**Abstract**

**References**

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286 Effective and Sustainable Hydraulic Fracturing

[1] Itasca *UDEC (Universal Distinct Element Code)*Version 5.0, Itasca Consulting Group,

[2] Bunger, A. P, Jeffrey, R. G, Kear, J, & Zhang, X. Experimental Investigation of the In‐ teraction among Closely Spaced Hydraulic Fractures. Presented at the 45th US Rock Mechanics/Geomechanics Symposium held in San Francisco, California, (2011). June

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The recently developed Unconventional Fracture Model (UFM\*) simulates complex hydraulic fracture network propagation in a formation with pre-existing closed natural fractures, and explicitly models hydraulic injection into a fracture network with multiple propagating branches [1]. The model predicts whether a hydraulic fracture front crosses or is arrested by a natural fracture it encounters, which defines the complexity of the generated complex hydraulic fracture network.

While taking into account the leakoff of the fracturing fluid into the formation, the leakoff into the natural fractures should also be considered, especially in low-matrix permeability condi‐ tions. The transmissibility of natural fractures can become significant, and the fracturing fluid can penetrate into natural fractures. Different regions can coexist along the invaded natural fracture: hydraulically opened region filled with fracturing fluid, region of still closed natural fracture invaded by fracturing fluid due to natural fracture permeability, and the region of natural fracture filled with original reservoir fluid.

Explicit modelling of hydraulic fractures interacting with permeable natural fractures becomes extremely complicated with the necessity to account for conservation of fluid mass, pressure drop along natural fractures, leak-off into the formation from natural fracture walls, pressure sensitive natural fracture permeability, properties of natural fractures, fluid rheology, while tracking the interface of each region along invaded natural fracture. A main challenge is integrating this hydraulic fracture/natural fracture interaction modelling into the overall hydraulic fracture network propagating scheme without losing model effectiveness and CPU performance.

© 2013 Kresse and Weng; 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.

The updated UFM model with enhancement to account for leakoff into the natural fractures will be presented.

the leakoff coefficient is highly pressure dependent. As the pressure exceeds the closure stress on the fissure (*p* > *p fo*), the entire fissure opens, yielding an accelerated leakoff condition. The estimation of the critical pressure in PKN-type HF (exceeding closing pressure *p* > *p fo*) to open a vertical fissure has been given through the function of the principal horizontal stresses and

Hydraulic Fracturing in Formations with Permeable Natural Fractures

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A more detailed description of the effects from natural fissures in reservoirs where natural fissures are the primary source of permeability is provided in [23]. The enhanced rate of fluid loss throughout the treatment is predicted, with leakoff accelerating as the fracturing pressure increases. The increase in fluid pressure in the fissures reduces the effective normal stress acting to close the fissures and hence increases their permeability. For hydraulic fracturing purposes, the effect of the magnified permeability is reflected as an increase in fluid-leakoff coefficient. The fluid-leakoff in the presence of natural fissures could be as high as 2 to 3 times that for normally occurring pressure – dependent leakoff behaviour, even under the net

For slightly elevated pressures NF porosity begins to open as the pore pressure increases because the elevated pressure relieves some of the net stress on the asperity contacts. Several models of this process have been developed. For example, [26] predicts the change in NF permeability resulting from changes in stress and pressure. This model have been validated

Among existing HF models accounting for the permeability of intercepted natural frac‐ tures mention [10] which couples fluid flow, elastic deformation, and frictional sliding to obtain a solution which depends on the competition between fractures for the permeabili‐ ty enhancements. The effect of initially closed but conductive fracture is specifically addressed. The possible scenarios for evolution of fracture opening and fluid transport in closed NFs implemented in [10] are shown in Figure 1. The initial aperture *w <sup>0</sup>* along a closed pre-existing NF corresponds to its residual conductivity. It is equal to the effective aperture for the parallel plate model. The initial conductivity of a closed natural fracture arises from the fact that its surfaces are rough and mismatched at fine scale, i.e. the aperture *w <sup>0</sup>* is related to the fracture porosity. With increasing the fluid pressure, the hydraulic aperture will slightly change due to micro structural change in the natural fracture, although the fracture still remain closed and carries some contact stresses. In the end, fracture will be opened mechanically as the fluid pressure exceeds the normal stress acting on the fracture. In this case, the effective hydraulic conductivity is equal to the sum of both hydraulic aperture and mechanical opening since the fracture opening augments the initial hydraulic aperture, as shown in Figure 1. Zhang's model also considers the possibility of frictional sliding through the Coulomb frictional law, and accounts for three types of contact behaviour at fracture surface: fracture is opened, fracture is closed but surface is in sticking

Poisson ratio [20].

pressure conditions.

and used in numerous studies [23].

mode, and fracture is closed but in sliding mode.
