A modified Ergun equation for application in packed beds with bidisperse and polydisperse spherical particles.

Accurately predicting gas pressure drop in packed beds is challenging in various industrial processes due to the size dispersity of bed particles. The original Ergun equation has been widely used for predicting gas pressure drop in packed beds of monosized spherical particles. Here, we aim to evaluate its prediction accuracy for non-monosized spherical particle beds and propose a modified Ergun-type correlation to consider involved particle-size-dispersity effects. Specifically, we focus on conditions where the tube-to-particle diameter ratio is larger than 14, and the particle Reynolds number, R e p , ranges from 26 to 561. An experimentally validated numerical approach that couples computational fluid dynamics and the discrete element method is used to obtain the gas pressure drop for various beds, showing that the original Ergun equation (with the Sauter mean diameter, d 32 , a common choice in both academia and industry, used as the average particle diameter) yields a predication discrepancy of up to 30%. Accordingly, we propose a novel correlation by using different particle sizes in different terms, revealing the distinct physics of the flow past a sphere in different regimes. In the inertial term, the use of d 32 is reasonable as it considers both volume and surface area of the particles, analogous to the corresponding body and surface forces on the sphere in this regime. In the viscous term, however, the surface-diameter mean, d 21 , which emphasizes particle surface area and geometric effect, is used because it describes the dominant skin frictional surface force in viscous flow. The modified Ergun equation demonstrates improved predictions for bidisperse packed beds by reducing the largest discrepancy to 4%, and can be applied to polydisperse beds as well. Moreover, the proposed correlation aligns well with the original Ergun equation, i.e., the monosized limit, in the investigated R e p range. [Display omitted] • Ergun equation shows limited prediction accuracy for non-monosized packed beds. • It overlooks dense packing (or low porosity) effects in non-monosized packings. • A modification is proposed by using different particle sizes in different terms. • The modified Ergun equation improves prediction, reducing discrepancy to under 4%. [ABSTRACT FROM AUTHOR]