In this paper, we demonstrate how a practical control problem with multiple control/optimization objectives and various operating constraints is formulated in the theoretical framework of state estimation based model predictive control (SEMPC) proposed by Lee et al. We use the shell control problem (SCP) of a heavy oil fractionator as case study. The shell control problem embodies most of the critical elements of challenging industrial process control problems (e.g. unmeasured disturbances, model uncertainty, input/output constraints, optimization objective conflicting with control requirements, failure-prone sensors, secondary measurements, nonsquare system, etc.) and therefore serves as a good test problem for investigation of potential benefits and pitfalls of the new technique. We demonstrate in the case study that, while the theory for the new model predictive control (MPC) technique is rigorously laid out, it is nontrivial for practicing engineers to formulate various practical objectives correctly within the theoretical framework to realize all the potential performance improvements of SEMPC over conventional MPC. By formulating and analyzing a series of different SEMPC controller designs for SCP, this paper highlights some of the possible difficulties that engineers may encounter in applying SEMPC to practical control problems and shows how these difficulties are overcome most efficiently.