Immersed particle method for fluid–structure interaction

Rabczuk, Timon; Gracie, Robert; Song, Jeong‐Hoon; Belytschko, Ted

doi:10.1002/nme.2670

Cited by 365 publications

(111 citation statements)

References 39 publications

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“…Numerical simulation [17][18][19][20][21][22][23][24][25][26][27][28] would avoid some of the randomness in laboratory experiments and could reflect the effect of critical parameters on hydraulic fracturing characteristics. Many works have been carried out to investigate the influence of some important parameters on hydraulic fracturing by numerical simulation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Influence of In-Situ Stress Ratio, Injection Rate and Fluid Viscosity on Hydraulic Fracture Propagation Using a Distinct Element Approach

Zhang

et al. 2016

Energies

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Numerical simulation is very useful for understanding the hydraulic fracturing mechanism. In this paper, we simulate the hydraulic fracturing using the distinct element approach, to investigate the effect of some critical parameters on hydraulic fracturing characteristics. The breakdown pressure obtained by the distinct element approach is consistent with the analytical solution. This indicates that the distinct element approach is feasible on modeling the hydraulic fracturing. We independently examine the influence of in-situ stress ratio, injection rate and fluid viscosity on hydraulic fracturing. We further emphasize the relationship between these three factors and their contributions to the hydraulic fracturing. With the increase of stress ratio, the fracture aperture increases almost linearly; with the increase of injection rate and fluid viscosity, the fracture aperture and breakdown pressure increase obviously. A low value of product of injection rate and fluid viscosity (i.e., Qµ) will lead to narrow fracture aperture, low breakdown pressure, and complex or dispersional hydraulic fractures. A high value of Qµ would lead wide fracture aperture, high breakdown pressure, and simple hydraulic fractures (e.g., straight or wing shape). With low viscosity fluid, the hydraulic fracture geometry is not sensitive to stress ratio, and thus becomes a complex fracture network.

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Section: Introductionmentioning

confidence: 99%

Numerical Investigation of Influence of In-Situ Stress Ratio, Injection Rate and Fluid Viscosity on Hydraulic Fracture Propagation Using a Distinct Element Approach

Zhang

et al. 2016

Energies

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“…Nevertheless, this approach can lead to ill-conditioning if the elements cut by the boundary are too small, and the accuracy of the method is typically limited by the approximate geometry representation. Another related method is the Immersed Particle Method [26], which is based on the same concept as IFEM but has been developed for modelling fluid-structure interaction. In [36], a surface reconstruction from scanned image using B-spline is presented.…”

Section: Introductionmentioning

confidence: 99%

Volumetric parametrization from a level set boundary representation with PHT-splines

Chan

Anitescu

Rabczuk

2017

Computer-Aided Design

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A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a splinebased representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C 1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems.

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“…Many models in early stages, such as Perkins-Kern (PK) model [3], Perkins-Kern-Nordgren (PKN) model [4], Khristianovich-Geertsma-Deklerk (KGD) mode [5], pseudo-3D models, and planar-3D models [6], cannot be used in simulating the propagation of complex fracture network. To meet the need of hydraulic fracturing design, many numerical models, such as the finite element method [7], extended finite element method [8], discrete element method [2] and mesh less method [9][10][11][12][13][14] have been developed in recent years. For example, Zhuang and Rabczuk et al [12][13][14] proposed a meshless method that is able to treat the nucleation of fractures and complex patterns involving fracture processes may not be the same because the fractures that have been created or reopened during fluid injection may partially close during production after fluid pressure dissipates [37].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study on the Formation of Shear Fracture Network

Zhang

2016

Energies

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Shear fracture network is important to the hydraulic fracturing treatment of a shale gas reservoir. In this paper, the formation of shear fracture network is investigated by a Displacement Discontinuity Method (DDM) based model. The results show that the sliding of fracture surface is irreversible but may change significantly after fluid pressure dissipates. The final sliding distance is different for natural and hydraulic fractures. Most of the shear fractures are natural fractures while the newly formed hydraulic fractures tend to be totally closed after pressure dissipates. The effects of in situ stress are investigated. The affected area reaches its maximum value when the maximum principle stress direction is perpendicular to the principal fracture direction. The effects of the injection rate are also investigated. The increasing of the injection rate is helpful in increasing the fracture aperture, but has no effect on the final sliding distance. Moreover, the effects of the injection rate on the affected area depend on the connectivity of natural fractures. The affected area increases with the injection rate when the connectivity is poor but decreases slightly with injection rate when the connectivity is good.

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Immersed particle method for fluid–structure interaction

Cited by 365 publications

References 39 publications

Numerical Investigation of Influence of In-Situ Stress Ratio, Injection Rate and Fluid Viscosity on Hydraulic Fracture Propagation Using a Distinct Element Approach

Numerical Investigation of Influence of In-Situ Stress Ratio, Injection Rate and Fluid Viscosity on Hydraulic Fracture Propagation Using a Distinct Element Approach

Volumetric parametrization from a level set boundary representation with PHT-splines

Numerical Study on the Formation of Shear Fracture Network

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