**1. Introduction**

It is believed that complexity of the resulting fracture network during hydraulic fracturing treatments in formations with pre-existing natural fractures is caused mostly by the interaction between hydraulic and natural fractures. Natural fractures can be important for hydrocarbon production in the majority of low-permeability reservoirs, particularly where the permeability of the rock matrix is negligible. Understanding and proper modelling of the mechanism of hydraulic-natural fractures interaction is a key to explain fracture complexity and the micro‐ seismic events observed during HF treatments, and therefore to properly predict production.

When hydraulic fracture (HF) intercepts natural fracture (NF) it can cross the NF, open (dilate) the NF, or be arrested at NF. If hydraulic fracture crosses natural fracture, it remains planar, with a possibility to open the intersected NF if the fluid pressure at the intersection exceeds the effective stress acting on the NF. If the HF does not cross the NF, it can dilate and eventually propagate into the NF, which leads to more complex fracture network.

The interaction between HF and NF depends on in-situ rock stresses, mechanical properties of the rock, properties of natural fractures, and hydraulic fracture treatment parameters including fracturing fluid properties and injection rate. During the last decades, extensive theoretical, numerical, and experimental work has been done to investigate, explain, and use the rules controlling HF/NF interaction [3-17]. A new crossing model [2] recently implemented in UFM is able to predict the crossing behaviour of HF at the NF accounting for the effects of fluid properties and NF permeability [18].

One of the important effects of natural fractures is enhanced leakoff, which can lead to a premature screenout during proppant injection. In a formation with low-matrix-permeability, the transmissibility of natural fissures can be significantly higher than that of the reservoir matrix. The fracturing fluid can readily penetrate into natural fissures during the fracturing process and maintain a pressure nearly equal to the pressure in the primary fracture [19].

The concept that natural fractures (fissures) could alter leakoff has been a subject of numerous studies [20-24] with considering the fissure opening conditions or pressure-sensitive leakoff conditions. It was often reported that permeability of natural fractures is pressure dependent [23, 25, 26].

The ways that elevated pressure could affect natural fractures have been described in [27]. Fissures with rough surfaces and minimal mineralization are most likely highly sensitive to the net stress pushing on them. Under virgin reservoir conditions (when the pressure *p* within the fissure equals the initial reservoir pressure *p ini*), the effective stress is fairly high and the open channels formed by mismatched fracture faces are most likely deformed and nearly closed. As the pressure in the fissure increases because of leakoff of the high-pressure fractur‐ ing fluid (*p* > *p ini*), the net closure stress is reduced and the fissure porosity opens. In this regime, 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 Poisson ratio [20].

The updated UFM model with enhancement to account for leakoff into the natural fractures

It is believed that complexity of the resulting fracture network during hydraulic fracturing treatments in formations with pre-existing natural fractures is caused mostly by the interaction between hydraulic and natural fractures. Natural fractures can be important for hydrocarbon production in the majority of low-permeability reservoirs, particularly where the permeability of the rock matrix is negligible. Understanding and proper modelling of the mechanism of hydraulic-natural fractures interaction is a key to explain fracture complexity and the micro‐ seismic events observed during HF treatments, and therefore to properly predict production. When hydraulic fracture (HF) intercepts natural fracture (NF) it can cross the NF, open (dilate) the NF, or be arrested at NF. If hydraulic fracture crosses natural fracture, it remains planar, with a possibility to open the intersected NF if the fluid pressure at the intersection exceeds the effective stress acting on the NF. If the HF does not cross the NF, it can dilate and eventually

The interaction between HF and NF depends on in-situ rock stresses, mechanical properties of the rock, properties of natural fractures, and hydraulic fracture treatment parameters including fracturing fluid properties and injection rate. During the last decades, extensive theoretical, numerical, and experimental work has been done to investigate, explain, and use the rules controlling HF/NF interaction [3-17]. A new crossing model [2] recently implemented in UFM is able to predict the crossing behaviour of HF at the NF accounting for the effects of

One of the important effects of natural fractures is enhanced leakoff, which can lead to a premature screenout during proppant injection. In a formation with low-matrix-permeability, the transmissibility of natural fissures can be significantly higher than that of the reservoir matrix. The fracturing fluid can readily penetrate into natural fissures during the fracturing process and maintain a pressure nearly equal to the pressure in the primary fracture [19].

The concept that natural fractures (fissures) could alter leakoff has been a subject of numerous studies [20-24] with considering the fissure opening conditions or pressure-sensitive leakoff conditions. It was often reported that permeability of natural fractures is pressure dependent

The ways that elevated pressure could affect natural fractures have been described in [27]. Fissures with rough surfaces and minimal mineralization are most likely highly sensitive to the net stress pushing on them. Under virgin reservoir conditions (when the pressure *p* within the fissure equals the initial reservoir pressure *p ini*), the effective stress is fairly high and the open channels formed by mismatched fracture faces are most likely deformed and nearly closed. As the pressure in the fissure increases because of leakoff of the high-pressure fractur‐ ing fluid (*p* > *p ini*), the net closure stress is reduced and the fissure porosity opens. In this regime,

propagate into the NF, which leads to more complex fracture network.

fluid properties and NF permeability [18].

[23, 25, 26].

will be presented.

288 Effective and Sustainable Hydraulic Fracturing

**1. Introduction**

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 pressure conditions.

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 and used in numerous studies [23].

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 mode, and fracture is closed but in sliding mode.

The approach given in [10] is based on boundary element method and rigorously models HF interaction with permeable NF. It is computationally expensive, and is applicable for analysis of limited (small) number of HF/NF interactions. For a more general complex fracture network model like UFM which deals with a large number (order of thousands) of natural fractures, the CPU time is important and model should be computationally efficient while still being

Hydraulic Fracturing in Formations with Permeable Natural Fractures

http://dx.doi.org/10.5772/56446

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The important aspect of HF/NF interaction is shear slippage of NF faces. The possibilities of shear slippage in natural fractures due to change of stress field (in isolated natural fractures) or during HF/NF interactions, and the influence of shear slippage on fracture aperture change and dilation have been a subject of experimental and numerical studies [10, 15, 17, 30, 34-37]. The conditions for shear slippage and the corresponding shear displacement (apertures) have been investigated [36], and the estimation of permeability of NF with changing effective normal stress is done by [11,38]. The shear slippage effect during HF/NF interaction is also

This paper describes how leakoff into the natural fractures during HF/NF interaction (crossing or arresting before NF opens) is integrated into the complex hydraulic fracture model UFM.

A complex fracture network model, referred to as Unconventional Fracture Model (UFM), had recently been developed [1, 39, 40]. The model simulates the fracture propagation, rock deformation, and fluid flow in the complex fracture network created during a treatment. The model solves the fully coupled problem of fluid flow in the fracture network and the elastic deformation of the fractures, which has similar assumptions and governing equations as conventional pseudo-3D fracture models. Transport equations are solved for each component of the fluids and proppants pumped. A key difference between UFM and the conventional planar fracture model is being able to simulate the interaction of hydraulic fractures with preexisting natural fractures, i.e., determine whether a hydraulic fracture propagates through or is arrested by a natural fracture when they intersect and subsequently propagates along the

To properly simulate the propagation of multiple or complex fractures, the fracture model takes into account the interaction among adjacent hydraulic fracture branches, often referred to as "stress shadow" effect. It is well known that when a single planar hydraulic fracture is opened under a finite fluid net pressure, it exerts a stress field on the surrounding rock that is proportional to the net pressure. The details of stress shadow effect implemented in UFM are

The branching of hydraulic fracture when intersecting natural fracture gives rise to the development of a complex fracture network. A crossing model that is extended from the Renshaw-Pollard [12] interface crossing criterion, applicable to any intersection angle, has been developed, validated against the experimental data [16, 17], and was integrated at first in the

physically correct.

included in current approach.

**2. UFM model specifics**

natural fracture.

given in [40].

**Figure 1.** Evolution of natural fracture opening [10]

The HF models [28-32] do not account for permeability of natural fractures explicitly. The 2D model in [33] uses approach from [13] to simulate interaction between induced propagating fracture and natural fracture. A modified leak-off model for an intersecting fracture based on poro-elasticity was introduced to account for the increased leakoff at the intersections. A poroelastic solution for the stresses in the HF/NF interaction zone has been used as a basis for hydraulic/natural fracture interaction criteria. A fully coupled finite element based approach was used to simulate HF propagation in a poroelastic formation with existing natural fractures. The approach given in [10] is based on boundary element method and rigorously models HF interaction with permeable NF. It is computationally expensive, and is applicable for analysis of limited (small) number of HF/NF interactions. For a more general complex fracture network model like UFM which deals with a large number (order of thousands) of natural fractures, the CPU time is important and model should be computationally efficient while still being physically correct.

The important aspect of HF/NF interaction is shear slippage of NF faces. The possibilities of shear slippage in natural fractures due to change of stress field (in isolated natural fractures) or during HF/NF interactions, and the influence of shear slippage on fracture aperture change and dilation have been a subject of experimental and numerical studies [10, 15, 17, 30, 34-37]. The conditions for shear slippage and the corresponding shear displacement (apertures) have been investigated [36], and the estimation of permeability of NF with changing effective normal stress is done by [11,38]. The shear slippage effect during HF/NF interaction is also included in current approach.

This paper describes how leakoff into the natural fractures during HF/NF interaction (crossing or arresting before NF opens) is integrated into the complex hydraulic fracture model UFM.
