General correlation for pressure drop through randomly-packed beds of spheres with negligible wall effects

Pressure drop in fixed beds has been studied for over a century and a large number of conflicting correlations exist in the literature. Contributing factors to these differences include the use of particles of different shapes, the presence of wall effects in beds of low tube-to-particle diameter ratio (N) and parameter fitting over limited ranges of modified Reynolds number Re-m = pvdp/mu(1-epsilon). The present work, in contrast, considers the entire Reynolds number range for perfect spheres in unbounded (high-N) random-packed beds. An asymptote-based correlation has been developed based on published data for extremely high Rem and on new particle-resolved computational fluid dynamics (PRCFD) results for extremely low Rem. The resulting equation is given by Delta P/L dp/pv(2) epsilon 3/(1-epsilon) = 160:0/Re-m (0.922+16Re(m)(0:46)) Re-m/(Re-m+52). This equation fits a literature data set of 541 points with average error 5.66%, and shows correct limits for both high and low Re-m.