Microcrack connectivity in rocks: a real-space renormalization group approach for 3D anisotropic bond percolation Article Swipe

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Renormalization group Percolation (cognitive psychology) Anisotropy Group (periodic table) Condensed matter physics Bond Space (punctuation) Percolation threshold Physics Statistical physics Computer science Business Mathematical physics Quantum mechanics Psychology Neuroscience Electrical resistivity and conductivity Operating system Finance

Ya-Pu Zhao , Jiangce Chen , Quanzi Yuan , Che-Min Cheng ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.1088/1742-5468/2016/01/013205 · OA: W2539737732

The onset of microcrack conductivity in anisotropic rocks, which is a concern in hydraulic fracturing, was treated as a three-dimensional (3D) bond percolation problem where the bonds in the three orthogonal directions are presented with different probabilities. A real-space renormalization group (RNG) approach was expanded to calculate the critical behavior in this percolation problem, which was demonstrated to have improved accuracy for estimating critical points. A 3D phase diagram for the anisotropic percolation problem was obtained to present the relation between rock permeability and crack density, which is suitable for the needs of engineering for its accuracy and visualization.