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Modeling of fracture induced stress under arbitrary pressure distribution and its application in hydraulic fracturing
PENG Yu, LI Yongming, ZHAO Jinzhou
(State Key Laboratory of Oil & Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China)
Abstract:
A new fracture induced stress model was established that can calculate the stress distribution around a section of the fracture under local pressure, in which complex analysis and the Westergaard stress function in fracture mechanics were applied. Superposition of the above model to the whole hydraulic fracture, a novel model that can compute the induced stress around the fracture under arbitrary pressures was then developed. The simulation results show that the new model has high calculation accuracy, and the classical model can be as a special case of the new model. In the simulation of the influence of pressure drop, asymmetric propagation and net pressure undulate on the induced stress, the results show that, when the pressure drop is taken into consideration, the possibility for the formation of a fracture net is decreasing rapidly from wellbore to fracture tip, but the stability of natural fractures is increasing significantly. Asymmetric propagation can lead to a compressive stress section skewing to the short half fracture, while the stress distribution far from the fracture is still symmetrical to the mid-perpendicular. The affection of the net pressure undulate is within one fifth of the half fracture length. So in this case, the average pressure can be taken into the classical model to calculate the stress distribution far from the fracture face.
Key words:  hydraulic fracturing  induced stress  net pressure  asymmetric propagation  mathematical model