Chadam 9704567 Reactive flows in porous media may undergo shape instabilities in the reaction (equivalently, porosity/permeability change) front. Because flow changes are coupled to these instabilities, it now appears to be the case that this reaction-infiltration mechanism plays an important role in many strategically significant problems (see below). The investigator models such phenomena as coupled nonlinear partial-ordinary differential equations and as moving free boundary problems and investigates the importance of the role played by dispersive effects, geomechanical effects, boundary and inertial effects, layered and random media, concentration dependent diffusivity and permeability and surface reactions. Basic existence, uniqueness and regularity of the coupled system of equations are studied as well as the sharp interface limit. The loss of stability of high-symmetry solutions is studied using bifurcation theory and numerical simulation. These mathematical models of goechemical processes and the results listed above have direct application to many problems in the petroleum, mining and waste management industries. For example, in enhanced oil recovery, the loss of stability of the spherical reaction front at the injection well often leads to fingering of the reactants directly to the removal site completely bypassing the oil. Moreover the dissolution and reprecipitation of the porous media by the reactants can sometimes lead to complete plugging at the injection well requiring expensive redrilling. Similar processes can explain observed reductions in the effectiveness of bioremediation of environmental wastes or predict the observed, but previously unexpected, rapid encroachment of nuclear and chemical wastes on sensitive environments. By calculating the shape of redox fronts, these methods can also be used (avoiding expensive drilling) to locate lens-shaped (roll-front) uranium deposits. Funding for the project is provided by the progra m of Applied Mathematics and the Office of Multidisciplinary Activities in MPS and by the Hydrologic Sciences program in EAR.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Michael H. Steuerwalt
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University of Pittsburgh
United States
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