Ergun equation flow-rate effects

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. 

Figures 14 and 15 show the normalized pressure drop factor for a densely packed bed of monosized spherical particles. For Rem < 7,fv is fairly independent of Rern, and at high Rem values, it increases fairly linearly with Rem. The data points are the experimental results taken from Fand et al. (110), where the bed diameter is D = 86.6 mm and the particle diameter is ds = 3.072 mm. One can observe that the 2-dimen-sional model of Liu et al. (32), referred to as equation 107, agrees with the experimental data fairly well in the whole range of the modified Reynolds number. From Figure 14, one observes a smooth transition from the Darcy s flow to Forchheirner flow regime. The one-dimensional model of Liu et al. (32) (i.e., equation 106) showed only slightly smaller fv value. Hence, the no-slip effect or two-dimensional effect for this bed is small. As shown in Figures 14 and 15, the Ergun equation consistently underpredicts the pressure drop. The deviation becomes larger when flow rate is increased.

The reactor is assumed to be adiabatic with plug flow. Axial dispersion can be ignored. Any effect of limitations of mass or heat transfer inside the catalyst pellet is lumped into the rate constants given in Table 1. The catalyst activity is assumed to be constant. Use the conversion of ethylbenzene or water in the set of continuity equations. Use the Ergun equation to describe the pressure drop. 

In order to estimate the rate of fluid flow through a porous material--e.g. the rate of water uptake in an absorbent polymer-either equation 1 or 4 can be used. In either case, the permeability of the material must be known or estimated. In most cases, no detailed knowledge of the geometry of the porous material is available. Therefore, general correlations between pore structure and permeability are often used. Dullien [5] and Happel and Brenner [10] present many of the functional forms that have been used to correlate permeability and porosity. The Kozeny-Carman equation, and its extension for Inertial effects, the Ergun equation, is the most widely encountered correlation. Detailed discussions of the derivation and application of Kozeny s original equation and Carman s modification are available [9, 5, 12]. 

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