Environmental contaminants in the subsurface include organics, heavy metals and radionuclides. There are several ways to remediate these contaminants: removal and cleaning of affected soils, geologic storage (such as Yucca Mountain for radionuclides), chemical in situ conversion or immobilization, and degradation or immobilization by soil microbes. Mathematical analysis and computer simulation have proved useful in design of remediation strategies and in evaluation of their performance. Effective as the present generation of modeling efforts have been, though, there is still much room for improvement, from creating more accurate conceptual models based on better understanding of underlying physical processes, to developing better analysis tools and more efficient numerical solvers. These matters are discussed within the context of in situ bioremediation modeling. A partial list of needs in that field include: more efficient multiphase flow algorithms for governing equations that change type over time in different parts of a domain; similarity methods, and regular and singular perturbation analysis of systems consisting of three or more coupled pdes (these would be helpful in verifying numerical solutions of complex nonlinear systems); solution methods for reactive systems which exhibit a range of time scales; biofilm structure and its interaction with the larger scale flow; exopolymers and particulates; microbial ecology, e.g.,incorporation of hierarchical features such as predator-prey chains; other pore scale processes, such as reactions at grain surfaces, and the feedback of dissolution/ precipitation/film growth to porosity and permeability. There are also constrained minimization problems, which encompass optimization, sensitivity analysis and inversion. Further, multi-scale, stochastic representations of soil/rock properties are more appropriate than deterministic, but the state of the art in solving stochastic partial differential equations, especially coupled nonlinear equations describing transport and reaction in realistic geologic stratigraphy, is still primitive, but full of opportunity.
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