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The effect of recycle on a linear reactor
Author(s) -
Schmeal W. R.,
Amundson Neal R.
Publication year - 1966
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690120628
Subject(s) - eigenfunction , eigenvalues and eigenvectors , dispersion (optics) , péclet number , fourier series , operator (biology) , fourier transform , mathematical analysis , boundary value problem , mathematics , function (biology) , isothermal process , mechanics , chemistry , physics , thermodynamics , optics , quantum mechanics , biochemistry , repressor , transcription factor , gene , evolutionary biology , biology
The theoretical transient behavior of an isothermal packed bed or tubular reactor with direct recycle is investigated. It is shown that the recycle effect, coupled with the phenomenon of axial dispersion, causes waves in the reactant concentration to travel through the bed when the feed concentration undergoes a step change. The waves have a length almost equal to the bed length and they travel with the velocity of the fluid. The behavior of the waves is very insensitive to the value of the Peclet number. The pertinent linear differential equation is solved by the method of generalized Fourier transforms and the boundary conditions are such that the Sturm‐Liouville theorem cannot be used. The operator is nonself‐adjoint and the eigenfunctions are not mutually orthogonal. The eigenvalues, which are complex, are found by means of the argument principle. Sample calculations are presented of the first one hundred terms of the Fourier expansion of a solution function and this is compared to a simplified approximate series which is developed.