Heterogeneity, permeability patterns, and permeability upscaling: Physical characterization of a block of Massillon sandstone exhibiting nested scales of heterogeneity

Over 75,000 permeability measurements were collected from a meter-scale block of Massillon sandstone, characterized by conspicuous cross bedding that forms two distinct nested-scales of heterogeneity. With the aid of a gas minipermeameter, spatially exhaustive fields of permeability data were acquired at each of five different sample supports (i.e. sample volumes) from each block face. These data provide a unique opportunity to physically investigate the relationship between the multi-scale cross-stratified attributes of the sandstone and the corresponding statistical characteristics of the permeability. These data also provide quantitative physical information concerning the permeability upscaling of a complex heterogeneous medium. Here, a portion of the data taken from a single block face cut normal to stratification is analyzed. Results indicate a strong relationship between the calculated summary statistics and the cross-stratified structural features visible evident in the sandstone sample. Specifically, the permeability fields and semivariograms are characterized by two nested scales of heterogeneity, including a large-scale structure defined by the cross-stratified sets (delineated by distinct bounding surfaces) and a small-scale structure defined by the low-angle cross-stratification within each set. The permeability data also provide clear evidence of upscaling. That is, each calculated summary statistic exhibits distinct and consistent trends with increasing sample support. Among these trends are an increasing mean, decreasing variance, and an increasing semivariogram range. Results also clearly indicate that the different scales of heterogeneity upscale differently, with the small-scale structure being preferentially filtered from the data while the large-scale structure is preserved. Finally, the statistical and upscaling characteristics of individual cross-stratified sets were found to be very similar owing to their shared depositional environment; however, some differences were noted that are likely the result of minor variations in the sediment load and/or flow conditions between depositional events