J. Lang, B. Erdmann, Adaptive Linearly Implicit Methods for Heat and
Mass Transfer, Report ZR-00-21 (2000), Konrad-Zuse-Zentrum Berlin.
Brine Transport in Porous Media
High-level radioactive waste is often disposed in salt domes. The safety
assessment of such a repository requires the study of groundwater flow
enriched with salt. The observed salt concentration can be very high with
respect to seawater, leading to sharp and moving freshwater-saltwater fronts.
In such a situation, the basic equations of groundwater flow and solute
transport have to be modified (Hassanizadeh and Leijnse, 1988). We use
the physical model proposed by Trompert, Verwer, and Blom (1993) for a
non-isothermal, single-phase, two-component saturated flow. It consists
of the brine flow equation, the salt transport equation, and the temperature
equation.
Two important features of the model are that in the incompressible case
the PDE-system is of index 1 and the salt transport equation is usually
dominated by the advection term. In practice, global Peclet numbers can
range between 102 and 104.
In the following, we present some results obtained for injection of warm brine
into a porous medium filled with fresh water. Two gates are used in the two-dimensional
case. The sharp solution fronts are resolved satifactorily using locally
refined meshes. The evolution of the variable time steps and the number of spatial
discretization points reflects nicely the high dynamics at the beginning both
time and space, while larger time steps and coarser grids are selected in the final
part of the simulation.
Two-dimensional brine-transport. Distribution of salt concentration
at t=500, 5000, 10000, and 20000 with corresponding spatial grids.
Two-dimensional brine transport. Evolution of time steps and number
of spatial discretization points for TOLt=TOLx=0.005.
A typical result for a three-dimensional pollution with salt water injected
through a small slit at the top of a tank
is shown in the next figure. The pollutant is slowly transported by a flow
through the tank while sinking to the bottom. The steepness of the solution
is higher in the back of the pollution front, which causes fine meshes
in this region. Despite the dominating convection terms no wiggles are
visible, especially at the inlet.
Three-dimesional brine transport. Level lines of the salt concentration
in a particular plane after two hours (top) and four
hours (middle), and corresponding spatial grids in the neighborhood of the inlet (bottom).
Adiabatic Flow of a Homogeneous Gas
The figure shows a typical two-dimensional Barenblatt solution.
