Rock Mech Rock Eng (2018) 51:653–660 https://doi.org/10.1007/s00603-017-1346-4 TECHNICAL NOTE PKN Solution Revisit: 3‑D Hydraulic Fracture Size and Stress Anisotropy Effects 1,2,4 3 2 Jincai Zhang · Yushuai Zhang · Shangxian Yin Received: 31 March 2017 / Accepted: 14 October 2017 / Published online: 24 October 2017 © Springer-Verlag GmbH Austria 2017 Keywords PKN model · Hydraulic fracture · Fracture 1 Introduction width · 3-D FEM modeling · 3-D PKN empirical solution Hydraulic fracturing is a very important stimulation tech- List of symbols nology which enables the operators to produce from those c Stress anisotropy factor tight and extremely low-permeable reservoirs (e.g., shale D Reservoir depth oil and shale gas plays). For hydraulic fracturing design, E Young’s modulus of the rock the hydraulic fracture volume needs to be calculated. The FEM Finite element method PKN solution (Perkins and Kern 1961; Nordgren 1972) H Fracture height has widely been applied in calculating the induced fracture H R eservoir thickness width by hydraulic fracturing. The PKN solution is a 2-D L Fracture length analytical solution with assumption of plane strain defor- p Downhole treatment pressure mation in the vertical plane. Perkins and Kern assumed PKN Perkins and Kern fracture that each vertical cross section acts independently; i.e., R Hole
Rock Mechanics and Rock Engineering – Springer Journals
Published: Oct 24, 2017
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