Originally Posted by G0to60
Could be one of the vacuum lines for the brake system. Perhaps the one that goes between the engine bay and rain tray.
This is the culprit which is likely #5 in the earlier schematic.
The location of this piece is between the back of the motor and the firewall, directly under the 'Y' pipe where it hangs a left towards the air box.
In the picture attached you can see where the hose that runs to the firewall (right facing arrow) has two little orange "valves" on it and it fits into the plastic cylinder (larger, left facing arrow) lower in the picture. It's just glued in and when the glue gets old and brittle (2002 with 187,000 miles) things start to fall apart. Mine just broke apart. It seems this is a common issue with the S4 guys, particularly guys running high boost (my allroad is stock).