**Numerical Modeling 1**

**Chapter 35**

**The XFEM With An Explicit-Implicit Crack Description For**

The Extended Finite Element Method (XFEM) approach is applied to the coupled problem of fluid flow, solid deformation, and fracture propagation. The XFEM model description of hydraulic fracture propagation is part of a joint project in which the developed numerical model will be verified against large-scale laboratory experiments. XFEM forms an important basis towards future combination with heat and mass transport simulators and extension to more complex fracture systems. The crack is described implicitly using three level-sets to evaluate enrichment functions. Additionally, an explicit crack representation is used to up‐ date the crack during propagation. The level-set functions are computed exactly from the ex‐ plicit representation. This explicit/implicit representation is applied to a fluid-filled crack in an impermeable, elastic solid and compared to the early-time solution of a plane-strain hy‐

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,

© 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,

distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

**Hydraulic Fracture Problems**

C. Clauser and T. P. Fries

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

draulic fracture problem with a fluid lag.

**1. Introduction**

**Abstract**

N. Weber, P. Siebert, K. Willbrand, M. Feinendegen,

Additional information is available at the end of the chapter
