Application of overall Thiele modulus of an assemblage of catalyst pellets of different shapes and properties to the design of catalytic reactors

Abstract The design and optimization of continuous catalytic reactors necessitate accurate prediction of the residence time required for certain reactant conversion, which is intrinsically linked to the effectiveness factor of the catalyst pellets. This work presents a robust and generalized methodology for calculating this time in mixed (CSTR) and plug flow (PFR) reactors by integrating a novel, simplified expression for the overall catalyst effectiveness factor based on the overall Thiele modulus developed by the authors. The core of this approach is a straightforward correlation for the pellet effectiveness factor, derived from a generalized Thiele modulus that is applicable to catalysts of any shapes and sizes. We demonstrate the application of this model by conducting a systematic comparative analysis of CSTR and PFR performance across a spectrum of reaction conditions, including different reaction orders, fractional volume changes, and conversion levels. A key finding is that for all positive reaction orders, a PFR consistently outperforms a CSTR, requiring a smaller residence time to achieve the same conversion, with the performance gap widening significantly for high conversions and higher reaction orders. Furthermore, for reactions with orders below unity, catalytic systems exhibit a markedly higher space-time requirement ratio between CSTR and PFR compared to homogeneous systems, highlighting the profound impact of intra-catalyst diffusion effects on reactor selection. The proposed method provides a computationally efficient and accurate framework for rapid catalyst screening and reactor design. The proposed method operates under the assumptions of isothermal conditions, negligible inter-particle mass transfer resistance, and is particularly suited for catalyst beds or configurations where the bulk fluid concentration is well-defined at the surface of each pellet.