(657a) Integrated Redundancy, Storage and Maintenance Policy Design Optimization for Reliable ASU Based on Markov Chain – a Game Theoretic Solution Approach

Ye, Y. - Presenter, The Dow Chemical Company
Grossmann, I., Carnegie Mellon University
Pinto, J. M., Linde plc
Ramaswamy, S., Praxair, Inc.
Plant availability has always been a critical consideration for the design and operation of chemical processes as it represents the expected fraction of normal operating time, which impacts directly the ability of meeting customer demands. The failure of a key unit is likely to cause the shut-down of the entire plant. For Air Separation Units (ASUs) that continuously supply gas customers through pipelines, a disruption can cause great loss. Currently, discrete event simulation tools are used to evaluate the reliability/availability of selected redundancy levels to simulate the behavior of every asset in a plant using historical maintenance data and statistical models (Sharda and Bury, 2008). However, this approach cannot systematically consider all possible design alternatives, not to mention other strategies to increase availability as it would be the case in an optimization approach.

A number of optimization works have been reported to optimize the reliability of chemical plants. Pistikopoulos et al. (2001) and Goel et al. (2003b) formulate an MILP model for the selection of units with different reliability and the corresponding production and maintenance planning for a fixed system configuration. Terrazas-Moreno et al. (2010) formulate an MILP model using Markov chains to optimize the expected stochastic flexibility of an integrated production site by the selection of pre-specified alternative plants and the design of intermediate storage. Kim (2017) presents a reliability model for k-out-of-n systems without repair using a structured continuous-time Markov Chain, which is solved with a parallel genetic algorithm. As an improvement, our recent mixed-integer framework (Ye et al., 2019) models the stochastic failure-repair process of the superstructure of the ASU process as a continuous-time Markov Chain, and simultaneously optimizes the redundancy selection and the maintenance policy.

This work extends the idea of our aforementioned recent work (Ye et al., 2019) to incoporate liquid storage as another strategy for increasing reliability besides considering redundant equipment and condition-based maintenance. To be specific, three strategies over design and maintenance are considered to increase the availability of the system. For design, we can install parallel units for certain processing stages, such that when the primary unit fails, the other units can fill in its place in order to reduce system downtime. Another reliable design strategy is to store liquid products which can be vaporized to meet pipeline demands during plant downtimes. The units will also go through periodic inspections, and condition based maintenance if the inspection result indicates that the equipment will fail shortly. Through this strategy the system can avoid a number of repairs, which are more costly than maintenances in terms of both time and money. Decisions to be made include redundancy selection for each processing stage, storage tank size selction for each product, and inspection interval selection for each failure mode of each processing stage.

Direct handling of this combinatorial problem results in either an intractable MILP to cover the entire super state space of the Markov Chain, or else on a large non-convex MINLP with exponential functions and many multilinear terms. Therefore, we propose an efficient solution approach that poses the problem as a team game, where the processing stages are the players who make decisions regarding their respective design and maintenance strategies in order to optimize a same system objective, the team outcome. The solution approach is initialized with a suboptimal solution within a one percent gap to the global optimum, and then iteratively improved by expanding the potential solution pool. The stopping criterion is the team game Nash Equilibrium, where no single stragety deviation can improve the team outcome. The gap bounding is proved under the assumption that the reliability data (failure rates and repair rates) of single units remain to be of the same orders of magnitude.

The computational results of the reliable design of the ASU shows that the game theoretic solution approach can achieve the identical result as the directly formulated MILP model in much shorter time. In addition, a series of perturbed problems are solved to illustrate that although a Nash Equilibrium may not imply the global optimum, they are identical for these representative cases.


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Terrazas-Moreno, S., Grossmann, I. E., Wassick, J. M., and Bury, S. J. (2010). Optimal design of reliable integrated chemical production sites. Computers & Chemical Engineering, 34(12):1919-1936.

Kim, H. (2017). Optimal reliability design of a system with k-out-of-n subsystems considering redundancy strategies. Reliability Engineering & System Safety, 167:572 – 582.

Ye, Y., Grossmann, I. E., Pinto, J. M., & Ramaswamy, S. (2019). Modeling for reliability optimization of system design and maintenance based on Markov chain theory. Computers & Chemical Engineering 124:381-404.