SEDIMENTOLOGY AND PERMEABILITY VARIATION OF SHALLOW-MARINE SANDSTONES, STRAIGHT CLIFFS FORMATION (UPPER CRETACEOUS), SOUTHERN UTAH: THE FRACTAL/FACIES CONCEPT FOR REPRESENTING NATURAL HETEROGENEITY

For the past two decades, geologists and subsurface hydrologists have been studying permeability variation in sediments. Stochastic hydrologists typically deal with stationary random processes, while geologists describe aquifer properties in terms of depositional processes and modification (facies creation). Although geologic studies support the fact that deterministic processes play a dominant role in the creation of sedimentary property distributions, chaotic processes play an important role also. The signature of chaotic processes is fractal scaling of property values, and this type of scaling is exhibited by non-stationary random processes with stationary (space-independent) increments. Thus one way to integrate sedimentary geology and stochastic hydrology is to apply fractal-based concepts within facies structure.

Large-scale sedimentological study, combined with small-scale field measurement of permeability, for part of the Upper Cretaceous Straight Cliffs Formation near Escalante, Utah, provides insight to understanding facies-dependent permeability variation. Using a newly designed drill-hole mini-permeameter probe, 516 permeability measurements were made in triplicate at a sample spacing of 15 cm for two facies within this unit: lower shoreface bioturbated sandstone and upper shoreface cross-bedded sandstone. Incorporating the sedimentological results, analytical property distribution methods were conditioned to the outcrop data for characterizing heterogeneity. Increments (differences in values) of natural log permeability over set distances between measurements were analyzed. The analysis shows that the outcrop permeability data display the property of "scaling" in fractal theory, and that stochastic fractal structure is present.

Results of this study demonstrate facies-dependent variations in permeability and scale and support a new concept for representing natural heterogeneity, which is called the fractal/facies concept (Lu et al., in press, Hydrogeology Journal). The significance of this concept is its application to selecting realistic property values, such as permeability, between known values. The fractal/facies approach offers an alternative to using variograms for predicting subsurface properties or generating property realizations.