Spatial variability of flow parameters in a stratified sand

Abstract

The spatial variability in porosity, hydraulic conductivity, compressibility, and various grain size fractions is analyzed for several sets of samples from the Quadra Sand. This unit is a well-sorted, medium grained, horizontally stratified sand with relatively few silt or gravel interbeds. Both random and uniformly spaced sample plans are used. The heterogeneity of the flow parameters is characterized by frequency histograms and their estimated moments, by their sample autocorrelation functions, and the estimated power spectra. Emphasis is placed on the nature of the spatial dependence between neighboring values of the flow parameters. A nearest neighbor stochastic process model is fit to the data to consider its adequacy in describing the spatial dependence within the porosity and hydraulic conductivity sequences. Even though the Quadra Sand is relatively uniform, a fairly complex spatial structure is observed. A simple monotonically decaying autocorrelation function may not adequately represent the spatial continuity. Statistical anisotropy is observed in both the extent of the spatial autocorrelation and in its functional form. Results show the importance of scale in constructing a probability model to describe the spatial variability.