In this study, a computational framework is extended for the simulation of the interaction of hydro-fractures with material interfaces. Using the extended finite element method (X-FEM), the equilibrium equation of the bulk is solved in conjunction with the hydro-fracture inflow and continuity equations using the staggered Newton method. The lubrication theory is applied to model the hydro-fracture inflow, where the hydro-fracture permeability is incorporated by means of the cubic law. Specific enrichment strategy is elaborated on the basis of the Eigen-function expansion method so as to achieve at high resolution for the stress field at singular zones. The competition between different interaction scenarios is explored through the application of the Ming-Yuan & Hutchinson's penetration/deflection criterion. Finally, the robustness of the proposed framework is investigated by means of numerical simulation.
Hydraulic fracturing technique is a well-known engineering process in which permeable fractures are driven within low permeability formations by means of highly pressurized fluid injection. Since first introduced in 1950s, hydraulic fracturing has been the common practice in enhancing oil and gas recovery from tight reservoirs (Detournay & Cheng 1993). Geertsma & de'Klerk (1969), Spence & Sharp (1985), and Khristianovic & Zheltov (1955) were amongst the first who presented simplified analytical solutions to the hydraulic fracturing problem. Numerical approaches on the other hand have proven to be a versatile tool in tackling with the wide range of complicated mechanisms involved in hydraulic fracturing treatments, namely the hydro-mechanical coupling, matrix permeability, fluid-lag, and domain inhomogeneities (e.g. Detournay & Cheng 1993, Boone & Ingraffea 1990, Secchi & Schrefler 2012). A step forward in the numerical simulations of hydraulic fracturing has been due to the advanced mesh independent implementations in the context of X-FEM framework (e.g. Réthoré et al. 2007, Khoei et al. 2014, Vahab & Khalili 2018a,b).