WHY DID SUDICKY (1986) FIND EXPONENTIAL SPATIAL CORRELATION IN PERMEABILITY AT THE BORDEN SITE?

Sudicky (1986) and Woodbury and Sudicky (1991) modeled the spatial correlation of permeability at the Borden site with exponential functionals. Using these exponential permeability correlation models within a model for the second-order moments on plume spreading (Dagan, 1989) allowed them to represent the spreading of the Borden chloride plume. Following from such successful demonstrations of macrodispersion theory, an exponential spatial correlation of permeability has commonly been assumed as the stochastic theory has been further developed. However, the reasons why the spatial correlation of permeability should be exponential have generally not been explored. In unconsolidated sediments, an exponential structure can arise because permeability falls into different statistical modes. These modes correspond to different sedimentary unit types, and the unit types correspond to episodic changes in sediment deposition. Sampling across such units gives rise to a non-differentiable permeability series. In such deposits, the global spatial correlation of permeability can largely be explained by the univariate statistics for permeability (mean, variance) within unit types together with the architecture of the unit types as represented by transition probabilities. When sampling across repeated occurrences of unit types, the shape of the global permeability correlation structure is largely controlled by the transition probabilities for those unit types. The transition probabilities will have an exponential shape if the coefficient of variation in the length of the unit types is relatively large, and the global spatial correlation of permeability will follow with an exponential shape.