This paper is concerned with the problem of a radial penny-shaped hydraulic fracture transverse to a borehole. Compressibility and borehole radius effects are considered as possible candidates to explain the early unstable phase of the fracture growth observed during laboratory experiments conducted with low viscosity fluids. The fracture grows in an impermeable elastic material under conditions where it can be assumed that the fluid is inviscid. The pressure gradient along the fracture is, therefore, zero. A solution is proposed in terms of dimensionless fluid pressure, fracture radius and inlet opening. It is shown that the problem depends only on a dimensionless time τ and on a dimensionless borehole radius α. With time, the solution evolves between two asymptotic regimes where the solution is self-similar. Compressibility effects control the solution at small time while the solution at large time is dominated by material toughness. A built-in instability is identified in the system of equations describing the problem and a criterion is proposed to predict the occurrence of an unstable growth step after fracture breakdown. The potential for unstable growth depends on the initial flaw length, the fluid compressibility, the volume of fluid and the material elastic modulus.
|Original language||English (US)|
|Number of pages||14|
|Journal||Strength, Fracture and Complexity|
|State||Published - 2005|