Evolution of Wellbore Pressure During Hydraulic Fracturing in a Permeable Medium

In hydraulic fracturing tests, the initial crack length and the compressibility of the injection system have a significant effect on the initiation and propagation of the fracture. Numerical or theoretical models that ignore the compressibility of the injection system are unable to accurately predict fracture behavior. In this paper, a 2D analytical/numerical model based on linear elastic fracture mechanics is presented for the initiation and propagation of hydraulic fracturing from two transversely symmetrical cracks in a borehole wall. It is assumed that the fracture is driven by compressible inviscid fluid in a permeable medium. To solve the problem, the governing equations are made dimensionless and the problem is solved in the compressibility–toughness-dominated propagation regime. According to the results, the initial crack length and the compressibility of the injection system have a significant effect on fracture initiation behavior. When the initial flaw length is small or compressibility effects are important, the initiation of the fracture is accompanied by instability and the occurrence of a sudden decrease in borehole pressure and a sudden increase in crack length. If the initial crack length is large or the compressibility effects are negligible, the crack propagation is stable. The leak-off coefficient has no effect on the pressure level required for crack propagation, but with an increase in leak-off, more time is required to reach the conditions for crack propagation. The results obtained in this paper provide good insights into the design of hydraulic fracturing processes.