Permeability upscaling measured on a block of Berea Sandstone: Results andinterpretation

To physically investigate permeability upscaling, over 13,000 permeability values were measured with four different sample supports (i.e., sample volu mes) on a block of Berea Sandstone. At each sample support, spatially exhau stive permeability datasets were measured subject to consistent flow geomet ry and boundary conditions, with a specially adapted minipermeameter test s ystem. Here, we present and analyze a subset of the data consisting of 2304 permeability values collected from a single block face oriented normal to stratification. Results reveal a number of distinct and consistent trends ( i.e., upscaling) relating changes in key summary statistics to an increasin g sample support. Examples include the sample mean and semivariogram range that increase with increasing sample support and the sample variance that d ecreases. To help interpret the measured mean upscaling, we compared it to theoretical models that are only available for somewhat different flow geom etries. The comparison suggests that the nonuniform flow imposed by the min ipermeameter coupled with permeability anisotropy at the scale of the local support (i.e., smallest sample support for which data is available) are th e primary controls on the measured upscaling. This work demonstrates, exper imentally, that it is not always appropriate to treat the local-support per meability as an intrinsic feature of the porous medium, that is, independen t of its conditions of measurement.