**Abstract**

[9] USEPA R-04-003 Appendix A Hydraulic Fracturing White PaperJune (2004).

Fracturing and Geothermal Energy, (1983). , 59-74.

6/01/2013)

400 Effective and Sustainable Hydraulic Fracturing

[10] Rummel, F, & Kappelmayer, O. The Falkenberg Geothermal Frac Project: Concepts and Experimental Results, In: Nemat-Nasser S, Abé H., Hirakawa S (ed) Hydraulic

[11] Wired Science: Energy Company Plans to Frack a Volcanoreported 10.04.(2012). http://www.wired.com/wiredscience/2012/10/newberry-volcano-fracking/accessed

[12] Johnson, S. M, & Morris, J. P. Hydraulic Fracturing Mechanisms In Carbon Seques‐ tration Applications, 43rd U.S. Rock Mechanics Symposium & 4th U.S.- Canada Rock

[13] Yan Jun FengXiu Wei Shi, Hydraulic Fracturing Process: Roles of In Situ Stress and

Mechanics Symposium, June July 1, (2009). Asheville, North Carolina, 28.

Rock Strength, (2012). Advanced Materials Research, 616-618, 435

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 and a 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 between the 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 over the wellbore radius, the ratio between the wellbore radius and a length-scale associated with the 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.
