If the system is totally sealed I would agree, but in our aquariums it never is. There is water flowing through the skimmer. There is also (at least in my RO skimmer) vent holes in the skimmer cup lid. And finally, my skimmer outlet pipe blows out air which is replaced from...somewhere?
But back to my original question, IF the system is completely sealed, what is pumping through your skimmer if you're using a recirculating CO2 scrubber? Assuming your air is Nitrogen, Oxygen (and 1% Argon), recirculating the skimmer air will continually draw out CO2. Assuming as you say it also no longer contains Oxygen, are you only recirculating pure Nitrogen? Clearly the air in a recirculating CO2 scrubber contains far less CO2 because the media lasts at least 2x longer (from my personal observations).
Then there is the question of how it actually effects the Oxygen content of your tank water. If indeed it is continuing to pull CO2 out of your tank water, wouldn't that in effect be increasing the Oxygen % of your tank water? One replaces the other right?
A tank like mine, rimless with an open top, an open sump and huge flow, there is significant air exchange even without a skimmer.
Has anyone actually measured the Oxygen content of their tank water before and after installing a recirculating CO2 scrubber?
There's nothing controversial about my claim of no oxygenation from recirculating skimmer air, except how low the O2 would get at night and how high it would get during the day without the gas exchange a skimmer causes (and whether either value is significant). The basic process effects are simple chemistry (Raoult's Law).
FWIW, no one claimed that there is no O2 in the recirculating air. If there's was somehow, that would be a disaster.
In a closed system of recirculating air, the air will track the O2 level in the water. It will never get super low, but also will never add much just because the tank water dropped in O2.
Water flowing through the skimmer is not relevant, since it is what is potentially going to be low in O2 to begin with.
CO2 entering or leaving the water has zero effect on O2 or any other gas (except an acidic or basic gas such as ammonia).
As far as I know, I am the only one to point out the basic chemistry problem of a recirculating skimmer, and it was never used much until BRS (not chemists) began to push the idea. SO I know of no data on O2 in recirculating skimmers.
But there is data on O2 in skimmerless vs skimmed tanks, so it is clear that in some cases, skimmers do help bring up low O2 levels at night:
"Aquaria can and do become hypoxic at night and such a state may pose a risk to hypoxia-intolerant organisms. Cloudy water in shipping containers and tanks is a cause for concern as oxygen levels are measured to decline rapidly and to very low levels."
"Airstones and skimmers appear to be a very effective means of oxygenating small water volumes. Their effect on larger water volumes appears to be less. While the effect may be relative, the larger tanks and systems described here utilized powerful skimming or air pumps, and to gain an equivalent amount of oxygen as occurs in small water volumes would likely require air pumps or skimmers far larger than those commonly employed by aquarists."