Topological impact of constrained fracture growth

The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.

[1]  Martin T. Dove Structure and Dynamics , 2003 .

[2]  M. Newman,et al.  Why social networks are different from other types of networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M E J Newman,et al.  Community structure in social and biological networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[4]  Assaf P. Oron,et al.  Flow in rock fractures: The local cubic law assumption reexamined , 1998 .

[5]  Carl E. Renshaw,et al.  Connectivity of joint networks with power law length distributions , 1999 .

[6]  Chrystel Dezayes,et al.  3D model of fracture zones at Soultz-sous-Forêts based on geological data, image logs, induced microseismicity and vertical seismic profiles , 2010 .

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  S. P. Neuman,et al.  Trends, prospects and challenges in quantifying flow and transport through fractured rocks , 2005 .

[9]  B. Berkowitz Characterizing flow and transport in fractured geological media: A review , 2002 .

[10]  Ove Stephansson,et al.  Fundamentals of discrete element methods for rock engineering , 2007 .

[11]  P. Davy,et al.  Percolation parameter and percolation-threshold estimates for three-dimensional random ellipses with widely scattered distributions of eccentricity and size , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  M E J Newman Assortative mixing in networks. , 2002, Physical review letters.

[13]  M. Basta,et al.  An introduction to percolation , 1994 .

[14]  Alex Hansen,et al.  Network topology of the desert rose , 2015, Front. Phys..

[15]  M. Cacas,et al.  Nested geological modelling of naturally fractured reservoirs , 2001, Petroleum Geoscience.

[16]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Sigmund Mongstad Hope,et al.  Topology of fracture networks , 2012, Front. Physics.

[18]  K. Sneppen,et al.  Specificity and Stability in Topology of Protein Networks , 2002, Science.

[19]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[20]  Steven M Gorelick,et al.  Effective permeability of porous media containing branching channel networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[22]  Xavier Sanchez-Vila,et al.  Point-to-point connectivity, an abstract concept or a key issue for risk assessment studies? , 2008 .

[23]  B. Efron The jackknife, the bootstrap, and other resampling plans , 1987 .

[24]  Olivier Bour,et al.  Connectivity properties of two‐dimensional fracture networks with stochastic fractal correlation , 2003 .

[25]  Géraldine Pichot,et al.  Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN) , 2012 .

[26]  L. R. da Silva,et al.  Self-organized percolation in multi-layered structures , 2010 .

[27]  H. Jourde,et al.  A three-dimensional model to simulate joint networks in layered rocks , 2002 .

[28]  Alex Hansen,et al.  Fracture networks in sea ice , 2014, Front. Physics.

[29]  Shilpa Chakravartula,et al.  Complex Networks: Structure and Dynamics , 2014 .

[30]  P. Davy,et al.  A model of fracture nucleation, growth and arrest, and consequences for fracture density and scaling , 2013 .

[31]  Philippe Renard,et al.  Issues in characterizing heterogeneity and connectivity in non-multiGaussian media , 2008 .

[32]  C. Darcel,et al.  Flow in multiscale fractal fracture networks , 2006, Geological Society, London, Special Publications.

[33]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  Robert C. Wolpert,et al.  A Review of the , 1985 .

[35]  R. Horne,et al.  Discrete Fracture Network Modeling of Hydraulic Stimulation: Coupling Flow and Geomechanics , 2013 .

[36]  H. Jourde,et al.  A three-dimensional model to simulate jointnetworks in layered rocks , 2002 .

[37]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[38]  D. F. Marks,et al.  An introduction , 1988, Experientia.

[39]  Anders Winberg,et al.  Site descriptive modelling during characterization for a geological repository for nuclear waste in Sweden , 2008 .

[40]  Claudio Castellano,et al.  Defining and identifying communities in networks. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[41]  Olivier Bour,et al.  A likely universal model of fracture scaling and its consequence for crustal hydromechanics , 2010 .

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

[43]  N. Odling,et al.  Scaling of fracture systems in geological media , 2001 .

[44]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[45]  Mark Newman,et al.  Networks: An Introduction , 2010 .