One element of this price rise is on the supply side, especially with Saudi Arabia and Russia apparently maintaining a production cut agreement they have. Rumors from OilPrice.com suggest there may be cheating on these agreements to come. But for now these two are holding the line on the supply side.
More important has been the increase on the demand side, which looks set to continue rising for at least the near future. I have posted previously on how global carbon emissions appear to have bottomed around April 7, with them rising since, if still well below pre-pandemic levels. Burning fossil fuels is a major source of these emissions, so it is quite possible that oil demand has been rising since around then, even though it was 10 days after then that oil prices did their brief plunge into negative territory.
According to OilPrice.com it is China that is leading this increase in oil demand. It was the first economy to drop due to the pandemic, with its oil demand declining about 40% during February. However, it looks that China's demand has returned as of May to a level 92% of its peak prior to the pandemic. That is substantial, while leaving more room for further growth.
Another nation with a large economy making an even sharper turnaround is India. In early April at the beginning of its two month lockdown its demand declined by 60%, but now it is estiimated that in June its demand will return fully to its pre-pandemic level.
US demand has also made a turnaround, although it did not decline as much and is recovering more slowly. But its demand is rising and will almost certainly continue to do so, if not at a rate that would happen if there were a V-style economic recovery.