58th Annual Report on Research 2013 Under Sponsorship of the ACS Petroleum Research Fund

In 2013 the PI was awarded the Junior Scientist Prize of the Society of Applied and Industrial Mathematics Activity Group on Geosciences. This award recognizes the PI's "outstanding contributions to mathematical analysis and computational methods for waves in complex subsurface applications." While the prize was based on work completed before the award period of this grant, the work enabled by this grant has allowed the PI to continue to develop the same advanced mathematical methods and to apply them to problems in reactive transport in the subsurface and compare them with experimental data. For this reason work completed under this award has been presented in the award lecture to illustrate future directions.  In the second year the grant has fully or partially supported four separate research projects.

1) Reactive transport with ion-exchange

In the first year, 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. This work has continued into the second year although the student has not been officially paid on the grant and the work was completed and has been submitted for publication to Water Resources Research in September 2013. In Venkatraman  et al. (2013) we have derived semi-analytic solutions for these complex reactive transport systems and for the first time we have been able to match complex geochemical patterns due to multiple displacement fronts observed experimental by Voeglin et al. (2000) and Valoochi et al. (1981). This work has also been presented by the graduate student at the Gordon 2012 Conference on Flow and Transport in Permeable Media in Switzerland and by the PI at the 2012 conference on Computational Methods for Water Resources in Urbana Champaign.

2) Reactive transport with pH-dependent  adsorption

The PRF-grant partially supported collaboration between Dr. Prigiobbe and the PI 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 hydrofracking of shale gas exploitation. In a first publication, Prigiobbe et al. (2012), we showed that pH dependence fundamentally changes the morphology of the reactive transport front 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. In the last year, we have extended the analysis to a more complete model of pH-dependent reactive transport. In Prigiobbe et al. (2012) the proton concentration was based on charge balance, however, many current models for surface complexation are not charge balanced.  In this case, the total proton concentration in the fluid, the so-called acidity, has to be modeled directly.

Therefore we have extended the theory to include the balance equation for the acidity, which leads to a more direct nonlinear coupling between the partial differential equations. The structure of the acidity model is even richer and the description of this structure has lead to a new publication Prigiobbe et al. (2013) that has been accepted for publication and is currently in print. The results have also been presented at Fall Meeting of the American Geophysical Union 2012.

3) Noble gas partitioning during natural gas migration

In the first year, 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 during the migration of natural gas in porous media. The work completed under this grant developed the semi-analytic solutions for the gas composition profiles. These initial results have been promising enough to obtain additional DOE funds to begin experimental work to demonstrate the gas composition patterns experimentally. This experimental work is ongoing, and once it is completed a publication acknowledging both grants will be submitted.

4) Exchange flows across faults

In the second, year the grant has supported my graduate student Kyung-won Chang. Kyung-won is working on the leakage of low-pH brines from deep geological CO2 storage. The leakage of such brines into shallower potable aquifers could mobilize contaminants that are currently strongly absorbed at low-pH and hence pose a threat to groundwater quality. While the mobilization of the contaminants in the aquifer is described by the pH-dependent adsorption theories described above the actual leakage flux of low-pH brine is determined by buoyancy driven exchange flow along the leakage path. Kyung-won is developing a scaling argument for the leakage flux as function of the geometry and properties of the leakage path and the driving density difference. He has been able to show that hydrodynamic dispersion limits the leakage flux and he is currently working an effective theory for a heterogeneous leakage path. Preliminary results have been presented at Fall Meeting of the American Geophysical Union 2012.

The research on has directly influenced my graduate teaching, through a reactive transport class based on the theory of hyperbolic conservation laws. In particular the analysis of ternary ion-exchange will be used as a key example in class, because it illustrates the basic theory and allows comparison with experimental data.

The grant has allowed the PI to demonstrate the feasibility and validity of this theoretical approach. This has already led to additional funding from the Department of Energy to experimentally confirm theoretical prediction on noble gas enrichment during natural gas transport.

The PI considers the work on pH-dependent sorption the most innovative and plans to continue this work in the future. The main challenge is the extension of the theory to proper surface complexation models that allow for variable surface charge and to perform high quality laboratory experiments to test the theory. The PI is in the process of writing a proposal to the National Science Foundation.