Thanks for the replies. There were only a couple so I'll just summarize here.
Looks like the best way to do what I want is to create different "fill volume" parts (most easily done in a family table) which represent the volume at different stages then use the Display@Time function to turn on or off only the fill volumes required at any point in time. Another way would be to add a transparency characteristic to the part using Trans@Time which could make it fade in and out if desired. It's a bit of work to set up either way but it seem like the most practical methods and can be done entirely inside Pro/E.