3D contaminant transport in saturated flow media

Hi every one!
First of all, I apologize in advanced for my english...
So, I`m routing a 3D model with steady flow and transient transport. My BC for transport is a concentration of 1780 mg/l in a 400 m2 area. Whem I simulate that, I can see there is a lot of numerical instability for transport contaminants, because in some layers there is only negative concentration and below them there is a layer with small concentration, but representative ones. My elements have about 1m lengh and 5 m thickness.
Here there are more details:
Longitudinal dispersivity = 10 m
Transversal dispersivity = 1m
I've tried different upwinding techniques and the problem remains.
Could anyone help me on this?
Thanks

With this element size, the instabilities are not likely caused by a too coarse discretization, this is why the upwinding techniques do not help either. It's hard to determine the cause for the oscillations without actually seeing the model. Nevertheless I'd recommend to check for parameter contrasts, e.g., very high/very low hydraulic conductivities; furthermore, it would be good to check the time-stepping procedure. If you're applying large fixed time steps, you are most likely better off switching to automatic time stepping. 

Peter,
In fact our problem had two layers with a big contrast in hydraulic conductivities. Maybe that's why when we discretized vertically even more around that transition we had better results, without the problems told before.
Thanks a lot,
Julia