X-FEM modelling of hydraulic fracturing

J. LUCERO, M. LUEGE, A.ORLANDO; C.TORRIJOS

Congreso; 1st Pan-American Congress on Computational Mechanics and XI Argentine Congress on Computational Mechanics; 2015

A computational model based on the extended finite element method (XFEM)is developed for hydraulic fracture analysis in porous media. The porous media equationsare obtained by applying the balance equations of mass and momentum for both solid andfluid phase and assuming the Biot-Coussy poroelastic constitutive equations for modellingthe behaviour of the solid phase, whereas the Darcy's law is employed to describe the fluidtransport within the intact part. As opposite, the flow through the crack is modelled bygeneralizing the Poiseuille's law for viscous fluids to the flow between two parallel plates,and assuming the conductivity dependent on the dynamic viscosity and the crack openingdisplacement. The full coupled equations between the flow and the displacement field ofthe matrix are obtained by applying the mass balance equations within the discontinuity.The displacement field, pressure, and the discontinuities are approximated in the spaceusing the XFEM, whereas the time discrete scheme is obtained by applying the backwardEuler method. The resulting discrete nonlinear equations are solved by applyingthe Newton-Raphson's method. A model problem of hydraulic fracturing is analysed, by looking particularly at its behaviour, near the crack-tip. Numerical experiments on the convergence with respect to mesh discretization and orientation are also presented.