Prof. John T. Foster
The Hildebrand Department of Petroleum & Geosystems Engineering
The University of Texas at Austin

A Finite Deformation Formulation for Reacting Porous Media With Volume Change

ABSTRACT: A finite-deformation theory is developed for reacting porous media consisting of a fluid and two solid phases (reactant and product). The central contribution is a kinematic and constitutive framework that distinguishes reaction-induced volume changes that merely fill pore space from those that generate stress in the solid skeleton. This distinction is introduced through a distention-based decomposition of the deformation and a free-energy split into isochoric and distention components. The theory also accounts for the evolving mechanical character of the skeleton by allowing its effective strength to update continuously as reactant is converted to product. In addition, a generalized Darcy-like relative flux is derived that consistently incorporates fluid consumption by reaction and a thermodynamic driving force through the gradient of the exchange potential tau, a feature missing from standard reactive transport theories. The governing equations are formulated in the reference configuration and cast in weak form for finite element implementation. Verification against analytical and standard poromechanics benchmarks demonstrates consistency of the formulation, and, in the small-strain, nonreactive limit, the theory reduces to Biot poromechanics.

BIOGRAPHY: John T. Foster is a professor in the Hildebrand Department of Petroleum and Geosystems Engineering at The University of Texas at Austin. He is also affiliated with the Department of Aerospace Engineering and Engineering Mechanics and the Oden Institute for Computational Engineering and Sciences. His research focuses on computational mechanics, poromechanics, and multiphysics models for subsurface systems.