The system studied in this thesis is called the Low Rise Return system and uses a partly filled marine drilling riser with a variable mud level which is used control the bottom holes pressure.Initially main components of the Low Riser Return System are listed and explained. Then the performance characteristics of the system are explored. Level movements in riser during level increase and decrease at constant mud pump rates are explained along with the effect of mud pump rate on maximum level increase and decrease rates.A simple simulator is then presented that calculates the bottom hole pressure when pump rates are changed. The simulator includes a function that enables it to simulate lost circulation scenarios.The simulator is used to simulate some preferred scenarios. First a pressure increase and decrease at constant mud pump rates are simulated. Then it is shown how a faster pressure decrease can be achieved by temporarily lowering the mud pump rate. Next simulations are shown where changes in mud level are used to compensate for changes in equivalent circulation density as mud pump rates are changed. Finally simulations are run that demonstrate how mud level can be reduced to cure lost circulation scenarios. Results and lessons learned are then discussed.