Chapter 4 Fluid Flow through Packed Bed of Particles...Defining equivalent height of filter cake and...
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U i C h a p t e r 4 F l u i d F l o w t h r o u g h P a c k e d B e d o f P a r t i c l e s 4 . 1 P r e s s u r e D r o p - F l o w R e l a t i o n s h i p ( 1 ) L a m i n a r F l o w F l u i d f l o w t h r o u g h a p a c k e d b e d : s i m u l a t e d b y f l u i d f l o w t h r o u g h a h y p o t h e t i c a l t u b e s ∴ (- Δ p ) H = 32 μ U D 2 ⇒ (- Δ p ) H e = K 1 μ U i D 2 e H a g e n - P o i s e i l l e e q u a t i o n S u b s t i t u t i n g s u i t a b l e r e l a t i o n s ∴ (- Δ p ) H = 180 μ U x 2 (1- ε ) 2 ε 3 C a r m a n - K o z e n y e q u a t i o n ( 2 ) G e n e r a l E q u a t i o n f o r T u r b u l e n t a n d L a m i n a r F l o w E r g u n e q u a t i o n (- Δ p ) H = 150 μ U x 2 (1- ε ) 2 ε 3 + 1.75 ρ f U 2 x (1- ε ) ε 3 L a m i n a r T u r b u l e n t L a m i n a r f l o w f o r Re *= xU ρ f μ (1- ε ) < 10 T u r b u l e n t f l o w f o r Re *= xU ρ f μ (1- ε ) > 2000 o r f *= 150 Re * + 1.75 w h e r e f *≡ (- Δ p ) H x ρ f U 2 ε 3 (1- ε )
Transcript of Chapter 4 Fluid Flow through Packed Bed of Particles...Defining equivalent height of filter cake and...
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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
