A typical hydraulic fracturing operation in a naturally fractured rock was simulated by using the Discrete Element Method, DEM (Cundall and Strack, 1979). In this model, a field-derived Discrete Fracture Network (DFN) was superimposed on an intact rock particle model to create a Synthetic Rock Mass (SRM). This SRM resembled both the mechanical (Pierce et al., 2007) and hydraulic (Hazzard et al., 2002) behavior of a specific naturally fractured rock mass. Fluid injection was simulated with this calibrated model to determine the geometry and orientation of the induced hydraulic fracture(s); also, the interaction between the pre-existing natural fracture network and the hydraulically induced fracture(s) was studie.


Hydraulic fracturing is a technology that has been utilized for more than 50 years in the oil and gas industry. It was originally used for stimulating relatively stiff and homogeneous formations; which typically behaved as linear elastic materials. Accordingly, hydraulic fracturing theory based on linear fracture mechanics was developed to model the hydraulic fracturing process. Assumptions such as the existence of a bi-wing, perfectly planar, symmetrical fractures are commonplace in current standard hydraulic fracturing simulators. Nonetheless, an increasingly important segment of the industry is currently stimulating naturally fractured formations (e.g. tight gas sands, and gas shales); where the assumptions of linear elasticity, simple fluid leak-off, and planar hydrofrac geometry (used in standard simulators) fail to hold. Furthermore, the physics of the interaction between the hydraulically-induced fracture(s) and the natural fractures in the rock is often disregarded. Finding modeling alternatives for this process is critical for the development and production of naturally fractured reservoirs, as hydraulic fracturing is commonly used as the main stimulation technique to increase deliverability and improve economics. Most hydraulic fracturing treatments carried out in naturally fractured rocks render rather unexpected results, as standard numerical models fail to correctly predict fracturing pressures and resulting fracture geometry. A worldwide survey on fracturing pressures by the Delft Fracturing Consortium (Papanastasiou, 1997), indicated that net pressures encountered in the field commonly are 50% to 100% higher than their corresponding values predicted by conventional fracturing simulators. The implementation of hydraulic fracturing operations in naturally fractured rocks has not been accompanied by modeling techniques tailored specifically for this kind of formations. In most cases, such models undergo a period of “calibration”, in order to reproduce the results obtained in the field.


Potyondy and Cundall (2004) showed that the mechanical behavior of a rock can be conceptually represented as a cemented granular assembly; where both the grain and the cement can deform and may eventually fail. They proposed the use of a Bonded Particle Model (BPM) to represent the behavior of real rock. In such model, the rock is discretized as an assembly of disks (2D) or spheres (3D); held together by intergranular bonds (see Fig. 1). Both, the microscale2 geometrical (e.g. size distribution, shape) and mechanical (e.g. stiffness, strength) properties of the particles and the bonds can be selected to match the overall mechanical behavior of a given rock.

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