(532dz) A New Correlation for Pressure Drop through Unbounded Randomly Packed Beds of Spherical Catalyst Particles over the Entire Range of Reynolds Number

Pressure drop in fixed bed reactors has been studied for over a century and many conflicting correlations exist in the literature. Contributing factors to this disagreement 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=ρvd_p/μ(1-ε). To avoid these problems, we restricted attention to perfect spheres in unbounded (high-N) random-packed beds. A new asymptote-based correlation based on data for extremely high Re_m and new particle-resolved computational fluid dynamics (PRCFD) results for extremely low Re_m is presented.

The equation fits a literature data set of 541 points with average relative error of 5.64% and shows correct limits for both high and low Re_m.

In comparison, the Ergun equation¹ has average relative error of 19.6% and a limit that is too high as Re_m→∞, and incorrectly predicts f_v=f_k Re_m decreases linearly as Re_m→0. It provides reasonable agreement with data for the range 10≤Re_m≤500, in which many experiments are performed. The KTA equation², developed by the nuclear industry, has a good average relative error of 7.2%, but predicts that f_k→0 as Re_m→∞ which is qualitatively incorrect. It provides a good approximation for 0.03≤Re_m≤10⁵, very similar to the equation of Erdim et al. (2015)³ which shares the KTA strengths and weaknesses. Both latter correlations also have f_v increasing with Re_m^0.9 approximately as Re_m increases from 0, which is also incorrect. Our new correlation gives the correct high and low Re_m behavior (see Figs. 1 and 2) and has better overall relative error.

References

1. Ergun S. Fluid flow through packed columns. Chem. Eng. Prog. 1952;48:89-94.
2. Nuclear Safety Standards Commission (KTA), 1981.
3. Erdim E, Akgiray Ö, Demir İ. A revisit of pressure drop-flow rate correlations for packed beds of spheres. Powder Technology 2015;283:488–504.