Flow through Packed 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.

1. Friction in flow through beds of solids (Flow through Packed (fixed) beds)

In many technical processes, liquids or gases flow through beds of solid particles. Important examples are filtration and two-phase countercurrent flow of liquid and gas through packed towers.

Pressure drop in flow of fluids through packed beds:

Flow through packed (fixed) bed can be regarded as fluid past some no. of submerged objects. In this case let us assume all the particles are spherical in shape having uniform size of diameter Dp and volume Vp.

Assume the packed bed length is L, volume is V and fluid is entering the bed with superficial velocity uo.  

Take porosity of the bed is ε, which is defined as,

We know that for non-circular ducts, we can use the Darcy formulae if we replace the diameter in both the friction factor and the Reynolds number with Hydraulic (equalent) diameter Deq.

Calculation of Hydraulic diameter:

Hydraulic diameter = 4 rH

And rH = cross sectional area perpendicular to flow/wetted perimeter

For a uniform duct this is a constant. For a packed bed it varies from point to point. But if we multiply both the cross sectional area and the perimeter by the length of the bed, it becomes,

But,

Hydraulic diameter = Deq = 4 rH

                                                For spherical particles,                              

Frictional losses through channel flow given as,

Here ‘f’ is the fanning friction factor and ‘u’ is the velocity through the channel.

The velocity through the packed bed = u = u0/ ε, (From continuity equation, u0 A = u εA)

Where u0 is superficial or approaching velocity of fluid.

Case1: For laminar flow (Re ≤ 1.0)

By substituting u and Deq in the above equation,

The above equation doesn’t consider the fact that the channels are actually irregular and not straight and parallel. For accounting the above fact it is found from experiments that 72 should be replaced by 150.

This equation is called Kozeny-Carman equation.

Case2: For turbulent flow (Re > 1000)

From experiments it has been found that, 3f = 1.75

The above equation is called Burke-Plummer equation.

Case3: For all regimes

 An equation covering the entire range of flow rates can be achieved by assuming that the viscous losses and the kinetic energy losses are additive.

So, the pressure drop per unit length of the packed bed is,

The above equation is called Ergun equation.

Note: The above Ergun equation is also can be written as, where,

     and

The below graph gives relation between f and Re

2. FLUIDIZATION

Fluidization refers to those gas-solids and liquid-solids system in which the solid phase is subjected to behave more or less like a fluid by the upwelling current of gas or liquid stream moving through the bed of solid particles.

A fluidized bed is a packed bed through which fluid flows at such a high velocity that the bed is loosened and the particle-fluid mixture behaves as though it is a fluid. Thus, when a bed of particles is fluidized, the entire bed can be transported like a fluid, if desired. Both gas and liquid flows can be used to fluidize a bed of particles.

(A). Conditions for Fluidization:

Consider a vertical tube partly filled with fine granular particles as shown in the figure. The tub is open at the top and has a porous plate to support the bed of particles and to distribute the flow uniformly. Assume that fluid is admitted at the bottom of the tube with superficial velocity of u0.

At first, when there is no flow, the pressure drop is zero, and the bed has a certain height. As the velocity gradually increases from zero the pressure drop gradually increases while the bed height remains fixed. This is a region where the Ergun equation for a packed bed can be used to calculate the pressure drop.

When the point A is reached, the bed starts expanding in height while the pressure drop becomes constant and no longer increases as the superficial velocity is increased. This is when the pressure drop across the bed counterbalances the net downward forces. As the velocity is increased further, the bed continues to expand in height, but the pressure drop stays constant.

If the flow velocity to the fluidized bed is reduced gradually the pressure drop remains constant, and the bed height decreases following the line BC. However, the final bed height may be greater than the initial value for the fixed bed, since solids dumped in a tube tend to pack more tightly than solids settling slowly from a fluidized state. Here, actually point B is considered as the minimum fluidization velocity.

Minimum fluidization velocity:

The velocity at which the pressure drop across the packed bed equals to the net downward forces is called minimum fluidization velocity. At this point the packed bed becomes fluidized bed. This is also sometimes referred to as the velocity at incipient fluidization.

(B). Pressure drop across the fluidized bed:

At minimum fluidization,

the net forces acting upon

the particle is zero

FD + Fb - Fg = 0

 FD = Fg - Fb

= mg - mfg = mg – (Vf) g

= mg – (Vp) g

= mg – (m/P) g

= mg (1-/P)

= P (1- ) V g (1-/P)

FD = (P -) g (1- ) V

P *A = (P -) g (1- ) V

P = (P -) g (1- ) V/A

P = (P -) g (1- ) L

= (P -) g (1- )

Fluidization starts at a point when the bed pressure drop exactly balances the net downward forces (gravity minus buoyancy forces) on the bed packing, so

p = (s - ) g L (1-)

This is the equation for the pressure drop across the fluidized bed.

At minimum fluidization, Pressure drop across the fluidized bed

equals to the pressure drop across the packed bed.  That means

we can relate the pressure drop across the bed to the Ergun equation.

Case1: For smaller particles (laminar flow, Re ≤ 1.0)

For very small particles (Re ≤ 1.0), only the laminar flow term of the Ergun equation is significant.

Case2: For larger particles (turbulent flow, Re > 1000)

For large particles (Re > 1000), only the turbulent flow term of the Ergun equation is significant.

Minimum porosity:  When we increase the fluid velocity the porosity of the bed also increases with the bed height. The porosity of the bed when true fluidization becomes is called the minimum porosity for fluidization (M).

The general equation for minimum porosity is given as, M = 1- 0.356 (log Dp – 1)

Where Dp is the particle diameter in microns.

Bed height: When the fluid velocity is increased above the minimum required for fluidization, the bed expands, and the porosity increase. If the cross sectional area of the vessel doesn’t change with height, the porosity is a direct function of the height of the bed.

(C). Advantages and disadvantages of Fluidization:

Advantages:

1. The chief advantage of fluidization is perfect contact of the fluid with all parts of the solid particles.
2. It prevents segregation of the particles by thoroughly agitating the bed.
3. Tremendous solid circulation takes place fro top to bottom of the fluidized bed ensuring rapid mixing of solids.
4. Proper mixing ensures:

1. No temperature gradients (no hot spots) even in large reactors with quite exothermic or endothermic reactions
2. Very high heat and mass transfer rates
3. High reaction rates in solid catalyzed reactions

5. In solid catalyzed reactions the conversion may be 2 to 10 times more in fluidized bed than in fixed bed
6. Liquid like behavior, easy to control and automate

Disadvantages:

1. The chief disadvantage of fluidization is greater power requirement because of higher pressure drop in fluidized beds
2. Serious erosion of pipe lines and vessel containers
3. Attrition of solid particles (loss of catalyst)
4. Need for larger reactor sizes and for recovery system
5. No-uniform flow patterns, so difficult to control

(D). Applications of Fluidization:

1. The largest-scale industrial application of fluidization is the catalytic cracking of heavy crude oil fractions to manufacture gasoline in petroleum industry, which is developed in World War-II.
2. Fluidized-Bed incineration: Fluidized bed system is commonly employed for incineration of solid wastes – like salty sludges left from most waste treatments.
3. Fluidized-Bed coal conversion: Fluid-bed pressurized gasifier is used to convert coal into a clean fuel gas.
4. Fluidized-Bed oil conversion: Fluidized-bed hydrozenator (FBH) is used to manufacture synthetic natural gas (SNG) from crude oil.
5. Fluidized-Bed drying: Loose granular solids, pasty mass and even liquid materials may be dried at a high rate in dryers with a fluidized bed system. Examples are drying of coal, cement, rock and limestone etc.

Other applications include:

6. Ore roasting such as sulfur, copper, cobalt and zinc sulfide ores
7. Manufacturing of cement
8. Manufacture of ethylene oxide from ethylene
9. Extraction of oil from oil-shale
10. Drying, coating and sizing of crystals
11. Transportation of solids etc.

(E). Types of Fluidization:

1. Particulate fluidization
2. Bubbling (or) Aggregative fluidization
3. Slugging fluidization
4. Spouted-bed fluidization

1. Particulate fluidization 

Particulate fluidization occurs in liquids and is characterized by even bed fluidization. As the velocity of the liquid is increased past the minimum fluidization velocity, the bed expands uniformly and density at a given velocity is same in all sections of the bed. In this type of fluidization the particles move individually. This occurs when the density difference of the solids and fluid is less and where the particles are small size.

       Particulate (or)    

    smooth fluidization

Merits:

1. Uniform momentum, heat and mass transfer

ε (Void fraction)

2. Equipments are smaller than in bubbling fluidization,

      so, investment cost is less.

3. Fixed flow patterns, so easy to control and also maintenance cost is less
4. Particles can’t escape from the bed unlike in the case of bubbling

      fluidization. So there is no problem of pollution to the environment

Demerits:

1. Pressure drops are higher as both viscous and kinetic losses have

       to be considered. So, power requirement is more.

2. Can be operated only at low velocities, so, less production rate
3. Separation of solids from fluids is relatively difficult and costly than

      aggregative fluidization

Application: Used in, 

1. Catalytic cracking of petroleum fractions

 Liquid

2. Oil industries
3. Slurry transportation (Ex: coal with water)

2. Bubbling (or) Aggregative fluidization

Bubbling fluidization occurs in gas-fluidized beds and is characterized by uneven bed fluidization. At superficial velocities much greater than Vmf most of the gas passes through the bed as bubbles or voids, which are almost free of solids, and only a small fraction of the gas flows in the channels between the particles. The density at a given velocity is not uniform at all the sections of the bed.

This occurs when the density difference of the solids and fluid is more and where the particles are large in size.

Merits:

1. Perfect fluid-solid contact (Gas can easily penetrate through the pores of the solid than the liquid in particulate fluidization)
2. Pressure drops are lower as kinetic losses only have to be considered. So, power requirement is less.
3. Can be operated at higher velocities, so, more production rate
4. Separation of solids from fluids is relatively easier and cheaper than particulate fluidization.

Demerits:

1. Non-uniform momentum, heat and mass transfer
2. Equipments are larger than in particulate fluidization, so, investment cost is more.
3. Complex flow patterns, so difficult to control and also maintenance cost is more
4. Particles can escape from the bed unlike in the case of particulate fluidization. So there is a problem of pollution to the environment (Ex: fly ash)
5. Large fluid velocities are required to lift the particles (as slip conditions between gas and solid prevail)

Applications: Used in,

1. Coal gasification
2. Biomass gasification
3. Pneumatic transportation
4. Fluidized-Bed coal conversion: Fluid-bed pressurized gasifier is used to convert coal into a clean fuel gas.
5. Fluidized-Bed drying: Loose granular solids, pasty mass and even liquid materials may be dried at a high rate in dryers with a fluidized bed system. Examples are drying of coal, cement, rock and limestone etc.

3. Slugging fluidization

When the particles are fluidized in a tall narrow vessel, same bubbling fluidization becomes slugging fluidization. This occurs particularly with the large particles.

Because of slip condition the rising particles will fall down and aggregate themselves at the bottom. Then the next batch fluid has to lift the aggregated particles. So larger bubble forms and sometimes if the diameter of the vessel is too small it occupies the entire cross section of the vessel.

Slugging can be avoided by going for smaller size of the particles and by using shallow beds of solids.

4. Spouted-bed fluidization

This is a desired one unlike the slugging fluidization.

 A spouted bed can be formed in vertical column where the fluid jet blows

vertically upward along the centerline of the column thus forming a spout in which there are fast moving fluid and entrained particles. The remainder of the particles bed, the annulus between spout and the column wall, is densely packed with particles moving slowly downwards and radially inwards.

Merits: 

Its success is attributed to its solids circulation characteristics and excellent gas-particle contact.

Demerits: 

The main disadvantage of spouted bed system is high pressure drop due to the expansion and friction through the inlet nozzle. This high pressure drop is due to the fact that all of the air is forced into the bed through inlet nozzle.

Applications: 

The spouted bed has been used in mainly in drying operation. Other applications are granulation, catalytic polymerization, residue treatment and coating of several materials.