Organic Rankine cycles (ORCs) offer a high structural design flexibility. The best process structure can be identified via the optimization of a superstructure, which considers design alternatives simultaneously. In this contribution, we apply deterministic global optimization to a geothermal ORC superstructure, thus guaranteeing to find the best solution. We implement a hybrid mechanistic data-driven model, employing artificial neural networks as thermodynamic surrogate models. This approach is beneficial as we optimize the problem in a reduced space using the optimization solver MAiNGO. We further introduce redundant constraints that are only considered for the lower-bounding problem of the branch-and-bound algorithm. We perform two separate optimizations, one maximizing power output and one minimizing levelized cost of electricity. The optimal solutions of both objectives differ from each other, but both have three pressure levels. Global optimization is necessary as there exist suboptimal local solutions for both flowsheet configuration and design with fixed configurations.

Global deterministic process optimization problems have recently been solved efficiently in a reduced-space by automatic propagation of McCormick relaxations (Bongartz and Mitsos, J. Global Optim, 2017). However, the previous optimizations have been limited to simplified thermodynamic property models. Herein, we propose a method that learns accurate thermodynamic properties via artificial neural networks (ANNs) and integrates those in deterministic global process optimization. The resulting hybrid process model is solved using the recently developed method for deterministic global optimization problems with ANNs embedded (Schweidtmann and Mitsos, J. Optim. Theory Appl., 2018). The optimal operation of a validated steady state model of an organic Rankine cycle is solved as a case study. It is especially challenging as the thermodynamic properties are given by the implicit Helmholtz equation of state. The results show that modeling of thermodynamic properties via ANNs performs favorable in deterministic optimization. This method can rapidly be extended to include properties from existing thermodynamic libraries, based on models or data.