Mechanical and Civil Engineering Seminar

Mechanical and Civil Engineering Seminar Series

Title: Reaction Fronts in Porous Media

Abstract:

The theory of systems of hyperbolic conservation laws provides a powerful framework to understand multi-component reactive transport in porous media. Under the assumption of local chemical equilibrium and in the limit of negligible hydrodynamic dispersion, reactive transport is governed by the n × n system of quasi-linear PDE's

(c + z(c))t + cx = 0,

where z(c) is the equilibrium constraint between the total concentrations of the components in the pore fluid, c, and the total concentrations of the components in (or sorbed onto) the solid, z. The Riemann problem is self-similar in x/t and allows (semi-) analytic solutions for non-linear reactions. This has been exploited in the Theory of Chromatography for isotherm-based reactions.

I will present an extension of the theory to modern surface complexation reactions, which include the electrostatics at the surface. These reactions govern the pH of pore fluids and the mobility of contaminants in the subsurface. The non-linearity introduced by surface complexation reactions is not genuinely non-linear and introduces new transport phenomena, such as composite waves. The analytic solutions also provide an excellent match to experiments over a wide range of compositions, illustrating the utility the theoretical framework in realistic systems.

Bio:

Marc Hesse is a computational geoscientist interested in the dynamics of porous media in geological and environmental processes. Due to his broad training, his work bridges the classical solid-earth sciences, the environmental sciences and energy geosciences. Marc initially studied Geology at the Technical University of Munich and the University of Edinburgh where he has developed an interest in a broad range of geological phenomena. Recognizing the importance of fluid dynamics and mathematical modeling in the study of porous media Marc shifted towards applied mathematics and its applications in the geosciences during his graduate education at the Massachusetts Institute of Technology, the University of Cambridge, and Stanford University and during his postdoc at Brown University. In 2009 Marc joined the Jackson School of Geosciences and the Oden Institute of Computational Engineering and Sciences at the University of Texas

NOTE: At this time, in-person Mechanical and Civil Engineering Lectures are open to all Caltech students/staff/faculty/visitors.