Numerical solution techniques for reaction parameter sensitivity coefficients in multicomponent subsurface transport models.

摘要

In recent years, a number of numerical models have been developed to simulate the reactive transport of contaminants in groundwater. These models are subject to uncertainty due to parameter measurement error and due to the spatial variability of properties in the subsurface environment. Parameter sensitivity coefficients, which are defined as the partial derivatives of the concentration with respect to the model parameters, provide a quantitative measure of the impact of these uncertainties. The focus of this dissertation is to develop efficient and accurate methods for calculation of reaction parameter sensitivity coefficients in a multicomponent subsurface transport model. The model simulates the coupled effects of two-dimensional steady-state groundwater flow, equilibrium aqueous speciation reactions, and kinetically-controlled interphase reactions, such as sorption and biodegradation.;For reactive transport, the state equations consist of a nonlinear PDE for each aqueous component and a nonlinear ODE for each immobile component; these differential equations are coupled together through reaction source/sink terms. The corresponding sensitivity equations take the form of a system of linear PDEs and ODEs. Codes are developed to compare the practice of solving the entire system of sensitivity equations to applying the operator splitting approach to solve the sensitivity equations. Codes are also developed to compare the direct and adjoint methods of calculating reaction parameter sensitivity coefficients in batch and transport problems. CPU time comparisons for example transport problems indicate that direct calculation of sensitivity coefficients is much more efficient than the calculation of sensitivity coefficients by direct perturbation. These comparisons also demonstrate that operator splitting results in a significant reduction in simulation time. Reaction parameter sensitivity coefficients are calculated for a series of example transport problems. These examples include a cobalt-NTA problem with kinetic sorption and biodegradation and a uranium-quartz system with mass transfer-limited surface complexation reactions. The computed sensitivity coefficients are used to gain insight into the relative significance of reaction processes and to rank individual reaction parameters in terms of importance. Sensitivity coefficients are also used to quantify the degree of coupling between components.