Propagation of a planar hydraulic fracture perpendicular to the isotropy plane of a transversely isotropic material

We investigate the case of a hydraulic fracture (HF) propagating perpendicular to the isotropy plane of a transversely isotropic material: a relevant configuration for the growth of HFs in sedimentary rocks where fractures are propagating vertically across layers. We extend the implicit level set algorithm originally developed for the propagation of planar 3D HF in isotropic media to transverse isotropy (TI) of elasticity and toughness. Contrary to the isotropic case, the near-tip plane strain elastic relation depends on the angle α between the local propagation direction and the isotropy plane. We present an analytical solution for an elliptical HF in the toughness dominated regime and use it to benchmark our numerical solver. For a TI elastic material, we investigate HF growth for two different assumptions: isotropic material toughness or isotropic critical fracture energy. In both cases, we compare the fracture aspect ratio obtained by our numerical results with simplified estimations based on the minimization of the variation of local stress intensity factor (or energy release rate) under the assumption of an elliptical fracture. Our numerical results show that for both assumptions, the fracture aspect ratio inversely scales with the ratio of plane-strain elastic modulus in the two orthogonal directions of the material frame with a different exponent. However, the fracture is never strictly elliptical, except for a very peculiar form of toughness anisotropy.

Propagation of fluid driven fractures in transversely isotropic material

Fatima-Ezzahra Moukhtari

The propagation of fluid driven fractures is used in a number of industrial applications (well stimulation of unconventional reservoirs, development of deep geothermal systems) but also occurs naturally (magmatic dyke intrusion). While the mechanics of hydraulic fractures (HF) in isotropic media is well established, the impact of the anisotropy of natural rocks on HF propagation is still far from being understood. Sedimentary rocks like shales and mudstones are ubiquitous in upper earth crust which are made of fine layers which result in transverse isotropy. In the framework of continuous mechanics, these rocks are commonly modelled as a transverse isotropic media (TI). In addition, a large number of fluids used in HF are non-Newtonian. They typically exhibit a shear-thinning behavior which can be reproduced by different rheological models with varying levels of accuracy (Carreau, power law, Ellis). In this thesis, we focus on hydraulic fractures in impermeable TI media. We assume that the fracture propagates normal to the isotropy plane without any further assumption on its shape. This configuration is relevant for normal and strike-slip stress regimes where the minimum in-situ stress is horizontal. We combine a boundary element and a finite volume method with an implicit level set scheme to model the growth of three dimensional planar HF. Both anisotropy of elasticity and fracture energy/toughness are accounted for. This algorithm couples a finite discretization of the fracture with the solution for a steadily moving hydraulic fracture in the tip region. We show that the near tip elastic operator has a similar expression than in the isotropy pending the use of a near-tip elastic modulus which now depends on the local propagation direction with respect to the isotropy plane. Using this numerical model we quantify the fracture elongation as a function of both the elastic and fracture toughness anisotropies. The elongation is maximal in the toughness dominated regime. The transition of the viscosity to the toughness regime occurs faster along the arrester direction, thus promoting fracture elongation. In parallel, we report laboratory experiments of HF growth in cubic samples of slate Del Carmen under true-triaxial confinement. We were able to propagate a planar HF perpendicular to the bedding planes only when the initial stress normal to bedding was 20 times larger than the other two stresses. For both regimes, the fracture surfaces are very rough with a self-affine behavior in the direction of the bedding and a stationary state in the direction normal to bedding. We also investigate the effect of a non-Newtonian rheology on HF growth. We solve the problem of steadily moving semi-infinite HF driven by a Carreau fluid. We use a Gauss-Chebyshev method for elasticity combined with finite differences for lubrication flow and solve the resulting non-linear system with the Newton Raphson method. The solution exhibits four asymptotic regions: a linear elastic fracture mechanics (lefm) asymptote near the tip, high-shear rate Newtonian and power law asymptotes in an intermediate region and a low-shear Newtonian asymptote in the far field. For the same dimensionless toughness, the fluid lag is smaller than for a Newtonian fluid of low shear rate viscosity. We show that simpler rheological models (Ellis and power law) cannot capture the complete solution, which accounts for the full rheological behavior.

EPFL2020

Propagation of fluid driven fractures in transversely isotropic material

Fatima-Ezzahra Moukhtari

EPFL2020