Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model

This paper considers the problem of a fluid-driven fracture propagating in a permeable poroelastic medium. We develop a zero-thickness finite element to model the fracture. The fracture propagation is governed by a cohesive zone model and the flow within the fracture by the lubrication equation. The hydro-mechanical equations are solved with a fully coupled approach, using the developed zero-thickness element for the propagating fracture and conventional bulk finite elements for the surrounding medium. The numerical results are compared to analytical asymptotic solutions under zero fluid lag assumption in the four following limiting propagation regimes: toughness-fracture storage, toughness-leak-off, viscosity-fracture storage and viscosity-leak-off dominated. We demonstrate the ability of our cohesive zone model in simulating the hydraulic fracture in all these propagation regimes.

► We model the propagation of a fluid-driven fracture in a permeable poroelastic rock. ► We demonstrate the ability of cohesive finite element to handle fracture propagation. ► The agreement between our numerical results and analytical solutions is very good. ► We investigate the influence of the medium permeability on the fracture propagation. ► At high permeability, both back-stress and diffusion pattern affect the propagation.