The geostatistical characteristics of the borden aquifer

Abstract

A complete reexamination of Sudicky's (1986) field experiment for the geostatistical characterization of hydraulic conductivity at the Borden aquifer in Ontario, Canada is performed. The sampled data reveal that a number of outliers {low In (K) valuest are present in the data base. These low values cause difficulties in both variogram estimation and determining population statistics. The analysis shows that assuming either a normal distribution or exponential distribution for log conductivity is appropriate. The classical, Cressie/Hawkins and squared median of the absolute deviations {SMAD) estimators are used to compute experimental variograms. None of these estimators provides completely satisfactory variograms for the Borden data with the exception of the classical estimator with outliers removed from the data set. Theoretical exponential variogram parameters are determined from nonlinear (NL) estimation. Differences are obtained between NL fits and those of Sudicky (1986). For the classical-screened estimated variogram, NL fits produce an In (K) variance of 0.24, nugget of 0.07, and integral scales of 5.1 m horizontal and 0.21 m vertical along A-A'. For B-B' these values are 0.37, 0.11, 8.3 and 0.34. The fitted parameter set for B-B' data {horizontal and vertical) is statistically different than the parameter set determined for A-A'. We 'also evaluate a probabilistic form of Dagan's (1982, 1987) equations relating geostatistical parameters to a tracer cloud's spreading moments. The equations are evaluated using the parameter estimates and covariances determined from line A-A' as input, with a velocity equal to 9.0 cm/day. The results are compared with actual values determined from the field test, but evaluated by both Freyberg (1986) and Rajaram and Gelhar (1988). The geostatistical parameters developed from this study produce an excellent fit to both sets of calculated plume moments when combined with Dagan's stochastic theory for predicting the spread of a tracer cloud. INTRODUCTION Sudick2y [ 1986] described the results of a sampling program in which a large number of hydraulic conductivity measurements were taken along two transects at the site of an daborate tracer test performed in the Borden aquifer in Ontario, Canada. These measurements, combined with a derailed evaluation of the dispersion characteristics of the injected tracer cloud [Freyberg, 1986], provided a unique opportunity to examine the validity of modern stochastic theories of contaminant transport that have emerged over the past decade. Based on the field data and subsequent geostatistica! inferences, Sudiclo, [1986] computed mean values, variances and integral scales for the underlying log conductivity distribution of the Borden aquifer. Then, by using these quantities as input to stochastic transport theories by Dagan [1982, 1987] and Gelhar and Axness [1983], the predicted field-scale flow and dispersion parameters were shown to be consistent with the observed evolution of the tracer plume as interpreted by Freyberg [1986]. The geostati...

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