**1. Introduction**

Understanding the mechanics of propagation of hydraulic fracture (HF) in naturally fractured reservoirs is critical to both petroleum and geothermal applications. The objective of fluid injection in these applications varies from creating HF to increasing the permeability of the surrounding rock mass, or "stimulation" of the reservoir. During stimulation, several mech‐ anisms can lead to permeability enhancement, including:


© 2013 Riahi and Damjanac; 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.

**•** Initiation and propagation of HF, which also results in increase in fracture network connectivity.

sampling or mapping domain — i.e.,*P*21=∑ *l*

DFN domain.)

was disregarded.

**3. Numerical approach**

model at constant rate.

*<sup>i</sup>* / *<sup>L</sup>* <sup>2</sup>

Numerical Study of Interaction Between Hydraulic Fracture and Discrete Fracture Network

Considering the computational requirements of the numerical tool used in this study, it was impractical to represent DFNs with the same level of complexity as that observed in the field. Therefore, the DFN realizations were simplified or filtered. The objective of the filtering process was to reduce the geometrical complexity while preserving the relevant characteristics of the DFN. In the adopted approach, DFN realizations were simplified first by disregarding fractures with a length smaller than a prescribed threshold. The minimum fracture length cutoff is determined based on the length scale of the analysed problem. Also, to conform to what is often observed in the field, closely spaced, sub-parallel fractures (sometimes generated by the Poisson process used for generation of the fracture locations in the synthetic DFN) are disregarded. The latter criterion is based on the field observations and the reasoning that the stress field around a fracture prevents occurrence of sub-parallel fractures in its vicinity. Finally, in this study, the variation of fracture orientation about the mean for each fracture set

The flow characterises of the DFN are determined by identifying the clusters and evaluating overall DFN connectivity. A cluster is a group of fractures that are connected to each other; no fracture inside a cluster intersects a fracture belonging to a different cluster. A fully connected DFN is defined as the DFN with one cluster extending to the boundaries of the domain. The partially and sparsely connected DFNs were created by decreasing the fracture density and

The numerical analyses of this study are carried out using a distinct-element modelling approach. Simulations were completed using distinct element code *UDEC*[1]. In this approach, the fractured formation is represented by an assembly of intact rock blocks separated by a preexisting discrete fracture network. The numerical simulations are performed using a fully coupled hydromechanical model. Fluid flow can only occur within the fractures, separating the impermeable blocks. Initially, the formation is dry. The fluid is injected in the centre of the

The rock blocks are modelled as elastic and impermeable. The pre-existing fractures are represented explicitly. They are discontinuities which deform elastically, but also can open and slip (as governed by the Coulomb slip law) as a function of pressure and total stress.

*UDEC* can simulate fracture propagation along the predefined planes only. In order to simulate propagation of an HF, the trajectory of the fracture should be defined explicitly in the model prior to simulations. In this model, the HF is assumed to be planar, aligned with the direction of the major principal stress. The two "incipient surfaces" of the plane of the HF initially are bonded with a strength that is equivalent to specified fracture toughness. Propagation of the HF corresponded to breaking of these bonds. Clearly, the assumption of propagation of the

visually inspecting the size of formed clusters relative to the size of the model.

, where L is the linear dimension of the

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The focus of this work is on the numerical modelling of fluid injection into the fractured rock mass and interaction between HF and the discrete fracture network. A series of comparative studies were performed to establish the effect of various in-situ parameters, including geometrical properties of the DFN, such as the level of connectivity and fracture size distri‐ bution, and operational parameters such as injection rate. In addition to qualitative evaluation of results, the model responses are compared in terms of a series of indices that were evaluated during injection. These indices include:


It is believed that the characteristics of the DFN have a critical effect on the response of a naturally fractured reservoir to fluid injection. Explicit representation of the DFN with realistic characteristics is thus important in the numerical modelling. Numerous realizations of different DFNs have been generated statistically and represented explicitly in the model.
