Vol. 25, No. 3 (2026), Sim26886 https://doi.org/10.24275/rmiq/Sim26886

Variable-order fractional diffusion-reaction in porous catalyst pellets under progressive deactivation: A numerical comparative study

 

Authors

R. Soto-Soto, L. Vicente, A.E. Rodriguez-Mata

Abstract

Classical diffusion-reaction models for porous catalyst pellets usually assume Fickian transport with constant effective diffusivity. However, catalyst deactivation caused by coke deposition, fouling, poisoning, or sintering progressively modifies the pore network and may induce anomalous subdiffusive transport. In this work, a variable-order fractional diffusion-reaction model is proposed for an isothermal flat-slab catalyst pellet with a first-order irreversible reaction. The classical time derivative is replaced by a Caputo derivative of time-dependent order $\alpha(\tau)$, defined by the exponential law α (τ)=α ∞+(1-α∞)exp(-λτ), which represents the transition from fresh Fickian transport to aged subdiffusive behavior. The model is solved using an implicit L1 finite-difference scheme and compared with the classical Crank--Nicolson solution. The transient catalyst effectiveness factor is used as the main performance indicator. Numerical results show that the variable-order model predicts slower reactant penetration and lower transient effectiveness during catalyst aging, demonstrating that classical models may overestimate catalyst performance under progressive transport degradation.

Keywords

variable-order fractional calculus; anomalous subdiffusion; catalyst deactivation; effectiveness factor; diffusion-reaction model.

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