(740d) Optimal Start-up of Cryogenic Air Separation Units

Cryogenic air separation plants are used for industrial-scale production of high purity components of air. They are highly energy intensive processes, which has motivated the development of demand response strategies to adapt their operation in response to fluctuating energy prices (Cao, Swartz and Flores-Cerrillo, 2016; Pattison et al., 2016; Zhang et al., 2018), as well as the investigation of design characteristics that limit the plant’s agility (Cao et al., 2015). The start-up of air separation units (ASUs) warrants particular consideration within this context. ASUs are tightly heat integrated and have slow dynamics, resulting in start-up times on the order of 20 hours or more during which electricity is consumed with limited revenue generation. In the current environment of electricity price deregulation, it may be economically advantageous for ASUs to be shut down over periods of particularly high electricity prices, resulting in more frequent start-ups than before. This creates an incentive to minimize start-up time.

Ruiz et al (1988) identified three stages for distillation column start-up: the discontinuous phase which represents discontinuous changes in variables; the semi-continuous phase which captures nonlinear continuous change; and the last phase characterized by linear continuous change. With an initial point corresponding with the third start-up phase identified by Ruiz et al (1988), Woinaroschy (2008) used iterative dynamic programming for start-up time minimization of rigorous distillation column models. Using a sequential NLP approach and simulated annealing, Wonzy & Li (2004) minimized start-up time of rigorous distillation columns initialized from the semi-continuous phase. Also starting with the semi-continuous phase and using a rigorous column model, de la Fuente & Tlacuahuac (2007) explored start-up time minimization using a simultaneous dynamic optimization approach on reactive distillation columns. Raghunathan et al., (2003) included discontinuities in their start-up formulation for cryogenic distillation of natural gas and converted the dynamic problem to a Mathematical Program with Equilibrium Constraints (MPEC). Also capturing discontinuity, however using simulation studies, Miller et al (2008) demonstrated start-up time minimization using additional reflux in the cryogenic distillation of air.

In this work, we consider a multiproduct air separation plant. The multiproduct plant considered has a lower column (LC), an upper column (UC), and a side rectifier. The UC produces high purity oxygen and nitrogen while the side rectifier, which does an oxygen-argon separation, produces a high purity argon product. Two of the products (nitrogen and argon) have purities measured in parts per million (ppm). The ASU also makes use of multi-stream heat exchanger (PHX) and integrated reboiler condenser (IRC) which results in a high degree of heat integration. This study investigates the development of a plant-wide high-fidelity first-principles dynamic model for dynamic optimization of a multi-product ASU start-up. The model is coded in gPROMS and based on the work done by Cao et al. (2016). This new model captures discontinuities that naturally arise during the start-up sequence. These include liquid overflow, change in vapor flow dynamics due to the closing of downcomers, toggling between open-loop and closed-loop control of liquid levels in sumps and reboilers, and opening and closing of vents. Moreover, operator logic such as the opening of valves and control of flows, is also modelled. These discontinuities could be treated as discrete decisions. However, considering the size of the model (in excess of 10,000 variables) and complexity, the discontinuities are instead approximated using smoothing functions. Using a combination of hyperbolic tangent functions and linear transition functions, non-smoothness was removed from the model to obtain a DAE system. Modelling appearance and disappearance of phases is computationally expensive (Raghunathan et al., 2003). A workaround used by Miller et al. (2008) was to initialize trays with negligible but computationally significant amounts of liquid and assume negligible vapor holdup on stages, a technique also used in this study. Minimization of start-up time is indirectly achieved by minimizing an economic objective tied to start-up costs. The results of the dynamic optimization provide control variable trajectories such as air flow rate. This paper will describe the dynamic ASU model with a particular focus on the discontinuity handling, its use in start-up simulation, and its incorporation within a dynamic optimization framework.

References

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