A plane‐strain hydraulic fracture driven by a shear‐thinning Carreau fluid

We study the propagation of a plane-strain hydraulic fracture driven by shear thinning fluid following Carreau rheology. restrict to impermeable medium case and quantify in details impact on growth shear-thinning properties between low high shear-rates Newtonian limits. derive several dimensionless numbers governing evolution solution. The notably depends ratio two limiting viscosities, index, toughness characteristic time-scale capturing instant at which inside reaches low-shear rate plateau. solve problem numerically using Gauss-Chebyshev methods for spatial discretization coupled hydro-mechanical fully implicit time integration scheme. solution evolves from an early self-similar equals one large-shear viscosity late transition period (corresponding part rheology) exhibits features similar power law rheology, albeit quantitatively different. Comparisons predictions obtained with power-law model confirm its inadequacy realistic fluids used practice compared more physical rheology: plateau rates cannot be neglected.