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This paper focuses on the application of steady-state operability to Model Predictive Control (MPC) of the Shell Heavy Oil Fractionator (SHOF) control problem. Operability for non-square systems is a relatively new area in the literature, and investigation into its applicability for higher order dimensions has not yet been addressed. This was done primarily to assess steady-state operability as a tool for evaluating the steady-state performance of high-order non-square systems. New theory and techniques have, however, been developed in the process. For non-square systems there are a number of alternatives in selecting the type (e.g. set-point, zone/interval and funnel) and number of controlled variables. This paper aims to investigate how operability can help the control designer to select these controlled variables (CVs) whilst ensuring robustness to expected disturbances. Different options are assessed for the SHOF, and conclusions and recommendations are made regarding how the concept of operability might be improved.