Raziuddin Khaleel

Evaluation of Van Genuchten–Mualem Relationships to Estimate Unsaturated Hydraulic Conductivity at Low Water Contents

Predicting contaminant migration within the vadose zone, for performance or risk assessment, requires estimates of unsaturated hydraulic conductivity for field soils. Hydraulic conductivities, K, were experimentally determined as a function of volumetric moisture content, θ, for Hanford sediments. The steady state head control method and an ultracentrifuge method were used to measure K(θ) in the laboratory for 22 soil samples. The van Genuchten model was used to fit mathematical functions to the laboratory-measured moisture retention data. Unsaturated conductivities estimated by the van Genuchten–Mualem predictive model, using the fitted moisture retention curve and measured saturated hydraulic conductivity, Ks, were compared to those obtained by a scaled-predictive method that uses a single K(θ) measurement as a match point near the dry regime. In general, the measured K values and those predicted from van Genuchten–Mualem relationships showed considerable disagreement. This suggests that the use of laboratory-measured Ks results in an inadequate characterization of K(θ) for the desired range of moisture content. Deviations between the measured and predicted K were particularly severe at relatively low moisture contents; for some samples, there were differences in excess of 2 orders of magnitude at low θ. However, use of the same moisture retention curve-fitting parameters and a single steady state head control-based K(θ) measurement near the dry regime resulted in considerable improvement. In fact, for the coarse-textured soils considered in this study, results indicate that a K∥θ) measurement near the dry regime must be used to obtain reliable estimates of unsaturated K at low θ. The study provided important insight on application of two different experimental techniques of measuring unsaturated conductivities.

An evaluation of analytical solutions to estimate drawdowns and stream depletions by wells

Analytical solutions for computing drawdowns and streamflow depletion rates often neglect conditions that exist in typical stream-aquifer systems. These conditions can include (1) partial penetration of the aquifer by the stream, (2) presence of a streambed clogging layer, (3) aquifer storage available to the pumping well from areas beyond the stream, and (4) hydraulic disconnection between the stream and the well. A methodology is presented for estimating extended flow lengths and other parameters used to approximate the increased head losses created by partially penetrating streams and clogging layer resistance effects. The computed stream depletion rates and drawdown distributions from several analytical solutions (Theis, 1941; Glover and Balmer, 1954; Jacob, 1950; Hantush, 1965) were compared to those obtained using a two-dimensional groundwater flow model. The stream geometry was approximated as a semicircle. Numerical simulation results indicate that, because of the use of simplifying assumptions, the analytical solutions can misrepresent aquifer drawdown distributions and overestimate stream depletion rates. Assuming that a correct simulation of the stream depletion phenomenon is provided by the numerical model, the error associated with each of the simplifying assumptions was determined. At a time of 58.5 days after pumping began, errors in computed stream depletion rates due to neglect of partial penetration were 20%, those due to neglect of clogging layer resistance were 45%, and those due to neglect of storage in areas beyond the stream were 21%. Neglecting hydraulic disconnection had only a minor effect (i.e., an error of 1% only at a time of 58.5 days after pumping began) on computed stream depletion rates and a noticeable effect on aquifer drawdown distributions.

Variability of Gardner's α for coarse‐textured sediments

Vadose zone soils in arid regions often contain a high gravel fraction (>2 mm size). This paper examines, for coarse-textured soils, variability of the slope α of Gardners [1958] unsaturated hydraulic conductivity K versus matric potential ψ relation, K = Kseαψ. The steady state head control method was used to obtain unsaturated K for tensions as high as 386 cm. A total of 79 samples were analyzed in the laboratory; the gravel fraction for the 41 gravelly samples ranged from 20 to 71% (by weight); the remaining 38 samples were sandy with no gravel fraction. The measured K values for the gravelly samples fall within a narrow range and are well within the range of measured K values for the sandy samples. The bulk of both gravelly and sandy samples can be described using a single-slope exponential model; Gardners α and the intercept K0 are based on a least squares fit to the late time measurements at lower ψ. The mean and variance of α for the gravelly samples are lower compared with the sandy type. The α values for the gravelly soils follow a normal distribution, whereas the K0 estimates and the laboratory-measured Ks follow lognormal distributions. For the sandy type, α, K0, and Ks follow lognormal distributions. The α values appear to be related to the median particle diameter d50 and the slope of the particle size distribution. A clear reduction in variability of α is apparent with an increase in d50, suggesting that the unsaturated K and α variability for the gravelly soils can be estimated within narrow ranges. The flow-weighted characteristic pore size λm is clearly dependent on the soil type; λm values for the gravelly soils are characterized by a smaller mean and variance than for the sandy type. This helps explain the finding that the range in unsaturated K for the gravelly soils is less than for the sandy type. At higher tensions the mean and variance of α and lnK0 as well as the cross correlation between α and lnK0 are important inputs to stochastic models of unsaturated flow. The implications of their variability on flow in heterogeneous media are discussed.

A Markov chain model for characterizing medium heterogeneity and sediment layering structure

[1] By leveraging use of ‘‘soft’’ data (e.g., initial moisture content, qi), this study applies the transition probability (TP) based Markov chain (MC) model to sediment textural classes for characterizing the medium heterogeneity and sediment layering structure. The TP/MC method is evaluated by simulating the vadose zone moisture movement at a field site, where the stratigraphy consists of imperfectly stratified soil layers. Soil heterogeneity is characterized via spatial variability of the geometry of soil textural classes. When the qi measurements, which carry signature about medium heterogeneity and stratigraphy, are not included in the TP/MC model, it is not possible to identify the horizontal TP. The qi measurements, when transformed into soil classes, are necessary in mapping the soil layering structure prevalent at the site. The soil hydraulic parameters for each soil class are treated deterministically and are estimated on the basis of core samples. To evaluate uncertainty in characterizing geometry of the soil classes, multiple conditional realizations of the soil classes are generated. A Monte Carlo simulation shows that the simulated mean moisture contents agree well with corresponding field observations. The observed splitting of the moisture plume in a coarse sand layer that is sandwiched between two fine-textured layers, the southeastward movement of the plume during the redistribution period, and the near-zero fluid flux below the bottom fine layer are adequately simulated. Spatial variability of the field-measured moisture content is sufficiently captured by the 95% confidence intervals calculated from the Monte Carlo simulations. Investigating the effect of data conditioning on the simulated results shows that a reduction of conditioning data does not necessarily deteriorate simulation results if other conditioning data exist within the mean length of the soil classes. The TP/MC method is flexible so that other types of site characterization data (e.g., geophysical data) can be incorporated as they become available.

Quantification of uncertainty in pedotransfer function-based parameter estimation for unsaturated flow modeling

[1] While pedotransfer functions (PTFs) have long been applied to estimate soil hydraulic parameters for unsaturated flow and solute transport modeling, the uncertainty associated with the estimates is often ignored. The objective of this study is to evaluate uncertainty of the PTF-estimated soil hydraulic parameters and its effect on numerical simulation of moisture flow. Contributing to the parameter estimation uncertainty are (1) the PTF intrinsic uncertainty caused by limited data used for PTF training and (2) the PTF input uncertainty in pedotransfer variables (i.e., PTF inputs). The PTF intrinsic uncertainty is assessed using the bootstrap method by generating multiple bootstrap realizations of the soil hydraulic parameters; the realizations follow normal or lognormal distributions. The PTF input variables (i.e., bulk density and soil texture) are obtained using the cokriging technique. The PTF input uncertainty is quantified by assuming that the cokriging estimates follow a normal distribution. Our results show that the PTF input uncertainty dominates over the PTF intrinsic uncertainty and determines the spatial distribution of the PTF parameter estimation uncertainty. When the parameter estimation uncertainty is included, the spatial variability of the measured soil hydraulic parameters is better captured. This is also the case for the observed moisture contents, whose spatial variability is well bracketed by the prediction intervals. However, this is only possible after the PTF input uncertainty is considered. These results suggest that additional sample acquisition for the PTF input variables would have a more favorable impact on reduction of the parameter estimation uncertainty than collecting additional soil hydraulic parameter measurements for PTF development.

A Catalog of Vadose Zone Hydraulic Properties for the Hanford Site

The purpose of this catalog is to integrate all available soil physics data and information from vadose zone characterization and performance assessments into one useable, scientifically defensible document.

Scale and directional dependence of macrodispersivities in colonnade networks

Macrodispersion in discrete colonnade network models is investigated using a series of Monte Carlo type numerical experiments. The numerical simulations consider fluid flow and advective transport through a square flow region of a two-dimensional network of hexagonal colonnades. Macrodispersivities are calculated as a function of the scale and orientation of the square flow region within the larger, parent geometry. Particle tracking, with flux-weighted tracer injection and monitoring, is used to generate experimental residence time distributions (RTDs). The method of moments is used to characterize the longitudinal tracer spreading. The simulated RTDs are utilized to examine the macrodispersive behavior in colonnade networks (column diameter, 1 m) with lognormally distributed fracture apertures (b, in millimeters). The network models are assumed to consist of open fractures with μln b = −1.945 and σln b = 0.896; this translates to an equivalent continuum log-conductivity variance (σln K2) of 3.67. Based on an ensemble average of 100 realizations, the slope for spatial variance versus scale of observation ranges from 3.15 to 3.36 m for varying orientations of the hydraulic gradient. For ensemble-averaged data, the varying orientations appear to have little effect on the macrodispersive behavior. For single-realization experiments, the computed macrodispersivities are directionally dependent at a length scale as large as 30 times the column diameter (and probably much beyond). The computed asymptotic and preasymptotic macrodispersivities are compared with available stochastic solutions for two-dimensional isotropic heterogeneity in the horizontal plane. The ensemble-based numerical data are in excellent agreement with the solutions of Dagan (1984, 1988) and Gelhar and Axness (1983). However, for individual realizations, nonergodic behavior is clearly apparent in the near-source, evolving region of transport, and the numerical data are quite variable between realizations. The study provides important insight on applicability of stochastic continuum theories to discrete colonnade network models having σln K2 much greater than 1.

Equivalent porosity estimates for Colonnade Networks

Using a particle-tracking procedure, numerical simulations are performed to evaluate the asymptotic limits and the length scale requirements for equivalent porosity estimates of discrete colonnade networks. The simulation results are used to determine differences between the scale requirements for equivalent hydraulic conductivities and porosities. The directional dependence of the equivalent porosity is investigated using a polar plot. For a continuous network of hexagonal colonnades with uniform apertures, the asymptotic porosity estimates become directionally dependent; the numerical values compare favorably with those based on theoretical considerations. With uniform apertures, the porosity values drop sharply whenever a fracture set is perpendicular to the applied gradient and thereby becomes nonconductive. With lognormally distributed apertures, the effect of a particular fracture sets being perpendicular to the gradient is overshadowed by the effect of distributed velocities, and the asymptotic limit for the equivalent porosity ellipse approaches that of a circle. For colonnade network models with filled or unfilled apertures, the computed length scale requirements for equivalent porosity approximation are slightly smaller than those for equivalent hydraulic conductivity. The study provides guidance in selecting an acceptable block size for use in a continuum model of ground water flow and transport through colonnade networks.