Applications of the Cluster Statistics

Abstract

This chapter presents a conceptually straightforward treatment of spatial correlations of “random” heterogeneous media, but does not intend to capture at this point even a majority of the actual behavior. A great deal of work still needs to be done since what has been accomplished so far neglects the expected geological complications due to patterns of deposition (on a wide range of scales), dewatering, alteration, deformation, and fracture. The fundamental point of this chapter will be that even if a medium itself does not exhibit correlations, the transport properties of this medium will be correlated over distances which can be very large. In fact a simple physical result emerges, namely that the length scale of correlations in the measurement of a conduction process is directly proportional to the size of the volume of measurement (Hunt, 2000), known in the hydrologic community as the “support” volume. This result is observed over 3–4 orders of magnitude of length, i.e. over 10+ orders of magnitude of the volume. Nevertheless there is as yet no proof that the percolation theoretical calculation is at the root of this experimental result.