Abstract
In this study, we propose a novel trust-region funnel (TRF) optimisation framework for process systems that integrate external black-box models, such as rigorous models, within equation-oriented (EO) formulations. The framework is applied to optimise a synthetic natural gas production process combining direct air capture and catalytic CO2 conversion using dual-function material (DFM) technology, with the objective of minimising the total annualised cost. The problem is formulated in Pyomo and solved using IPOPT, treating the DFM reactor as an external black-box model. The TRF method achieves substantial improvements compared to published mixed-integer nonlinear programming and direct nonlinear programming approaches, reducing capture cost from 460 USD to 426 USD per tonne of CO2. Key design improvements include reducing the number of DFM units per train by one-third and achieving a 22% reduction in DFM capital costs. These results highlight the TRF framework's ability to overcome numerical challenges and unlock economically superior designs for next-generation carbon capture and utilisation systems.