Add water to it and you make acid. Cut the PH before you use the rug Dr.
Add water to what and make acid? Wood ash is a source of alkali if anything. The carbonized content is difficult to completely get out of any rug as it is not soluble, though mechanical flushing can get some of it.
Oh, it’s a good idea that when the rug has dried after shampooing, apply a Scotchgard type spray.