A variational approach to the numerical simulation of hydraulic fracturing under in-situ stresses
Conferences
Overview
Overview
abstract
Most hydraulic fracturing simulation approaches apply propagation criteria to an individual fracture
along prescribed path(s). In practice, however, the
modeling of hydraulic fracturing in reservoir stimulation requires handling interactions between multiple
natural or induced fractures growing along unknown
paths, and changes in fracture pattern and network.
In this paper, we extend the work of Bourdin et al
2012 and focus on the effectof in-situ stresses on
crack path in 2D and 3D, and revisit the verification
work against analytic solution with more realistic
units. The approach is based on Francfort and Marigo's variational approach to fracture (Francfort and
Marigo, 1998). The main idea is to recast Griffith's
criterion for a single fracture growth into a global
energy minimization problem. The energy we consider consists of the sum of surface and bulk terms
accounting for the energy dissipated by a growing
crack and the mechanical energy, including the work
of residual (in-situ) stresses and pressure force
against the fracture walls. To be more specific, we
search the minimum of the total energy under any
admissible fracture sets and kinematically admissible
displacement field. Our focus is on quasi-static crack
propagation propagation encountered during hydraulic fracturing process, which we model as a rate independent process. This approach does not need any
a priori knowledge of the crack path, or any additional hypotheses concerning fracture nucleation or activation. We claim that it provides a mathematically
rigorous and mechanistically sound unified framework accounting, derived from first principles, and
accounting for new fractures nucleation, existing
fractures activation, and full fracture path determination such as branching, kinking, and interaction between multiple cracks. It is no surprise that having no
a priori hypothesis or knowledge on fracture geometry comes at the cost of numerical complexity. To
overcome the complexities associating with handling
of large and complex fracture patterns, we propose an
approach based on a regularized model where fractures are represented by a smooth function.
In this paper, we first show series of comparison cases of the variational fracture simulation against analytical solutions. We demonstrate our approach's ability to predict complex behaviors such as turning fracture under in-situ earth stresses and the interactions
of multiple fractures.
