(710e) Uncertainty Analysis and Optimization of a Solvent-Based Post-Combustion Carbon Capture Process Under Uncertainty

Amine-based post-combustion capture is a well-studied and well-accepted technology for carbon capture from point sources. One promising novel technology in this field is the PZ/AFS process that has the advanced flash stripper (AFS) process modification and uses piperazine (PZ) as the solvent [1]. In a previous work, we had developed an equation-oriented, nonlinear model of this process in the IDAES-PSE modeling framework [2, 3], which was validated by comparing with pilot plant performance data. Deterministic optimization was performed to identify the optimal design and conditions for varying plant capacities, capture targets and flue gas sources with an aim to improve the economic viability of this process. It was also observed that the model was well convergent under a wide range of conditions [2].

However, such a process model includes many inherently uncertain parameters, and disregarding uncertainty might cause the optimal solution that is obtained to be suboptimal or even infeasible in real life operation. Therefore, the aim of this work is to apply optimization under uncertainty techniques to mitigate the risk in our designs stemming from various sources of parametric uncertainty in our model. In this study, we focus on epistemic uncertainties of parameters used in the column and heat exchanger models that are associated with properties whose values are either calculated from experimental correlations or those that are assumed to be constant by simplifying assumptions. These include the overall heat transfer coefficient, equilibrium law constants, reaction rate constants, and the density of solvent, among other parameters.

We first leveraged the deterministic optimization capabilities of our equation-oriented model to conduct a systematic sensitivity analysis and uncertainty propagation relating to these parameters. One-way sensitivity analysis is conducted, where each parameter is varied one at a time around their nominal value and sampled at multiple points over a predetermined range, allowing us to observe nonlinearities between the inputs and outputs, whenever present [4]. By comparing cost-optimal designs in light of different uncertainty realizations, the sensitivity of cost of capture to the latter was analyzed. Having performed this analysis on all the parameters in a systematic manner, from highest to lowest levels of the model, we were able to rank the uncertain parameters that were most impactful. These findings help us to reduce the scope of our optimization under uncertainty problem and ensure its eventual tractability.

We next focus on applying rigorous nonlinear robust optimization techniques to identify solutions that remain immune to the aforementioned uncertainties, where it is assumed that all the uncertain data resides in an uncertainty set [5]. These sets were compiled with the highest-impact parameters and the shape and size of the sets were determined based on the result of these sensitivity analyses as well as based on the data reported in literature for certain parameters. Robust process designs were obtained using the solver PyROS, which is based on the Generalized Robust Cutting-Set algorithm and is suitable for large-scale nonlinear models with irremovable equality constraints [6, 7]. For this, we adapted our deterministic model to feature first-stage degrees of freedom (e.g., equipment sizing variables) as well as second-stage, recourse variables, to include the make-up of PZ and water, two bypass ratios, steam, and cooling water flowrates. With this capability, we were able to create price of robustness curves that elucidate the costs associated with a sequence of increasingly robust optimal designs. This study, therefore, provides insights on which uncertainties are the most critical in terms of our ability to commit to designs with a high degree of confidence in the current design cycle as well as what is the amount of funds worth investing to reduce epistemic uncertainty before committing to a final design.

References:

[1] GT Rochelle, Y Wu, E Chen, K Akinpelumi, KB Fischer, T Gao, CT Liu, and JL Selinger. Pilot Plant Demonstration of Piperazine with the Advanced Flash Stripper. International Journal of Greenhouse Gas Control, 84:72–81 (2019)

[2] I Akkor, SS Iyer, J Dowdle, L Wang, CE Gounaris. Mathematical Modeling and Economic Optimization of a Piperazine-Based Carbon Capture Process (2024, Forthcoming)

[3] A Lee, JH Ghouse, JC Eslick, CD Laird, JD Siirola, MA Zamarripa, D Gunter, JH Shinn, AW Dowling, D Bhattacharyya, LT Biegler, AP Burgard, DC Miller. The IDAES process modeling framework and model library – Flexibility for process simulation and optimization. Journal of Advanced Manufacturing and Processing 3.3 e10095 (2021)

[4] V Spek, et al. Uncertainty analysis in the techno-economic assessment of CO2 capture and storage technologies. Critical review and guidelines for use. International Journal of Greenhouse Gas Control, 100, 103113 (2020)

[5] BL Gorissen, I Yanıkoglu, and D Hertog. A practical guide to robust optimization. Omega, 53:124–137 (2015)

[6] NM Isenberg, P Akula, JC Eslick, D Bhattacharyya, DC Miller, and CE Gounaris. A generalized cutting-set approach for nonlinear robust optimization in process systems engineering. AIChE Journal, 67(5):e17175 (2021)

[7] NM Isenberg, JAF Sherman, JD Siirola, and CE Gounaris. PyROS: Nonlinear Robust Optimization in Pyomo (2024, Forthcoming)