Assuming space is cold and empty ...
The ring that you drop into the bottom of the ocean will settle, eventually, to the bottom. Assuming it lands appropriately (e.g., with "This side up" up), it'll start draining water into the other ring and keep doing so almost forever. It if doesn't land right-side up, everything below will still happen, it'll just end relatively quickly.
The other ring will have a jet of water shooting from it that nigh-immediately crystallizes into ice. Unless it runs into something, it'll just keep moving forward forever, leaving a trail of ice behind it (think Iceman traveling).
Not much will happen to the original world; in the deep places of the ocean is where you find natural portals to the Elemental Plane of Water, which will continually replenish any lost sea water.
If the submerged ring itself lands in a portal, then you'll have a portal from the elemental plane of water into deep space, with roughly the same effects (assuming your portal rings are capable of crossing planar barriers; please consult your magician).