**1. Introduction**

The large scale conversion of geothermal energy into electrical energy using natural formations as heat exchangers depends on the coincidental occurrence of heat, fluid and permeability. This is valid for only a few locations on earth. Enhanced Geothermal System (EGS) propose to engineer the controlled creation of a heat exchanger between two wells in deep hot rocks, increasing the number of possible locations on earth. Water can be let circulate between the two wells, heat up while passing through the hot rock and be cooled down on the surface for

© 2013 Weber et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

power generation. Yet this engineering of the heat exchanger has to be improved such that the outcome can be predicted within specified uncertainties.

events occurring during crack formation and propagation by means of ultrasonic transducers.

The XFEM With An Explicit-Implicit Crack Description For Hydraulic Fracture Problems

http://dx.doi.org/10.5772/56383

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**Figure 1.** Large- scale tri-axial testing facility under construction, able to apply up to 30 MPa vertically and 15 MPa

Preliminary tests were performed on concrete samples of smaller size (15 x 15 x 15 cm3

recently been extended to granite and basalt. Acoustic events were recorded during fracture creation and propagation. The experiments indicated the need to lower the compressive energy induced before breakdown. Further, instead of water and light oil, fluids of higher viscosity will be used from now on to enlarge the regime of fracture propagation (see Figure 2c) and to consider the lag of scaling. Optimization of acoustic emission monitoring is continuously

Hydraulic fracture propagation is based at least on three physical processes. A fluid flow within the fracture imposes a pressure load on the fracture surfaces. As a result, the rock undergoes a (mechanical) deformation and the fracture starts to propagate when a critical condition is reached [1]. Depending on the different modeling assumptions, this critical condition can be defined by the fracture toughness or another stress-based criterion. The following assumptions are usually made for the hydraulic fracture model [1]: I) the fluid flow is governed by the lubrication theory, II) solid deformation is modeled using the theory of

) and

horizontally

ongoing.

**3. Governing equations**

**2.2. Small-scale**

Material parameters will be derived from standard rock mechanical tests.

The extension to more complex fracture scenarios as well as the integration with other software for risk assessment simulations requires a computer resource moderate modeling of fracture propagation. The extended finite element method (XFEM) forms a good basis for this. It has been applied to various problems within the area of fracture mechanics. The XFEM allows for the consideration of a priori knowledge about the solution of a hydraulic fracture problem into the approximation space through the addition of enrichment functions [10]. It enables, thereby, the accurate approximation of fields that involve jumps, kinks, singularities, and other nonsmooth features within elements [2, 6, 11]. The developed numeric model will be verified against large-scale laboratory experiments. However, the focus of the present paper will lie on the progress in using XFEM for hydraulic fracture modeling. An XFEM approach in combi‐ nation with an explicit and implicit crack description is applied to a plane-strain hydraulic fracture problem. The implicit description is given by three level-set functions defined in [5] and enables a simple evaluation of the enrichments. In contrast, the explicit crack description is used to perform the crack update. Given the explicit interface, the level-set functions for each propagation step can be calculated straightforward.

The paper is organized as follows: After a short description of the laboratory part of the joint project in Section 2, the governing equations for a hydraulic fracture problem in its basic form are presented in Section 3. Models are discussed for the solid deformation, fluid flow, and fracture propagation. In Section 4, an XFEM formulation with an explicit-implicit interface description is introduced and the discretization of these governing equations is carried out. Numerical results are presented in Section 5. Finally, Section 6 concludes this paper.
