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

Abstract

International audienceThis 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

Numerical methods for hydraulic fracture propagation: A review of recent trends

“…Such an approach is, of course, attractive from a theoretical point of view as it does not rely on the assumptions behind Carter's leak-off. In the limit of negligible poroelastic coupling and small rock diffusivity (compared to the injection duration), the results obtained are similar to the Carter's leak-off model (Carrier and Granet, 2012;Kovalyshen and Detournay, 2013). Poroelastic effects are obviously important when the injection duration is similar to the rock diffusion time-scales.…”

“…Instead of utilizing Carter's leak-off approximation, one can instead simulate the reservoir as a porous medium and couple the equations of poroelasticity with the flow in the deformable hydraulic fracture (Boone and Ingraffea, 1990;Carrier and Granet, 2012). Such an approach is, of course, attractive from a theoretical point of view as it does not rely on the assumptions behind Carter's leak-off.…”

“…Cohesive zone models have been widely used for fracture nucleation and growth in elastic and poroelastic solids (Simoni and Secchi, 2003;Papanastasiou, 2011, 2013;Yao et al, 2015;Carrier and Granet, 2012;Chen, 2012;Yao et al, 2015). The cohesive zone model originates from the theory proposed by Dugdale (1960) and Barenblatt (1962) to overcome the stress singularity ahead of the fracture tip.…”

The enhanced local pressure model for the accurate analysis of fluid pressure driven fracture in porous materials

“…Segura and Carol [14,15] introduced a hydro-mechanical coupling formulation using zero-thickness interface elements with double nodes based on the FEM. Carrier and Granet [16] also used interface elements but included an additional degree of freedom for the pressure in the fracture. Recently, also advancements were made in continuum based hydraulic fracturing simulations using a phase-field approach [17].…”

Investigação Do Fraturamento Hidráulico Por Modelagens Analítica E Numérica

“…O modelo da zona coesiva (MZC) para fraturas, originalmente proposto por Barrenblatt (1962) e Dugdale (1960), tem sido amplamente usado com sucesso para simular processos de fraturamento em rochas (Cheng 2009,2012, Zielonka 2013, Carrier 2012, Shen 2012. Este modelo postula a existência de uma zona de processo de fratura caracterizada por uma lei coesiva de tensão de tração vs separação na ponta da fratura.…”