  Vugs are small to medium-sized cavities inside rock, which have significant
effects on the fluid flow in rock. Moreover, the presence of vugs may have
non-trivial impacts on the geomechanical behavior of rock. How to quantify and
analyze such effects is still an opening problem. To this end, we derive a
macroscopic poroelastic model for a single-phase viscous fluid flow through a
deformable vuggy porous medium. At first, a vuggy porous medium is divided into
two parts: the porous matrix and vugs. Then, we model the hydro-mechanical
coupling process on the fine scale using Biot's equations within porous matrix,
Stokes equations within the vugs, and an extended Beavers-Joseph-Saffman
boundary condition on the porous-fluid interface. Next, based on the
homogenization theory, we obtain a macroscopic Biot's equations governing the
hydro-mechanical coupling behavior of vuggy porous media on larger scale.
Subsequently, the macroscopic poroelastic coefficients, such as the effective
Darcy permeability, effective Young's modulus and effective Biot coefficient,
can be computed from three cell problems. Finally, several numerical examples
are designed to demonstrate the computational procedure of evaluating the
geomechanical behavior of vuggy porous media.
