The property is owned by the Cornwall Kerosene & Tar company. If the player tries to enter, then the guards will warn them to leave, resulting in a gunfight if the player does not comply. After the mission "American Fathers II" in the fourth chapter, this will no longer be the case.
In the mission "Pouring Forth Oil II", Arthur is tasked with stealing an oil wagon from the refinery, which he needs in order to conduct a train robbery with John Marston. This mission is technically optional, as John will do it instead if the player does not do it in time.
Later, in the mission "American Fathers II", Arthur is tasked by Eagle Flies to steal an important document to do with oil under the Wapiti Indian Reservation. Arthur sneaks into the refinery at night by hiding in a wagon and makes his way to the office, where he finds the foreman, Danbury. Arthur retrieves the document and makes his way out, but slips on the roof in the rain, where he is found by the guards. Luckily, Eagle Flies causes an explosion which helps he and Arthur to escape.
In the mission "My Last Boy", the oil fields are the site of a battle between the Army and the Indians. With the Van der Linde gang's help, the Indians miraculously manage to win the battle and Colonel Favours is slain, but Eagle Flies is mortally wounded and the Wapiti Indians are forced to flee the country.
Visiting the oil fields in 1907 reveals that the site has been abandoned. There is an absence of both workers and guards, while the damage done to the place in the battle eight years prior is still evident.