Interpretation of Response Data by the Dispersion Model

Here we wish to determine the axial diffusivity from response measurements, in preparation for using the dispersion model for conversion calculations. According to this model, the actual reactor can be represented by a tubular-flow reactor in which axial dispersion takes place according to the effective diffusivity D. It is supposed that the axial velocity u and the concentration are uniform across the diameter, as in a plug-flow reactor. 

Imagine that a step function of inert tracer concentration Cq is introduced into the feed at 0 = 0. By solving the transient mass balance, we can 

Canceling dividing by AzA6, and taking the limit as Az 0 gives 

If no axial dispersion occurs in the feed line, the proper boundary condition at z = 0 is 

CHAPTER 6 DEVIATIONS FROM IDEAL REACTOR PERFORMANCE 

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SECTION 6-5 INTERPRETATION OF RESPONSE DATA BY THE DISPERSION MODEL ... 

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