Fixed bed and fluidized bed - PowerPoint PPT Presentation

• 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

• 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)

• 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 ==> volumetric flow rate

Ap,

Vp

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

• Sphericity <=> specific surface area <=> 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 ==> larger surface area

As,

Vs

Rings (Raschig,etc)

Tarus saddle

Pall Ring

• 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
• ==> all particles have exactly same specific surface area

• 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)

• 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

• 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

• 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)

• 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

• To calculate the pressure drop, use Force balance

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

• Until now, we haven’t said anything about laminar flow. So the above equations are valid for both laminar and turbulent flows

• 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

• 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

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

• 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?

• Force balance: Substitute for t etc.

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

• Pressure drop

• Specific surface area vs “average diameter”

• Define “average Dia” of particle as

• Some books (BSL) use Dp

In terms of specific surface area

In terms of average particle diameter

• 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)

f

Re

• However

• Pressure drop and shear stress equations

• Only the expression for shear stress changes

• For high turbulence (high Re),

Hence, force balance

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

• We have already developed an expression for contact area

In terms of average particle diameter

In terms of specific surface area

Ergun Equation for packed bed

• 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!

Ergun Equation for packed bed

• 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

• 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...

Reynolds number for packed bed

• Multiply by 3 on both sides (why?)

• Packed bed friction factor = 3 f

Eqn in McCabe and Smith

• 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?

• 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

• Sphericity vs Void Fraction

1

f

~0.4

0

1

e

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

• 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

• Empirical correlation for porosity

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

• 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

80

• Range of operation depends on Ar

40

R

0

100

104

108

Ar

• Criteria for aggregate fluidization
• Semi empirical

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