Approximation of nuclear contaminant transport through porous media

Nuclear contaminant transport in porous media is considered. Of particular interest is a model of nuclear contaminants that arise in a finite decay chain; that is, except for the final element in the chain, each element decays into another harmful substance. From conservation of mass for the mixture, an elliptic equation for pressure is derived. Conservation of the displacing fluid leads to a convection-dominated parabolic equation for the concentration of each contaminant. One of the objectives of this thesis is to develop a new variant of the Modified Method of Characteristics (MMOC) such that the mass of each component is conserved. This is accomplished using a Modified Method of Characteristics with Adjusted Advection (MMOCAA). Convergence in L2 is proved. Next, a derivation of a differential system describing the flow of a single phase slightly compressible fluid in a multiscale, naturally-fractured reservoir is presented. First, the macroscopic equations for a triple-porosity model are obtained through two successive steps: homogenization over the microscopic level leads to a mesoscopic description, which is further homogenized to lead to a nested description of the macroscopic flow. The model obtained is an extension of the dual porosity counterpart. Further, a model for the ( N + 1)-scale problem in a fractured medium is derived. The well-posedness of each of these models is proved