Simple Reaction with Segregation in a Batch Reactor

Consider a simple chemical reaction in a batch reactor. The reaction rate in terms of the intensity of mixing, , is given by: , where and are the instantaneous concentrations, and are the mean concentrations, and and are the initial concentrations of species and . The governing equation is the following:
.
This equation can be written in dimensionless form as:
, where is the initial concentration ratio, is the dimensionless time, is the mixing time, is the dimensionless concentration, is the Damköhler number (a dimensionless number that is a measure of the reaction time versus mixing time), and is the degree of segregation.
This Demonstration displays the dimensionless concentration versus the dimensionless time for various values of the Damköhler number and the initial concentration ratio. It is straightforward to see that the steady-state dimensionless concentration is independent of the Damköhler number. The Damköhler number has an influence only on how fast this steady-state dimensionless concentration is reached. This steady-state dimensionless concentration is equal to When , there is an analytical expression for the dimensionless concentration, which is given by:
, with .

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J. Ingham, I. J. Dunn, E. Heinzle, and J. E. Prenosil, Chemical Engineering Dynamics, 2nd ed., Weinheim, Germany: Wiley-VCH, 2000 pp. 450–451.
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