An assessment of the role of transient flow on the dispersion of non-reactive solutes in porous media, a numerical study

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Farrell, David Anthony
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The current study utilized a numerical simulation experiment, involving the finite element modelling of groundwater flow and mass transport equations to examine the impact of flow transients on solute dispersion processes in hydrogeologic environments, with emphasis on dispersion processes observed at the Borden tracer test site. The numerical approach utilized a limited Monte Carlo simulation in which the flow boundary conditions were treated as temporal but deterministic whereas the hydraulic conductivity was treated as a heterogeneous, second-order stationary, randomly correlated process. Parameters were based on data collected at the Borden tracer test site. Analysis of the results the transverse spreading of individual plumes was commonly enhanced under transient flow conditions compared to steady-state flow conditions. However, the magnitude of the enhancement varied within and across realizations, making prediction difficult. In the longitudinal direction enhanced spreading is inconsistently observed. As part of this study, matrix methods for solving the system of equations which result from the finite element discretization of the mass transport equation were investigated. Emphasis was focussed on the performance of the Amoldi modal reduction method (AMRM) relative to the Laplace Transform Galerkin (LTG) method. Again the results were inconsistent in that for some classes of problems the AMRM greatly outperformed the LTG method, whereas in other cases the results were reversed. For the more realistic case of steady-state flow and mass transport in heterogeneous second-order stationary randomly correlated hydraulic conductivity fields, the AMRM greatly outperformed the LTG method. Based on these results a "shift" version of the AMRM was implemented and evaluated to improve the approximation of the eigenvalues of the problem and increase the convergence rate of the method. The results showed that some shifts could improve the convergence of the AMRM, whereas other shifts could degrade the convergence. Estimation of an "optimal" shift was shown to be difficult (perhaps inefficient) since the optimal shift varies with the number of Amoidi vectors considered, the material properties of the problem, the discretization of the domain, and the solution time considered. However, when utilized, the optimal shift was shown to improve convergence, especially when only a few Amoldi vectors were utilized. (Abstract shortened by UMI.)