Packed beds of spheres

Flow Through a Packed Bed of Spheres. The Ergun Equation (46), gives the pressure drop through a packed bed of spheres 2... 

For packed beds of spheres of different diameters or of non-spherical particles, and equivalent diameter has to be formed... 

Gillespie, B.M. Crandall, E.D. Carberry, J.J. Local and average interphase heat transfer coefficients in a randomly packed bed of spheres. Amer. Inst. Chem. Eng. J. 14 (1968) 483-490... 

For packed beds of spheres, the porosity is generally larger near the bounding solid surface, resulting in an increase in the local velocity (component parallel to the surface) and the local Reynolds number. 

If the continuum treatment is to be employed, we must first identify the elements that make up the system. The choice of elements might be obvious (as in the case of a packed bed of spheres) or some simplifying assumptions might have to be made. Common simplifying assumptions are assuming the system to be made up of cylinders of infinite length (for fibrous media) or assuming arbitrary convex-surfaced particles to be spheres of equivalent cross section or volume. Then the properties of an individual particle can be determined. If the system cannot be broken down into elements, then we have no choice but to determine its radiative properties experimentally. 

FIGURE 9.19 Prediction and experimental results of Chung et al. [120] for condensation (in a packed bed of spheres) at a bounding vertical impermeable surface. The large Bo results of Cheng [116] are also shown. 

Colver (1980) observed experimentally that the bulk resistivity of a packed bed of spheres less than about 65 pm takes on a pseudocontinuum behavior. 

Mass transfer to a single sphere in a packed bed of spheres d = sphere diameter F = superficial velocity Re = vd/v Sh = kd/D... 

Hicks, R. E., Pressure drop in packed beds of sphere, Ind. Eng. Chem. Fundam., 9, 500, 1970... 

A gas oil is cracked at 630°C and 1 atm by passing vaporized feed through a packed bed of spheres of silica-alumina catalyst with radius = 0.088 cm. For a feed rate of 60 cm liquid/cm, .hr, a SO percent conversion is found. The following data are also knovm ... 

K. Ridgway and K. J. Tarbuck, Voidage fluctuations in randomly-packed beds of spheres adjacent to a containing wall, Chem. Eng. Sci., 1968, 23, 1147-1155. 

Only a very few experimental data on the cocurrent flow of gas and flowing solids through the packed bed have been reported. Kiel [10] studied the cocurrent gas-soHds downflow over regularly stacked packing, while Barysheva et al. [21] used a packed bed of spheres in their experimental investigations. 

For packed bed of spheres, Barysheva et al. [21] found that flowing particle mean residence time is essentially independent of gas flow rate. Mean solids velocity decreases with an increase of flowing particles diameter, this effect becoming more pronounced at higher solids flow rates. Further, flowing solids velocity decreases with an increase in flowing solids flow rate. This is a consequence of the interaction between individual flowing solids particles. 

For a Reynolds number range of 10-10000 for gases in a packed bed of spheres (D4), the recommended correlation with an average deviation of about +20% and a maximum of about -T50% is... 

Gunjal PR, Ranade VV, Chaudhari RV. Computational study of a single-phase flow in packed beds of spheres. AIChE Journal 2005 51 365-378. 

Figure 6.1 Friction factor versus Reynolds number plot for fluid flows through a packed bed of spheres...

The zero vorticity cell model has been extended numerically to intermediate Reynolds numbers for spheres (LeClair and Hamielec, 1968), and both the zero vorticity and the free-surface cell models (unmodified) to spheroids at low Reynolds numbers (Epstein and Masliyah, 1972). However, these extensions are more applicable to immobilized packed beds than to fluidized beds, and only in the absence of turbulence, which for unexpanded, fixed packed beds of spheres develops at Re > 110—150 (foils and Hanratty, 1966). 

For a packed bed of spheres, the minimum value of the Sherwood number for reactant A (Sh = pdp/DA, of 3.8 (for Rep—>0) can be used (Section 3.2.2.2). Thus we can estimate the minimum values of for porous and non-porous catalysts (first-order reaction). For porous particles we obtain based on Eq. (4.5.17) ... 

The void fraction in packed beds of spheres has been correlated by Haughey and Beveridge [1969] in the following way ... 

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