Description: |
The modeling of coupled mechanics and flow in porous media attracts researchers from different
areas and is of great
importance in a diverse range of engineering fields.
Land subsidence, due to consolidation or compaction, which is often caused by exploitation of
subsurface resources,
has often been a concern for reservoir engineers. Understanding the effects of groundwater
pumping or oil extraction
and its impact on the environment has been motivating extensive studies in subsurface flow and
geomechanics modeling.
Another major application arises in sequestration of carbon in saline aquifers.
In stress-sensitive reservoirs, variation of the effective stress resulting from fluid production
may induce deformation of the rocks and cause permeability reduction.
This effect may significantly reduced expected productivity.
We consider the numerical solution of a coupled geomechanics and a stress-sensitive reservoir flow
model.
The equations used for the model were formulated on the basis of Darcy's law and the conservation
principles for mass and linear momentum.
The permeability tensor used in the model is stress-dependent.
The work focuses on deriving convergence results for the numerical solution of this nonlinear
partial differential system.
Here we combine a mixed finite element for Darcy flow and Galerkin finite element for elasticity.
We start by deriving error estimates in a continuous-in-time setting. Theoretical convergence
error estimates in a discrete-in-time setting are also
in the scope of this investigation. We perform numerical experiments
for verifying our
theory and modeling some realistic engineering applications.
Area(s):
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