(614e) Optimal Planning and Operation of Cryogenic Air Separation Columns Considering Uncertain Demands and Product Transitions

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:

[1]  White, V., Perkins, JD., Espie, DM.,
(1996). Switchability analysis. Computers chem. Eng., 20, 469.

[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