Sedimentation & filtration

Present by : Ngoc Tran Shamia salih

Hong Nguyen

Sedimentation

Sedimentation is the natural process in which particles is carried to the bottom of a body of water and forms a solid layer

Sedimentation

Purpose

To measure the diameter of the particles

At fixed time intervals samples were taken from the suspension at different depth

Industrial use

Water treatment

Food industry

In geology

Blood test

Hydrometer Hydrometer is used to determine the

specific gravity or relative density of liquids

It is normally made of glass and it is usually weighted with mercury or lead shot to make it flow upright.

Hydrometer

The operation of hydrometer is based on Archimedes’ principle

The lower the density of the substances, the further the hydrometer will sink

Hydrometer

There are different types of hydrometer used based on the density of the liquid

variety of scales of hydrometer used depending on what you want to measure

A Type of Hydrometer

Procedure Measure a white solid powered (20g)

Procedure Fill a 1000ml cylinder with 900ml of

water

Procedure

Pour the white powder into the cylinder and shake it until the water and the powder are evenly distributed

Procedure Then place the hydrometer into the

cylinder

Procedure Measure the temperature

Then set the timer

Measure the height of the hydrometer at 0 seconds

And then start recording the height in time intervals until the height is constant

p

eB

amFforcebuoyantThe

:.1

2:.2

2pOD

D

AuCFforcedragThe

mgFforcegravityThe G :.3

Motion of sphere particle

DBG FFFdt

dumforceofSum :.4

m

uACg

m

uACgg

dt

du pD

p

ppD

p 2

)(

2.5

22

0.6 dt

dutakingbysettlingnalgravitatioFor

pfpD

ppt AC

mguvelocitySettlingTherfore

)(2

:

If the particles are sphere of diameter Dp

At low Reynolds numbers the drag coefficient varies inversely with Re of particle

MOTION OF SPHERE PARTICLE

6:.1

3ppgDmparticleofMass

4:.2

2p

p

DAparticleofArea

fD

pfpt C

DguvelocitySettling

3

)(4:

18

)(3&

Re

242gD

uDuFC fptptDD

Re=G*D/µ)

To calculate values of effective depth from the equation: L = L1 + 0.5(L2 -VB /A) or table 2

L1 : distance along the stem of the hydrometer from the top of the bulb to the mark for a hydrometer reading.

L2 : overall length of the hydrometer bulb (L2 = 14.0 cm)

V B :volume of hydrometer bulb (V B = 67.0 cm3)

A = cross-sectional area of sedimentation cylinder (A = 27.8 cm2)

To find the value correction factor α from table 1

To find K value from table 3

CALCULATION DIAMETER OF THE PARTICLE

SG=2.53 α=1.024

%100)(

% 1

pM

bLP

Reading L1=10 L=14.7

At 220C & SG=2.53 K=0.01307

CALCULATION & ANALYSIS

t

LKDp %100

)(% 1

pM

bLP

Temperature : 22 0C

Volume (ml) 900ml

Dry mass (gram) 20g

Concentration: 22%

SG : 2.53g/cm3

K (Table 3) 0.01307

a (Correction Factor Gs) 1.024

b (Correction Factor Temp)

4.4

T (min)Actual

reading Effective L D (mm) % P

0 20 13.04

1 18 13.37 0.05 69.63

2 17 13.53 0.04 64.51

3 15 13.86 0.03 54.27

4 14 14.02 0.03 49.15

5 12 14.34 0.02 38.91

6 11 14.51 0.02 33.79

7 10 14.67 0.02 28.67

8 9 14.83 0.02 23.55

9 8 15.00 0.02 18.43

10 7 15.16 0.02 13.31

11 6 15.32 0.02 8.19

12 6 15.32 0.02 8.19

0 2 4 6 8 10 12 1411.50

12.00

12.50

13.00

13.50

14.00

14.50

15.00

15.50

16.00

f(x) = 0.897557613913866 ln(x) + 13.0126256633382R² = 0.9471580873965f(x) = 13.0591584665652 x^0.0624606743875519R² = 0.954148973226955

f(x) = 0.187002197802198 x + 13.2449142857143R² = 0.975805758487322

Height Vs. Time

Time (min)

L (

mm

)

THEORY OF FILTRATION

Filtration is a very important step in the entire process of solid-liquid separation which can be sub-divided into four major stages

(1) Pretreatment

(2) Solids concentration

(3) Solids separation

(4) Post-treatment

Types of filtration

Basically, there are two types of filtration (1) Depth filters - used for deep bed

filtration where particle deposition takes place inside the medium and cake deposition on the surface is undesirable.

(2) Surface filters – Used for cake filtration where the solids are deposited in the form of a cake on the up-stream side of a relatively thin filter medium.

Rotary Filtration

Purpose: To separate water and solid

A pre-coat is a layer of fine particular material added on to the filter septum before filtration to form a coating cake

Rotary vacuum filter drum

+ consist of a drum rotating in a tub of liquid to be filtered.

+ pre –coat

+vacuum sucks liquid and solids onto the drum pre- coat surface .

+ the solids adhere to the outside of the drum

+ knife cut the solid out of drum .

The knife advances automatically as the surface is removed.

https://www.youtube.com/watch?v=4MFI-JFhBAU&feature=youtu.be

The pump • Vacuum filtration usually

involves the use of a vacuum filter flask, a filter trap, a water pump

• the liquid is sucked down into the filter flask by the action of the water pump, and any excess liquid that overflows out of the filter flask is caught in the filter trap

Procedure

Fill the tank with the mixture Turn on the valve for water go to the

pump Turn off all the valves which are drain

out the water from the tank, pump, and drum.

Turn on the main switch and all the buttons.

Continue

Vacuum pump Agitator drive Filter drive Pre-coat drive Filtrate pump

Valve for water come to the pump

(blue)valve for water drain out the tank after finish

(green )valve control the water go to the pump

Drain valve

Valves drain out all water after finish

The filter-cake resistance

specific resistance the local porosity and permeability (or specific resistance), as well as the constitutive relations for the drag force between the phases and the solid matrix stress are required to obtain the numerical solution of the equations.

The medium resistance is a function of the medium itself and the material being filtered.

Resistance arises from the filter cloth, mesh, or bed, and to this is added the resistance of the filter cake as it accumulates.

The filter-cake resistance is obtained by multiplying the specific resistance of the filter cake, that is its resistance per unit thickness, by the thickness of the cake. R = µr(Lc + L)

THE PROPERTIES OF A FILTER CAKE

The key properties of a filter cake are the cake porosity and permeability

The cake porosity (ε ) is a measure of the fluid capacity of the formed cake or the fraction of a porous medium available for fluid flow.

The cake permeability ( k ) is an indication of how easily the fluid can pass through its voids under an applied pressure gradient.

The extent of permeability is determined by the porosity of the medium and also the sizes of pores in its internal structure.

θ: Angle comprising the sector immersed in the suspension

Dry cake

Wet cake

Batch filtration

Rotary filtration

MASS BALANCE FOR THE SOLID IN THE CAKE

Solids accumulate in cake = Solids removed from suspension. LAԐ the volume of water in the cake

The volume of water contained in the LAԐ is much smaller than VF1 the volume of filtrate.

PRESSURE DROP DURING CAKE FILTRATION

)2

(1 2

msck

mcsc

FF RPXtf

RtXAt

V

A

Q

PXtf

tXAt

V

A

Q sck

csc

FF

21

PXtf

tAt

XVX

A

QG SCk

CC

SFS

FF

21

Fraction Submergence of drum surface θ/2π : fk

Time cycle 2π/ω : tc

The time immersion period in each cycle : t= tc * fk

Rotation velocity ω (rad/s)

If the Rm is very small

Amount of solid

Rotary Vacuum Filtration

Filtration Flux

θ: Angle comprising the sector immersed in the suspension

CONCLUSION

The diameter of the particle The concentration of the particles The cake permeability ( k ) is an indication of how easily the fluid can pass

through its voids under an applied pressure gradient

The cake porosity (ε ) is a measure of the fluid capacity of the formed cake or the fraction of a porous medium available for fluid flow Pressure drop

Total pressure drop: P drop cross filter & P drop due to filter medium

Specific cake resident: the local porosity and permeability

The speed of the drum rotation ω The filtrate flow rate

The amount of solid

PXtf

tXAt

V

A

Q sck

csc

FF

21

PXtf

tAt

XVX

A

QG SCk

CC

SFS

FF

21

References

Unit Operations textbook Dr. Lo Dr. JangMr. Minh TranFriend: Codyhttp://www.engineering-resource.comhttp://www.filtration-andseparation.comhttp://www.engr.uky.edu

QUESTIONS