Fixed bed and fluidized bed

1
Fixed bed and fluidized bed

• Ref BSL, McCabe Smith

• Why fixed (or fluidized) bed?
• Expensive Catalyst
• enzyme (immobilized)
• Large Surface area
• Used in reaction/adsorption/ elution (for example)

• Goal Expression for pressure drop, try some
  examples

2
Fixed bed

• Filled with particles
• Usually not spherical
• To increase surface area
• To increase void fraction
• To decrease pressure drop
• For analytical calculation, assume all particles
  are identical
• Usable, because final formula can be modified by
  a constant factor (determined by experiment)

3
Fixed bed

• What are important parameters?
• (For example, for adsorption of a protein from a
  broth)
• rate of adsorption (faster is better)
• saturation concentration (more is better)
• From the product requirement (eg X kg per day),
  density and product concentration in broth gt
  volumetric flow rate

4
Fixed bed

• Assume quick adsorption (rate of adsorption is
  high)
• Calculate the surface area of particles needed
  for operation

• Sphericity ltgt specific surface area ltgt average
  particle diameter

• Sphericity
• Volume of particle Vp
• Surface Area of particle Ap
• Surface Area of sphere of same volume (Vs Vp)
  As
• Sphericity As/Ap
• May be around 0.3 for particles used in packed
  beds
• lower sphericity gt larger surface area

As, Vs
5
Fixed bed

• Specific surface area
• Ap /Vp
• Minimal value for sphere
• Some books use S to denote area (instead of A)
• Assume all the particles are identical
• gt all particles have exactly same specific
  surface area

6
Fixed bed

• What is the pressure drop we need, to force the
  fluid through the column?
• (i.e. what should be the pump spec)
• We know the volumetric flow rate (from adsorption
  equations, productivity requirements etc)
• We know the area per particle (we assume all
  particles are identical). And the total area for
  adsorption (or reaction in case of catalytic
  reactor).
• Hence we can calculate how many particles are
  needed
• Given a particle type (eg Raschig ring) , the
  approximate void fraction is also known (based on
  experimental results)

7
Fixed bed

• What is void fraction?
• Volume of reactor VR
• Number of particles Np
• Volume of one particle Vp
• Volume of all the particles Vp Np
  VALL-PARTICLES

• Knowing void fraction, we can find the reactor
  volume needed
• Alternatively, if we know the reactor volume and
  void fraction and the Vp, we can find the number
  of particles

8
Fixed bed

• To find void fraction experimentally
• Prepare the adsorption column (or reactor....)
  and fill it with particles
• Fill it with water
• Drain and measure the quantity of water
• ( void volume)
• Calculate void fraction

9
Fixed bed

• Since we know Vp, Np, e, we can find VR
• Choose a diameter and calculate the length (i.e.
  Height) of the column (for now)
• In normal usage, both the terms height and
  length may be used interchangeably (to mean the
  same thing)
• Adsorption rate, equilibrium and other parameters
  will also influence the determination of height
  diameter
• To calculate the pressure drop
• Note columns with large dia and shorter length
  (height) will have lower pressure drop
• What can be the disadvantage(s) of such design ?
  (tutorial)

10
Fixed bed

• To calculate the pressure drop
• You want to write it in terms of known quantities
• Length of column, void fraction, diameter of
  particles, flow rate of fluid, viscosity and
  density
• Obtain equations for two regimes separately
  (turbulent and laminar)
• Consider laminar flow

• Pressure drop increases with
• velocity
• viscosity
• inversely proportional to radius
• Actually, not all the reactor area is available
  for flow. Particles block most of the area. Flow
  path is not really like a simple tube
• Hence, use hydraulic radius

11
Fixed bed - pressure drop calculation (Laminar
flow)

• To calculate the pressure drop, use Force balance

• Resistance due to Shear
• Find Contact Area
• Find shear stress

• Until now, we havent said anything about laminar
  flow. So the above equations are valid for both
  laminar and turbulent flows

12
Fixed bed - pressure drop calculation (Laminar
Flow)

• Find contact area

• To calculate the shear stress, FOR LAMINAR FLOW

• Here V refers to velocity for flow in a tube

• However, flow is through bed, NOT a simple tube

13
Fixed bed - pressure drop calculation (Laminar
Flow)

• Find effective diameter (i.e. Use Hydraulic
  radius), to substitute in the formula
• Also relate the velocity between particles to
  some quantity we know

• To find hydraulic radius ( and hence effective
  dia)

• Hydraulic diameter

14
Fixed bed - pressure drop calculation (Laminar
Flow)

• Vavg is average velocity of fluid in the bed,
  between particles
• Normally, volumetric flow rate is easier to find

15
Fixed bed - pressure drop calculation (Laminar
Flow)

• Can we relate volumetric flow rate to Vavg ?
• Use a new term Superficial velocity (V0)

• I.e. Velocity in an empty column, that will
  provide the same volumetric flow rate
• Can we relate average velocity and superficial
  velocity?

16
Fixed bed - pressure drop calculation (Laminar
Flow)

• Force balance Substitute for t etc.

• Volume of reactor (say, height of bed L)

17
Fixed bed - pressure drop calculation (Laminar
Flow)

• Pressure drop

• Specific surface area vs average diameter

• Define average Dia of particle as

• Some books (BSL) use Dp

18
Fixed bed - pressure drop calculation (Laminar
Flow)

• Pressure drop

• However, using hydraulic radius etc are only
  approximations
• Experimental data shows, we need to multiply the
  pressure requirement by 2 (exactly 100/48)

19
Fixed bed - pressure drop calculation (Turbulent
Flow)

• Pressure drop and shear stress equations

• Only the expression for shear stress changes

• For high turbulence (high Re),

20
Fixed bed - pressure drop calculation (Turbulent
Flow)

• We have already developed an expression for
  contact area

21
Fixed bed - pressure drop calculation (Turbulent
Flow)

• Value of K based on experiments 7/24

• What if turbulence is not high?
• Use the combination of laminar turbulent
  pressure drops valid for all regimes!

22
Fixed bed - pressure drop calculation (Laminar OR
Turbulent Flow)

• If velocity is very low, turbulent part of
  pressure drop is negligible
• If velocity is very high, laminar part is
  negligible

• Some texts provide equation for friction factor

23
Fixed bed - pressure drop calculation (Laminar OR
Turbulent Flow)

• For pressure drop, we multiplied the laminar part
  by 2 (based on data) . For the turbulent part,
  the constant was based on data anyway.
• Similarly...

24
Fixed bed - pressure drop calculation (Laminar OR
Turbulent Flow)

• Multiply by 3 on both sides (why?)

• Packed bed friction factor 3 f

Eqn in McCabe and Smith
25
Example

• Adsorption of Cephalosporin (antibiotic)
• Particles are made of anionic resin(perhaps resin
  coatings on ceramic particles)
• void fraction 0.3, specific surface area 50
  m2/m3(assumed)
• column dia 4 cm, length 1 m
• feed concentration 2 mg/liter (not necessary to
  calculate pressure drop, but needed for finding
  out volume of reactor, which, in this case, is
  given). Superficial velocity about 2 m / hr
• Viscosity 0.002 Pa-s (assumed)
• What is the pressure drop needed to operate this
  column?

26
Fixed Bed

• What is the criteria for Laminar flow?
• Modified Reynolds Number
• Turbulent flow- Inertial loss vs turbulent loss
• Loss due to expansion and contraction
• Packing uniformity
• In theory, the bed has a uniform filling and a
  constant void fraction
• Practically, near the walls, the void fraction is
  more

• Ergun Eqn commonly used, however, other empirical
  correlations are also used
• e.g. Chilton Colburn eqn

0.8
e
0.4
0.2
Edge
Center
Edge
27
Fixed Bed

• Sphericity vs Void Fraction

1
f
0.4
0
1
e
28
Fixed Bed

• Alternate method to arrive at Ergun equation (or
  similar correlations)
• Use Dimensional analysis

29
Fluidized bed

• When the fluid (moving from bottom of the column
  to the top) velocity is increased, the particles
  begin to move at (and above) a certain
  velocity.
• At fluidization,
• Weight of the particles pressure drop (area)
• Remember to include buoyancy

30
Fluidized bed Operation

• Empirical correlation for porosity

• Types of fluidization Aggregate fluidization vs
  Particulate fluidization
• Larger particles, large density difference
  (rSOLID - rFLUID) gt Aggregate fluidization
  (slugging, bubbles, etc)
• gt Typically gas fluidization
• Even with liquids, lead particles tend to
  undergo aggregate fluidization
• Archimedes number

31
Fluidized bed Operation

• Porosity increases
• Bed height increases
• Fluidization can be sustained until terminal
  velocity is reached
• If the bed has a variety of particles (usually
  same material, but different sizes)
• calculate the terminal velocity for the smallest
  particle
• Range of operability R
• Minimum fluidization velocity incipient
  velocity (min range)
• Maximum fluidization velocity terminal velocity
  (max range)
• Other parameters may limit the actual range
  further
• e.g. Column may not withstand the pressure, may
  not be tall enough etc
• R Vt/VOM
• Theoretically R can range from 8.4 to 74

32
Fluidized bed Operation
80

• Range of operation depends on Ar

40
R
0
100
104
108
Ar
33
Fluidized bed Operation

• Criteria for aggregate fluidization
• Semi empirical

• Particulate fluidization
• Typically for low Ar numbers
• More homogenous mixture