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Approximation methods to evaluate the effect of axial dispersion in isothermal flow reactors
Author(s) -
Houghton Gerald
Publication year - 1962
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450400503
Subject(s) - taylor dispersion , dimensionless quantity , isothermal process , nonlinear system , dispersion (optics) , taylor series , chemistry , differential equation , perturbation (astronomy) , mathematical analysis , boundary value problem , thermodynamics , mechanics , diffusion , mathematics , physics , quantum mechanics , optics
Two quasi‐analytical methods are given for the approximate solution of the nonlinear differential equation governing the effect of longitudinal dispersion on the concentration profile in an isothermal flow reactor with reaction orders other than zero or first. The first method converts the nonlinear differential equation and its boundary conditions into a nonlinear integral equation which is solved by iteration, while the second method generates approximate solutions by considering axial dispersion as a perturbation on the reaction kinetics. By using the perturbation method a dimensionless group has been generated that is characteristic of the interaction between axial diffusion and reaction kinetics. It is also demonstrated that an axial dispersion coefficient characteristic of Taylor diffusion can be applied in the presence of a reaction of any order and that the effect of depletion of concentration by chemical reaction is to aid in the reduction of radial concentration gradients.