ИСТИНА

Fracture tip model is an essential part of numerical simulators of hydraulic fracture (HF) propagation (e.g., Planal3D approach). The main purpose of the tip model is to accurately resolve the coupled physical processes (e.g., rock breakage, fluid pressure drop in the viscous fluid flow in the fracture, fluid exchange between fracture and the rock), which have O(1) influence on the HF propagation, but may occur on a lengthscale too small to be efficiently captured in a coarse grid simulator. The tip solution parametrized by the fracture front velocity can be integrated into a numerical simulator as a “tip element”, e.g., allowing to resolve the fracture front advance at each time step of the simulation. The current work is devoted to the construction of the near-tip solution of a fluid-driven fracture propagating in a permeable elastic reservoir rock with account for pressure-dependence of the fluid exchange between the fracture and the reservoir. The fracture tip model is represented by a semi-infinite fracture moving with a constant velocity. We account for the usual coupling between the two dissipative processes in the HF propagation: the rock breakage and the viscous fluid flow. The model also accounts for three possible fluid balance mechanisms: storage in the fracture, leak-in and leak-off from the fracture. The leak-in of the pore fluid into the fracture arises naturally at/near the tip, as the new crack volume is continuously created at the advancing fracture front, only to be eventually leaked-off back into the formation at some distance behind the front as the fluid pressure recovers. This process results in a pore fluid circulation cell/cavity adjacent to the propagating HF tip [see also, Detournay and Garagash 2003]. In this work, we obtain and fully characterize the general numerical solution for opening and pressure along the semi-infinite fracture within the problem parameteric space, identifying the parametric domains corresponding to the various limiting regimes of the HF propagation. Utilising the proposed model, we assess the impact of pore fluid leak-in and associated near-tip circulation cavity on the hydraulic fracture propagation, and explore limitations of the widely-used, pressure-independent leak-off approximation (i.e., “Carter’s law”).