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Modeling fracture porosity development using simple growth laws
Author(s) -
Bloomfield John P.,
Barker John A.,
Robinson Nicola
Publication year - 2005
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.2005.0039.x
Subject(s) - aperture (computer memory) , tortuosity , exponent , fracture (geology) , porosity , sigma , geometry , materials science , physics , mechanics , mathematics , composite material , acoustics , linguistics , philosophy , quantum mechanics
A model of porosity development has been developed to investigate general relationships between simple fracture aperture growth laws and fracture porosity in evolved fracture arrays in aquifers. The growth of fracture apertures in two‐dimensional orthogonal arrays with initially spatially uncorrelated lognormal aperture distributions has been studied, where aperture growth rate is proportional to an exponent of the flow rate through each fracture. The evolved arrays show geometrical phase changes as a function of the aperture growth rate exponent, e , and the standard deviation of the initial aperture distribution, σ z . Low values of e and σ z lead to bimodal aperture distributions, where apertures parallel to flow are preferentially enlarged. At moderate values of e and σ z , there is a transition to a regime of more complex geometries consisting of networks of channel‐like structures of preferentially enlarged apertures. At larger values of e , array‐spanning channel‐like paths of preferentially enlarged apertures develop, where the tortuosity of the channel‐like paths is a linear function of σ z . Following an initial growth phase, during which dynamically stable aperture configurations develop, arrays undergo simple amplification. The geometry of the evolved aperture fields is diverse and they can be highly complex; consequently, parameterization and prediction of their evolution in terms of the initial aperture distributions and growth rate laws is not trivial.