2f show that the finger spacing, , does not vary significantly with Δ and increases monotonically with increasing k. Figures 3a to 3c show the same results in terms of standard dimensionless quantities and demonstrate that the scaling does not collapse the data into unique functions of Ra m . Fitting a power law for the flux to the entire data set shows a sublinear scaling, Sh ∼ Ra 0.75 m (see Figure S10), similar to previous experiments (Neufeld et al, 2010;Wang et al, 2016). However, there is a clear distinction in behavior, if results are grouped by d (Figure 3a) or by Δ (Figure 3b).…”

Section: Experimental Setup and Resultsmentioning

confidence: 87%

Effect of Dispersion on Solutal Convection in Porous Media

Liang

Wen

Hesse

et al. 2018

Geophysical Research Letters

109

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Solutal convection in porous media is thought to be controlled by the molecular Rayleigh number, Ra m , the ratio of the buoyant driving force over diffusive dissipation. The mass flux should increase linearly with Ra m and the finger spacing should decrease as Ra −1∕2 m. Instead, our experiments find that flux levels off at large Ra m and finger spacing increases with Ra m . Here we show that the convective pattern is controlled by a dispersive Rayleigh number, Ra d , balancing buoyancy and dispersion. Increasing the bead size of the porous medium increases Ra m but decreases Ra d and hence coarsens the pattern. While the flux is predominantly controlled by Ra m , the anisotropy of mechanical dispersion leads to an asymmetry in the pattern that limits the flux at large bead sizes.Plain Language Summary Pattern formation in simple physical systems is intriguing, and convection in porous media is an example that was thought to be well understood. Convection is controlled by the balance between buoyant driving forces and dissipative mechanisms such as diffusion that smear out the concentration and hence density differences. Here we use simple laboratory experiments to show that the convective pattern is controlled by a different process than previously thought. A Rayleigh number based on mechanical dispersion, which is independent of fluid properties, predicts the flow pattern of solutal convection in bead packs.

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Section: Experimental Setup and Resultsmentioning

confidence: 87%

Effect of Dispersion on Solutal Convection in Porous Media

Liang

Wen

Hesse

et al. 2018

Geophysical Research Letters

109

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“…Assuming the steady state in the distribution of the concentration in the most extended finger, we evaluated the transverse dispersion coefficient by mass conservation for cylindrical control volume of the finger. Details of the scheme used to estimate the transverse dispersion are found in Nakanishi et al (2016) and Wang et al (2016). Figure 6 plots the transverse dispersion against the Péclet number defined as Pe = (vdp)/(φD0), where v is the finger extension velocity.…”

Section: Onset Timementioning

confidence: 99%

“…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;…”

Section: Introductionmentioning

confidence: 99%

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

Wang¹,

Nakanishi²,

Teston³

et al. 2018

JFST

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In this study, density-driven natural convection in porous media associated with Rayleigh-Taylor instability was visualized by X-ray computed tomography to investigate the effect of the thickness of the diffusing interface on convection. The thickness of the interface was changed by molecular diffusion with time, and the effective diffusivity in a porous medium was estimated. Compared with the thick interface, for the thin interface, many fine fingers formed and extended rapidly in a vertical direction. The onset time of natural convection increased proportionally with the thickness of the interface, being correlated with Rayleigh number and Péclet number. For the thinner initial interface, the finger number density increased more rapidly after onset and reached a higher value. Next, we discussed the mass transport in Rayleigh-Taylor convection to show how dispersion affects mass transport based on finger extension velocity and concentration in fingers. Increasing the interface thickness delayed the onset of convection, while the finger extension velocity remained the same. The reduced finger extension velocity changed nonlinearly with the Péclet number, reflecting the effect of dispersion. High transverse dispersion and longitudinal dispersion quickly reduced finger density. Transverse dispersion between ascending and descending fingers decreased the density; the density decreased linearly along the finger on both sides of the symmetric plane. As a result, the Sherwood number was proportional to the Rayleigh number, whereas the coefficient changed nonlinearly with Péclet number because of dispersion, reflecting the nonlinear dependences of the reduced velocity and the reduced density difference on Péclet number.

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“…Spreading delineates the spatial extent of a solute plume and is important in a number of engineering and scientific fields. It describes the movement of dissolved CO 2 after subsurface injection [ Xiao et al ., ; Wang et al ., ; Nakanishi et al ., ], and the extent of a contaminant groundwater plume [ Mayer et al ., ; Kitanidis and McCarty , ]. Mixing describes dilution, or the interaction of separate chemical components by concentration gradients and diffusion.…”

Section: Introductionmentioning

confidence: 99%

Observations of the impact of rock heterogeneity on solute spreading and mixing

Boon

Bijeljic

Krevor

2017

Water Resources Research

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Rock heterogeneity plays an important role in solute spreading and mixing in hydrogeologic systems. Few observations, however, have been made that can spatially resolve these processes in 3-D, in consolidated rocks. We make observations of the spatially resolved steady state concentration of a sodium iodide solute while flowing brine through cylindrical rock cores using X-ray CT imaging. Three rocks with an increasing level of heterogeneity are chosen: a Berea sandstone, a Ketton carbonate, and an Indiana carbonate. The impact of heterogeneity on solute transport is analyzed by: (1) quantifying spreading and mixing using metrics such as the transverse dispersion coefficient, the dilution index, the reactor ratio, and the scalar dissipation rate and (2) visualizing and analyzing flow structures such as meandering, flow-focusing, and flow-splitting using isoconcentration contour maps. The transverse dispersion coefficient, D t , and the variation in D t throughout the rock core, increases with Pecl et number (Pe) and rock heterogeneity. The reactor ratio indicates that mixing is Fickian for the Berea sandstone and Ketton carbonate, but diverges for the Indiana carbonate. The temporal evolution of the scalar dissipation rate, a measure of the mixing rate, remains close to that of Fickian mixing for the Berea and Ketton rocks but not for the Indiana. Heterogeneous rock features are observed to cause meandering, focusing, or splitting of the plume depending on Pe.

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Three-dimensional structure of natural convection in a porous medium: Effect of dispersion on finger structure

Cited by 59 publications

References 43 publications

Effect of Dispersion on Solutal Convection in Porous Media

Effect of Dispersion on Solutal Convection in Porous Media

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

Observations of the impact of rock heterogeneity on solute spreading and mixing

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