(521ei) Wall Effects on Pressure Drop through Randomly Packed Beds of Spherical Catalyst Particles

An asymptote-based correlation for pressure drop in unbounded packed beds of spheres over a wide Re-range was (Dixon, 2023):

f_k ≡ (ΔP/L)(d_p/ρv²)(ε³/(1-ε)) = 160/Re_m + (0.922 + 16Re_m^-0.46) Re_m / (Re_m +60.0)

The limit as Re_m → ∞ is lower than that suggested in standard correlations such as that of Ergun.

For packed beds with strong wall effects, the pressure drop has been claimed to increase at low Re and decrease at high Re, compared to that in unbounded beds (Eisfeld and Schnitzlein (2001)). In this work we use particle-resolved CFD (PRCFD) in the viscous region at low Re to show that the widely accepted correction by Mehta and Hawley (1969) overestimates the effect, and an improved correction formula is given, based on the work of Carman (1937). In the inertial region at high Re a careful analysis of the widely disagreeing literature data shows that many studies present inconsistent values for void fraction, which has a strong effect on pressure drop. The accepted data shows reasonable agreement with the Dixon correlation above, with only small decreases for very low values of tube-to-particle diameter ratio (N) in the inertial range. High-Re PRCFD simulations are being conducted to determine whether the wall effect on fixed bed pressure drop in the inertial range is real, or whether it was invoked to compensate for the wrong limit as Re increases.

References

1. Dixon AG. General correlation for pressure drop through randomly-packed beds of spheres with negligible wall effects. AIChE J. e18035 (2023).
2. Carman PC. Fluid flow through granular beds. Trans Inst Chem Engrs. 15:150-66 (1937).
3. Eisfeld B, Schnitzlein K. The influence of containing walls on the pressure drop in packed beds. Chem Eng Sci. 56:4321-4329 (2001).
4. Mehta D, Hawley MC. Wall effect in packed columns. Ind Eng Chem Proc Des Dev. 8:280-282 (1969).