Analysis and Optimization of Multistage Mixed Refrigerant Systems Using Generalized Disjunctive Programming

The synthesis and optimization of multistage mixed refrigerant systems is a highly challenging and complex problem. It is computationally expensive, highly non-linear, and highly sensitive to changes in composition of refrigerant mixture. Attempts to build a superstructure optimization model using mixed-integer non-linear programming (MINLP) may lead to computational difficulty arising from non-linear and non-convex functions. In this paper, a novel generalized disjunctive programming model formulation is proposed based on a multistage mixed refrigerant system. The model is developed based on mass, energy, phase equilibria, and thermodynamic relations. The main aim is to minimize the required shaft work of the system. The created model formulation is quite systematic and maintains the problem's logical structure. As a result, advanced solution methods such as the logic-based branch and bound may be used to solve the models. This ensures that the solution is sought in reduced space contrary to the full scale for the case of MINLP models. The proposed model is applied on the single mixed refrigerant (SMR) process, and shaft work results obtained are better than those in two referenced literature cases by atmost 25.6% and 13.6%. In addition, it is also applied on a two-stage mixed refrigerant (MR) system, and all results validated by simulation in Aspen Hysys. Model and Hysys results compare with differences of not more than 5.9% ad 1.81% for the SMR and two stage cases respectively. A shaft work consumption comparison of the SMR and two stage yields 24.92 MW versus 23.71 MW, a reduction of 4.9% with introduction of an additional stage. For Aspen Hysys results, a similar comparison yields 26.15 MW versus 24.138 MW, a reduction of 7.7%. The results demonstrates the effectiveness and efficiency of the formulation.