Shorter Communications
Expressions (IS), ( 19) are the generalized versions of the con-Departmen! of Chemical Engineering Y. C. YORTSOS* stant activity case (Aris [4]) for the case of variable diffusivity University of Southern California T. T. TSOTSIS and catalytic activity. Notice that due to the non linearity of the Los Angeles problem, the additive property of the resistances is not valid any CA 90007 longer. Both relations ( 19), (1%) are valid for any geometry, U.S.A. activity or diffusivity profiles, and order of reaction kinetics.
A similar analysis can be applied in a rather straightforward * manner to the case of generalized isothermal kinetics. However the formulas derived are not as easy to use as in the previous two cases.
CONCLUSlONs
The relationship between the effectiveness factors for the Robin and Dirichlet problems for a catalyst with variable catalytic activity was studied. It was shown that for a single isothermal reaction with first order kinetics the additive property of the resistances first established by Aris [4] for the constant activity case, i.e. GJ D K L u x a rl ; NOTATION external concentration, moles Lw3 effective diffusivity, L't-' rate constant, t-' characteristic length, L concentration, dimensionless position coordinate, dimensionlees catalytic activity, dimensionless effectiveness factor, dimensionless mass transfer coefficient, dimensionless Thiele modulus, dimensionless 1 1 L m=m+Yu+s)
is always valid, for any catalytic activity or effective diffusivity profiles. Modified versions of this relationship for isothermal pth order kinetics were also derived. Such relationships allow for the direct evaluation of the effectiveness factor of the Robin problem from the effectiveness factor of an associated Dirichlet problem, for any activity or effective diffusivity profiles, and they could be important in problems of reactor sensitivity and control.