Continuum approximation of large reaction mixtures in reactors with backmixing

The growing need to produce ultraclean fuels from hydrocarbon mixtures such as petroleum fractions and residues has put increasing pressure on refiners to achieve deep conversions. It is imperative to be able to predict the behavior of such mixtures at high conversions as functions of their properties and reactor type. To this end, treating the reaction mixture as a continuum greatly simplifies the analysis and modeling of the conversion process. However, the continuum approximation can become invalid at very high conversions. Previously, we examined the validity of the approximation for various reactions in plug flow reactors. The validity conditions for first‐order reaction mixtures in reactors with different mixing intensities are developed. In general, backmixing widens the range of validity. In certain cases, the continuum approximation is valid at arbitrarily high conversions. © 2014 American Institute of Chemical Engineers AIChE J, 61: 159–165, 2015