Hydromechanical Modeling of Nonplanar Three-Dimensional Fracture
Propagation Using an Iteratively Coupled Approach
Abstract
Accurate numerical modeling of fracture propagation and deflection in
porous media is important in the development of geo-resources. To this
end, we propose a novel modeling framework to simulate nonplanar
three-dimensional (3-D) fracture growth within poroelastic media, using
an iteratively coupled approach based on time-/scale-dependent fracture
stiffness. In this approach, the propagating fractures are explicitly
tracked and fitted at each growth step using triangular elements that
are independent of the matrix discretized by hexahedral grids. The
finite volume/finite element method (FVFEM) is employed to solve the
hydro-mechanical system, based on the embedded discrete fracture model
(EDFM). The calculated pressure in fractures and the stress state of the
host grid of the embedded fractures constitute the boundary conditions
for the boundary element method (BEM). The BEM module, in turn, renders
the evolving fracture stiffness and aperture for the FVFEM module.
Finally, the total stresses and the fracture-tip displacements are
computed at the end of each time step to estimate the velocity and
direction of newly created fractures ahead of the fracture tip. The
proposed model is first validated against analytical solutions. Then, in
three different examples, results are shown from the fracture’s
footprint under layered stress conditions, simultaneous propagation of
two nonplanar 3-D fractures, and the mechanical interaction of en
échelon arrays. This work presents an efficient framework to simulate
propagation of nonplanar fractures, and establishes the foundation to
build an integrated simulator for fracture propagation, proppant
transport, and production forecasting in unconventional formations.