I painted my ceiling beams white that were previously dark brown. The circles you are talking about are from tannins in the wood seeping through. It was very difficult to paint my beams. I didn't realize what kind of work I was in for..haha. But it was a learning experience. The best paint for wood like this is an oil based paint. It adheres much better and prevents less seepage.(sorry if spelled wrong}. A good primer like Zinsser Bullseye 123 paint for all surfaces works really well before the top coat.. The circles are exactly what I experienced after I primed and painted before using oil base. So much work! Live and learn!! lol..