A magnetic thermometric method is used to determine cross-sectional average axial catalyst temperature profiles for superparamagnetic nickel 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.
A modified Hartshorn inductance bridge is used to follow changes in the magnetization of superparamagnetic samples in order to determine their average temperature. The thermometry is performed in the temperature range of 475–525 K. During routine experiments, the rms noise voltage in the bridge is approximately 300 nV when the primary coil is excited by a 200 mA rms current at a frequency of 47 Hz. This corresponds to a signal-to-noise ratio of 3000 and a temperature sensitivity of 0.015 K for typical samples studied.
Map algebras are used for the manipulation of spatial data and form the basis for many types of spatial analyses and modeling efforts. The most basic form of a map algebra applies the same function (e.g., addition, subtraction) across the study area. To account for local variation of modeling parameters, we present a spatially dynamic map algebra to demonstrate the need for and utility of algebraic functions where the function is determined based on a specific and relative location. The need for such an algebra comes from the growth of complex models where the values of variables or parameters are not fixed across space. Locally derived parameters are not new, as shown by geographically weighted regression. This type of algebra is needed in cases of complex models, such as those found in flow networks, where network dynamics vary across space. This includes hydrologic processes, movement of people and goods, and the transmission of ideas. We test the approach on a case study of nitrogen flow in the Niantic River watershed, Connecticut. Findings show that the results from a spatially dynamic map algebra can differ from a fixed function. Fixed functions can result in model outputs that under‐ or overestimate by up to 50%.
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