We investigate the initiation and early-stage propagation of an axi-symmetric hydraulic fracture from a wellbore drilled in the direction of the minimum principal stress in an elastic and impermeable formation. Such a configuration is akin to the case of a horizontal well anda hydraulic fracture transverse to the well axis in an open hole completion. In addition to the effect of the wellbore on the elasticity equation, the effect of the injection system compressi-bility is also taken into account. The formulation accounts for the strong coupling betweenthe elasticity equation, the flow of the injected fluid within the newly created crack and the fracture propagation condition. Dimensional analysis of the problem reveals that three di-mensionless parameters control the entire problem: the ratio of the initial defect length overthe wellbore radius, the ratio between the wellbore radius and a length-scale associated withthe fluid stored by compressibility in the injection system during the well pressurization,and finally the ratio of the time-scale of transition from viscosity to toughness dominated propagation to the time-scale associated with compressibility effects. A fully coupled nu-merical solver is presented, and validated against solutions for a radial hydraulic fracture propagating in an infinite medium. The influence of the different parameters on the transi-tion from the near-wellbore to the case of a hydraulic fracture propagating in an infinite me-dium is fully discussed.

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