**Author details**

B. Damjanac, C. Detournay, P.A. Cundall and Varun

Itasca Consulting Group, Inc., Minneapolis, Minnesota, USA

### **References**


[3] Itasca Consulting GroupInc. PFC2D (Particle Flow Code in 2 Dimensions), Version 4.0. Minneapolis: Itasca; (2008).

**Chapter 42**

**Testing and Review of Various Displacement**

Hyunil Jo and Robert Hurt

http://dx.doi.org/10.5772/56445

**Abstract**

Additional information is available at the end of the chapter

merical simulations for field engineering applications.

**Discontinuity Elements for LEFM Crack Problems**

The numerical modeling of hydraulic fractures in unconventional reservoirs presents signifi‐ cant challenges for field applications. There remains a need for accurate models that field personnel can use, yet remains consistent to the underlying physics of the problem [1]. For numerical simulations, several authors have considered a number of issues: the coupling be‐ tween fracture mechanics and fluid dynamics in the fracture [2], fracture interaction [3-5], proppant transport [6], and others [7-9]. However, the available literature within the oil and gas industry often ignores the importance of the crack tip in modeling applications devel‐ oped for engineering design. The importance of accurate modeling of the stress induced near the crack tip is likely critical in complex geological reservoirs where multiple propagat‐ ing crack tips are interacting with natural fractures. This study investigates the influence of various boundary element numerical techniques on the accuracy of the calculated stress in‐ tensity factor near the crack tip and on the fracture profile, in general. The work described here is a part of a long-term project in the development of more accurate and efficient nu‐

For this investigation, the authors used the displacement discontinuity method (DDM). The numerical technique is applied using constant and higher-order elements. Further, the au‐ thors also applied special crack tip elements, derived elsewhere [10], to capture the square root displacement variation at the crack tip, expected from Linear Elastic Fracture Mechan‐ ics (LEFM). The authors expect that special crack tip elements will provide the necessary flexibility to choose other tip profiles. The crack tip elements may prove instrumental for ef‐ ficient modeling of the different near-tip displacement profiles exhibited by Viscosity-Domi‐ nated or Toughness-Dominated regimes in hydraulic fracture propagation. As others have

> © 2013 Jo and Hurt; 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.

