# (273a) A Computational Tool for Applying Optimization Under Uncertainty on Advanced Process Simulators

- Conference: AIChE Annual Meeting
- Year: 2018
- Proceeding: 2018 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Tuesday, October 30, 2018 - 8:00am-8:19am

Accurately modeling complex chemical engineering processes (e.g., solid sorbent-based carbon capture plants) requires rigorous large-scale models. Optimizing these models with traditional mathematical optimization tools is challenging, especially when uncertainty is analyzed (Reddy et al., 2017). For instance, having uncertain variables with continuous distributions increases the size of the optimization problem, which in turn increases the computational burden. FOQUS can potentially reduce the time required for implementing OUU, thus making OUU more feasible, with its alternative approach of using process simulator models within an OUU framework.

The capabilities of FOQUS are demonstrated with the design and OUU of a solid sorbent-based carbon capture system for a coal-fired power plant, which was simulated in Aspen Custom Modeler (ACM). The uncertainties originate from material characterization (e.g., solid sorbent particle diameter and heat transfer coefficients) and from the operation of the power plant (e.g., the inlet flue gas flow rate). The reaction kinetic parameters for this system are well-studied, and a previous study found that the uncertainty of these parameters had negligible effect on the performance of the carbon capture plant (Eslick et al., 2015).

The objective of this study is to minimize the expected value of the cost of electricity (COE) while maintaining a minimum of 90% CO_{2} capture. FOQUS uses a two-stage stochastic optimization framework, where the equipment design variables are the first-stage variables, and the operating variables are the second-stage variables. The parameter uncertainty distributions are represented by generating scenarios with different values of the uncertain parameters. The problem is solved as a nested optimization problem. In the first stage, a derivative-free optimization algorithm in FOQUS adjusts the values of the first-stage variables to be the same across all scenarios. Nested inside that optimization, the optimization algorithm in the process simulator is used to adjust the values of the second-stage variables. Second-stage variables are not required to be the same across all scenarios, which means that they provide recourse to uncertainties. Leveraging the optimization algorithm provided by the process simulator improves the performance of the solution method, and the second-stage optimization problems can be run in parallel, using the parallel simulation job queuing capabilities of FOQUS.

To highlight the importance of considering the uncertainties of variables prior to designing the plant, the expected value of the COE obtained from OUU is compared against the expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) (Birge and Louveaux, 2011). The EVPI compares the expected value of the COE obtained from the case where the values of both the equipment design variables and the operating variables can be adjusted to respond to the perturbation in the value of the uncertain variable (i.e., the ideal but unrealistic situation) against the expected value of the COE obtained from executing OUU. A negative value of the EVPI suggests that the expected value of the COE generated from the ideal case is smaller compared to the expected value of the COE generated from performing OUU. On the other hand, the VSS compares the expected value of the COE obtained from executing OUU against the expected value of the COE obtained from the case where the carbon capture plant is built using the values of the equipment design variables that were optimized without any uncertainty considerations, and then when the uncertainties are introduced, only the values of the operating variables were optimized to minimize the expected value of the COE. A negative value of the VSS suggests that the expected value of the COE generated from performing OUU is smaller compared to the expected value of the COE generated from building the plant using the values of the equipment design variables generated after optimization without considering the uncertainty.

For the case where the value of the particle diameter is perturbed from -25% to +25% from the base case, the EVPI is -0.8 USD/MWh, and the VSS is -4.8 USD/MWh. Building the carbon capture plant using the values of the equipment design variables obtained from OUU instead of those obtained without performing OUU improves the flexibility of the plantâ€™s operation, thus reducing technical risk. These results show that FOQUS can easily facilitate OUU analyses in a simulation-optimization framework.

**References**

Birge, J.R., Louveaux, F., 2011. Introduction to Stochastic Programming, second ed. Springer Science+Business Media, LLC, New York, NY, USA.

Eslick, J.C., Tong, C., Ng, B., Lee, A., Dowling, A.W., Mebane, D.S., Chen, Y., Miller, D.C., 2015. Optimization under uncertainty with rigorous process models. 2015 AIChE Annual Meeting; 8â€“13 November 2015; Salt Lake City, UT, USA.

Miller, D.C., Agarwal, D., Bhattacharyya, D., Boverhof, J., Chen, Y., Eslick, J., Leek, J., Ma, J., Mahapatra, P., Ng, B., Sahinidis, N.V., Tong, C., Zitney, S.E., 2017. Innovative computational tools and models for the design, optimization and control of carbon capture processes, in: Papadopoulos, A.I., Seferlis, P. (Eds.), Process Systems and Materials for CO_{2} Capture: Modelling, Design, Control and Integration. John Wiley & Sons Ltd, Chichester, UK, pp. 311â€“342.

Miller, D.C., Syamlal, M., Mebane, D.S., Storlie, C., Bhattacharyya, D., Sahinidis, N.V., Agarwal, D., Tong, C., Zitney, S.E., Sarkar, A., Sun, X., Sundaresan, S., Ryan, E., Engel, D., Dale, C., 2014. Carbon Capture Simulation Initiative: A case study in multiscale modeling and new challenges. Chemical and Biomolecular Engineering 5, 301â€“323.

Reddy, S.S., Sandeep, V., Jung, C.-M., 2017. Review of stochastic optimization methods for smart grid. Frontiers in Energy 11 (2), 197â€“209.