Optimal Control of the Sabatier Process in Microchannel Reactors

TL;DR

The paper tackles PDE-constrained optimization of a Sabatier microchannel reactor by coupling a 3D reacting-flow model with a computationally efficient 1D reduction. It uses parameter identification against experimental data to calibrate kinetic constants and validates the 1D model against the 3D reference with relative errors below 1%. Two optimization problems are solved: maximizing outlet CO2 conversion with wall-temperature control at fixed flow, and maximizing mass throughput under a state constraint with variable flow and wall temperature, both demonstrating substantial yield improvements. The work provides a practical computational framework via cashocs for adjoint-based optimization and offers insights into temperature profiling and flow management for improved reactor performance, with plans to extend to more detailed kinetics and larger networks.

Abstract

We consider the optimization of a chemical microchannel reactor by means of PDE constrained optimization techniques, using the example of the Sabatier reaction. To model the chemically reacting flow in the microchannels, we introduce a three- and a one-dimensional model. As these are given by strongly coupled and highly nonlinear systems of partial differential equations (PDEs), we present our software package cashocs which implements the adjoint approach and facilitates the numerical solution of the subsequent optimization problems. We solve a parameter identification problem numerically to determine necessary kinetic parameters for the models from experimental data given in the literature. The obtained results show excellent agreement to the measurements. Finally, we present two optimization problems for optimizing the reactor's product yield. First, we use a tracking-type cost functional to maximize the reactant conversion, keep the flow rate of the reactor fixed, and use its wall temperature as optimization variable. Second, we consider the wall temperature and the inlet gas velocity as optimization variables, use an objective functional for maximizing the flow rate in the reactor, and ensure the quality of the product by means of a state constraint. The results obtained from solving these problems numerically show great potential for improving the design of the microreactor.

Figures (7)

• Figure 1: Schematic of the problem setting with inlet part $\Omega^\text{in}$ (blue) and catalytic reaction part $\Omega^\text{reac}$ (orange).
• Figure 2: Properties of the Sabatier reaction for stoichiometric inlet conditions.
• Figure 3: History of the numerical optimization.
• Figure 4: Simulated and measured CO2 conversion for the experiments from Engelbrecht2017CarbonEngelbrecht2017Experimentation.
• Figure 5: Relative errors between the 1D and 3D model.