A theory of macrodispersion for the scale-up problem

Glimm, James; Lindquist, W. Brent; Pereira, Felipe; Zhang, Qiang

doi:10.1007/bf00613272

Cited by 88 publications

(69 citation statements)

References 16 publications

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“…Note that the approximation for 1 v in equation (12) has been shown to work well for the range of variance of hydraulic conductivity <1.0, as considered here (e.g., Bellin et al, 1992;Glimm et al, 1993;Hsu et al, 1996). Highly heterogeneous porous media is outside the scope of this paper.…”

Section: Using Higher-order Approximationmentioning

confidence: 92%

A Note on Upscaling Retardation Factor in Hierarchical Porous Media with Multimodal Reactive Mineral Facies

et al. 2015

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We present a model for upscaling the time-dependent effective retardation factor, ) ( t R , in hierarchical porous media with multimodal reactive mineral facies. The model extends the approach by Deng et al. (2013) in which they expanded a Lagrangian-based stochastic theory presented by Rajaram (1997) in order to describe the scaling effect of ) ( t R . They used a firstorder linear approximation in deriving their model to make the derivation tractable. Importantly, the linear approximation is known to be valid only to variances of 0.2. In this article we show that the model can be derived with a higher-order approximation, which allows for representing variances from 0.2 to 1.0. We present the derivation, and use the resulting model to recalculate ) ( t R for the scenario examined by Deng et al. (2013).

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Section: Using Higher-order Approximationmentioning

confidence: 92%

A Note on Upscaling Retardation Factor in Hierarchical Porous Media with Multimodal Reactive Mineral Facies

et al. 2015

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“…The constantby-parts absolute permeability field is defined on a 64 versus 32 versus 32 uniform grid. Each layer is taken to be (the log of) a realization of a (Gaussian) random fractal field (see Glimm et al, 1992Glimm et al, , 1993 with moderately large heterogeneity strength where the mean permeability value is prescribed as 100 millidarcy. The data below are held fixed in all flow studies:…”

Section: Numerical Experimentsmentioning

confidence: 99%

Carbon Sequestration Monitoring Activities

Frost¹

2010

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“…0. Bellin et al, 1992;Follin, 1992;Glimm et al, 1993;Rubin, 1997]. Note that these studies have been conducted by using Gaussian models of spatial variability and that slightly different limits of validity have been suggested because of different acceptance criteria and numerical schemes.…”

Section: Application To Planar Flowmentioning

confidence: 99%

Spatial moments analysis of kinetically sorbing solutes in aquifer with bimodal permeability distribution

Massabò

Bellin

Valocchi

2008

Water Resources Research

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[1] We analyze the influence of the formation structure upon transport of nonreactive and kinetically sorbing solutes in heterogeneous porous formations. Formation structure is represented through a bimodal distribution of hydraulic conductivity with two scales of spatial variability, which is a simplified, yet realistic, model of spatial variability. Kinetic sorption is modeled using a linear reversible rate expression. We derive new closed-form solutions of the second ergodic spatial moments of a kinetically sorbing solute. Although these solutions are obtained through a perturbation expansion in term of logconductivity variance, they are not limited to any particular model of spatial variability. We show that the formation structure, as described by the bimodal model, has a significant impact on plume moments of a non-reactive tracer at moderate contrast between mean hydraulic conductivity of the two hydrofacies, when the two scales of variability have comparable weight. On the contrary, the impact diminishes when bimodality weakens at both low and high contrast. As expected, the large time asymptotic longitudinal macrodispersion coefficient is influenced by the structure only through the variance and integral scale of log-conductivity, and thus the result for the bimodal model is identical to that of a unimodal Gaussian field sharing the same second-order statistics. The impact of kinetic sorption depends upon the plume travel time since injection. At early times, sorption kinetics tends to accentuate the difference between the longitudinal macrodispersivity in bimodal and unimodal fields, while at later times the difference is minimal because overall macrodispersivity is dominated by the spreading caused by nonequilibrium sorption. In a bimodal formation transverse macrodispersivity peaks later and declines to zero slower than in a Gaussian unimodal field with the same second-order statistics. These results demonstrate that even a very simplified facies model, such as the bimodal model relying on a statistical distribution of high-and low-conductivity zones, has important impacts upon global parameters describing the migration of nonreactive and reactive tracers. Consequently, larger effects are expected for quantities such as early arrival times and BTC tailing which are more directly influenced by the spatial patterns of high hydraulic conductivity than global parameters, such as macrodispersivity. Furthermore, these solutions contribute to bridge the gap between stochastic modeling and applications, since bimodal fields can be obtained to honor soft data typically available in applications, for example through conditional simulations using stratigraphic information from well logs.Citation: Massabó, M., A. Bellin, and A. J. Valocchi (2008), Spatial moments analysis of kinetically sorbing solutes in aquifer with bimodal permeability distribution, Water Resour. Res., 44, W09424,

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A theory of macrodispersion for the scale-up problem

Cited by 88 publications

References 16 publications

A Note on Upscaling Retardation Factor in Hierarchical Porous Media with Multimodal Reactive Mineral Facies

A Note on Upscaling Retardation Factor in Hierarchical Porous Media with Multimodal Reactive Mineral Facies

Carbon Sequestration Monitoring Activities

Spatial moments analysis of kinetically sorbing solutes in aquifer with bimodal permeability distribution

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