This study compares PI and MPC controls via a computer simulation for a gas recovery unit (GRU), which consists of three distillation columns operated in series: a de-ethanizer, a depropanizer and a debutanizer. In addition, the de-ethanizer feed is preheated by the bottoms product from the de-ethanizer, which causes additional process coupling. Rigorous models are developed for the columns including column pressure dynamics and heat transfer dynamics. The process is a highly coupled system and has interactive constraints that determine the feasible operating regions. A decentralized PI control system with override controls for the constraints was designed and implemented on the GRU simulator and was compared with an industrial MPC controller. The MPC controller was observed to outperform the decentralized control system due to its multivariable constraint control capability. Since the simulator is available to other university researchers, it can serve as a challenge problem for multivariable control and identification. Three MPC controllers with different strategies for controlling the bottom level of the first column were implemented on the GRU process. The first MPC controller does not directly control the level, the second one moves the setpoint to the PI level controller, and the third one controls the level directly by manipulating the flow. The results show that including level into the MPC controller improves composition control for cases in which the manipulated variable for the level control has a significant impact on compositions.