An X-FEM technique in modeling hydro-fracture interaction with naturally-cemented faults

•X-FEM implementation of hydro-fracture evolution in fractured formations.•Formulation of fracturing flow distribution throughout fracture network.•A novel non-dimensionalisation strategy for the hydraulic fracturing problem.•Hydro-fracture interaction scenarios with idealized naturally-cemented faults. In this paper, an enriched finite element method is presented to model the interaction between the hydraulically-driven fracture and the pre-existing naturally-cemented fault within an impermeable domain. The inflow and continuity equations of the fluid phase are solved throughout the discontinuities in conjunction with the momentum balance equation of the bulk using a sequential manner based on the staggered Newton algorithm. The frictional contact behavior along the overlapped zone of the naturally-cemented fault is modeled through the extended–FEM penalty scheme. The effect of cementation bond along the natural fault is incorporated employing a modified Coulomb law to derive the cementation tractions. Various interaction scenarios are recognized based on a novel approach accounting for the effect of fracturing fluid diversion into the intersected fracture network. Finally, several numerical examples are presented in order to illustrate the performance and accuracy of the proposed computational algorithm. Accordingly, it is shown by increase in natural fracture length, the probability of hydro-fracture arrest is increased. Meanwhile, the shear resistance of the natural interface plays the key role in development of the penetration scenario.