Gas-liquid cylindrical cyclone separators are widely used in several applications, including bulk separation of hydrocarbons. Recently, these separators have been considered for subsea separation because of their low weight and compact design. However, disadvantages associated with their design are the resulting fast dynamics and small operational volume, which make them highly sensitive to flow variations. There are two possible approaches for dealing with this problem: (1) increasing the operational volume or (2) improved control. The fast dynamics necessitates a fast and computationally inexpensive control algorithm. Therefore, in this paper, we consider a newly proposed nonlinear dynamic model containing unmeasured parameters to design a model predictive control algorithm for real-time offset-free optimal control, i.e., improved transient handling and product quality optimization. Offset-free optimal control is achieved by augmenting the states with integral error states of the controlled variables. The MPC algorithm with and without state feedback from the estimator is compared in simulations, both achieving offset-free optimal control.