9459

Concentration and Temperature Profiles in an Axially Dispersed Adiabatic Tubular Reactor

This Demonstration computes the concentration and temperature profiles in a tubular reactor for low Péclet numbers ( using the shooting method (blue solid curve), as well as the orthogonal collocation method with shifted Legendre polynomials and eight internal collocation points (the red dots). Perfect agreement is obtained (see the first two snapshots).
For large values of the number, the reactor behavior approaches that of a plug flow reactor (PFR), and in the limit as , the system become singular. Consequently the boundary value problem becomes increasingly stiff with increasing . For , the shooting method fails to converge. Thus for , only orthogonal collocation results are shown (see red dots). To assess the accuracy of the collocation method, we computed the residual error for the temperature and concentration profiles. The residual error is shown in the plots; it measures how closely the solution satisfies the ordinary differential equations and boundary conditions. We also compared our results with data taken from [1] at (blue circles), as can be seen in the last two snapshots. The concentration profile is in good agreement with [1], but our temperature profile is at best only in qualitative agreement.

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DETAILS

An axially dispersed, adiabatic tubular reactor obeys the following dimensionless mass and energy balance equations:
,
.
This is an example of a split-boundary value problem (BVP) with:
at ,
at ,
at ,
at .
Assume that the dimensionless heat of reaction is equal to and that the reaction rate is given by: .
is a dimensionless group analogous to the axial Péclet number () for the energy balance. In the present Demonstration, we take , for simplicity and in order to compare with data given in [1].
Reference
[1] M. E. Davis and R. J. Davis, Fundamentals of Chemical Reaction Engineering, New York: McGraw–Hill, 2003.
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