An approximate solution for toughness-dominated near-surface hydraulic fractures

• Published in: International journal of fracture Vol. 168; no. 1; pp. 93 - 100
• Main Authors: Mathias, Simon A., Fallah, Arash S., Louca, Luke A.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2011; Springer; Springer Nature B.V
• Subjects: Applied sciences; Approximation; Asymptotic methods; Automotive Engineering; Characteristics of producing layers. Reservoir geology. In situ fluids; Characterization and Evaluation of Materials; Chemistry and Materials Science; Civil Engineering; Classical Mechanics; Computer simulation; Crack propagation; Crude oil, natural gas and petroleum products; Crude oil, natural gas, oil shales producing equipements and methods; Crystalline rocks; Earth sciences; Earth, ocean, space; Energy; Exact sciences and technology; External geophysics; Fluid flow; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fuels; Fundamental areas of phenomenology (including applications); Geophysics. Techniques, methods, instrumentation and models; Hydraulic fracturing; Hydraulics; Materials Science; Mathematical analysis; Mathematical models; Mechanical Engineering; Original Paper; Physics; Prospecting and production of crude oil, natural gas, oil shales and tar sands; Solid mechanics; Specific surface; Structural and continuum mechanics; Surface energy; Blister crack; Hydraulic fracture; Fracture mechanics; Free-surface effects; Rupture; Free surface; Modeling; Hydraulic fracturing; Fracture toughness; Blistering; Fracture surface; Asymptotic approximation; Fracture energy; Fractography; Surface energy; Crack; Internal pressure
• ISSN: 0376-9429; 1573-2673
• DOI: 10.1007/s10704-010-9559-5

Asymptotic solutions for fracture opening, volume and specific surface energy for small and large fracture radii are presented from the literature. By comparison to numerical simulation of static circular fractures subject to constant and uniform internal pressures, it is found that a good approximation for fracture opening, for intermediate fracture radii, is obtained from a power mean (with exponent 1/2) of the small and large fracture radii limiting cases. The power mean equation for fracture opening is used to derive corresponding equations for fracture volume, specific surface energy and mode I and II stress intensities. These are then combined to form an approximate solution to describe the propagation of circular toughness-dominated near-surface hydraulic fractures, suitable for small, large and intermediate fracture radii. The approximate solution is shown to closely approximate results from equivalent numerical simulation.