From what I understand the Logwood dye turns the barrels darker black in color. I have some Logwood powder that I haven't tried yet. The last few barrels that I did for myself are Damascus and I didn't use it. This barrel is Stub Twist and I don't see how the Logwood would have helped to make it darker.
I believe you use 2-4 ozs. of Logwood powder to 2-3 gallons of water.

I know trappers use it on new traps and well as reconditioning old ones. They boil them and then dip them in the Logwood solution.