Reports: DNI851230-DNI8: The Interpretation of Geochemical Patterns Through the Hyperbolic Theory for Reactive Transport in Porous Media

Marc A. Hesse, PhD, University of Texas (Austin)

The theory of hyperbolic conservation laws provides a basis for the rational understanding of complex reaction fronts that develop during reactive transport in porous media. This theory has already been successfully applied to chromatographic problems in chemical engineering and to enhanced oil recovery problems in petroleum engineering but is currently rarely used to understand reactive transport in porous media. In the last year we have been extending the theory to several environmental problems of great societal importance. The PRF-grant has supported three separate research projects detailed below.

The PRF-grant partially supported a collaboration with Dr. Prigiobbe to extended the existing theory to pH dependent sorption reactions. These type of reaction are control the migration of many pollutants including radionuclides and heavy metals in the subsurface. These problems have recently received renewed attention due to concerns of groundwater contamination due to hydro-fracking of shale gas exploitation. We were able to show that pH dependence fundamentally changes the nature of the problem and introduces new phenomena that are not present in classical systems. In particular, pH dependent systems allow ‘composite waves', i.e. wave that are combinations of shocks (compressive) and rarefactions (expansive). In contrast, in classical competitive sorption, the waves are either shocks or rarefactions, which are sometimes referred to as contamination and remediation waves in the environmental literature. The results have been presented at Fall Meeting of the American Geophysical Union 2011 and the conference on Computational Methods in Water Resources 2012 and have been published in the peer-reviewed literature in 2012, see the list of publications.

The PRF-grant fully supported the work of graduate student Ashwin Venkatraman to work with the PI to extend the theory to ternary heterovalent ion-exchange in natural systems. Ion-exchange controls major element composition of many coastal aquifer, in particular the fragile aquifers of barrier islands along the Gulf of Mexico that have been strongly affected by the recent oil spill. Experimental data by Voeglin et al. (2000) demonstrate that ternary systems can lead to very complex geochemical patterns due to multiple displacement fronts. Hyperbolic theory offers an opportunity to understand and analyze these patterns. The aim of our work on the ternary ion-exchange is to match the experimental observations by Voeglin with analytic solutions. This work is currently in progress but initial results have been able to match several of the experimental profiles. The theory also shows that the available experimental data do not sample all four qualitatively different solutions that are possible in a ternary system. This shows how the theory we are developing could be used to guide experimentation so that it explores the full range of behaviors.

The PRF-grant partially supported the work of graduate student Kiran Sathaye to work with the PI to study the noble gas distributions that develop as noble gases partition between CO2 and water during two-phase flow in porous media. This work is ongoing and but preliminary results have compared derived and compared analytic solutions that treat the noble gas as a tracer or as component contributing to the volume of the phases. Our results show that the tracer limit is degenerate and leads to qualitatively different behavior. A small bank of concentrated noble gas at the gas front is replaced with a spike (delta function) in the tracer limit. Since the interpretation of most noble gases requires the interpretation of noble gas ratios the spikes forming in the tracer limit may lead to errors.

The research on has directly influenced my graduate teaching, because I am developing a class on reactive transport in porous media based on the theory of hyperbolic conservation laws. The class has been taught twice to 21 and 14 students and has been a success. The particular research topics discussed above will be integrated into the class as results mature. In particular the project on ternary ion-exchange will be used as a key example in class.

The grant has allow the PI to investigate a new area where he had no previous results and it would have been hard to gain funding from other agencies. However, if the work continues to progress well it should provide a sound foundation for grants from other agencies. The PI is currently discussing with Dr. Prigiobbe to submit an NSF proposal to extend the theoretical work on pH-dependent sorption.