Formulas to find oil fields

Fractals have provided a rich source of new ideas when applied to the study of the earth, mainly through the recognition that many natural phenomena are scale invariant, ie their form is similar when studied at different scales. Thus the shapes of coastlines have become a classical example of fractal geometry. This book contains a series of research papers and reviews which illustrate how fractal concepts can be used to quantify the spatial heterogeneity of different geological features in an attempt to improve approaches to the exploration for and production of hydrocarbons.

New concepts can influence the search for oil and gas by either directly predicting and locating their occurrence or by improved understanding of the processes which led to their formation and accumulation. This book illustrates both approaches.

In regions that have been extensively explored for hydrocarbons, information about the size and distribution of oil fields is important and may be of use in new areas of exploration. In the first part of this book various authors, including Benoit Mandlebrot and the two editors, examine data on the size of fields and compare them to the power-law (or Pareto) distribution model. In its most easily used form, this states that the number (N) of fields exceeding a size (s) is N = C s-D, where C is a constant and D is the fractal dimension.

In a mature oil province, data generally support the validity of the model, although problems exist in both defining the sizes of fields and in ensuring that all fields of a given size have been found. Christopher Barton and Scholz provide a nice illustration of how early exploration of a region in Texas led to the discovery of the big fields, with subsequent "in filling" of numerous small fields. By the time a few hundred fields have been discovered the power-law distribution is apparent.

How can this fractal distribution of field sizes be put to practical use? Clearly if the parameters C and D, and the size of the largest field are known or can be estimated from early discoveries, then it is a simple matter to calculate the number of fields above a size deemed to be economically exploitable. This is an important element in any decision to invest in further exploration, but a more difficult decision is knowing where to drill. Paul La Pointe suggests that the fractal distribution of oil and gas may help such decision making.

These predictions may keep oil company executives happy, but fractals offer the geologists new insights into the complex processes which form oil fields. Fractal methods may be used to analyse the sequence of strata and their reservoir properties, thus aiding correlation and facies interpretation, either directly from rock sequences or from properties logged in wells. The recognition that many geophysical signals are examples of fractal noise can be used to improve well log and seismic interpretation, the cornerstones of petroleum exploration and reservoir interpretation.

The physics of fracturing and fluid flow is highly nonlinear; fractal methods are beginning to provide greater understanding of reservoir behaviour and need to be incorporated into the simulation of reservoirs.

There are informative, up-to-date discussions of all of these important topics in this book. There are some important areas not covered, such as the fractal nature of faults, which control many oil fields and are important in production, but this topic is well covered in the recent literature. This book should be of interest to a wide range of geologists.

David J. Sanderson is professor of geology, University of Southampton.