Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution

Abstract

Permeability upscaling is physically investigated by making over 31,000 permeability measurements on a meter‐scale block of volcanic tuff. The experiments are made possible by a specially adapted minipermeameter test system. Here we present and analyze 5185 permeability values, corresponding to five different sample supports (i.e., sample volumes) collected from one of the six block faces. The results show that the measured spatial permeability patterns, bimodal permeability distribution, and semivariogram structure/length scales are closely related to the strong textural contrast characterizing the tuff sample (i.e., highly porous pumice fragments embedded in a tight rock matrix). Each of the summary statistics shows distinct and consistent trends with increasing sample support (i.e., upscaling). As the sample support increases, the mean and variance decrease according to a power law relation, and the semivariogram range increases linearly, while the general structure of the semivariogram (isotropic, spherical model) remains unchanged. Interpretation of these results is pursued from two very different points of view; one addresses upscaling of the ensemble statistics, while the second examines upscaling from a local or pointwise perspective. We find the general upscaling trends exhibited by the ensemble statistics (given above) to be consistent with the basic concepts of volume averaging, albeit nonlinear volume averaging. The bimodal characteristics of the tuff sample and the nonuniform flow conditions imparted by the minipermeameter contribute to the nonlinearity. The local analysis reveals strong variability in permeability upscaling from point to point throughout the sampling domain. Specifically, the permeability upscaling exhibited by zones rich in pumice is very different from zones dominated by matrix, unless the averaging volume is significantly larger than the spatial correlation scale.