Temperature distribution in a chemical reactor

Abstract

A chemical reactor has 1250 sections and it is possible to calculate a theoretical temperature for each section. These have a distribution across sections with mean 452 °C and standard deviation 22 °C; the distribution is closely approximated by a normal distribution in the range 390–520 °C. For a variety of reasons, measured temperatures depart from the theoretical ones, the discrepancies being partly random and partly systematic. The temperature is measured in 20 sections and Table D.1 gives the measurements and the corresponding theoretical values. It is known further that the measured temperature in a section deviates from the ‘true’ temperature by a completely random error of measurement of zero mean and standard deviation 3 °C. Special interest attaches to the number of channels in the reactor with `true’ temperature above 490 °C.

Fictitious data based on a real investigation.