Determination of Kinetic Parameters in Laminar Flow Reactors. I. Theoretical Aspects

Summary This article describes the development of a numerical tool for the simulation, the estimation of parameters and the systematic experimental design optimization of chemical flow reactors. The goal is the reliable determination of unknown kinetic parameters of elementary reactions from measurements in a wide range of (laminar) flow conditions, from low to high temperature and from low to high pressure. The corresponding experiments have been set-up in the physical-chemistry group of J. Wolfrum at the PCI, Heidelberg; see the article Hanf/Volpp/Wolfrum [24] in this volume. The underlying mathematical model is the full set of the compressible Navier-Stokes equations accompanied by the balance equations for the chemical species. This system is discretized by a finite element method with mesh adaptivity driven by duality-based a posteriori error estimates (‘DWR method’); see the article Becker et al. [12] in this volume. The parameter estimation uses the Lagrangian formalism by which the problem is reformulated as a nonlinear saddle-point boundary value problem which is solved on the discrete level by the Newton or Gauß-Newton method. The contents of this article is as follows: Introduction Mathematical model Numerical approach The low-temperature flow reactor The high-temperature flow reactor A step towards optimal experimental design Conclusion and outlook References Appendix