Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

Landman, Anke Jannie; Johannsen, Klaus; Schotting, R. J.

doi:10.1016/j.advwatres.2007.05.016

Cited by 15 publications

(19 citation statements)

References 34 publications

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“…This has been confirmed for longitudinal dispersivity by Landman et al (2007a) and Watson et al (2002a).…”

Section: Resultssupporting

confidence: 69%

“…Watson et al (2002b) obtained a higher value for the case of longitudinal dispersion in a similar porous medium, e.g., m = 1.44. In the case of longitudinal dispersion, Landman et al (2007a) estimated a one order of magnitude reduction in the scaled macro-dispersivity for a relatively small gravity number, e.g., N g = 1.6. In the case of transverse dispersion for the same porous medium properties, this reduction is limited to 20% for a high gravity number, e.g., N g = 16.…”

Section: Density-affected Apparent Dispersivitymentioning

confidence: 99%

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Modeling Transverse Dispersion and Variable Density Flow in Porous Media

et al. 2008

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A two-dimensional numerical model is used to study the nonlinear behavior of density gradients on transverse dispersion. Numerical simulations are conducted using d 3 f , a computer code for simulation of density-dependent flow in porous media. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersivity. Changing salt concentration significantly affects fluid properties. This physical behavior of the fluid involves a non-linearity in modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from the tracer case due to the spatial variation of permeability, described by statistical parameters, at the local-scale. Indeed, the presence of vertical flow velocities induced by permeability variations is responsible for the reduction of the mixing zone width in the steady state in the case of a high density gradient. Uncertainties in the model simulations are studied in terms of discretization errors, boundary conditions, and convergence of ensemble averaging. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and limitations of the nonlinear model of Hassanizadeh (1990) and Leijnse (1995) (Adv Water Resour 18(4):203-215, 1995) in heterogeneous porous media are investigated. We found that the main cause of the nonlinear behavior of dispersion, which is the interaction between density contrast and vertical velocity, needs to be explicitly accounted for in a macro-scale model.

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“…This has been confirmed for longitudinal dispersivity by Landman et al (2007a) and Watson et al (2002a).…”

Section: Resultssupporting

confidence: 69%

Section: Density-affected Apparent Dispersivitymentioning

confidence: 99%

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

et al. 2008

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“…Modeling of non-dilute systems in porous medium systems has received considerable attention in the literature both because of intrinsic interest [e.g., 9, 12, 13, 19–21] and also because of the many important applications that fall into this category of model [e.g., 10, 11, 17]. A rich, recent experimental literature has contributed as well to helping better understand the physicochemical phenomena of interest in these complex systems.…”

Section: Discussionmentioning

confidence: 99%

“…The application of concern is the movement of a potentially concentrated solution consisting of a dense brine. This application has been the focus of significant recent research [e.g., 9, 12, 13, 19–21] with the appropriate model for flow and transport considered an open question. In addition, interesting aspects of this application can be considered and ultimately compared to laboratory data, while ignoring certain complicating aspects of closure that would emerge in the most general model.…”

Section: Model Closurementioning

confidence: 99%

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 5. Single-fluid-phase transport

Gray

Miller

2009

Advances in Water Resources

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This work is the fifth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.

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“…More broadly, unstable systems and problems with sharp interfaces continue to challenge and motivate research into improved numerical methods (Gotovac et al, 2007; Johannsen et al, 2006; Landman et al, 2007a; Younes et al, 2009). It seems clear that high-resolution simulation of dense, viscous fluids in complex porous medium systems remains difficult and that care is needed in applying existing simulators to such systems.…”

Section: Introductionmentioning

confidence: 99%

Dense, viscous brine behavior in heterogeneous porous medium systems

Wright

Pedit

Gasda

et al. 2010

Journal of Contaminant Hydrology

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The behavior of dense, viscous calcium bromide brine solutions used to remediate systems contaminated with dense nonaqueous phase liquids (DNAPLs) is considered in laboratory and field porous medium systems. The density and viscosity of brine solutions are experimentally investigated and functional forms fit over a wide range of mass fractions. A density of 1.7 times, and a corresponding viscosity of 6.3 times, that of water is obtained at a calcium bromide mass fraction of 0.53. A three-dimensional laboratory cell is used to investigate the establishment, persistence, and rate of removal of a stratified dense brine layer in a controlled system. Results from a field-scale experiment performed at the Dover National Test Site are used to investigate the ability to establish and maintain a dense brine layer as a component of a DNAPL recovery strategy, and to recover the brine at sufficiently high mass fractions to support the economical reuse of the brine. The results of both laboratory and field experiments show that a dense brine layer can be established, maintained, and recovered to a significant extent. Regions of unstable density profiles are shown to develop and persist in the field-scale experiment, which we attribute to regions of low hydraulic conductivity. The saturated-unsaturated, variable-density ground-water flow simulation code SUTRA is modified to describe the system of interest, and used to compare simulations to experimental observations and to investigate certain unobserved aspects of these complex systems. The model results show that the standard model formulation is not appropriate for capturing the behavior of sharp density gradients observed during the dense brine experiments.

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Density-dependent dispersion in heterogeneous porous media Part I: A numerical study

Cited by 15 publications

References 34 publications

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 5. Single-fluid-phase transport

Dense, viscous brine behavior in heterogeneous porous medium systems

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