Ergun equation, flow prediction

The following data are reported for the flow of air through beds of granular aetivated carbon. Compare the pressure drops with values predicted using the Ergun equation and predict the pressure drops for both sizes at air velocities of 100 and 200 ft/min. 

The pressure drop across a packed bed in laminar flow scales like the pressure drop across an open tube in laminar flow. In the turbulent limit, the Ergun equation predicts... 

Although Ergun equation is widely accepted in predicting the pressure drop for flow-through porous media, it is a known fact that the Ergun equation or its modified forms overpredict the pressure drop by as much as 100% at high porosity and underpredict the pressure drop by as much as 300% for low porosity medium such as sandstones (31). A more accurate equation has been developed by Liu et al. (32) based on a revised Kozeny-Carman theory. 

Figure 20 shows the calculated pressure drop factor and the experimental values. We observe that the model of Liu et al. (32) predicts the experimental pressure drop both in the Darcy s flow regime, the transition, and the Forchheimer regimes. The two-dimensional model gives a much better prediction than that using the one-dimensional model. The Ergun equation significantly overpredicts the experimental data. 

The pressure drop for concurrent downflow of gas and liquid in a packed bed can be predicted using correlations of the Lockhart-Martinelli type [22]. The pressure drop for each phase flowing separately through the bed is calculated using the Ergun equation [Eq. (3.64)], and these values define a parameter x ... 

In practice, the Ergun equation is often used to predict packed bed pressure gradient over the entire range of flow conditions. For simplicity, this practice is followed in the Worked Examples and Exercises in this chapter. 

Ergun showed that Eq. (7,22) fitted data for spheres, cylinders, and crushed solids over a wide range of flow rates. He also varied the packing density for some materials to verify the (1 — e) /e terra for the viscous loss part of the equation and the (1 — s)/e term for the kinetic-energy part. Note that a small change in e has a very large effect on Ap, which makes it difficult to predict Ap accurately and to reproduce experimental values after a bed is repacked. 

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