Numerical Solution Techniques for Reaction Parameter Sensitivity Coefficients in Multicomponent Subsurface Transport Models
Tebes-Stevens, Caroline Louise
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https://hdl.handle.net/2142/83467
Description
Title
Numerical Solution Techniques for Reaction Parameter Sensitivity Coefficients in Multicomponent Subsurface Transport Models
Author(s)
Tebes-Stevens, Caroline Louise
Issue Date
1998
Doctoral Committee Chair(s)
Valocchi, Albert J.
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Biogeochemistry
Language
eng
Abstract
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.
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