A variational hydraulic fracturing model coupled to a reservoir simulator

• A variational approach extended to hydraulic fracturing in porous media.
• Simulation of multiple complex fractures regardless of their modes of propagation.
• Hydraulic-fracture model coupled to an existing reservoir simulator.
• Model has been tested against the Sneddon’s closed form solutions in 2D and 3D.
• Turning, branching, and merging of hydraulic fractures were demonstrated.
• Impacts of pre-existing fracture with unilateral contact condition were studied.

A variational fracture model coupled to an external reservoir simulator through variable exchange is presented. While convergence is not optimal without Jacobian matrices with which fully coupling can provide, the presented coupling scheme is versatile enough that the reservoir simulator could be easily replaced with any other simulator. A variational approach to fracture is introduced first by comparison to the classic Griffith criteria, and is then expanded to include poro-elasticity and in-situ stresses that are required in hydraulic applications. The coupled code has been tested against existing analytical solutions of fluid-driven fracture propagation. Finally, illustrative examples are shown to demonstrate that the methodology's ability to simulate multi fracture interaction with the unified approach for turning and merging fractures.