Experimental investigation on backflow of power-law fluids in planar fractures

In hydrofracturing, we model the backflow of a non-Newtonian fluid in a single flat-walled fracture of planar geometry and support our conceptualization with laboratory experiments. We consider a power-law fluid, a spatially homogeneous fracture aperture, and its variation in time depending on the internal fluid pressure and the elastic relaxation of the walls. The relationship between the latter quantities may be linear, akin to a Winkler soil, or nonlinear, due to the progressive softening or stiffening of the boundary associated with the properties of the surrounding rock. The result is an integrodifferential problem that generally admits a closed-form solution, albeit implicit for some quantities. In particular, a comparison is conducted between the drainage time in the present configuration and point drainage in radial geometry. The approach is generalized by introducing a leak-off, i.e., a loss of fluid at the fracture boundaries that accelerates the fracture closure, when compared to the no leak-off case. To validate the theoretical results, 14 experiments are conducted with an ad hoc replica of a rectangular fracture of aspect ratio 2.5–2.7, with a maximum height of ≈2 mm; the elastic reaction of the walls is due to o-rings, also sealing the fracture without adding friction disturbances. Fluids with different rheology, both Newtonian and shear-thinning, are associated with different boundary conditions of external pressure and overload. The match between theory and experiments is fairly good, with discrepancies of a few percent essentially due to the approximations of the theoretical model, and, for shear-thinning fluids, to the simplified constitutive equation.