FILTRATION OPERATION

IN. NURUL HASYIMAH MOHD AMIN

OBJECTIVES

• • • At the end of this lessons, students should be able to: Explain filtration process Explain basic operation of plate and frame filter press.

Determine the cake resistance, filter medium resistance and cake thickness.

INTRODUCTION

Filtration

may be defined as the separation of solids from liquids by passing a suspension through a permeable medium which retains the particles.

Figure 1.

Schematic diagram of filtration system

INTRODUCTION

• • • • •

INTRODUCTION

At initial stage, particles are deposited in the surface layers of the cloth to form the true filtering medium The cake gradually build up on the medium.

The resistance to flow progressively increases.

The pores of filter medium are larger than the particles which are to be removed.

In laboratory, filtration is often carried out using a form of Buchner funnel .

INTRODUCTION

1.0

0.8

PES25 (TG) PVDF (TG) PES25 (TG-FA) PVDF (TG-FA) 0.6

0.4

0.2

0.0

0 10 20 30 40 50 60 70

time (min)

Figure 5.2 Normalised flux decline for glycerine  water solutions with TG and TG  FA using PES25 and PVDF membranes

TYPES OF FILTRATION

1. Surface filters 2. Depth filters

1.SURFACE FILTERS

used for cake filtration in which the solids are deposited in the form of a cake on the up-stream side of a relatively thin filter medium.

Figure2.

Mechanism of cake filtration

TYPES OF FILTRATION PROCESS

•

Cake filtration

 This process applied based on the accumulation of the solute on the filter surface in a cake form.  It is expected that the concentration of the solute is high  Thus they can block the pores as well as located on the previously deposited and already arrived solute layer.  It is used for the case of larger solute than the pore size which can not enter the pore.

2.DEPTH FILTERS

used for deep bed filtration in which particle deposition takes place inside the medium and cake deposition on the surface is undesirable.

Figure 3.

Mechanism of deep bed filtration

* Also known as clarifiers.

* The particles of solid are trapped inside the filter medium.

FACTORS WHICH INFLUENCE THE RATE OF FILTRATION • • • • • • Pressure drop ( ∆P ) Area of filtering surface ( A ) Viscosity of filtrate ( v ) Resistance of filter cake ( α ) Resistance of filter medium ( R m ) Properties of slurry ( μ )

• • •

PURPOSE OF FILTRATION

To remove and recycle the filtrate.

To make the material or solids more suitable for handling.

To reduce the cost of transportation.

PLATE AND FRAME FILTER PRESS

PLATE AND FRAME FILTER PRESS: BASIC OPERATION

• This press is made up of two units, known respectively as plates and frames, with a filter medium, usually filter cloth, between the two. • The frame is open, with an inlet for the slurry, while the plate has grooved surface to support the filter cloth, and with an outlet for the filtrate.

The operation • • The slurry enters the frame from the feed channel, The filtrate passes through the filter medium on to the surface of the plate while the solids form a filter cake in the frame. • The filtrate then drained down the surface of the plate , between the projections on the surface and escapes from the outlet. • Filtration is continued until the frame is filled with filter cake, when the process is stopped , the frame emptied, and the cycle re started.

PLATE AND FRAME FILTER PRESS: BASIC OPERATION

• • • • • The process of Filtration will continue either until Filtrate no longer flows out of the discharge or if it is observed that the Pressure of Filtration suddenly rises. The increase in Pressure is the result of the Frame to be full of solid and prohibit Slurry to enter further. In this situation, the Filter can be called as ‘jammed’ Therefore, the Plate and Frame need be open in order to remove the Filter Cake from the Filter Medium. The Filter Cake which has been removed will be collected by dropping to a conveyor or a storage bin while the Filter Medium need to be washed for the next Filtration Cycle

FILTRATION SYSTEM

• •

PRINCIPLES OF CAKE FILTRATION

Constant-pressure filtration

: The pressure drop is held constant and the flow rate allowed to fall with time

Constant-rate filtration

: The pressure drop is progressively increased and the flow rate is held constant

• • • •

PRINCIPLES OF CAKE FILTRATION

In cake filtration, the liquid passes through 2 resistances: the cake and filter medium.

The filter medium resistance is only during the early stages of cake filtration.

The cake resistance is zero at the start and increases with time as filtration proceeds.

If the cake is washed after it is filtered, both resistances are constant during the washing period and that of the filter medium is usually negligible.

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE

Filter cake Slurry flow Filtrate dL L Fig 5.3: Section through a filter cake Filter medium

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE

• The flow of filtrate through the packed bed of cake can be described by Poiseuille’ Law assuming laminar flow in the filter channel 

p

  32  (

L

2 

p L



D

2 32 

D

2 

L

1 )  

p L

 32 

D

2 SI unit English unit (5.1) (5.2) (5.3)

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE Where ∆p ν D L μ g c pressure drop in N/m 2 (lb f /ft 2 ) open tube velocity in m/s (ft/s) diameter in m (ft) length in m (ft) viscosity in Pa.s or kg/m.s (lb m /ft.s) 32.174 lb m .ft/lb f .s

2

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • From Carman – Kozeny assuming laminar flow is relation; the pressure drop in the cake by  

p c L



k

1  ( 1    3 ) 2 (

s o

) 2 (5.4)  

p c L

 4 .

17  ( 1    3 ) 2 (

s o

) 2 (5.5)

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE Where k 1 μ L ν constant (4.17) viscosity of filtrate in Pa.s (lb m /ft.s) linear velocity based on filter area in m/s (ft/s) thickness of cake in m (ft) S 0 specific surface area of particle area per volume of solid particle (m 2 /m 3 ) ε void fraction or porosity of cake

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • The linear velocity is based on the empty cross sectional area is; • Where V t A   1

dV A dt

filter area in m 2 (ft 2 ) total filtrate collected in m 3 (ft 3 ) time in s (5.6)

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • The thickness of cake, L may be related to the volume of filtrate by a material balance.

L



A

( 1

C



s V

 ) 

p

(5.7) • • C s = kg solids/m 3 of filtrate ρ p = density of solid particles in the cake (kg/m 3 )

The fluid passes through the filter medium, which offers resistance to its passage, under the influence of a force which is the pressure differential across the filter .

rate of filtration = driving force/resistance

-(  P) or Pressure drop

rate of filtration = driving force/resistance

Filter cake (  ) Filter medium (R m ) Viscosity (  )

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • Substitute (5.6) into (5.4) and using (5.7) to eliminate L

dV Adt

 

k

1 ( 1    )(

s p p

 3

p c

/ 

p

) 2 

C s V A

   

p c C s V A

• Where α is the cake resistance in m/kg (ft/lb m ) (5.8)

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • The cake resistance can be defined as  

k

1 ( 1   )(

s p



p

 3 / 

p

) 2 (5.9) • For the filter medium resistance,

dV Adt

   

p R m f

(5.10)

• • BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE The filter medium resistance may vary with the pressure drop, since the higher liquid velocity caused by a large pressure drop may force additional particles of solid into the filter medium.

It also varies with the age and cleanliness of the filter medium.

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • Since the resistances of cake and filter medium are in series, equation (5.8) and (5.10) can be combined; • where

dV Adt

   

p



C s V



A R m



p

 

p c

 

p f

(5.11)

BASIC THEORY OF FILTRATION: PRESSURE DROP OF FLUID THROUGH FILTER CAKE • The volume of filtrate V related to accumulated dry cake solids m c

m c



C s V

 1    

c x m F m c

 

c x V

• Where slurry c x is the mass fraction of solids in the ρ is the density of filtrate (5.12)

FILTRATION EQUATION FOR CONSTANT PRESSURE FILTRATION: BATCH FILTRATION • Equation (5.11) can be rearrange;

dt dV



A

2 

C s

(  

p

)

V

 

A

(  

p

)

R m

(5.14)

dt dV



K c V

 1

q o

(5.15)

FILTRATION EQUATION FOR CONSTANT PRESSURE FILTRATION: BATCH FILTRATION • K c is in s/m 6 (s/ft 6 )

K c



A

2 

C s

(  

p

) SI unit

K c



A

2 

C

(  

p s

)

g c

English unit

FILTRATION EQUATION FOR CONSTANT PRESSURE FILTRATION: BATCH FILTRATION • 1/q o is in s/m 3 (s/ft 3 ) 1

q o

 

R m A

(  

p

) SI unit 1

q o



A

(  

R m



p

)

g c

English unit

FILTRATION EQUATION FOR CONSTANT PRESSURE FILTRATION: BATCH FILTRATION • The time of filtration is

t



K c V

2 2  1

q o V

• Dividing by V

V t



K c V

2  1

q o

(5.17) (5.18)

• • • FILTRATION EQUATION FOR CONSTANT PRESSURE FILTRATION: BATCH FILTRATION A plot of t/V versus V will be linear with a slope equal to K c /2 and intercept of 1/q 0 .

From the plot, the values of α values of slope and intercept.

and R m may be calculated from the Often the first point on the graph does not fall on the line and is omitted.

• • • FILTRATION EQUATION FOR CONSTANT PRESSURE FILTRATION: BATCH FILTRATION A plot of t/V versus V will be linear with a slope equal to K c /2 and intercept of 1/q 0 .

From the plot, the values of α values of slope and intercept.

and R m may be calculated from the Often the first point on the graph does not fall on the line and is omitted.

EXAMPLE 5.1:

Laboratory filtrations conducted at constant pressure drop on a slurry of CaCO3 in H2O gave the data shown in table below. The filter area was 440 cm 2 , the mass of solid per unit volume of filtrate was 23.5 g/L and the temperature was 25˚C. Evaluate the quantities  and R m as a function of pressure drop (  of water = 0.886 cP)

EXAMPLE 5.1:

FILTRATE VOLUME (l)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

TEST 1

17.3

41.3

72.0

108.3

152.1

201.7

TEST 2

6.8

19.0

34.6

53.4

76.0

102.0

131.2

163.0

TEST 3

6.3

14.0

24.2

37.0

51.7

69.0

88.8

110.0

134.0

160.0

TEST 4

5.0

11.5

19.8

30.1

42.5

56.8

73.0

91.2

111.0

133.0

156.8

182.5

TEST 5

4.4

9.5

16.3

24.6

34.7

46.1

59.0

73.6

89.4

107.3

• • • •

WASHING OF FILTER CAKES AND TOTAL CYCLE TIME

The washing of a cake after the filtration cycle has been completed takes place by displacement of the filtrate and by diffusion.

To calculate washing rates, it is assumed that the conditions during washing are the same as those that existed at the end of the filtration.

It is assumed that the cake structure is not affected when wash liquid replaces the slurry liquid in the cake.

The total filter cycle time is the sum of the filtration time + the washing rate + the cleaning time.

WASHING OF FILTER CAKES AND TOTAL CYCLE TIME

• For constant pressure filtration, using the same pressure in washing as in filtering; the final filtering rate is; •

dV

Where

dt

  

dV dt

  

f



K c V f

1  1

q o f

is the washing rate in m 3 /s (ft 3 /s) V f (5.19) is the total volume of filtrate for the entire period at the end of filtration in m 3

CONTINUOUS FILTRATION

• • In a continuous filter, the feed, filtrate and cake move at steady constant rates.

The resistance of the filter medium is generally negligible (1/q compared with the cake resistance.

o = 0)

CONTINUOUS FILTRATION

0 

t dt



K c

0 

V VdV t



K c V

2 2 (5.20) (5.21)

CONTINUOUS FILTRATION

• In a rotary drum filter, the filter time is less than the total cycle time, t .

c

t



ft c



f n

(5.22) • Where f is the fraction of the cycle used for the cake formation (fraction submergence of the drum surface in the slurry)

CONTINUOUS FILTRATION

flowrate



V At

c

   2

f

(  

p

)

t

c



C

s

   1 / 2 (5.23)

CONTINUOUS FILTRATION

• When short cycle times are used and/or filter medium resistance is relatively large, the term 1/q o must be included.

t



ft c



K c V

2 2  1

q o V

(5.24)

FILTRATION EQUATION FOR CONSTANT RATE FILTRATION

• • If the slurry is fed to the filter by a positive displacement pump.

Equation (5.11) can be rearranged  

p

 

C s A

2

dV dt

 

V

 

R m A dV dt



K v V



C

(5.25)

FILTRATION EQUATION FOR CONSTANT RATE FILTRATION

• Where

K v

    

C s A

2

dV dt

   SI unit

K v

   

C s A

2

g c dV dt

  • K v is in N/m 5 (lb f /ft5) English unit

FILTRATION EQUATION FOR CONSTANT RATE FILTRATION

C

 

R m A dV dt C

   

R m Ag c dV dt

  C is in N/m 2 (lb f /ft 2 ) SI unit English unit

FILTRATION EQUATION FOR CONSTANT RATE FILTRATION

• • • • Assuming that the cake is incompressible, K v and C are constant characteristic of the slurry, cake , rate of filtrate flow and so on.

Plot of -∆p versus the total volume of filtrate, V gives a straight line.

The slope is K v and the intercept is C.

The pressure increases as the cake thickness increases and the volume of filtrate collected increases.

FILTRATION EQUATION FOR CONSTANT RATE FILTRATION

• • The equation can be rearranged in terms of -∆p and time, t.

Total volume related to the rate and total time as;

V



t dV dt

(5.26)

FILTRATION EQUATION FOR CONSTANT RATE FILTRATION

• Substitute equation (5.26) into (5.25)  

p

    

C s A

2

dV dt

2   

t

 

R m A dV dt

(5.27)