On the undrained and drained hydraulic fracture splits

The simulation of hydraulic fracturing (HF) involves the solution of a hydro-mechanically coupled system. This article presents a new iterative sequential coupling algorithm, the undrained HF split, that improves the simulation of HFs in impermeable media. A poromechanics analogy is used to derive a stable split for the hydro-mechanically coupled system in which the mechanical subproblem is solved first. The proposed undrained HF split is applied to the simulation of cohesive HFs in an impermeable elastic medium. The cubic law is used as the constitutive model for simulating fluid flow in fractures. A minimum hydraulic aperture is assumed in the cohesive tip zone, where the mechanical aperture smoothly vanishes. While general in its nature, the undrained HF splitting scheme is employed within the context of a two-dimensional eXtended finite element model for the fractured solid, and a regular finite element model for fluid in the fracture. The undrained HF split is successfully used to simulate self-similar plane strain HFs as well as the propagation of HFs from a wellbore under anisotropic stress conditions. Fracture trajectories and local alteration of stress field are investigated. The solution of the undrained HF split converges to the same solution as the fully coupled model, whereas the commonly used P -> W sequential algorithm, referred to in this article as the drained HF split, generates spurious oscillations and fails to converge in many problems. The undrained HF split is shown to be stable and robust in applications where the drained HF split is unstable.