A BLEVE does not need oxygen to become an explosion. The explosion occurs with the rupture of a tank (that has been heated, increasing the internal pressure and thus increasing the boiling point of the liquid inside, so that it remains liquid). This causes a loss of rapid loss of pressure, which in turn rapidly decreases the boiling point of the liquid, thus causing a sizable part of the liquid to almost immediately boil and cause an expanding "cloud" of gas.

When this occurs, you have an explosion that can propel parts of a steel propane tank up to 1/2 mile (at least).