A natural gradient experiment on solute transport in a sand aquifer: 2. Spatial moments and the advection and dispersion of nonreactive tracers

Abstract

The three‐dimensional movement of a tracer plume containing bromide and chloride is investigated using the data base from a large‐scale natural gradient field experiment on groundwater solute transport. The analysis focuses on the zeroth‐, first‐, and second‐order spatial moments of the concentration distribution. These moments define integrated measures of the dissolved mass, mean solute velocity, and dispersion of the plume. Moments are estimated from the point observations using quadrature approximations tailored to the density of the sampling network. The estimators appear to be robust, with acceptable sampling variability. Estimates of the mass in solution for both bromide and chloride demonstrate that the tracers behaved conservatively, as expected. Analysis of the first‐order moment estimates indicates that the experimental tracer plumes traveled along identical trajectories. The horizontal trajectory is linear and aligned with the hydraulic gradient. The vertical trajectory is curvilinear, concave upward. The total vertical displacement is small, however, so that the vertical component of the mean solute velocity vector is negligible. The estimated mean solute velocity is identical for both tracers (0.091 m/day) and is spatially and temporally uniform for the first 647 days of travel time. After 647 days of transport, the plume apparently encountered a relatively large‐scale heterogeneity in the velocity field, leading to a distinct vertical layering, and slowing the rate of advance of the center of mass of the plume as a whole. The estimated horizontal components of the covariance tensor evolve over time in a manner consistent with the qualitative shape changes observed from plots of the concentration data. The major principal axis, initially aligned roughly perpendicular to the hydraulic gradient, rotates smoothly over time until it is nearly aligned with the mean solute velocity vector, as the plume itself elongates and orients its long axis with the direction of movement. Plots of the components of the covariance tensor as functions of time show evidence of what is commonly called “scale‐dependent” dispersion: the rate of growth of the covariance over time is not linear. The theoretical results of G. Dagan (1984) calibrate well to the estimated covariance data for the first 647 days of transport. The calibrated values of the parameters of the hydrualic conductivity distribution closely match independently measured values from the site. The asymptotic longitudinal dispersivity obtained from the calibration is 0.49 m, although asymptotic conditions were apparently not reached. The estimated covariance terms for the last sampling session, 1038 days after injection, are inconsistent with the earlier data and with the Dagan model, particularly for the transverse and off‐diagonal components. This behavior is probably attributable to the observed large‐scale heterogeneity in the velocity field.

Estimation and upscaling of dual-permeability model parameters for the transport of E. coli D21g in soils with preferential flow

“…It should be emphasized that virtual fields are a simplified representation of the natural environment. Nevertheless, the stream tube model has often been used to approximate flow and transport at the field scale (e.g., Dagan, 1984;Freyberg, 1986;Gelhar and Axness, 1983;Kabala and Sposito, 1991;Russo, 1991;Sposito and Barry, 1987) and available experimental data are generally consistent with this approach (Dean and Foran, 1992;Evans and Owens, 1972;Guzman et al, 2009). Furthermore, the estimated mean and variance in microbial concentrations are needed for risk assessment.…”

“…A variety of stochastic methods have been used to describe solute transport in heterogeneous flow fields (e.g., Dagan, 1984;Freyberg, 1986;Gelhar and Axness, 1983;Kabala and Sposito, 1991;Russo, 1991;Sposito and Barry, 1987). In a simplified stochastic modeling approach the field may be viewed as a series of independent stream tubes with their hydraulic conductivity and/or other selected parameters described using probability density functions (PDFs) (Dagan, 1993;Jury and Roth, 1990).…”

Pumping tests in networks of multilevel sampling wells: Motivation and methodology

“…Unfortunately, the description of spatial variations in K on a scale of relevance for contaminant transport investigations has proven to be a difficult task. Although tracer tests performed in networks of multilevel sampling wells can be the source of valuable information about K variations [e.g., Freyberg, 1986 ever, depends critically on the connectivity of regions of high or low hydraulic conductivity, conditions which cannot be reliably determined even from a suite of single-well tests because of the lack of sensitivity of these tests to just such features. While some success has been obtained in describing patterns of K variation outside of the near-well region using geophysical techniques (to characterize major lithologic structures) in conjunction with tracer data (to estimate the hydraulic properties of the geophysically delineated zones), the dependence of this approach on data from costly tracer experiments limits its practical utility.…”

“…A new field method for the estimation of spatial variations in K between wells, hydraulic tomography, has been independently proposed by several investigators [e.g., Bohling, 1993;Tosaka et al, 1993;Gottlieb and Dietrich, 1995]. As shown in Figure 1, this method essentially consists of the performance of a series of short-term pumping tests in which the position of the stressed interval in the pumping well, isolated with packers, is varied between tests to produce a "crossed" streamline pattern similar to the crossed ray paths of a typical cross-hole seismic tomography experiment [e.g., Peterson et al, 1985].…”

Effective Parameters, Effective Processes: From Porous Flow Physics to In Situ Remediation Technology

“…A more subtle effect becomes apparent when placing a localized plume of enhanced liquid saturation into the medium, and permitting it to flow in response to gravitational force. Plume behaviok is analyzed by evaluating s p a t i a l moments (Sahimi et al, 1986a, b;Freyberg, 1986;Essaid et al, 1993). An effective transverse dispersivity for a localized plume is then calculated as…”