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flow in fractured media: A modified renormalization method
Author(s) -
Gavrilenko Pierre,
Guéguen Yves
Publication year - 1998
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/97wr03042
Subject(s) - scaling , renormalization group , renormalization , statistical physics , scale (ratio) , flow (mathematics) , permeability (electromagnetism) , percolation (cognitive psychology) , scaling law , percolation theory , fracture (geology) , geology , mechanics , mathematics , physics , geotechnical engineering , geometry , chemistry , conductivity , mathematical physics , quantum mechanics , biochemistry , neuroscience , membrane , biology
We present a methodology to account for fluid flow from microscales to macroscales in fractured media. Renormalization group (RG) theory coupled to a percolation approach provides a convenient tool to allow dealing with the complex connectivity of fracture systems and with the intricate relationship between the various scales involved and the observation scale. This method also provides us with a way to describe scale dependence of permeability ( K ). Two‐ and three‐dimensional calculations can be performed for broad distributions of both conductances and fracture lengths. Here we introduce what we call a “modified renormalization” method. This method is then tentatively applied to the upper crust where many scales of fractures are present. The results are discussed relative to the 3‐ to 4‐orders‐of‐magnitude increase in permeability which has been reported by some authors from sample scale to regional scale, and we examine how our model could be used to predict possible scaling laws.