Prediction of axial dispersion in plug-flow reactors using a simple method

In most full-scale plug-flow reactors, the flow usually is nonideal because of entrance and exit flow disturbances and axial dispersion. Axial dispersion refers to the degree of back mixing and molecular diffusion of fluid elements in the process stream in the axial direction. In this article, an analytical solution is developed for plug flow reactors with dispersion numbers varying from complete-mix (infinity dispersion) to ideal plug-flow reactors (zero dispersion) to facilitate the design of treatment processes such as stabilization ponds and using first-order removal kinetics. An attempt has been made to formulate a simple-to-use method which is easier than existing approaches, less complicated with fewer computations, for accurate and rapid estimation of effluent and influent concentration ratios in plug flow reactor (percentage remaining) as a function of plug flow dispersion factor (from zero to infinity), first-order reaction constant and hydraulic detention time. The average absolute deviations between the reported data and the proposed correlations are found to be less than 1.8% demonstrating the excellent performance of proposed tool. The tool developed in this study can be of immense practical value for engineers and scientists to have a quick check on the percentage remaining in plug flow reactors at various conditions. In particular, process engineers would find the predictive tool to be user-friendly with transparent calculations involving no complex expressions.