scholarly journals Phase Field Model of Hydraulic Fracturing in Poroelastic Media: Fracture Propagation, Arrest, and Branching Under Fluid Injection and Extraction

2018 ◽  
Vol 123 (3) ◽  
pp. 2127-2155 ◽  
Author(s):  
David Santillán ◽  
Ruben Juanes ◽  
Luis Cueto-Felgueroso
2020 ◽  
Vol 54 (3) ◽  
pp. 1003-1023
Author(s):  
Annika Bach ◽  
Liesel Sommer

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.


2020 ◽  
Vol 24 (5) ◽  
pp. 1767-1782 ◽  
Author(s):  
Lin Ni ◽  
Xue Zhang ◽  
Liangchao Zou ◽  
Jinsong Huang

Abstract Modeling of hydraulic fracturing processes is of great importance in computational geosciences. In this paper, a phase-field model is developed and applied for investigating the hydraulic fracturing propagation in saturated poroelastic rocks with pre-existing fractures. The phase-field model replaces discrete, discontinuous fractures by continuous diffused damage field, and thus is capable of simulating complex cracking phenomena such as crack branching and coalescence. Specifically, hydraulic fracturing propagation in a rock sample of a single pre-existing natural fracture or natural fracture networks is simulated using the proposed model. It is shown that distance between fractures plays a significant role in the determination of propagation direction of hydraulic fracture. While the rock permeability has a limited influence on the final crack topology induced by hydraulic fracturing, it considerably impacts the distribution of the fluid pressure in rocks. The propagation of hydraulic fractures driven by the injected fluid increases the connectivity of the natural fracture networks, which consequently enhances the effective permeability of the rocks.


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