Scaling of fracture connectivity in geological formations

A new method to quantify fracture network connectivity is developed and applied to analyze two classical examples of fault and joint networks in natural geological formations. The connectivity measure accounts for the scaling properties of fracture networks, which are controlled by the power law length distribution exponent a, the fractal dimension D and the fracture density. The connectivity behavior of fracture patterns depends on the scale of measurement, for a D + 1. Analysis of the San Andreas fault system shows that a < D+1 and that the connectivity threshold is reached only at a critical length scale. In contrast, for a typical sandstone joint pattern, a ≈ D + 1, which is on the cusp where the connectivity threshold is highly sensitive to the minimum fracture length in the system.

[1]  Olivier Bour.  Transferts de fluides dans les milieux fractures : effets d'echelle , 1996 .

[2]  Olivier Bour,et al.  On the connectivity of three‐dimensional fault networks , 1998 .

[3]  D. Sornette,et al.  Some consequences of a proposed fractal nature of continental faulting , 1990, Nature.

[4]  T. Madden,et al.  Microcrack connectivity in rocks: A renormalization group approach to the critical phenomena of conduction and failure in crystalline rocks , 1983 .

[5]  J. Long,et al.  From field data to fracture network modeling: An example incorporating spatial structure , 1987 .

[6]  C. C. Barton.  Fractal Analysis of Scaling and Spatial Clustering of Fractures , 1995 .

[7]  Tamaz Chelidze,et al.  Percolation and fracture , 1982 .

[8]  G. Marsily,et al.  Water penetration through fractured rocks: Test of a tridimensional percolation description , 1985 .

[9]  Olivier Bour,et al.  Clustering and size distributions of fault patterns: Theory and measurements , 1999 .

[10]  Brian Berkowitz,et al.  Structure, flow, and generalized conductivity scaling in fracture networks , 1998 .

[11]  Paul Segall,et al.  Joint formation in granitic rock of the Sierra Nevada , 1983 .

[12]  E. Hauksson,et al.  Role of fluids in faulting inferred from stress field signatures , 1999, Science.

[13]  Patience A. Cowie,et al.  Determination of total strain from faulting using slip measurements , 1990, Nature.

[14]  Yves Guéguen,et al.  Percolation networks and fluid transport in the crust , 1991 .

[15]  Olivier Bour,et al.  Connectivity of random fault networks following a power law fault length distribution , 1997 .

[16]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[17]  N. P. Christensen,et al.  Variations in fracture system geometry and their implications for fluid flow in fractures hydrocarbon reservoirs , 1999, Petroleum Geoscience.

[18]  Noelle E. Odling,et al.  Scaling and connectivity of joint systems in sandstones from western Norway , 1997 .

[19]  Philippe Davy,et al.  On the Frequency-Length Distribution of the San Andreas Fault System , 1993 .

[20]  K. Furlong,et al.  Seismic Evidence for a Lower-Crustal Detachment Beneath San Francisco Bay, California , 1994, Science.

[21]  Chin-Fu Tsang,et al.  Channel model of flow through fractured media , 1987 .

[22]  C. Renshaw.  Influence of subcritical fracture growth on the connectivity of fracture networks , 1996 .