Analytical solution for propagation of hydraulic fracture with Barenblatt's cohesive tip zone

摘要

In the paper, a model of a hydraulic fracture with a tip cohesive zone according to the Barenblatt's approach is considered. The particular case of inviscid fracturing fluid and impermeable rock is studied analytically. Dependencies on time of the fracture length, injection pressure, and fracture opening at the well-bore are obtained, and compared with the corresponding dependencies for a brittle (elliptic-tip) hydraulic fracture. It is proved that on the assumption of finite-ness of the cohesive stresses action range, the cohesive zone length cannot also exceed a certain limit value. The limit form of the cohesive zone is obtained, and the limit fracture toughness is evaluated. It is shown that effective fracture toughness tends to the limit value as power function of fracture length with index -1/2.