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Theoretical Models for the Effective Electrical Conductivity of Transversely Isotropic Rocks With Inclined Penny‐Shaped Cracks
Author(s) -
Yan Han,
Han Tongcheng,
Fu LiYun
Publication year - 2020
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1029/2020jb020371
Subject(s) - transverse isotropy , electrical resistivity and conductivity , anisotropy , isotropy , conductivity , materials science , composite material , geology , geotechnical engineering , geometry , optics , mathematics , physics , quantum mechanics
The existence of cracks can significantly influence the electrical properties of rocks, and electrical exploration has been applied for the detection and characterization of cracks. However, the premise is the knowledge of the quantitative effects of cracks on the electrical properties of fractured rocks, and theoretical models have provided means to obtain such knowledge. In this work, we derive explicit theoretical models for the anisotropic electrical conductivity of transversely isotropic (TI) rocks with inclined and rotated cracks, as well as cracks with random orientation distribution. Based on the developed models, we study systematically and quantitatively the effects of the crack properties and distributions on the anisotropic electrical conductivity of cracked rocks. We show that for TI rocks with aligned cracks, the inclination angle of the cracks affects both the vertical and the horizontal electrical conductivities, whereas the rotation angle only influences the horizontal electrical conductivity, although both the two angles can lead to the global rotations of the principal axes of the electrical conductivity tensor. On the other hand, the conductivity of TI rocks containing randomly distributed cracks remains transversely isotropic. For both aligned and randomly distributed cracks, the increasing crack volume fraction can linearly increase the electrical conductivity of the effective rocks, and cracks with lower aspect ratio show more significant effects on the electrical conductivity. The knowledge of the effects of the cracks on the TI rocks obtained in this study can be applied for more accurate interpretation of the electrical exploration data to better characterize cracked formations.