  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.
