Does the barrel have any kind of injection system for adding CO2?
When the beer is in a sealed fermenter, it is giving off CO2 through the yeasts breaking down the sugars. This forms a layer above the surface of the beer and prevents oxygen from reaching it.
Now that this process is complete (more or less), then it is very easy for oxygen to come into contact with the fermented wort. Either inject CO2 into the barrel or if that is not possible, bottle it. It will condition just as well in bottles.