Private blockchains are completely uninteresting. (By this, I mean systems that use the blockchain data structure but don’t have the above three elements.) In general, they have some external limitation on who can interact with the blockchain and its features. These are not anything new; they’re distributed append-only data structures with a list of individuals authorized to add to it. Consensus protocols have been studied in distributed systems for more than 60 years. Append-only data structures have been similarly well covered. They’re blockchains in name only, and -- as far as I can tell -- the only reason to operate one is to ride on the blockchain hype.