Short-Cut Method for the Estimation of Isothermal Effectiveness Factors

The computation of effectiveness factors (EFs) is commonly used for simplifying heterogeneous models of catalytic processes. To do this, the reaction rate in a catalyst pellet is expressed by its rate under surface/bulk conditions multiplied by a functional factor, namely, the EF. When many EF evaluations are required, it is desirable to dispose of short-cut methods to alleviate the computational burden. Existing short-cut methods are based on the availability of analytical solutions for a related linear, but nonhomogeneous, approximation to the nonlinear kinetics. However, the nonhomogeneous term can lead to spurious solutions, such as the presence of negative concentration values. This paper proposes a derivation of the EF short-cut method as an iteration procedure in the average concentration. On the other hand, aimed at avoiding negative concentration values, the proposed linear boundary-value problem is equipped with a nonactive region. In this way, the short-cut method is composed of two nonlinear equations on the average concentration and the position of the boundary between the active and nonactive regions. Numerical results show that such a modification increases the prediction capacity of EF short-cut methods for a practically acceptable Thiele modulus region.