Stochastic analysis of the contaminant transport problem and adaptive estimation of the conductivity field from tracer data

Fei-Wen Deng, Purdue University

Abstract

A 3-D stochastic analysis of the contaminant transport problem in groundwater is developed in the spirit of Naff (1990). The new derivation is more general and simpler than the previous analyses. The fast-Fourier transformation (FFT) is used extensively to obtain numerical estimates of the mean concentration and various spatial moments. Data from both Borden and Cape Cod experiments are used to test the FFT/Stochastic model. Results are comparable to results obtained by other methods, and to the experiments themselves. An adaptive estimation scheme is used to obtain the integral scale and variance of the log-fluctuating conductivity based on the FFT/Stochastic model and a Kalman-like filter. The filter incorporates prior estimates of the unknown parameters with tracer data to adaptively obtain improved estimates as the tracer evolves. Synthetic concentration data are generated to test the methodology. The rate of convergence of the scheme depends on prior information, the temporal frequency of sampling, and tracer sampling locations. Tracer moment data from the Cape Cod experiment are used to validate the methodology. The results show that a significant improvement in the prior estimates of the conductivity can lead to a substantial improvement in the ability to predict plume movement. The form of the covariance function of the conductivity can be identified from the robustness of the estimation with respect to the prior estimates. Both the longitudinal and transverse spatial moment data are important to the estimation. The approach provides a cost-effective alternative to the classical head based approach for obtaining the fluctuating conductivity.

Degree

Ph.D.

Advisors

Cushman, Purdue University.

Subject Area

Civil engineering

COinS