The spatial variability of hydraulic conductivity at the site of a long-term tracer test performed in the Borden aquifer was examined in great detail by conducting permeability measurements on a series of cores taken along two cross sections, one along and the other transverse to the mean flow direction. Along the two cross sections, a regular-spaced grid of hydraulic conductivity data with 0.05 m vertical and 1.0 m horizontal spatial discretization revealed that the aquifer is comprised of numerous thin, discontinuous lenses of contrasting hydraulic conductivity. Estimation of the three-dimensional covariance structure of the aquifer from the log-transformed data indicates that an exponential covariance model with a variance equal to 0.29, an isotropic horizontal correlation length equal to about 2.8 m, and a vertical correlation length equal to 0.12 m is representative. A value for the longitudinal macrodispersivity calculated from these statistical parameters using three-dimensional stochastic transport theory developed by L. W. Gelhar and C. L. Axness (1983) is about 0.6 m. For the vertically averaged case, the two-dimensional theory developed by G. Dagan (1982Dagan ( , 1984 yields a longitudinal di. spersivity equal to 0.45 m. Use of the estimated statistical parameters describing the In (K) variability in Dagan's transient equations closely predicted the observed longitudinal and horizontal transverse spread of the tracer with time. Weak vertical and horizontal dispersion that is controlled essentially by local-scale dispersion was obtained from the analysis. Because the dispersion predicted independently from the statistical description of the Borden aquifer is consistent with the spread of the injected tracer, it is felt that the theory holds promise for providing meaningful estimates of effective transport l•arameters in other complex-structured aquifers. terns. Because sufficient concentration measurements are sometimes unavailable in practical situations and because source boundary conditions are often unknown, a dispersivity value obtained by model calibration can become highly uncertain. The dispersivity in these cases can only be regarded as a curve-fitting parameter. Recent developments in the theory of contaminant transport recognize the complexity of groundwater systems by regarding the fundamental physical and chemical properties of earth materials that affect local solute transport as stochastic processes or as spatial random fields. Then by solving a stochastic form of the governing groundwater flow and mass transport equations in which random hydraulic parameters are represented statistically, average macroscale transport parameters are derived for the purpose of making large-scale transport predictions [Gelhar, 1985]. These macroscale parameters are intrinsically related to the statistical parameters describing complex three-dimensional heterogeneity of a medium's hydraulic properties, with the relationship being determined from the solution of the stochastic equations. Examples of the appro...

A general analytical solution is developed for the problem of contaminant transport along a discrete fracture in a porous rock matrix. The solution takes into account advective transport in the fracture, longitudinal mechanical dispersion in the fracture, molecular diffusion in the fracture fluid along the fracture axis, molecular diffusion from the fracture into the matrix, adsorption onto the face of the matrix, adsorption within the matrix, and radioactive decay. Certain assumptions are made which allow the problem to be formulated as two coupled, one-dimensional partial differential equations: one for the fracture and one for the porous matrix in a direction perpendicular to the fracture. The solution takes the form of an integral which is evaluated by Gaussian quadrature for each point in space and time. The general solution is compared to a simpler solution which assumes negligible longitudinal dispersion in the fracture. The comparison shows that in the lower ranges of groundwater velocities this assumption may lead to considerable error. Another comparison between the general solution and a numerical solution shows excellent agreement under conditions of large diffusive loss. Since these are also the conditions under which the formulation of the general solution in two orthogonal directions is most subject to question, the results are strongly supportive of the validity of the formulation. tant attenuation mechanism exists in the form of molecular diffusion into the solid matrix [Golubev and Garibyants, 1971]. This mechanism acts to reduce contaminant concentrations in the fracture and thereby delays the migration of the contaminant.

Sudicky and Frind [1982] considered the physically important process of contaminant transport in a fractured porous medium. They developed analytic expressions for contaminant concentrations within equally spaced parallel fractures as well as within the matrix of the porous rock material. However, their expressions for the contaminant concentration in the porous matrix are incorrect, both for the general case with dispersion in the fracture and the simplified instance where dispersion is ignored. (Also note the error in their (35b); the term should be exp (-R2z/v) instead of exp (R2z/v)). We present the correct solutions in this paper. The steady state expressions given by Sudicky and Frind for concentrations in the porous matrix are correct. It must be emphasised that the main results illustrated and discussed by Sudicky and Frind are not affected by these errors, since they did not evaluate the expressions obtained for the porous matrix. The notation and numbering of equations used by Sudicky and Frind is retained in the working here. Where any differences occur, a definition will be given. Equations developed here are identified with numbers of the form (1'). Two errors can be identified in the expressions given by Sudicky and Frind for the concentration in the porous matrix. The first, an omission, relates to the concentration at the fracture wall, while the second stems from an error in integration. Any solution to a boundary value problem must, by definition , satisfy the imposed boundary conditions. The condition imposed at the interface between the fracture and the porous matrix is stated as c'(b, z, t) = c(z, t) (1') However, the solution given for the porous matrix (equation (31)) satisfies c'(b, z, t)= 0 (2') for all times. This indicates an omission in the solution given by Sudicky and Frind. The Laplace inversion in (29) is incomplete , since for x = b the result incorrectly gives L-•{1} =0 (Y) where L-• is the inverse Laplace transform operator. Equation (29) is therefore only correct for x > b. For x-b the inversion yields a delta function •5(t) and must be included in the overall solution (31). Sudicky and Frind make no covering statement, claiming (29) or (31) to be valid only in the region x > b. This immediately resolves the discrepancy between (1') and (2'), since the integrand in (31) is discontinuous at x = b. However, while both equations (29) and (30) are correct for x > b, a second error is apparent in expressions (31) and (36b). The time integration, in proceeding from (30) to (31), was performed incorrectly. Although they noted it earlier, Sudicky and Frind ignored the presence of u[T(0] in the kernel of the time integration of (30) by retaining the lower integral limit as zero. Here we have used the notation u[T0:)] = 0 •: < A r (4') u[T0:)] = 1 z > A Y where TOO = •:-A Y. Clearly the inclusion of (4') necessitates integration from A Y to t, not zero to t. This error by Sudicky and Frind required the introduction of the parameter fl'. In the correct solution it does not appear. Upon c...

Distinct plumes of septic system‐impacted ground water at two single‐family homes located on shallow unconfined sand aquifers in Ontario showed elevated levels of Cl−, NO3−, Na+, Ca2+, K+, alkalinity, and dissolved organic carbon and depressed levels of pH and dissolved oxygen. At the Cambridge site, in use 12 years, the plume had sharp lateral and vertical boundaries and was more than 130 m in length with a uniform width of about 10 m. As a result of low transverse dispersion in the aquifer, mobile plume solutes such as NO3− and Na+ occurred at more than 50 percent of the source concentrations 130 m downgradient from the septic system. At the Muskoka site, in use three years, the plume also had discrete boundaries reflecting low transverse dispersion. After 1.5 years of system operation, the Muskoka plume began discharging to a river located 20 m from the tile field. Almost complete NOs attenuation was observed within the last 2 m of the plume flowpath before discharge to the river. This was attributed to denitrification occurring within organic matter‐enriched riverbed sediments. The very weakly dispersive nature of the two aquifers was consistent with the results of recently reported natural‐gradient tracer tests in sands. Therefore, for many unconfined sand aquifers, the minimum distance‐to‐well regulations for permitting septic systems in most parts of North America should not be expected to be adequately protective of well‐water quality in situations where mobile contaminants such as NOs are not attenuated by chemical or microbiological processes.