Geostatistical analysis of aquifer heterogeneity from the core scale to the basin scale: A case study

Abstract

This study examines the spatial variability of conductivity within the sandstone Wabiskaw member of the Lower Cretaceous, Middle Mannville in the Alberta Basin. The Wabiskaw is an important regional hydrostratigraphic unit. Vertical variability within the aquifer is characterized by downhole variograms of log conductivity from core measurements. They are found to exhibit pseudoperiodic structures due to alternating sand and shale layers. Horizontal spatial variability is characterized using variograms of log transmissivity and indicator data. These variograms show a steady increase in spatial variability over length scales ranging from 400 m to 100 km, characteristic of self‐similar or fractal behavior. They also reveal distinct correlation structures related to both high and low transmissivity depositional features. This study also considers the upscaling of conductivity vertically, from the core to the well scale, and horizontally, from the well to the basin scale. It is shown that traditional vertical upscaling of conductivities by arithmetic averaging causes an overestimation of transmissivity in two‐dimensional areal flow models. An alternative approach, based on power averaging, is proposed. Transmissivities derived by vertical upscaling of core measurements are compared with values derived from drill‐stem tests in the same well. No correlation between these quantities is observed. An average transmissivity for the Wabiskaw in the study area is determined by geometric spatial averaging; however, the highly clustered spatial distribution of well locations requires a weighting of sample values using ordinary kriging.