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Thomas Wick - One of the best experts on this subject based on the ideXlab platform.
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an iterative staggered scheme for phase field brittle Fracture Propagation with stabilizing parameters
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Mats Kirkesaether Brun, Thomas Wick, Inga Berre, Jan Martin Nordbotten, Florin Adrian RaduAbstract:Abstract This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle Fracture Propagation models, where the Fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.
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an error oriented newton inexact augmented lagrangian approach for fully monolithic phase field Fracture Propagation
SIAM Journal on Scientific Computing, 2017Co-Authors: Thomas WickAbstract:The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field Fracture Propagation. Phase-field Fracture consists of two coupled partial differential equations, and it is well known that the underlying energy functional is nonconvex and sophisticated algorithms are required. For the incremental, spatially discretized problem, we employ an adaptive error-oriented Newton algorithm which works as an inner loop within an inexact augmented Lagrangian iteration. The latter approach relaxes the crack irreversibility constraint, which is an inequality constraint in time. Six numerical tests and benchmarks are consulted to demonstrate the performance of the algorithmic techniques. Specifically, the fully monolithic approach is compared to a quasi-monolithic approach in which the phase-field is approximated through extrapolation in the displacement equation. These comparisons are done in terms of certain quantities of interest and computational cost. Moreover, fea...
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a primal dual active set method and predictor corrector mesh adaptivity for computing Fracture Propagation using a phase field approach
Computer Methods in Applied Mechanics and Engineering, 2015Co-Authors: Timo Heister, Thomas Wick, Mary F. WheelerAbstract:Abstract 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 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 predictor-corrector 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.
Florin Adrian Radu - One of the best experts on this subject based on the ideXlab platform.
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an iterative staggered scheme for phase field brittle Fracture Propagation with stabilizing parameters
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Mats Kirkesaether Brun, Thomas Wick, Inga Berre, Jan Martin Nordbotten, Florin Adrian RaduAbstract:Abstract This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle Fracture Propagation models, where the Fracture evolution is tracked by a phase field variable. The model we consider is a two-field variational inequality system, with the phase field function and the elastic displacements of the solid material as independent variables. Using a penalization strategy, this variational inequality system is transformed into a variational equality system, which is the formulation we take as the starting point for our algorithmic developments. The proposed scheme involves a partitioning of this model into two subproblems; phase field and mechanics, with added stabilization terms to both subproblems for improved efficiency and robustness. We analyze the convergence of the proposed scheme using a fixed point argument, and find that under a natural condition, the elastic mechanical energy remains bounded, and, if the diffusive zone around crack surfaces is sufficiently thick, monotonic convergence is achieved. Finally, the proposed scheme is validated numerically with several bench-mark problems.
Hanyi Wang - One of the best experts on this subject based on the ideXlab platform.
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Hydraulic Fracture Propagation in naturally Fractured reservoirs: Complex Fracture or Fracture networks
Journal of Natural Gas Science and Engineering, 2019Co-Authors: Hanyi WangAbstract:Abstract All reservoirs are Fractured to some degree. Depending on the density, dimension, orientation and the cementation of natural Fractures and the location where the hydraulic fracturing is executed, pre-existing natural Fractures can impact hydraulic Fracture Propagation and the associated flow capacity. Understanding the interactions between hydraulic Fracture and natural Fractures is crucial in estimating Fracture complexity, stimulated reservoir volume (SRV), drained reservoir volume (DRV) and completion efficiency. However, what hydraulic Fracture looks like in the subsurface, especially in unconventional reservoirs, remain elusive, and many times, field observations contradict our common beliefs. In this study, a global cohesive zone model is presented to investigate hydraulic Propagation in naturally Fractured reservoirs, along with a comprehensive discussion on hydraulic Fracture Propagation behaviors in naturally Fractured reservoirs. The results indicate that in naturally Fractured reservoirs, hydraulic Fracture can turn, kink, branch and coalesce, and the Fracture Propagation path is quite complex, but it does not necessarily mean that Fracture networks can be created, even under low horizontal stress difference, because of strong stress shadow effect and flow-resistance dependent fluid distribution. Perhaps, ‘complex Fracture’, rather than ‘Fracture networks’, is the norm in most unconventional reservoirs.
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Numerical modeling of non-planar hydraulic Fracture Propagation in brittle and ductile rocks using XFEM with cohesive zone method
Journal of Petroleum Science and Engineering, 2015Co-Authors: Hanyi WangAbstract:In this study, we present a fully coupled non-planar hydraulic Fracture Propagation model in permeable medium based on the Extended Finite Element Method (XFEM), and the arbitrary solution-dependent Fracture path cam be determined by solving a set of discontinuity equations. The Cohesive Zone Method (CZM), which is able to model crack initiation and growth by considering process zone effects, is implemented at the crack tip to enable the modeling of Fracture Propagation in both brittle and ductile formations. The method represents a useful step towards the prediction of non-planar, complex hydraulic Fractures and can provide us a better guidance of design wells and hydraulic Fractures that will better drain reservoir volume in formation with complex stress conditions and heterogeneous properties.
Jun Xie - One of the best experts on this subject based on the ideXlab platform.
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A 3-D Hydraulic Fracture Propagation Model Applied for Shale Gas Reservoirs with Multiple Bedding Planes
Engineering Fracture Mechanics, 2020Co-Authors: Jun Xie, Jizhou Tang, Yu Fan, Rui Yong, Lihua Zuo, Xing ChenAbstract:Abstract Rock layering, a critical factor in determining Fracture height growth, is pervasive in Longmaxi shale formation in the southwest of China. This formation has characteristics of large burial depth, low porosity and multiple bedding layers that hamper reaching the target Fracture height even after increasing the pumping rate and treatment size. Hence, it becomes much significant to develop a Fracture Propagation model considering the effect of bedding layers on Fracture height growth. This paper introduces a coupled 3-D hydraulic Fracture Propagation model and investigates the influence of shear displacement discontinuities along bedding planes on Fracture height growth. Our model addresses rock deformation and fluid flow. Rock deformation is governed by a fully three-dimensional displacement discontinuity method (3D DDM). The fluid flow model employs a finite difference method (FDM) being able to capture fluid movement along vertical Fractures and bedding planes. Additionally, a Propagation criteria determines whether the Fracture would penetrate bedding planes. In this paper, we selected two different Fracture geometries and analyzed profiles of Fracture width, pressure and two types of shear displacement discontinuities. From numerical investigations, we found that the maximum width can be obtained at the junction after the vertical Fracture penetrated the bedding planes as a result of the decrement of the compressive stress acting on the bedding planes. As the Fracture penetrates the bedding planes, a certain amount of fluid would leak into the planes, which leads to Fracture height containment. Moreover, the slope utilized for characterizing the correlation between leak-off volume and Fracture height, is regarded as a tool to identify the number of BPs that Fracture penetrates through. This paper illustrates the potential application of our 3-D Fracture Propagation model for Longmaxi shale formation with multiple bedding layers. Shear displacements along bedding planes are regarded as a primary mechanism of Fracture height containment.
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Numerical Study of Simultaneous Multiple Fracture Propagation in Changning Shale Gas Field
MDPI AG, 2019Co-Authors: Jun Xie, Haoyong Huang, Yu Sang, Yu Fan, Juan ChenAbstract:Recently, the Changning shale gas field has been one of the most outstanding shale plays in China for unconventional gas exploitation. Based on the more practical experience of hydraulic fracturing, the economic gas production from this field can be optimized and gradually improved. However, further optimization of the Fracture design requires a deeper understanding of the effects of engineering parameters on simultaneous multiple Fracture Propagation. It can increase the effective Fracture number and the well performance. In this paper, based on the Changning field data, a complex Fracture Propagation model was established. A series of case studies were investigated to analyze the effects of engineering parameters on simultaneous multiple Fracture Propagation. The Fracture spacing, perforating number, injection rate, fluid viscosity and number of Fractures within one stage were considered. The simulation results show that smaller Fracture spacing implies stronger stress shadow effects, which significantly reduces the perforating efficiency. The perforating number is a critical parameter that has a big impact on the cluster efficiency. In addition, one cluster with a smaller perforating number can more easily generate a uniform Fracture geometry. A higher injection rate is better for promoting uniform fluid volume distribution, with each cluster growing more evenly. An increasing fluid viscosity increases the variation of fluid distribution between perforation clusters, resulting in the increasing gap between the interior Fracture and outer Fractures. An increasing number of Fractures within the stage increases the stress shadow among Fractures, resulting in a larger total Fracture length and a smaller average Fracture width. This work provides key guidelines for improving the effectiveness of hydraulic Fracture treatments
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numerical investigation of effect of natural Fractures on hydraulic Fracture Propagation in unconventional reservoirs
Journal of Natural Gas Science and Engineering, 2018Co-Authors: Jun Xie, Haoyong Huang, Bo Zeng, Jizhou TangAbstract:Abstract Field observations show that natural Fractures are commonly presented in unconventional reservoirs, acting as planes of weakness that divert hydraulic Fracture Propagation and generate complex Fracture geometry. We systematically investigated the impacts of natural Fractures on net injection pressure, Fracture geometry, fluid volume distribution, and induced stresses using a complex Fracture Propagation model. The model fully couples rock deformation and fluid flow in the Fractures, perforations, and the wellbore. A simplified three-dimensional displacement discontinuity method is used to calculate multiple Fracture interaction within stages as well as between stages and wells. Fluid volume distribution between each Fracture is automatically calculated during pumping based on fluid resistance. The simulation results show that when a hydraulic Fracture diverts into a natural Fracture, the net injection pressure is elevated, resulting in width enlargement of the Fracture segment before the natural Fracture and reduction of total Fracture length. Much less fluid flows into the Fracture wing that diverts into the natural Fracture. Due to a larger compressional stress exerting on the natural Fracture, Fracture width of the Fracture segment on the natural Fracture is restricted, which significantly affects proppant transport and distribution. Additionally, differential stress, approach angle, length of natural Fractures, and relative position of natural Fractures are critical parameters affecting elevation of net injection pressure as well as Fracture width enlargement and restriction before and on natural Fractures. As differential stress and approach angle increase, higher net injection pressure is required, shorter Fracture length is created, and width enlargement and restriction before and on natural Fractures are more severe. Deviation of Fracture Propagation from the original path is greatly affected by the length of natural Fractures. The larger the natural Fracture, the more deviation from the original path. This study highlights the behaviors of a hydraulic Fracture diverting into a natural Fracture and the final Fracture geometry.
Bruce Jamieson - One of the best experts on this subject based on the ideXlab platform.
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Fracture Propagation propensity in relation to snow slab avalanche release validating the Propagation saw test
Geophysical Research Letters, 2008Co-Authors: Dave Gauthier, Bruce JamiesonAbstract:[1] The ‘Propagation Saw Test’ (PST) was designed to assess the Fracture Propagation propensity of weak snowpack layers in relation to snow slab avalanche release. Its predictions were tested against independent field observations of weak layer Fracture initiation and slope-scale Fracture Propagation (e.g., avalanche release). A total of 170 tests were performed at 23 sites. Approximately 76% of tests correctly predicted the observed slope-scale Fracture Propagation or lack thereof; however, 20% of tests predicted that Propagation would not occur at sites that had recently propagated Fractures. The predictive accuracy of the dataset improves if only test columns approximately 1.0 m long are selected. Critical Fracture energy release rate calculations show that the lowest values are found in snowpacks where Fractures initiated but did not propagate. This suggests that physical descriptions of Propagation propensity in weak snowpack layers should include a sustainability term.
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towards a field test for Fracture Propagation propensity in weak snowpack layers
Journal of Glaciology, 2006Co-Authors: Dave Gauthier, Bruce JamiesonAbstract:Slab avalanche release requires Fracture initiation and Propagation in a weak snowpack layer. While field tests of weak-layer strength are useful for Fracture initiation, the challenge remains to find a verified field test for Fracture Propagation. We introduce the two current versions of a field test for Fracture Propagation propensity, and report results of testing conducted in the Columbia Mountains of British Columbia, Canada, during the winter of 2005. By extending the column of a stability test approximately 3 m in the downslope direction, the test method allows for the development of a flexural wave in the slab, and thereby maintains the contribution of this wave and the associated weak-layer collapse to the Fracture process. Fracture lengths collected on a day and location where the Propagation propensity of the snowpack was locally high show a bimodal distribution, with approximately 50% of observed Fractures similar to those collected in stable snowpacks, and approximately 50% with much longer Fracture lengths.
