A. The operator has a privilege over the property described in R.S. 9:4883 to secure payment of all obligations incurred in the conduct of operations which the non-operator is personally bound to pay or reimburse.
B. A non-operator has a privilege over the property described in R.S. 9:4883 to secure payment of all obligations owed to him by the operator from the sale or other disposition of hydrocarbons of the non-operator produced from the well.