FM 304

Batch Settling of Solid Slurries

Name of the group: A7

Student Information

07002035 Kshitij Gupta

07002036 Mayank Sharma

07002037 Anasuya Mandal

07002038 Mukul Bansal

07002039 Sumit Chandra Prasad

Date of submission: 25th

September 2009

Motivation Settling is the process by which particulates settle to the bottom of a liquid and form a sediment.

Particles that experience a force, either due to gravity or due to centrifugal motion will tend to move

in a uniform manner in the direction exerted by that force. For gravity settling, this means that the

particles will tend to fall to the bottom of the vessel, forming a slurry at the vessel base.

Settling is an important operation in processes such as

• Mining

• Wastewater treatment

• Biological science

• Food processing

Aim Vertical Cylinders: Obtain the batch settling data for the given calcium carbonate slurry (i.e. the

settling rate versus concentration of slurry), and demarcate the different settling regimes (‘free

settling” and ‘hindered settling’).

Inclined Cylinders: Obtain the batch settling data in the free settling regime for different angles (100

and 150). Observe the flow patterns during the settling.

Apparatus Vertical settling cylinder, inclined settling cylinder, glass rod, stop watch

Reagents: Water, Calcium Carbonate

Summary of Procedure

Vertical Cylinder:

1. Note the initial concentration of slurry in the measuring cylinder (gm/lt).

2. Record the initial height of the slurry bed below the clear liquid before mixing.

3. Agitate the system thoroughly using the glass rod provided.

4. Repeat noting the slurry level at two min. intervals till the level of slurry reaches a constant

height. This height should be equal to the original height of slurry noted.

5. Carry out this exact same procedure for the second vertical cylinder simultaneously.

Tilted Cylinder:

1. Fix the angle of the cylinder to 100. Note the initial concentration of slurry (gm/lt).

2. Record the initial height of the slurry bed below the clear liquid before mixing.

3. Agitate the system thoroughly using the glass rod provided.

4. As soon as the system is thoroughly mixed, note the slurry level.

5. Repeat noting the slurry level at two min. intervals till the level of slurry reaches a constant

height. This height should be equal to the original height of slurry noted.

6. Repeat the entire procedure for cylinder inclination 150.

Theory

The terminal velocity of the particle is affected by many parameters, i.e. anything that will alter the

particle's drag. Hence the terminal velocity is most notably dependent upon

• Grain size,

• The shape (roundness and sphericity) and

• Density of the grains

• The viscosity and density of the fluid.

For vertical cylinders:

For a particle in a dilute solution, there are only three forces acting on the particle. There is a

downward force of gravity and upward forces of buoyancy and viscous drag. The free body diagram

of a particle can be given as:

The particle keeps on accelerating under the effect of gravity. The drag

force, however is a function of the particle velocity. When the velocity reaches

such a value that the drag and the buoyant forces together equal the force of

gravity, the particle stops accelerating. This constant velocity the particle has

achieved is called the terminal velocity of the particle. This velocity is affected by

the grain size, shape (roundness & sphericity), density of grains as well as the

viscosity and density of the fluid. Writing a force balance on a particle which has

achieved its terminal velocity ut:

Where Fg=gravitational force, Fb=buoyant force and Fd=viscous drag.

Substituting the relevant values of the forces,

r=radius of the particle, =density of the particle, =density of the fluid, =viscosity

solving for ut, we get,

Consequently,

Drag coefficient CD:

Fd Fb

Fg

These equations hold till such time as the settling is in the free regime. When the

concentration increases beyond a point, the settling passes from the free regime to the hindered

regime. For the hindered regime, the settling velocity is given by the empirical equation:

The concentration is given by

During the free fall regime,

For inclined cylinder:

With inclined cylinders, the rate of settling increases with the angle of inclination. This effect

was discovered by Boycott in 1920. This effect is observed because as a result of the inclination, the

total sedimentation path is shortened. As a consequence, the rate of settling increases. The theory

explaining this effect was proposed by Ponder-Nakamura and Kuroda (PNK theory). This theory is

based on the increased projected area available for settling. The volumetric rate of increase of clear

fluid (S) is given, according to this theory by:

Where,

S=Volumetric rate of settling

W=width of cylinder

b=breadth of cylinder

H=height of liquid column

=inclination of the cylinder with the surface

The rate of change of height is given by:

H(t)

H0

b

b

H0 H(t)

Observations:

Vertical Cylinders : Time

(mins) Column 1 Column 2

dh/dt (col

1)

dh/dt (col

2)

Concentration

1 (25*Ho/H)

Concentration

2 (12.5*Ho/H)

eps1 =

(1-C/rho)

eps2 = (1-

C/rho)

0 23 16

2 425 441 13.5 24.5 27.65 13.32 0.99 0.99

4 398 392 14 24.5 29.52 14.99 0.99 0.99

6 370 343 12.5 25 31.76 17.13 0.99 0.99

8 345 293 13.5 20.5 34.06 20.05 0.98 0.99

10 318 252 14 19.5 36.95 23.31 0.98 0.99

12 290 213 12.5 25.5 40.52 27.58 0.98 0.99

14 265 162 11 23.5 44.34 36.27 0.98 0.98

16 243 115 13.5 25 48.35 51.09 0.98 0.98

18 216 65 12 19.5 54.40 90.38 0.97 0.96

20 192 26 12.5 1.5 61.20 225.96 0.97 0.90

22 167 23 11 0.5 70.36 255.43 0.97 0.88

24 145 22 12.5 0 81.03 267.05 0.96 0.88

26 120 22 11.5 0.5 97.92 267.05 0.95 0.88

28 97 21 11 0.5 121.13 279.76 0.94 0.87

30 75 20 10.5 0.5 156.67 293.75 0.93 0.86

32 54 19 1.5 0 217.59 309.21 0.90 0.86

34 51 19 1 0 230.39 309.21 0.89 0.86

36 49 19 1.5 0.5 239.80 309.21 0.89 0.86

38 46 18 1 0 255.43 326.39 0.88 0.85

40 44 18 1 0 267.05 326.39 0.88 0.85

42 42 18 1 0 279.76 326.39 0.87 0.85

44 40 18 0.5 0.5 293.75 326.39 0.86 0.85

46 39 17 1 0 301.28 345.59 0.86 0.84

48 37 17 1 0 317.57 345.59 0.85 0.84

50 35 17 0.5 0 335.71 345.59 0.85 0.84

52 34 17 1 0 345.59 345.59 0.84 0.84

54 32 17 1 0.5 367.19 345.59 0.83 0.84

56 30 16 0 0 391.67 367.19 0.82 0.83

58 30 16 0.5 0 391.67 367.19 0.82 0.83

60 29 16 0 0 405.17 367.19 0.81 0.83

62 29 16 0.5 0 405.17 367.19 0.81 0.83

64 28 16 0 0 419.64 367.19 0.81 0.83

66 28 16 0 0 419.64 367.19 0.81 0.83

68 28 16 0.5 0 419.64 367.19 0.81 0.83

70 27 16 0 0 435.19 367.19 0.80 0.83

72 27 16 0 0 435.19 367.19 0.80 0.83

74 27 16 0.5 0 435.19 367.19 0.80 0.83

76 26 16 0 0 451.92 367.19 0.79 0.83

78 26 16 0 0 451.92 367.19 0.79 0.83

80 26 16 0 0 451.92 367.19 0.79 0.83

82 26 16 0 0 451.92 367.19 0.79 0.83

84 26 16 0 0 451.92 367.19 0.79 0.83

86 26 16 0.5 0 451.92 367.19 0.79 0.83

88 25 16 0 0 470.00 367.19 0.78 0.83

90 25 16 0 0 470.00 367.19 0.78 0.83

92 25 16 0 0 470.00 367.19 0.78 0.83

94 25 16 0 0 470.00 367.19 0.78 0.83

96 25 16 0 0 470.00 367.19 0.78 0.83

Calculations

For Vertical Cylinders :

From the graphs, the terminal velocities for the two vertical cylinders are:

Cylinder 1: Ut= 12.40 mm/min

Cylinder 2: Ut= 23.01 mm/min

Cylinder 1: Dp= 14.89 μm

Cylinder 2: Dp= 20.28 μm

Inclined Cylinders :

Time

(mins)

(Tilted

10°)

(Tilted

15°)

Vertical

Height

(mm) – H1

* cos10

Vertical

Height

(mm) – H2

* cos15

dH/dt1 dH/dt2 C1 C2 Ut1 Ut2 S1 S2

0 11 11 10.83 10.63

2 88 86 86.66 83.07 3.50 3.45 12.50 12.79 2.98 2.94 355.40 350.00

4 81 78 79.77 75.34 3.00 2.95 13.58 14.10 2.56 2.52 304.63 300.00

6 75 72 73.86 69.55 3.50 3.45 14.67 15.28 2.98 2.94 355.40 350.00

8 68 64 66.97 61.82 3.00 2.95 16.18 17.19 2.56 2.52 304.63 300.00

10 62 58 61.06 56.03 2.50 2.46 17.74 18.97 2.13 2.10 253.86 250.00

12 57 52 56.13 50.23 2.50 2.46 19.30 21.15 2.13 2.10 253.86 250.00

14 52 47 51.21 45.40 2.00 1.97 21.15 23.40 1.70 1.68 203.08 200.00

16 48 43 47.27 41.54 2.50 2.46 22.92 25.58 2.13 2.10 253.86 250.00

18 43 40 42.35 38.64 1.00 0.98 25.58 27.50 0.85 0.84 101.54 100.00

20 41 37 40.38 35.74 1.50 1.48 26.83 29.73 1.28 1.26 152.31 150.00

22 38 34 37.42 32.84 1.00 0.98 28.95 32.35 0.85 0.84 101.54 100.00

24 36 32 35.45 30.91 1.00 0.98 30.56 34.38 0.85 0.84 101.54 100.00

26 34 31 33.48 29.94 1.00 0.98 32.35 35.48 0.85 0.84 101.54 100.00

28 32 28 31.51 27.05 1.00 0.98 34.38 39.29 0.85 0.84 101.54 100.00

30 30 27 29.54 26.08 0.50 0.49 36.67 40.74 0.43 0.42 50.77 50.00

32 29 26 28.56 25.11 1.00 0.98 37.93 42.31 0.85 0.84 101.54 100.00

34 27 24 26.59 23.18 0.50 0.49 40.74 45.83 0.43 0.42 50.77 50.00

36 26 23 25.61 22.22 0.50 0.49 42.31 47.83 0.43 0.42 50.77 50.00

38 25 22 24.62 21.25 0.50 0.49 44.00 50.00 0.43 0.42 50.77 50.00

40 24 21 23.64 20.29 1.00 0.98 45.83 52.38 0.85 0.84 101.54 100.00

42 22 20 21.67 19.32 0.50 0.49 50.00 55.00 0.43 0.42 50.77 50.00

44 21 19 20.68 18.35 0.50 0.49 52.38 57.89 0.43 0.42 50.77 50.00

46 20 18 19.70 17.39 0.00 0.00 55.00 61.11 0.00 0.00 0.00 0.00

48 20 18 19.70 17.39 0.50 0.49 55.00 61.11 0.43 0.42 50.77 50.00

50 19 17 18.71 16.42 0.00 0.00 57.89 64.71 0.00 0.00 0.00 0.00

52 19 17 18.71 16.42 0.50 0.49 57.89 64.71 0.43 0.42 50.77 50.00

54 18 16 17.73 15.46 0.00 0.00 61.11 68.75 0.00 0.00 0.00 0.00

56 18 16 17.73 15.46 0.00 0.00 61.11 68.75 0.00 0.00 0.00 0.00

58 18 15 17.73 14.49 0.00 0.00 61.11 73.33 0.00 0.00 0.00 0.00

60 18 15 17.73 14.49 0.50 0.49 61.11 73.33 0.43 0.42 50.77 50.00

62 17 15 16.74 14.49 0.00 0.00 64.71 73.33 0.00 0.00 0.00 0.00

64 17 15 16.74 14.49 0.50 0.49 64.71 73.33 0.43 0.42 50.77 50.00

66 16 15 15.76 14.49 0.00 0.00 68.75 73.33 0.00 0.00 0.00 0.00

68 16 14 15.76 13.52 0.00 0.00 68.75 78.57 0.00 0.00 0.00 0.00

70 16 14 15.76 13.52 0.50 0.49 68.75 78.57 0.43 0.42 50.77 50.00

72 15 14 14.77 13.52 0.00 0.00 73.33 78.57 0.00 0.00 0.00 0.00

74 15 13 14.77 12.56 0.00 0.00 73.33 84.62 0.00 0.00 0.00 0.00

76 15 13 14.77 12.56 0.00 0.00 73.33 84.62 0.00 0.00 0.00 0.00

78 15 13 14.77 12.56 0.00 0.00 73.33 84.62 0.00 0.00 0.00 0.00

80 15 12 14.77 11.59 0.00 0.00 73.33 91.67 0.00 0.00 0.00 0.00

82 15 12 14.77 11.59 0.00 0.00 73.33 91.67 0.00 0.00 0.00 0.00

84 15 11 14.77 10.63 0.50 0.49 73.33 100.00 0.43 0.42 50.77 50.00

86 14 11 13.79 10.63 0.00 0.00 78.57 100.00 0.00 0.00 0.00 0.00

88 14 11 13.79 10.63 0.00 0.00 78.57 100.00 0.00 0.00 0.00 0.00

90 14 11 13.79 10.63 0.00 0.00 78.57 100.00 0.00 0.00 0.00 0.00

92 14 11 13.79 10.63 0.00 0.00 78.57 100.00 0.00 0.00 0.00 0.00

94 14 11 13.79 10.63 0.00 0.00 78.57 100.00 0.00 0.00 0.00 0.00

96 14 11 13.79 10.63 7.00 6.89 78.57 100.00 5.96 5.87 710.79 700.01

Results

Vertical Cylinders

For Cylinder 1 (50 gm CaCO3)

• Terminal Velocity: 12.40 mm/min

• Transition from free to hindered settling at 217.59 gm/lt

• Particle diameter(Dp) : 14.89 µm

• Value of n: 11.53

For Cylinder 2 (25 gm CaCo3),

• Terminal Velocity: 23.01 mm/min

• Transition from free to hindered settling at 225.96 gm/lt

• Particle diameter(Dp) : 20.28 µm

• Value of n: 18.45

Tilted Cylinders

For Cylinder at 100

• Terminal Velocity: 2.757 mm/min

• Particle diameter(Dp) : 22.2 µm

For Cylinder at 150

• Terminal Velocity: 3.001 mm/min

• Particle diameter(Dp) : 23.17 µm

Discussion and conclusions

1. The rate of settling increase as the angle of inclination of the cylinder increase as a result of

increase in surface area or equivalently a decrease in sedimentation path.

2. The terminal velocity is higher in the free settling regime due to less interaction between

particles as well as with the wall.

3. The terminal velocity of a particle depends upon various parameters such as geometry, density

of fluid etc.

Sources of Error and Precautions

1. The initial solution may not be completely homogeneous due to imperfect stirring which may

lead to unexpected settling rates.

2. The particles of Calcium Carbonate are not perfectly spherical.

3. The boundary between the clear solution and the part with particles is not very clear during the

initial stages of free settling, especially in the low concentration cylinder.

4. There may be an error in time measurement during the experiment.

5. The particle diameter vary between 2 to 20 microns but not constant as assumed during the

experiment.

Recommendations

Stronger light source can be provided to discern the separation layer.