R2Chem: Renewables-to-Chemicals Process Networks
To reduce the CO2 emissions in process and energy supply industries, the massive use of renewable energy and the substitution of fossil-based feedstocks implementing efficient Renewables-to-Chemicals (R2Chem) conversion systems is essential. Due to the variety of feedstocks and process technologies, there are several potential pathways for converting renewable energy into valuable target products.
To avoid binary decision variables, we introduce in  an elegant problem formulation in terms of continuous process scope variables, with the overall approach visualised in Fig. 1. All constraints (equalities, inequalities), as well as the objective function, are formulated as linear expressions in terms of the (purely continuous) decision variables, namely the fluxes of mass, energy, heat, and work as well as the extent variables [2-3]. The objective function contains the Total Annualized Costs (TAC) and penalty terms for direct and indirect CO2 emissions.
For the target product methanol, we have shown that a good compromise between production cost and emissions is achieved by using natural gas or biogas as a feedstock source. The compromise is particularly good when the required energy comes from renewable sources. Net consumption of CO2 by the overall production system is possible if renewable energy sources are exploited while using CO2 as a feedstock source at the same time. When using fossil fuels, a unfavourable CO2 balance is unavoidable due to the high indirect CO2 emissions. The high indirect CO2 emissions are caused by the energy supply, such as electricity and heat. In addition to the economic challenges of using CO2 as a feedstock, the environmental impact depends on the energy source used. The main advantage of the proposed methodology is the ability to quickly determine an optimal process system within a superstructure in which many alternative process configurations are embedded. So far, the method has been used for optimizing process systems for the production of methanol  and formic acid . In addition, we have extended our network approach to the level of a single process as well as to individual process units . This approach allows detailed process design and more precise estimation of entropy production inside each process and process unit.
More recently, the continuous process extent network formulation was extended by adding a linear heat-integration model to serve as the basis for the so-called FluxMax approach [6,7]. The idea behind the FluxMax approach is to decouple the non-linearities of chemical potential calculations (e.g. enthalpy, entropy) from the optimization problem. The decoupling is done by discretizing the thermodynamic state space and calculating the potentials in these discrete points a priori. These discrete points are connected by linear reaction-extent-based elementary process functions, which lead to a convex network flow optimization problem. With such a formulation, process design and heat integration can be considered parallel, leading to new, unintuitive process configurations, as exemplified on the energy-optimal methanol production process design  and the production of hydrogen cyanide .
Further study into the methanol production pathway, as one of the main target molecules, demonstrated the flexibility of the FluxMax approach in its application for distillation unit design . The extra degrees of freedom introduced by the FluxMax, compared to the conventional distillation column design equations (MESH), allowed identifying energy-optimal methanol/water distillation column designs by adding extra inter-stage heat transfer area as an option to reduce the energy consumption of the column.
Since June 2021, the PSE Group contributes to the BMBF-funded project PtX-Wind which is part of H2Mare. In PtX-Wind, the offshore generation of Power-to-X (PtX) products, namely methane, methanol, ammonia, and Fischer-Tropsch products, are under research. For this case, it is necessary to evaluate the overall process chains from generating green hydrogen via electrolysis and capturing the required feedstocks to the refinement of the target products.
In the scope of the BMBF project, the PSE Group is cooperating with other project partners on the development of a process control system, particularly on the creation of a digital twin (Fig. 2). With the help of the digital twin, information about individual PtX process steps and the entire plant network can be gained before a physical offshore plant will exist. In that light, the PSE Group will contribute its expertise in modelling, simulation, and optimization using different tools, including mechanistic modelling, data-driven methods and hybrid modelling.
Further information about the project PtX-Wind can be found on the webpage of the Wasserstoff-Leitprojekte .
 Schack, D., Rihko-Struckmann, L., & Sundmacher, K. (2018). Linear programming approach for structure optimization of Renewables-to-Chemicals (R2Chem) production networks. Industrial & Engineering Chemistry Research, 57(30), 9889-9902.
 Schack, D., Rihko-Struckmann, L., & Sundmacher, K. (2016). Structure optimization of Power-to-Chemicals (P2C) networks by linear programming for the economic utilization of renewable surplus energy. In: 26th European Symposium on Computer Aided Process Engineering, pp. 1551-1556.
 Schack, D., Rihko-Struckmann, L., & Sundmacher, K. (2017). Economic linear objective function approach for structure optimization of Renewables-to-Chemicals (R2Chem) networks. In: 27th European Symposium on Computer Aided Process Engineering, pp. 1975-1980.
 Schack, D., & Sundmacher, K. (2018). Techno-ökonomische Optimierung des Produktionsnetzwerkes für die Synthese von Ameisensäure aus erneuerbaren Ressourcen. Chemie-Ingenieur-Technik, 90(1-2), 256-266.
 Liesche, G., Schack, D., Rätze, K.H.G., & Sundmacher, K. (2018). Thermodynamic network flow approach for chemical process synthesis. In: 28th European Symposium on Computer Aided Process Engineering, pp. 881-886.
 Schack, D., Liesche, G., & Sundmacher, K. (2020) The FluxMax approach: Simultaneous flux optimization and heat integration by discretization of the thermodynamic state space illustrated on methanol synthesis process. Chemical Engineering Science 215, 115382
 Liesche, G., Schack, D., & Sundmacher, K. (2019) The FluxMax approach for simultaneous process synthesis and heat integration: Production of hydrogen cyanide. AIChE Journal 65(7), e16554
 Schack D., Jastram A., Liesche G., Sundmacher K. (2020) Energy-Efficient Distillation Processes by Additional Heat Transfer Derived from the FluxMax Approach. Front. Energy Res. 8,134
 Bundesministerium für Bildung und Forschung. Wie Partner im Leitprojekt H2Mare Wasserstoff direkt auf hoher See produzieren wollen [Online]. Available at: https://www.wasserstoff-leitprojekte.de/leitprojekte/h2mare (Accessed: 02 November 2021)