Principles and Practice of Engineering PE Chemical Reference Handbook by National Council of Examiners for Engineering and Surveying (NCEES) (z-lib.org)

Chapter 6: Fluid Mechanics

Flow Coefficient (C) and Orifice Loss Coefficient

C= Corifice
1 − b4

Incompressible Flow

Vo = C Aorifice 2 gc DP
t

Compressible Flow

Vo = Y C Aorifice 2 gc DP
t

where Y = expansion factor

6.4.3.2 Flow Nozzle Meter

1.00

d2 d2 0.2
2
0.4
0.6

0.98

d2 d1 Cnozzle β = d—1— = 0.8
0.96 d2 DISCHARGE COEFFICIENT

Cnozzle FOR NOZZLE METERS

FLOW 0.94
104 105 106 107 108
NOZZLE METER Re

Flow Coefficient (C)

C= Cnozzle
1 − b4

Incompressible Flow

Vo = C Anozzle 2 gctDP

Compressible Flow
Vo = Y C Anozzle 2 gctDP

where Y = expansion factor

©2020 NCEES 282

Chapter 6: Fluid Mechanics

6.4.3.3 Venturi Flow Nozzle Meter
The venturi discharge coefficient is a function oPf RthEeSsSpUeRciEficMgEeAoSmUeRtEryMoEfNtThe meter.

FLOW

Flow Coefficient (C)

C= Cventuri
1 − b4

Incompressible Flow

Vo = C Aventuri 2 gctDP

Compressible Flow

Vo = Y C Aventuri 2 gc DP
t

where Y = expansion factor

6.4.3.4 Pitot Tube Flow Meter

P1 P2

STATIC TUBE

FLOW

PITOT TUBE
(OR IMPACT TUBE)

P1 measures the static pressure. Assuming elevation effects are negligible, P2 is the stagnation pressure:
u2
P1 + t gc
2

Therefore:

u= 2 gc _P2 − P1i
t

©2020 NCEES 283

Chapter 6: Fluid Mechanics

6.4.3.5 Permanent Pressure Loss in Flow Meters VENA CONTRACTA
PB
FLOW RESTRICTION
PA

FLOW PVC
PA
PERMANENT
PRESSURE

LOSS

PB

P vc

Pressure Loss Across Restrictive Flow Meters: The permanent pressure loss (or nonrecoverable pressure drop) across a restrictive
flow meter (e.g., orifices and nozzles) is the difference between the upstream pressure, PA, (the static pressure not influenced by
the device, or roughly one pipe diameter upstream), and the pressure measured downstream of the device where the static pressure
recovery is complete, PB (approximately six pipe diameters downstream).

For a given measured differential pressure, ΔP (e.g., radius or flange taps for an orifice), the permanent pressure loss can be
estimated by:

PA − PB = DPKKJK 1 − b4 `1 − Cd2j − Cd b2 NO
L 1 − b4 `1 − Cd2j + Cd b2 OO
P

where

Cd = coefficient of discharge for the device (e.g., Corifice and Cnozzle)
For orifice plates and nozzles, the flow coefficient, K, can be approximated

K=f 1 − b4`1 − Cd2j − 1 2
Cd b2
p

Source: ASME MFC-3M-2004, Measurement of Fluid Flow in Pipes Using Orifice, Nozzle, and Venturi

©2020 NCEES 284

Chapter 6: Fluid Mechanics

6.4.3.6 Weir Meters V-Notch Weir (90o Notch)
L
Rectangular Weir—Suppressed
L

HH

Vo = C L H 3 Vo = C H 5
2 2

where C = 3.33 ft 0.5 where C = 2.5 ft 0.5
sec sec

C = 1.84 m 0.5 C = 1.4 m 0.5
s s

Rectangular Weir—Contracted
L

H

Vo = C _L − 0.2H 3

iH 2

where C = 3.33 ft 0.5
sec

C = 1.84 m 0.5
s

©2020 NCEES 285

Chapter 6: Fluid Mechanics

6.5 Tables Pipe Dimensions and Weights
Weights are based on carbon steel pipe
Pipe Size OD
inches inches Identification Wall Thickness Weight Inside Diameter
mm mm
Steel Stainless inches mm lbm kg inches mm
1/8 0.405 Steel ft m
6 10.3 Iron Schedule
Pipe No. Schedule
1/4 0.54
8 13.7 10 10S 0.049 1.24 0.19 0.28 0.307 7.82
STD 40 0.269 6.84
3/8 0.675 XS 80 40S 0.068 1.73 0.24 0.37 0.215 5.84
10 17.1
80S 0.095 2.41 0.31 0.47 0.410 10.40
1/2 0.840 0.364 9.22
15 21.3 10 10S 0.065 1.65 0.33 0.49 0.302 7.66
STD 40
XS 80 40S 0.088 2.24 0.43 0.63 0.545 13.80
0.493 12.48
80S 0.119 3.02 0.54 0.80 0.423 10.70

10 10S 0.065 1.65 0.42 0.63 0.710 18.00
STD 40 0.674 17.08
XS 80 40S 0.091 2.31 0.57 0.84 0.622 15.76
0.546 13.84
80S 0.126 3.20 0.74 1.10 0.464 11.74
0.252 6.36
5 5S 0.065 1.65 0.54 0.80
10 0.920 23.40
STD 40 10S 0.083 2.11 0.67 1.00 0.884 22.48
XS 80 0.824 20.96
160 40S 0.109 2.77 0.85 1.27 0.742 18.88
XX 0.612 15.58
80S 0.147 3.73 1.09 1.62 0.434 11.06

0.188 4.78 1.31 1.95 1.185 30.10
1.097 27.86
0.294 7.47 1.72 2.55 1.049 26.64
0.957 24.30
5 5S 0.065 1.65 0.69 1.03 0.815 20.70
10 0.599 15.22
STD 40 10S 0.083 2.11 0.86 1.28
XS 80 1.530 38.90
3/4 1.050 160 40S 0.113 2.87 1.13 1.69 1.442 36.66
20 26.7 XX 1.380 35.08
80S 0.154 3.91 1.48 2.20 1.278 32.50
1.160 29.50
0.219 5.56 1.95 2.90 0.896 22.80

0.308 7.82 2.44 3.64 1.770 45.00
1.682 42.76
5 5S 0.065 1.65 0.87 1.29 1.610 40.94
10 1.500 38.14
STD 40 10S 0.109 2.77 1.41 2.09 1.338 34.02
XS 80 1.100 28.00
1 1.315 160 40S 0.133 3.38 1.68 2.50
25 33.4 XX
80S 0.179 4.55 2.17 3.24

0.250 6.35 2.85 4.24

0.358 9.09 3.66 5.45

5 5S 0.065 1.65 1.11 1.65
10
STD 40 10S 0.109 2.77 1.81 2.69
XS 80
1-1/4 1.660 160 40S 0.140 3.56 2.27 3.39
32 42.2 XX
80S 0.191 4.85 3.00 4.47

0.250 6.35 3.77 5.61

0.382 9.70 5.22 7.77

5 5S 0.065 1.65 1.28 1.90
10
STD 40 10S 0.109 2.77 2.09 3.11
XS 80
1-1/2 1.900 160 40S 0.145 3.68 2.72 4.05
40 48.3 XX
80S 0.200 5.08 3.63 5.41

0.281 7.14 4.86 7.25

0.400 10.15 6.41 9.55

©2020 NCEES 286

Chapter 6: Fluid Mechanics

Pipe Dimensions and Weights (cont'd)
Weights are based on carbon steel pipe

Pipe Size OD Identification Wall Thickness Weight Inside Diameter
inches inches
mm mm Steel Stain- inches mm lbm kg inches mm
less Steel ft m
2 2.375 Iron Schedule Schedule
50 60.3 Pipe No.

5 5S 0.065 1.65 1.61 2.39 2.245 57.00
10 2.157 54.76
STD 40 10S 0.109 2.77 2.64 3.93 2.067 52.48
XS 80 1.939 49.22
160 40S 0.154 3.91 3.66 5.44 1.687 42.82
XX 1.503 38.16
80S 0.218 5.54 5.03 7.48
2.709 68.78
0.344 8.74 7.47 11.11 2.635 66.90
2.469 62.68
0.436 11.07 9.04 13.44 2.323 58.98
2.125 53.94
5 5S 0.083 2.11 2.48 3.69 1.771 44.96
10
STD 40 10S 0.120 3.05 3.53 5.26 3.334 84.68
XS 80 3.260 82.80
2-1/2 2.875 160 40S 0.203 5.16 5.80 8.63 3.068 77.92
65 73 XX 2.900 73.66
80S 0.276 7.01 7.67 11.41 2.624 66.64
2.300 58.42
0.375 9.53 10.02 14.92
3.834 97.38
0.552 14.02 13.71 20.39 3.760 95.50
3.548 90.12
5 5S 0.083 2.11 3.03 4.52 3.364 85.44
10 2.728 69.30
STD 40 10S 0.120 3.05 4.34 6.46
XS 80 4.334 110.08
3 3.5 160 40S 0.216 5.49 7.58 11.29 4.260 108.20
80 88.9 XX 4.026 102.26
80S 0.300 7.62 10.26 15.27 3.826 97.18
3.624 92.04
0.438 11.13 14.34 21.35 3.438 87.32
3.152 80.06
0.600 15.24 18.6 27.68
4.506 114.46
5 5S 0.083 2.11 3.48 5.18 4.290 108.96
10 3.580 90.94
3-1/2 4 STD 40 10S 0.120 3.05 4.98 7.41
90 101.6 XS 80 5.345 135.76
XX 40S 0.226 5.74 9.12 13.57 5.295 134.50
5.047 128.20
80S 0.318 8.08 12.52 18.64 4.813 122.24
4.563 115.90
0.636 16.15 22.87 34.03 4.313 109.54
4.063 103.20
5 5S 0.083 2.11 3.92 5.84
10
STD 40 10S 0.120 3.05 5.62 8.37
XS 80
4 4.5 120 40S 0.237 6.02 10.8 16.08
100 114.3 160
XX 80S 0.337 8.56 15.00 22.32

0.438 11.13 19.02 28.32

0.531 13.49 22.53 33.54

0.674 17.12 27.57 41.03

4-1/2 5 STD 40 40S 0.247 6.27 12.55 18.67
115 127 XS 80
XX 80S 0.355 9.02 17.63 26.24

0.710 18.03 32.56 48.45

5 5S 0.109 2.77 6.36 9.46
10
STD 40 10S 0.134 3.40 7.78 11.56
XS 80
5 5.563 120 40S 0.258 6.55 14.63 21.77
125 141.3 160
XX 80S 0.375 9.53 20.80 30.97

0.500 12.70 27.06 40.28

0.625 15.88 32.99 49.12

0.750 19.05 38.59 57.43

©2020 NCEES 287

Chapter 6: Fluid Mechanics

Pipe Dimensions and Weights (cont'd)
Weights are based on carbon steel pipe

Pipe Size OD Identification Wall Thickness Weight Inside Diameter
inches inches
mm mm Steel Stain- inches mm lbm kg inches mm
less Steel ft m
6 6.625 Iron Schedule Schedule
150 168.3 Pipe No.

7 7.625 5 5S 0.109 2.77 7.59 11.31 6.407 162.76
175 193.7 10 6.357 161.50
STD 40 10S 0.134 3.40 9.30 13.83 6.065 154.08
8 8.625 XS 80 5.761 146.36
200 219.1 120 40S 0.280 7.11 18.99 28.26 5.501 139.76
160 5.187 131.78
9 9.625 XX 80S 0.432 10.97 28.60 42.56 4.897 124.40
225 244.5
0.562 14.27 36.43 54.21 7.023 178.40
10 10.75 6.625 168.30
250 273 0.719 18.26 45.39 67.57 5.875 149.24

11 11.75 0.864 21.95 53.21 79.22 8.407 213.56
275 298.5 8.329 211.58
STD 40 40S 0.301 7.65 23.57 35.10 8.125 206.40
XS 8.071 205.02
XX 80S 0.500 12.70 38.08 56.69 7.981 202.74
7.813 198.48
0.875 22.23 63.14 94.00 7.625 193.70
7.437 188.92
5 5S 0.109 2.77 9.92 14.78 7.187 182.58
10 7.001 177.86
20 10S 0.148 3.76 13.41 19.97 6.875 174.64
30 6.813 173.08
STD 40 0.250 6.35 22.38 33.32
60 8.941 227.12
XS 80 0.277 7.04 24.72 36.82 8.625 219.10
100 7.875 200.04
120 40S 0.322 8.18 28.58 42.55
140 10.482 266.20
XX 0.406 10.31 35.67 53.09 10.420 264.62
160 10.250 260.30
80S 0.500 12.70 43.43 64.64 10.136 257.40
10.020 254.46
0.594 15.09 51.00 75.92 9.750 247.60
9.562 242.82
0.719 18.26 60.77 90.44 9.312 236.48
9.062 230.12
0.812 20.62 67.82 100.93 8.750 222.20
8.500 215.84
0.875 22.23 72.49 107.93
11.000 279.44
0.906 23.01 74.76 111.27 10.750 273.10
10.000 254.04
STD 40S 0.342 8.69 33.94 50.54

XS 80S 0.500 12.70 48.77 72.60

XX 0.875 22.23 81.85 121.85

5 5S 0.134 3.40 15.21 22.61
10
20 10S 0.165 4.19 18.67 27.78
30
40 0.250 6.35 28.06 41.76
STD 60
XS 80 0.307 7.80 34.27 51.01
100
120 40S 0.365 9.27 40.52 60.29
XX 140
160 80S 0.500 12.70 54.79 81.53

0.594 15.09 64.49 95.98

0.719 18.26 77.10 114.71

0.844 21.44 89.38 133.01

1.000 25.40 104.23 155.10

1.125 28.58 115.75 172.27

STD 40S 0.375 9.53 45.60 67.91

XS 80S 0.500 12.70 60.13 89.51

XX 0.875 22.23 101.72 151.46

©2020 NCEES 288

Chapter 6: Fluid Mechanics

Pipe Dimensions and Weights (cont'd)
Weights are based on carbon steel pipe

Pipe Size OD Identification Wall Thickness Weight Inside Diameter
inches inches
mm mm Steel Stain- inches mm lbm kg inches mm
less Steel ft m
12 12.75 Iron Schedule Schedule
300 323.8 Pipe No.

14 14 5S 0.156 3.96 21.00 31.24 12.438 315.88
350 355.6 12.390 314.66
10S 0.180 4.57 24.19 35.98 12.250 311.10
16 16 12.090 307.04
400 406.4 20 0.250 6.35 33.41 49.71 12.000 304.74
30 11.938 303.18
STD 0.330 8.38 43.81 65.19 11.750 298.40
40 11.626 295.26
XS 40S 0.375 9.53 49.61 73.86 11.374 288.84
60 11.062 280.92
80 0.406 10.31 53.57 79.71 10.750 273.00
100 10.500 266.64
XX 120 80S 0.500 12.70 65.48 97.44 10.126 257.16
140
160 0.562 14.27 73.22 108.93 13.624 346.04
13.500 342.90
0.688 17.48 88.71 132.05 13.376 339.76
13.250 336.54
0.844 21.44 107.42 159.87 13.124 333.34
13.000 330.20
1.000 25.40 125.61 186.92 12.812 325.42
12.500 317.50
1.125 28.58 139.81 208.08 12.124 307.94
11.812 300.02
1.312 33.32 160.42 238.69 11.500 292.10
11.188 284.18
10S 0.188 4.78 27.76 41.36
15.624 396.84
10 0.250 6.35 36.75 54.69 15.500 393.70
20 15.376 390.56
STD 30 0.312 7.92 45.65 67.91 15.250 387.34
40 15.000 381.00
XS 40S 0.375 9.53 54.62 81.33 14.688 373.08
60 14.312 363.52
80 0.438 11.13 63.50 94.55 13.938 354.02
100 13.562 344.48
120 80S 0.500 12.70 72.16 107.40 13.124 333.34
140 12.812 325.42
160 0.594 15.09 85.13 126.72

0.750 19.05 106.23 158.11

0.938 23.83 130.98 194.98

1.094 27.79 150.93 224.66

1.250 31.75 170.37 253.58

1.406 35.71 189.29 281.72

10S 0.188 4.78 31.78 47.34

10 0.250 6.35 42.09 62.65
20
STD 30 0.312 7.92 52.32 77.83
XS 40
60 40S 0.375 9.53 62.64 93.27
80
100 80S 0.500 12.70 82.85 123.31
120
140 0.656 16.66 107.60 160.13
160
0.844 21.44 136.74 203.54

1.031 26.19 164.98 245.57

1.219 30.96 192.61 286.66

1.438 36.53 223.85 333.21

1.594 40.49 245.48 365.38

©2020 NCEES 289

Chapter 6: Fluid Mechanics

Pipe Dimensions and Weights (cont'd)
Weights are based on carbon steel pipe

Pipe Size OD Identification Wall Thickness Weight Inside Diameter
inches inches
mm mm Steel Stain- inches mm lbm kg inches mm
less Steel ft m
18 18 Iron Schedule Schedule
450 457 Pipe No.

20 20 10S 0.188 4.78 35.80 53.31 17.624 447.44
500 508 17.500 444.30
10 0.250 6.35 47.44 70.57 17.376 441.16
22 22 20 17.250 437.94
550 559 STD 0.312 7.92 58.99 87.71 17.124 434.74
30 17.000 431.60
24 24 XS 40S 0.375 9.53 70.65 105.17 16.876 428.46
600 610 40 16.500 418.90
60 0.438 11.13 82.23 122.38 16.124 409.34
80 15.688 398.28
100 80S 0.500 12.70 93.54 139.16 15.250 387.14
120 14.876 377.66
140 0.562 14.27 104.76 155.81 14.438 366.52
160
0.750 19.05 138.30 205.75 19.564 496.92
19.500 495.30
0.938 23.83 171.08 254.57 19.250 488.94
19.000 482.60
1.156 29.36 208.15 309.64 18.812 477.82
18.376 466.76
1.375 34.93 244.37 363.58 17.938 455.62
17.438 442.92
1.562 39.67 274.48 408.28 17.000 431.80
16.500 419.10
1.781 45.24 308.79 459.39 16.062 407.98

10S 0.218 5.54 46.10 68.61 21.564 547.92
21.500 546.30
10 0.250 6.35 52.78 78.56 21.250 539.94
STD 20 21.000 533.60
XS 30 40S 0.375 9.53 78.67 117.15 20.250 514.54
19.750 501.84
40 80S 0.500 12.70 104.23 155.13 19.250 489.14
60 18.750 476.44
80 0.594 15.09 123.23 183.43 18.250 463.74
100 17.750 451.04
120 0.812 20.62 166.56 247.84
140 23.500 597.30
160 1.031 26.19 209.06 311.19 23.250 590.94
23.000 584.60
1.281 32.54 256.34 381.55 22.876 581.46
22.624 575.04
1.500 38.10 296.65 441.52 22.062 560.78
21.562 548.08
1.750 44.45 341.41 508.15 20.938 532.22
20.376 517.96
1.969 50.01 379.53 564.85 19.876 505.26
19.312 490.92
10S 0.218 5.54 50.76 75.55

10 0.250 6.35 58.13 86.55
STD 20
XS 30 40S 0.375 9.53 86.69 129.14

60 80S 0.500 12.70 114.92 171.10
80
100 0.875 22.23 197.60 294.27
120
140 1.125 28.58 251.05 373.85
160
1.375 34.93 303.16 451.45

1.625 41.28 353.94 527.05

1.875 47.63 403.38 600.67

2.125 53.98 451.49 672.30

10 10S 0.250 6.35 63.47 94.53
STD 20 40S 0.375 9.53 94.71 141.12
XS 80S 0.500 12.7 125.61 187.07

30 0.562 14.27 140.81 209.65
40 0.688 17.48 171.45 255.43
60 0.969 24.61 238.57 355.28
80 1.219 30.96 296.86 442.11
100 1.531 38.89 367.74 547.74
120 1.812 46.02 429.79 640.07
140 2.062 52.37 483.57 720.19
160 2.344 59.54 542.64 808.27

©2020 NCEES 290

Chapter 6: Fluid Mechanics

Pipe Dimensions and Weights (cont'd)
Weights are based on carbon steel pipe

Pipe Size OD Identification Wall Thickness Weight Inside Diameter
inches inches
mm mm Steel Stain- inches mm lbm kg inches mm
less Steel ft m
26 26 Iron Schedule Schedule
650 660 Pipe No.

28 28 10 0.312 7.92 85.68 127.36 25.376 644.16
700 711 STD 25.250 640.94
XS 20 40S 0.375 9.53 102.72 152.88 25.000 634.60
30 30
750 762 80S 0.500 12.70 136.30 202.74 27.376 695.16
27.250 691.94
32 32 10 0.312 7.92 92.35 137.32 27.000 685.60
800 813 STD 26.750 679.24
40S 0.375 9.53 110.74 164.86
20 29.376 746.16
30 0.500 12.70 146.99 218.71 29.250 742.94
29.000 736.60
0.625 15.88 182.90 272.23 28.750 730.24

10 10S 0.312 7.92 99.02 147.29 31.376 797.16
STD 40S 0.375 9.53 118.76 176.85 31.250 793.94
XS 20 80S 0.500 12.70 157.68 234.68 31.000 787.60
30.750 781.24
30 0.625 15.88 196.26 292.2 30.624 778.04

10 0.312 7.92 105.69 157.25 33.376 848.16
STD 33.250 844.94
XS 20 40S 0.375 9.53 126.78 188.83 33.000 838.60
32.750 832.24
30 80S 0.500 12.70 168.37 250.65 32.624 829.04
40
0.625 15.88 209.62 312.17 35.376 898.16
35.250 894.94
0.688 17.48 230.29 342.94 35.00 888.60

10 0.312 7.92 112.36 167.21 41.250 1047.94
STD 41.000 1041.60
34 34 XS 20 40S 0.375 9.53 134.79 200.82
850 864 47.250 1199.94
30 80S 0.500 12.70 179.06 266.63 47.000 1193.60
40
0.625 15.88 222.99 332.14

0.688 17.48 245.00 364.92

36 36 10 0.312 7.92 119.03 176.97
900 914 STD
XS 20 40S 0.375 9.53 142.81 212.57
42 42
1050 1067 80S 0.500 12.70 189.75 282.29

48 48 30 0.375 9.53 166.86 248.53
1200 1219
60 0.500 12.70 221.82 330.21

30 0.375 9.53 190.92 284.25

60 0.500 12.70 253.89 377.81

©2020 NCEES 291

Chapter 6: Fluid Mechanics

Size OD 24ga 22ga 20ga Tubing Sizes (U.S.) 9ga 7ga 1/4" 3/8"
(inches) (inches) Gauge (nominal inches) 0.148 0.180 0.250 0.375
0.022 0.028 0.035
0.206 0.194 18ga 16ga 14ga 12ga 11ga 1.364 1.640
0.331 0.319 0.430 Inside Diameter (inches) 1.454 2.015
0.444 0.555 1.579 2.140
0.680 0.049 0.062 0.083 0.109 0.120 1.604 2.515
0.805 1.704 2.640
1/4 0.2500 0.930 0.402 0.376 0.334 0.532 0.510 1.954 2.765
3/8 0.3750 0.980 0.527 0.501 0.459 0.657 0.635 2.079 3.140
1/2 0.5000 1.055 0.652 0.626 0.584 0.782 0.760 2.204 3.390
5/8 0.6250 1.180 0.777 0.751 0.709 0.832 0.810 2.579 3.640
3/4 0.7500 1.243 0.902 0.876 0.834 0.907 0.885 2.704 4.140
7/8 0.8750 1.305 0.952 0.926 0.884 1.032 1.010 2.829 4.640
1 1.0000 1.430 1.027 1.001 0.959 1.095 1.073 3.204 5.890
1.050 1.0500 1.555 1.152 1.126 1.084 1.157 1.135 3.454
1-1/8 1.1250 1.590 1.215 1.189 1.147 1.282 1.260 3.704
1-1/4 1.2500 1.680 1.277 1.251 1.209 1.407 1.385 4.204
1-5/16 1.3125 1.805 1.402 1.376 1.334 1.442 1.420 4.704
1-3/8 1.3750 1.830 1.527 1.501 1.459 1.532 1.510
1-1/2 1.5000 1.930 1.562 1.536 1.494 1.657 1.635
1-5/8 1.6250 1.652 1.626 1.584 1.682 1.660
1.660 1.6600 1.777 1.751 1.709 1.782 1.760
1-3/4 1.7500 1.802 1.776 1.734 2.032 2.010
1-7/8 1.8750 1.902 1.876 1.834 2.157 2.135
1.900 1.9000 2.152 2.126 2.084 2.282 2.260
2 2.0000 2.277 2.251 2.209 2.657 2.635
2-1/4 2.2500 2.402 2.376 2.334 2.782 2.760
2-3/8 2.3750 2.751 2.709 2.907 2.885
2-1/2 2.5000 2.902 2.876 2.834 3.282 3.260
2-7/8 2.8750 3.001 2.959 3.532 3.510
3 3.0000 3.376 3.334 3.782 3.760
3-1/8 3.1250 3.584 4.282 4.260
3-1/2 3.5000 3.834 4.782 4.760 4.000
3-3/4 3.7500 4.334 6.010 4.500
4 4.0000 4.834 5.750
4-1/2 4.5000
5 5.0000 5.500
6-1/4 6.2500

©2020 NCEES 292

Chapter 6: Fluid Mechanics

Size OD 24ga 22ga 20ga Tubing Sizes (Metric) 9ga 7ga 1/4" 3/8"
(mm) Gauge (nominal mm) 3.800 4.600 6.400 9.600
0.600 0.700 0.900
1/4" 6.4 5.2 5.0 18ga 16ga 14ga 12ga 11ga 34.6 41.6 101.5 139.6
3/8" 9.5 8.3 8.1 10.9 Inside Diameter (mm) 36.9 51.2 114.2
1/2" 12.7 11.3 14.1 40.1 54.3 146.0
5/8" 15.9 17.3 1.300 1.600 2.100 2.800 3.100 40.7 63.9
3/4" 19.1 20.4 43.2 67.0
7/8" 22.2 23.6 10.1 9.5 8.5 49.6 70.2
1" 25.4 24.9 13.3 12.7 11.7 52.8 79.7
1.050" 26.7 26.8 16.5 15.9 14.9 13.5 12.9 55.9 86.1
1-1/8" 28.6 30.0 19.6 19.0 18.0 16.6 16.0 65.5 92.4
1-1/4" 31.8 31.6 22.8 22.2 21.2 19.8 19.2 68.6 105.1
1-5/16" 33.4 33.2 24.1 23.5 22.5 21.1 20.5 71.8 117.8
1-3/8" 35.0 36.3 26.0 25.4 24.4 23.0 22.4 81.3 149.6
1-1/2" 38.1 39.5 29.2 28.6 27.6 26.2 25.6 87.7
1-5/8" 41.3 40.4 30.8 30.2 29.2 27.8 27.2 94.0
1.660" 42.2 42.7 32.4 31.8 30.8 29.4 28.8 106.7
1-3/4" 44.5 45.9 35.5 34.9 33.9 32.5 31.9 119.4
1-7/8" 47.7 46.5 38.7 38.1 37.1 35.7 35.1
1.900" 48.3 49.0 39.6 39.0 38.0 36.6 36.0
2" 50.8 41.9 41.3 40.3 38.9 38.3
2-1/4" 57.2 45.1 44.5 43.5 42.1 41.5
2-3/8" 60.4 45.7 45.1 44.1 42.7 42.1
2-1/2" 63.5 48.2 47.6 46.6 45.2 44.6
2-7/8" 73.1 54.6 54.0 53.0 51.6 51.0
3" 76.2 57.8 57.2 56.2 54.8 54.2
3-1/8" 79.4 60.9 60.3 59.3 57.9 57.3
3-1/2" 88.9
3-3/4" 95.3 69.9 68.9 67.5 66.9
4" 101.6 73.6 73.0 72.0 70.6 70.0
4-1/2" 114.3
5" 127.0 76.2 75.2 73.8 73.2
6-1/4" 158.8 85.7 84.7 83.3 82.7

91.1 89.7 89.1
97.4 96.0 95.4
110.1 108.7 108.1
122.8 121.4 120.8

152.6

©2020 NCEES 293

7 MASS TRANSFER

7.1 Symbols and Definitions

Symbols

Symbol Description Units (U.S.) Units (SI)
A
A Area ft2 or in2 m2
Absorption factor
dimensionless

a Effective interfacial mass-transfer area per unit volume ft2 m2
ft3 m3

B Bottom product flow rate lb mole mol
c Concentration hr s

lb mole mol
ft3 m3

cp Heat capacity Btu J K = m2
lbm-cF kg : s2 : K
D Distillate flow rate
lb mole mol
DAB Mass diffusivity (diffusion coefficient) hr s
D, d Diameter
ft2 m2
E Efficiency hr s
F Feed flow ft or in. m
f Ratio of vapor-phase flow to feed flow (fraction vaporized)
f Darcy friction factor dimensionless

f Fugacity of a pure component lb mole mol
hr s
dimensionless
dimensionless

lbf P=a mN=2 kg
in2 m : s2

fti Fugacity of a component i in a mixture lbf P=a mN=2 kg
in2 m : s2

©2020 NCEES 294

Chapter 7: Mass Transfer

Symbol Symbols (cont'd) Units (U.S.) Units (SI)
Description mol
lb mole s
G Gas flow rate (stripper/absorber) hr mol
s
GS Gas flow rate, solute-free basis lb mole m
g Gravitational acceleration hr s2
ft J
gt Molar Gibbs free energy mol
sec2
Btu
lb mole

H Henry's Law constant lbf P=a mN=2 kg
in2 m : s2
Btu
DH Heat input hr W= sJ= kg : m2
s3
h Height ft or in.
h Head loss, pressure drop ft or in. m

h Specific enthalpy Btu m
lbm
J = m2
Btu kg s2
lb mole
ht Molar specific enthalpy J
Dh Specific enthalpy change mol

Btu J = m2
lbm kg s2

Dhvap Latent heat of vaporization Btu J = m2
HTU lbm kg s2
Height of a transfer unit
j Colburn Factor ft or in. m
Molar flux of component A per area
jA Distribution coefficient for phase equilibrium dimensionless
K Liquid flow (for a flash, in a column, stripper, or absorber)
L lb mole mol
ft2- hr m2 : s

dimensionless

LS Liquid flow rate, solute-free basis lb mole mol
hr s
l Length, distance
m Mass lb mole mol
m General phase equilibrium coefficient hr s
m Slope of the operating line or slope of the equilibrium line m
ft or in.
MW Molecular weight
lbm kg
N Number of stages
n Number of moles dimensionless
no Molar flow per area, molar flux
NTU Number of transfer units dimensionless

P Pressure lbm kg
lb mole mol

dimensionless

lb mole mol

lb mole mol
ft2- hr m2 : s

dimensionless

lbf P=a mN=2 kg
in2 m : s2

©2020 NCEES 295

Chapter 7: Mass Transfer

Symbol Symbols (cont'd) Units (U.S.) Units (SI)
Description

Pc Critical pressure lbf P=a mN=2 kg
in2 m : s2

Pr Reduced pressure dimensionless

P* Three-phase equilibrium pressure lbf P=a mN=2 kg
in2 m : s2

p Partial pressure lbf P=a mN=2 kg
in2 m : s2

psat Saturation pressure, or vapor pressure lbf P=a mN=2 kg
/ Poynting correction factor in2 m : s2
q Ratio of liquid-phase flow to feed flow
dimensionless

dimensionless

Qo Heat duty Btu W= sJ= kg : m2
hr s3

q Ratio of liquid-phase flow to feed flow (fraction not dimensionless
vaporized)

R Reflux ratio dimensionless

R Universal gas constant Btu J
lb mole -cR mol : K
S Boil-up ratio
S Stripping factor dimensionless
T Temperature
Tc Critical temperature dimensionless
Tr Reduced temperature
u Velocity °R or °F K or °C

V Volume °R or °F K or °C

V Vapor flow (for a flash, in a column, stripper, or absorber) dimensionless

ft m
sec s

ft3 m3

lb mole mol
hr s

vt Molar volume ft3 m3
lb mole mol

v Specific volume ft3 m3
lbm kg

Dv Specific volume change during phase change ft3 m3
lb mole mol
X Mole ratio in liquid phase (solute-free basis)
x Mole fraction in liquid phase dimensionless
Y Mole ratio in vapor phase (solute-free basis)
y Mole fraction in vapor phase dimensionless
Z Compressibility factor
z Mole fraction in the feed dimensionless
z Distance or length
dimensionless
a Interfacial area per unit volume
dimensionless

dimensionless

ft or in. m

ft2 m2
ft3 m3

©2020 NCEES 296

Chapter 7: Mass Transfer

Symbols (cont'd)

Symbol Description Units (U.S.) Units (SI)

aij Relative volatility for components i and j dimensionless
d Film thickness
g Activity coefficient ft or in. m

dimensionless

g Surface tension, interfacial tension lbf N = kg
in. m s2

e Void fraction dimensionless

m Dynamic viscosity cP or lbm Pa : s = kg
ft-sec m:s

r Density lbm kg
ft3 m3
zi Fugacity coefficient i of a pure component in the vapor phase
dimensionless

zt i Fugacity coefficient i of a component in a mixture in the dimensionless
vapor phase

zd Volume fraction of the dispersed phase (holdup) dimensionless

7.2 Fundamentals of Mass Transfer

7.2.1 Diffusion

Fick's Law of Diffusion: Molar Flux

jA = − DAB dcA
dz

Mass transport due to diffusion and bulk flow:

no A = no xA + jA = (no A + no B) xA − c DAB dxA
dz

no B = no xB + jB = (no A + no B) xB − c DBA dxB
dz

where

no A = molar flux of species A
no = bulk flow

©2020 NCEES 297

Chapter 7: Mass Transfer

Rules of Thumb for Diffusion Coefficients at 25°C

DAB c ft 2 m DAB c m 2 m
sec s

In Gases 0.43 × 10–4 – 2.4 × 10–4 0.4 × 10–5 – 2.2 × 10–5
Air 1.8 × 10–4 – 8.1 × 10–4 1.7 × 10–5 – 7.5 × 10–5
Hydrogen 0.32 × 10–4 – 1.7 × 10–4 0.3 × 10–5 – 1.6 × 10–5
Carbon dioxide
In Liquids 0.75 × 10–8 – 2.2 × 10–8 0.7 × 10–9 – 2.0 × 10–9
Gases in water 1.3 × 10–8 – 3.2 × 10–8 1.2 × 10–9 – 3.0 × 10–9
Acids in water 0.43 × 10–8 – 1.5 × 10–8 0.4 × 10–9 – 1.5 × 10–9
Organics in water 1.6 × 10–8 – 3.2 × 10–8 1.5 × 10–9 – 3.0 × 10–9
Organic solvents

Diffusion Coefficient (Pressure and Temperature Dependence)

For dilute, binary gas systems, changes in the diffusion coefficient can be predicted at any temperature and at any pressure below

25 atm by:

P1 T2 3 XD_T1i
P2 T1 2 XD_T2i
DAB_T2, P2i = DAB_T1, P1ie oe
o

where

DAB(T, P) = diffusion coefficient as a function of pressure and temperature
ΩD(T) = the "collision integral" for molecular diffusion, which is a dimensionless function of temperature and
of the intermolecular potential field for one molecule of A and one molecule of B.

Collision Integral for Diffusion as a Function of Dimensionless Temperature
3.0

Collision integral, ΩD 2.5

2.0

1.5

1.0

0.5

0.0 2.0 4.0 6.0 8.0 10.0
0.0 Dimensionless temperature, kT/εAB

Source: Fundamentals of Momentum, Heat, and Mass Transfer, James R. Welty, Gregory L. Rorrer, and David G. Foster.
Copyright © 2015 John Wiley & Sons, Inc. Reproduced with permission of John Wiley & Sons, Inc.

where

k = Boltzmann constant
εAB = Leonard-Jones force constant

©2020 NCEES 298

Chapter 7: Mass Transfer

Integrated Fick's Law
Steady-state equimolar counterdiffusion of two components (No bulk flow, DAB = DBA, ideal gas):

no A = DAB (cA − cA,i) = c DAB (xA − xA,i)
d d

For an ideal gas:

no A = DAB (pA − pA,i) = DAB P (yA − yA,i)
d RT d RT

where

i = conditions at the interface

d = film thickness

Steady-state diffusion of A through a stagnant film (no B = 0)

no A = c DAB ln f 1 − xA p
d 1 − xA,i

where

xA,i = concentration of A at the interface

xA = concentration of A at distance z from the interface

Concentration profile:

ln f 1 − xA p = z ln f 1 − xA,b p
1 − xA,i d 1 − xA,i

where

xA,b = concentration of A in the bulk fluid
z = distance from the interface

For an ideal gas:

no A = DAB P ln f 1 − yA p = DAB P yA,i − yA
d RT 1 − yA,i d RT ylm

ylm = `1 −lynA``1j1−−−`y1yAA−,ijjyA,ij, plm = `P − pAj − `P − pA,ij

ln `P − pAj
`P − pA,ij
where

ylm = logarithmic mean of the mole fractions in the gas phase and at the interface

plm = logarithmic mean of the partial pressures in the gas phase and at the interface

For diffusion of one component through a multicomponent mixture, the equation above with an effective diffusion coefficient can

be used:

/DA,mix = 1 − yA
yj

j ! A DAj

©2020 NCEES 299

Chapter 7: Mass Transfer

7.2.2 Mass-Transfer Coefficients

Definitions of the Mass-Transfer Coefficient

System Mole Fraction Concentration Pressure

Equimolar counter-diffusion, liquid no A = kx DxA no A = kc DcA

kx = c DAB kc = DAB
d d

Equimolar counter-diffusion, ideal gas no A = k y DyA no A = kc DcA no A = kG DpA

Diffusion through a stagnant film, liquid ky = DAB P kc = DAB kG = DAB
d RT d d RT
Diffusion through a stagnant film, ideal gas
Diffusion through a stagnant film, ideal gas, no A = kxl DxA no A = kcl DcA
mass-basis
k xl = c DAB kcl = DAB
d clm d clm

no A = k yl DyA no A = kc DcA no A = kGl DpA

k yl = DAB P kc = DAB kGl = d DAB
d R T ylm d clm R T plm

mo A = k yl DyA

k yl = DAB P MWA
d R T ylm

where clm = cAo − cA
cAo − cAi
ln cA − cAi

kc = mass-transfer coefficient for liquid (concentration basis)
kG = mass-transfer coefficient for gas (pressure basis)
kx = mass-transfer coefficient for liquid (mole fraction basis)
ky = mass-transfer coefficient for gas (mole fraction basis)
kc' = mass-transfer coefficient for liquid (concentration basis), corrected for inert component
kG' = mass-transfer coefficient for gas (concentration basis), corrected for inert component
kx' = mass-transfer coefficient for liquid (mole fraction basis), corrected for inert component
ky' = mass-transfer coefficient for gas (mole fraction basis), corrected for inert component

©2020 NCEES 300

Chapter 7: Mass Transfer

7.2.3 Convective Mass Transfer

Reynolds analogy between momentum, heat, and mass transfer with Colburn correction:

jM = kG dt n 2/3
Gl DAB
n

jH = h d c pn 2/3
c p GM k
n

For flow through straight tubes and across plane surfaces:

jM= j=H f
8

For turbulent flow around cylinders:

jM = jH # f
8

where

f = Darcy friction factor

GM = mass flux in lbm or kg
ft2 -hr m2 : s

G' = molar flux

h = heat-transfer coefficient in Btu or W
hr- ft2 -o F m2 : K

jH = Colburn heat-transfer factor

jM = Colburn mass-transfer factor

k = thermal conductivity in Btu or W
hr- ft -oF m:K

kG = gas-phase mass-transfer coefficient

©2020 NCEES 301

Chapter 7: Mass Transfer

Other correlations for the mass-transfer coefficient:

Mass Transfer1 for Simple Situations

Fluid Motion Range of Conditions Equation
Inside circular pipes
Re = 4000–60,000 jM = 0.023 Re–0.17
Unconfined flow parallel to Sc = 0.6–3000 Sh = 0.023 Re0.83 Sc1/3
flat plates2
Re = 10,000–400,000 jM = 0.0149 Re–0.12
Sc > 100 Sh = 0.0149 Re0.88 Sc1/3

Transfer begins at leading jM = 0.664 Rex–0.5
edge
Rex < 50,000 Nu = 0.037 Re 0.8 Pr 0.43 e Pr0 0.25
x 0 Pri
Rex = 5 × 105–3 × 107 o
Pr = 0.7–380

Between above equation and

Rex = 2 × 104–5 × 105 Nu = 0.0027 Rex Pr 0.43 e Pr0 0.25
Pr = 0.7–380 0 Pri
o

Confined gas flow parallel Ree = 2600–22,000 jM = 0.11 Ree–0.29
to a flat plate in a duct

4C = 0–1200 See note 4.
n
Liquid film in wetted-wall
tower, transfer between ripples suppressed
liquid and gas
4C = 1300–8300 = # 10 −5)c 4C 1.506
n Sh (1.76 n
m Sc0.5

Perpendicular to single Re = 400–25,000 kG P Sc 0.56 = 0.281 ^Relh0.4
cylinders Sc = 0.6–2.6 Gl

Rel = 0.1–105 Nu = 80.35 + 0.34^Relh0.5 + 0.15^Relh0.58BPr0.3
Pr = 0.7–1500

RellSc0.5 = 1.8–600,000 Sh = Sh0 + 0.347_RellSc0.5i0.62
Sc = 0.6–3200
Past single spheres 2.0 + 0.569 (GrM Sc)0.250 GrM Sc < 108
2.0 + 0.0254 (GrM Sc)0.333 GrM Sc 2 108
Sh0 = * Sc 0.244 4

Rell = 90–4000 jM = jH = 2.06 ^ Rellh−0.575
Sc = 0.6 f

Rell = 5000–10,300 jM = 0.95jH = 20.4 ^Rellh−0.815
Sc = 0.6 f
Through fixed beds of
pellets3 Rell =0.0016–55 jM = 1.09 ^Rellh−2/3
Sc = 168–70,600 f

Rell = 5–1500 jM = 0.250 ^Rellh−0.31
Sc = 168–70,600 f

1. Average mass-transfer coefficients throughout, for constant solute concentrations at the phase surface.
Generally, fluid properties are evaluated at the average conditions between the phase surface and the bulk fluid. The heat-
mass-transfer analogy is valid throughout.

2. Mass-transfer data for this case scatter badly but are reasonably well represented by setting jM = jH.

©2020 NCEES 302

Chapter 7: Mass Transfer

3. For fixed beds, the relation between e and dp is a = 6^1–fh , where a is the specific solid surface, surface per
volume of bed. For mixed sizes: dp

/n ni d 3
pi

dp = i=1
n
/
ni d 2
pi

i=1

4. For small rates of flow or long contact times:

kL,av d = Shav . 3.41
DAB

For large Reynold numbers of short contact times:

C 1
6DAB l 2
kl,av = e rtd
o

Shav = c 3 d 1
2r l
Re Scm2

Total absorption rate from the average kL:
ury d
NA,av = l `crA,l − cA0j = kL,av `cA,i − crAjM

`cA,i − crAjM = `cA,i − SSSSSTRSSc``Acc0AAj,,−ii −−`cccrAAA,,0iljj−VWWWWWWXWcrA,lj
where ln

a = specific surface of a fixed bed of pellets, pellet surface/volume of bed

cA,i = concentration of A at the interface
cA0 = concentration of A at the approach, or initial, value
c A = bulk-average concentration of A
c A,l = bulk-average concentration of A across length l

DAB = molecular diffusivity of A in B

dc = diameter of a cylinder

de = equivalent diameter of a noncircular duct = 4 (cross-sectional area)/perimeter

dp = diameter of a sphere; for a nonspherical particle, diameter of a sphere of the same surface as the particle
3 Dt 2
GrM = Grashof number for mass transfer g l t d t
n n

k = mass-transfer coefficient

kl,av = average mass-transfer coefficient across length l
l = length

NA,av = average mass-transfer flux of A at, and relative to, a phase boundary

©2020 NCEES 303

Chapter 7: Mass Transfer

ni = a number, dimensionless
Nu
= Nusselt number hd
Pr k
cp n
= Prandtl number k

Pr0 = Prandtl number at the approach, or initial, value

Pri = Prandtl number at the interface

Re = Reynolds number dG or lG
n n

Re' = Reynolds number for flow outside a cylinder dnc G
dp G
Re'' = Reynolds number for flow past a sphere n

Ree = Reynolds number for flow in a noncircular duct denG

Rex = Reynolds number with x as the length dimension xG
n

n
Sc = Schmidt number t DAB

Sh = Sherwood number kl
DAB

Sh0 = Sherwood number at the approach, or initial, value

Shi = Sherwood number at the interface
u y = bulk average velocity in the y direction (parallel to the direction of flow)

C = mass flow rate per unit width

d = thickness of a layer

e = void fraction

Source: Republished with permission of McGraw-Hill, from Mass Transfer Operations, Robert Treybal, 3rd ed.,
New York,1987; permission conveyed through Copyright Clearance Center, Inc.

7.2.4 Mass Transfer Between Phases for Dilute Systems LIQUID PHASE INTERFACE VAPOR PHASE
T, ptot
no A = kL (x − xi) = kG (yi − y) = klL (c − ci) = klG (pi − p)

=kL k=lL tr L and kG klG P

yi − y = kL = klL tr L = Ll HTUG
x − xi kG klG P Gl HTUL
x
where xi yi
y
G' = molar flux (gas phase)

HTUL = height of a transfer unit based on liquid-phase CONCENTRATION OF CONCENTRATION OF
resistance X APPROACHING Y APPROACHING
THE INTERFACE THE INTERFACE
HTUG = height of a transfer unit based on vapor-phase
resistance

i = subscript meaning concentration at interface

kL = liquid-phase mass-transfer coefficient (mole fraction basis)

©2020 NCEES 304

Chapter 7: Mass Transfer

klL = liquid-phase mass-transfer coefficient (concentration basis)
kG = gas-phase mass-transfer coefficient (mole fraction basis)
klG = gas-phase mass-transfer coefficient (partial pressure basis)
L' = molar flux (liquid phase)

pi = partial pressure
tr L = average molar density of liquid phase

In most types of separation equipment, the interfacial area for mass transfer cannot be accurately determined, and transfer coef-
ficients based on volume of the device are used:

1 = 1 + m and 1 = 1 + 1
KG a kG a kL a KL a m kG a kL a

where

a = effective interfacial mass-transfer area per unit volume, in ft2 or m2
ft3 m3

KG = overall gas-phase mass-transfer coefficient

KL = overall liquid-phase mass-transfer coefficient

m = slope of equilibrium line

Overall Mass-Transfer Coefficients KL and KG for Dilute Systems

no A = KL (x − xeq) = KG (yeq − y)
where

xeq = liquid mole fraction in equilibrium with vapor phase
yeq = vapor mole fraction in equilibrium with liquid phase

Overall Mass-Transfer Coefficients for Dilute Systems

Gas Phase Liquid Phase

Equilibrium: y = m • x 1 = 1 + m 1 = 1 + 1
Use for: KG kG kL KL m kG kL

High solubility, low m; Low solubility, high m;

gas-phase resistance is controlling liquid-phase resistance is controlling

7.2.5 Mass Transfer Between Phases for Concentrated Systems

no A = ktL (x − xi) = ktG (yi − y) = Kt L (x − xeq) = Kt G (yeq − y)
xBM yBM eq eq
x BM y BM

xBM = (1 − x) − (1 − xi) x eq = (1 − x) − (1 − xeq)
BM
_1 − xi _1 − xi
ln _1 − xij ln _1 − xeqi

yBM = (1 − y) − (1 − yi) y eq = (1 − y) − (1 − yeq)
`1 − yj BM `1 − yj

ln `1 − yij ln `1 − yeqj

©2020 NCEES 305

Chapter 7: Mass Transfer

=ktG k=G yBM klG P yBM
=ktL k=L xBM
k lL t xBM

L

yi − y = kL = ktL yBM = LM HTUG yBM
x − xi kG ktG xBM GM HTUL xBM

where
ktG = gas-phase mass-transfer coefficient for concentrated systems
Kt G = overall gas-phase mass-transfer coefficient for concentrated systems
ktL = liquid-phase mass-transfer coefficient for concentrated systems
Kt L = overall liquid-phase mass-transfer coefficient for concentrated systems

xBM = logarithmic-mean solvent concentration between bulk and interface
yBM = logarithmic-mean gas concentration between bulk and interface
L' = molar flux (liquid phase)

G' = molar flux (gas phase)

HTUL = height of a transfer unit based on liquid-phase resistance

HTUG = height of a transfer unit based on vapor-phase resistance
tr L = average molar density of liquid phase

Overall Mass-Transfer Coefficients Kt L and KtG for Concentrated Systems

1 = yBM 1 + xBM 1 (yeq − yi)
Kt G eq ktG eq ktL (x − xi)
y BM y BM

1 = xBM 1 + yBM 1 (xi − xeq)
Kt L eq ktL eq ktG (yi − y)
x BM x BM

7.2.6 Height of a Transfer Unit

=HTUG k=G aGyl BM Gl
ktG a

=HTU L k=L aLxl BM Ll
ktL a

HTUOG = Gl = Gl = yBM HTUG + mGl xBM HTUL
eq Kt G a eq Ll eq
KG a y BM y BM y BM

HTUOL = Ll = Ll = xBM HTUL + Ll yBM HTUG
eq Kt L a eq mGl eq
KL a x BM x BM x BM

©2020 NCEES 306

Chapter 7: Mass Transfer

where

HTUG = height of a transfer unit based on vapor-phase resistance
HTUOG = height of an overall vapor-phase mass-transfer unit
HTUL = height of a transfer unit based on liquid-phase resistance
HTUOL = height of an overall liquid-phase mass-transfer unit

Height Equivalent to One Theoretical Plate (HETP)

If equilibrium line and operating line are parallel c mGl = 1 m, then:
Ll

HETP = HTU

If equilibrium line and operating line are straight, but not parallel, then:

HTUOG mGl − 1
HETP Ll
=
mGl
ln c Ll m

7.2.7 Mass Transfer with Reaction

Consider a reaction between a dissolving gas A and a liquid-phase reactant B, with q moles of B reacting per mole of A,
so that:

nA + mB " Products

q = m
n

where

q = number of moles of B reacting per mole of A

CAL and CBL = molar concentrations of A and B, respectively, in the liquid

The rate of reaction of A, JL, is then given by

JL = knm C n C m
AL BL

m3 m + n− 1
mol
where knm = reaction velocity constant, in d n

JL has units, moles/sec/unit volume of liquid. Alternatively,

J = knm C n C m fL
AL BL

JL is the rate of reaction and has units of mol , n and m are the orders of reaction in A and B, and fL is the liquid
s : m3

hold-up fraction. A "reaction time" tR can be defined as

tR = (n + 1)

2knm C (n − 1) C m
AL BL

The mass transfer of A in the liquid is given by

J = kL a (C * − CAL)
AL

©2020 NCEES 307

Chapter 7: Mass Transfer

where

J = reaction rate in moles/sec/unit volume of reactor

C * = dissolved gas concentration in liquid bulk in mol
AL m3

kL = interphase mass-transfer coefficient in m
s

a = gas-liquid interphase surface area/unit dispersion volume in 1
m

J is the rate of reaction and has units of mol . A mass-transfer "diffusion time," tD, can be defined as
tD s : m3
DAL
= 2
k L

where DAL = diffusivity of A in the liquid

If a fast reaction is occurring near the interface within the "diffusion film," it will enhance the mass-transfer rate, and the equation
for the mass transfer of A into liquid, above, becomes

J = k * a (C * − CAL)
L AL

* C AL) (n − 1) m 1
AL BL 2
k * = =2DAL knm (C − C G
L
n+1

where k * = enhanced liquid-film mass-transfer coefficient in m
L s

©2020 NCEES 308

Chapter 7: Mass Transfer

Various Gas-Liquid Reaction Regimes and Parameters of Importance

Regime Conditions Important Variables Concentration Profiles
I Kinetic control
Slow reaction Rate \ eL LIQUID
\ knm FILM
II Diffusion control
Moderately fast reaction in \ `C A* Ljn GAS CA*L BULK
bulk of liquid, CAL . 0 CBL
tD 1 0.02 \ `C * jm
III Fast reaction tR BL CAL

0.02 1 tD 1 2 Independent of a
tR (if a is adequate)
Independent of kL

Rate \ a
\ kL

\ C * CBL
AL CA*L
Design so that
Independent of knm CAL
eL 2 100 DAL Independent of eL
a kL (if eL is adequate)
Rate \ a

Reaction in film, CAL . 0 21 tD 1 CBL \ knm CBL
(pseudo first order in A' ) tR CA*L
q C * A* Ljc n + 1 m
IV Very fast reaction AL 2 CAL
General case of III \ `C
CBL
CBL 22 C * Independent of kL CA*L
AL Independent of eL
Rate \ a
tD
21 tR depends on

CBL + C * kL knm C * CBL CAL
AL AL
Independent of eL CBL
CA*L
V Instantaneous reaction Rate \ a
\ kL CAL
Reaction at interface;
controlled by transfer of tD 22 CBL Independent of C *
B to interface from bulk, tR AL
J \ kL a
q C * Independent of knm
AL Independent of eL

Reprinted from Mixing in the Process Industries, 2nd ed., N. Harnby, M.F. Edwards, and A.W. Nienow, "Gas-Liquid
Dispersion and Mixing," p. 352, © 1992, with permission from Elsevier.

©2020 NCEES 309

Chapter 7: Mass Transfer

7.3 Vapor-Liquid Separations

7.3.1 Batch Distillation

Rayleigh Equation

# #nf dn = ln nf = xf dx
n n0 x0 y−x
n0

where

nf = moles in still at end of run
n0 = initial moles in still
xf = mole fraction in liquid phase at end of run
x0 = initial mole fraction in liquid phase in still

Relative Volatility Equation

a AB = c y m
d11 x
y n
− x

−

where

aAB = relative volatility
y = mole fraction of light component in vapor phase

Rearranging:

y = 1 + a AB x 1) x
(a AB −

Therefore,

ln nA = a AB ln nB
n0A n0B

where

nA = moles of liquid "A" left in the still at any time
nB = moles of liquid "B" left in the still at any time
0 = time zero

aAB = relative volatility

Operating Line for Batch Distillation With Reflux

yn+1 = RD xn + xD
RD + 1 RD + 1

where

RD = reflux ratio based on the distillate rate
x = liquid composition

©2020 NCEES 310

Batch Distillation Apparatus Chapter 7: Mass Transfer

Batch Distillation Apparatus
Q• C CONDENSER

N DISTILLATE
N-1 ACCUMULATOR
N-2

1
2 COLUMN
3

REBOILER
Q• R

7.3.2 Continuous Distillation

7.3.2.1 Theoretical Stage
An ideal theoretical stage has the following characteristics:

1. It operates in steady state and has a liquid product and a vapor product.

2. All vapor and liquid entering the stage are intimately contacted and perfectly mixed.

3. Total vapor leaving the stage is in equilibrium with total liquid leaving the stage.

For a single binary distillation stage, the following balances and equilibrium relationships apply.

Overall mass balance: Vn Ln–1
Fn + Vn + 1 + Ln − 1 = Vn + Ln
Fn (yn) (xn–1) ΔHn
Component mass balance:
zn Fn + yn + 1Vn + 1 + xn − 1 Ln − 1 = ynVn + xn Ln (zn) STAGE n

(yn+1) (xn)

Vn+1 Ln

©2020 NCEES 311

Chapter 7: Mass Transfer

Energy balance:
htf,n Fn + htV,n + 1Vn + 1 + htL,n − 1 Ln − 1 + DHn = htV,nVn + htL,n Ln

where
ht = molar specific enthalpy
Fn = feed flow to stage n
Vn = vapor flow leaving stage n
Ln = liquid flow leaving stage n
DHn = heat input to stage n

7.3.2.2 Constant Molal Overflow
When the molar heats of vaporization of the components are nearly equal, the molar flow rates of the vapor and liquid are nearly
constant in each section of the column.
In the rectifying section, the following assumptions then apply:
==L L=0 L1 L=n and V V1 = Vn
And in the stripping section, the following assumptions then apply:
L=l L=N Lm and V=l V=N Vm
where
L = liquid flow in the rectifying section
V = vapor flow in the rectifying section
Ll = liquid flow in the stripping section
V l = vapor flow in the stripping section
N = total number of stages
m = stage in stripping section
n = stage in rectifying section

©2020 NCEES 312

Chapter 7: Mass Transfer

7.3.2.3 Column Material Balance Stage Model for Distillation

F Q• c CONDENSER
zF V1 STAGE 0

L0 D
XD
V1 L0
RECTIFYING SECTION STAGE 1

V2 L1

Vn Ln-1
STAGE n

Vn+1 Ln

Vf Lf-1
STAGE f (FEED)

Vf+1 Lf

STRIPPING SECTION VM LM-1
VM+1 STAGE M

LM

VN LN-1
STAGE N

LN VN+1

LN REBOILER
Q• R STAGE N+1

313 B
XB

©2020 NCEES

Chapter 7: Mass Transfer

Overall mass balance:
F=D+B

Component mass balance:
zF F = xD D + xB B

Ratios:

D = zF − xB
F xD − xB

B = xD − zF
F xD − xB

For the rectifying section, the following balances apply:

D = V1 − L0 = Vn + 1 − Ln
xD D = y1V1 − x0 L0 = yn + 1Vn + 1 − xn Ln

For the stripping section, the following balances apply:

B = LN − 1 − VN = Lm − Vm + 1
xB B = xN − 1 LN − 1 − yNVN = xm Lm − ym + 1Vm + 1

7.3.2.4 Graphical Solution for Binary Distillation (McCabe-Thiele Diagram)

McCabe-Thiele Diagram for Binary Distillation With Constant
Molal Overflow and Constant Relative Volatility

1 y1
x - INTERCEPT (y = 1)

EQUILIBRIUM CURVE

EA xD

y' D RECTIFYING
y - INTERCEPT (x = 0) OPERATING LINE

y = MOLE FRACTION IN VAPOR C q LINE
x'

yN zF 1
B y=x
yN+1
STRIPPING
xN OPERATING LINE
0 xB
x = MOLE FRACTION IN LIQUID
0

©2020 NCEES 314

Chapter 7: Mass Transfer

Equations for the McCabe-Thiele Diagram

Name Equations
Equilibrium Line
Operating Line for y = 1 + ax − 1)
the Rectifying x (a
Section
yn + 1 = L xn + xD D = L xn + xD D = R xn + xD = L xn + c1 − L mxD
A V V L+D L+D R+1 R+1 V V

Operating Line for Slope: L = R y-Intercept (x = 0): Reflux Ratio:
the Stripping V R+1
Section yx=0 = xD = xD D R = L = V −D = xD −1
R+1 L+D D D yx=0
B
Ll xB B Ll xB B S+1 xB Ll xB
Feed Line Vl Vl Ll − Ll − B S S B
ym + 1 = xm − = B xm − = xm − = Ll xm − Ll
C B B
− 1 − 1

Ll = `1 − f j + `R + 1 − f j xF − xB
B xD − xF

Slope: x-Intercept (y = 1): Boil-up Ratio:

Ll = S+1 = xB + Ll −1 S = Vl = Ll −1 = xy = 1 − xB
Vl S B B B 1 − xy=1
xy=1 Ll

B

y= f − 1 x + zF = q x − zF
f f − q−1
q 1

Feed Condition:

q = mole fraction liquid in feed

= mqlar enthalpy to cqnvert feed to saturated vapqr
molar enthalpy of vaporization

f = mole fraction vapor in feed

q+f=1

Slope: Intercept:

f − 1 = q For zF $ `1 − f j
f −
q 1
zF zF
xy = 0 = 1 −f = q

For zF # `1 − f j

yx = 1 = zF + f − 1 = q − zF
f q−1

Intersection of Feed xI = e zF − xD o f ^R + 1h
Line/ f R+1 1 +R−f
Operating Lines
yI = zF +e zF − xD o ` f − 1j^R + 1h
D f f R+1 1+R−f

©2020 NCEES 315

Chapter 7: Mass Transfer

Name Equations for the McCabe-Thiele Diagram (cont'd)
Intersection of Feed Equations
Line/
Equilibrium Line For constant a:

E xl = − 1 >a 1 1 + f zF − _a − af f − 1jH + 1 >a 1 1 + zF − _a − af f − 2 − _a − zF −
2 − −1 1i` 4 − f−1 1i` 1i`
1jH f 1j

yl = xle f − 1 o+ zF
f f

Operating Line for y=x
Total Reflux
Rmin = xD − yl
Operating Line for yl − xl
Minimum Reflux

Circled A, B, C, D, and E in table above refer to the previous graph, "Binary Distillation With Constant Molal Overflow."

7.3.2.5 Feed Conditions
The feed condition is defined by
Ll = L + q F = L + `1 − f j F
V = V l + `1 − qj F = V l + f F

Feed Conditions

Feed Condition Values for f and q Flows at Feed Location Feed Line in McCabe-Thiele
Subcooled Liquid
f<0

f = − cpL (Tb − TF) LV
Dhvap F

q>1

q = 1 + cpL (Tb − TF)
Dhvap
L' V'

©2020 NCEES 316

Chapter 7: Mass Transfer

Feed Conditions (cont'd)

Feed Condition Values for f and q Flows at Feed Location Feed Line in McCabe-Thiele

Bubble Point f=0
(Saturated Liquid)
q=1 LV
F

Partially Vaporized 0<f<1 L' V'
0<q<1
V
L
F

Dew Point f=1 L' V'
(Saturated Vapor) q=0
LV
F

Superheated Vapor f>1 L' V'
V
f = 1 + cpV (TF − Td)
Dhvap L
F
q<0
L' V'
q = − cpV (TF − Td)
Dhvap

where
cpL = heat capacity of the liquid
cpV = heat capacity of the vapor
TF = temperature of the feed
Tb = bubble point temperature of the liquid
Td = dew point temperature of the vapor

©2020 NCEES 317

Chapter 7: Mass Transfer

7.3.2.6 Condensers

Types of Condensers

Total Condenser Partial Condenser

A total condenser does not represent a theoretical stage. A partial condenser represents a theoretical stage.

V1 STAGE 0 Vy22 STAGE 1
y1
V1 D
STAGE 1 V1 y1 STAGE 2 V2 y2 V1 y0 = yD
L1 x1 Lx00
Lx11
D
x0 = xD A THEORETICAL STAGE
NOT A THEORETICAL STAGE

EQUILIBRIUM LINE

y y y1 b a
y1 b y2 d c
a
OPERATING LINE

c e x = y1
x1
x1 x0
x
x
The triangle indicated by cde represents the top stage of
The triangle indicated by abc represents the top stage of the distillation column, and the triangle indicated by abc
the distillation column. represents the partial condenser.
Heat Duty: Qo TC = V1 Dhvap = D (R + 1) Dhvap
Heat Dut=y: Qo PC L=1 Dhvap D R Dhvap

For subcooled reflux:

If the reflux is subcooled, a portion of the vapor entering the top stage of the column will condense, providing heat to increase the
liquid temperature to the bubble point. The additional amount of liquid that is condensed inside the column is determined by:

DL = LER cpR _T1 − TRi
Dhvap

Effective reflux ratio (also called internal reflux ratio) for the stages in the column:

L = LER + DL = LER>1 + cpR _TD1 −hvTapRiH
D D
D

The temperature of the top stage in the column, T1, may be estimated as equal to the bubble point of the external reflux.

©2020 NCEES 318

Chapter 7: Mass Transfer

where
T1 = temperature of top stage
TR = temperature of the reflux
LER = external reflux (LER = RD)
DL = rate of liquid condensed on top stage of the column
cpR = heat capacity of the reflux

7.3.2.7 Reboilers

Types of Reboilers

Reboiler Without Mixing Reboiler With Mixing

If the vapor effluent from the reboiler is in equilibrium If liquid effluent from the reboiler mixes with the liquid
with the bottom product, then the reboiler represents a from the bottom stage of the column, the reboiler does not
theoretical stage. Other examples: kettle reboiler, internal represent a theoretical stage.
heating coil.

LN LN
VAP
VN+1

LIQ
LN+1

BOTTOM PRODUCT BOTTOM PRODUCT

©2020 NCEES 319

Chapter 7: Mass Transfer

Types of Reboilers

Reboiler Without Mixing Reboiler With Mixing

y y
yN
b
a

yN+1 d c b a
yN

ec

x N+1 xN x N–1 x x N x N–1 x

The triangle indicated by abc represents the bottom stage The triangle indicated by abc represents the bottom stage of
of the distillation column and the triangle indicated by cde the distillation column.
represents the reboiler.
Heat D=uty: Qo R V=R Dhvap S B Dhvap
Heat Duty: Qo R = VN + 1 Dhvap = S B Dhvap

Heat Duty: Qo R = B =`R + 1 − f j xF − xB − f G Dhvap
xD − xF

7.3.2.8 Minimum Reflux

Underwood Method With No Distributed Nonkey Components
The Underwood method assumes constant relative volatilities and constant molal overflows, and it requires a trial-and-error solution.

First, by trial-and-error, find a value for φ that is between the relative volatilities of the light key and heavy key components. The

relative volatilities are based on a characteristic temperature for the column, such as the bubble-point temperature of the distillate or

the flashed feed temperature at the column pressure. The heavy key is the reference component j for the relative volatilities of each

component i.

/1 − q = aij zFi = / fi
aij − {

Second, calculate the value of Rmin from:
aij xDi
/Rmin + 1 = aij − {

where

zFi = mole fraction of component i in the feed

q = moles of feed to stripping section per mole of feed

aij = relative volatility between components i and j
φ = adjustable parameter, which has no physical significance

fi = fraction of component i in the feed that is vaporized

xDi = mole fraction of component i in the distillate

©2020 NCEES 320

Chapter 7: Mass Transfer

7.3.2.9 Minimum Theoretical Stages
The Fenske equation applies when the relative volatility is constant across the column. If the relative volatility varies across the
column, a geometric mean of the range of values for the relative volatility may be used as an approximation. For example:
aij = `atop abotj1/2
or
aij = `atop amid abotj1/3

For a binary separation, the Fenske equation for the number of stages (including any theoretical stages represented by the con-
denser and reboiler) at total reflux is

ln =1 xD 1 − xB G
− xD xB
Nmin =
ln a

For a multicomponent separation­­with the light key indicated by i and the heavy key indicated by j, the Fenske equation is

ln > xDi xBj H
xDj xBi
Nmin =
ln aij

where Nmin = minimum number of stages, including any theoretical stages represented by the condenser and reboiler

7.3.2.10 Shortcut Estimates for Number of Theoretical Stages

Estimated Number of Theoretical Stages: Gilliland Correlation

Gilliland Correlation

1.0
0.8
0.6

0.4

0.2

N – Nmin 0.1
N+1 0.08
0.06

0.04

0.02 0.10 0.2 0.4 0.6 1.0

0.01 R – Rmin
0.01 0.02 0.04 R+1

Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical
Engineering, 5th ed., New York: McGraw-Hill, 1993.

©2020 NCEES 321

Chapter 7: Mass Transfer

Estimated Number of Theoretical Stages: Underwood Correlation
The Underwood correlation can be used for constant volatility and partial reflux.

Underwood Correlation

Rectifying Section (Top) Stripping Section (Bottom)

0 # K1 # 1, K2 2 1 K1 1 0, 0 # K2 # 1

V = R+1 V `R + 1 + f j xF − xB − f
L R L xD − xF
=
xF − xB
`1 − f j + ` R + 1 − f j xD − xF

xD b =− xB −
R+1 xF − xB
b = `R + 1 − f j xD xF − f

K1,2 = − 1 fb V 1 − a12 V p ! 1 fb V 1 − a12 V 2 − b V
2 L L 4 L L L
− − p a12 − 1
a12 − 1 a12 − 1

Intersection of feed line with operating lines: xI = e xF − xD o f ^R + 1h
f R+1 1 +R−f

NR = llnnSSSSSSTRS__(xx1DI+−−(KaKa1111i2i2_−_VLKK122)−−K1xx)DI2iiVWWWWXWWW NS = llnnRTSSSSSSS__(1xxBI+−−(KKaa1111i2i2_−_VLKK122)−−K1xx)BI2iiVWWWWXWWW

where = intercept of the operating line with the vertical axis
b = number of stages in the rectifying section
NR = number of stages in the stripping section
NS

7.3.3 Absorption and Stripping

For dilute solutions (xsolvent . 1), use solute-free basis for the concentrations (X, Y) and the flow rates (GS, LS):

YA = yA = pA pA XA = 1 xA
1 − yA Ptot − − xA

GS = G `1 − yAj = _1 G LS = L _1 − xAi = _1 L
+ YAi + XAi

©2020 NCEES 322

Chapter 7: Mass Transfer

Absorption and Stripping

Absorber Stripper
Feed Xin
Feed Yin GS, Yout LS, Xin
For fresh stripping gas: Yin = 0
For fresh solvent: Xin = 0

GS, Yin LS, Xout

Material Balance

Yout = Yin − LS ` Xout − Xinj and Xout = Xin − GS `Yout − Yinj
GS LS

Equilibrium Line (EQ): y = m x

YEQ = 1 + mX mi or XEQ = m + Y − 1i
X _1 − Y _m

Operating Line (OL) Operating Line (OL)

Y = LS X + Yin − LS Xout Y = LS X + Yout − LS Xin
GS GS GS GS

Minimum Flow Minimum Flow

LS,min = GS `Yin − Youtj GS,min = LS ` Xin − Xoutj

m + Yin − 1 i − Xin m + m Xin − 1 i − Yin
Yin _m Xin _m

Diagram Diagram

Yin BOTTOM EQ Y eq (Xin ) EQ
TOP
OL Yout Ls
Gs,min OL
Yout TOP
Yin BOTTOM Xin
Ls,min Xout
Gs

Xin Xout X eq(Yin)

Absorption Factors: Equilibrium Equations: Stripping Factors:
General:
A = L y=mx S = mG
mG L

A = L Vapor/Liquid: y = K x S = KG
KG L

A = Ptot L Henry's Law: y = H x S = HG
HG Ptot Ptot L

A= Ptot L Raoult's Law: y= psat x S= psat G
psatG Ptot Ptot L

©2020 NCEES 323

Chapter 7: Mass Transfer

Absorption and Stripping (cont'd)

Absorber Stripper

Efficiency Efficiency

e Ls o Xout − Xin e Gs o Yout − Yin
Gs Xeq _Yini − Xin Ls Yeq _ Xini − Yin
E = min = E = min =

e Ls o e Gs o
Gs Ls
act act

Theoretical Stages A−1XWWWWWWVW TheoreticaNlSS=taglnesSRSSSSSST_1 −1WWXVWWWWW
ln SSSSSSSRT_1
− A−1 i 8Yin − Yeq _ XiniB + − S−1i 8Xin − Xeq _ XiniB + S
8Yout − Yeq _ XiniB 8Xout − Xeq _ XiniB
NA =
ln ^ Ah ln ^S h

NA = Yout − Yin for A=1 NS = Xout − Xin for A=1
Yeq _ Xini − Yout Xeq _ Xini − Xout

NTU (Number of Transfer Units) NTU (Number of Transfer Units)

NTUOY = Yin − Yout NTUOX = Xin − Xout
DYlm DXlm

DYlm = 8Yin − Yeq _ XoutiB − 8Yout − Yeq _ XiniB DXlm = 8Xin − Xeq _YoutiB − 8Xout − Xeq _YiniB
ln>YYoinut−−YYeqeq__XXouintiiH ln> XXoinut−−XXeqeq__YYouintiiH

where
DYlm = log-mean concentration difference in the vapor phase (solute-free basis)
DXlm = log-mean concentration difference in the liquid phase (solute-free basis)
NTUOY = overall number of transfer units based on the gas phase
NTUOX = overall number of transfer units based on the liquid phase

7.4 Design of Columns

7.4.1 Trayed Columns 324
7.4.1.1 Primary Tray Design Parameters

• Number of passes
• Tray spacing
• Tray type
• Outlet weir type and height
• Downcomer type and area
• Clearance under downcomer
• Hole size, valve size, or bubble cap size and style
• Fractional hole area for sieve and valve trays
• Tray pressure drop

©2020 NCEES

Chapter 7: Mass Transfer

• Tray efficiency
• Tray capacity
• Tray hydraulics (flooding)
Tray sizing calculations are performed at points where the column loading is expected to be the highest and lowest in each
section. Typically, these are
• The top tray
• Above every feed, product draw-off, and point of heat addition or removal
• Below every feed, product draw-off, and point of heat addition or removal
• The bottom tray
• At any point in the column where the calculated vapor or liquid loading peaks

Starting Dimensions for Cross-Flow Sieve Trays

Dimension (units) Vacuum Atmospheric Pressure

Tray spacing (in.) 24 24 24

Downcomer area (% column) 5 10 15

Active area (% column) 90 80 70

Hole area (% active) 12 10 8

Weir height (in.) 122

Hole diameter (in.) 0.25 0.25 0.25

Downcomer clearance (in.) 0.5 1.0 1.5

Source: Copyright ©2008. From Albright's Chemical Engineering Handbook by Lyle F. Albright.
Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.

Criterion Tray Selection
Vapor-Handling Capacity
Liquid-Handling Capacity Criteria for Selecting a Distillation Column Device
Mass-Transfer Efficiency Details

Flexibility Entrainment flooding. At incipient flooding, the minimum column diameter is fixed.

Pressure Drop Fixes the size of downcomers. Downcomer backup can lead to flooding.

Cost Sets required height for a given number of theoretical stages. Efficiency can be a func-
tion of column diameter.
Design Limitations
Of concern when the column must be operated under a wide range of feed rates or when
Special Concerns future capacity needs must be considered in the initial design.

Low pressure drop is critical for vacuum columns, especially when a low bottoms tem-
perature must be maintained.

Consider total cost of the system, including auxiliary equipment; a more expensive
device may lead to lower operating costs.

Device should be proven commercially. Also, the user needs to understand how the
device was designed (if by a vendor).

Fouling, corrosion, ease of installation or removal, potential foaming problems,
adequate residence time for reactions, special heat-transfer needs.

Source: Copyright ©2008. From Albright's Chemical Engineering Handbook by Lyle F. Albright.
Reproduced by permission of Taylor and Francis Group, LLC, a division of Informa plc.

©2020 NCEES 325

Chapter 7: Mass Transfer

7.4.1.2 Common Types of Distillation Trays
Bubble Cap Tray (left) and Various Caps (right)


Source: Republished with permission of McGraw-Hill, from Mass Transfer Operations, Robert Treybal,
3rd ed., New York,1987; permission conveyed through Copyright Clearance Center, Inc.
Sieve Tray (left) and Dual-Flow Tray (right)

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister,
New York, 1992; permission conveyed through Copyright Clearance Center, Inc.
Bubble Cap Trays

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York,

1992; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 326

Chapter 7: Mass Transfer
Sieve Trays

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister,
New York, 1992; permission conveyed through Copyright Clearance Center, Inc.
Valve Trays

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister,
New York, 1992; permission conveyed through Copyright Clearance Center, Inc.

7.4.1.3 Comparison of Common Types of Distillation Trays

Comparison of the Common Tray Types

Feature Sieve Trays Valve Trays Bubble Cap Trays Dual-Flow Trays
Capacity Very high
Efficiency High High to very high Moderately high Lower than other types

Turndown High High Moderately high Low; even lower than sieve
trays; unsuitable for variable
Entrainment About 2:1; About 4–5:1; some Excellent; better load operation
not gener- special designs achieve than valve trays;
Pressure Drop ally suitable (or claim) 10:1 or more good at extremely Low to moderate
for operation low liquid rates
under variable Low to moderate
loads

Moderate Moderate High; about 3 times
higher than sieve
trays

Moderate Moderate; early designs High
somewhat higher; recent
designs same as sieve
trays

©2020 NCEES 327

Chapter 7: Mass Transfer

Comparison of the Common Tray Types (cont'd)

Feature Sieve Trays Valve Trays Bubble Cap Trays Dual-Flow Trays
Cost
Maintenance Low About 20 percent higher High; about 2–3 Low
Fouling Tendency than sieve trays times the cost of
Effects of Corrosion sieve trays
Availability of
Design Information Low Low to moderate Relatively high Low
Other
Low Low to moderate High; tends to col- Extremely low; suitable where
Main Applications lect solids fouling is extensive and for
slurry handling

Low Low to moderate High Very low

Well-known Proprietary, but informa- Well-known Some information available
tion readily available

Instability sometimes occurs in
large diameter (> 8 ft) columns

Most columns Most columns, services Extremely low-flow Capacity revamps where
when turn- where turndown is im-
down is not portant conditions; where efficiency and turndown can be
critical
leakage must be sacrificed; highly fouling and

minimized corrosive services

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992;
permission conveyed through Copyright Clearance Center, Inc.

7.4.1.4 Hydraulic Model for Trays

The Hydraulic Model for Trays
TRAY ABOVE
AN

ADT

hcl FROTH hw
ADB AB

LIQUID AND GAS
LIQUID WITH BUBBLES

TRAY BELOW

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York,
1992; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 328

Chapter 7: Mass Transfer

Tray Area Symbol Tray Area Definitions
Total tower cross- Definition
sectional area
Net area AT The inside cross-section area of the empty tower without downcomers or trays

Bubbling area AN Total cross-section area minus the area at top of the downcomer; also referred to as
free area; represents smallest area available for vapor flow in the intertray spacing
Hole area
Total tower cross-section area minus total downcomer area, downcomer seal area,
Slot area AB and any other nonperforated regions; also referred to as the active area (Aa); repre-

Open slot area sents the area available to vapor flow near the tray floor
Fractional hole area
Downcomer top area Ah Total area of perforations on the tray; smallest area available for vapor passage
Downcomer bottom Total vertical curtain area for all valves through which vapor passes in a horizontal
area
AS direction as it leaves the valves, based on the narrowest opening of the valves; small-
est area available for vapor flow on a valve tray

ASo Slot area when all valves are fully opened

Af Ratio of hole area to bubbling area (in sieve trays) or slot area to bubbling area (in
valve trays)

ADT Area at top of downcomer

ADB Area at bottom of downcomer

7.4.1.5 Definitions of Vapor Load

Several different parameters are used for characterization of the vapor load.

ft 3 m 3
sec s
The vapor load (Vload), in or , is

Vload = CFS tG
tL − tG

where

CFS = vapor flow rate at conditions, in ft 3 or m3
sec s

rL, rG = densities of the liquid and gas phases, respectively

The F-factor for gas loading, in ft d lbm 0.5 or m e kg 0.5 , is
sec ft3 s m3
n o

F = u tG

where u = superficial linear gas velocity

The C-factor for gas loading, in ft or m , is
sec s
tG
C=u tL − tG

In practice, the F-factor and the C-factor may be based on bubbling area AB, net area AN, or some other area, depending on the
source of data and correlations. Care must be taken to use the correct area basis, depending on the source.

These terms are related as follows:

C = Vload = F
A tL − tG

©2020 NCEES 329

Chapter 7: Mass Transfer

7.4.1.6 Definitions of Liquid Load

The tray liquid load QL, in gpm or m 3 , is
in. hr :
VoL m
LW
QL =

where

VoL = liquid volumetric flow rate, in gal or m3
min s

LW = outlet weir length, in inches or meters

The downcomer liquid load QD, in gpm or ft or m , is
ft 2 sec s

QD = VoL
ADT

7.4.1.7 Flow Regimes on Trays

Flow Regimes

FLOODING

Cs, VAPOR LOAD / A, ft/ s SPRAY

FROTH

EMULSION

BUBBLE

LIQUID FLOW RATE PER WEIR LENGTH

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York,
1992; permission conveyed through Copyright Clearance Center, Inc. .

ENETXRCAEISNSIMVEENT Tray Performance Diagram

ENTRAINMENT FLOODING

AREA OF DOWNCOMER FLOODING
SATISFACTORY OPERATION

VAPOR FLOW RATE WEEP POINT
EXCESSIVE WEEPING

DUMP POINT

LIQUID FLOW RATE

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York, 1992;
permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 330

Chapter 7: Mass Transfer

7.4.1.8 Column Flooding

Effect of Design Parameters on Flooding

Design Parameters That Spray Entrainment Froth Entrainment Downcomer Backup Downcomer Choke
Lower Flooding Point Flooding
Flooding Flooding Flooding
Low bubbling area
XX X
Low fractional hole area (<
8%) XX X

Low tray spacing XX X
XX
High weirs (> 4 in) XX

Small weir length X

Small clearance under X
downcomer

Small downcomer top area

Source: Republished with permission of McGraw-Hill, from Distillation Design, Henry Z. Kister, New York,
1992; permission conveyed through Copyright Clearance Center, Inc.

7.4.1.9 Entrainment Flooding

The correlations for entrainment given below are based on C-factors, specifically the Souders and Brown constant

CSB at the entrainment flood point, in ft or m .
sec s

CSB,flood = uS,flood tG
tL − tG

where uS,flood = superficial gas velocity at the entrainment flood point

Fair's Entrainment Flooding Correlation

CSB at the entrainment flood point, in ft or m
sec s

CSB,flood = u N, flood c 20 0.2 e tG 0.5
c tL − tG
m o

where uN,flood = superficial gas velocity at the entrainment flood point based on the net area AN
γ = surface tension, in dyne/cm

CSB,flood and uN,flood are based on the net area AN. The correlation is applicable to sieve trays, valve trays, and
bubble cap trays.

These restrictions apply:

1. System is nonfoaming or low-foaming.

2. Weir height is less than 15 percent of tray spacing.

3. Sieve-tray perforations are 13 mm (1/2 in.) or less in diameter.

4. Ratio of slot (bubble cap), perforation (sieve), or full valve opening (valve plate) area Ah to active area Aa is 0.1 or
greater. Otherwise the value of uN,flood should be corrected using the following table:

©2020 NCEES 331