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Chapter 4 Fluid Flow through Packed Bed of

Particles

4.1 Pressure Drop - Flow Relationship

(1) Laminar Flow

Fluid flow through a packed bed: simulated by fluid flow through a

hypothetical tubes

∴ (- Δ p )H

=32μU

D 2

⇒ (- Δ p )H e

=K 1μU i

D2e

Hagen-Poiseille equation

Substituting suitable relations

∴ (- Δ p )H

= 180μU

x2

( 1- ε ) 2

ε 3

Carman-Kozeny equation

(2) General Equation for Turbulent and Laminar Flow

Ergun equation

(- Δ p )H

= 150μU

x2

( 1- ε ) 2

ε 3 + 1.75ρfU

2

x( 1 - ε )ε 3

Laminar Turbulent

Laminar flow for Re *=xU ρ fμ ( 1 - ε )

< 10

Turbulent flow for Re *=xU ρ fμ ( 1- ε )

> 2000

or

f*=150Re*

+1.75

where f * ≡(- Δ p )H

xρfU

2

ε 3

( 1- ε )

Filtrate

Filter cake

Slurry

Filter medium

Filtrate

Filter cake

Slurry

Filter medium

Batch Continuous

P r e s s u r e

Filtration

Filter Press

Shell-and-Leaf FiltersAutomatic Belt Filters

V a c u u m

FiltrationDiscontinuous Vacuum Filters

Rotary Drum Filters

Horizontal Belt FiltersCentrifugal

FiltrationBatch Types Continuous Types

Types of liquid filters

Friction factor

Figure 4.1

(3) Nonspherical Particles

x sv (surface-volume diameter) instead of x

Worked Example 4.1

4.2 Filtration

For filtration theory and practice, see

http://coel.ecgf.uakron.edu/~chem/fclty/chase/

FILTRATION%20FUNDAMENTALS_files/frame.htm

(1) Introduction

Filter media : Canvas cloth, woolen cloth, metal cloth, glass,

cloth, paper, synthetic fabrics

Filter aids : To avoid cake plugging

- Diatomaceous silica, perlite, purified woolen cellulose, other

inert porous solids

- By either adding slurry (increasing cake permeability)

or precoating the filter media surface

(2) Incompressible Cake

For cake filter

From laminar part of Ergun equation

(- Δ p )H

=150μU ( 1 - ε ) 2

x 2ε 3

where L : cake thickness

x : surface-volume diameter of particle

* For compressible filter cake,

dpdL

= r cμU

where r c: a function of pressure difference

By defining cake resistance r c

r c=150 ( 1 - ε ) 2

x2ε 3

,

(- Δ p )H

= r cμU

where U=1AdVdt

V: volume of slurry fed to filter

Also defining φ(volume formed by passage of unit volume filtrate)

φ= HAV

,

dVdt

=A 2 (- Δ p )r cμφV

Including the resistance of filter medium,

since the resistances of the cake and the filter medium are in

series,

(- Δ p ) = (- Δ p m )+ (- Δp c )

↓

1AdVdtr cμHc

By analogy for the filter medium

(-Δ p m )=1AdVdtr mμHm

∴ (- Δ p )=1AdVdt

( r m μH m+ r cμH c)

Defining equivalent height of filter cake and volume of filtrate

r mH m= r c H eq and H eq=φV eqA

where V eq: volume of filtrate passing to create a cake of thickness

H eq

∴ 1AdVdt

=(- Δ p)A

r cμ(V+V eq )φ

Constant rate filtration

1AdVdt

=(-Δ p)A

r cμ(V+V eq )φ= constant

Constant pressure filtration

Integrating

tV

=r cφμ

A 2(- Δ p ) ( V2 +V eq)

Worked Example 4.2

(3) Washing the Cake

Figure 4.2