A consistent phase field model for hydraulic fracture propagation in poroelastic media

2020 ◽  
Vol 372 ◽  
pp. 113396
Author(s):  
Liang-Ping Yi ◽  
Haim Waisman ◽  
Zhao-Zhong Yang ◽  
Xiao-Gang Li
Keyword(s):  
Hydraulic Fracture ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Fracture Propagation ◽  
Poroelastic Media ◽  
Hydraulic Fracture Propagation

A phase-field model of hydraulic fracture in saturated binary porous media

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 539-540
Author(s):  
Mangesh Pise ◽  
Jochim Bluhm ◽  
Jörg Schröder
Keyword(s):  
Porous Media ◽  
Hydraulic Fracture ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model

A Γ-convergence result for fluid-filled fracture propagation

2020 ◽  
Vol 54 (3) ◽  
pp. 1003-1023
Author(s):  
Annika Bach ◽  
Liesel Sommer
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Discontinuous Galerkin ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Fracture Propagation ◽  
Convergence Result ◽  
Elastic Media ◽  
Γ Convergence

In this paper we provide a rigorous asymptotic analysis of a phase-field model used to simulate pressure-driven fracture propagation in poro-elastic media. More precisely, assuming a given pressure p ∈ W 1,∞ (Ω) we show that functionals of the form $$ E(\vec{u})={\int }_{\mathrm{\Omega }} e(\vec{u}):\mathbb{C}e(\vec{u})+p\nabla \cdot \vec{u}+\left\langle \nabla p,\vec{u}\right\rangle\enspace \mathrm{d}x+{\mathcal{H}}^{n-1}({J}_{\vec{u}}),\enspace \vec{u}\in \mathrm{G}{SBD}(\mathrm{\Omega })\cap {L}^1(\mathrm{\Omega };{\mathbb{R}}^n) $$ can be approximated in terms of Γ-convergence by a sequence of phase-field functionals, which are suitable for numerical simulations. The Γ-convergence result is complemented by a numerical example where the phase-field model is implemented using a Discontinuous Galerkin Discretization.

scholarly journals Effect of Vugs on Hydraulic Fracture Propagation with Phase Field Method

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 4) ◽  
Author(s):  
Qingdong Zeng ◽  
Wenzheng Liu ◽  
Jun Yao
Keyword(s):  
Hydraulic Fracture ◽  
Phase Field ◽  
Fracture Propagation ◽  
Finite Element Approximation ◽  
Field Method ◽  
Fracture Pattern ◽  
Carbonate Reservoirs ◽  
Phase Field Method ◽  
Element Approximation ◽  
Hydraulic Fracture Propagation

Abstract The interaction between hydraulic fracture and vugs affects the formed fracture pattern, which is of great significance for developing carbonate reservoirs efficiently. To investigate the effect of vugs on hydraulic fracture propagation, a hydromechanical coupling model is established based on the phase field method. Fluid flow in the porous media with vug is described by using phase field indicator functions. The pressure, displacement, and phase fields are solved by finite element approximation and iterative method, and the proposed model is validated against analytical solution. Some influencing factors including vug geometry and property are analyzed, and results show that the vug has important impact on hydraulic fracture propagation. The fracture diverts to the vug, and it could propagate across a small vug but be arrested by a large vug. As the distance between fracture and vug increases, the effect becomes weaker until it disappears. Besides, the modulus of vug fillings determines the fracture propagation pattern. The increase of vug filling modulus makes the fracture direct crossing difficult. The study could provide some guidance for hydraulic fracturing design of carbonate reservoirs.

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