A magnetic thermometric method is used to determine cross-sectional average axial catalyst temperature profiles for superparamagnetic neckel catalyst beds during ethane hydrogenolysis, an exothermic reaction. Each solid temperature profile is determined from an axial profile of cross-sectional average magnetization and is represented by a polynomial. In turn, each magnetization profile is determined from voltage data obtained as the bed is moved through an AC permeameter. A Fredholm equation of the first kind, “regularized” using a minimum variance constraint, is inverted to determine the magnetization profile.
The determination of the axial temperature profile for a reactor operating at 11.0% conversion is detailed. It provides a good test of the method used. Some limitations of the method are highlighted by attempts to analyze data from a reactor operating at complete conversion. The potential for model parameter estimation is discussed.