DATE:29/3/2023 EXPT NO:9

PRESSURE DROP THROUGH A PACKED BED

AIM:

a) To study the pressure drop through a packed bed.

b) To determine the pressure drop per unit length of bed.

c) To plot a logarithmic graph between modified Reynolds number VS modified friction factor

INTRODUCTION:

Packed bed provides a large surface area of contact between two fluids and is thus extensively
used in distillation, extraction, adsorption etc. As the fluid passes through the bed, it does so
through the voids present in the bed. The void forms continuous channel throughout the bed.
The flow may be laminar through some channels.

THEORY:

The Ergun equation expresses the friction factor in a packed column as a function of the modified
Reynolds number as

The Friction factor for laminar regime from Kozeny –Carman equation can be expressed as

Modified Reynolds number (Rem) is defined as

PROCEDURE:

a) Allow the water to flow down from the bottom to top in the packed bed

b) Regulate flow of water by mean of valves

c) Record the flow rates of water from rotameter

d) Note the pressure drop across the bed using manometer

e) Repeat the same procedure at different flow rates of water

GIVEN DATA:

D = 0.05m A = 1.964x10-3m2

Sp = 4.95 x 10-4m2 d0 = 0.009m g =

9.81m/s2 di = 0.006m

𝜌= 1000kg/m3 Lp = 0.009m

Dp = 0.00847m L1 = 0.36m

𝜖 = 0.66 𝜑s = 0.455m

𝜇 = 8.29x10-4Ns/m2

OBSERVATIONS:

Observation Table

Volumetric Full length H(mm) Half Length H (mm)

S. No
Flow rate
Forward Reverse Forward Reverse
1 200 62.15 62 36 37
2 250 87.7 80 48 43
3 300 118.7 107 62 58
4 350 146.5 134 80 75
5 400 177.1 156 120 87
6 450 225.4 200 120 102
7 500 280.1 229 140 124
8 550 321.7 267 160 153
9 600 374.8 319 181 170
10 650 417 374 210 208
11 700 496 430 230 240
12 750 549 573 254 271
13 800 609 581 282 305
14 850 673 596 320 340
15 950 731 717 230 363

f) After the experiments turn off all the valves and switch off the equipment
FORMULAE:

1. Surface area =

2. Volume Vp =

3. Sphericity of particle

4. Discharge of water = (fw × 10-3) / 3600

5. Velocity of water V = Q/A

6. Modified (NRe)m =

7. Ergun friction factor f =

8. Pressure drop per unit length of bed ∆P/L = h*9.81*1000

SAMPLE CALCULATIONS

For full length, forward:

Q = LPH*10-3/3600

= 5.56*10-5 m3/s

V = Q/A = 5.56*10-5/1.964*10-3

= 28.29*10-3 m/s

NRE
= 398.5

Ergun f =

= 1.92

𝛥𝑝/𝐿=𝜌𝑔ℎ/𝐿 = 103*9.81*62.15*10-3/0.36

= 1694

Exp fp 0.66)

= 7.11

Calculation Table for Friction Factor

 Experimental Experimental
Vx ergun Fp(full) Fp(half)
S.No. Q x 10^5 NRE
10^-3 f
Forward Reverse Forward Reverse
1 5.56 28.29 398.5 1.92 7.11 7.09 8.23 8.46
2 6.94 35.36 498.1 1.89 6.42 5.85 7.03 6.29
3 8.33 42.43 597.7 1.86 6.03 5.44 6.30 5.89
4 9.72 49.50 697.3 1.85 5.47 5.00 5.97 5.60
5 11.11 56.57 797.0 1.84 5.06 4.46 6.86 4.97
6 12.50 63.65 896.6 1.83 5.09 4.52 5.42 4.61
7 13.89 70.72 996.2 1.82 5.12 4.19 5.12 4.54
8 15.28 77.79 1095.8 1.81 4.86 4.04 4.84 4.63
9 16.67 84.86 1195.5 1.81 4.76 4.05 4.60 4.32
10 18.06 91.93 1295.1 1.80 4.51 4.05 4.55 4.50
11 19.44 99.00 1394.7 1.80 4.63 4.01 4.29 4.48
12 20.83 106.08 1494.3 1.80 4.46 4.66 4.13 4.41
13 22.22 113.15 1593.9 1.79 4.35 4.15 4.03 4.36
14 23.61 120.22 1693.6 1.79 4.26 3.77 4.05 4.30
15 25.00 127.29 1793.2 1.79 4.13 4.05 2.60 4.10

For half length: f =

For full length: f =

Qx Vx ergun ΔP/L (full) ΔP/L (half)
S.no 10^-5 10^-3 NRE f Forward Reverse Forward Reverse
1 5.56 28.29 398.49 1.92 1694 1690 1962 2017
2 6.94 35.36 498.11 1.89 2390 2180 2616 2344
3 8.33 42.43 597.73 1.86 3235 2916 3379 3161
4 9.72 49.50 697.35 1.85 3992 3652 4360 4088
5 11.11 56.57 796.97 1.84 4826 4251 6540 4742
6 12.50 63.65 896.59 1.83 6142 5450 6540 5559
7 13.89 70.72 996.21 1.82 7633 6240 7630 6758
8 15.28 77.79 1095.83 1.81 8766 7276 8720 8339
9 16.67 84.86 1195.46 1.81 10213 8693 9865 9265
10 18.06 91.93 1295.08 1.80 11363 10192 11445 11336
11 19.44 99.00 1394.70 1.80 13516 11718 12535 13080
12 20.83 106.08 1494.32 1.80 14960 15614 13843 14770
13 22.22 113.15 1593.94 1.79 16595 15832 15369 16623
14 23.61 120.22 1693.56 1.79 18339 16241 17440 18530
15 25.00 127.29 1793.18 1.79 19920 19538 12535 19784

RESULT AND DISCUSSION:

Pressure drops for packed bed for full length and half-length was calculated. We plot ln(Nre)
vs ln(f) graph which has negative slope. We can also conclude that as pressure drop increases,
flow rate also increases.

CONCLUSION:

We have inferred that experimental friction factor is directly proportional to ∆P/L and pressure
drop increases as flow rate increases. We use these principles widely in chemical engineering
field. This concept can be used in catalytic reactions.

NOMENCLATRE:

Q = Discharge, m3 /s

𝜑s = Sphericity

D = 0.05m

Sp = Surface area of particle, m2

d0 = Outer diameter, m di

= Inside diameter, m f = Ergun

friction factor

𝜌= Density of water, kg/m3

𝜇 = Viscosity of water, N s/m2

A = Area of cross section of pipe, m2

Tabulation for graph plotting

ln(f) ln(Nre)
 0.65 5.99
0.63 6.21
0.62 6.39
0.61 6.55
0.61 6.68
0.60 6.80
0.60 6.90
0.59 7.00
0.59 7.09
0.59 7.17
0.59 7.24
0.59 7.31
0.58 7.37
0.58 7.43
0.58 7.49

Log(f) vs Log(Nre)
0.66
0.65
0.64
0.63
0.62
0.61
0.60
0.59
0.58
5.80 6.00 6.20 6.40 6.60 6.80 7.00 7.20 7.40
Log(Nre)

Graph Plotted with Logarithmic Modified Friction and Logarithmic Modified NRe