Summary

The main objective of this experiment was to verify the Richardson-Zaki equation for

liquid-solid fluidization beds and to study the flow pattern and calculate the pressure drop

characteristics of gas-solid fluidization beds. Water-sand system was used for liquid-solid

fluidization & air-resin system was used for gas-solid fluidization. For liquid-solid system, bed

height and superficial velocities were determined. Logarithmic plot of superficial velocity vs.

voidage were plotted for both increasing and decreasing velocities. From the plot values of

terminal settling velocity, minimum fluidization velocity and Richardson-Zaki index were

determined for both increasing and decreasing velocities. The values of ut, umf and n varied

from 0.192-0.2354m/s, 0.01547-0.01844 m/s and 2.7007-3.1382 respectively. Corresponding

theoretical values were also obtained from the (R/u2) (ud/) 2 vs. Re plot. The values of

ut, umf and n were 0.186 m/s, 0.019m/s and 2.628 respectively. For gas-solid fluidized bed,

pressure drops for corresponding superficial velocities of air were recorded and the graphical

relation between pressure drop and superficial air velocity were showed in plot. The flow

regimes for different flow rates in gas-solid fluidization bed were shown in neat sketches.

Experimental Setup

The following diagrams show the experimental setup for this experiment.

Figure 1: Schematic diagram for a liquid-solid fluidization bed.

Figure 2: Schematic diagram for 2-D and 3-D gas-solid fluidization beds.

Flow Regimes:

Figure 3: Flow regimes for 2-D gas-solid fluidization bed.

Observed Data

Fixed bed height = 1.2 inch

Weight of sample sand = 280g

Inner diameter of gas-solid tube = 6 inch

Initial height of bed without fixed bed height = 3 inch

Mesh Number of sand = -12+14

Room temperature = 26C

Column diameter of liquid-solid tube = 2 inch

Table 1: Observed Data for liquid-solid fluidization

No.

Of

Obs.

Increasing Flow Rate Decreasing Flow Rate

Mass of

Water

+

Bucket

(Kg)

Time

(s)

Height of the

bed

(inch)

Mass of

Water +

Bucket

(Kg)

Time

(s)

Height of

the bed

(inch)

1 0.85 30.6 3.85 5.2 30.6 8.85

2 1.05 30.5 3.8 5.05 30 8.7

3 1.125 30.25 3.875 5 30.1 8.35

4 1.3 30.5 3.975 4.6 30 7.85

5 1.35 30.5 4 3.55 30.1 6.3

6 1.5 30.2 4.2 2.4 30 5.05

7 1.62 30.5 4.35 1.9 30 4.6

8 2.3 30.5 4.8 1.55 30 4.15

9 3.45 30.8 6.2 - - -

10 4.12 30.7 7.15 - - -

11 4.8 31 8.4 - - -

12 5.2 30.5 9.1 - - -

Table 2: Observed Data for gas-solid fluidization

No.

Of

Obs.

Flow rate

Of air

(L/min)

Height of the manometric

fluid (CCl4)

Left

(inch)

Right

(inch)

1 80 21.1 19.95

2 120 21.2 19.95

3 160 21.2 19.8

4 200 21.2 19.75

5 240 21.3 19.7

6 280 21.35 19.7

7 320 21.4 19.65

8 360 21.5 19.6

9 400 21.55 19.5

10 440 21.6 19.4

Calculated Data

Table 3: Calculated data for flow rate, velocity and voidage for liquid-solid fluidization bed.

Obs.

No.

Height of

fluidization

bed

(m)

Mass flow

rate

(Kg/s)

Volumetric

flow rate

(m3/s)105

Superficial

Velocity

(m/s)

Voidage

For Increasing Flow Rate

1 0.09779 0.017973856 1.80318E-05 0.008896681 0.367273

2 0.09652 0.024590164 2.46694E-05 0.012171614 0.358947

3 0.098425 0.027272727 2.73606E-05 0.013499426 0.371355

4 0.100965 0.032786885 3.28926E-05 0.016228818 0.38717

5 0.10160 0.03442623 3.45372E-05 0.017040259 0.3910

6 0.10668 0.039735099 3.98632E-05 0.019668038 0.4200

7 0.11049 0.043278689 4.34182E-05 0.02142204 0.4400

8 0.12192 0.06557377 6.57851E-05 0.032457637 0.4925

9 0.15748 0.102272727 0.000102602 0.050622848 0.607097

10 0.18161 0.124429967 0.000124831 0.061590216 0.659301

11 0.21336 0.14516129 0.000145629 0.071851785 0.7100

12 0.23114 0.160655738 0.000161174 0.07952121 0.732308

For Decreasing Flow Rate

13 0.22479 0.160130719 0.000160647 0.079261337 0.724746

14 0.22098 0.158333333 0.000158844 0.078371669 0.7200

15 0.21209 0.156146179 0.000156649 0.077289074 0.708263

16 0.19939 0.143333333 0.000143795 0.070946984 0.689682

17 0.16002 0.107973422 0.000108321 0.053444572 0.613333

18 0.12827 0.07000000 7.02256E-05 0.034648527 0.517624

19 0.11684 0.053333333 5.35052E-05 0.026398878 0.470435

20 0.10541 0.041666667 4.1801E-05 0.020624123 0.413012

21 0.1016 0.026578073 2.66637E-05 0.013155587 0.3910

22 0.10033 0.013266998 1.33098E-05 0.006566885 0.383291

Table 4: Data for pressure drop and superficial air velocity for Gas-Solid fluidization bed.

Obs.

No.

Pressure

Drop

(m)

Flow rate of

Air

(m3/s)103

Superficial

Air Velocity

(m/s)

1 0.02921 0.00133 0.0730994

2 0.03175 0.00200 0.1096491

3 0.03556 0.00267 0.1461988

4 0.03683 0.00333 0.1827485

5 0.04064 0.00400 0.2192982

6 0.04191 0.00467 0.255848

7 0.04445 0.00533 0.2923977

8 0.04826 0.00600 0.3289474

9 0.05207 0.00667 0.3654971

10 0.05588 0.00733 0.4020468

Sample Calculation:

For liquid - solid fluidized bed

Experimental calculation:

Column diameter, D1 = 2 in. = 0.0508m.

Column area, A1 = 4

D1

2 = 4

(0.0508)2 = 0.0020268m2.

Temperature of water = 230 C.

Density of water, W = 996.787 Kg/m3

Assuming, mf = 0.42

K = H0 (1- mf ) = 0.09779 (1-0.42) m = 0.056718m

For observation no.5 (at decreasing height):

Mass of water, W = 3.25 Kg

Time, t = 30.1 s.

Mass flow rate, .

m = t

W =

1.30

25.3 Kg/s = 0.107973 Kg/s.

Volumetric Flow Rate, V=

.

m

W =

0.1079734

996.787= 10.8321410-5 m3/s

Superficial velocity, u = 1

.

A

V =

10.83214105

0.0020268 m/s = 0.05344m/s.

Height of the bed, H = 0.16002 m.

Voidage, = 1-H

K = 1-

16002.0

0.056718 = 0.64555

From superficial velocity vs. voidage graph for increasing velocity,

ut = 0.192m/s

umf = 0.01844m/s

n = 2.7007

From superficial velocity vs. voidage graph for decreasing velocity,

ut = 0.2354m/s

umf = 0.01547m/s

n = 3.1382

Theoretical calculation:

Temperature of water = 260 C.

Density of water, W = 996.787 Kg/m3

Viscosity of water, W = 9.3210-4 Kg/ms

g = 9.81 m/s2.

Particle diameter, dp = 1.52410-3m.

Particle density, s = 2.16103 Kg/m3.

Assuming, 0 = 0.42

22

Re''

u

R

W =

2

3

3

)(2

W

WsWp gd

=24

3

)1032.9(3

)787.9962160(81.9787.996001524.02

= 30900.3

Ret = 305. [From 22

Re''

u

R

W vs. Re graph]

Ret = W

Wtpud

ut = Wp

Wt

d

Re =

787.996001524.0

1032.9305 4

= 0.187123 m/s.

umf = 0.0055W

pWs

mf

mf gd

23

)(

1

= 0.00554

23

1032.9

001524.081.9)787.9962160(

42.01

42.0

= 0.01998 m/s.

n = mf

t

mf

u

u

ln

)ln(

= 42.0ln

)187123.0

01998.0ln(

= 2.5787

For gas - solid fluidized bed

Column diameter, D2 = 6 in. = 0.1524 m.

Column area, A2 = 4

D2

2 = 4

0.15242 = 0.01824m2.

For observation no.10

Air flow rate, q = 440 L/min = 100060

440

cm3/s =7.33 310 m3/s.

Superficial velocity of air, u = 2A

q =

01824.0

10 7.33 -3 m/s = 0.40204 m/s.

Pressure drop P = 0.05588 m CCl4

Graphs:

Figure 4: Variation of Superficial Velocity with voidage (Increasing flow rate).

y = 0.192x2.7007

0.001

0.01

0.1

1

0.1 1

Sup

erfi

cial

Vel

oci

ty (

m/s

)

Voidage

Variation of Superficial Velocity with voidage (Increasing flow rate)

0.192

0.42

0.0184

4

Figure 5: Variation of Superficial Velocity with voidage (decreasing flow rate).

y = 0.2354x3.1382

0.001

0.01

0.1

1

0.1 1

Sup

erfi

cial

Vel

oci

ty (m

/s)

Voidage

Variation of Superficial Velocity with voidage (decreasing flow rate)

0.42

0.01547

0.2354

Figure 6: Change of pressure drop with Superficial Air velocity for 3-D gas-solid

fluidization bed.

0.01

0.1

0.01 0.1 1

Pre

ssu

re D

rop

(m C

Cl 4

)

Superficial Air Velocity(m/s)

Pressure drop vs. Superficial Air velocity for 3-D gas-solid fluidization bed

Results and Discussion:

The result of this experiment has been submitted in a tabular form as follows

Table 7: Table for results

Topics

Experimental values

for velocity

Theoretical

values Increasing Decreasing

Minimum fluidization

velocity (ms-1)

0.01844 0.01547 0.01998

Terminal settling

velocity (ms-1)

0.192 0.2354 0.123713

Richardson-Zaki index 2.7007 3.1382 2.5787

Pressure drop in gas-solid fluidization ranges from 1.15 inch CCl4 to 2.20 inch CCl4 for

different air flow rates.

In this experiment two different types of graph have been plotted which are as follows

Velocity vs voidage in logarithmic coordinates (for increasing and decreasing velocity)

Pressure drop vs air velocity in logarithmic coordinates

When a fluid is passed upwards through a bed of solids, the pressure drop across the bed will

be directly proportional to the rate of flow. But when the frictional drag on the particles

becomes equal to their apparent weight (actual weight less buoyancy), the particles become

rearranged so that they offer less resistance to the flow of fluid and the bed starts to expand.

This process continues as the velocity is increased, with the total frictional force remaining

equal to the weight of the particles, until the bed has assumed the loosest stable form of packing.

Therefore, the curve between velocity vs voidage in logarithmic coordinate will be a straight

line and such a curve was also obtained in our experiment. All the curves plotted are straight

line with positive slopes. This kind of profiles agrees with literature. As the experiment was

performed for a specific range of fluid velocity, some portion of the curve was not obtained.

The pressure drop across a bed of solids will be directly proportional to the rate of flow

when a fluid is passed upwards through it. But when the frictional drag on the particles becomes

equal to their apparent weight (actual weight less buoyancy), the particles become rearranged

so that they offer less resistance to the flow of fluid and the bed starts to expand. This process

continues as the velocity is increased, with the total frictional force remaining equal to the

weight of the particles, until the bed has assumed the loosest stable form of packing.

Therefore, the curve between velocity vs voidage in logarithmic coordinate will be a straight

line and such a curve was also obtained in this experiment. All the curves plotted are straight

line with positive slopes. This kind of profiles agrees with literature. As the experiment was

performed for a specific range of fluid velocity, the packed bed region and pneumatic transport

were not observed.

For liquid-solid fluidization the superficial velocity vs. voidage plot in logarithmic scale

for both the increasing and decreasing height shows straight line with a slope which was the

Richardson-Zaki index. The Richardson-Zaki indexes found in the experiment were in the limit

of empirical value 2.7007-3.1382. The pressure drop vs. velocity graph for gas-solid

fluidization shows like a straight line with positive slope. This indicates pressure drops

increases linearly with flow rate or velocity.

From results, it is apparent that the experimental values deviate somewhat from the

theoretical values. Some reasons can be pointed out to explain these discrepancies.

At higher superficial velocity of the fluid, the bed height was fluctuating too much. So, it was

very difficult to take the height of the bed and the average height was taken.

Throughout the calculation, the particles were assumed to be perfectly spherical. But sand

particles used in the experiment were not spherical.

In this experiment the results were calculated both theoretically and experimentally.

The discrepancies between the theoretical and experimental values were not so high. However,

the little difference could be result for the following factors -

Volumetric flow rate and corresponding bed height were measured manually. So it

could happen that some mistakes were made which affected the result of the

experiment.

Again some phenomena like channeling, slugging attrition of particle occurred due to

which the results varied.

Fluidized beds have a wide range of applications in chemical and petroleum industries.

One of the main practical advantages of fluidization is connected with the liquid-like flowing

properties of fluidized beds. Indeed it appears particularly simple and economical to transport

solid particles through pipes, to control the bed height by overflow or to circulate from one bed

to another by gravity, thus avoiding the use of standard solid handling equipment, which is

often mechanically complex and expensive to operate. This mechanism is used in the

production of vinyl chloride, melamine, poly - ethylene, ploy - propylene etc. It has its

application in the catalytic cracking of petroleum and also in filtrate washing. Therefore,

studying this experiment can help to get a conscious understanding of using the basic principles

of fluidization in process industries.