Density-dependent dispersion in heterogeneous porous media Part II: Comparison with nonlinear models

Landman, Anke Jannie; Schotting, R. J.; Егоров, А. Г.; Demidov, Denis

doi:10.1016/j.advwatres.2007.05.017

Cited by 14 publications

(26 citation statements)

References 25 publications

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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%

“…These efforts have included posited non-linear dispersion relationships [9] and multiscale models based upon homogenization [13]. None of the models advanced to date appear to provide a first-principles based approach capable of fitting the observed data for dispersion in a non-dilute system under varying velocities, mass fractions, and media conditions.…”

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%

“…Although some approaches to non-Fickian dispersion have been proposed [e.g., 8, 9, 13], an apparent void exists in deriving macroscale species transport models based upon a microscale flow and transport equations, appropriate microscale thermodynamics, rigorous averaging of conservation and thermodynamic equations that maintains consistency across scales, and a general, consistent procedure for closing the models at the macroscale. In fact, no such macroscale models with a strong theoretical foundation have been derived for either the non-dilute situation or the dilute limit.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Model Closurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…In particular, this is true when the main flow direction is perpendicular to the gravity direction. As illustrated by Landman et al (2007b), the increase in heterogeneity acts in an opposite manner. • The effect of gravity on transverse dispersion, i.e., D T , is more pronounced when Pe T and N g are large.…”

Section: Density-affected Apparent Dispersivitymentioning

confidence: 95%

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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Effects of Heterogeneity, Connectivity, and Density Variations on Mixing and Chemical Reactions Under Temporally Fluctuating Flow Conditions and the Formation of Reaction Patterns

Pool

Dentz

2018

Water Resources Research

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Solute mixing, spreading, and fast chemical reactions in aquifers are strongly influenced by spatial variability of the hydraulic properties, temporal flow fluctuations, and fluid density differences. We study the coupling of heterogeneity, transient forcing, and density‐driven flow on mixing and chemical reactions between two fluids of different density under a stable stratification. We consider the reaction of the fast dissolution of calcite. We find that temporal fluctuations and heterogeneity cause strong local enhancement of the mixing and reaction rates and this impact increases with the degree of connectivity of hydraulic conductivity. The global mixing and reactivity, however, are on the order of or smaller than their homogeneous counterparts due to heterogeneity‐induced fluid segregation. The local maxima of the mixing and reaction rates are found to be located around strongly stretched regions corresponding to high velocity zones where dispersive mass transfer mechanisms are increased by dispersion. We also find that density variations compress the interface, which in turn emphasizes local maxima in mixing and reaction rates. Numerical results provide evidence that the stretching of the interface induced by spatial heterogeneity and transient effects coupled with density variations lead to the formation of complex patterns of reactive hotspots, zones of enhanced reaction efficiency, and that its distribution is directly linked to the deformation properties and topology of the flow field. These results provide new insights into the role of spatial and temporal variability on the mixing and reaction efficiency as well as the formation of reactive geochemical patterns in actual environmental systems.

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Density-dependent dispersion in heterogeneous porous media Part II: Comparison with nonlinear models

Cited by 14 publications

References 25 publications

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

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

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

Effects of Heterogeneity, Connectivity, and Density Variations on Mixing and Chemical Reactions Under Temporally Fluctuating Flow Conditions and the Formation of Reaction Patterns

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