Analysis of solute transport in flow fields influenced by preferential flowpaths at the decimeter scale

Several recent studies at the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, have indicated that the relative preferential flowpaths and flow barriers resulting from decimeter-scale aquifer heterogeneities appear to have a dominant effect on plume-scale solute transport. Numerical experiments are thus conducted in this study to explore the key characteristics of solute transport in two-dimensional flow fields influenced by decimeter-scale preferential flowpaths. A hypothetical but geologically plausible network of 10 cm wide channels of high hydraulic conductivity is used to represent the relative preferential flowpaths embedded in an otherwise homogeneous aquifer. When the hydraulic conductivity in the channels is 100 times greater than that in the remaining portion of the aquifer, the calculated concentration distributions under three source configurations all exhibit highly asymmetrical, non-Gaussian patterns. These patterns, with peak concentrations close to the source and extensive spreading downgradient, resemble that observed at the MADE site tracer tests. When the contrast between the channel and nonchannel hydraulic conductivities is reduced to 30:1 from 100:1, the calculated mass distribution curve starts to approach a Gaussian one with the peak concentration near the central portion of the plume. Additional analysis based on a field-scale model demonstrates that the existence of decimeter-scale preferential flowpaths can have potentially far-reaching implications for ground water remediation. Failure to account for them in numerical simulation could lead to overestimation of the effectiveness of the remedial measure under consideration.     

Inverse modelling using PS‐InSAR data for improved land subsidence simulation in Las Vegas Valley,Nevada

Las Vegas Valley has had a long history of groundwater development and subsequent surface deformation. InSAR interferograms have revealed detailed and complex spatial patterns of subsidence in the Las Vegas Valley area that do not coincide with major pumping regions. This research represents the first effort to use high spatial and temporal resolution subsidence observations from InSAR and hydraulic head data to inversely calibrate transmissivities (T), elastic and inelastic skeletal storage coefficients (S_ke and S_kv) of the developed‐zone aquifer and conductance (CR) of the basin‐fill faults for the entire Las Vegas basin. The results indicate that the subsidence observations from InSAR are extremely beneficial for accurately quantifying hydraulic parameters, and the model calibration results are far more accurate than when using only groundwater levels as observations, and just a limited number of subsidence observations. The discrepancy between distributions of pumping and greatest levels of subsidence is found to be attributed to spatial variations in clay thickness. The Eglington fault separates thicker interbeds to the northwest from thinner interbeds to the southeast and the fault may act as a groundwater‐flow barrier and/or subsidence boundary, although the influence of the groundwater barrier to this area is found to be insignificant. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of snow structure on water flow and solute transport

Water flow through a melting snow pack modifies its structure and stability and affects the release of water and nutrients into soils and surface waters. Field and laboratory observations indicate a large spatial variability on various scales of the liquid water content and flow, a dominant system feature currently not included in numerical models. We investigated experimentally water and dye tracer movement through microstructurally different snow pack horizons and the persistence of preferential flow paths. Naturally rounded snow of varying grain size was artificially packed to obtain well known conditions by sieving it into rectangular bins. Surface melt was induced with infrared lamps. The flow paths were visualized with tracers and liquid water content was monitored with time domain reflectometry probes. Vertical cuts through the snow pack were imaged. The dye tracer patterns allowed the two flow regimes ‘matrix flow’ and ‘preferential flow’ to be distinguished. Matrix flow is apparently dominated by film and capillary flow in the unsaturated snow matrix. The capillary barrier effect at a boundary between a fine over a coarse textured layer on matrix flow in snow was confirmed. In contrast, preferential flow appears as well‐defined flow fingers that advance from 0·1 to 1 cm s^?1. During a melt phase, the advancing flow fingers enlarge and are only partially time invariant. It remains to be shown whether the continuum concept, including the Darcy–Buckingham law is apt to describe the extremely non‐linear nature of water flow and the travel time of solutes in snow under conditions of melt water percolation. Probably, snow packs that include faceted crystals and large variations in bulk density, feature more pronounced capillary barriers and preferential flow triggering, but also stronger impeding of fingers by lateral dispersion. Further, triggering and persistence of preferential flow is complicated by the usually transient infiltration rate. Copyright © 2004 John Wiley & Sons, Ltd.     

物理场多重分形谱理论模型的数值模拟研究

利用二维双标度三分非空集对物理场多重分形谱进行了理论模型的数值模拟研究。模拟结果表明：随着物理量空间分布不均匀性的增大，不同模型参数下的理论分形谱曲线变陡，Dq值域范围变宽。利用多重分形谱曲线的形态特征，可进一步了解是“稀疏区”还是“密集区”起主导作用，这对于从理论上把握物理和化学场分布特性具有重要意义。     

Reactive barriers: hydraulic performance and design enhancements

The remediation of contaminated ground water is a multibillion-dollar global industry. Permeable reactive barriers (PRBs) are one of the leading technologies being developed in the search for alternatives to the pump-and-treat method. Improving the hydraulic performance of these PRBs is an important part of maximizing their potential to the industry. Optimization of the hydraulic performance of a PRB can be defined in terms of finding the balance between capture, residence time, and PRB longevity that produces a minimum-cost acceptable design. Three-dimensional particle tracking was used to estimate capture zone and residence time distributions. Volumetric flow analysis was used for estimation of flow distribution across a PRB and in the identification of flow regimes that may affect the permeability or reactivity of portions of the PRB over time. Capture zone measurements extended below the base of partially penetrating PRBs and were measured upgradient from the portion of aquifer influenced by PRB emplacement. Hydraulic performance analysis of standard PRB designs confirmed previously presented research that identified the potential for significant variation in residence time and capture zone. These variations can result in the need to oversize the PRB to ensure that downgradient contaminant concentrations do not exceed imposed standards. The most useful PRB design enhancements for controlling residence time and capture variation were found to be customized downgradient gate faces, velocity equalization walls, deeper emplacement of the funnel than the gate, and careful manipulation of the hydraulic conductivity ratio between the gate and the aquifer.     

Influence of variable salinity conditions in a tidal creek on riparian groundwater flow and salinity dynamics

While recent studies have revealed that tidal fluctuations in an estuary significantly affect groundwater flows and salt transport in the riparian zone, only seawater salinity in the estuary has been considered. A numerical study is conducted to investigate the influence of estuarine salinity variations on the groundwater flow and salt dynamics in the adjacent aquifer to extend our understanding of these complex and dynamic systems. Tidal salinity fluctuations (synchronous with estuary stage) were found to alter the magnitude and distribution of groundwater discharge to the estuary, which subsequently impacted on groundwater salinity patterns and residence times, especially in the riparian zone. The effects of salinity fluctuations were not fully captured by adopting a constant, time-averaged estuarine salinity. The modelling analysis also included an assessment of the impact of a seasonal freshwater flush in the estuary, similar to that expected in tropical climates (e.g. mean estuary level during flood significantly greater than average), on adjacent groundwater flow and salinity conditions. The three-month freshwater flushing event temporarily disrupted the salt distribution and re-circulation patterns predicted to occur under conditions of constant salinity and tidal water level fluctuations in the estuary. The results indicate that the salinity variations in tidal estuaries impact significantly on estuary–aquifer interaction and need to be accounted for to properly assess salinity and flow dynamics and groundwater residence times of riparian zones.     

Influence of heterogeneity on unsaturated hydraulic properties (2) – percentage and shape of heterogeneity

In subsurface porous media, the soil water retention curve (WRC) and unsaturated hydraulic conductivity curve (UHC) are two important soil hydraulic property curves. Spatial heterogeneity is ubiquitous in nature, which may significantly affect soil hydraulic property curves. The main theme of this paper is to investigate how spatial heterogeneities, including their arrangements and amounts in soil flumes, affect soil hydraulic property curves. This paper uses a two‐dimensional variably saturated flow and solute transport finite element model to simulate variations of pressure and moisture content in soil flumes under a constant head boundary condition. To investigate the behavior of soil hydraulic property curves owing to variations of heterogeneities and their arrangements as well, cases with different proportions of heterogeneities are carried out. A quantitative evaluation of parameter variations in the van Genuchten model (VG model) resulting from heterogeneity is presented. Results show that the soil hydraulic properties are strongly affected by variations of heterogeneities and their arrangements. If the pressure head remains at a specific value, the soil moisture increases when heterogeneities increase in the soil flumes. On the other hand, the unsaturated hydraulic conductivity decreases when heterogeneities increase in the soil flumes under a constant pressure head. Moreover, results reveal that parameters estimated from both WRC and UHC also are affected by shapes of heterogeneity; this indicates that the parameters obtained from the WRC are not suitable for predicting the UHC of different shapes in heterogeneous media. Copyright © 2011 John Wiley & Sons, Ltd.     

The Role of Heterogeneities as a Tuning Parameter of Earthquake Dynamics

We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity (quasidynamic model). The model produces a brittle-ductile transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: (1) high stress drop barriers in near-vertical directions and (2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations.on leave from CNRS Rennes, France     

Delineating alluvial aquifer heterogeneity using resistivity and GPR data

Conceptual geological models based on geophysical data can elucidate aquifer architecture and heterogeneity at meter and smaller scales, which can lead to better predictions of preferential flow pathways. The macrodispersion experiment (MADE) site, with >2000 measurements of hydraulic conductivity obtained and three tracer tests conducted, serves as an ideal natural laboratory for examining relationships between subsurface flow characteristics and geophysical attributes in fluvial aquifers. The spatial variation of hydraulic conductivity measurements indicates a large degree of site heterogeneity. To evaluate the usefulness of geophysical methods for better delineating fluvial aquifer heterogeneities and distribution of preferential flow paths, a surface grid of two-dimensional ground penetrating radar (GPR) and direct current (DC) resistivity data were collected. A geological model was developed from these data that delineate four stratigraphic units with distinct electrical and radar properties including (from top to bottom) (1) a meandering fluvial system (MFS); (2) a braided fluvial system (BFS); (3) fine-grained sands; and (4) a clay-rich interval. A paleochannel, inferred by other authors to affect flow, was mapped in the MFS with both DC resistivity and GPR data. The channel is 2 to 4 m deep and, based on resistivity values, is predominantly filled with clay and silt. Comparing previously collected hydraulic conductivity measurements and tracer-plume migration patterns to the geological model indicates that flow primarily occurs in the BFS and that the channel mapped in the MFS has no influence on plume migration patterns.     

Stochastic evaluation of subsurface contaminant discharges under physical,chemical, and biological heterogeneities

A finite element 2D Monte Carlo approach is used to evaluate the sensitivity of groundwater contaminant discharges to a Damkohler number ω and spatial variability in aquifer hydraulic conductivity, initial microbial biomass concentrations, and electron acceptor/donor concentrations. Bioattenuation is most sensitive to spatial variations in incipient biomass and critical electron donors/acceptors for ω ≥ 1 (i.e., when pore-water residence times are high compared to the time needed for microbial growth or contaminant attenuation). Under these conditions, critical reaction processes can become substrate-limited at multiple locations throughout the aquifer; which in turn increases expected contaminant discharges and their uncertainties at monitored transects. For ω ≤ 0.2, contaminant discharge is not sensitive to incipient biomass variations. Physical heterogeneities expedite plume arrival and delay departure at transects and in turn attenuate peak discharges but do not affect cumulative contaminant discharges. Physical heterogeneities do, however, induce transect mass discharge variances that are bimodal functions of time; the first peak beings consistently higher. A simple stream tube model is invoked to explain the occurrence of peaks in contaminant discharge variance.     

Predicting Pesticide Attenuation in a Fractured Aquifer Using Lumped‐Parameter Models

Neighboring springs draining fractured‐rock aquifers can display large differences in water quality and flow regime, depending on local variations of the connectivity and the aperture size distribution of the fracture network. Consequently, because homogeneous equivalent parameters cannot be assumed a priori for the entire regional aquifer, the vulnerability to pollution of such springs has to be studied on a case by case basis. In this paper, a simple lumped‐parameter model usually applied to estimate the mean transit time of water (or tracer) is presented. The original exponential piston‐flow model was modified to take land‐use distribution into account and applied to predict the evolution of atrazine concentration in a series of springs draining a fractured sandstone aquifer in Luxembourg, where despite a nationwide ban in 2005, atrazine concentrations still had not begun to decrease in 2009. This persistence could be explained by exponentially distributed residence times in the aquifer, demonstrating that in some real world cases, models based on the groundwater residence time distribution can be a powerful tool for trend reversal assessments as recommended for instance by current European Union guidelines.     

Modeling of Plume Capture by Continuous, Low-Permeability Barriers

Modeling was performed to simulate ground water flow through reactive barriers of lower hydraulic conductivity than the surrounding aquifer to determine the plume capture widths. As a plume approaches such a barrier, it spreads laterally. Therefore, to intercept an entire plume, the barrier must be wider than the upgradient width of the undisturbed plume. The results indicate that, for practical values of barrier thickness and plume width, hydraulic conductivities ten-fold less than that of the aquifer can be accommodated by making the width of the barrier approximately 20% greater than the upgradient width of the plume. Barrier hydraulic conductivities one-hundred-fold less than that of the aquifer may require barrier widths up to twice the width of the upgradient plume for plumes 100 feet wide (33 m) and as little as 1.1 times for plumes 1000 feet wide (325 m). The results presented here lend support to the view that novel emplacement methods that create zones of slightly lower hydraulic conductivity than the native aquifer may be viable alternatives to the excavation-and-backfill approaches which have thus far been used for installing permeable reactive barriers.     

Interpreting velocities from heat-based flow sensors by numerical simulation

We have carried out numerical simulations of three-dimensional nonisothermal flow around an in situ heat-based flow sensor to investigate how formation heterogeneities can affect the interpretation of ground water flow velocities from this instrument. The flow sensor operates by constant heating of a 0.75-m-long, 5-cm-diameter cylindrical probe, which contains 30 thermistors in contact with the formation. The temperature evolution at each thermistor can be inverted to obtain an estimate of the ground water flow velocity vector using the standard interpretive method, which assumes that the formation is homogeneous. Analysis of data from heat-based flow sensors installed in a sand aquifer at the Former Fort Ord Army Base near Monterey, California, suggested an unexpected component of downward flow. The magnitudes of the vertical velocities were expected to be much less than those of the horizontal velocities at this site because the sensors were installed just above a clay aquitard. Numerical simulations were conducted to examine how differences in thermal conductivities may lead to spurious indications of vertical flow velocities. We found that a decrease in the thermal conductivity near the bottom of the sensor can perturb the temperature profiles along the instrument in such a manner that analyses assuming homogeneous thermal conductivity could indicate a vertical flow component even though flow is actually horizontal. This work demonstrates how modeling can be used to simulate instrument response to formation heterogeneity and shows that caution must be used in interpreting data from such devices.     

Estimating Preferential Flow in Karstic Aquifers Using Statistical Mixed Models

Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory‐scale Geo‐HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow‐dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit‐like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study.     

Seismic attenuation in porous rocks with random patchy saturation

Saturation of porous rocks with a mixture of two fluids has a substantial effect on seismic‐wave propagation. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves due to the mechanism of wave‐induced fluid‐flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a regular way. However, recent experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Based on an approximation for the coherent wavefield in random porous media, we develop a model which assumes a continuous distribution of fluid heterogeneities. As this continuous random media approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental data. We also show how to relate the random functions to experimentally measurable parameters.     

Comparative review of theoretical models for elastic wave attenuation and dispersion in partially saturated rocks

Saturation of porous rocks with a mixture of two fluids (known as partial saturation) has a substantial effect on the seismic waves propagating through these rocks. In particular, partial saturation causes significant attenuation and dispersion of the propagating waves, due to wave-induced fluid flow. Such flow arises when a passing wave induces different fluid pressures in regions of rock saturated by different fluids. As partial fluid saturation can occur on different length scales, attenuation due to wave-induced fluid flow is ubiquitous. In particular, mesoscopic fluid flow due to heterogeneities occurring on a scale greater than porescale, but less than wavelength scale, is responsible for significant attenuation in the frequency range from 10 to 1000 Hz.Most models of attenuation and dispersion due to mesoscopic heterogeneities imply that fluid heterogeneities are distributed in a periodic/regular way. In 1D this corresponds to periodically alternating layering, in 3D as periodically distributed inclusions of a given shape (usually spheres). All these models yield very similar estimates of attenuation and dispersion.Experimental studies show that mesoscopic heterogeneities have less idealized distributions and that the distribution itself affects attenuation and dispersion. Therefore, theoretical models are required which would simulate the effect of more general and realistic fluid distributions.We have developed two theoretical models which simulate the effect of random distributions of mesoscopic fluid heterogeneities. The first model assumes that one fluid forms a random ensemble of spherical inclusions in a porous medium saturated by the other fluid. The attenuation and dispersion predicted by this model are very similar to those predicted for 3D periodic distribution. Attenuation (inverse quality factor) is proportional to ω at low frequencies for both distributions. This is in contrast to the 1D case, where random and periodically alternating layering shows different attenuation behaviour at low frequencies. The second model, which assumes a 3D continuous distribution of fluid heterogeneities, also predicts the same low-frequency asymptote of attenuation. However, the shapes of the frequency dependencies of attenuation are different. As the 3D continuous random approach assumes that there will be a distribution of different patch sizes, it is expected to be better suited to modelling experimental results. Further research is required in order to uncover how to relate the random functions to experimentally significant parameters.     

Scale effect and calibration of contaminant transport models

The influence on solute transport of the small-scale spatial variation of aquifer hydraulic conductivity (K) was analyzed by comparing results from fine-grid (2 m by 2 m) simulations of a synthetic heterogeneous aquifer to those from coarse-grid (8 m by 4 m) simulations of an equivalent homogeneous aquifer. Realizations of the K field of the heterogeneous aquifer were generated, using the Monte Carlo approach, from a lognormal distribution with mean log K of 2 (K in m/d) and three levels of log K variance of 0.1, 0.5, and 1.0. Numerical simulation results show that the average standard deviation of point concentrations increased from 1.21 to 5.78 when the value of log K variance was increased from 0.1 to 1.0. The average discrepancy between modeled concentrations (obtained from a coarse-grid deterministic numerical simulation) and the actual mean point concentrations (obtained from fine-grid Monte Carlo numerical simulations) increased from 0.91 to 4.23 with the increase in log K variance. The results from this study illustrate the uncertainty in predictions from contaminant transport models due to their inability to simulate the effects of heterogeneities at scales smaller than the model grid.     

Spatial weighting functions: transient hydraulic tests and heterogeneous media

To improve understanding of property measurements in heterogeneous media, an energy-based weighting function concept is developed. In (assumed) homogeneous media, the instrument spatial weighting function (ISWF) depends only on the energy dissipation distribution set up by the measurement procedure and it reduces to simply inverse sample volume (uniform weighting) for 1-D parallel flow case (ideal permeameter). For 1-D transient flow in homogeneous media, such as with slug tests, the ISWF varies with position and time, with 95% of the total weighting contained within 115 well radii, even late in the test. In the heterogeneous case, the determination of the ISWF is connected to the problem of determining an equivalent hydraulic conductivity (K), where the criterion for equivalence is based on equal energy dissipation rate rather than equal volume discharge. The discharge-based equivalent K (K(E)) and the energy-based equivalent K in heterogeneous media (K(eh)) are not equal in general, with K(eh) typically above the nodal arithmetic mean K. The possibly more fundamental problem is that as one makes K measurements in heterogeneous media at different locations or on different cores of heterogeneous materials, the ISWF will be heterogeneity dependent, implying that the averaging process resulting in the equivalent K value also varies with position. If the testing procedure is transient, then the averaging process varies with time. This suggests a fundamental ambiguity in the interpretation of hydraulic conductivity measurements in heterogeneous media that may impact how we approach modeling and prediction in a practical sense (Molz 2003). Further research is suggested.