Aku,
The problem is related to the weighting options used at the grid block interfaces. See pages 135-136 of the TOUGH2 user manual for a discussion. In the Solution Controls dialog, select the Weighting tab. Change the Mobility at Interface to "Harmonic Weighted", The Permeability at Interface to "Harmonic Weighted", the Density at Interface to "Average of Adjacent Elements", and the Diffusive Flux at Interface to "Coupled Harmonic Weighting". Your problem will then run quickly and the solution appears reasonable.
However, it would be helpful to have a deeper discussion on the numerical solution that makes these changes in weighting necessary. Perhaps inviting Karsten Pruess to discuss this would be useful. You could send your model (the saturation.dat file) to him and ask.
Daniel Swenson, Thunderhead Engineering