On the undrained and drained hydraulic fracture splits

Abstract

Summary 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.

A convergence study of monolithic simulations of flow and deformation in fractured poroelastic media

“…However, the rate of convergence decreases and it appears to stagnate around the used convergence criterion. This behaviour has also been observed in literature for the iterative undrained hydraulic fracturing split . Adding the final two terms further enhances the rate of convergence.…”

“…Since Equation is linear, it exactly accounts for the pressure changes caused by fluid being absorbed due to the opening of the fracture. This is comparable to the undrained hydraulic fracturing split, which has improved convergence and stability compared to the drained split …”

“…This inflow is then assumed constant, and the new displacements and interstitial fluid pressures are calculated. In the case of an impermeable porous medium, this corresponds to the P → W /drained hydraulic fracturing split …”

“…Staggered and iterative schemes have been applied successfully for the simulation of poroelastic problems, allowing for the combination of separate solvers developed for the fluid problem and the resolution of the displacements. Simulation of pressurised fractures in nonporous media has shown the ability of iterative schemes to yield stable solutions in spite of large nonlinearities introduced by the fracture . This was achieved by applying an undrained hydraulic fracture split, taking into account the changes in the fluid pressure caused by the fracture opening while solving for the displacements of the solid constituent.…”

Direct simulation vs subgrid scale modelling of fluid flow in fractured or fracturing porous media

“…First, an iteration of the porous domain with a Newton-Raphson scheme is carried out. To approximate the influence of the fracture flow, an undrained assumption is used in which the pressure inside the fracture is altered due to changes in the fracture height [17,28]. Using Eq.…”