Seminar | From Pore-Filling Reactions to Multicomponent Reservoir Mechanics: A Finite-Deformation Mixture Theory

Join us for a seminar with John T. Foster, professor in UT Austin’s Hildebrand Department of Petroleum and Geosystems Engineering and Department of Aerospace Engineering and Engineering Mechanics. Foster will discuss a new framework for connecting reactive transport, porous-media mechanics and reservoir flow, with applications ranging from chemical reactions and phase transformations to coupled geomechanical simulations.

Abstract

Reactive transport and geomechanics are commonly developed from different primary variables and constitutive assumptions. When these models are coupled directly, it can become difficult to determine whether a pressure, stress, flux, or source term follows from a balance law, a constraint, or a constitutive closure. In this talk, I will present a thermodynamically consistent theory for multicomponent, multiphase porous media undergoing finite deformation, chemical reaction, and phase transformation. The formulation is developed in the reference configuration of the solid skeleton from phase and component mass balances, momentum balances, a constrained variational principle, and the entropy inequality. A central feature is a distention-based kinematic description that distinguishes reaction products that occupy available pore space fromreaction-induced volume changes that deform and stress the load-bearing skeleton. The theory also produces state-dependent effective properties and nonlinear Biot coupling, accounts for momentum carried by transferred mass, and yields a generalized Darcy-typeflux containing pressure, mechanical, and exchange-potential driving forces. Standard compositional flow, black-oil flow, and classical poromechanics emerge as special cases of the general formulation.I will then specialize the theory to an incompressible, fully saturated three-phase mixture consisting of a pore fluid, a solid reactant, and a solid product. Fully coupled finite-element simulations illustrate drained and undrained reactions, permeability-controlled transient contraction and recovery, the Mandel problem, and the evolution of deformation as reaction changes the composition and stiffness of the solid skeleton. If time permits, I will also discuss preliminary extensions to a partially saturated four-phase system containing a compressible gas. These examples show how a common mixture-theory framework can connect reservoir flow, geomechanics, and reactive phase change while retaining equation-level thermodynamic consistency.

Bio

John T. Foster is a Professor in the Hildebrand Department of Petroleum and Geosystems Engineering and the Department of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin. He is also a core faculty member of the Oden Institute for Computational Engineering and Sciences and holds the George H. Fancher Professorship in Petroleum Engineering. He earned his B.S. and M.S. degrees in mechanical engineering from Texas Tech University and his Ph.D. from Purdue University. Before entering academia, he spent seven years at Sandia National Laboratories. His research combines continuum mechanics, numerical methods, and high-performance computing, with applications in geomechanics, fracture, porous-media transport, and multiscale modeling. He is a registered Professional Engineer in Texas