An algorithm for the simulation of curvilinear plane‐strain and axisymmetric hydraulic fractures with lag using the universal meshes

Grossman-Ponemon, Benjamin E.; Lew, Adrián J.

doi:10.1002/nag.2896

Cited by 9 publications

(5 citation statements)

References 48 publications

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“…We solve the fully coupled problem numerically using the method presented in Grossman-Ponemon and Lew (2019). All simulations were run in a square domain with a domain edge length of L = 100a c .…”

Section: Methodsmentioning

confidence: 99%

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Logarithmic growth of dikes from a depressurizing magma chamber

Grossman-Ponemon¹,

Heimisson²,

Lew³

et al. 2019

Preprint

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Dike propagation is an intrinsically multiphase problem, where deformation and fluid flow are intricately coupled in a fracture process. Here we perform the first fully-coupled simulations of dike propagation in two dimensions, accounting for depressurization of a circular magma chamber, dynamic fluid flow, fracture formation, and elastic deformation. Despite the complexity of the governing equations we observe that the lengthening is well explained by a simple model $a(t) = c_1 \log(1+t/c_2)$, where $a$ is the dike length, $t$ is time, and $c_1$ and $c_2$ are constants. We compare the model to seismic data from 8 dikes in Iceland and Ethiopia and, in spite of the assumption of plane strain, we find good agreement between the data and the model. In addition, we derive an approximate model for the depressurization of the chamber with the dike length. These models may help forecast the growth of lateral dikes and magma chamber depressurization.

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Section: Methodsmentioning

confidence: 99%

“…We now comment on modifications to the algorithm in Grossman-Ponemon and Lew (2019) to account for the depressurization of the volcanic chamber and the pressure boundary condition at the inlet of the dike.…”

Section: Methodsmentioning

confidence: 99%

Logarithmic growth of dikes from a depressurizing magma chamber

Grossman-Ponemon¹,

Heimisson²,

Lew³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…In terms of changes to orientation, several different criteria are typically employed, such as the maximum hoop stress criteria (Erdogan and Sih 1963;Williams and Ewing 1972;Finnie and Saith 1973) or the maximum energy release rate condition (Ewing et al 1976;Cotterell 1965;Hussain et al 1974). Examples of works from the hydraulic fracture field employing such criteria include He and Zhuang (2018), Jang et al (2020) and Grossman-Ponemon and Lew (2019).…”

Section: Governing Equations For Hydraulic Fracturementioning

confidence: 99%

A multi-resolution approach to hydraulic fracture simulation

et al. 2022

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We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

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“…Other issues associated with modeling this complex phenomenon include the presence of different layers of rock formation; variation of the in situ confining stress; leakage of hydraulic fluid; effect of temperature and shear on the rheology of the fracture fluid; the movement of the suspended sorted sand within the fracture; and so forth 5 . As a result, several models for the simulation of hydraulic fracture propagation have been developed to date 5–26 . The injection rate of the fracturing fluid, rock properties, and rheology are the main input parameters for these models, while the geometry, path, and fluid pressure are some of the output of the simulations 27 …”

Section: Introductionmentioning

confidence: 99%

Propagation mechanisms and parametric influence in multiple interacting hydraulic fractures: A 3‐D G/XFEM hydro‐mechanical modeling

Mukhtar

Shauer

Duarte

2022

Num Anal Meth Geomechanics

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Using a robust three‐dimensional generalized/eXtended finite element method (G/XFEM) algorithm, this paper presents a comprehensive study on multiple hydraulic fracture propagation and their interactions under different treatment conditions. Aimed at capturing the complex multiphysics behavior, the resulting nonplanar fracture footprints under mixed‐mode conditions are simulated using a formulation, which couples the solid/rock domain equations and the fluid flow within the fractures/crevices. Due to the small length scale of the fracture process zone relative to the surrounding formation size, as typically encountered in tight shale reservoirs, linear elastic fracture mechanics based on a regularized Irwin criterion is adopted to describe the fractured solid/rock response while a power law is used for the fluid flow by assuming a Newtonian fluid behavior. Equipped with the capability for mesh adaptivity and automatic time step search algorithms, the G/XFEM utilized to discretize the resulting system of coupled nonlinear equations allows the adoption of independent meshes for the background solid domain and the fracture surfaces without any matching/compatibility requirement between the two. Fracture propagation directions are decided based on the modes I, II, and III stress intensity factors that are extracted using the displacement correlation method. The presented model is first applied to a pair of misaligned fractures and then to an array of en échelon fractures for qualitative verification against a literature prediction by the boundary element method (BEM) and an observed field behavior, respectively. Next, simulation of several sets and configurations of multiple hydraulic fractures, resulting in a total of 23 parametric studies, are carried out to investigate the influences of fracture spacing, injection fluid viscosity, number of fracture clusters, and the type of remote stress conditions.

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An algorithm for the simulation of curvilinear plane‐strain and axisymmetric hydraulic fractures with lag using the universal meshes

Cited by 9 publications

References 48 publications

Logarithmic growth of dikes from a depressurizing magma chamber

Logarithmic growth of dikes from a depressurizing magma chamber

A multi-resolution approach to hydraulic fracture simulation

Propagation mechanisms and parametric influence in multiple interacting hydraulic fractures: A 3‐D G/XFEM hydro‐mechanical modeling

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