Isogeometric analysis of fracture propagation in saturated porous media due to a pressurised non-Newtonian fluid

A model has been developed to simulate fractures which are pressurised using a non-Newtonian (power-law) fluid. The flow in the surrounding, deformable porous medium is described with a non-Newtonian fluid as well. The resulting model can represent the propagation of pressurised fractures, leak-off and the interstitial fluid pressure in a saturated porous medium. The resulting equations have been discretised using Non-Uniform Rational B-Splines (NURBS), cast into a traditional finite element datastructure using Bézier extraction. It is shown that lumped integration of the fracture inflow terms is needed to obtain non-oscillatory results for the fluid velocity normal to the discontinuity, and an integration scheme has been derived to prevent non-physical fluid leak-off from the fracture tips. Simulations have been carried out for a typical hydraulic fracture problem. The results show the dependence of the fluid leak-off and the fracture tip pressure on the power-law fluid index. Shear-thinning fluids result in a larger amount of fluid leak-off compared to Newtonian fluids, but their lower effective viscosity results in a higher pressure at the fracture tip. These effects influence the propagation velocity of the pressurised fracture, and thus demonstrate the importance of properly modelling the non-Newtonian character of pressurising fluids.