Analysis of a fully coupled geomechanics and reservoir flow model with stress-dependent permeability
 
 
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):
Date:  2008-12-18
Start Time:   11:30
Speaker:  Sílvia Barbeiro (CMUC)
Place:  5.5
Research Groups: -Numerical Analysis and Optimization
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