ABSTRACT:

This paper revisits the problem of an elliptical planar fracture in a transversely isotropic (TI) material. Transverse isotropy can be used to represent the behavior of finely layered shale formations subject to hydraulic fracturing (HF). In contrast to isotropic homogeneous formations, in which penny-shaped vertical fractures are produced, the elastic anisotropy changes the aspect ratio of fractures. The latter aspect ratio of a uniformly pressurized (or ‘dry’) elliptical crack can be estimated for given TI elastic parameters. We extend this result to hydraulically driven fractures by using the near-tip asymptotic solutions of the crack for different regimes of propagation. The crack aspect ratios for the toughness-dominated regime, the viscosity-dominated regime, and the regime determined by yield stress of Hers chel-Bulkley fluid are calculated. The aspect ratio for the toughness-dominated regime is in agreement with the known solution for the ‘dry’ crack, while for other regimes the aspect ratio is different.

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