A new semi-empirical model for pressure drop prediction in a packed bed of smooth and rough particles: Derivation and verification

The accurate prediction of pressure drop in packed beds is fundamental to numerous chemical, mechanical, and environmental engineering applications. While traditional models such as the Ergun equation and Reynolds number-based correlations have been widely employed, they suffer from inherent limitations and lack a unified framework bridging packed beds and empty conduits. This paper presents a comprehensive derivation of the Quinn Fluid Flow Model (QFFM), a novel theoretical framework developed from first principles. The QFFM establishes a universal linear relationship between the normalized dimensionless pressure gradient (PQ) and the fluid current (CQ), expressed as PQ=k1+k2CQ. A key innovation is the conceptualization of any closed conduit as a “packed conduit” via the Hypothetical Q-Channel (HQC) and the wall normalization coefficient (λ), which inherently incorporates the effects of tortuosity, viscous boundary layers, and surface roughness. By unifying the description of flow through packed beds, the new semi-empirical model offers a robust, physics-based alternative to conventional semi-empirical correlations, validated across diverse flow regimes and particle morphologies.