Contaminant Transport in Unsaturated Heterogeneous Formations

Leaking nuclear waste repositories in unsaturated soils can be of significant impact to the environment due to transient water infiltration. In order to investigate this problem through numerical simulations we have developed a simulator which takes into account the interaction of radionuclide plumes and two-phase (air-water) flows. We introduce an operator splitting scheme which allows us to solve the governing equations with appropriate numerical methods. For the advective transport of solute plumes we employ eulerian-lagrangian techniques. We approximate the two-phase flow problem combining a conservative, second order, non-oscillatory central scheme [1] for saturation transport with mixed finite elements for both diffusion and velocity calculations [2]. Numerical simulations in heterogeneous porous media are presented. For the approximation of the advective transport of solute plumes we compare the Modified Method of Characteristics (MMOC) [3], the Locally Conservative Eulerian-Lagrangian Method (LCELM) [4], and a new, locally conservative lagrangian procedure developed by the authors. Our numerical experiments indicate that the new procedure produces more accurate predictions than the other methods; moreover, it is virtually free of numerical diffusion. References: [1] N. Nessyahu and E. Tadmor, Non-Oscillatory Central Differencing for Hyperbolic Conservation Laws, J. Comput. Phys., 87, vol. 2, pp. 408-463, 1990. [2] J. Douglas, Jr. and F. Furtado and F. Pereira, On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs. Comput. Geosc., 1, pp. 155-190, 1997. [3] J. Douglas, Jr. and T. Rusell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J. Num. Anal., vol.19, pp. 871-885, 1982. [4] J. Douglas, Jr., F. Pereira, and L. M. Yeh, A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media. Comput. Geosc., 4 , pp. 1-40, 2000.