Estimation of the Axial Dispersion Coefficient

The axial dispersion coefficient can be determined experimentally, for instance, by finding the numerical value of the Peclet number, in impulse or step-response experiments. This is, however, possible, provided that experimental equipment (reactor) is available to carry out the experiments. This is not always the case. If no reactor experiments can be performed, the best approach is to estimate the value of the axial dispersion coefficient firom the available correlations. 

In tube reactors with laminar flow profiles, the axial dispersion coefficient (D) is related to the molecular diffusion coefficient (Dm), the average flow velocity, and the tube diameter (d)  

The above equation is valid for the values of Reynolds number below 2000 only. By incorporating the Peclet number (Pe) for a tube, Pcr = wd/D, the same relation can be expressed using two dimensionless quantities, namely, the Reynolds number (Re) and Schmidt number (Sc) [5]  

The advantage of using the kind of correlations presented above is that the Peclet number can be estimated from the flow velocity and from easily measured physical material parameters ( X, p,r m) only. 

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Although the above method can give a simple evaluation of Peclet number for the system, the tailing in the RTD curve can cause significant inaccuracy in the evaluation of the Peclet number. Michell and Furzer67 suggested that a better estimation of the axial dispersion coefficient is obtained if the observed RTD is statistically fitted to the exact solution of the axial dispersion model equation with appropriate boundary conditions. For example, a time-domain solution to the partial differential equation describing the dispersion model, i.e.,... 

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