Introductory Theory on Fluidization

2. THEORY

2.1 Packed columns and Fixed Beds

A packed column consists of specifically shaped particles contained within a column. Generally a packed column is used to bring two phases in contact with one another. Normally one fluid will wet the packing and flow as a film over its surface. The second fluid will pass through the remaining volume of the column. This promotes a high interfacial area between the two phases and a high degree of turbulence between the two fluids. The fluid's can be liquid or gas, and can be entered into the column either at the top or bottom. Figure 1 represents a typically layout used for fluidization.

figure 1: Typical packed column set up used for fluidisation

A packed column is constructed using a metal, glass, ceramic or plastic shell preferably with a corrosion resistant lining. The column should be mounted as vertical as possible to promote even liquid distribution. The packing material or bed rests on a support plate that should be designed to offer minimal resistance to the passage of fluids (75% free area is recommended for the passage of gas ,(Richardson, J. F. & Harker, J.H. with Backhurst, J.R.( 2002)).

It is important to be able to predict the pressure drop over a packed column for the various flow rates of the fluids. These criteria are used extensively in plant design. Packed columns in which the solids are stationary relative to each other are referred to as fixed.

The first experimental work with fixed beds was carried out by Darcy (Darcy, H.P.G. (1856)) in 1830 in Dijon and translated into English in 2004 (Bobeck, P. (2004)). His work resulted in the "Darcy's Law" relationship, which can be expressed as equation 1.

(1)

Here, B is termed the permeability coefficient and is dependent

only on the physical properties of the bed. is the viscosity of the fluid and is the bed thickness. is the average velocity of the fluid and is the pressure drop.

Alternatively the expression for fluid flow through a fixed bed is given by equation 2, the Carmen-Kozeny equation,(Richardson, J. F. & Harker, J.H. with Backhurst, J.R.( 2002)).

(2)

2.2.1 Fluidised Beds

When a fluid is passed downwards through a bed at any flow, no relative movement occurs between the particles unless the initial layout of the particles was unstable. Where the flow is streamline, the bed will behave as a fixed bed and can be treated with the fixed bed equations. When a fluid is passed upwards through a bed, the bed will behave as a fixed bed only at relatively low flow rates. A simple force balance on a particle, figure 2, shows competing forces.

figure 2. A force balance on a particle in a bed.

Thus when the frictional drag forces are equal to the apparent weight of the particle, the bed will begin to rearrange in order to minimize the resistance to the flow of fluid. As are result, the bed will expand and a corresponding increase in the bed voidage will be observed. This bed expansion will increase as the flow of the fluid is increased, until the bed assumes it's loosest stable packing. If the fluid flow is then increased further, the particles separate from one another and the bed is considered fluidised.

The superficial velocity at which minimum fluidisation occurs is referred to as the minimum fluidising velocity. The pressure drop behaves as it would for a fixed bed until the minimum superficial fluidising is reached. Above this velocity of flow, the pressure drop will tend to be constant. This is demonstrated in figure 3.

figure 3: A log graph of pressure drop versus superficial velocity.

As shown in figure 3, when the flow rate is increased of the fluid from start, the pressure drop increases as per the fixed bed equations. When the bed begins to expand, the gradient decreases until a maximum pressure drop is reached. This maximum occurs due to the static frictional forces between the particles that must be overcome. After this point, as the fluid flow rate is increased, the pressure drop remains constant.

When the process is reversed, and the flow rate is decreased, the pressure drop no longer reaches a maximum. Rather the pressure drop remains constant until the minimum superficial fluidizing velocity is reached at the minimum fluidizing point. At this point the particles are just resting on one another and after this point, the bed behaves as a fixed bed. Note from figure 2 that the return pressure drop is less than the increasing velocity pressure drop. This result is due to the fact that the bed will settle at the maximum porosity, and unless disturbed, the voidage and bed height will remain at this maximum value.

A more general expression for fluid flow through beds is the Ergun Equation, based on a friction factor correlation. Equation 3 ,(Richardson, J. F. & Harker, J.H. with Backhurst, J.R.( 2002)), is a version of this.

Ð"P = 150(1 - e)2 мU + 1.75(1 - e) сfU2 (3)

H e3 d2 e3 d

This equation can be used for fixed or fluidised beds. Here the voidage (e) and H (bed height) are those specific to the minimum fluidisation velocity at the minimum fluidisation point. In general the Ergun equation tends to over predict the pressure drop for a fluidised system. For a bed of spherical particles, the voidage