This paper addresses the application of a new MPC to a distillation system where isobutane and light butenes are separated from butane and heavier compounds. This system is located in the alkylation unit of an oil refinery. The MPC considered here is based on the infinite horizon MPC extended to the case where the system has stable and integrating modes. The controller is developed based on a particular state space model in the incremental form, which considers the existence of time delays. The proposed controller provides nominal stability to the closed loop system. Practical tests in a distillation system show that the performance of the new controller, which can be extended to consider robustness to model uncertainty is similar to the performance of the conventional MPC with finite prediction horizon.