Cryogenic air separation units (ASUs) are an essential utility supplier to a number of industries, including chemicals, metal processing, electronics and water treatment. Electricity to operate compressors is the main utility required for the process and accounts for a large portion of the operating costs . Optimal production scheduling is crucial for minimizing operating costs in an environment where the process is subject to time-varying electricity prices. Generally, production levels are increased at times when prices are low; excess production of nitrogen and oxygen is liquefied and stored so that the products can be used to satisfy demand when grid demand and electricity prices are at a peak . This operating paradigm effectively amounts to storing energy in the form of the latent heat removed from the cryogenic products . ASUs also typically supply their gas products to customers through a pipeline system, and it is important to ensure that the product quality satisfies the customer requirements during production rate transitions. Equivalently, an optimal transition pathway between two operating points, that does not violate any constraints in product quality (e.g., the impurity level) or operation (e.g., flooding in the distillation column), must be established [4, 5].
Motivated by the above, we introduce a novel integrated scheduling and dynamic optimization framework for air separation processes. Our approach consists of including a (low order) dynamic model of the ASU in the scheduling calculation as a means to avoid quality and process constraint violations. In particular, we proceed by (i) identifying a low-order model from historical operating data, that captures the dynamics of variables relevant to the scheduling calculation and (ii) developing of an integrated scheduling and control formulation for the ASU process using this model. This is a significant departure from the traditional scheduling calculation which contains limited (and typically static) information about the dynamic performance of the process.
We illustrate our framework using a detailed model of an ASU for the production of nitrogen. We discuss several continuous- and discrete-time data-driven modeling options and their implementation in the integrated scheduling and optimization framework, as well as sequential and simultaneous strategies for solving the resulting mixed-integer dynamic optimization problem. Our results show that accounting for process dynamics at the scheduling level allows for a better exploitation of real-time energy prices, and leads to improvements in ASU operating profit.
 R. C. Pattison and M. Baldea, Optimal Design of Air Separation Plants with Variable Electricity Pricing. In Proceedings of the 8th International Conference on Foundations of Computer-Aided Process Design, Computer Aided Chemical Engineering, 34:393-398, 2014.
 M. G. Ierapetritou, D. Wu, J. Vin, P. Sweeney, and M. Chigirinskiy, Cost Minimization in an Energy- Intensive Plant Using Mathematical Programming Epproaches. Industrial & Engineering Chemistry Research, 41(21):5262-5277, 2002.
 Q. Zhang, I.E. Grossmann, C.F. Heuberger, A. Sundaramoorthy, J.M. Pinto, Air Separation with Cryogenic Energy Storage: Optimal Scheduling Considering Electric Energy and Reserve Markets, AIChE Journal, 61(5):1547-1558, 2015.
 Y. Cao, Design for Dynamic Performance: Application to an Air Separation Unit, MSc Thesis, McMaster University, 2011.
 Y. Cao, C. Swartz, M. Baldea, Design for Dynamic Performance: Application to an Air Separation Unit, In Proceedings of the American Control Conference, 2683-2688, 2011.