(419d) Mixed-Integer Nonlinear Programming Models for Optimal Design of Reliable Chemical Plants

Ye, Y., Carnegie Mellon University
Grossmann, I., Carnegie Mellon University
Pinto, J. M., Linde plc
Ramaswamy, S., Praxair, Inc.
Mixed-integer nonlinear programming models for optimal design of reliable chemical plants

Yixin Ye1, Ignacio E. Grossmann1, Jose M. Pinto2, Sivaraman Ramaswamy2

1Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213

2Business and Supply Chain Optimization R&D, Praxair, Danbury, CT 06810



Plant availability has always been a critical consideration for the design and operation of chemical processes, for 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. An effective way to reduce the impact of equipment breakdown on the entire plant is to install back-up units in the design phase. Current state-of-the-art design reliability (regarding number and selection of back-up units) for these plants or other chemical processes is to use simulation tools to assess different design alternatives. Currently, discrete event simulation tools are used to evaluate reliability/availability of selected alternatives in terms of equipment redundancy, additional inventory and preventive maintenance to simulate the behavior of every asset in a plant using historical maintenance data and statistical models (Sharda and Bury, 2008). However, this approach does not systematically consider all the alternatives as it would be the case in an optimization approach.

Research has been done to quantitatively analyze the reliability of chemical plants (Thomaidis and Pistikopoulos, 1995). Goel et al. (2003b) consider both design and planning of production and maintenance in an MILP model with variable reliability parameters and fixed system configuration. Aguilar et al. (2008) address reliability issue in utility plant design and operation and report the optimization result of an MILP model for a specific example considering two failure situations. Terrazas-Moreno et al. (2010) formulate an MILP model using Markov chains to optimize the selection of alternative plants and the design of intermediate storage for an integrated production site.

However, there are virtually no general mixed-integer programming models proposed for the optimal design of reliable chemical processes. In response to this gap, this work develops optimization models for reliable design of chemical plants, where the major trade-off considered is between plant availability and the investment cost of back-up equipment. Mixed-integer models are formulated to select redundant equipment for serial systems in terms of availability, in order to maximize system availability (i.e. probability that the system performs without failures), and hence sales revenue, while minimizing the total cost of the system.

First, we consider a basic scenario where all the stages need only one unit to work properly. A set of potential units for each stage are given with certain availabilities (i.e. the probability of finding the unit available), operating priorities, which means that a unit can only become active when all installed units that have higher priorities have failed, and cost rates. Based on the parameters provided above, the relationship between the availability of stage and its design decision is established. On the basis of the basic scenario, an additional standby strategy is applied. Here, two units each with half capacity can work at the same time in one stage, such that when one of them fails, there is still half of the original output left. System availability is also redefined to capture the new situations of having partial capacity.

Two non-convex MINLP models for maximizing system net profit are formulated regarding the two situations, respectively. In addition, another non-convex -constrained MINLP model is formulated for the first scenario by maximizing availability and minimizing the total cost. It is shown that this model can be reformulated as a convex MINLP in order to generate the corresponding Pareto-optimal solutions.

The proposed MINLP models are applied to several case studies that include sensitivity analysis of the availabilities predicted for each unit. Furthermore, the proposed models for availability evaluation are incorporated in the synthesis of methanol and hydro-alkylation processes that involve optimizing their flowsheet superstructures.


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Goel, H. D., Grievink, J., and Weijnen, M. P. (2003b). Integrated optimal reliable design, production, and maintenance planning for multipurpose process plants. Computers & chemical engineering, 27(11):1543-1555.

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