Cryogenic air separation columns, which are widely used in industry, consume a large amount of energy producing significant quantities of high-purity nitrogen, oxygen and argon. In order to meet the requirement of different customers, the production rate and product purities have to be changed rather frequently. Rising material and energy costs, as well as uncertain market and load demands are pushing increased research into the flexible design and operation of cryogenic air separation columns^[1-6].

Existing research has focused on the implementation of suitable control strategies to guarantee effective transition between different operating conditions^{[1-4, 6]}. However, a second area to consider is the optimal planning and operation of these air separation systems in order to avoid large or frequent transitions. This problem is difficult for two main reasons. First, it requires optimization formulations that consider correlated uncertainties in the demands and product transitions. Second, the coupled nature of cryogenic air separation systems gives rise to an extremely complex and highly nonlinear model. Nonlinear programming formulations and advanced large-scale algorithms provide a rigorous framework for addressing both of these problems.

Adopting a purely multi-scenario approach that requires the satisfaction of customer demands and constraints on controlled transitions over all the scenarios can lead to solutions that are far too conservative (and expensive). Instead, we combine the multi-scenario approach with Chance-Constrained Programming to obtain more cost effective solutions that are acceptable with regards to the uncertainty. This study presents a multi-scenario mathematical formulation and advanced solution approach for optimal planning and operation with uncertain demands and transitions using chance constraints. A rigorous nonlinear process model is used for the coupled cryogenic air separation system, which considers mass and energy balances, phase equilibrium, and system hydraulics. To effectively solve such large-scale nonlinear problem, we present a parallel internal decomposition approach^[6-8] based on the existing primal-dual interior-point NLP solver, IPOPT ^[9]. Optimal solutions with different inventory and uncertainty distribution assumptions will be discussed, along with the impact of different customer satisfactory levels. Furthermore, as demonstrated by this problem, the parallel interior-point approach is shown to be scalable to many processors.

References:

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[2]  Roffel, B., Betlem, BHL., de Ruijter, JAF. (2000). First principles dynamic modeling and multivariable control of a cryogenic distillation process. Computers chem. Eng., 24, 111.

[3]  Bian, S., Henson, M., Belanger P., Megan L., (2005) Nonlinear state estimation and model predictive control of nitrogen purification columns. Ind. Eng. Chem. Res., 44, 153.

[4]  Seliger B., et al., (2006) Modeling and dynamics of an air separation rectification column as part of an IGCC power plant. Sep. Purif. Technol. 49, 136.

[5]  Miller, J., Luyben, WL., M., Belanger P., Blouin, S., Megan L., (2008) Improving agility of cryogenic air seapration plants, Ind. Eng. Chem. Res., 47, 394

[6]  Zhu, Y., Laird, CD., A parallel algorithm for structured nonlinear programming, foundations of computer-aided process operations (FOCAP-O), Boston, Massachusetts, USA, July 2008.

[7]  Laird, CD., Biegler, LT. (2006). Large-scale nonlinear programming for multi-scenario optimization. proceedings of the int. conference on high performance scientific computing, Hanoi, Vietnam.

[8]  Zavala, VM., Laird, CD., Biegler LT. (2007) Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems. in press, Chem. Eng. Sci.

[9]  Wächter A., Biegler LT. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Programm., 106, 25