I don't mean to be discouraging, but sometimes people just start off in the wrong direction with something, and from what I'm seeing this is one of those times.
Don't get me wrong, I think it would be an interesting challenge to see if it would be possible to set up a filter system for a small pond that would work adequately, but frankly I think just using one 55 gallon barrel full of any kind of media will be inadequate for such a small volume of water.
On top of that I see that you've built an OSB (oriented strand board) deck around the pond. Besides pooping in the water ducks love to splash around in the water a LOT, and with all that splashing going on they are going to get a lot of water on to that OSB board and it's quickly going to rot out, not that the ducks are going to mind, but it won't take long before the fancy deck you made for them is falling apart.
Years ago I had ducks and I set up a pond about the same size, but my solution was to build the pond on a high spot and install a large diameter drain with a pipe running out the side that had a screw cap and the end of the pipe. Every few days I'd open the cap and let all the filthy water run out. Then I'd spray down the pond and put the cap back on and set up a sprinkler beside the pond and let it run till the pond filled up again. The ducks seemed to enjoy the sprinkler as much as the pond full of water, in fact before the pond was even full they had the water filthy already. The pond was concrete and had a concrete berm all the way around which of course wouldn't rot, but it also helped prevent them from tracking as much dirt and mud into the pond.
If you are going to go ahead with your 55 gal barrel system, your primary focus should be mechanical filtration. You want to mechanically filter the water well before running it through any sort of bio-media, otherwise you'll simply overwhelm the bio-media with gunk and it won't function properly, and you'll have to removing it all the time to clean it which is something you don't really want to do with bio-media. So my suggestion would be to set a large screen on top of the barrel, like the one pictured bellow, and flow the water through that before it goes to the bio-media, and empty that screen as frequently as possible. Then run the water through your bio-media in a shower type system, meaning that the media is not submerged in water. This allows for much better bio conversion then submerged media because the bio-film (nitrifying bacteria) get much more oxygen then submerged media system, and the showering process also tends to help clean the bio-media of gunk better.
Google Bakki Shower
Don't get me wrong, I think it would be an interesting challenge to see if it would be possible to set up a filter system for a small pond that would work adequately, but frankly I think just using one 55 gallon barrel full of any kind of media will be inadequate for such a small volume of water.
On top of that I see that you've built an OSB (oriented strand board) deck around the pond. Besides pooping in the water ducks love to splash around in the water a LOT, and with all that splashing going on they are going to get a lot of water on to that OSB board and it's quickly going to rot out, not that the ducks are going to mind, but it won't take long before the fancy deck you made for them is falling apart.
Years ago I had ducks and I set up a pond about the same size, but my solution was to build the pond on a high spot and install a large diameter drain with a pipe running out the side that had a screw cap and the end of the pipe. Every few days I'd open the cap and let all the filthy water run out. Then I'd spray down the pond and put the cap back on and set up a sprinkler beside the pond and let it run till the pond filled up again. The ducks seemed to enjoy the sprinkler as much as the pond full of water, in fact before the pond was even full they had the water filthy already. The pond was concrete and had a concrete berm all the way around which of course wouldn't rot, but it also helped prevent them from tracking as much dirt and mud into the pond.
If you are going to go ahead with your 55 gal barrel system, your primary focus should be mechanical filtration. You want to mechanically filter the water well before running it through any sort of bio-media, otherwise you'll simply overwhelm the bio-media with gunk and it won't function properly, and you'll have to removing it all the time to clean it which is something you don't really want to do with bio-media. So my suggestion would be to set a large screen on top of the barrel, like the one pictured bellow, and flow the water through that before it goes to the bio-media, and empty that screen as frequently as possible. Then run the water through your bio-media in a shower type system, meaning that the media is not submerged in water. This allows for much better bio conversion then submerged media because the bio-film (nitrifying bacteria) get much more oxygen then submerged media system, and the showering process also tends to help clean the bio-media of gunk better.
Google Bakki Shower