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

Permeability upscaling is physically investigated by making over 31,000 per meability measurements on a meter-scale block of volcanic tuff. The experim ents 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 p atterns, bimodal permeability distribution, and semivariogram structure/len gth scales are closely related to the strong textural contrast characterizi ng the tuff sample (i.e., highly porous pumice fragments embedded in a tigh t rock matrix). Each of the summary statistics shows distinct and consisten t trends with increasing sample support (i.e., upscaling). As the sample su pport increases, the mean and variance decrease according to a power law re lation, and the semivariogram range increases linearly, while the general s tructure of the semivariogram (isotropic, spherical model) remains unchange d. Interpretation of these results is pursued from two very different point s of view; one addresses upscaling of the ensemble statistics, while the se cond 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 nonl inear volume averaging. The bimodal characteristics of the tuff sample and the nonuniform flow conditions imparted by the minipermeameter contribute t o the nonlinearity. The local analysis reveals strong variability in permea bility upscaling from point to point throughout the sampling domain. Specif ically, the permeability upscaling exhibited by zones rich in pumice is ver y different from zones dominated by matrix, unless the averaging volume is significantly larger than the spatial correlation scale.