The Evidence for and Implications of a Fractal Distribution of Petroleum Reserves

Abstract

ABSTRACT This paper presents preliminary empirical and physical evidence that oil and gas field sizes are fractally distributed. Further, the paper shows that this evidence predicts a fractal dimension greater than 1.0, which implies that larger quantities of hydrocarbons exist in smaller fields than in larger fields. If this hypothesis is true more hydrocarbons remain undiscovered in smaller fields than have been discovered to date, even in mature areas. If the hypothesis is false, the outlook for mature areas is not nearly so optimistic. The paper also presents a list of "key questions" that should be answered before one could be certain of a fractal distribution of reserves, and it gives a reliable estimate of the distribution's dimension. INTRODUCTION In the past few years, there has been a veritable boom in the application of fractal geometry to the description of geologic phenomena. Lakes, faults, topography, river basin sizes, river bends, river lengths, river discharges, dunes, earth quakes, island sizes, shore lines, diamond distribution, ore deposits, porosity, pore element cross-sections, sand-shale thickness and frequencies, sandstone grain size frequency, sedimentary structures, rainfall, and mountain ranges have all been shown to be fractally distributed.1–4 This fractal order inherent in many of nature's processes could also apply to petroleum reserves. The current consensus in the literature is that petroleum reserves follow a log-normal distribution. These studies sight empirical evidence that shows a good statistical fit between the log-normal distribution and observed field sizes. Davis and Chang5 summarize some problems with the current situation of relying on empirical data to estimate remaining reserves: "The information contained in the size distribution of discovered fields is not adequate to predict the number of pools remaining in a basin," and "In the absence of any physical theory to derive a hypothetical pool-size distribution, it seems a tremendous leap of faith to assume that a fairly restrictive family of distributions… can be used to model all petroleum basins." Fractal geometry can possibly provide a physical theory, in addition to empirical evidence, for estimating remaining petroleum reserves. This paper presents both physical and empirical evidence that petroleum reserves are distributed fractally. The reason that this is important is that if we understand whether reserves are fractally distributed and if we know the fractal dimension, then we can show if more ultimate reserves exist in larger or smaller flelds. The answer to this question has important implications for exploration in mature areas. For example, if more reserves exist in smaller fields, then, with appropriate improvements in exploration and production technology, more petroleum lies undiscovered (albeit in smaller fields) than has been discovered to date. Otherwise, the future for mature areas is not nearly as bright. This paper presents an argument for the use of fractal methods to investigate the answers to these questions. Because of the scope of this subject, however, this paper is just the beginning of this investigation—it actually raises more questions than it answers. These questions are important because their answers would determine if petroleum reserves are fractally distributed, and the fractal dimension of the distribution.