Pressurized-Fracture Propagation using a Phase-Field Approach Coupled to a Reservoir Simulator

Wick, Thomas; Singh, Gurpreet; Wheeler, Mary F.

doi:10.2118/168597-ms

Cited by 10 publications

(6 citation statements)

References 13 publications

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“…Our findings in Figure 10 show the evolution of bulk (20) and crack energies (21) for Case 1 and Case 3. The results illustrate the expected behavior: As long as the crack does not grow (up to t = 0.0095s), there is only an increase in bulk energy.…”

Section: Single Edge Notched Shear Testmentioning

confidence: 96%

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A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Heister

Wheeler²,

Wick

2015

Computer Methods in Applied Mechanics and Engineering

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362

352

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In this paper, we consider phase-field-based fracture propagation in elastic media. The main purpose is the development of a robust and efficient numerical scheme. To enforce crack irreversibility as a constraint, we use a primal-dual active set strategy, which can be identified as a semi-smooth Newton's method. The active set iteration is merged with the Newton iteration for solving the fully-coupled nonlinear partial differential equation discretized using finite elements, resulting in a single, rapidly converging nonlinear scheme. It is well known that phase-field models require fine meshes to accurately capture the propagation dynamics of the crack. Because traditional estimators based on adaptive mesh refinement schemes are not appropriate, we develop a predictorcorrector scheme for local mesh adaptivity to reduce the computational cost. This method is both robust and efficient and allows us to treat temporal and spatial refinements and to study the influence of model regularization parameters. Finally, our proposed approach is substantiated with different numerical tests for crack propagation in elastic media and pressurized fracture propagation in homogeneous and heterogeneous media.

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Section: Single Edge Notched Shear Testmentioning

confidence: 96%

“…In addition, Biot's coefficient is chosen as α = 0. Both terms appear in situations as investigated in [20,21,22].…”

Section: The Energy Functionalmentioning

confidence: 99%

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Heister

Wheeler²,

Wick

2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

362

352

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“…This is an important example motivated by practical applications. Examples with varying geomechanics parameters have been presented in [16,13] as well as in [24] to couple phase-field fracture propagation with a reservoir simulator.…”

Section: Fracture Propagation In a Heterogeneous Porous Mediummentioning

confidence: 99%

Phase-field modeling of a fluid-driven fracture in a poroelastic medium

2015

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International audienceIn this paper we present a phase field model for a fluid-driven fracture in a poroelastic medium. In our previous work, the pressure was assumed given. Here we consider a fully coupled system where the pressure field is determined simultaneously with the displacement and the phase field. To the best of our knowledge, such a model is new in the literature. The mathematical model consists of a linear elasticity system with fading elastic moduli as the crack grows, which is coupled with an elliptic variational inequality for the phase field variable and with the pressure equation containing the phase field variable in its coefficients. The convex constraint of the variational inequality assures the irreversibility and entropy compatibility of the crack formation. The phase field variational inequality contains quadratic pressure and strain terms, with coefficients depending on the phase field unknown. We establish existence of a solution to the incremental problem through convergence of a finite dimensional approximation. Furthermore, we construct the corresponding Lyapunov functional that is linked to the free energy. Computational results are provided that demonstrate the effectiveness of this approach in treating fluid-driven fracture propagation

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“…The goals are to observe the pressure and the radius with respect to time. An extension of this setting to heterogeneous materials is discussed in [47].…”

Section: A Propagating Penny-shape Crack In Three Dimensionsmentioning

confidence: 99%

A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium

Mikelić¹,

Wheeler²,

Wick³

2015

Multiscale Model. Simul.

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216

138

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The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and nonplanar propagation in possibly heterogeneous media. In this paper, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a generalized parabolic diffraction problem. Here, the phase-field variable is used as an indicator function to combine reservoir and fracture pressure. The resulting three-field framework (elasticity, phase field, pressure) is a multiscale problem that is based on the Biot equations. The proposed numerical solution algorithm iteratively decouples the equations using a fixed-stress splitting. The framework is substantiated with several numerical benchmark tests in two and three dimensions.

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Pressurized-Fracture Propagation using a Phase-Field Approach Coupled to a Reservoir Simulator

Cited by 10 publications

References 13 publications

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach

Phase-field modeling of a fluid-driven fracture in a poroelastic medium

A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium

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