--> Abstract: The Fractal Nature of Hydrocarbon Deposits, 1: Size Distributions, by C. H. Scholz and C. C. Barton; #91004 (1991)

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The Fractal Nature of Hydrocarbon Deposits, 1: Size Distributions

SCHOLZ, CHRISTOPHER H., Lamont-Doherty Geological Observatory and Department of Geological Sciences, Columbia University, Palisades, NY, and CHRISTOPHER C. BARTON, U.S. Geological Survey, Denver, CO

Fractal phenomena define scale invariant sets of objects that obey power-law size distributions. Thus, if oil deposits are fractal, the number of deposits of volume V, N(V), would, within a defined space, obey a relation N(V) = aV(-D), where the exponent D is known as the fractal dimension. Such a defined space might be the play, the basin, the province, or the world. We have examined a number of datasets for regions in mature states of exploration. In such regions we may expect that most of the larger deposits have been discovered so that the upper part of the distribution of discoveries approximately reflects the size distribution of original deposits. We find the size distributions of oil deposits to obey the fractal size distribution quite well, down to some field size where the d stribution of discovered fields is truncated for economic reasons. This distribution appears to hold at all hierarchical levels we have studied to date: the distribution of pools in a small play--the Cardium Scour of Alberta; in a large play--the Frio Standplain of the Gulf Coast; fields in basins--the Permian basin and the western Gulf of Mexico; and fields in larger territorial units--fields in the lower 48 states and giant fields (globally). The misconception that oil fields are lognormally distributed appears to reflect an artifact of the economic truncation of the datasets. In contrast to a lognormal distribution, there is no mean field size for a fractal distribution.

Within any defined space the volume of oil must be finite, thus the size distribution must be convergent. Since the maximum field within the space can always be defined but the minimum field size is arbitrary, the requirement that (Sigma)V be finite means for the fractal distribution that D be less than 2. In the cases we have studied, D is in the range 1.6-1.8; so this convergence requirement is satisfied. Thus, most of the oil is contained in the largest fields, even though there are many more small fields. Therefore, if for a given region all the larger fields have been discovered or can be estimated from a discovery process model, a robust estimate can be made of the total remaining oil in the region and of its distribution within fields of different sizes.

 

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