CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
Publication 22-CNA-001

Energetic Formulation of Large-Deformation Poroelasticity

Mina Karimi
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA
minakari@andrew.cmu.edu

Mehrdad Massoudi
National Energy Technology Laboratory (NETL)
Pittsburgh, PA

Noel J. Walkington
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
noelw@andrew.cmu.edu

Matteo Pozzi
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA

Kaushik Dayal
Center for Nonlinear Analysis
Department of Civil and Environmental Engineering
Department of Materials Science and Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik.Dayal@cmu.edu

Abstract: The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework.

Get the paper in its entirety as  22-CNA-001.pdf

«   Back to CNA Publications