[Furface]

It all depends. At our indoor, we have two sessions, but the tournament is a "Single" Portsmouth, so most people enter for only one session. The results are overall over both sessions. Some enter both sessions - and pay two entry fees - but their score in the second session cannot count, because of rules in sighters (effectively they have had 66 earlier!)
However, some tournaments use a Double Portsmouth, which is exactly that. Entrants shoot two Portsmouth rounds, usually with a break between. In this case you enter for both sessions and cannot compete unless you take part in both.
There is a third option, combining the two. Two sessions of single Portsmouths; overall prizes for the singles, as in the first option; also prizes for the double, contestants for which would not be allowed sighters for teh second half, I presume.