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

Mikelić, Andro; Wheeler, Mary F.; Wick, Thomas

doi:10.1007/s10596-015-9532-5

Cited by 160 publications

(144 citation statements)

References 20 publications

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“…[16][17][18][19] In hydraulic fracturing, the pressure induced by the fluid within the crack is responsible for the propagation of fracture. [16][17][18][19] In hydraulic fracturing, the pressure induced by the fluid within the crack is responsible for the propagation of fracture.…”

Section: Overview Of Related Researchmentioning

confidence: 99%

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

Sudhakar

Wall

2018

Numerical Methods in Fluids

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Summary We present a novel method to model large deformation fluid‐structure‐fracture interaction, which is characterized by the fact that the fluid‐induced loads lead to fracture of the structure and the fluid medium fills the resulting crack opening; the mutual interaction between the crack faces and the surrounding fluid contributes substantially to the overall dynamics. A mesh refitting approach is used to model the quasi‐static fracture of the structure, and a robust embedded interface formulation is used to solve the fluid flow equations. The proposed method uses a strongly coupled partitioned scheme with Aitken's Δ2 method as convergence accelerator. Selected numerical examples of increasing complexity are presented to evaluate the performance of the proposed fluid‐structure‐fracture coupling algorithm. The most difficult simulation of the reported examples involves a number of complex phenomena: mixed‐mode crack propagation through the structure, fluid starts to fill the crack opening, complete fracture of the structure into two pieces of which one is carried away by the flow.

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Section: Overview Of Related Researchmentioning

confidence: 99%

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

Sudhakar

Wall

2018

Numerical Methods in Fluids

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“…Pop et al [124] employed nonlinear transmission conditions for reactive flow in fractured media. Recently, the phase field modeling of flow in fractured media has been considered by Lee et al [125] and Mikelić et al [126,127]. The embedded discrete fracture models have been employed by Li and Lee [128] and Moinfar et al [129] discretized the complex fractures into a number of segments while the matrix is treated as structured grids.…”

Section: Discrete Fracture Modelmentioning

confidence: 99%

Flow and Transport in Tight and Shale Formations: A Review

et al. 2017

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A review on the recent advances of the flow and transport phenomena in tight and shale formations is presented in this work. Exploration of oil and gas in resources that were once considered inaccessible opened the door to highlight interesting phenomena that require attention and understanding. The length scales associated with transport phenomena in tight and shale formations are rich. From nanoscale phenomena to field-scale applications, a unified frame that is able to encounter the varieties of phenomena associated with each scale may not be possible. Each scale has its own tools and limitations that may not, probably, be suitable at other scales. Multiscale algorithms that effectively couple simulations among various scales of porous media are therefore important. In this article, a review of the different length scales and the tools associated with each scale is introduced. Highlights on the different phenomena pertinent to each scale are summarized. Furthermore, the governing equations describing flow and transport phenomena at different scales are investigated. In addition, methods to solve these equations using numerical techniques are introduced. Cross-scale analysis and derivation of linear and nonlinear Darcy's scale laws from pore-scale governing equations are described. Phenomena occurring at molecular scales and their thermodynamics are discussed. Flow slippage at the nanosize pores and its upscaling to Darcy's scale are highlighted. Pore network models are discussed as a viable tool to estimate macroscopic parameters that are otherwise difficult to measure. Then, the environmental aspects associated with the different technologies used in stimulating the gas stored in tight and shale formations are briefly discussed.

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“…Filling in the discretized form in the balance Eqs. [23][24][25][26] give the continuous equations as…”

Section: Discretizationmentioning

confidence: 99%

“…Other methods that considered hydraulic fracturing in porous media are, e.g. based on interface elements with a cohesive zone [24], remeshing techniques [25] and phase field approaches [26]. The phase field method incorporates complex fracture patterns and 3D fractures directly into a model based on the variational approach [27].…”

Section: Introductionmentioning

confidence: 99%

On the numerical simulation of crack interaction in hydraulic fracturing

et al. 2017

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In this paper, we apply the enhanced local pressure (ELP) model to study crack interaction in hydraulic fracturing. The method is based on the extended finite element method (X-FEM) where the pressure and the displacement fields are assumed to be discontinuous over the fracture exploiting the partition of unity property of finite element shape functions. The material is fully saturated and Darcy's law describes the fluid flow in the material. The fracture process is described by a cohesive tractionseparation law, whereas the pressure in the fracture is included by an additional degree of freedom. Interaction of a hydraulic fracture with a natural fracture is considered by assuming multiple discontinuities in the domain. The model is able to capture several processes, such as fracture arrest on the natural fracture, or hydraulic fractures that cross the natural fracture. Fluid is able to flow from the hydraulic fracture into the natural fracture. Two numerical criteria are implemented to determine whether or not the fracture is crossing or if fluid diversion occurs. Computational results showing the performance of the model and the effectiveness of the two criteria are presented. The influence of the angle between a hydraulic fracture and a natural fracture on the interaction behaviour is compared with experimental results and theoretical data.

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

Cited by 160 publications

References 20 publications

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

A strongly coupled partitioned approach for fluid‐structure‐fracture interaction

Flow and Transport in Tight and Shale Formations: A Review

On the numerical simulation of crack interaction in hydraulic fracturing

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