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.

A large-scale field experiment on natural gradient transport of solutes in groundwater has been conducted at a site in Borden, Ontario. Well-defined initial conditions were achieved by the pulse injection of 12 m s of a uniform solution containing known masses of two inorganic tracers (chloride and bromide) and five halogenated organic chemicals (bromoform, carbon tetrachloride, tetrachloroethylene, 1,2-dichlorobenzene, and hexachloroethane). A dense, three-dimensional array of over 5000 sampling points was installed throughout the zone traversed by the solutes. Over 19,900 samples have been collected over a 3-year period. The tracers followed a linear horizontal trajectory at an approximately constant velocity, both of which compare well with expectations based on water table contours and estimates of hydraulic head gradient, porosity, and hydraulic conductivity. The vertical displacement over the duration of the experiment was small. Spreading was much more pronounced in the horizontal longitudinal than in the horizontal transverse direction; vertical spreading was very small. The organic solutes were retarded in mobility, as expected. ford University advised on the selection of organic compounds; Gary Hopkins was instrumental in the design and implementation of the experiment. Kent Keller, Stephanie O'Hannesin, Ernie Kaleny, and Bill Blackport (University of Waterloo) contributed greatly during the instrumentation of the site and the collection of the samples. Other collaborators from the University of Waterloo included

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A geometric simulation method was used to develop a three-dimensional, highly detailed synthetic representation of point bar sediments in the Wabash River system. Geometric simulation methods, in comparison to well-known second-order stochastic methods, offer the advantage of being more closely related to depositional processes, which are often similarly conceptualized (i.e., described in terms of shapes of discrete bed forms, trends in grain size, and spatial relationships of defined geologic facies). Multiple scales of geometric variation were defined within a sedimentologically prescribed framework, and shapes of discrete geometric elements were established at each scale. The selected shapes were based on published field studies including sedimentological bed form studies and trench studies in active point bar sediments. The parameterization of the shapes allowed for random variability of the shape descriptors; discrete shapes were then generated and assimilated by computer. Hydraulic conductivity values were assigned to the discrete elements based on reports of observed variations in grain size and field measurements of hydraulic conductivity. The synthetic model, referred to as a numerical aquifer, is being used as the basis for extensive numerical experimentation to study the relationship between natural spatial structure and subsurface flow and transport. CriteriaGeological plausibility. The intended use of the numerical aquifer is as an assumed ground truth for the study of spatial structure and its impacts on flow and transport. Therefore it must be geologically plausible and arguably realistic. This requires that its construction represent variations in hydraulic conductivity in a manner consistent with relevant depositional processes, shapes and scales of depositing bed forms, field observations of stratification geometries and grain size variations, and actual measurements of hydraulic conductivity. 3259 3260 SCHEIBEAND FREYBERG: GEOMETRIC SIMULATION OF NATURAL POROUS MEDIA Cross sectionsof the numerical aquifer should give to the trained eye of a geologist the same qualitative visual impression as photographs and sketches of outcrops. Spatial resolution. It is widely accepted that variability at the pore scale can be adequately represented by scale-averaged parameters such as hydraulic conductivity and dispersivity at the scale of centimeters, corresponding to the laboratory scale of Dagan [1986]. At larger scales, however, it is not clear that similar constructs are well defined. Some investigators have defined scales, larger than the laboratory scale, below which variability can be neglected [e.g., Durlofsky, 1991; Dykaar and Kitanidis, 1992], but these depend on an assumed statistical homogeneity at small scales. Sedimentary deposits, however, are often highly structured at small scales and may not be well represented by statistically homogeneous models. The influence of small-scale sedimentary structure on flow in petroleum reservoirs is known to be significant [Weber, 1982[Weber, , 1986], but it...