Global optimization is desirable for the design of chemical and energy processes as design decisions have a significant influence on the economics. A relevant challenge for global flowsheet optimization is the incorporation of accurate thermodynamic models. A promising alternative to conventional thermodynamic property models is the integration of data-driven surrogate models into mechanistic process models and deterministic global optimization in a reduced space. In our previous works, we trained artificial neural networks (ANNs) on thermodynamic data and included the surrogate models in the global flowsheet optimization of subcritical organic Rankine cycles (ORC). In this work, we extend the framework to the optimization of transcritical ORCs operating at a supercritical high pressure level and subcritical low pressure level. We train separate ANNs for supercritical and subcritical thermodynamic properties. ANNs with a small number of neurons can learn the thermodynamic properties to sufficient accuracy. We identify the optimal working fluid among 122 available fluids in the thermodynamic library CoolProp via a deterministic global optimization of the hybrid process model using the solver MAiNGO. The results show that the process can be optimized efficiently and that transcritical operation can enable high power generation.

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.

The performance of an organic Rankine cycle (ORC) relies on process design and operation. Simultaneous optimization of design and operation for a range of working fluids (WFs) is therefore a promising approach for WF selection. For this, deterministic global process optimization can guarantee to identify a global optimum, in contrast to local or stochastic global solution approaches. However, providing accurate thermodynamic models for a large number of WFs while maintaining computational tractability of the resulting optimization problems are open research questions. We integrate accurate thermodynamic and transport properties via artificial neural networks (ANNs) and solve the design problems with MAiNGO in a reduced-space formulation. We illustrate the approach for an ORC process for waste heat recovery of a diesel truck. After an automated preselection of 122 WFs, ANNs are automatically trained for the 37 selected WFs based on data retrieved from the thermodynamic library CoolProp. Then, we perform deterministic global optimization of design and operation for every WF individually. Therein, the trade-off between net power generation and investment cost is investigated by multiobjective optimization. Further, a thermoeconomic optimization finds a compromise between both objectives. The results show that, for the given conditions, monoaromatic hydrocarbons are a promising group of WFs. In future work, the proposed method and the trained ANNs can be applied to the design of a variety of energy processes.

Numerical optimization is very useful for design and operation of energy processes. As the design has a major impact on the economics of the system, it is desirable to find a global optimum in the presence of local optima. So far, deterministic global optimization with detailed thermodynamic models incorporated has been limited to single fluid energy systems. We extend our previously presented approach [Schweidtmann et int Mitsos, COMPUT CHEM ENG (2019)] from single-species working fluids to binary mixtures with variable composition. First, we create accurate thermodynamic data for two selected binary mixtures using a thermodynamic library. Using this data, we train artificial neural networks, select them based on desired accuracy, and include them in the process model. The resulting hybrid model is then optimized with the open-source solver MAiNGO. We perform thermodynamic optimizations of geothermal power plants, considering both organic Rankine and Kalina cycle. For each cycle, we identify the globally optimal design, operation, and working fluid composition for the selected binary fluid mixtures within tractable CPU times. We show how a second mixture component enables improved ORC performance.

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.

Deterministic global optimization of process flowsheets has so far mostly been limited to simplified thermodynamic models. Herein, we demonstrate a way to integrate accurate thermodynamic models for the optimal process design of an organic Rankine cycle (ORC) via the use of artificial neural networks (ANNs). We generate training data using the thermodynamic library Coolprop and learn thermodynamic properties. The ANNs are subsequently embedded in the process design optimization problem in a reduced-space, which is solved to global optimality using our in-house optimization software MAiNGO. The importance of accurate thermodynamics is illustrated for the design of an ORC for geothermal power generation. We show that the use of an accurate thermodynamic model leads to different design decisions in comparison to a simplified model. Furthermore, we investigate the influence of the network architecture and complexity on accuracy, optimization results and computational performance.

beta version is available open-source works well for problems formulated in reduced space runs on parallel computing can be extended to the user's needs can be used as general-purpose solver.

We recently demonstrated the potential of deterministic global optimization in a reduced-space formulation for flowsheet optimization. However, the consideration of implicit unit operations such as flash calculations is still challenging and the solution of complex flowsheets incorporating such operations can be intractable. We show that the solution of flash equations can be integrated in global optimization via artificial neural networks (ANNs). Thus, flash calculations are no longer performed within the flowsheet optimization. Instead, flash equations are solved offline and then learned using ANNs. ANNs have been used successfully in the literature to learn flash equilibria but have not yet been included in deterministic global optimization for this task. We embed the ANNs in a hybrid model and use deterministic global optimization to solve it. In addition, we utilize deterministic global optimization to calculate a guaranteed worst-case accuracy of ANNs compared to a rigorous model. We demonstrate the proposed approach on an illustrative five-component vapor-liquid equilibrium flash using our in-house solver MAiNGO.