This one can take a while to install, even though the download itself is quite small.
On my Mac mini (2011) it took almost an hour, and most of that time was just sitting at the black screen with silver Apple logo, underneath which there was text along the lines of, “Installation in progress. Calculating time remaining...” For some, it may sit in that state for some time (over half an hour in my case.) So, my advice is to just be patient, leave it alone, and not restart your system, for those that run into the same thing. Otherwise, you will be rebooting in recovery mode and reinstalling macOS, as restarting at that point will most likely put your system in an unusable state.
Took less than 5 minutes to install on my mid2012 15” Unibody MacBook Pro.
(Both systems have SATA3-connected SSDs in them (same model and capacity.) While my MacBook Pro was fresh-installed with 10.13 when it released last fall, the Mac mini has always gone through upgrade steps from Yosemite onwards, including a restore from Time Machine backup when I put the SSD in it. So, maybe that has something to do with it.)