**Multiscale Modeling**

**Chapter 29**

**Provisional chapter**

**Fluid-Driven Fracture in a Poroelastic Rock**

to be applicable for injection operations over long periods of time.

be equal to zero implies that the fluid pressure inside the fracture is uniform.

**Fluid-Driven Fracture in a Poroelastic Rock**

Hydraulic fracturing is commonplace in the geo-industry, whether designed or unintended; e.g., stimulation of hydrocarbons reservoirs [1, 2], disposal of waste water [3], waterflooding operations [4], enhanced oil recovery by injection of CO2 [5], and preconditioning of rock mass in the mining industry [6, 7]. Nonetheless, modeling of hydraulic fracturing usually relies on oversimplified assumptions [1, 8]; in particular, fluid leak-off is often studied within Carter's model [9] that assumes that the transport of the filtrate and the porous fluid through the porous medium is one-dimensional. While this assumption is quite reasonable in the case of short treatments such as hydraulic fracturing of a hydrocarbons reservoir [2], it is unlikely

This study is part of an ongoing effort to rigorously introduce large-scale 3D diffusion in a model of hydraulic fracture. The increase of pore pressure around the fracture caused by fluid leak-off from the fracture leads to an expansion of the porous medium. This expansion can be accounted for by the introduction of the so-called backstress [10, 11]. By definition, the backstress would be the stress induced across the fracture plane if the fracture were closed. Here we restrict our investigation to the toughness-dominated regime of propagation, for which the viscosity of the fluid is negligible. In other words we assume that the energy spent for hydraulic fracturing is mainly due to the rock damage rather than due to dissipation associated with viscous flow of the fracturing fluid. Setting the fracturing fluid viscosity to

Previous works on the toughness-dominated regimes with leak-off include a detailed examination of the case of the Carter's leak-off model by means of scaling and asymptotic analyses [12] and an analysis of a "stationary" 3D leak-off under conditions of very slow fracture propagation, when the pore pressure around the fracture is always in equilibrium [13]. A model for the plane strain propagation of a natural fracture through a porous medium was proposed by [14], who introduced an efficient approach to calculate of the fluid exchange

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

©2012 Kovalyshen and Detournay, licensee InTech. This is an open access chapter 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 Kovalyshen and Detournay; 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,

Yevhen Kovalyshen and Emmanuel Detournay

Additional information is available at the end of the chapter

Yevhen Kovalyshen and Emmanuel Detournay

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56460

10.5772/56460

**1. Introduction**

**Provisional chapter**
