Scale Models of Packed Tubular Reactors

The rules given by Damkohler (Dl) for changing the scale of catalytic reactors without changing the course of the reaction were derived primarily by dimensional analysis. A better idea of the requirements for scaling up can be obtained by a detailed examination of the coefficients in the differential equations and boundary conditions describing the reactor, with the independent variables in the equations transformed to a modified reciprocal space velocity and a dimensionless radial variable. In an exact scale model, these coefficients are all the same as they are in 

The parameters nominally at our disposal are the diameter of the reactor, the mass velocity, and the particle diameter. The problem of changing the scale will be discussed from the point of view of an engineer who wants to match the performance of two reactors of different diameters, and who must then choose a corresponding mass velocity and an accessible—and acceptable—combination of particle diameter and activity of catalyst. 

In all that follows, it will be assumed that neither radiation nor molecular conduction will affect the performance of a scale model. If either is so important that its variation cannot be ignored, no useful scale model can be designed. 

This substitution is made, and the terms involving the rates are multiplied by the activity factor a. After some rearranging, the equations take the form 

As the model is to be constructed so that the intensive properties of the reacting fluid are to be invariant to the change of scale, such quantities as the heat capacity and the rate and heat of reaction are also invariant. In his treatment of packed catalytic reactors, Bosworth [see (B8), p. 318] assumes that the diffusivities and the thermal conductivity remain constant when the scale is changed. Since these quantities are approximately proportional to the mass velocity and the particle diameter, the resulting rules for scaling can not be correct. The presence of 

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