Abstract: Fractal Size and Spatial Distribution of Hydrocarbon Accumulations--Implications for Resource Assessment and Exploration Strategies

Christopher C. Barton

Hydrocarbon accumulations vary in size and in spatial clustering over scales ranging from one to six orders of magnitude. A proper mathematical description of these variations is needed in order to forecast the size, number, and spatial clustering of undiscovered, conventionally recoverable hydrocarbon deposits. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. Accumulation size/frequency data sets extending over six orders of magnitude, from small fields in a play to giant fields of the world, are found to be fractal with the fractal dimension ranging between 2.43 and 2.98; this allows the size and number of undiscovered accumulations to be forecast.

The spatial distribution of hydrocarbon fields is also found to be fractal, and this is used to constrain the design of exploration and development strategies. Fractal analyses of spatial distribution have been performed on quarter-mile-square cells classified as hydrocarbon bearing (production and shows combined) or dry in 1,600-square-mile portions of the Denver and Powder River basins that have been extensively drilled. These analyses were limited to cells drilled to a single stratigraphic interval 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 Denver and Powder River Basins are 1.5 and 1.4, respectively, and the fractal dimensions of the dry ells are 1.8 and 1.7. The fractal dimension for the pattern of all cells drilled is 1.8 for both basins, which suggests that historic drilling strategies used in these basins approaches a fractal dimension of 2.0. Such a high dimension suggests excess drilling which could result from a number of drilling strategies, including random drilling with no geologic input. A computer program has been developed that compares the success of historic exploration and development strategies with fractal-based geometric strategies. The latter prove to be a much more successful strategy for finding the subtle stratigraphic traps that may not be definable using geophysical techniques. Knowledge of the fractal dimension of a reservoir prior to drilling provides both a basis for selecting and also a crite ion for halting a drilling strategy that is matched to the spatial fractal dimension of the reservoir; such matched strategies indicate a more efficient and economical method than historical practice.

AAPG Search and Discovery Article #90986©1994 AAPG Annual Convention, Denver, Colorado, June 12-15, 1994