(184f) Systematic Analysis, Design and Optimization of Heterogeneously Catalyzed Gas Phase Reaction Processes

In order to determine the optimal reaction conditions of a process, most often heuristics, attainable region approaches or rigorous optimization methods are applied. One of the most successful methods for solving the reactor synthesis problem is the rigorous optimization of a reactor superstructure. However, the obtained networks consist usually of several connected ideal standard reactors, such as CSTR and PFTR. Due to the large number of reactors required to build such networks, the obtained solutions can hardly be realized in practice. In addition, not all process intensification measures such as the distributed dosing of a reactant, increasing the area for heat transfer or the interface area in a multiphase reaction systems can be investigated easily with the aforementioned methods.

In this contribution, we propose a new methodology for the analysis, design and optimization of chemical reactors. This approach is not based on the use of standard reactors. It is intended for the investigation of all kind of process intensification measures, for example to obtain an optimal temperature profile in the reactor.

The method is a multi-level approach. On the first level, the investigation is based on tracking a fluid element on its way through the process [1]. The state of the fluid element at the reactor inlet is fixed. At the reactor outlet specific states are constrained and measures for the reactor performance, such as the conversion, are enforced. The task is to find the optimal way of the fluid element with respect to a certain objective, such as minimum residence time or maximum selectivity. In order to optimize the process route, certain process variables, which are taken to be variable over time, are optimized. Hence, the fluid element is optimally manipulated at every time along its path through the reactor. On this level of the proposed methodology, only system inherent limitations, for example constraints which are imposed by the catalyst, are considered. Technical limitations due to the reactor design are not yet included in the model. This gives rise to the maximum potential, which can be obtained by controlling the investigated process variable. In terms of process intensification, the effect of several measures such as perfect heat control using a microreactor or distributing a reactant over the reactor length can be investigated without extensive modeling of all technical constraints.

On the next level of the proposed method, the model is converted to a reactor model with ideal flow field (no backmixing) and technical limitations for heat and mass transfer are considered. By comparing the different optimization levels the loss in the objective by these technical limitations can be quantified.

For every level, a dynamic optimization problem has to be solved to obtain the optimal process route. The balance equations of the problem are discretized to yield a large scale NLP problem. This problem is solved using state-of-the-art NLP solvers, such as IPOPT and CONOPT. It consists of equality and inequality constraints as well as initial and final conditions. The equality constraints are the discretized balance equations and the kinetic expressions for the reaction rate and for the heat and mass transport. Technical limitations impose most often additional inequality constraints.

In order to illustrate this method, the heterogeneously catalyzed gas phase oxidation of SO₂ to SO₃ is investigated. Sulfur trioxide is one of the major bulk chemicals and is being used to produce sulfuric acid. For the intensification of the SO₂-oxidation process the energy efficiency and the reduction of investment costs are the most important aspects.

Considering this example, several variables affecting the reaction rate can be identified. In this reaction system, the reaction temperature is the most important variable, but other variables such as the partial pressure of SO₂ and O₂ are also important. In order to control the fluid temperature at every point in the reactor, the heat flux must be adjusted locally. This can be achieved by manipulating the local values of the heat transfer area, the heat transfer coefficient or the temperature difference between cooling media and fluid. One or more of these variables must be adjusted along the reactor to obtain the optimal heat flux at every point. For example, the heat exchange area can be changed locally be using a non-conventional reactor design. A non-uniform coolant temperature can be obtained by changing the cooling strategy from a constant cooling temperature, e.g. by using a boiling liquid as coolant, to a counter-current cooling strategy. By dividing the reactor into a few segments and applying different coolant strategies in each segment almost every temperature profile can be achieved in the reactor. In such a way, the optimal temperature profile, which is calculated by solving the dynamic optimization problems, can be approximated. Of course, this approach is not limited to optimizing the temperature profile, but can also be used for other process intensification measures. It yields the optimal process route with respect to the investigated objective and control variables as a benchmark for any technical approximation. In addition, the obtained profiles indicate how the optimal reactor must be designed.

To sum up, the described framework for the analysis, design and optimization of chemical reaction processes is very well suited to determine the quantitative effect of different process intensification measures. The multi-level approach yields the optimal reaction route as well as the influence of technical limitations. On the basis of the optimal route, new reactor concepts for smaller and more intelligent apparatuses can be derived.

Literature:

[1] Freund, H.; Sundmacher, K.; Chem. Eng. Process., 2008, 47(12), 2051.