Filtration p 2011annot(1)

8/3/2019 Filtration p 2011annot(1)

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Motivation

Aims and background

Filtration description

General filtration equation

Summary

Filtration

Solid-Fluids Systems

E Ventura-Medina

E Ventura-Medina Filtration
http://find/http://goback/


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Motivation

Aims and background



Summary

Outline

1 Motivation

2 Aims and background

3 Filtration description

Using packed beds to model filtration

4 General filtration equation

Cake resistance dependence with pressure dropConstant pressure filtration

Constant rate filtration

Scale-up



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Motivation

Aims and background



Summary

Outline

1 Motivation







Scale-up



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Motivation

Aims and background



Summary

Outline

1 Motivation







Scale-up



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Motivation

Aims and background



Summary

Outline

1 Motivation







Scale-up


M i i


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Motivation

Aims and background



Summary

Applications

Physical separationof solids from the

fluid

Dewatering of

sludges

Food processing


M ti ti


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Motivation

Aims and background



Summary

Industrial Filter Press


Motivation


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Motivation

Aims and background



Summary

Objectives and prior knowledge I

This topic aims to:

introduce the general filtration equation as a tool to

describe filtration processes,

introduce the concept of specific cake resistance and filtermedium resistance and how to obtain theses parameters

from laboratory filtration data,

show the dependence of specific cake resistance with

pressure drop changes,show calculations for filtration process operating under

constant filtration rate and constant pressure drop,

show calculations for filtration scale-up.


Motivation


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Motivation

Aims and background



Summary

Objectives and prior knowledge II

Prior knowledge:

fluid flow through packed beds

concept of driving force and rate changes

concept of compressible/incompressible fluids


Motivation


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Motivation

Aims and background



Summary


Outline

1 Motivation





Cake resistance dependence with pressure drop

Constant pressure filtration


Scale-up


Motivation


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Motivation

Aims and background



Summary


From a packed bed to a filter cake

Carman-Kozeny equation:

P

L

= 150v

dp2

(1 )2

3

for filtration we can write:

PcL

= 1v(1 )2

3a2sv

L : thickness of the cake

v : velocity of filtrate based on the empty cross-sectional area

Pc : Pressure drop across the cake

asv = 6/dp


Motivation


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Motivation

Aims and background



Summary



Pc = 1v(1 )2

3asv

2 L

v =Q

A=

1

A

dV

dt

Pc = 11A

dVdt

(1 )23

asv2 L


Motivation


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Aims and background



Summary



Pc = 1v(1 )2

3asv

2 L

v =Q

A=

1

A

dV

dt

Pc = 11

A

dV

dt

(1 )2

3asv

2 L

Material balance of solids:

LA(1 )p = C(V + LA)

p: density of the particlesC: mass of solids per volume of liquid

LA V

then

L =CsV

A(1 )p

Cs: mass of solids per volume of

filtrateE Ventura-Medina Filtration

Motivation


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Aims and background



Summary


Filter cake resistance

Pc =

CsV

A(1 )p

1

1

A

dV

dt

(1 )2

3asv

2

can be written as

1

A

dV

dt=

Pc

CsV

A

with

=1(1 )asv

2

p3

: specific cake resistance


Motivation


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Aims and background



Summary


Filter medium resistance

1A

dVdt

= PfRm

with

Rm: resistance of the filter medium and pipes going in and out

of the filter


MotivationCake resistance dependence with pressure drop


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Aims and background



Summary




Scale-up


1

A

dV

dt=

P

CsV

A+ Rm

(1)

where

CsV =Cx

1 mCxV

Cx: mass fraction of solids in slurry

m: mass ratio of wet cake to dry cake

: density of the filtrate


Motivation

Ai d b k dCake resistance dependence with pressure drop


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Aims and background



Summary




Scale-up


1

A

dV

dt=

P

CsV

A+ Rm

(1)

where

CsV =Cx

1 mCxV

Cx: mass fraction of solids in slurry

m: mass ratio of wet cake to dry cake

: density of the filtrate


Motivation

Ai d b k dCake resistance dependence with pressure drop


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Aims and background



Summary

p p p



Scale-up

Outline

1 Motivation








Scale-up


Motivation

Aims and backgroundCake resistance dependence with pressure drop


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Aims and background



Summary

p p p



Scale-up

Specific cake resistance

=1(1 )asv

2

p3

It is a function of porosity and specific surface area of the

solids asvIt depends on the pressure of the system

= 0(P)s (2)

0 and sare empirical constants obtained by gathering data of vs. P

= (P) = incompressible cake


Motivation

Aims and backgroundCake resistance dependence with pressure drop


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Aims and background



Summary



Scale-up


=1(1 )asv

2

p3



= 0(P)s (2)




MotivationAims and background



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Aims and background



Summary



Scale-up


=1(1 )asv

2

p3



= 0(P)s (2)







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Aims and background



Summary



Scale-up

Outline

1 Motivation








Scale-up




C fil i


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Aims and background



Summary



Scale-up

Operation at constant pressure I

The general filtration equation:

1

A

dV

dt

=P

CsVA

+ Rm

can be re-arrange when the pressure drop is constant so:

dt

dV =

Cs

A2(P)V +

A(P)Rm

integrating from initial time (t= 0,V = 0) to a given time (t,V)




C t t filt ti


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g



Summary



Scale-up

Operation at constant pressure II

t0

dt =V

0

CsA2(P)

V + A(P)

Rm

dV

t

V=

CsA2(P)

V

2+

A(P)Rm






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g



Summary



Scale-up

Resistance for Constant pressure filtration I

Example

A CaCO3 slurry in water at 298 K and concentration Cs =23.47 kg/m3 is filtered in a plate-and-frame filter press with an

area A=0.0439 m2

at constant pressure (P=338 kPa).Determine the specific cake resistance and the filter mediumresistance Rm from the experimental data given below.

t[s] V 103 [m3]

4.4 0.498

9.5 1.00016.3 1.501

24.6 2.000

34.7 2.498

t[s] V 103 [m3]

46.1 3.002

59.0 3.50673.6 4.004

89.4 4.502

107.3 5.009






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Summary



Scale-up

Resistance for Constant pressure filtration II

Finding t/V

t[s] V 103 [m3] t/V 103 [s/m3]

4.4 0.498 8.84

9.5 1.000 9.5016.3 1.501 10.86

24.6 2.000 12.30

34.7 2.498 13.89

46.1 3.002 15.36

59.0 3.506 16.8373.6 4.004 18.38

89.4 4.502 19.86

107.3 5.009 21.42






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Summary



Scale-up

Resistance for Constant pressure filtration III

Plotting t/V versus V



Fil i d i i




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Summary



Scale-up

Resistance for Constant pressure filtration IV

From plot t/V versus V

B= 6400 s/m3

Kp/2=3.00 106 s/m6.

therefore

= 1.863 1011 m/kg

Rm = 10.63 1010 m1



Filt ti d i ti




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Summary

Co sta t p essu e t at o


Scale-up

Outline

1 Motivation


3 Filtration descriptionUsing packed beds to model filtration





Scale-up







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Summary

p


Scale-up

Operation at constant rate I

The general filtration equation:

1

A

dV

dt=

P

CsV

A + Rm

can be re-arrange when the rate of filtration is constant so:

P = CsA2

dV

dtV + Rm

A

dV

dt

can be written as







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Summary


Scale-up

Operation at constant rate II

P = KvV + C

with

Kv =CsA2

dV

dt

; C =

RmA

dV

dt







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Summary


Scale-up

Outline

1 Motivation


3 Filtration descriptionUsing packed beds to model filtration



Constant pressure filtrationConstant rate filtration

Scale-up







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Summary


Scale-up

From laboratory data to large scale

The filter cake resistance , can be considered constant ifoperating both filters (laboratory and large scale) at the

same pressure.

The filter medium resistance in many cases can be

neglected or considered constant throughout a range of

conditions if insufficient data is available

Cake compressibility might be important and should betaken into account when possible.





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Summary

Summary

We have studied:

the general filtration equation as a tool to describe filtration

processes,

the concept of specific cake resistance and filter mediumresistance and how to obtain theses parameters from

laboratory filtration data,

the dependence of specific cake resistance with pressure

drop changes,

the calculations carried out for a filtration process under

constant filtration rate and constant pressure drop.

calculations that are carried out for filtration scale-up.





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p


Summary

Background to revise

fluid flow through packed bedsconcept of driving force and rate changes

concept of compressible/incompressible fluids


Documents

Filtration p 2011annot(1)