Spatial Variability Of Hydraulic Conductivity Research Articles

LA CONDUCTIVIDAD HIDRAULICA EN FASE SATURADA COMO HERRAMIENTA PARA EL DIAGNOSTICO DE LA ESTRUCTURA DEL SUELO

Hydraulic conductivity in the saturated phase was determined in order to diagnose the structural characteristics of Hapludand and Palehumult submitted to different management and located in a series of volcanic soils with a varied pedological development. Spatial variation in hydraulic conductivity in the saturated phase increases in the more structured soils. It's magnitude depends on the amount of coarse porosity.Managements that decrease coares pores reduce the capacity to conduce water.The sites where hydraulic conductivity in the saturated phase experiments big changes after aprolonged flow also show low stability of aggregates. As the volcanic ash soils show a more advanced pedological development, coarse porosity diminishes and with it hydraulic conductivity. In a parallel manner, there is a decrease of the stability of water aggregates and a increase in the variation of hydraulic conductivity of the continuous flow.

Dual-tracer transport experiments in a physically and chemically heterogeneous porous aquifer: effective transport parameters and spatial variability

In order to investigate the effects of reactive transport processes within a heterogeneous porous aquifer, two small-scale forced gradient tracer tests were conducted at the ‘Horkheimer Insel’ field site. During the experiments, two fluorescent tracers were injected simultaneously in the same fully penetrating groundwater monitoring well, located approximately 10 m from the pumping well. Fluoresceine and Rhodamine WT were used to represent the classes of practically non-sorbing and sorbing solutes, respectively. Multilevel breakthrough curves with a temporal resolution of 1 min were measured for both tracers at different depths within the pumping well using fibre-optic fluorimeters. This paper presents the tracer test design, the fibre-optic fluorimetry instrumentation, the experimental results and the interpretation of the measured multilevel breakthrough curves in terms of temporal moments and effective transport parameters. Significant sorption of Rhodamine WT is apparent from the effective retardation factors. Furthermore, an enhanced tailing of Rhodamine WT breakthrough curves is observed, which is possibly caused by a variability of aquifer sorption properties. The determined effective parameters are spatially variable, suggesting that a complex numerical flow and transport modelling approach within a stochastic framework will be needed to adequately describe the transport behaviour observed in the two experiments. Therefore, the tracer test results will serve in future work for the validation of numerical stochastic transport simulations taking into account the spatial variability of hydraulic conductivity and sorption-related aquifer properties.

Spatial Variability of Hydraulic Conductivity in a Cultivated Field at Different Times

Farming practices and climatic patterns may alter soil surface hydraulic conductivity (K) both spatially and at different times during a season. This study quantified spatial variability and spatial dependence of ponded and tension K measurements in a cultivated field at different times. Paired small-base infiltrometers (76-mm diameter) were used at four pressure heads (5, −30, −60, and −150 mm) to measure K across a transect four times during one and a half growing seasons (1–2 July 1991, 12–13 Aug. 1991, 29–30 Apr. 1992, and 28–29 May 1992). A natural log transformation best normalized ponded K data, but ln(K + 1) was better for the tension data. Periodicity was apparent for K at a head (h) of −150 mm, with a significant period of 46 m for July 1991, 147 m for April 1992, and 96 m for May 1992. The periods for the three dates may be three different harmonics. The July periodicity was consistent with expected wheel traffic patterns from the previous harvest; K measurements would have coincided with wheel tracks every 46 m for the July 1991 measurement date. Periodicity for other dates had no apparent cause. For ponded K, only within-pair data were spatially correlated (0.6–0.8 m). At a head of −150 mm, K values were spatially correlated over distances of 6.6, 16.8, and 0.6 m for the measurements of July 1991, April 1992, and May 1992, respectively. Correlation distances were intermediate for K-30 and K-60. Since spatial correlation and periodicity varied with measurement date, one set of transect measurements was not adequate to describe spatial variability of K.

不連続性岩盤内の透水性の不均一性と流れの局所化について

This paper describes a relationship between heterogeneous permeability profile and the geometry of localized flow paths based on a laboratory experiment. A 30cm cube of chert containing multiple sets of natural fractures is used for the study. Each of the six faces of the block is divided into 25 hydraulically isolated subpanels, i.e. 150 subpanels in total, which are connected to a separate flow line for control or monitoring. The pressure and flow responses under different boundary conditions are inverted to provide information on the spatial variation of hydraulic conductivity. It has been shown that, because of the wide variation in permeability, the limited number of high permeability zones are creating localized flow paths which controll the overall flow characteristics in a fractured chert block.

Ground-probing radar as a tool for heterogeneity estimation in gravel deposits: advances in data-processing and facies analysis

Pleistocene gravely braided-river deposits in river valleys constitute a large fraction of the natural ground-water reservoirs in Switzerland. The knowledge of the distribution and variability of hydraulic conductivity within these deposits are key factors for the estimation of water residence times and of description of large-scale mixing procesess in aquifers such as macrodispersion. It has been shown elsewhere that the spatial variability of hydraulic conductivity is related to the composition and the characteristic dimensions of sedimentary structures, which are themselves related to the dynamics of ancient braided-river systems. In many contamination problems, sedimentological information is sparse and drill-core descriptions and pumping-tests only give a limited picture of the geometry of inhomogeneities. The ground-probing radar (GPR) method is a promising tool for resolving changes of physical properties in gravel deposits at the scale of natural inhomogeneities arising from changing sedimentary composition. However, the main limitation of GPR is the rapid attenuation of electromagnetic waves in subsurface sediments such as gravels, which leads to a limited penetration of the order of 10 to 15 m for a 250 MHz antenna. The objectives of our present work are: 1. (1) To show how digital processing methods similar to reflection seismics may be applied for velocity and profile processing. These methods can improve both the resolution of radar profiles, in particular at greater depths, and the determination of velocity distributions from CDP experiments. 2. (2) To examine whether and to what extent the characteristic lithofacies of Pleistocene gravel deposits can be recognized as mappable reflection patterns on ground-probing radar (GPR) reflection profiles in order to gain information about the geometry of inhomogeneities. Using modern digital data processing methods, such as band pass, high- or low-cut filtering, deconvolution and velocity analysis, much more significant information can be obtained from the recorded GRP field data-sets. Our results demonstrate that on GPR reflection images the basic fluvial forms such as (1) pool deposits generated at the junction of two channels, and (2) channel deposits may be distiguished. Their shape and characteristic spatial dimensions may be recognized from a series of profiles in different directions. Because the method can detect changes in the water content, the reflection image may be related even to small changes in the degree of saturation of the sediments. Thus reflectors can indicate the changing composition of sediments.

Numerical simulations of Twin Lake Natural‐Gradient Tracer Tests: A comparison of methods

The primary objectives of the Twin Lake experiments have been to study geologic heterogeneities and field‐scale dispersion and to provide data for developing and evaluating groundwater flow and transport models. The experiment reported here was undertaken in 1987–1988 to expand the studies of heterogeneity and dispersion from a 40‐m scale investigated in 1983 to a full 270‐m scale from the point of tracer injection to the groundwater discharge zone. The hydrogeologic setting, the experimental and analytical methods, and the interpretation of experimental data are the topics of discussion in this paper. The 1983 and 1987–1988 tracer tests were used to evaluate the predictive abilities of various numerical groundwater flow and transport models. The modeling is done along the mean flow direction in the vertical plane. The two‐dimensional finite‐element modeling was successful in simulating the hydraulic head distribution but not the groundwater motion or the tracer transport. In addition, owing to the advection‐dominated nature of the groundwater flow, the transport simulation suffered from numerical dispersion. Significant improvements in simulations were obtained using method‐of‐characteristics‐and random‐walk‐based computer models. The influence of dimensionality on the transport simulation was evaluated by comparing the two‐ and three‐dimensional random‐walk simulations. It was found that over the first 40 m along the mean flow path, the three‐dimensional simulation does not reproduce the plume migration any better than the two‐dimensional simulation does. Random‐walk simulations of the transport observed in the 1983 and 1987–1988 tests are also done on the basis of the advection‐dispersion equation and tracer test‐derived velocities without invoking the concept of hydraulic conductivity and Darcy's law. These simulations were found to be superior to simulations based on the coupled flow and transport models. It was also found that the simulated hydraulic head distribution is insensitive to spatial variations in hydraulic conductivity and the simulated groundwater velocity distribution is inappropriate for transport modeling. It was concluded that the advection‐dispersion models of the local‐scale transport perform better in predicting the tracer migration at the Twin Lake aquifer using measured velocities rather than velocities simulated by a flow model.

Transport of cobalt(2+) in a physically and chemically heterogeneous porous medium

The fate of radionuclides in the subsurface is of critical importance to the planning, siting, and evaluation of repositories for radioactive wastes. Mathematical models are an integral component of this process. An accurate understanding of radionuclide transport is required to successfully formulate and use these models. It is wellknown that the subsurface is both physically and chemically heterogeneous. Recent research has shown that the resultant spatial variability of hydraulic conductivity and of sorption capacity can significantly affect solute transport in the subsurface. The impact of hydraulic conductivity variability and sorption capacity variability on the transport of radionuclides is, therefore, of great interest. Very few well-controlled, experimentally based laboratory investigations of the transport of radionuclides in physically and chemically heterogeneous porous media have been reported in the literature. The purpose of this paper is to report the preliminary results of such an investigation. We present results obtained for transport of Co2+ in a column packed with two media of differing hydraulic conductivities and sorption capacities. In addition to being influenced by these heterogeneities, transport of the Co2+ is also influenced by rate-limited diffusive mass transfer and nonequilibrium sorption.

Probability Distributions for Hydraulic Conductivity of Compacted Soil Liners

This paper describes an analysis of hydraulic conductivity data collected from 57 landfill liners and covers throughout North America. Statistical characteristics of the data are summarized, and goodness‐of‐fit analyses are performed on each set to determine a distributional form that can be used to describe spatial variability of hydraulic conductivity. The statistics of hydraulic conductivity are shown to vary widely. The mean varied from 2.9×10-9 to 1×10-5cm/s, the coefficient of variation varied between 27 and 767, the coefficient of skewness between −0.23 and 7.7, and the coefficient of kurtosis from 1.75 to 58. Goodness‐of‐fit tests show that the two‐parameter log‐normal hypothesis is often rejected. The traditional two‐parameter log‐normal distribution is compared to four alternative distributions: the three‐parameter log‐normal, generalized extreme value (GEV), the three‐parameter gamma, and inverse Gaussian. The analyses show that the three‐parameter log‐normal and GEV result in superior fits to ...

Neural network‐based screening for groundwater reclamation under uncertainty

Uncertainty due to spatial variability of hydraulic conductivity is an important issue in the design of reliable groundwater remediation strategies. Using groundwater management models based on a stochastic approach to groundwater flow, where the log‐hydraulic conductivity is represented as a random field, is a frequently studied technique for the design of aquifer remediation in the presence of uncertainty. Such an approach employs the solution of a management model for a large set of equally probable realizations of the hydraulic conductivity. However, only a few out of the large set of realizations are critical to the final outcome of the design. The spatial distribution of the hydraulic conductivity values in a realization, and the degree of variation of the hydraulic conductivity values within a realization are identified as two important features that determine the level of criticalness of a realization. The association between the hydraulic conductivity pattern and the level of criticalness is not known explicitly and needs to be captured for efficient screening. The screening approach presented here utilizes the pattern classification capability of a neural network and its ability to learn from examples. It is shown that incorporation of only a few critical realizations in a groundwater management model can yield highly reliable remediation designs. The application of the screening tool in a pump‐and‐treat design problem is illustrated via two examples.

Comparison of Several Interpolators for Smoothing Hydraulic Conductivity Data in South West Iran

Hydraulic conductivity is an important factor in the design of subsurface drainage systems. The high spatial variability of hydraulic conductivity prevents the identification of homogeneous zones to which uniform drain spacing can be assigned. This study was conducted to determine the suitability of several interpolators for smoothing hydraulic conductivity data. Interpolation techniques used were ordinary and universal kriging, trend surface, moving average, and distance weighted moving average. The precision of interpolation was measured by cross-validation using the mean absolute error (MAE) between interpolated and observed values. The data set consisted of 383 auger hole hydraulic conductivity measurements from a 16,000 ha area in South West Iran. The semi-variogram was characterized by a range of influence of 4.5 km and a nugget effect corresponding to 67% of the sill. Values of MAE ranged from 1.373 to 2.159 m d1 depending on the method and the number of neighbors used in the interpolation. The best methods were ordinary kriging, universal kriging with a linear drift, and squared distance weighted moving average, for which the MAE values were 1.373, 1.383, and 1.392 m d1, respectively. Although the MAE values of these three methods were similar, the interpolated surfaces were very different. Because of its precision of interpolation and the smoothness of the interpolated surface, ordinary kriging was the most appropriate method for smoothing hydraulic conductivity data in this area.

Field study of dispersion in a heterogeneous aquifer: 2. Spatial moments analysis

Analysis is performed of a 20‐month natural gradient tracer study in the saturated zone of a highly heterogeneous aquifer. Graphical presentation of concentration distributions versus time and spatial moments analysis reveal dramatically non‐Gaussian behavior and a systematic mass loss. Implications of the mass loss on plume moments is analyzed through sensitivity studies. The moments data are interpreted by applying two simple models: (1) pure advection from a continuous source, and (2) advection plus dispersion in a converging nonuniform flow field. A longitudinal dispersivity of 5–10 m is estimated from the latter model and is somewhat larger than the value of about 1.5 m calculated by Rehfeldt et al. (this issue) using the stochastic theory of Gelhar and Axness (1983) based on independent measurements of the spatial variation of hydraulic conductivity. The dispersivity of 5–10 m is an order of magnitude larger than values measured at recently studied field sites (Borden and Cape Cod) with less heterogeneity, but an order of magnitude lower than would be computed from the moments data if the flow is presumed to be uniform.

Field study of dispersion in a heterogeneous aquifer: 3. Geostatistical analysis of hydraulic conductivity

Observations of the spatial variability of hydraulic conductivity at a tracer test site, located at Columbus Air Force Base in Mississippi, are presented. Direct measurements of hydraulic conductivity of the heterogeneous alluvial aquifer at the site were made using borehole flowmeter logging, slug tests, and a laboratory permeameter to test undisturbed soil cores. Indirect methods estimating hydraulic conductivity were also evaluated, including soil grain size analyses, surface geophysical surveys, and mapping of sediment facies. The spatial covariance of the 2187 hydraulic conductivity values obtained with the borehole flowmeter method was examined. The log hydraulic conductivity variance (σln2K) and the horizontal and vertical correlation scales (λh and λv) of 4.5, 12.8 m, and 1.6 m, respectively, were estimated assuming second‐order stationarity of the conductivity field. The covariance parameters are uncertain with bounding values that are 24–76% above or below the estimate. Covariance parameters estimated with more limited nonflowmeter data were within the same magnitude as those obtained using the extensive flowmeter data, suggesting that data from a variety of methods may be used to provide approximate values of the autocovariance parameters. Nonstationarity of the ln K field was examined by removing three‐dimensional polynomial trend surfaces and calculating variograms of the residuals. Significantly lower estimates for σln2K, λh and λv of 2.7, 4.8 m, and 0.8 m, respectively, were obtained from the third‐order log conductivity residuals. After trend removal, the bounding parameter values differ 15–44% from the estimated values. Accounting for unsteady flow and the uncertainty in the covariance parameters of the third‐order log conductivity residuals, the calculated longitudinal and horizontal transverse macrodispersivities ranged from 1.5 m to 1.8 m and 0.3 m to 0.6 m, respectively.

Spatial variability of hydraulic conductivity of an unconfined sandy aquifer determined by a mini slug test

The spatial variability of the hydraulic conductivity in a sandy aquifer has been determined by a mini slug test method. The hydraulic conductivity ( K) of the aquifer has a geometric mean of 5.05 × 10 −4 m s −1 , and an overall variance of 1n K equal to 0.37 which corresponds quite well to the results obtained by two large scale tracer experiments performed in the aquifer. A geological model of the aquifer based on 31 sediment cores, proposed three hydrogeological layers in the aquifer concurrent with the vertical variations observed with respect to hydraulic conductivity. The horizontal correlation length of the hydraulic conductivity has been determined for each of the three hydrogeological layers and is found to be small (1–2.5 m). The asymptotic longitudinal dispersivity of the aquifer has been estimated from the variance in hydraulic conductivity and the horizontal correlation length, to be in the range of 0.3–0.5 m compared with a value of 0.42 m obtained in one of the tracer tests performed.

A stochastic model of solute transport in groundwater: Application to the Borden, Ontario, Tracer Test

Results from the Borden tracer test are used to evaluate the performance of the stochastic model developed by Graham and McLaughlin (1989a, b). The model assumes that spatial variations in hydraulic conductivity induce variations in a steady state velocity field which, in turn, induce variations in solute concentration. Analytical expressions for the unconditional ensemble moments of velocity are derived from the unconditional ensemble moments of log hydraulic conductivity. The velocity moments are related to the ensemble moments of concentration by a set of coupled partial differential equations. The dependent variables in these equations are the concentration mean and covariance and the velocity‐concentration covariance (or macrodispersive flux). Macrodispersion is not assumed to be Fickian. The moment equations are solved with a dual‐grid finite element algorithm. The nonstationary concentration covariances obtained from the finite element solution provide the information needed to condition estimates of velocity and concentration on a small set of concentration measurements. In the Borden application considered here conditioning is performed sequentially, at 85 days and at 260 days after the injection of a pulse of conservative tracer (chloride). The conditional mean concentration provides a better estimate of the true chloride concentration than the unconditional mean. The concentration variance and macrodispersive flux both decrease at conditioning times but gradually increase after the solute plume moves out of the sampling grid. The performance of the stochastic model, as indicated by an analysis of measurement residuals, is generally consistent with the model's own estimates of concentration uncertainty.

Correction to “Comment on ‘Effective Groundwater Model Parameter Values: Influence of Spatial Variability of Hydraulic Conductivity, Leakance, and Recharge’ by J. J. Gómez‐Hern´ndez and S. M. Gorelick” by Rachid Ababou and Eric F. Wood

Correction to “Comment on ‘Effective Groundwater Model Parameter Values: Influence of Spatial Variability of Hydraulic Conductivity, Leakance, and Recharge’ by J. J. Gómez‐Hern´ndez and S. M. Gorelick” by Rachid Ababou and Eric F. Wood

Reply [to “Comment on ‘Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge’ by J. J. Gómez‐Hernández and S. M. Gorelick”

Reply [to “Comment on ‘Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge’ by J. J. Gómez‐Hernández and S. M. Gorelick”

Reply to comment on 'Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge' by R. Ababou and E. F. Wood

Reply to comment on 'Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge' by R. Ababou and E. F. Wood

Comment on "Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, Leakance, and recharge" by J. Gomez-Hernandez and S. Gorelick

Comment on "Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, Leakance, and recharge" by J. Gomez-Hernandez and S. Gorelick

Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: From data to design

Most optimization models for groundwater quality management have ignored the effects of uncertainty due to spatial variability of hydraulic conductivity. Here we explicitly incorporate this uncertainty into a procedure for the optimal design of aquifer remediation strategies. Local hydraulic conductivity and head data are used to quantify the uncertainty which is traced through to target a reliable remediation design. The management procedure is based on the stochastic approach to groundwater flow and contaminant transport modeling, in which the log‐hydraulic conductivity is represented as a random field. The remediation design procedure has two steps. The first is solution of the stochastic inverse model. Maximum likelihood and Gaussian conditional mean estimation are used to characterize the random conductivity field based on the hydraulic conductivity and hydraulic head measurements. Based on this statistical characterization, conditional simulation is used to generate numerous realizations (maps) of spatially variable hydraulic conductivity that honor the head and conductivity data. The second step is solution of the groundwater quality management model. Two management model formulations are presented. The first, termed the multiple realization management model, simultaneously solves the nonlinear simulation‐optimization problem for a sampling of hydraulic conductivity realizations. It is shown that reclamation design based on as few as 30 conductivity realizations can provide reliable (over 90%) remediation strategies. The second model, termed the Monte Carlo management model, solves the nonlinear simulation‐optimization problem individually for a sampling of hydraulic conductivity realizations. This provides a relationship between pumping (cost) and reliability. Each of the management models is linked with the stochastic inverse model, and each is demonstrated for two cases: (1) the available data are limited to hydraulic conductivity measurements and (2) both hydraulic conductivity and hydraulic head measurements are used.

A comparison of travel time and concentration approaches to modeling transport by groundwater

Two approaches to characterize transport by groundwater are compared: the common one in which solute movement is represented in terms of concentration as function of space and time and that of a travel-time probability distribution function (p.d.f.), defined as the probability of crossing of a compliance surface by a solute particle. First, the connection between the two representations is established: the travel-time p.d.f. is proportional to the mass of solute which has crossed the surface at time t. The implication of ergodicity of concentration upon travel-time distribution is discussed. The application of travel-time approach is illustrated for Fickian transport of an inert solute in a heterogeneous aquifer. The influence of spatial variability of hydraulic conductivity and of parameters estimation errors are examined separately. The relative merits of the two approaches are examined.