Math Challenge - ABV of iced beer

This may not be possible, but I thought I'd give it a try. I have a 10.5% stout I don't like much, so I put a gallon of it in the freezer. I collected the first 32 ounces that easily thawed and came out of the ice. I saved the other 32 ounces and thawed that as well.

Here are the readings:

Initial beer: 1.095 OG / 1.021 FG (added whiskey to bring it to 10.5% from 9.9%)
Melted ice: 1.009 in hydrometer, 1.023 with refractometer

I thought I could use the morebeer refractometer spreadsheet in reverse to calculate the ABV of the melted ice. I know the FG, and I have the refractometer reading, so I thought I could calculate the OG, and thus the ABV. However, it tells me that my OG on the melted ice is 1.000, and the FG is 1.009. Negative ABV??

Ok, that's the puzzle. It isn't that important, as the iced beer is pretty tasty and definitely stronger, but I thought I'd try the math anyway. Any thoughts?

 

Update - I just tried the beersmith calculator. If I plug in my refractometer and hydrometer readings there, I get an ABV of 1.77% for the iced leftovers. That seems about right!

This means my concentrated version is about 19.2% I believe.

 

Meh, slightly better. That isn't saying much though. Now that I know it works, I'll do it again with a tastier beer.

 

Very interesting - thanks for the link. It seems like everyone does this slightly different. I'm liking my process of measuring the ABV of the residual melted ice though. It seems much more exact than a simple hydrometer reading of the residual. There is alcohol present in this as well, so a hydrometer alone isn't very useful.

I'm currently attempting to concentrate the 19.2% further, but it doesn't want to freeze. Looks like I'll have to wait for Minnesota winter for further concentration...