Multi-phase fracturing fluid leakoff model for fractured reservoir using extended finite element method

• A novel XFEM for multi-phase fluid flow in fractured porous media is proposed.
• The refined functions allow the discontinuities in the pressure derivatives.
• The cumulative fluid leakoff is linearly related to time for fissured reservoir.
• The model can be coupled with hydro-mechanical for fracture propagation.

Fracturing fluid leakoff into natural fractures determines the propagation of a hydraulically-driven fracture, especially for slick-water fracturing in unconventional reservoirs. This paper proposes a multi-phase model of fluid flow in a fractured porous medium using the extended finite element method (XFEM), and investigates the effects of pre-existing natural fissures on fracturing fluid leakoff. This model introduces an absolute value of signed distance function and appropriate branch functions to refine the local discontinuities in the modeled pressure derivatives across the fractures. This local refinement is independent of the matching grid and is easily incorporated into XFEM-based stress analysis for crack propagation modeling. A numerical example is provided, in which the cumulative leakoff volume versus exposure time behavior for a single natural fracture with different intersection angles with a hydraulic fracture is investigated, along with that of a single non-intersected natural fracture at different distances from a hydraulic fracture. In addition, the leakoff behavior into a pre-existing fracture is compared with that into matrix rock. These comparisons indicate that the cumulative leakoff volume is linearly proportional to the square root of the leakoff time for matrix rock unaffected by fractures, while it is linearly proportional to the leakoff time in the case of non-intersected fractures.