Okay...for the transfer of o2 from the bubbles of a submersed aeration system...as Sue mentioned, the bubble column created is a cheap inexpensive way to lift water from the bottom to the surface and allow that water to off-gas the hydrogen sulfide and carbon dioxide gases.
Bottom aeration in my opinion has always been the wrong description other than it moves the higher oxygen water from the surface and "CIRCULATES" it back to the bottom. Bottom Circulators should be a better term.
The transfer of oxygen into the water from a bottom aeration system is less than 5%. The numbers Sue gave were from the diffuser manufacturer who tested the diffuser in "Clean Water with ALL oxygen removed from the water". Therefore the water had a desire or an attratction to absorb oxygen. That is why the numbers are so high.
Place those same diffusers in a pond that contains other concentrations in the water column and the oxygen transfer is greatly reduced. Add to that just as mentioned above that it is so difficult to get oxygen into the water when other compounds are present and the transfer is greatly reduced.
For emergency aeration, floating ciruclator of some sort or I have even had our customers back their boat into the water, leave it hooked to the trailer and start the motor and splash the water, are better choices.
For long term circulation and evening out the oxygen curves, a bottom aeration (circulator) is a better choice.
In your case Donnie, I think the system was undersized for the potential nutrient shock load that happened. This one would have even caught us too. Ted said you had a turnover of 4X per day and I personally would have thought that to be enough. Those cows must be eating some rich stuff!
We will have to re-think the potential shock load when dealing with live stock watershed.
I'm sure this entire post has helped novices but it has helped us pros too. Thank you.