Mixing and stretching efficiency in steady and unsteady groundwater flows

Weeks, Scott W.; Sposito, Garrison

doi:10.1029/98wr02535

Cited by 54 publications

(42 citation statements)

References 16 publications

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“…We refer to the latter process as mixing. Note that our definition of mixing differs from that of Weeks and Sposito [1998], who defined it as the stretching of the plume surface because of differences in advective transport. We think that our definition of mixing is more useful in the context of multicomponent reactive transport when different plumes belong to different compounds which may react when mixed Oya and Valocchi, 1998].…”

Section: Paper Number 1999wr900354mentioning

confidence: 74%

Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments

Cirpka¹,

Kitanidis²

2000

Water Resources Research

157

135

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Abstract. Breakthrough curves of a conservative tracer in a heterogeneous twodimensional aquifer are analyzed by means of their temporal moments. The average velocity and the longitudinal macrodispersion coefficient of the equivalent onedimensional aquifer obtained through cross-sectional averaging of concentration can be defined from the first and second central moments of a breakthrough curve integrated over the outflow boundary of the domain. On the basis of an integrated breakthrough curve, one cannot distinguish between actual solute dilution, which involves concentration reduction, and variability of arrival times among parts of the plume at different crosssectional positions. Analyzing the temporal moments of breakthrough curves at a "point" within the domain gives additional information about the dilution of the tracer. From these local first and second central moments an apparent seepage velocity Va and an apparent dispersivity of mixing aa can be derived. For short travel distances, aa equals the local-scale longitudinal dispersivity. It increases with the travel distance but much more slowly than the macrodispersivity. At the large-distance limit, aa may eventually reach the level of macrodispersivity. Lenses of high conductivity where groundwater flow converges are identified as regions of preferential enhanced mixing. The spatial distribution of these regions causes a high degree of variability of a a within a domain, indicating a high degree of uncertainty in the quantification of dilution at early stages. In an accompanying paper [Cirpka and Kitanidis, this issue] the results of conservative tracer transport are utilized for the study of mixing-controlled reactive transport. [1996, 1998] showed the relation between dilution and the decay of concentration fluctuations. For a conservative compound the spatial variability of advection controls spreading. However, local dispersion plays a decisive role in determining the rate of fluctuation decay and the speed with which dilution catches up with spreading. If we observed two nonsorbing compounds that initially did not occupy the same space and we considered spreading exclusively, the mass of the two compounds would remain in their specific, and separated, water volumes moving with groundwater flow. The compounds would never occupy the same volume, and the plumes would not overlap. By contrast, if we consider dilution, the volume occupied by each compound increases and overlapping of the two plumes becomes possible. We refer to the latter process as mixing. Note that our definition of mixing differs from that of Weeks and Sposito [1998], who defined it as the stretching of the plume surface because of differences in advective transport. We think that our definition of mixing is more useful in the context of multicomponent reactive transport when different plumes belong to different compounds which may react when mixed Oya and Valocchi, 1998].As already stated, dilution leads to mixing. However, if we consider the introduction of a highly mobile comp...

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Section: Paper Number 1999wr900354mentioning

confidence: 74%

Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments

Cirpka¹,

Kitanidis²

2000

Water Resources Research

157

135

View full text Add to dashboard Cite

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“…The mixing efficiency generally depends on the spatial variability of hydraulic conductivity (or transitions) between zones of highly contrasting hydraulic conductivities. Weeks and Sposito [1998] showed that mixing is driven by unsteady advection, which acts to stretch and fold fluid filaments in such a manner that plume boundary areas become highly irregular. Weeks and Sposito [1998] showed that the mixing of a solute plume by unsteady groundwater flow, in an aquifer with pronounced hydraulic conductivity variation, would be most effective if chaotic path lines were induced.…”

Section: Key Features Of Geometry and Nonlinear Dynamics Of Flow Thromentioning

confidence: 99%

Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives

Faybishenko

2004

Reviews of Geophysics

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[1] The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short-and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.

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“…Whenever H is constant and does not depend on data values, the quality of the reconstruction in areas with complex geometries is low. To solve this problem, Takeda et al 29 proposed to locally rotate and scale H to ensure that weight is concentrated along concentration isolines 14) where the overbar stands for averaging over the pixels adjacent to x i , and μ is a global smoothing parameter. This filter is nonlinear because H i depends now on the solution through ∇u.…”

Section: ■ Introductionmentioning

confidence: 99%

Visualization of Mixing Processes in a Heterogeneous Sand Box Aquifer

Castro-Alcalá

Fernàndez-García

Carrera

et al. 2012

Environ. Sci. Technol.

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Mixing is increasingly recognized as a critical process for understanding and modeling reactive transport. Yet, mixing is hard to characterize because it depends nonlinearly on concentrations. Visualization of optical tracers in the laboratory at high spatial and temporal resolution can help advance the study of mixing processes. The solute distribution is obtained by analyzing the relationship between pixel intensity and tracer concentration. The problem with such techniques is that grain borders, light fluctuations, and nonuniform brightness contribute to produce noisy images of concentrations that cannot be directly used to estimate mixing at the local scale. We present a nonparametric regression methodology to visualize local values of mixing from noisy images of optical tracers that minimizes smoothing in the direction of concentration gradients. This is achieved by weighting pixel data along concentration isolines. The methodology is used to provide a full visualization of mixing dynamics in a tracer experiment performed in a reconstructed aquifer consisting of two materials with contrasting hydraulic properties. The experiment reveals that mixing is largest at the contact area of regions with different permeability. Also, the temporal evolutions of mixing and dilution rates are significantly different. The mixing rate is more persistent than the dilution rate during tracer invasion, and the opposite is true during flushing, which helps in understanding the complementary nature of these two measures.

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Mixing and stretching efficiency in steady and unsteady groundwater flows

Cited by 54 publications

References 16 publications

Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments

Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments

Nonlinear dynamics in flow through unsaturated fractured porous media: Status and perspectives

Visualization of Mixing Processes in a Heterogeneous Sand Box Aquifer

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