Estimation of the three-dimensional anisotropic spatial covariance of log permeability using single-hole and cross-hole packer test data from fractured granites

Abstract

The log permeability spatial covariance function is usually estimated by semivariogram analysis of local log permeability measurements. In the presence of statistical anisotropy, however, this method is sometimes impractical because it requires a large number of measurements. In this thesis, a methodology is developed which overcomes this difficulty by combining results from both small-scale and large-scale field tests. In particular, data from single-hole packer tests conducted in vertical boreholes drilled into granite near Oracle, Arizona, are combined with cross-hole test results to determine the three-dimensional covariance structure of the local log permeability field. The combination is based on a theoretical relationship between the effective permeability tensor of a rock mass and the spatial variability of local log permeabilities within the rock mass.