A critical review of dispersivity observations from 59 different field sites was developed by compiling extensive tabulations of information on aquifer type, hydraulic properties, flow configuration, type of monitoring network, tracer, method of data interpretation, overall scale of observation and longitudinal, horizontal transverse and vertical transverse dispersivities from original sources. This information was then used to classify the dispersivity data into three reliability classes. Overall, the data indicate a trend of systematic increase of the longitudinal dispersivity with observation scale but the trend is much less clear when the reliability of the data is considered. The longitudinal dispersivities ranged from 10−2 to 104 m for scales ranging from 10−1 to 105 m, but the largest scale for high reliability data was only 250 m. When the data are classified according to porous versus fractured media there does not appear to be any significant difference between these aquifer types. At a given scale, the longitudinal dispersivity values are found to range over 2–3 orders of magnitude and the higher reliability data tend to fall in the lower portion of this range. It is not appropriate to represent the longitudinal dispersivity data by a single universal line. The variations in dispersivity reflect the influence of differing degrees of aquifer heterogeneity at different sites. The data on transverse dispersivities are more limited but clearly indicate that vertical transverse dispersivities are typically an order of magnitude smaller than horizontal transverse dispersivities. Reanalyses of data from several of the field sites show that improved interpretations most often lead to smaller dispersivities. Overall, it is concluded that longitudinal dispersivities in the lower part of the indicated range are more likely to be realistic for field applications.

Observations of the spatial variability of hydraulic conductivity at a tracer test site, located atColumbus 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 (cr•2n •c) and the horizontal and vertical correlation scales (An and X,) 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 nonfiowmeter 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 In K field was examined by removing three-dimensional polynomial trend surfaces and calculating variograms of the residuals. Significantly lower estimates for cr•2n K, An and A• 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.

Results are presented for a large-scale natural gradient tracer experiment conducted in a heterogeneous alluvial aquifer at a site near Columbus, Mississippi. The study was initiated with a 48-hour pulse injection of 10 m 3 of groundwater containing bromide and three organic tracers (pentaftourobenzoic acid, o-trifiuoromethylbenzoic acid, and 2,6-diflourobenzoic acid). Over a 20-month period, seven comprehensive samplings of the tracer plume were performed at approximately 1-to 4-month intervals using an extensive three-dimensional sampling well network. The dominant feature of the tracer plume that evolved during the study was the highly asymmetric concentration distribution in the longitudinal direction. This asymmetry was produced by accelerating groundwater flow along the plume travel path that, in turn, resulted from an approximate 2-order-of-magnitude increase in the mean hydraulic conductivity between the near-field and far-field regions of the site. The Columbus study is distinct from previous natural gradient experiments because of the extreme heterogeneity of the aquifer, the large-scale spatial variations in groundwater velocity, and the extensive set of hydraulic conductivity measurements for the aquifer.

The dispersion of a solute plume resulting from unsteady flow in three-dimensional, heterogeneous porous media was analyzed using stochastic continuum theory. Asymptotic stochastic solutions of the perturbed unsteady flow and solute transport equations were used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three-dimensional, statistically anisotropic input covariance describing the hydraulic conductivity and an input covariance describing the temporal variability of the mean hydraulic gradient. The flow equation was approximated by neglecting the influence of internal storage due to medium and fluid compressibility (specific storage, S s • 0). The predictive expression for the macrodispersivity tensor is the sum of two components: a spatial variability component identical to previous steady state theory and an unsteady component. Two special cases of unsteady flow were examined: variation only in the magnitude and variation only in the direction of the hydraulic gradient. Gradient magnitude variation produces a slightly larger longitudinal macrodispersivity than does the steady flow case, whereas gradient direction variation produces a significantly larger transverse macrodispersivity. Longitudinal and horizontal transverse macrodispersivities predicted with the unsteady stochastic theory were shown to be of a magnitude similar to observed values from the Borden, Cape Cod, and Columbus tracer experiments. 1964; Gelhar and Axness, 1983; Molz et al., 1986; Dagan, 1984, 1989; Neuman et al., 1987]. Near the source of contamination, solute shoots out along pathways of large hydraulic conductivity, but lags behind in regions of small K. Accurate modeling of this advection-dominated nearsource behavior requires a detailed understanding of the local heterogeneity. Much farther from the source, the solute disperses more rapidly than expected from laboratory measurements of dispersion [Anderson, 1979; Gelhat et al., 1985, 1992]. This enhanced field-scale mixing is caused, in large part, by the variability of K. Detailed measurement of the heterogeneous K field for use in advection-dominated models with laboratory-scale dispersivities is an unrealistic alternative for large-scale problems. Deterministic modeling of solute transport in a heterogeneous aquifer with only laboratory-scale dispersivity would require at least four cells per hydraulic conductivity correlation length [Ababou et al., 1989]. Thus, over 2 billion cells would be required to describe the Cape Cod sewage plume [LeBlanc, 1984], which is 3500 m long, 1000 m wide, and 25 m thick in an aquifer with horizontal and vertical correlation lengths of 3.5 and 0.19 m, respectively [Hess et al., 1992]. Of course, one should always obtain as much information about the flow system as resources will allow and incorporate that information into any modeling effort. Nonetheless, some form of advection-dispersion model with field-scale macro-1Now at Illinois State Water Survey, Office of Ground Water Quality,...

Interest in geothermal energy production has grown rapidly in recent years due to the increasing demand for clean, renewable, domestic energy. Recent publications have suggested that geothermal energy from Enhanced Geothermal Systems could satisfy a large portion of the energy needs in the U.S. if the technology were implemented on a large scale. Pertinent to this goal are many of the lessons learned from the pioneering Hot Dry Rock project aimed at producing usable energy form the heat of the earth, conducted from 1970 to 1995at Fenton Hill, New Mexico, USA. During this project, the Los Alamos National Laboratory created and tested two reservoirs at depths in the range of 2.8 to 3.5 km in crystalline rock formations underlying the Fenton Hill site. Thermal energies in the range of 3-10 MWt were produced demonstrating the technical feasibility of the concept. Many important lessons were learned regarding the creation, engineering and operation of such subsurface systemsthese lessons will prove valuable as the geothermal community moves towards the goal of realizing the immense potential of this ubiquitous renewable energy resource.The purpose of this paper is to provide a brief, easy to read overview of this pioneering project.