ABSTRACT: Fractal Geometry and Reservoir Characterization

Ute C. Herzfeld

Application of mathematics in geology to date is still widely restricted to parametrical statistics of collected data, the insufficiency of which is due to its derivation from fields alien to earth sciences. In attempting to design satisfactory mathematical models, problems arise from the discrepancy between the complexity of geological features and the lack of understanding of the underlying structures and processes. The development of geostatistics from miner's estimation techniques accounting for the spatial origin of data noted a significant step toward geologically relevant but yet not physical models.

Although further developed geomathematical methods generally are more widely accepted and found more useful by practitioners, one should not hesitate to venture from tradition toward more adventurous concepts. A potential for analytical modeling in geology lies in fractal geometry, fractals being defined as objects of noninteger (Hausdorff) dimension by Hausdorff in 1919 and rediscovered as "the geometry of nature" by Mandelbrot in the 1960s. Although early examples of fractals stem from earth sciences (length of a coastline, Brownian landscape), the role of fractals in geology presently has only experimental and descriptive character.

The properties of self-similarity and the transitional status between deterministic and stochastic (random) variables (being a point of debate among geoscientists) make fractal sets suitable for use in reservoir characterization. Geometrical patterns apparent at different scales associated with the levels of information encountered during reservoir exploration may reveal a form of similarity across scale that results from one complex geological mechanism.

AAPG Search and Discovery Article #91003©1990 AAPG Annual Convention, San Francisco, California, June 3-6, 1990