Multi-Scale Physics-Based Numerical Modeling of Hydraulic Fracturing Treatment for Unconventional Shale Reservoirs

Abstract

Numerical modeling of the hydraulic fracturing process is a complex and highly non-linear problem that requires special treatment of the far-field and the near-wellbore fracture propagation. In this study, I developed an efficient numerical simulator called FracMod to model the far-field fracture propagation and used the commercial application to investigate the fracture initiation in the immediate vicinity of the wellbore.

I used the displacement discontinuity method (DDM), a branch of the boundary element method (BEM), to model the rock deformation and the far-field fracture propagation. To improve the accuracy of the estimation of the fracture width, I implemented higher-order quadratic elements and special square root tip elements to describe the two-dimensional fractures and used biquadratic elements to describe the three-dimensional fractures.

The governing non-linear fluid flow equations were approximated by the finite difference method, they were solved by the Newton-Raphson method and were iteratively coupled with the rock deformation scheme. I validated the numerical scheme of fracture propagation that I developed against the Perkins-Kern-Nordgren (PKN) and the Khristianovic-Geertsma-de Klerk (KGD) analytical models.

Monitoring techniques for hydraulic fracturing, such as fiber optics, radioactive tracers, and core analysis, imply the initiation of multi-stranded fracture "swarms" and longitudinal fractures in the near-wellbore region. I used the FracMod fracturing simulator to mimic the crosswell fiber optics response in the presence of fracture swarms.

Additionally, I used commercial software for describing near-well fracture behavior to explain the complex fracture morphology in this region by performing simulation studies covering both synthetic and field cases. This study provided insights into the impact of the perforation parameters and patterns, injection rate, cement thickness, stress anisotropy, and formation heterogeneity on fracture morphology. The results of this study led to recommendations for promoting transverse fracture initiation and reducing fracture breakdown pressure.