Multiscale Modeling of the Hydromechanical Behavior of Fractured
Reservoirs
Multiscale, Fractured Reservoirs, Homogenization, Reservoir
Simulation
A significant part of petroleum, gas, and geothermal reservoirs contain natural fractures
that impact their performance. When these discontinuities fall on the sub-seismic scale, it
is a challenge to incorporate them into numerical models, because the computational costs
of their explicit representation are usually too high. Popular solutions that deal with the
effect of these small-scale fractures are the dual-porosity approaches and classical flow-
based upscaling. However, while the dual-porosity models disregard the geometrical
complexity of real fracture networks, traditional upscaling can not capture the dynamic
influence of the fractures, whose permeabilities change continuously during the
reservoir’s productive life. This thesis is dedicated to the multiscale hydro-mechanical
modeling of reservoirs containing complex fracture networks. The adopted multiscale
method is an adaptation of the multi-level Finite Element Method (FEM), which solves
both the macroscale and the microscale numerically and couples them according to the
principles of homogenization. The modification proposed here is called the multi-level
Box method because it replaces the FEM with the Box method, also called the control-
volume FEM. Contrary to upscaling techniques, this method can capture the dynamic
influence of the heterogeneities on the large-scale behavior without the need of defining
equivalent constitutive laws. At the level of the REV, the fractures are generated
stochastically and represented by interface elements. Major modifications were made to
an open-source code to make the hydro-mechanical simulation of elastoplastic fractures
possible. A new statistics-based methodology based on the Central Limit Theorem was
proposed to define the REV of random fractured media. Also, two methods used to
impose periodic boundary conditions on periodic and non-periodic meshes were adapted
to domains containing interface elements. The developed tools and methods were applied
to a synthetic case of depletion inspired by a real naturally fractured chalk reservoir. The
multiscale method was able to represent the loss of productivity caused by depletion and
the anisotropic evolution of the pore pressure field.