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%0 Thesis %A Weber, Nikolai %T The XFEM for hydraulic fracture mechanics %I Rheinisch-Westfälische Technische Hochschule Aachen %V Dissertation %C Aachen %M RWTH-2016-11062 %P 1 Online-Ressource (xv, 131 Seiten) : Illustrationen, Diagramme %D 2016 %Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2017 %Z Dissertation, Rheinisch-Westfälische Technische Hochschule Aachen, 2016 %X The aim of this thesis is the numerical treatment of the hydraulic fracturing process based on the extended finite element method (XFEM). Three main physical phenomena are considered: a viscous fluid flows into an existing crack, the crack propagation due to the fluid pressurization, and solid deformation due to internal and external loads. The XFEM accurately accounts for the displacement jumps across the crack surface which is numerically interpreted as a discontinuity. This is achieved by locally enriching the approximation space with discontinuousfunctions such as the sign function. The singular behavior at the crack tip is captured by adding four tip-enrichment functions. Thus, the crack is not required to align with the element edges of the finite element mesh and no remeshing is necessary for crack propagation. A twofold crack description is utilized to properly incorporate the enrichments and to perform the crack update. First, a level-set method with three level-set functions is used to describe the crack implicitly. Thereby, the enriched location can be determined and the level-set functions aredirectly used to evaluate the enrichments. Moreover, a local coordinate system at the crack tip can be formulated based on the implicit description. Second, an explicit crack description is used on the basis of a triangular mesh. The crack update is then performed by adding additional elements to the existing mesh at those crack front locations where propagation takes place. Since the crack front represents a moving boundary, its location is easily tracked as the exact crack front position is given throughout the whole simulation. Since both descriptions are easily transformed into each other, they complement one another extremely well. This combines the advantages of the evaluation of the enrichment functions with the implicit and the crack update with the explicit description. The fluid flow equations on the crack surface are described using a finite element method on triangular meshes. additionally, the mesh is locally refined in the crack front region in order to accurately capture the steep gradient in the pressure field. The finite element formulation is extended to the case of arbitrarily curved cracks. A local coordinate system on the surface is introduced in order to properly transform and integrate the fluid flow equations. This approach is implemented and verified for transport equations on curved surfaces. The governing equations are coupled iteratively and, therefore, maintain the flexibility of treating each model part independently. At each propagation step, the coupled equations are solved such that the propagation condition is met and the crack is updated. When the fluid front does not reach the crack front, both fronts are tracked separately. In this case, the fluid front moves forward until the propagation condition is satisfied and then a new propagation step can be performed. This thesis presents a fully coupled modeling approach that allows arbitrary crack growth in three-dimensional space. Another focus is on the treatment of transport equations on manifolds and the associated fluid-induced crack propagation. The coupled problem is verified against simplified analytical solutions and against experimental results that were obtained from fracturing rock samples of the size 30 × 30 × 45 cm³. An initial penny-shaped crack is assumed and the verification focuses on the pressure response for the pressure buildup and propagation phase. Since no satisfying agreement in the pressure curve close to the breakdown pressure is achieved, the fluid flow model is extended to capture the non-linear effects of the system due to the compressibility. The simulation results obtainedwith this approach agree well with the experimental results. %F PUB:(DE-HGF)11 %9 Dissertation / PhD Thesis %R 10.18154/RWTH-2016-11062 %U https://publications.rwth-aachen.de/record/679277