Phase-field modeling of proppant-filled fractures in a poroelastic medium

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

doi:10.1016/j.cma.2016.02.008

Cited by 88 publications

(50 citation statements)

References 77 publications

(172 reference statements)

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“…The linear equations are solved with parallel Message Passing Interface (MPI)‐based iterative solvers (GMRES) with block‐diagonal preconditioning, and at each timestep, a simple line search algorithm is applied. For more detailed algorithm, the reader is referred to previous studies …”

Section: Global Numerical Algorithmmentioning

confidence: 99%

“…BC0 is used as the reference (see Figure ) so that the effect of remote stresses is not considered as the previous studies do …”

Section: Numerical Examplesmentioning

confidence: 99%

“…Simulations are performed with the boundary conditions BC0‐BC3 to investigate their effect on fracture propagation. It has been seen that BC0 gives stable solutions without causing coupling failure . As for BC1 and BC2 , we assign the stress boundary conditions P 1 and P 2 ( P 1 > P 2 ), representing the maximum and minimum horizontal principal stresses, S Hmax and S hmin , respectively.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Figure shows the phase‐field representation. Recently, this phase‐field approach has been applied to hydraulic fracture modeling …”

Section: Introductionmentioning

confidence: 99%

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The effect of stress boundary conditions on fluid‐driven fracture propagation in porous media using a phase‐field modeling approach

Shiozawa

Lee

Wheeler

2019

Num Anal Meth Geomechanics

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Summary A phase‐field approach for fluid‐driven fracture propagation in porous media with varying constant compatible stress boundary conditions is discussed and implemented. Since crack opening displacement, fracture path, and stress values near the fracture are highly dependent on the given boundary conditions, it is crucial to take into account the impact of in situ stresses on fracturing propagation for realistic applications. We illustrate several numerical examples that include the effects of different boundary conditions on the fracture propagation. In addition, an example using realistic boundary conditions from a reservoir simulator is included to show the capabilities of our computational framework.

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Section: Global Numerical Algorithmmentioning

confidence: 99%

“…BC0 is used as the reference (see Figure ) so that the effect of remote stresses is not considered as the previous studies do …”

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

“…Figure shows the phase‐field representation. Recently, this phase‐field approach has been applied to hydraulic fracture modeling …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effect of stress boundary conditions on fluid‐driven fracture propagation in porous media using a phase‐field modeling approach

Shiozawa

Lee

Wheeler

2019

Num Anal Meth Geomechanics

Self Cite

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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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Investigation of wing crack formation with a combined phase‐field and experimental approach

Lee

Reber

Hayman

et al. 2016

Geophysical Research Letters

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Fractures that propagate off of weak slip planes are known as wing cracks and often play important roles in both tectonic deformation and fluid flow across reservoir seals. Previous numerical models have produced the basic kinematics of wing crack openings but generally have not been able to capture fracture geometries seen in nature. Here we present both a phase‐field modeling approach and a physical experiment using gelatin for a wing crack formation. By treating the fracture surfaces as diffusive zones instead of as discontinuities, the phase‐field model does not require consideration of unpredictable rock properties or stress inhomogeneities around crack tips. It is shown by benchmarking the models with physical experiments that the numerical assumptions in the phase‐field approach do not affect the final model predictions of wing crack nucleation and growth. With this study, we demonstrate that it is feasible to implement the formation of wing cracks in large scale phase‐field reservoir models.

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Phase-field modeling of proppant-filled fractures in a poroelastic medium

Cited by 88 publications

References 77 publications

The effect of stress boundary conditions on fluid‐driven fracture propagation in porous media using a phase‐field modeling approach

The effect of stress boundary conditions on fluid‐driven fracture propagation in porous media using a phase‐field modeling approach

Flow and Transport in Tight and Shale Formations: A Review

Investigation of wing crack formation with a combined phase‐field and experimental approach

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