HYDRAULIC FRACTURING MODELING BY UTILIZING IMPROVED EXTENDED FINITE ELEMENT METHOD

A novel enrichment formulation is presented for modeling coupled fluid-driven fracture propagation. The proposed method is based on the extended finite element method with modifications to incorporate variable stress singularity at the crack tips to account for the transition between toughness-dominated and viscous-dominated regimes. These enrichment functions are inspired by the asymptotic analytical solutions. Additionally, a consistent enrichment function is introduced for fluid pressure calculations close to the fracture tip.

To validate the proposed method, the numerical results are compared with the analytical solutions for two extreme propagation regimes. A superconvergent method is also proposed to calculate the energy release rate at the fracture tips for the general variable singularity. Mesh independency of the proposed method is verified and the convergence with the rate of 0.58 has been achieved for the coupled model using this method. The shear lag approximation is utilized to incorporate the height effect into the proposed method to describe the evolution of the fracture geometry more realistically.

The proposed method does not require high mesh concentration at the tip regions to achieve high numerical accuracy and is fully parallelized to expedite computation. High numerical accuracy with short execution time is crucial for simulating complicated geometries such as interacting hydraulic fractures or interaction a hydraulic fracture with pre-existing natural fractures. Hence, an example of fracture propagation in presence of multiple pre-existing fractures is presented to show a successful application of the model for predicting fracturing performance in Barnett Shale.