Porous Media

Responsible: Jens Lang, Bodo Erdmann, Rainer Roitzsch
Cooperation: J. Verwer, J. Blom, CWI Amsterdam
Literature: 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.
2dbrine_w_500.gif 2dbrine_w_5000.gif
2dbrine_w_10000.gif 2dbrine_w_20000.gif
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.

3dbrine_gzoom_7200.gif 3dbrine_gzoom_14400.gif
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.
Initial and Final Solution (t=0.05)

Last update: July 2007
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