(459g) Economies of Numbers Formulations for Optimal Process Family Design of Carbon Capture Systems

Enabling rapid, widespread deployment of many process variants across a range of design requirements is key to ensuring the widespread availability of critical decentralized technologies such as carbon capture systems. Unfortunately, traditional process design methods are not efficient for designing many similar variations of a process rapidly across a wide range of system requirements. Rather than considering each process variant as a separate design task, we have proposed viewing the entire set of variants as a “family.” In our work, we present rigorous optimization formulations that simultaneously design each variant within the family from a platform of available unit modules, largely inspired by product family and platform design.

According to Simpson et al. (2014), a product family is “a set of products that share one or more common ‘element(s)’ yet target a variety of different market segments.” This approach has shown documented success across many industries, including automobile, airplane, and tractor production (Simpson et al., 2014). We map this approach to process systems engineering, designing a family of process variants for a set of specified design conditions (such as capacity requirements, environmental conditions, etc.) using a combination of common unit modules selected from a platform while optimizing the remaining unique unit modules. Our approach simultaneously designs the family of process variants as well as the standardized modules that make up the platform. Standardizing modules within the platform captures economies of numbers, and by customizing that platform and variant designs we also draw on economies of scale.

Critical climate change goals cannot be met without the rapid deployment of point-source carbon capture processes at a large number of carbon-emitting sites. According to Wilberforce et al. (2019), the major challenge inhibiting widespread deployment of carbon capture is the high cost associated with the design, manufacturing, and deployment of the system. Design methods that decrease system costs, reduce project timelines, and enable the efficient design of many systems at once are key to ensuring the widespread availability of critical technologies such as carbon capture. A modular design scheme holds potential benefits for deploying process systems quickly and cost-effectively, deriving significant savings from economies of numbers by offering a limited catalog of small, mass-manufactured units. Economies of numbers is a well-documented savings phenomenon that captures how, as the number of times a unit is manufactured increases, the total labor cost decreases at a uniform rate (Argote and Epple, 1990). However, the downside to modular design is that, to meet operational requirements for each process variant, modular units are “stacked,” which eliminates economies of scale (Baldea, et al., 2017). By focusing solely on economies of scale or economies of numbers, design approaches can fall short of reaching optimal cost and time savings. This motivated our current approach, which blends customization and standardization to gain benefits from both a rigorous traditional design approach and efficiencies from a more modular design.

In previous work, we presented an efficient mixed-integer linear programming formulation by discretizing the design space (Zhang et al., 2022). The formulation resembles the P-median problem, lending us important convergence properties to solve large instances of this problem. We have also employed machine learning surrogates to design a process family of refrigeration systems (Stinchfield et al., 2023a) and a family of carbon capture systems (Stinchfield et al., 2023b). While our previous approaches required specification of the number of modules in the platform, we extend these formulations to automatically determine the best number of platform designs. In this work, we formulate a Mixed Integer Linear Program (MILP) that explicitly includes estimations for economies of numbers within the formulation, determining the optimal tradeoff between standardization and customization. This improves on previous approaches because this formulation no longer requires us to constrain the total number of unique module designs offered within the platform—it is now determined optimally. For our case study, we design 63 carbon capture variants each with a unique combination of flue gas flow rate and flue gas carbon dioxide concentrations. We optimally build a platform of absorber and stripper designs from which each of the 63 variants is built, while the rest of the carbon capture process for each variant is designed uniquely (i.e., heat exchanger, condenser, etc.). Our approach exploits both economies of scale and economies of numbers, reduces overall engineering design efforts, and significantly decreases manufacturing time and costs through selective standardization of units. In this presentation, we will show the new optimization formulations for process family design that include economies of numbers, and we will demonstrate the cost reductions possible using a carbon capture case study.

Disclaimer

This project was partially funded by the U.S. Department of Energy, National Energy Technology Laboratory an agency of the United States Government, through a support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Acknowledgments

This effort is part of the U.S. Department of Energy’s Institute for the Design of Advanced Energy Systems (IDAES) supported by the Office of Fossil Energy and Carbon Management’s Simulation-based Engineering/Crosscutting Research Program.

References

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[2] Baldea, M., Edgar, T. F., Stanley, B. L. & Kiss, A. A., ‘Modular manufacturing processes: Status, challenges, and opportunities’, AIChE journal 63.10 (2017), 4262–4272.

[3] Simpson, T.W., Jiao, J., Siddique, Z., Hölttä-Otto, K. Advances in Product Family and Product Platform Design [electronic Resource] : Methods & Applications 1st ed. 2014. Springer New York. doi:10.1007/978-1-4614-7937-6

[4] Stinchfield, G., Biegler, L.T., Eslick, J.C. , Jacobson, C., Miller, D.C., Siirola, J.D., Zamarripa, M.A., Zhang, C., Zhang, Q., Laird, C.D. “Optimization-based Approaches for Design of Chemical Process Families Using ReLU Surrogates” (2023a) In-proceedings of FOCAPO/CPC 2023.

[5] Stinchfield, G., Ammari, B.L., Morgan, J.C., Siirola, J.D., Zamarripa, M.A., Laird, C.D. “Optimization of Process Families for Deployment of Carbon Capture Processes using Machine Learning Surrogates” (2023b) Accepted to 33^rd ESCAPE.

[6] Wilberforce, Tabbi, et al. "Outlook of carbon capture technology and challenges." Science of the total environment 657 (2019): 56-72.

[7] Zhang, C., et al., 2022, Optimization-based design of product families with common components. Computer Aided Chemical Engineering, Proceedings of 14^th International Symposium on Process Systems Engineering (PSE 2021+). Volume 49, pp. 91-96. Elsevier.