Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/11171
Title: A priori error estimates for the numerical solution of a coupled geomechanics and reservoir flow model with stress-dependent permeability
Authors: Barbeiro, Sílvia 
Wheeler, Mary F. 
Keywords: Stress-sensitive reservoir problem; Poro-elasticity; Mixed finite elements; A priori error estimates
Issue Date: 2009
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 09-17 (2009)
Abstract: In this paper we consider the numerical solution of a coupled geomechanics and a stress-sensitive porous media reservoir flow model.We combine mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. This work focuses on deriving convergence results for the numerical solution of this nonlinear partial differential system. We establish convergence with respect to the L2-norm for the pressure and for the average fluid velocity and with respect to the H1-norm for the deformation. Estimates respect to the L2-norm for mean stress, which is of special importance since it is used in the computation of permeability for poroelasticity, can be derived using the estimates in the H1-norm for the deformation. We start by deriving error estimates in a continuous-in-time setting. A cut-off operator is introduced in the numerical scheme in order to derive convergence. The spatial grids for the discrete approximations of the pressure and deformation do not need be the same. Theoretical convergence error estimates in a discrete-in-time setting are also derived in the scope of this investigation. A numerical example supports the convergence results.
URI: http://hdl.handle.net/10316/11171
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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