To path indicator Subpages of “Research“ To navigation To quick access To footer with other services
To content
Logo des Lehrstuhls Reaction Engineering and Catalysis (REC)
Department Biochemical and Chemical Engineering
A metal device in a laboratory with various other devices. © Roland Baege​/​TU Dortmund

Model-Based Design of Optimal Reactors

Principal Investigator: Hannsjörg Freund

Researchers: Elodia Morales, Lutz Vogel-Lackenberg, Mathias Waldner

One of the main research focuses of the Chair of “Reaction Engineering and Catalysis” is the development of optimal catalytic reactors for implementing highly efficient chemical processes. The goal of this optimization is to achieve the highest possible yield of the desired product while minimizing energy and resource consumption. To achieve this, we utilize the Multi-Level Reactor Design (MLRD) concept developed by our group. This concept can be divided into four levels.

The reactor design framework based on the optimizations performed. Level 0 involves determining the reaction kinetics. Level 1 involves determining the optimal reaction pathway. Level 2 involves the optimal reactor design. Level 3 involves the reactor design, taking technical feasibility into account. © M. Kaiser ​/​ FAU
Illustration of the step-by-step process and the respective results of the optimizations performed at each level in Multi-Level Reactor Design (MLRD).

A prerequisite for model-based reactor design using MLRD is the description of the reactions taking place through a reaction kinetics model. Since this is a crucial first step, a separate area of research (reaction kinetics: experiments, network analysis, and modeling) is dedicated to this topic. Once a model with an adequate level of detail has been established to describe the actual reaction network, the process of identifying and analyzing the ideal reaction pathway in detail begins (Level 1).

To make it easier to understand, the MLRD concept will be illustrated using a simple, concrete example: the oxidation of sulfur dioxide (SO₂) to sulfur trioxide (SO₃). This reaction is a crucial step in the production of sulfuric acid using the double-contact process. At Level 1, the ideal reaction path up to a desired conversion is considered. The goal here is to minimize the reaction time required for this, so the aim is to achieve the highest possible reaction rate. According to Arrhenius, a high temperature is required for this. However, since the oxidation of SO₂ is an exothermic equilibrium reaction, the temperature must not be set too high to avoid limitations caused by an unfavorable equilibrium state. Thus, there is an optimal temperature at which the reaction should be carried out. This optimal reaction pathway is shown in the following diagram.

The figure shows a reaction rate (y-axis) versus temperature (x-axis) plot for the SO₂ oxidation reaction. The equilibrium position and the optimal reaction pathway are plotted on this graph. Additionally, the reaction rate profile in a technical adiabatic batch reactor is shown.
The first level (Level 1) of the MLRD methodology, using SO₂ oxidation as an example. Here, the optimal reaction process is determined. In addition, the reaction process is shown in simplified form in a technically adiabatic batch reactor with intermediate cooling.
The figure shows a reaction rate (y-axis) versus temperature (x-axis) plot for the SO₂ oxidation reaction. The equilibrium position and the optimal reaction pathway are plotted on this graph. In addition, the reaction rate curve is plotted, taking into account mass transfer phenomena with several residence times.
The second level (Level 2) of the MLRD methodology, using SO₂ oxidation as an example. At this level, transport processes are taken into account, which limits the maximum reaction rate under certain conditions.
The figure shows a reaction rate (y-axis) versus temperature (x-axis) plot for the SO₂ oxidation reaction. The equilibrium position and the optimal reaction pathway are plotted on this graph. Additionally, the reaction rate curve for a reactor subject to the limitations of a technical implementation is shown.
The third level (Level 3) of the MLRD methodology, using SO₂ oxidation as an example. Here, options for technical implementation are considered, and a specific reactor configuration is selected and optimized.

In addition to the ideal reaction path, the diagram for Level 1 shows the current state of the art in adiabatic batch reactors. The optimal reaction path is determined based on the assumption of unrestricted heat and mass transfer within the reactor. In reality, however, mass transfer limitations occur - particularly at high temperatures - which are taken into account at Level 2 of the MLRD methodology. At this stage, initial idealized reactor concepts are also incorporated into the analysis. The resulting reaction pathway deviates significantly from the optimal reaction pathway at high temperatures and low conversion rates.

In the final step (Level 3), the technical feasibility of the developed optimal reactor concept is determined. Here, the heat and mass transfer processes in the reactor - which, in reality, proceed at only finite rates due to technical constraints - as well as optimized temperature control play a decisive role. At this stage, various operating concepts are examined, and technically feasible control strategies are considered. The result is the optimal reaction control within the limits of technical feasibility.

The simple example presented here serves merely as an illustrative explanation. The MLRD methodology has been expanded over the past few years to include many substantial aspects and application possibilities. Thus, MLRD is equally applicable to highly complex reaction networks with up to approximately 70 reactions. Especially for such complex systems, the optimal solution is often highly counterintuitive and can no longer be predicted using heuristics.
 

Other successful applications of the MLRD methodology:

In addition, the optimization can also be performed using two-dimensional reactor models, provided that this is required due to strong radial gradients or is necessary for a better understanding of the results. Life-cycle optimization has also already been performed, in which the optimization takes into account the entire service life of a catalyst that deactivates over time. Conversely, this approach can also be used to optimize the service life of the catalyst and to compare different catalysts in terms of their service life.

Modeling Catalyst Deactivation
Modeling Catalyst Deactivation
Darstellung der Temperatur entlang der Reaktorachse bei unterschiedlichen Lastwechseln
Auftragung der Temperatur entlang der Reaktorachse bei unterschiedlichen Lastwechseln

Other successful applications of the MLRD methodology include the optimization of dynamically operated reactors, optimization under uncertainty, multi-objective optimization, the incorporation of rigorous diffusion models, and, in this context, the generalized consideration of the catalyst pellet for the integrated optimal design of the entire catalyst-reactor system.

Illustration of the Optimization Cycle Under Uncertainty © J. Maußner ​/​ FAU
Optimization Under Uncertainty

An additional extension involves the treatment of multiphase systems. The simpler case of rapid mass transfer between the phases can be considered analogously to the single-phase case (where the second phase serves merely as a reservoir). If, on the other hand, mass transfer limitations exist in the system, both phases must be explicitly taken into account in the modeling. In this context, the applicability and potential of the MLRD methodology for optimizing reactive separation devices were impressively demonstrated using the example of optimizing a chemical absorber.