ATS/TexasTree
ArboristSite Operative
The vessels of a ring-porous tree (such as a red oak) are generally larger and concentrated in the outermost layer of sapwood. These vessels are produced early in the season. This is significant because it affects a tree's susceptibility to vascular damage. Ring-porous vascular systems are very efficient, but are much more vulnerable to blockage. The elm's vulnerability to Dutch elm disease is an case in point.
In the case of this Red Oak, you may end up losing branches on the cut side of the tree if the vascular tissue has been completely severed. I say MAY - this is not a guarantee so don't go out and cut it down based off of my projection alone. If the tree were a larger dbh, I would think this cut to be less of an issue; however, since the cut went about 1/5 of the way in, it is very probable that the vascular tissue on that side of the tree is not going to be able to transport nutrients. The cut tissue will never heal. Trees are NOT like people. The tree will try to 'wall' off the damage and cover up ('heal') around the wound but, the cut portion will likely never transfer nutrients again.
As Arborpro stated above - a ring porous tree is likely to suffer significantly from this type of wound. Sealing of wounds is not the regeneration of vascular tissue. Water conducting vessels cut won't reconnect.
I don't think the tree will be "fine." I've seen too much damage and death in red oaks with just a few roots cut.
Because they are ring-porous, I've seen die back in the crown of a red oak in as little as a few hours on a hot summer day with a water stressed tree.
It scares the hell out of the trenching contractors when it happens and lets lay people understand that cutting roots (or trunks) can have dire consequences.
I sometimes wish all trees were ring porous so contractors and homeowners alike would respect trees and tree roots a little more.
The paper tape I mentioned ( also called Tree Wrap around here) is light brown in color with a black backing and is typically used by nurseries (needlessly) to wrap young tree trunks.
I have found that it can sometimes help trunk wounds if applied immediately after the bark is damaged when Uncle Henry backs the Desoto into Grannie's tree.
Several hours or days after the fact, I would question its efficacy.
Tree Wrap does kill mistletoe (by blocking sunlight) if you can keep the wrap on the affected limb for 2 growing seasons.