Elementary Process Functions (EPF) Methodology
State-of-the-art methods for chemical process design are based on (1) experience and model-supported heuristics, both of which are easy to apply and that lead to reasonable results for systems that are not too complex; (2) attainable region concepts, which typically make use of predefined ideal reactors to find an optimal reactor network, but are hard to apply to processes with integrated recycles; (3) rigorous optimization methods, in which either superstructures of units are optimized, requiring the solution of an MINLP problem, or dynamic programming approaches from which optimal temperature and concentration profiles along the reaction coordinate can be found. The main drawbacks of approaches (1) and (2) are the use of predefined process units and the difficulties in designing process systems with recycle loops. They are mostly used to design single-phase systems and select devices from a predefined set of solutions. In recent years, rigorous optimization methods have gained in popularity compared to other approaches. As a consequence, the superstructure optimization approach was applied to both homogeneous and multiphase systems. In contrast, the dynamic optimization approaches developed so far have not been used to derive optimal designs for devices or curtail the optimal design in advance.
In 2008, the PSE group proposed a novel approach, the Elementary Process Functions (EPF) methodology, for the optimal design of chemical production processes, illustrated in Figure 1 below. In its original form, the EPF approach is based on the idea that in each chemical process Lagrangian matter elements are manipulated along their travel route through the process by the action of mass, energy, and momentum fluxes. In terms of the process hierarchy, the consideration of matter elements is linked to the phase level. At this level, independent of specific devices or unit operations, we are able to determine an ideal process route via dynamic optimization at unlimited fluxes but with predefined system-inherent constraints, provided that we have access to adequate knowledge about the reaction kinetics. Then, on the process unit level the ideal process route is approximated by the application of a combination of existing devices or new tailor-made equipment. In the EPF methodology, this is achieved in a three-step procedure resulting in possible reactor candidates, operated either in semi-batch or continuous mode.
In recent years, we have extended the EPF process design concept in four main directions. On the Process Unit Level, a probabilistic approach was introduced to quantify the influence of parameter uncertainties on the process design and to increase robustness of optimal design solutions . Furthermore, alternative, indirect optimization approaches based on Pontryagin’s Minimum Principle (PMP) were investigated for process control. By presenting a remedy for its shortcomings for (path-)constrained problems, the PMP approach was successfully applied to semi-batch reactors indicating high computational efficiency . The application of parsimonious parameterization of the control variables  and its combination with Nonlinear Model Predictive Control (NMPC) of semi-batch reactors [4, 5] enables PMP to be a viable alternative to direct approaches.
For systematically deriving reactor network candidates while taking into account (back-)mixing characteristics, process wide recycling, and dosing of substrates, the Flux Profile Analysis was developed. By analyzing the optimal mass and energy control fluxes of a dynamic optimization of a (semi-)batch process, reactor-network candidates can be synthesized, bridging the conceptual gap between dynamic optimization of batch reactors and the superstructure-based synthesis of continuously operated reactor networks [6, 7].
An alternative view of the EPF methodology is presented in the FluxMax approach where a thermodynamic network flow problem is formulated as a directed graph containing discrete thermodynamic state nodes, elementary process nodes, and utility nodes [8, 9]. The calculation of the thermodynamic potentials (enthalpy, entropy, Gibbs energy) of the state nodes is decoupled from the solution of the network flow optimization problem, leading to a convex solution space and a globally optimal process design solution in the case of a convex (or convexified) objective function. An advantage of the FluxMax approach is its versatility and applicability across different lengthscales. The proof-of-concept for this approach was provided for the reactor and compressor cascade design of methanol synthesis at the Process Unit Level  and for the production of hydrogen cyanide at the Plant Level .In addition, its usefulness was shown also for the site-optimal production of methanol at the Production System Level .
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 Aydin, E., Bonvin, D., and Sundmacher, K. (2018) NMPC using Pontryagin’s Minimum Principle-Application to a two-phase semi-batch hydroformylation reactor under uncertainty. Computers & Chemical Engineering. 108 47–56.
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 Kaiser, N.M., Jokiel, M., McBride, K., Flassig, R.J., and Sundmacher, K. (2017) Optimal Reactor Design via Flux Profile Analysis for an Integrated Hydroformylation Process. Industrial & Engineering Chemistry Research. 56 (40), 11507–11518.
 Liesche, G., Schack, D., & Sundmacher, K., (2018). The FluxMax approach for simultaneous process synthesis and heat integration: Production of hydrogen cyanide. AIChE Journal, under review.
 Liesche, G., Schack, D., Rätze, K.H.G., & Sundmacher, K. (2018). Thermodynamic network flow approach for chemical process synthesis. In: 28 th European Symposium on Computer Aided Process Engineering , 881-886.
 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.