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66
Application of a Fractional AdvectionDispersion Equation
 Water Resour. Res
, 2000
"... A transport equation that uses fractionalorder dispersion derivatives has fundamental solutions that are Levy's #stable densities. These densities represent plumes that spread proportional to time , have heavy tails, and incorporate any degree of skewness. The equation is parsimonious s ..."
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Cited by 86 (22 self)
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A transport equation that uses fractionalorder dispersion derivatives has fundamental solutions that are Levy's #stable densities. These densities represent plumes that spread proportional to time , have heavy tails, and incorporate any degree of skewness. The equation is parsimonious since the dispersion parameter is not a function of time or distance. The scaling behavior of plumes that undergo Levy motion is accounted for by the fractional derivative. A laboratory tracer test is described by a dispersion term of order 1.55, while the Cape Cod bromide plume is modeled by an equation of order 1.65 to 1.8.
The Fractional AdvectionDispersion Equation: Development and Application
, 1998
"... The traditional 2ndorder advectiondispersion equation (ADE) does not adequately describe the movement of solute tracers in aquifers. This study examines and rederives the governing equation. The analysis starts with a generalized notion of particle movements, since the secondorder equation is tr ..."
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Cited by 27 (12 self)
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The traditional 2ndorder advectiondispersion equation (ADE) does not adequately describe the movement of solute tracers in aquifers. This study examines and rederives the governing equation. The analysis starts with a generalized notion of particle movements, since the secondorder equation is trying to impart Brownian motion on a mathematical plume at any time. If particle motions with longrange spatial correlation are more favored, then the motion is described by Lévy's family of &alpha;stable densities. The new governing (FokkerPlanck) equation of these motions is similar to the ADE except that the order (&alpha;) of the highest derivative is fractional (e.g., the 1.65th derivative). Fundamental solutions resemble the Gaussian except that they spread proportional to time 1/&alpha; and have heavier tails. The order of the fractional ADE (FADE) is shown to be related to the aquifer velocity autocorrelation function. The FADE derived here is used to....
Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests
 Transp. Por. Media
, 1999
"... The macrodispersion experiments (MADE) at the Columbus Air Force Base in Mississippi were conducted in a highly heterogeneous aquifer that violates the basic assumptions of local 2  order theories. A governing equation that describes particles that undergo Lvy motion, rather than Brownian motio ..."
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Cited by 20 (15 self)
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The macrodispersion experiments (MADE) at the Columbus Air Force Base in Mississippi were conducted in a highly heterogeneous aquifer that violates the basic assumptions of local 2  order theories. A governing equation that describes particles that undergo Lvy motion, rather than Brownian motion, readily describes the highly skewed and heavytailed plume development at the MADE site. The new governing equation is based on a fractional, rather than integer, order of differentiation. This order (#), based on MADE plume measurements, is approximately 1.1. The hydraulic conductivity (K) increments also follow a power law of order # = 1.1. We conjecture that the heavytailed K distribution gives rise to a heavytailed velocity field that directly implies the fractionalorder governing equation derived herein. Simple arguments lead to accurate estimates of the velocity and dispersion constants based only on the aquifer hydraulic properties. This supports the idea that the correct governing equation can be accurately determined before, or after, a contamination event. While the traditional ADE fails to model a conservative tracer in the MADE aquifer, the fractional equation predicts tritium concentration profiles with remarkable accuracy over all spatial and temporal scales.
Dispersion of groundwater age in an alluvial aquifer system. Water Resour. Res. 38 (article number 1198
, 2002
"... [1] Interpretation of groundwater ages typically rests on assumptions of minimal mixing of different water ages in the water samples. The effects of threedimensional, geologic heterogeneity on groundwater mixing and tracer concentrations, however, have not been evaluated. In this study, we use a se ..."
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[1] Interpretation of groundwater ages typically rests on assumptions of minimal mixing of different water ages in the water samples. The effects of threedimensional, geologic heterogeneity on groundwater mixing and tracer concentrations, however, have not been evaluated. In this study, we use a series of 10 detailed geostatistical realizations along with highresolution numerical groundwater flow and contaminant transport simulation to model distributions of groundwater ages and chlorofluorocarbon (CFC) ages at wells within a heterogeneous streamdominated alluvial fan aquifer system. Results show that groundwater reaching a well in the heterogeneous aquifer system typically consists of a wide distribution of groundwater ages (often spanning>50 years), even over short (<1.5 m) screened intervals. Additionally, simulated arithmetic mean groundwater ages do not correspond to mean ages estimated from simulated CFC concentrations. Results emphasize the potential ambiguity of ‘‘mean’ ’ groundwater ages estimated from environmental tracer concentrations in typically heterogeneous geologic systems. The significant dispersion of groundwater ages also implies that ultimate, maximum effects of nonpoint source, anthropogenic contamination of groundwater may not be reached until after many decades or centuries of gradual decline in groundwater quality. INDEX TERMS:
Ratelimited mass transfer or macrodispersion: Which dominates plume evolution at the Macrodispersion Experiment (MADE) site?, Water Resour
 Res
, 2000
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 19 (1 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Assessing groundwater vulnerability to contamination: providing scientifically defensible information for decision makers: U.S. Geological Survey Circular 1224
, 2002
"... Throughout the United States increasing demands for safe drinking water and requirements to maintain healthy ecosystems are leading policy makers to ask complex social and scientific questions about how to ..."
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Cited by 13 (0 self)
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Throughout the United States increasing demands for safe drinking water and requirements to maintain healthy ecosystems are leading policy makers to ask complex social and scientific questions about how to
Numerical simulation of tracer tests in heterogeneous aquifer
 J. Environ. Eng. 124 Ž
, 1998
"... ABSTRACT: A largescale, naturalgradient tracer test in a heterogeneous aquifer at a site near Columbus, Miss. is simulated using threedimensional (3D) hydraulic conductivity distributions derived from the borehole flowmeter test data. The simulated plume is more sensitive to the way the hydraulic ..."
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Cited by 7 (1 self)
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ABSTRACT: A largescale, naturalgradient tracer test in a heterogeneous aquifer at a site near Columbus, Miss. is simulated using threedimensional (3D) hydraulic conductivity distributions derived from the borehole flowmeter test data. The simulated plume is more sensitive to the way the hydraulic conductivity field is interpolated from the measured data than it is to the dispersivity value. The transport model with longitudinal dispersivities in the range of 15 m can reasonably reproduce the observed plume to a certain concentration limit, but fails to reproduce the significant spreading of the tracer at diluted concentrations as observed in the field. This modeling study illustrates the formidable challenges in modeling and monitoring contaminant transport in very heterogeneous aquifers and points to the needs for new, innovative monitoring techniques that can be applied to characterize the spatial and temporal variabilities in the aquifer properties at scales suitable for detailed transport modeling.
Spatial correlation of permeability in crossstratified sediment with hierarchical architecture
"... [1] Crossstratified deposits can give rise to a hierarchy of permeability modes, across scales, corresponding to a hierarchy of sedimentary unit types. The shape of the sample semivariogram for permeability can be largely controlled by the shape of the crosstransition probabilities of unit types h ..."
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[1] Crossstratified deposits can give rise to a hierarchy of permeability modes, across scales, corresponding to a hierarchy of sedimentary unit types. The shape of the sample semivariogram for permeability can be largely controlled by the shape of the crosstransition probabilities of unit types having the greatest contrast in permeability. The shape of those crosstransition probabilities can be, in turn, largely determined by the variance of the lengths of those unit types. A sufficient condition for an exponentiallike semivariogram is the repeated occurrence of unit types having both a contrast in permeability and a large length variance. These relationships are shown through writing the identities for spatial correlation of permeability in a hierarchical and multimodal form and as a function of the transition probabilities for the sedimentary unit types. These relationships are also illustrated through analyzing data representing crossstratified sediments within a point bar deposit. INDEX TERMS: 1829 Hydrology: Groundwater hydrology;
Transport behavior of groundwater protozoa and protozoansized microspheres in sandy aquifer sediments
 Appl. Environ. Microbiol
, 1995
"... Transport behaviors of unidentified flagellated protozoa (flagellates) and flagellatesized carboxylated microspheres in sandy, organically contaminated aquifer sediments were investigated in a smallscale (1 to 4m travel distance) naturalgradient tracer test on Cape Cod and in flowthrough colum ..."
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Transport behaviors of unidentified flagellated protozoa (flagellates) and flagellatesized carboxylated microspheres in sandy, organically contaminated aquifer sediments were investigated in a smallscale (1 to 4m travel distance) naturalgradient tracer test on Cape Cod and in flowthrough columns packed with sieved (0.5to 1.0mm grain size) aquifer sediments. The minute (average in situ cell size, 2 to 3 mm) flagellates, which are relatively abundant in the Cape Cod aquifer, were isolated from core samples, grown in a grass extract medium, labeled with hydroethidine (a vital eukaryotic stain), and coinjected into aquifer sediments along with bromide, a conservative tracer. The 2mm flagellates appeared to be near the optimal size for transport, judging from flowthrough column experiments involving a polydispersed (0.7 to 6.2 mm in diameter) suspension of carboxylated microspheres. However, immobilization within the aquifer sediments accounted for a log unit reduction over the first meter of travel compared with a log unit reduction over the first 10 m of travel for indigenous, freeliving groundwater bacteria in earlier tests. High rates of flagellate immobilization in the presence of aquifer sediments also was observed in the laboratory. However, immobilization rates for the laboratorygrown flagellates (initially 4 to 5 mm) injected into the aquifer were not constant and decreased noticeably with increasing time and distance of travel. The decrease in propensity for grain surfaces was accompanied by a decrease in cell size, as the flagellates presumably readapted to aquifer conditions. Retar