Use of variable-scale pressure test data to estimate the log hydraulic conductivity covariance and dispersivity of fractured granites near Oracle, Arizona

Application of modern stochastic theories to nonuniform geologic media requires, among other things, knowing the principal directions and correlation lengths of the log hydraulic conductivity covariance. To infer this information by standard geostatistical methods directly from point measurements of hydraulic conductivity in three-dimensional space is seldom possible due to a ubiquitous scarcity of data. To show how this difficulty can be overcome we use an example of fractured granitic rocks near Oracle, Arizona. At this site, hydraulic conductivities were measured on a small scale by packer tests and on a larger scale by cross-hole tests. The test results suggest that the measured hydraulic conductivities can be viewed as quantities defined over a continuum which are scalar on a local scale but exhibit large scale anisotropy due to spatial nonuniformity and the effect of fracture orientations. Based on this observation, the two sets of hydraulic conductivity data are related theoretically and the resulting expression is used to estimate the anisotropic covariance function of log hydraulic conductivities at the Oracle site. We then employ these parameters to calculate a Fickian dispersivity tensor for the Oracle granite by relying on the recent theory of Neuman et al. (1987a). Our results highlight the need to extend available stochastic theories to the domain of strongly nonuniform media the properties of which fluctuate with large amplitudes.