ARMA 12-441 Montney Shale Geomechanical Challenges : 2 D and 3 D FEM / DEM Numerical Simulations of a Layered Material Fracturing in Compression

In this study a series of numerical analysis have been carried out to assess the suitability of the FEM/DEM technique to simulate UCS test of a horizontally layered material, the Montney shale. The strength parameter of the Montney samples reported by Keneti and Wong (2011) were used as the input data to 2D and 3D models in the ELFEN program. When the failure criterion within the intact material was met in the model, a new crack was generated which could be visualized by remeshing the updated geometry with the pre-existing foliations and the new cracks. The results were analyzed in terms of the “global mechanical response” obtained by assessing if the fracturing response is comparable to the recorded behavior in the UCS test of the Montney shale. The entire fracturing process was shown to be simulated well by ELFEN during fractures initiation and propagation processes. stress-strain behaviour, initiation and propagation of fracture and fluid flow [6]. Predicting the geomechanical response of the shale material during hydraulic fracturing operation in the field needs better understanding of their geomechanical behaviour under laboratory testing as well as throughout simulation by numerical approaches. Fig. 1. Shale gas plays of North America [1]. Fig. 2. Montney-Doig resource plays [4]. There are many practical problems in jointed media where discontinuities are dominant in the analysis. The conventional numerical methods such as Finite Element Method (FEM), which are mostly continuity based, are clearly not suitable for using in such situations [7]. Thus, the methods such as discrete elements methods (DEM), Discontinuous Deformation Analysis (DDA) and combined Finite-Discrete Element Method (FEM/DEM) have been developed in the past to model a discontinuous media. In FEM/DEM, continuum behaviour is modeled through finite elements while discontinuous behaviour is analyzed by discrete elements [8]. The effect of layering and the direction of loading on the samples behaviour were studied by Mahabadi et al. [8] by employing a modified FEM/DEM research code presented in [9] by Munjiza. The applicability of the combined finite-discrete element method to model laboratory scale experiments was shown through their simulations of Brazilian disc tests for both a homogeneous rock and a layered rock. The results suggested that the presence of layers and direction of loading with respect to them plays a major role in mechanical behaviour of the models. Stefanizzi et al. [10] simulated a series of numerical analyses using the finite/discrete element code ELFEN and showed the suitability of this approach to simulate standard rock mechanics tests. ELFEN provides a unique ability to model fracture initiation and propagation, as it simulates the transition from continuum to discontinuum [10]. In this study, the uniaxial compression test conducted by Keneti and Wong [11-13] on Montney shale sample has been simulated by ELFEN (Rockfield Software, 2010). The results have been analyzed in terms of the “global mechanical response” obtained by evaluating if the fracturing response is realistically represented. 2. EXPERIMENTAL WORKS ON THE MONTNEY SHALE Keneti and Wong [11-14], investigated some geomechanical properties of the Montney shale throughout laboratory investigations. From their study, it was found that the pre-existing planes of weakness play a major role in failure and anisotropic behavior of the Montney shale. From the Brazilian and point load strength tests, the tensile strength in the horizontal direction was dominated by the bond strength of the intact structure (6-15.3 MPa), whereas that in the vertical direction was controlled by the existing natural beddings (0.7-2.8 MPa) [11 and 12]. Compressive strength, compressive elastic modulus in the vertical direction and Poisson’s ratio were measured from the unconfined compressive strength test as 99 MPa, 25 GPa, and 0.1, respectively. The final mode of fracture was mainly shearing at top and bottom of the sample, rather than the common vertical splitting around the core center [13]. Tensile and compressive elastic moduli in the horizontal direction were also measured from Brazilian test as 31 GPa and 40 GPa, respectively [12]. From the direct shear tests using double shear boxes, the Montney samples sheared through the foliation planes as well as through the rock material which resulted in higher shear strength parameters compared to the reported values for shale. From the results, the cohesion was found as 20 MPa and the peak friction angle was about 40 o [14]. 3. FEM/DEM MODELS FOR COMPRESSIVE LOADING OF THE MONTNEY SHALE The unconfined compression of cylindrical rock samples is widely performed in rock engineering projects in order to determine the uniaxial compressive strength, σc , and the elastic constants Young’s modulus, Ec , and Poisson’s ratio, θ, of the rock material. Although it seems to be a straightforward technique, great attention must be paid in interpreting results obtained in a uniaxial compressive test. Its results are affected by the rock composition, loading condition and the condition of the test samples. Even for rock having the same geological name, the test results will vary with the grain size, porosity, the nature and extent of cementing between the grains, degree of weathering and micro-fissuring, and the levels of pressure and temperature that the rock has been subjected to throughout its history [15]. The main feature of the test preparations should be to subject the testing sample to uniform boundary conditions with a uniform uniaxial stress. Consequently, a uniform displacement field would be generated all over the sample. However, the sample might be prevented from deforming uniformly due to “end effects”. The sample would be restrained near its ends due to friction between its ends and the loading platens and differences between the elastic properties of rock and steel. The result of such restraint is that shear stresses are developed at the contact area of the sample and the loading platen. This means that the axial stress is not always a principal stress and therefore, stresses within the sample are not uniaxial. As a consequence of the end effects, the stress distribution varies throughout the testing sample in a uniaxial compressive strength test as a function of the geometry of the sample. As the height to diameter (H/D) ratio increases, a greater proportion of the sample volume is subjected to an approximately uniform state of uniaxial stress. Therefore, it has been suggested that a H/D ratio of at least 2 should be used in uniaxial compression [15]. In the ELFEN model of the UCS test simulation, the geometry of the specimen was set same as the sample tested in the laboratory and its properties were also assigned the same as the obtained experimental results. The modeled specimen had a diameter of 76 mm and a height of 160 mm (i.e. the H/D ratio is 2.1). Location of each pre-existing fracture was found by Computer Tomography (CT) technique and presented in the model (Fig. 3). A homogeneous isotropic sample was also modeled for studying the failure process of the Montney in absence of the pre-existing weak planes. Fig. 3 Foliations in Montney cores observed in computer tomography analysis. The constant vertical velocities of 0.5 mm/s and 2 mm/s were applied to the 2D and 3D models, respectively, to simulate the compressive loading. These displacement rates were chosen only for the calculation time efficiency purpose in the numerical simulation. However, it is not representative of the real loading condition as the loading rate is normally much slower during the experiment. A mesh size of 10% of the unit length was assumed for the platens and the sample in 2D and 3D models. The platens outer boundaries were set free to move in the loading direction (vertical) and were fixed in the horizontal direction in 2D and 3D models. Therefore, the specimen could freely expand in a minimal end effect condition. The FEM/DEM code ELFEN only considers Mode I (tensile) fracture initiation and propagation. Therefore, only fractures created by exceeding the tensile strength of the material can be visualized. The Rankine Rotating crack model coupled with a Mohr-Coulomb failure criterion was assigned to simulate the material behavior in 2D and 3D models. Although it is practical in ELFEN code, the effects of heterogeneity was not considered in the current study as the objective of this study was investigation of the influence of the pre-existing cracks on failure of material in UCS test. Hence, the matrix was considered as homogenous and the discontinuity parameters Kn , Kt and μf were assigned to simulate the pre-existing weak planes in the 2D model. For the 3D model, weaker material properties were assigned to the preexisting cracks of 1mm thickness. The assumed fracture energy parameter was based on the author’s experience and the available literature. However, no sensitivity analysis was done on this critical parameter in current study. Table 1 summarizes the material properties used for the UCS test numerical simulation. Table 1. Properties of the matrix and pre-existing fractures in 2D and 3D numerical simulation of the UCS test Compressive Elastic Modulus (Ec), GPa 25 Poisson's Ratio (θ) 0.1 Friction Angle (φ) 31 Cohesion (C), MPa 20 Tensile Strength (σt), MPa 10 Fracture Energy (Gf), N/mm 0.003 Pre-existing Fractures Parameters in 2D Model: Kn , N/mm 3 2.5×10 4 Kt , N/mm 3 2.5×10 3