This is a good question. The fact that people are not buying the May future at -$37/bbl and selling the June contract at $20/bbl tells you that Cushing storage

This is a good question. The fact that people are not buying the May future at -$37/bbl and selling the June contract at $20/bbl tells you that Cushing storage must effectively be full and that the theoretical storage figures quoted in research are not practically usable (at least at short notice). It's very hard to imagine any practical means of storage that isn't wildly profitable to utilize for $57/bbl/month.