Dynamic effectiveness factor for catalyst particles.
The effectiveness factor (EF) is a nondynamic concept that has been demonstrated to be useful for the analysis and design of reaction-diffusion systems (e.g., catalyst particles). The aim of this paper is to introduce a dynamic EF factor (DEF) concept that extends the existing nondynamic one. In the first step, the standard EF is interpreted as a scaling factor that transforms total reaction rates from surface/bulk to catalyst particle conditions. Through the use of Fourier transform (i.e., frequency domain) to deal with time variations, the above interpretation is extended to dynamic conditions by defining the DEF as a linear operator transforming total reaction rate signals from surface/bulk to catalyst particle conditions. It is shown that the classical nondynamic EF concept is recovered in the steady-state limit of the DEF definition. Interestingly, the DEF can be easily computed from the nondynamic EF expressions by introducing a complex Thiele modulus. Results show that for reaction-diffusion processes where the diffusion mechanism is governed by Fick's law the magnitude of the DEF decreases with the frequency. This means that the best reaction rate performance is obtained when the process operates at steady-state (i.e., nondynamic) conditions. However, when a diffusion model with relaxation time is assumed to hold, resonant peaks at nontrivial frequencies can be displayed. Physically, this behavior implies that dynamic (e.g., periodic) operation of the reaction-diffusion process can yield better performance when compared with its nondynamic counterpart.