Optimal Start-Up of Air Separation Processes using Dynamic Optimization with Complementarity Constraints

Fluctuating electricity prices create an incentive for the flexible operation of electricity intensive processes, such as air separation units (ASUs). Shutting down an ASU during times with peak electricity prices has been claimed economically attractive but requires an efficient and largely automated start-up procedure. Previous works have considered simulations of plant start-ups and dynamic optimization of load scheduling near the nominal operation mode. Discrete events like the appearance of a liquid phase have impeded any rigorous ASU start-up optimization. In this work, we formulate the optimal start-ups as dynamic optimization problems with regularized algebraic complementarity constraints (Caspari et al., 2019b) using a mechanistic dynamic process model in Modelica. Our approach captures physical effects appearing during start-up like the appearance and disappearance of phases. We solve the resulting optimization problems with direct single-shooting using the dynamic optimization framework DyOS. We perform in-silico dynamic offline optimizations of an ASU start-up and consider different process modifications. We consider cold start-up optimizations, where the process medium is initialized at cryogenic conditions just before liquefaction. The results illustrate that the proposed approach can be applied to large-scale processes. The results show further that liquid assist operation reduced the optimal start-up time by about 70 % compared to the start-up without this modification.