Effectiveness factors for general reaction rate forms

Abstract
The great utility of the effectiveness factor concept to account for intraparticle diffusion lies in its simplicity of application. Unfortunately, the standard formulation leads to a separate relationship for each type of reaction rate form, which greatly complicates practical computations.A general asymptotic solution is given here which leads to the definition of a general modulus somewhat different in form from the standard one. The use of this general modulus tends to approximately bring together all of the various curves.To illustrate its use, a few new exact solutions for simple order reactions are derived and combined with existing solutions for both simple order and adsorption reaction rate forms. It is seen that all of the curves lie within a relatively narrow range. Thus the general modulus permits one to estimate the effectiveness factor for any arbitrary reaction from the existing curves.

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