When does physical price kick in more than futures?

let me know if this needs better wording. A few weeks ago, I was seeing online posts about physical price being actually 140$, I tried to find concrete data rather than attractive headlines/shitposting to no avail. In contrast to WTI/Brent futures hovering like the 90-110 range which is still high but not 140. Now that the last tankers pre-war are arriving, dispersing in the economy etc, should we be seeing a sharp price increase from lack of supply or will it be gradual like it's been for the past month or so?

Edit: this is for america sorry for now specifying, could apply other places as well