Natural fracture aperture-size, spacing, and stratigraphic variation in fracture density are factors determining the fluid-flow capacity of low-permeability formations. In this study, several facies were identified in a Woodford Shale complete section. The section was divided into four broad stratigraphic zones based on interbedding of similar facies. Average thicknesses and percentages of brittle and ductile beds in each stratigraphic foot were recorded. Also, five fracture sets were identified. These sets were split into two groups based on their trace exposures. Fracture linear intensity (number of fractures normalized to the scanline length [[Formula: see text]]) values were quantified for brittle and ductile beds. Individual fracture intensity-bed thickness linear equations were derived. These equations, along with the average bed thickness and percentage of brittle and ductile lithologies in each stratigraphic foot, were used to construct a fracture areal density (number of fracture traces normalized to the trace exposure area [[Formula: see text]]) profile. Finally, the fracture opening-displacement size variations, clustering tendencies, and fracture saturation were quantified. Fracture intensity-bed thickness equations predict approximately 1.5–3 times more fractures in the brittle beds compared with ductile beds at any given bed thickness. Parts of zone 2 and almost entire zone 3, located in the upper and middle Woodford, respectively, have high fracture densities and are situated within relatively organic-rich (high-GR) intervals. These intervals may be suitable horizontal well landing targets. All observed fracture cement exhibit a lack of crack-seal texture. Characteristic aperture-size distributions exist, with most apertures in the 0.05–1 mm (0.00016–0.0032 ft) range. In the chert beds, fracture cement is primarily bitumen or silica or both. Fractures in dolomite beds primarily have calcite cement. The average fracture spacing indices (i.e., bed thickness-fracture spacing ratio) in brittle and ductile beds were determined to be 2 and 1.2, respectively. Uniform fracture spacing was observed along all scanlines in the studied beds.
Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets
