Pressure drop flow through packed beds

We see that Apjl, the frictional pressure drop per unit depth of bed, is made up of two components. The first term on the right-hand-side accounts for viscous (laminar) frictional losses, cc pu. and dominates at low Reynolds numbers. The second term on the right-hand-side accounts for the inertial (turbulent) frictional losses, oc pu2, and dominates at high Reynolds numbers. For further information about flow through packed beds, see Chapter 7 An Introduction to Particle Systems . 

We further mention that at low values of the Reynolds number (that is at very low fluid velocities or for very small particles) for flow through packed beds the Sherwood number for the mass transfer can become lower than Sh = 2, found for a single particle stagnant relative to the fluid [5]. We refer to the relevant papers. For the practice of catalytic reactors this is not of interest at too low velocities the danger of particle runaway (see Section 4.3) becomes too large and this should be avoided, for very small particles suspension or fluid bed reactors have to be applied instead of packed beds. For small particles in large packed beds the pressure drop become prohibitive. Only for fluid bed reactors, like in catalytic cracking, may Sh approach a value of 2. 

Many empirical equations for predicting pressure gradients in countercurrent flow of gas and liquid are available in the literature.17,31,36 The pressure drop in countercurrent flow can be represented by an equation of the Carman-Kozeny type for flow through packed beds, Below the flooding point, the following equation is suggested36 and has been shown to agree well with experimental data ... 

The flow through the straight channels of the monolith matrix is subject to very low pressure drops in a packed bed with the same external geometric surface area the pressure drop may be greater by two or three orders of magnitude. 

Leva did extensive work on the pressure drop in packed beds of particles with various shapes [16]. He suggests the following equation for laminar flow through packed beds ... 

Pressure drop and liquid holdup are very important parameters, indispensable for the design of trickle-bed reactor (6, 7, 13, 16, 17, 19, 23, 27, 29, 30, 32, 42). Their values influence directly the interfacial parameters between the fluid phases and between liquid and solid pliases too. Many workers have proposed different correlations for predicting the two-phase pressure drop in co-current downward flow through packed beds (6, 17, 19, 23,... 

Flow through packed beds of solids is usually analyzed by considering such characteristics as the porosity of the bed and the sphericity of the particles, and Section 7.5.4.1 shows that the analysis of a filter is helped by considering how the deposit of precipitated solids changes those characteristics. In the other filters, the solids deposit as a cake on the filter medium. The resistances of the filter cake and medium are then additive. When the resistivity, or the resistance per unit thickness, of the cake remains constant throughout operation, the specific resistance increases linearly with the amount of solid deposited. Analytical solutions for the filtration rate are then possible. In the constant-rate case, the pressure drop encountered can be expressed as a function of time (Section 7.5.4.2). 

In most adsorption processes the adsorbent is contacted by the fluid phase in a packed column. Such variables as the particle size, fluid velocity, and bed dimensions determine the pressure drop and have an important impact on the economics of the process since they determine the pumping cost as well as the extent of axial mixing and the heat transfer properties. The hydrodynamics of flow through packed beds have been extensively studied, and detailed accounts may be found in many chemical engineering textbooks. The present review is therefore limited to a brief summary of the principal features of the flow behavior which are important in the design of fixed bed absorbers. 

The most popular pressure drop equation for flow through packed beds is that of Ergun [1952]. Ergun considered the packed bed to consist of a bundle of... 

Kozeny modeled a packed bed as a series of parallel, small diameter tubes of equal length and diameter [1]. Carman applied the work of Kozeny to experimentally determine pressure drops for the flow through packed beds [2]. This work produced the Carman-Kozeny equation for gas-phase pressure drop ... 

In the CFD modelling of membrane filtration process, membranes are usually modelled as a porous wall while the flow within a membrane is usually solved using both Navier-Stokes and Darqr equations (Ghidossi et al, 2006). A porous media model is widely used for determining the pressure loss during flow through packed beds, filter papers, perforated plates, flow distributors and tube banks (ANSYS, 2010). A momentum source term is added to the governing momentum equations, which creates a pressure drop that is proportional to the fluid velocity ... 

The Carman-Kozeny equation relates the drop in pressure through a bed to the specific surface of the material and can therefore be used as a means of calculating S from measurements of the drop in pressure. This method is strictly only suitable for beds of uniformly packed particles and it is not a suitable method for measuring the size distribution of particles in the subsieve range. A convenient form of apparatus developed by Lea and Nurse 22 1 is shown diagrammatically in Figure 4.4. In this apparatus, air or another suitable gas flows through the bed contained in a cell (25 mm diameter, 87 mm deep), and the pressure drop is obtained from hi and the gas flowrate from h2. 

Adsorbents are available as irregular granules, extruded pellets and formed spheres. The size reflects the need to pack as much surface area as possible into a given volume of bed and at the same time minimise pressure drop for flow through the bed. Sizes of up to about 6 mm are common. 

Column design and preparation incorporated previously described methods reported in the literature (39). Two different adsorbents were employed a 100/120 mesh crosslinked styrene/ divinylbenzene resin (Polypak P-Waters Associates) and a Woelm aniontropic activity grade alumina. These adsorbents were packed in 300 and 94 cm. stainless steel columns having a 1 mm. internal diameter. Pressure drop across the adsorbent bed was kept to a minimum (<0.02 atm.) by using a heated pressure reduction valve at the end of the column. Typical linear flow velocities through the columns were in the range of 0.27-2.17 cm/sec. 

Figure 1.13 illustrates flow through a bed packed with porous particles and ui and U2 are the EOF velocities through the small intraparticle pores and the larger interstitial channels, respectively. For pressure driven flow, assuming that the path length and the pressure drops are the same for the two cases the flow velocity varies as square of... 

Figure 1. Pressure drop in flow through packed and fluidized beds.

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