Fractal Heterogeneity of Clastic Reservoirs

Hans-Henrik Stolum

Significant improvements in understanding and predicting reservoir behavior would result if geological and simulation models could be efficiently integrated. This presentation outlines how that aim could be facilitated by using the fractal properties of reservoir rocks.

More precisely, shaly units within a marginal marine sand-shale sequence show a fractal distribution pattern. "Fractal" means the distribution is self-similar over a wide range of scales. This pattern is caused by depositional mechanisms, so the value of its fractal dimension is determined by the depositional environment. The complex studied consists of a rather poor reservoir unit with low connectivity between individual sand lenses and one good reservoir unit. The lithologic fractal dimension of the poor unit is 2.71, and the good unit is 2.82. This dimension, paired with a parameter directly related to the net/gross ratio (the shale factor) forms an excellent tool for quantitatively describing fractal heterogeneity.

This fractal pattern observed in one dimension (core) reflects a three-dimensional pattern. Areal photographs and satellite images of two marginal marine, tide-dominated depositional systems show distinct fractal patterns over several orders of scale (tens of meters to kilometers). That it is actually distinct lithologic facies (representing depositional environments) which are fractally distributed can be verified in one instance by reference to core data.

This implies that the fractal dimension of lithological patterns in conjunction with the shale factor is a direct measure of the facies-controlled anisotropy/heterogeneity of the reservoir rock. If generally valid, some interesting perspectives open up. Fractal heterogeneity could be described adequately for simulation purposes by only two parameters. If these parameters form an efficient measure of the effect of anisotropy/heterogeneity on permeability, they could readily be used in reservoir simulations.

AAPG Search and Discovery Article #91022©1989 AAPG Annual Convention, April 23-26, 1989, San Antonio, Texas.