In-situ measurement of permittivity distributions in reactors by cavity perturbation

The microwave cavity perturbation method is widely used for material parameter measurements in connection with small homogeneous samples. Its applicability to larger and inhomogeneous samples is uncertain, but highly desirable in connection with the in-situ condition monitoring of chemical reactors. We have investigated the problem of the reconstruction of axially inhomogeneous permittivity distributions in tubular reactors from measured cavity resonance frequencies of the reactor. It is shown that the use of a priori knowledge about the function class of the permittivity distribution, which in turn follows from assumptions about the chemical process inside the reactor, allows one to reconstruct the permittivity distribution based on a few resonances only. The resulting errors in the function parameters or in the permittivity values identified are on the order of 5%, as demonstrated by analytical and numerical calculations, by numerical experiments, and by laboratory experiments.