Flow through Packed Beds and Fluidized Beds

Chemical engineering operations commonly involve the use of packed and fluidized beds. These are devices in which a large surface area for contact between a liquid and a gas (absorption, distillation) or a solid and a gas or liquid (adsorption, catalysis) is obtained for achieving rapid mass and heat transfer, and particularly in the case of fluidized beds, catalytic chemical reactions. First, let us consider flow through a packed bed. Packed Beds:A typical packed bed is a cylindrical column that is filled with a suitable packing material. You can learn about different types of packing materials from Perrys Handbook. The liquid is distributed as uniformly as possible at the top of the column and flows downward, wetting the packing material. A gas is admitted at the bottom, and flows upward, contacting the liquid in a counter-current fashion. An example of a packed bed is an absorber. Here, the gas contains some carrier species that is insoluble in the liquid (such as air) and a soluble species such as carbon dioxide or ammonia. The soluble species is absorbed in the liquid, and the lean gas leaves the column at the top. The liquid rich in the soluble species is taken out at the bottom. From a fluid mechanical perspective, the most important issue is that of the pressure drop required for the liquid or the gas to flow through the column at a specified flow rate. To calculate this quantity we rely on a friction factor correlation attributed to Ergun. Other fluid mechanical issues involve the proper distribution of the liquid across the cross-section, and developing models of the velocity profile in the liquid film around a piece of packing material so that heat/mass transfer calculations can be made. Design of packing materials to achieve uniform distribution of the fluid across the cross-section throughout the column is an important subject as well. Here, we only focus on the pressure drop issue. The Ergun equation that is commonly employed is given below. fp = 150/Rep + 1.75Here, Here, the friction factor pf for the packed bed, and the Reynolds number pRe, are defined as follows. The various symbols appearing in the above equations are defined as follows. p: Pressure Drop L: Length of the Bed DP: Equivalent spherical diameter of the particle defined by DP = 6 : Density of the fluid : Dynamic viscosity of the fluid Vs: Superficial velocity = , where Q is the volumetric flow rate of the fluid and A is the cross-sectional area of the bed) :Void fraction of the bed ( is the ratio of the void volume to the total volume of the bed) Sometimes, we may use the concept of the interstitial velocity Vi, which is related to the superficial velocity by Vi = V s/ The interstitial velocity is the average velocity that prevails in the pores of the column. Two simpler results, each obtained by ignoring one or the other term in the Ergun equation also are in use. One is the Kozeny-Carman equation, used for flow under very viscous conditions.fp = 150/Rep when Rep The other is the Burke-Plummer equation, used when viscous effects are not as important as inertia. fp = 1.75, Rep 1,000It is suggested that the student simply use the Ergun equation.

Fluidisation & mapping of regimes:When a bed of solids is kept suspended by fluid up-flow, the bed can behave in various ways- i) smoothly fluidised; ii) Bubbling; iii) Slugging; iv) Spouting etc.

Before fluidisation of a particle bed in a column tower, the particles will form a fixed bed and fluidisation sets on when the velocity of the fluid ,either liquid or gas attains a minimum level and then with the increase of velocity , the process of fluidisation takes different form as mentioned above. Simultaneously with different degrees of increase of fluid velocities, the fluid pressure drop gradually increases with increasing velocities and at certain minimum value of the velocity , the bed starts expanding and pressure drops starts decreasing and at the onset fluidisation, the pressure drop becomes constant.

Fixed bed of particles:Characterization of particles of bed:The size of spherical particle can be measured without ambiguity; however, question arises with non-spherical particles. There are various ways of defining particle sizes. We can adopt deff that is useful for both flow and pressure drop.For particle size larger than or > 1 mm: This can be measured by means of caliper, micrometer, mass determination, if density is known. From these measurements, we can first calculate the equivalent spherical diameter, defined as follows:dsph = ( Diameter of spheres having the same volume as the particles)Various measures of non-sphericities are available, and are summarized in tables as under

Sphericity:Sphericity is defined as the ratio of surface of a sphere having the same volume as the particle to the surface of that particle.s = With this definition, s=1 for spheres & 0 < s