Technical Papers and Presentations

Over the past million years, several cold ages have occurred and thereby caused perma-frost conditions basically all over the present area of Germany. Since in Germany the safe-ty of a nuclear waste repository legally needs to be investigated for a period of one million years, the ground freezing effect of permafrost must be included in the long-term safety assessment with respect to the groundwater flow system. While in principle the ground freezing in the upper geosphere should shield the biosphere from possibly contaminated groundwater in deeper aquifers, there is the phenomenon of taliki (singular: talik) which is well-known from present-day permafrost regions. Taliki are locally unfrozen zones that can reach through the whole permafrost-induced frozen ground and thus may form a hydraulic shortcut between deep aquifers and the surface, thereby possibly concentrating the flux of harmful substances. The conditions for the forming of taliki and their long-term stability – highly important for the safety assessment – are largely unknown, though. A systematic numerical investigation needs several physical features to be considered. There is – groundwater flow that occurs in porous media even at subzero temperatures, – heat flow in porous media, and – temperature dependent phase change of the water. Several models for groundwater flow under permafrost conditions have been set up with COMSOL Multiphysics® in the past. However, these and other sources have not been entirely clear at justifying all aspects of the balance equations, the constitutive equations (CE) and the equations of state (EOS) that were used. A stringent mathematical framework including CE and EOS was therefore recently derived by the author and realised in the COMSOL Multiphysics® software using the Subsurface Flow Module. In particular, the interfaces Darcy’s Law and Heat Transfer in Porous Media were used and accurate formulations for the EOS at subzero temperatures implemented. To represent the phase change from water to ice, the phase change material node under the Heat flow interface was applied, but modified in the equation view mode to allow for a varying width of the transition zone. As a starting point, a generic 2d-axial symmetric model has been set up to simulate a lake in a granitic formation. The lake was treated as a porous medium with an extremely high porosity and permeability. The vertical boundary of the model was located far away from the lake to justify no flow boundary conditions for flow and heat transport. The mean heat flux from inner earth over Germany has been assigned to the bottom boundary and a tem-perature evolution reflecting the development of the last ice age to the top of the model. First results from modelling the ground temperatures down to a depth of 2000 m confirm a thermal shadowing of the cooling ground under large aquatic surface features. The rather simple model is thermally dominated by heat conduction, though, so that it didn’t show further signs of talik formation. However, the sensitivity of the processes involved leaves a wide field open for further analysis.