(392ar) Multiobjective Mixed-Integer Bayesian Optimization for the Use of Liquid Organic Hydrogen Carriers for Maritime Applications

Many engineering optimization problems can be characterized as costly "black-box" problems. These are situations where evaluations of the objective function are expensive, gradients are unavailable, and no cost-effective analytical models exist. Consequently, efficient optimization techniques that rely solely on function evaluations are required. Within Process Systems Engineering (PSE), optimization algorithms play a crucial role by guiding process design decisions based on various objectives. In this context, data-driven optimization techniques (Van De Berg et al., 2022), particularly Bayesian Optimization (BO), emerge as promising methods capable of efficiently addressing these challenging problems. BO is able to perform optimization with a reduced number of process evaluations and offers several possibilities for process design (e.g., constraints, multiobjective, mixed integer-continuous space) (Paulson and Tsay, 2024). The idea of BO is using a surrogate model, typically a Gaussian Process, to adjust the shape of objective functions based on the input variables. Then, the most promising points are considered for next function evaluations and the model is updated. In this work, BO is used for the optimization of the Liquid Organic Hydrogen Carriers (LOHCs) dehydrogenation module (DH) coupled with a Solid Oxide Fuel Cell (SOFC) fuel cell for maritime applications. The optimization of this system includes the evaluation of computationally expensive functions using black-box approach, black-box but measurable constraints, multiobjective optimization and the presence of binaries. Hence, a new process optimization methodology using BO is presented for the specific LOHCs case study.

The decarbonization of maritime sector, hard-to-electrify, is a priority. International Maritime Organization (IMO) sets net-zero emissions target by 2050 (IMO, 2023). Hydrogen has attracted attention. However, low volumetric density (Hydrogen Europe, 2021) and demanding and unsafe conditions for current storage technologies may difficult its application. At this point, LOHCs can store it under ambient conditions and reuse the oil infrastructure. They store hydrogen in the chemical structure of an organic liquid (hydrogenation) and release it (dehydrogenation). Using LOHCs as maritime fuels has been encouraged in some works. The potential combination with SOFC can produce electricity to meet ship engine demand and cover dehydrogenation heat (Gambini et al., 2024). However, a detailed process flowsheet for this concept has not been evaluated nor optimized yet. In this work, a detailed DH module and a combined heat and power (CHP) system with a SOFC is proposed for optimization. Different from other works, reaction units are modelled using rigorous reactor assessment (Prieto et al., 2023). Two technologies are proposed within a process superstructure: adiabatic and isothermal trickle bed reactors. The process conditions, equipment size and number of units for each type is to be determined. The optimization of a process design framework with these reactors is challenging (differential equations, non-linearities) and computationally expensive. Hence, process simulation is treated as a black-box function. Several objective functions critical for maritime applications are proposed such as investment and volume of process equipment, safety and efficiency. Hence, multiobjective BO is applied for process design. Reactors operating conditions (e.g., pressure, temperature, recycle) and design parameters (catalyst use and diameter) are considered as input variables. Unlike these, which are continuous, decision variables such as number of each reaction unit (integer) are also introduced. Hence, a BO framework is used for the optimization of this system considering its characteristics.

Primarily, several strategies are proposed to transform the traditional BO considering the presence of a continuous-integer space. These include the use of hybrid kernels and Genetic Algorithms for the optimization of the acquisition function. With this approach, the constrained single objective optimization of each of the functions is carried out. The results are 31.8 M$, 63.7 m³, 43.5 % system efficiency and 3.5 risk units (proposed in this work). Finally, using the same approach, constrained multiobjective BO is performed to reach a trade-off between the different opposing objective functions. A pareto front is built to find the most promising candidates to design the DH and CHP modules. Hence, LOHCs systems are evaluated for a future deployment and implementation in maritime sector.

Acknowledgements

The authors acknowledge the support from the Regional Government of Castilla y León (Junta de Castilla y León) and by the Ministry of Science and Innovation MICIN and the European Union NextGenerationEU/PRTR (H2MetAmo project-C17.I01.P01.S21) and the FPU, Spain grant (FPU21 /02413) to C.P.

References

Gambini, M., Guarnaccia, F., Manno, M., and Vellini, M. (2024). Feasibility study of LOHC-SOFC systems under dynamic behavior for cargo ships compared to ammonia alternatives. International Journal of Hydrogen Energy, 81, 81-92.

Hydrogen Europe (2021). How hydrogen can help decarbonise the maritime sector.

IMO, O. (2023). 2023 IMO strategy on reduction of GHG emissions from ships. In Resolution MEPC. 377 (80). International Maritime Organization London, UK.

Paulson, J. A., and Tsay, C. (2024). Bayesian optimization as a flexible and efficient design framework for sustainable process systems. Current Opinion in Green and Sustainable Chemistry, 100983.

Prieto, C., Sánchez, A., and Martín, M. (2023). A three-phase reactor assessment for the deployment of Liquid Organic Hydrogen Carriers (LOHCs): dybenzyltoluene and indoles mixture systems as case studies. Energy Conversion and Management, 294, 117548.

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