Fractal Characterization of a Fractured Chalk Reservoir--The Laegerdorf Case

STOLUM, HANS-HENRIK, ANDREAS G. KOESTLER, JENS FEDER, TORSTEIN JSSANG, and AMNON AHARONY, Stavanger, Norway

What is the matrix block size distribution of a fractured reservoir? In order to answer this question and assess the potential of fractal geometry as a method of characterization of fracture networks, a pilot study has been done of the fractured chalk quarry in Laegerdorf.

The fractures seen on the quarry walls were traced in the field for a total area of 200 X 45 m. The digitized pictures have been analyzed by a standard box-counting method. This analysis gave a fractal dimension of similarity varying from 1.33 for fractured areas between faults, to 1.43 for the fault zone, and 1.53 for the highly deformed fault gouge. The amplitude showed a similar trend. The fractal dimension for the whole system of fractures is 1.55. In other words, fracture networks in chalk have a nonlinear, fractal geometry, and so matrix block size is a scaling property of chalk reservoirs.

In terms of rock mechanics, we interpret the variation of the fractal dimension as follows: A small fractal dimension and amplitude are associated with brittle deformation in the elastic regime, while a large fractal dimension and amplitude are associated with predominantly ductile, strain softening deformation in the plastic regime. The interaction between the two regimes of deformation in the rock body is a key element of successful characterization and may be approached by seeing the rock as a non-Newtonian viscoelastic medium. The fractal dimension for the whole is close to a material independent limit that constrains the development of fractures.

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