Fractal Nature of Hydrocarbon Deposits, 2: Spatial Distribution

BARTON, CHRISTOPHER C., U.S. Geological Survey, Denver, CO, CHRISTOPHER H. SCHOLZ, Lamont-Doherty Geological Observatory and Department of Geological Sciences, Columbia University, Palisades, NY, and THOMAS A. SCHUTTER, PAUL R. HERRING, and WILLIAM J. THOMAS, U.S. Geological Survey, Denver, CO

Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension.

Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. We have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1600-mi portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. We have limited our analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimensions of the dry holes are 1.8 and 1.7, respectively. The fractal dimension for the patt rn of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir; such a strategy should prove more efficient and economical than current practice.

AAPG Search and Discovery Article #91004 © 1991 AAPG Annual Convention Dallas, Texas, April 7-10, 1991 (2009)