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

Over 75,000 permeability measurements were collected from a meter-scale blo ck of Massillon sandstone, characterized by conspicuous crossbedding that f orms two distinct nested scales of heterogeneity. With the aid of a gas min ipermeameter, spatially exhaustive fields of permeability data were acquire d at each of five different sample supports (i.e., sample volumes) from eac h block face. These data provide a unique opportunity to physically investi gate the relationship between the multiscale cross-stratified attributes of the sandstone and the corresponding statistical characteristics of the per meability. These data also provide quantitative physical information concer ning the permeability upscaling of a complex heterogeneous medium. Here, a portion of the data taken from a single block face cut normal to stratifica tion is analyzed. The results indicate a strong relationship between the ca lculated summary statistics and the cross-stratified structural features vi sibly evident in the sandstone sample. Specifically, the permeability field s and semivariograms are characterized by two nested scales of heterogeneit y, including a large-scale structure defined by the cross-stratified sets ( delineated by distinct bounding surfaces) and a small-scale structure defin ed by the low-angle cross-stratification within each set. The permeability data also provide clear evidence of upscaling. That is, each calculated sum mary statistic exhibits distinct and consistent trends with increasing samp le support. Among these trends are an increasing mean, decreasing variance, and an increasing semivariogram range. The results also clearly indicate t hat the different scales of heterogeneity upscale differently, with the sma ll-scale structure being preferentially filtered from the data while the la rge-scale structure is preserved. Finally, the statistical and upscaling ch aracteristics of individual cross-stratified sets were found to be very sim ilar because of their shared depositional environment; however, some differ ences were noted that are likely the result of minor variations in the sedi ment load and/or flow conditions between depositional events.