Enhancing environmental restoration predictive modeling in undersampled environments
New computational physics methods for estimating constitutive property parameterizations in ground water aquifers were developed and demonstrated in this project. The dynamical and statistical axioms of physics, embodied in partial differential equations (PDES) of kinetic theory, are employed to constrain interpolations of hydraulic head (pressure) and transmissivity (permeability) between sparsely measured datum points. These methods can apparently be applied in numerous approaches to parameter estimation. To demonstrate the basic concepts and techniques developed in this work, examples are considered for steady-state, two-dimensional, heterogeneous, ground water flow models, given (i) discrete borehole observations of hydraulic head and transmissivity and (ii) governing kinetic equations for Darcy flow behavior. Estimations of spatially dependent parameters from sparsely measured data are treated as mathematically ill- posed problems because infinitely many parameter distributions (realizations) that are consistent with the data generally exist. Potential difficulties associated with ill-posedness in mean flow realizations are mitigated by requiring that acceptable realizations respect the observed data, are solutions of forward and inverse PDEs for physical continuity, respect information sampling principles, and are distributed by spatial interpolations that themselves are optimal solutions of the governing PDEs between measured datum points. To accomplish these requisites, adaptive numerical grid Galerkin techniques were applied in a novel manner-one that calibrates (constrains) the forward and inverse PDE solutions to assume the observed values of head and transmissivity at measurement locations, while also interpolating the PDE solutions between the measurement locations with basis functions, optimizations, and adaptive grids that are indigenous to Galerkin methods. Long-standing problems associated with data sampling and noise were mitigated by introducing and solving additional regularizing PDEs that, in effect, spatially filter data interpolations simultaneously with the solution of data- constrained forward and inverse flow PDES, commensurate with information sampling and signal processing principles. Applications of these estimation techniques to synthetic data sets with known analytic solutions demonstrate attainable accuracy levels of the techniques in challenging problems and, more importantly, provide examples of the genuine effects of data undersampling, which is always an important factor in actual practice. Finally, practical realizations of aquifer transmissivity are computed for a field data set obtained in Superfund cleanup activities at Lawrence Livermore National Laboratory`s Livermore Site.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 289882
- Report Number(s):
- UCRL-ID-129568; ON: DE98058845; BR: EW2010302
- Resource Relation:
- Other Information: PBD: 25 Mar 1998
- Country of Publication:
- United States
- Language:
- English
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