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This paper presents an integrated methodology that utilizes the cohesive zone model ( CZM ) to simulate propagation of hydraulic fractures, and their interactions with pre-existing natural fractures. CZM has the advantage of capturing the non-elastic behavior of shales; usually induced by total organic carbon (TOC) as well as dissimilar mechanical properties of cemented natural fractures. At the intersection of an advancing hydraulic fracture and a stationary natural fracture, the hydraulic fracture may arrest, cross, or divert into a pre-existing natural fracture depending on the rock mechanical properties, magnitude and direction of rock principal stresses, and fracture intersection angle. The activation of natural fractures during hydraulic fracture treatments improves fracture complexity and expands reservoir drainage area, making stimulation treatments more effective. In this work, triaxiality effects are incorporated into the cohesive zone model. Utilizing triaxiality makes the traction separation law ( TSL ) tied to confining pressure and this ensures a more reliable transition from laboratory test environment to bottomhole conditions. We present a methodology to determine the cohesive properties or TSL characteristics of rock, after performing semicircular bending tests ( SCBT ). Finite element analysis ( FEA ) is then used to calibrate the cohesive properties of both rock and natural fractures. The calibrated parameters were utilized in a field-scale FEA to simulate the growth of complex fracture networks. The results show how fracture intersection angle and the nature of cemented materials inside the natural fractures might divert a hydraulic fracture initially propagating in a direction perpendicular to the minimum horizontal stress. The sensitivity analysis of primary parameters such as fluid viscosity, natural fracture distribution, fracture intersection angle, and differential stresses is implemented to provide a better insight into the performance of hydraulic fracturing jobs in naturally fractured reservoirs. Results indicate the importance of nonlinear fracture tip effects as in-situ stress differences increase. [ABSTRACT FROM AUTHOR]

A coupled extended finite element method (XFEM) is presented here for modeling propagation of fluid-driven fractures in different regimes including toughness- and viscosity-dominated regimes. The extended finite element method allows to model growth, and coalescence of arbitrary discontinuities (fractures) without requiring the mesh to conform to discontinuities nor significant refinement near the fractures. Fluid-driven fractures propagation is a coupled, nonlinear and non-local problem with moving boundary conditions. The proposed method is based on the extended finite element method with modifications to incorporate variable stress singularity at the crack tips for the transition between toughness-dominated and viscosity-dominated regimes. These modifications consist of enriched functions that are initially inspired by the asymptotic analytical solutions. The standard extended finite element approximation is enriched by adding near tip asymptotic solutions just for displacements, however the proposed method introduces a consistent enriched function for fluid pressure calculations close to the fracture tips to catch the singularity. Additionally, a technique is presented to remove singularity issue for required numerical integrations. Green's functions concept is proposed here to expedite calculations. To circumvent violation of partition of unity and parasitic terms in the approximation space induced by the blending elements at the edge of the enriched domain, the ramp function is utilized to improve the convergence rate. Stress intensity factors are calculated using a new contour integral method that can handle cases with different tip singularities. The proposed technique is verified with the cases that have analytical solutions. Some examples are presented to show the advantages of this technique in comparison to the regular XFEM. [ABSTRACT FROM AUTHOR]

The intersection of natural fractures with hydraulic fractures results in formation of complex fracture networks, including non-planar fractures or multi-stranded fractures. On one hand, opening of these natural fractures improves productivity of the formation; on the other hand, coalescence of these fractures into a hydraulic fracture makes pressure analysis and prediction of fracture growth very complicated. Overall, interactions between natural fractures and hydraulic fractures pose more challenges in the fracturing design and its execution. Investigation and understanding of their interaction are crucial in achieving successful fracture treatments in formations with pre-existing natural fracture network. In this paper, we will review the numerical works that have been done in the last decade to model opening of natural fractures during hydraulic fracturing, focusing especially on mechanical models that address propagation of hydraulic fractures in naturally fractures reservoirs. Linear elastic fracture mechanics, cohesive element methods and continuum damage mechanics techniques utilized to understand interaction of hydraulic fractures with natural fractures are discussed here based on their capability to reproduce experimental results and field observations. [ABSTRACT FROM AUTHOR]

We developed a method and presented it as a Mathematica code to calculate the stress and strain fields inside and outside of two interacting ellipsoidal inhomogeneities with arbitrary orientation with respect to each other, using the Eshelby technique. The Eshelby technique can be used to determine the elastic fields in and around these inhomogeneities. Assuming same material properties for one of the inclusions and the surrounding matrix, this code can be also used for the single inhomogeneity problem. Different geological features like faults and aquifers can be modeled as inhomogeneous inclusions. We start by reviewing Eshelby's solution for a single inclusion, a single inhomogeneity and a double inhomogeneity problem with the required formulation to calculate Eshelby tensors. Then, we describe our code structure and validate it with existing solutions in the literature and present numerical solutions. [ABSTRACT FROM AUTHOR]