**1. Introduction**

It is believed that complexity of the fracture network created during hydraulic fracturing treatments in formations with pre-existing natural fractures is caused mostly by the interaction between hydraulic and natural fractures. The understanding and proper modelling of the mechanism of hydraulic-natural fractures interactions are keys to explain fracture complexity and the microseismic events observed during hydraulic fracturing treatments, and therefore to properly predict production.

When a hydraulic fracture (HF) intercepts a natural fracture (NF) it can cross the NF, open (dilate) the NF, or be arrested at NF. If the hydraulic fracture crosses the natural fracture, it remains planar, with the 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. So the crossing criterion in general controls the complexity of the resulting fracture network.

The interaction between HF and NF depends on the in-situ rock stresses, mechanical properties of the rock, properties of natural fractures, and the 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 develop the rules controlling HF/NF interaction. Among the main contributions to this topic are the work listed in references [1-15].

Most of the existing crossing models do not take into account fluid properties due to the complexity of modelling fluid-solid interaction in the vicinity of the intersection, so crossing behaviour is explained purely from elasticity point of view. Field and laboratory observations, however, show that fluid properties are important and should be accounted for [9, 16].

It is well known that the microseismic events cloud is related to the hydraulic fracture propagation pattern which in turn strongly depends on the HF/NF interaction rules [17].

Figure 1 shows the microseismic events observed in the same well first treated with a crosslinked gel, and then re-fractured with slick water [16]. Cross-linked gel was pumped at 70 bpm for about 3 hours with sand concentration ramped up to 3 ppg. Most of the microseismic activity suggests longitudinal fracturing with only modest activation of natural fractures, resulting in a narrow stimulated network (less than 500 feet from the wellbore in many sections of the lateral), as seen in Figure 1a with resulting Stimulated Reservoir Volume ( SRV) equal to 430 million ft3 . During the full re-frac conducted the following day 60,000 bbl of slick water and 285,000 lb of sand was pumped at 125-130 bpm for most of the treatment lasting 6.5 hours. The stimulated network was approximately 1500ft wide and 3,000 ft long (Figure 1b) with considerable height growth and SRV of 1450 million ft3 . Clearly, the re-fracturing treatment stimulated a much larger volume of rock than the initial gel treatment (1450 million ft3 vs 430 million ft3 ), and showed the patterns of development that suggested the opening of both northeast and northwest trending fractures [ 16].

existing natural fractures. The influence of the stress field anisotropy, intersection angle, as well as natural fractures properties are also important and are discussed. The results are then compared with the simulations using the previous crossing model which does not ac‐

It is believed that complexity of the fracture network created during hydraulic fracturing treatments in formations with pre-existing natural fractures is caused mostly by the interaction between hydraulic and natural fractures. The understanding and proper modelling of the mechanism of hydraulic-natural fractures interactions are keys to explain fracture complexity and the microseismic events observed during hydraulic fracturing treatments, and therefore

When a hydraulic fracture (HF) intercepts a natural fracture (NF) it can cross the NF, open (dilate) the NF, or be arrested at NF. If the hydraulic fracture crosses the natural fracture, it remains planar, with the 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. So the crossing criterion in general controls the complexity of the resulting fracture

The interaction between HF and NF depends on the in-situ rock stresses, mechanical properties of the rock, properties of natural fractures, and the 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 develop the rules controlling HF/NF interaction. Among the main contributions to this topic

Most of the existing crossing models do not take into account fluid properties due to the complexity of modelling fluid-solid interaction in the vicinity of the intersection, so crossing behaviour is explained purely from elasticity point of view. Field and laboratory observations, however, show that fluid properties are important and should be accounted for [9, 16].

It is well known that the microseismic events cloud is related to the hydraulic fracture propagation pattern which in turn strongly depends on the HF/NF interaction rules [17].

Figure 1 shows the microseismic events observed in the same well first treated with a crosslinked gel, and then re-fractured with slick water [16]. Cross-linked gel was pumped at 70 bpm for about 3 hours with sand concentration ramped up to 3 ppg. Most of the microseismic activity suggests longitudinal fracturing with only modest activation of natural fractures, resulting in a narrow stimulated network (less than 500 feet from the wellbore in many sections of the lateral), as seen in Figure 1a with resulting Stimulated Reservoir Volume ( SRV) equal

and 285,000 lb of sand was pumped at 125-130 bpm for most of the treatment lasting 6.5 hours.

. During the full re-frac conducted the following day 60,000 bbl of slick water

count for the influence of fluid properties.

184 Effective and Sustainable Hydraulic Fracturing

**1. Introduction**

network.

to 430 million ft3

to properly predict production.

are the work listed in references [1-15].

**Figure 1.** Single-well microseismic event locations for XL gel stimulation and water-frac re-fracturing treatment, hori‐ zontal Barnett Shale well [16]

treatment

This field example indicates the importance of proper consideration of fluid properties when modelling the interaction of hydraulic fractures with pre-existing natural fractures. In general it is observed that for the same field conditions more viscous fluid tends to cross the natural fractures more easily, while slick water tends to penetrate into the natural fractures more easily and open them without crossing. Pumping rate as well as rock properties should also be taken into account.

The importance of fluid properties on the created hydraulic fracture network has been mentioned in some experimental and numerical studies [9, 18, 19]. The experimental study of the influence of flow rate and fracturing fluid viscosity on the hydraulic fracture geometry have been performed in [9] based on analysis of different *Qμ* value (product of the injection rate and fracturing fluid viscosity). The experiments show that with low *Qμ* value fluid tends to leak into the pre-existing discontinuities despite the influence of fluid pressure and once the discontinuity accepts fluid, the pressure can rise far above the confining stress without inducing new fractures. With large *Qμ* value the hydraulic fracture tends to cross natural fracture due to increase of the pressurization rate.

The influence of fluid injection rate and viscosity on the amount of the tensile failure in the rock with natural fractures has been investigated based on 3DEC DEM model in [18, 19]. For low viscosity fluid the amount of area failing in shear is dramatically higher than in the case with high viscosity. Their results show that an increase in injection rate greatly increases the amount of tensile failure within the model leading potentially to creating more fractures, while a lower injection rate favours the creation of shear failure resulting mostly in activating (opening) pre-existing natural fractures.

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 pre-existing natural fractures, i.e., determine whether a hydraulic fracture propagates through or is arrested by a natural fracture when they intersect and subsequently

Effect of Flow Rate and Viscosity on Complex Fracture Development in UFM Model

http://dx.doi.org/10.5772/56406

187

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 the hydraulic fracture at the intersection with the natural fracture gives rise to the development of a complex fracture network. A crossing model that is extended from the Renshaw-Pollard [10] interface crossing criterion, applicable to any intersection angle, has been developed [14], validated against the experimental data [15], and was integrated in the UFM. The previous crossing model, showing good comparison with existing experimental data, does

The new crossing model (OpenT) which accounts for the fluid properties is presented in short

There are a few analytical criteria describing the mechanical HF-NF interaction devel‐ oped in the past [10, 11, 13, 14]. With their relative simplicity they do not take into account the influence of the fluid injection into the hydraulic fracture and the fluid infiltration into the natural fracture after contact. These criteria were designed to capture the effect of the fracture approach angle, the NF friction coefficient and the anisotropy of the in-situ stresses. To improve the description of HF-NF interaction a new analytical model that takes the mechanical influence of the HF opening and the hydraulic permeability of the NF into

The analytical model of the HF-NF interaction (OpenT) solves the problem of the elastic perturbation of the NF at the contact with the blunted HF tip, which is represented by a uniformly open slot (i.e. giving its name OpenT) [21]. The opening of the HF at the junction point *w*T (blunted tip) develops soon after contact, and approaches the value of the average opening of the hydraulic fracture *<sup>w</sup>*¯, defined by the injection rate *<sup>Q</sup>* and the fluid viscosity *μ*. In a viscosity-dominated regime, the average opening of the KGD fracture with half-length *L*

propagates along the natural fracture.

not account for the fluid impact on the crossing pattern.

below and is implemented in a new version of UFM.

**3. New crossing model in UFM**

account has been developed.

and height *H* can be estimated as [25]

presented in [24].

A new analytical model, called OpenT, for hydraulic fracture interaction with a pre-existing discontinuity has been developed to predict the fracture crossing or deflection at the encoun‐ tered interface [20, 21]. The new physically rigorous criterion of fracture re-initiation at the discontinuity has been implemented, which combines both stress criterion and energy release rate. It has been shown that the OpenT model adequately predicts the fracture crossing of noncohesive frictional interfaces observed in various laboratory experiments with different interface orientations with respect to hydraulic fractures [21].

The new crossing model predicts the dimensions of open and sliding zones created at cohesive and non-cohesive interfaces after the intersection with a fluid-driven fracture. Such informa‐ tion can be valuable, for example, in passive microseismic monitoring of fracture treatments in naturally fractured formations. By thoroughly examining the stress field generated by the hydraulic fracture and activated open and sliding zones at the discontinuity, it was shown that the new fracture initiation point is shifted along the inclined interface. The model predicts the offset of a secondary fracture as a function of the geometrical, loading, and mechanical parameters of the system, such as the fracture-interaction angle, in-situ stress components and fracture toughness in rock.

New OpenT crossing model incorporates the influence of rock properties (local horizontal stresses, rock tensile strength, toughness, pore pressure, Young's modulus, Poisson ratio), natural fracture properties (friction coefficient, toughness, cohesion, permeability), intersec‐ tion angle between hydraulic and natural fractures, fracturing fluid properties (viscosity, tip pressure), and injection rate to define crossing rules.

This new OpenT model has been validated against laboratory experiments and against rigorous numerical models [3,20,21]. It was incorporated into the UFM model that simulates complex fracture network propagation in a formation with pre-existing natural fractures [22-24]. We present several UFM test cases showing the influence of injection rate and fluid viscosity on the generated hydraulic fracture footprint and production impact by comparing of two crossing criteria, the extended Renshaw & Pollard (hereafter referred as eRP) [14, 15] and the OpenT.
