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The original pseudo three-dimensional (P3D) model is extended to an arbitrary
stress contrast on the basis of the correspondence principle suggested. The principle employs
the similarity between solutions to plain-strain elasticity problems for (i) the crack,
corresponding to the central cross-sections of the P3D model, and (ii) the crack of the
Khristianovich-Geertsma-de Klerk (KGD) model, when the sizes and average openings of the
cracks are the same. This suggests using the propagation speeds of the KGD problem for
assigning the speed of the height growth of the P3D model. This approach is applicable in all
the cases when the KGD problem may be accurately solved; specifically, when accounting for
an arbitrary stress contrast.
Keywords: hydraulic fracturing, pseudo three dimensional (P3D) model, stress contrast |
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