One of Air Liquide's major business activities is the separation of air into its pure components: oxygen, nitrogen and argon. The products can be in either liquid or gaseous phase. The gas products are often supplied to various customers in a region via gas pipelines which connect the plants to the customers. Each plant may contain one or more of air separation units (ASU) which are at the heart of the air separation process. The production capability of each plant for the different products is determined by the plant layout and the design of each of the air separation units. ASUs are highly energy intensive. Hence, the operating margin of an air separation plant is highly susceptible to the rapid fluctuations in electricity prices. The customers usually take gases at different conditions, and thus the gas pipelines have to be operated at different pressure levels through the operation of downstream and network compressors. Further, customer demands are not always stable but varying. Given these two major factors of fluctuating prices and consumer demands, real-time optimization techniques are necessary to determine the most profitable way of operating gas pipeline networks while satisfying a variety of process and network constraints.
Real-time optimization of a network necessitates a quality model describing the underlying processes and network. Air separation units operate in a fashion that can be described only with highly nonlinear and nonconvex functional forms. Unfortunately, detailed first-principles models can be very large, posing a significant challenge for optimization algorithms. For the pipeline in this study, Air Liquide developed a model to describe both plant and pipeline operations using mass and energy balances and, through regression, on historical plant data. By combining overall mass and energy balances with regression, we were able to maintain the accuracy of the model while preventing the model size to grow too large.
The second set of modeling challenges are the process constraints that necessitate many discrete decisions such as whether certain compressors and air separation units should be turned on or off. Modelling these discrete decisions through the use of integer variables required us to use a mixed-integer nonlinear programming model. Due to nonconvexities this model possesses multiple local optima. Global optimization techniques were found necessary in order to avoid inferior locally optimal solutions. The model must be efficiently solved in reasonable time to allow for its use in real-time optimization. Further, the size of the model and numerical characteristics introduced through regression data pose considerable challenges for all global solvers. We overcame these challenges by pursuing a model reduction and scaling strategy that facilitated reliable and robust solutions to the model. Detailed computational results are presented showcasing a highly successful industry-academia collaborative effort between Air Liquide and Carnegie Mellon University to address several modeling and numerical solution challenges that arose in the context of this challenging pipeline operational problem.