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

Chapter 7: Mass Transfer

Ah uN,flood Correction Factor
Aa

0.10 1.00

0.08 0.90

0.06 0.80

Fair's Entrainment Flooding Correlation

0.7 PLATE SPACING
0.6
0.5 , ft/sec 0.5 36"

0.4 24"

ρG 0.3 18"
ρL – ρG
12"
20 0.2 0.2 9"
γ
6"

SB,C flood = uN, flood 0.1

0.07 0.02 0.03 0.05 0.07 0.1 0.2 0.3 0.5 0.7 1.0 2.0
0.06
0.05
0.04

0.03
0.01

FLV = _L ρG 0.5
G ρL

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

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Chapter 7: Mass Transfer

7.4.1.10 Downcomer Backup Flooding
The downcomer backup is determined by a pressure balance for the downcomer:

hdc = ht + hw + how + hhg + hda

where

hdc = height of clear liquid in downcomer, in inches liquid or mm liquid
ht = total tray pressure drop, in inches liquid or mm liquid
hw = height of weir at tray outlet, in inches liquid or mm liquid
how = height of liquid crest over weir, in inches liquid or mm liquid
hhg = liquid hydraulic gradient across tray, in inches liquid or mm liquid
hda = head loss due to liquid flow under downcomer apron, in inches liquid or mm liquid

The height of aerated liquid in the downcomer is determined by:

hldc = hdc
z dc
where

hldc = height of aerated liquid froth in downcomer, in inches froth or mm froth
zdc = relative froth density (froth density to liquid density)

To prevent downcomer backup flooding, the following criterion must be met:

where hldc 1 S + hW
S = tray spacing, in inches or millimeters

Downcomer Choke Flooding

Glitsch Correlation

The maximum clear liquid velocity at the downcomer entrance to avoid downcomer choke flooding is the lowest of the three fol-
lowing correlations:

`QD,maxj1 = 250 SF
`QD,maxj2 = 41 tL − tG SF
`QD,maxj3 = 7.5 S`tL − tGj SF

where

S = tray spacing, in inches or millimeters

SF = derating factor

QD,max = maximum downcomer liquid load, in gpm or ft or m
ft 2 sec s

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Chapter 7: Mass Transfer

Generalized Criteria for Maximum Downcomer Velocity

Maximum Downcomer Velocities

Foaming Example Clear Liquid Velocity in Downcomer, ft
Tendency sec
Low-pressure (< 100 psia) light hydrocarbons, stabilizers,
Low air-water simulators 18-in. 24-in. 30-in.
Medium Oil systems, crude oil distillation, absorbers, midpressure
High (100–300 psia) hydrocarbons Spacing Spacing Spacing
Amines, glycerine, glycols, high-pressure (> 300 psia) light
hydrocarbons 0.4–0.5 0.5–0.6 0.6–0.7

0.3–0.4 0.4–0.5 0.5–0.6

0.2–0.25 0.2–0.25 0.2–0.3

Source: From H.Z. Kister, Distillation Operation, Copyright © 1990, McGraw-Hill, Inc. As shown in Kister, Henry Z., Distillation
Design, New York: McGraw-Hill, 1992; permission conveyed through Copyright Clearance Center, Inc.

System Factors

Capacity Discount Factors for Foaming Systems

System Type Examples Factor
1.00
Nonfoaming 0.90
0.85
Fluorine systems Freon, BF3 0.73
Moderate foaming Oil absorbers, amine, and glycol regenerators 0.60
0.30
Heavy foaming Amine and glycol absorbers

Severe foaming MEK units

Foam-stable Caustic regenerators

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.

7.4.1.11 Tray Hydraulic Parameters

Hydraulic Parameters

how hhg
ht + hw + how + hda + hhg

hw

hd + hw + how + –12 hhg SIEVE TRAY h ow
h da
hhg P2 hw
β ( hw+ how ) + –12 hhg
P1
P1 – P2 = hd

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 334

Chapter 7: Mass Transfer

where
hd = dry tray pressure drop, in inches liquid or mm liquid
hda = head loss due to liquid flow under downcomer apron, in inches liquid or mm liquid
hhg = liquid hydraulic gradient across tray, in inches liquid or mm liquid
how = height of liquid crest over weir, in inches liquid or mm liquid
ht = total tray pressure drop, in inches liquid or mm liquid
hw = height of weir at tray outlet, in inches liquid or mm liquid
b = tray aeration factor in pressure drop equation, dimensionless

7.4.1.12 Tray Pressure Drop
The total pressure drop across a tray, ht:
ht = hd + hl
where hl = pressure drop through the aerated liquid on the tray, in inches liquid or mm liquid

7.4.1.13 Efficiency

The point efficiency is the ratio of the change of composition at a point to the change that would occur on a
theoretical stage:

EOG = f yn − yn − 1 p
eq
y n − yn − 1 po int

The Murphree tray efficiency applies to an entire tray instead of to a single point on a tray:

EMV = f yn − yn − 1 p
yneq − yn − 1
tray

Overall column efficiency:

EOC = Nt
Na

The overall column efficiency is related to the Murphree efficiency by:

EOC = ln 81 + EMV _m − 1iB with m = m V
ln m L

where

EOC = overall column efficiency
EOG = point efficiency for a tray
EMV = Murphree tray efficiency
Nt = number of theoretical stages in a column
Na = number of actual stages in a column
yneq = vapor mole fraction in equilibrium with the liquid

l = ratio of slope of equilibrium curve to operating line

©2020 NCEES 335

Chapter 7: Mass Transfer

7.4.2 Packed Columns
7.4.2.1 Primary Packing Design Parameters

• Type of tower separation
• Packing height
• Packing type and packing factors
• Tower pressure drop
• Flooding velocity calculation

7.4.2.2 Absorption and Stripping

Gas Absorption With Countercurrent Flow

Gi , YAi

Li , XAi

h=h

PACKING

G, YA L, XA dh

h=o
Go , YAo
Lo , XAo

©2020 NCEES 336

Chapter 7: Mass Transfer

Operating Line Above Equilibrium Line
BOTTOM
OF TOWER

YAo PINCH POINT
YA
SLOPE = L
YAi G MIN

EQUILIBRIUM
LINE (SLOPE = m)

OPERATING LINE
SLOPE = L

G

XAo (YAo / m) = (XAo ) MAX
XA

where
G = mass velocity of gas phase
L = mass velocity of liquid phase
XA = mass ratio A in liquid phase
YA = mass ratio A in gas phase
h = height of packing
i = dilute end
o = rich end

©2020 NCEES 337

Chapter 7: Mass Transfer

Desorption or Stripping With Countercurrent Flow
Go , YAo

Lo , XAo

h=h

PACKING

G, YA L, XA dh

h=o
Gi , YAi
L i , XA i

©2020 NCEES 338

Chapter 7: Mass Transfer
Operating Line Below Equilibrium Line

Y eq(XAo) EQUILIBRIUM LINE
YAo (MAX)
OPERATING LINE FOR
YAo
YA MINIMUM GAS FLOW

SLOPE = L MAX
G

PINCH TOP OF TOWER
POINT

OPERATING LINE

YAi XAi XAo
XA

Gas Absorption With Concurrent Flow

Go, YAo

Lo, XAo

h=h

G, YA L, XA dh

h=o
Gi , YAi
Li , XAi

©2020 NCEES 339

Chapter 7: Mass Transfer

Absorption Operation With Concurrent Flow

TOP OF TOWER

YAo OPERATING LINE
YAi L
YA (YAi ) MAX SLOPE = – G

– L MIN
G

EQUILIBRIUM LINE

XAo XAi
XA

Desorption or Stripping With Concurrent Flow
Go, YAo

Li , XAi h=h

Lo, XAo dh
h=o
©2020 NCEES
Gi , YAi

340

Chapter 7: Mass Transfer
Desorption or Stripping Operation With Concurrent Flow

YA EQUILIBRIUM
YAo LINE
YAi
OPERATING LINE

– L MIN
G

(YAi ) MAX XAi XAo
XA

7.4.2.3 Mass-Transfer Coefficients
NA = ky (yA – yAs)
NA = kx (xAs – xA)
NA = Kx (xA* – xA)
NA = Ky (yA – yA*)

where

NA = molar flux of A
kx, ky = individual mass-transfer coefficients
Kx, Ky = overall mass-transfer coefficients
xAs, yAs = solute mole fraction at interface in liquid and gas phase, respectively
xA* = mole fraction of solute in the liquid phase at equilibrium
yA* = mole fraction of solute in the gas phase at equilibrium
(NA)AVG Ai = (ky)AVG (yA – yAs) Ai
where Ai = total interfacial area
Ai =a A h

©2020 NCEES 341

Chapter 7: Mass Transfer

where
a = interfacial area per unit volume, in ft2
A = cross-sectional area, in ft2
h = height of packing, in ft

7.4.2.4 Packing Design

Operating Line

The equation for the operating line is

Go yAo − GyA = Lo xAo − LxA or yA = L xA + 1 (GyAo − Lo xAo)
G G

Packing Height of Transfer Unit

The height of packing is

h = HG # yAo (1 − yA)lm dyA and h = nG HG
(1 − yA) (yA − yAs)
yAi

where

nG = number of gas-phase transfer units
lm = log mean

The number of gas-phase transfer units is

nG = # yAo (1 − yA)lm dyA
(1 − yA) (yA − yAs)
yAi

where (1 − yA)lm = (1 − yA) + (1 − yAs) as an approximation
2

For dilute solutions, assume L, G, and slope m are constant.

HOG = HG + mG HL = mG HOL
L L

where HOG and HOL = height of overall transfer units in gas and liquid phases, respectively

L = A = absorption factor, which ranges from 1.0 to 1.4
mG

1 = S= stripping factor
A

m = Hl
P

where

P = absolute pressure

H l= Henry's constant

HOG = HOL
A

nOG = yAo − yAi and nOL = xAo − xAi

` yA − y * jlm ` x * − xAjlm
A A

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Chapter 7: Mass Transfer

where ` yA − yA* jlm = ` yA l−nySTRSSSSSS`A*`jyyoAA−−−`yyyA*A*Ajj−oi WWWVWWWWXyA* ji

and similarly for `xA* − xAjlm

For dilute solutions:

nOL = xAo − xAi
`xA − x A* jlm

Packing HETP
For gas absorption: h = nOG HOG
For gas stripping: h = nOL HOL
Also, h = NTP HETP
where

NTP = number of theoretical plates

HETP = height of an equivalent theoretical plate

ln RSSSSSSTSSSSd1 − HG nKKKKJLKKKKlnyyAAHoip−−GL HHppxxAAii ONOOOOOOO + H G WWVXWWWWWWWW
pL P p L

NTP =

=A m=LG m H A = p L
p H G

=S A1= HG
pL

ln SSSSSRTSSSSc1 − 1 m JLKKKKKKK xAo − yAi POOONOOOO + 1 WVWWWWWWWXW
S xAi − m S
yAi
NTP = m

ln (S)

where
A = absorption factor
S = stripping factor

Note: For absorption and stripping, calculations for tower height are the same, although the operating line slope will differ.

©2020 NCEES 343

Chapter 7: Mass Transfer

Height of Packing
=h N=TUOG HTUOG NTUOL HTUOL = NT HETP

where

HETP = height equivalent of a theoretical stage

HTUOG = height of an overall vapor-phase mass-transfer unit
HTUOL = height of an overall liquid-phase mass-transfer unit
NTUOG = overall number of transfer units based on gas phase
NTUOL = overall number of transfer units based on liquid phase
NT = number of theoretical stages
h = height of packing

Height of Overall Transfer Unit

HOG = Gs
Ky a (1 − yA)lm

where (1 − yA) lm = (1 − yA* ) − (1 − yA)
where
ln f 1 − yA* p
1 − yA

HOL = Ls
Kx a (1 − xA)lm

(1 − xA) lm = (1 − xA) − (1 − xA* )

ln f 1 − xA p
1 − xA*

Number of Gas-Phase Transfer Units

#nOG = yA0 `1 `1 − yAjlm yA* j dyA
yA1 − yAj` yA −

Using the log-mean average:

#nOG = 1 − yAi + yAo dyA
0.5 ln 1 − yAo yAi ` yA − yA* j

In dilute solutions:

nOG = yAo − yAi

` yA − y * jlm
A

where ` yA − yA* jlm = ` yA − yA* jbottom − ` yA − yA* jtop

ln ` yA − yA* jbottom
` yA − yA* jtop

©2020 NCEES 344

Chapter 7: Mass Transfer

Number of Liquid-Phase Transfer Units

#nOL = xAo _1 _1 − xAilm xAj dxA
xAi − xAi`xA* −

#nOL = 1 − xAo + xAo dxA
0.5 ln 1 − xAi xAi xA* − xA

Absorption With Reaction

Dissolved solute reacts with solvent in liquid phase if irreversible reaction:

nOG = ln yAo
yAi

7.4.2.5 Correlations for Mass-Transfer Coefficients
For insoluble gases that do not react chemically with the liquid:

Hx = 1 d Gn xx h nx 0.5
a t x Dvx
ne o

where
Hx = individual liquid-phase HTU
Gx = mass velocity of liquid
mx = viscosity of liquid
Dvx = diffusivity of liquid
rx = liquid density
a and h = constants given in the table below

Values of a and h in Equations1 for
Various Packing Materials at 77°F

Packing Type Packing Size (in.) a h
0.22
Rings 2 80

1.5 90 0.22
1 100 0.22

Saddles 0.5 280 0.35

0.375 550 0.46
1.5 160 0.28

1 170 0.28

0.5 150 0.28

Tile 3 110 0.28

1. All quantities in equations must be expressed in fps units if these values of a are used.

Source: McCabe, W.L., and J.C. Smith, Unit Operations of Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976.

©2020 NCEES 345

Chapter 7: Mass Transfer

The temperature effect of liquids on the HTU can be evaluated as:
Hx = Hxo e −0.013(T − To)

where

Hx = HTU at T °F
Hxo = HTU at To °F
T = final temperature in °F

To = initial temperature in °F

Henry's Law: y* = m x

x* = y
m

where m = Henry's Law Constant/Total Pressure

7.4.2.6 Packing Factors
Selection of packing is based primarily on packing factors and avoidance of flooding.

Packing Factors (ft–1)

PACKING FACTORS**
(WET AND DUMP PACKED)

TYPE OF PACKING MAT’L. NOMINAL PACKING SIZE (INCHES) 3 3½
¼ ⅜ ½ ⅝ ¾ 1 1 ¼ 1½ 2

SUPER INTALOX CERAMIC 60 30

SUPER INTALOX PLASTIC 33 21 16
145 98 52 40 22
INTALOX SADDLES CERAMIC 725 330 200

HY-PAK RINGS METAL 42 18 15

PALL RINGS PLASTIC 97 52 40 25 16
PALL RINGS METAL 70 48 28 20 16

BERL SADDLES CERAMIC 900 240 170 110 65 45

RASCHIG RINGS CERAMIC 1600 1000 580 380 255 155 125 95 65 37

RASCHIG RINGS METAL 700 390 300 170 155 115
1/32” WALL METAL 410 290 220 137 110 83 57 32

RASCHIG RINGS
1/16” WALL

EXTRAPOLATED 1/8” WALL F 3 OBTAINED IN 16" AND 30" I.D. TOWER
1/32” WALL 3/16” WALL DATA BY LEVA
1/16” WALL 1/4” WALL
3/32” WALL 3/8” WALL

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES 346

Chapter 7: Mass Transfer
Packing Factors: Stacked Packings & Grids

1000 DIAMOND PITCH CHECKER BRICK, 55%
800 SQUARE PITCH FREE SPACE

CROSS PARTITION DIAMOND PITCH GRID TILE (CERAMIC)
SQUARE PITCH CROSS PARTITION
600 SSIINNGGLLEESSPPIIRRAALLRRIINNGGSS( RINGS (SQUARE PITCH)

400

PACKING FACTOR– F RASCHIG RINGS 1/4'' WALL
(CERAMIC) 3/16'' WALL
200

5/16'' WALL

100 RASCHIG RINGS

80 (CERAMIC)

60 1'' x 1'' x 1/4''

40 1'' x 2'' x 1/4'' 3/8'' WALL

11/2'' x 11/2'' x 3/16'' RASCHIG RINGS

2'' x 2'' x 3/8'' (METAL 1/8'' WALL)

20 METAL GRID WOOD GRIDS
(1'' x 1'' x 1/16'')

4'' x 4'' x 1/2''

10 1'' 2'' 3'' 4''

NOMINAL PACKING SIZE – INCHES

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

Packing Factors: Screen Packing & Random Dumped Packing

1000 STEDMAN
800
600

400

PACKING FACTOR– F 200 QUARTZ ROCK 2'' SIZE
CANNON

100 GOODLOE
80 CROSS PARTITION
60 RINGS

40 TELLERETTES PANAPAK
MAS PAC FN-200

20 MAS PAC
FN-90
FROM MANUFACTURERS DATA
EXCEPT AS NOTED 4''
10

1'' 2'' 3''

NOMINAL PACKING SIZE - INCHES

©2020 NCEES Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

347

Chapter 7: Mass Transfer

7.4.2.7 Flooding and Pressure Drop

Generalized Pressure Drop Correlation

0.60

0.40 GENERALIZED PRESSURE DROP
CORRELATION

0.20 FLOODING LINE PARAMETER OF CURVES IS PRESSURE
11..5500 PDARROAPMIENTIENRCHOEFSCOUFRVWEASTEISRP/FROEOSTSUORFE
DPRAOCKPEIND IHNECIHGEHST OF WATER/FOOT
0.10 1.00

g .060 0.50
.040 0.25
G 2 F µ 0.1)

ρ

G

ρ .020
L 0.10

( .010

ρG

.006 0.05
.004

.002 .02 .04 .06 0.1 0.2 0.4 0.6 1.0 2.0 4.0 6.0 10.0
ρLρGρG
.001
.01

L 1
G 2

L = LIQUID RATE, lbm
sec-ft2
G = GAS RATE, lbm
sec-ft2
ρL = LIQUID DENSITY, lbm
ft3

ρG = GAS DENSITY, lbm
ft3

F = PACKING FACTOR

µ = VISCOSITY OF LIQUID, cP

g = GRAVITATIONAL ACCELERATION

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

Determination of column diameter D:

D= c 4 m d GA n where GA = actual gas flow rate of the packed column
r G

©2020 NCEES 348

Chapter 7: Mass Transfer
Pressure Drop Versus Gas Rate

4.0 5/8 RASCHIG RINGS (METAL) (1/32" WALL)
COLUMN DIA. = 15 in.

PACKING HEIGHT = 5.1 ft.

∆P~INCHES WATER / FT. PACKING 2.0

L = 20L,=0020L5,=00300,000
15,000
1.0 L = 2,000000 LL==4L8,,000=00000010000,00L0= 6,000000 DRY
0.8 =

0.6 12,000L

0.4 F = 190=

LIQUID RATE lbmL
0.2 AS PARAMETER ft2-hr

0.1 2 3 4 500 1000 2000 5000
100

AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

4.0 1/4-in. INTALOX SADDLES (CERAMIC)

COLUMN DIA. = 8 in.
PACKING HEIGHT = 4.4 ft.

2.0
∆P~INCHES WATER / FT. PACKING
L = 10,0001.0
LLLL===D=135,,,R1000000Y000000000000000.8
0.6

0.4

0.2 F = 725
0.1 20 LIQLUIQIDUIRDARTAETE lblsb.m/ft2,hr.
AS PAARSAPMAERTAEMREftT2-EhRr

40 60 80 100 200 400 600 1000
AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES 349

Chapter 7: Mass Transfer
Pressure Drop Versus Gas Rate (cont'd)

3/8 INTALOX SADDLES (PORCELAIN)

2.0

∆P~INCHES WATER / FT. PACKING 1.0 8,000000 LD=RL1Y,0=00030,000L000=0LL5=0=025,,000000000000
0.8
=
0.6
L
0.4 COLUMN DIA. = 8''in.6,000000
PACKING HEIGHT = 4.4'ft
F==333300=

0.2 LIQUID RATE lbmL
AS PARAMETER ft2-hr

0.1 100 200 300 500 1000 2000
50 AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

4.

COLUMN DIA. = 30 in.
PACKING HEIGHT = 10 ft.
NO.2 HY-PAK (METAL)
2.

∆P~INCHES WATER / FT. PACKING 1.
0.8
0.6

0.4
F==1188
L =L30=,40L00,=00L50=0,06000,0000 L =LD5R,=00Y010000,000
20,000

=

L

0.2 LIQUID RATE lbm
0.1 AS PARAMETER ft2-hr

100 2 3 4 500 1000 2000 5000

lbm
AIR MASS VELOCITY,

ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES 350

Chapter 7: Mass Transfer
Pressure Drop Versus Gas Rate (cont'd)

4.0 3" X 3" CROSS PARTITION RINGS – DUMPED

(CERAMIC)

2.0

∆P~INCHES WATER / FT. PACKING1.0
LLLLL===L==12=915,L0,06,220,,0=000L5000,00003=000000000,003005,000000.8
L = 4,5500000.6
L = 1,5500000.4
DRY
0.2 F = 78

0.1 LIQUID RATE lbm
100 AS PARAMETER ft2-hr

2 3 4 500 1000 2000

lbm
AIR MASS VELOCITY, ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

4.0 2 in. RASCHIG RINGS (CARBON STEEL)

COLUMN DIA. = 16 in.
PACKING HEIGHT = 6.0 ft.
CO-CCUURRRREENNTTFFLLOOWW
2.0

1.0∆P~INCHES WATER / FT. PACKING
0.6 DLRL=Y=1LI0L2,LN0=0,=E00L34000=,0L0,050=000,0600L0,0=000700,000
0.4

0.2 F = 57 lbm
0.1 ft2-hr
LIQUID RATE
100 AS PARAMETER

2 3 45 1000 2000 5000

AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES 351

Chapter 7: Mass Transfer
Pressure Drop Versus Gas Rate (cont'd)

1-11/-21-/i2n". INTALOX SADDLES (PORCELAIN)
COLUMN DIA. = 16 in.

PACKING HEIGHT = 6.2 ft.
"COC-CUURRRREENNTT"FFLLOOWW

4.0

∆P~INCHES WATER / FT. PACKING 2.0 LLL===78L060L,0=,00,=00504000000,0,00000
LL==120,0L,00=000300,0001.0
0.6
DRY L = 5,000000
0.4

0.2 LIQUID RATE lbm
AS PARAMETER ft2-hr

0.1 2 3 4 500 1000 2000 5000 10,000
100 lbm

AIR MASS VELOCITY, ft2-hr

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process
Products Division, 1972 (revised 2001).

∆P~INCHES WATER / FT. PACKING 4.0 1 in. INTALOX SADDLES (POLYPROPYLENE)40,L0=0500,000
COLUMN DIA. = 16 in.
PACKING HEIGHT = 6.0 ft.

2.0 COC-CUURRRREENNTTFFLLOOWW

1.0 L = 60,000

0.6

0.4
L= DLRL=Y=1LI20,N0,0E00000
30,000

=

L

0.2 F = 57 lbm
0.1 ft2-hr
LIQUID RATE
100 AS PARAMETER

2 3 45 1000 2000 5000

lbm
AIR MASS VELOCITY, ft2-hr

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process
Products Division, 1972 (revised 2001).

©2020 NCEES 352

Chapter 7: Mass Transfer

Pressure Drop Versus Gas Rate (cont'd)

4.0 2 in. INTALOX SADDLES (POLYPROPYLENE)
COLUMN DIA. = 16 in.
PACKING HEIGHT = 6.0 ft.
CO-CCUURRRREENNTTFFLLOOWW

2.0
∆P~INCHES WATER / FT. PACKING
DLRL=Y =1LLI02,=LN00,E3=0L000,40=L000,5=0L000,60=L000,70=L000,08=L000,90=000,1000000,00001.0
0.6
0.4

0.2 F = 21 lbm
0.1
LIQUID RATE
100 AS PARAMETER ft2-hr

2 3 45 1000 2000 5000

AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process
Products Division, 1972 (revised 2001).

1-1/2 -iinn.. PPAALLLL RRIINNGGSS ((CCAARRBBOONN SSTTEEEELL))

4.0

COLUMN DIA. = 16 in.
PACKING HEIGHT = 6.0 ft.
COCURRENT FLOW

2.0

1.0 LL==6700,0,00000

0.6

0.4
∆P~INCHES WATER / FT. PACKING
DRYLL=IL1N=0E,20L00,0=00300,0L0=04L0,=05000,000
F==2288
0.2 LLIIQQUUIDIDRRATAETELBS./FTl.b2,m- HR.
0.1 AS PAARSAPMAREATMEERTEfRt2-hr

100 2 3 45 1000 2000 5000

AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

©2020 NCEES 353

Chapter 7: Mass Transfer
Pressure Drop Versus Gas Rate (cont'd)

2 in. PALL RINGS (POLYPROPYLENE)
COLUMN DIA. = 16 in.
PACKING HEIGHT = 5.6 ft.
"CCOOC-CUURRRENENTTF"LFOLWOW

4.0

2.0 L = 120,000
∆P~INCHES WATER / FT. PACKINGL =L9L=L0=,=100107L0100,=0,00,60000000L,00=0080,000
LLL===2L310L0,=,00,=0500004,00000,0000001.0
0.6
DRY0.4

0.2 LIQUID RATE LBS./FT.2,
LIQHURI.DASRAPTAERAMElTbEmR
AS PARAMETER ft2-hr

0.1 2 3 4 500 1000 2000 5000 10,000
100

AIR MASS VELOCITY, lbm
ft2-hr

Source: Eckert, J.S., E.H. Foote, R.R. Nemunaitis, and L.H. Rollison, Akron, OH: Norton
Chemical Process Products Division, 1972 (revised 2001).

7.5 Liquid-Liquid Extraction

7.5.1 Fundamentals of Liquid-Liquid Extraction

7.5.1.1 Partition Ratio

The equilibrium partition ratio in mole fraction units is

K=io xy=ii c iraffinate
extract
c i

where

yi = mole fraction of solute i in the extract phase

xi = mole fraction of solute i in the raffinate phase

gi = activity coefficient of solute i in the indicated phase

The equilibrium partition ratio in mass ratio units Kil is

YX=iill e m extract o
solute
mextraction solvent
=Kil
m raffinate
e m solute o

raffinate solvent

where

Yil = ratio of mass solute i to mass extract solvent in extract phase

Xil = ratio of mass solute i to mass raffinate (feed) solvent in raffinate phase

m = mass flow rate, in lbm or kg
hr s

©2020 NCEES 354

Chapter 7: Mass Transfer

The advantage of using the solute-free basis is that the feed solvent and extraction solvent flows do not change
during the extraction.

7.5.1.2 Extraction Factor

On a McCabe-Thiele type of diagram, E is the slope of the equilibrium line divided by the slope of the operating

line F .
S

Ei = mi S
F

where

Ei = extraction factor

mi = local slope of the equilibrium line

S = mass flow rate of the solvent phase, in lbm or kg
hr s
kg
F = mass flow rate of the feed phase, in lbm or s
hr

For dilute systems with straight equilibrium lines, the slope of the equilibrium line is equal to the partition ratio:

mi = Kil

7.5.1.3 Separation Factor

The separation factor indicates the relative enrichment of a given component in the extract phase after one
theoretical stage of extraction.

f=fXXYYiijjllll ppreaxftfriancatte f Yil p Kil
Xil K jl
=a ijl =
Y jl
f X jl p

where aijl = separation factor for solute i with respect to solute j (mass ratio basis)

7.5.1.4 Interfacial Mass Transfer

no = ky (yint − y) no = koy (y* − y)
no = kx (xint − x) no = kox (x − x*)

where

no = molar flow per area

xint = mole fraction of solute i in the raffinate phase at the interface
x* = mole fraction of solute i in the raffinate phase in equilibrium with the extract phase
yint = mole faction solute i in the extract phase at the interface
y* = mole fraction of solute i in the extract phase in equilibrium with the raffinate phase

#NTUG = ye (1 − y)1m dy
ys (1 − y) (yint − y)

©2020 NCEES 355

Chapter 7: Mass Transfer

For dilute solutions:

NTUOL = xf − xr
(x − x*)1m

where
xf = mole fraction of solute i in the feed
xr = mole fraction of solute i in the raffinate
NTUG = number of transfer units based on gas phase
NTUOL = number of transfer units based on liquid phase
( )lm = log mean

7.5.2 Theoretical (Equilibrium) Stage Calculations

Countercurrent Extraction Cascade

F 'X f E 'Ye or Y1
FEED STAGE 1

X1 Y2
2

X n–1 Yn

n

Xn Yn+1

Xr–1 r –1
Yr
RAFFINATE STAGE
R 'X r r

S'Ys

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 356

Chapter 7: Mass Transfer

7.5.2.1 McCabe-Thiele Method
McCabe-Thiele Graphical Stage Calculation Using Bancroft Coordinates

2

1

WT. SOLUTE X f ' Ye
EXTRACTION-SOLVENT
EQUILIBRIU4M LINE 3 2 OPERATING LINE

WT.

Y' SLOPE = F '
S '

r PARTIAL STAGE
0 X r ' Ys

0 WT. SOLUTE 2
WT. FEED-SOLVENT
X'

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

For immiscible feed and extraction solvents, the operating line for the feed end (stage 1 to stage n) is

Y ln + 1 = Fl Xnl+ ElYel− Fl Xfl
Sl Sl

where

Xfl = mass ratio of solute in feed
Yel = mass ratio of solute in extract
El = mass flow rate of extraction solvent only

Fl = mass flow rate of feed solvent only

Sl = mass flow rate of extraction solvent only

For immiscible feed and extraction solvents, the operating line for the raffinate end (stage n to stage r) is

Ynl= Fl Xnl− 1 + SlYsl− Rl Xrl
Sl Sl

where
Xrl = mass ratio of solute in raffinate
Ysl = mass ratio of solute in solvent
Rl = mass flow rate of raffinate solvent only

©2020 NCEES 357

Chapter 7: Mass Transfer

The overall material balance is

Yel= Fl Xfl+ SlYsl− Rl Xrl
El

7.5.2.2 Kremser-Souders-Brown (KSB) Theoretical Stage Equation

For straight equilibrium and operating lines, the number of theoretical stages N is approximated by:

ln >f X f l− Ysl/ml pc1 − 1 m + 1 H
Xrl− Ysl/ml E E
for E = ml FSll, E Y= 1
N = ln E

where

N = number of theoretical stages

ml = local slope of equilibrium line in mass ratio units

Sl = mass flow rate of the solvent only (solute-free basis), in lbm or kg
hr s

Fl = mass flow rate of the feed solvent (solute-free basis), in lbm or kg
hr s

An alternate form is

Xfl− Ysl/ml = E N − 1/E for E Y= 1
Xrl− Ysl/ml 1 − 1/E

Xfl− Ysl/ml = N + 1 for E = 1
Xrl− Ysl/ml

Graphical solutions to the KSB equation are shown below. Note that the term for the abscissa is the inverse of the term used in the

KSB equation.

©2020 NCEES 358

Chapter 7: Mass Transfer

Graphical Solutions to the KSB Equation

1.0
0.8
0.6
0.4 N = 1

0.2 2
3
0.1 4
.08
.06 6
.04

.02

.01
.008
.006
X'r – Y's /m' .004
X'f – Y's /m' .002

.001
.0008
.0006
.0004

.0002 8
10
.0001
.00008
.00006
.00004

.00002 15 6 8 10

.00001 24
1
ε, EXTRACTION FACTOR

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 359

Chapter 7: Mass Transfer

In general, these equations are valid for any concentration range in which equilibrium can be represented by a linear relationship
Y = m X + b (written here in general form for any system of units). For applications that involve dilute feeds, the section of the
equilibrium line of interest is a straight line that extends through the origin where Yi = 0 at Xi = 0. In this case, b = 0, and the slope
of the equilibrium line is equal to the partition ratio where m = K.

The KSB equation also may be used to represent a linear segment of the equilibrium curve at higher solute concentrations. In this
case, the linear segment is represented by a straight line that does not extend through the origin, and m is the local slope of the
equilibrium lin=e, so b Y 0=and m Y K.

Furthermore, a series of KSB equations may be used to model a highly curved equilibrium line by dividing the analysis into linear
segments and matching concentrations where the segments meet. For equilibrium lines with moderate curvature, an approximate
average slope of the equilibrium line may be obtained from the geometric mean of the slopes at low and high solute concentra-
tions:

maverage . mgeometric mean = mlow mhigh

7.5.2.3 Stage Efficiency

po (%) = theoretical stages # 100
actual stages

p md = cd,n + 1 − cd,n

cd,n +1 − c *
d

po (%) = ln [1 + p md (E − 1)] # 100
ln E

where

po = overall stage efficiency
pmd = Murphree stage efficiency based on the dispersed phase

7.5.3 Rate-Based Calculations With Mass-Transfer Units

In most cases, the dominant mass-transfer resistance resides in the feed (raffinate) phase because the slope of the equilibrium line
usually is greater than one. In that case, the overall mass-transfer coefficient based on the raffinate phase may be written:

1 = 1 + 1
kor kr mevrol ke

where

ke = extract-phase mass-transfer coefficient, in ft or m
hr s

kr = raffinate-phase mass-transfer coefficient, in ft or m
hr s

kor = overall mass-transfer coefficient based on the raffinate phase, in ft or m
hr s

mevrol = local slope of equilibrium line (volumetric concentration basis)

©2020 NCEES 360

Chapter 7: Mass Transfer

The required contacting height of an extraction column is related to the height of a transfer unit and the number of transfer units

by:

#Zt = Vr x in dX = HTUor NTUor
kor a x out X − Xeq

where

Zt = total height of extractor

Vr = liquid velocity of raffinate phase, in ft or m
sec s
ft2 m2
a = interfacial area per unit volume, in ft3 or m3

Xeq = mass ratio in equilibrium with composition of extract phase

HTUor = height of overall transfer units (based on raffinate phase)

NTUor = number of transfer units (based on raffinate phase)

For straight equilibrium and operating lines, the number of transfer units is approximated by the Colburn equation:

lnSSSSSSSSRTSS KKJKKKKKLKK Xf l− Ysl PNOOOOOOOOO c1 − 1 m+ 1 WWWWWWWWVXWW
Xrl− ml E E
Ysl
NTUor = ml

1 − 1
E
where

=E m=l FSll, E Y 1

An alternate form is

Xfl− Ysl exp <NTUor c1 − 1 mF − 1
Xrl− ml E E
Ysl =
ml − 1
1 E

The height of a transfer unit is

HTUor = HTUr + HTUe
E

HTUr = Qr
Acol kr a

HTUe = Qe
Acol ke a

where

HTUr = height of a transfer unit due to resistance in the raffinate phase, in ft or m
HTUe = height of a transfer unit due to resistance in the extract phase, in ft or m
Acol = column cross-sectional area, in ft2 or m2

©2020 NCEES 361

Chapter 7: Mass Transfer

Qr = volumetric flow rate of the raffinate phase, in ft3 or m3
min s

Qe = volumetric flow rate of the extract phase, in ft3 or m3
min s

The relation between overall raffinate-phase transfer units from the Colburn equation and the number of theoretical stages from

the KSB equation is

NTUor = N # ln E for E Y= 1
1 for E = 1
1 − E

NTUor = N = Xfl− Ysl −1
Xrl− ml
Ysl
ml

7.5.3.1 Solute Reduction Factor, FR
The solute reduction factor FR, is an indication of process performance.

For a single-stage batch process or for one theoretical stage of a continuous process, the solute reduction factor is

Xin cE − 1 m
Xout E
FR = = for N = 1
1
c1 − E m

The required solvent-to-feed ratio is approximated by

S = FR − 1 for N = 1
F K

where

K = distribution coefficient for phase equilibrium

S = mass flow rate of the solvent phase (solute-free basis)

F = mass flow rate of the feed phase (solute-free basis)

Xin = ratio of mass solute i to mass raffinate solvent in the raffinate phase at the inlet of the raffinate

Xout = ratio of mass solute i to mass raffinate solvent in the raffinate phase at the outlet of the raffinate

Yout = ratio of mass solute i to mass extract solvent in the extract phase at the outlet of the solvent

Yin = ratio of mass solute i to mass extract solvent in the extract phase at the inlet of the solvent

For any extraction configuration, the concentration of solute in the extract is

Yout = Xin d1 − 1 n for Yin = 0
FR
c S m
F

For cross-flow extraction, in which the raffinate phase for each stage is contacted with fresh solvent, the solute reduction factor is

FR = c1 + E poN
N
m

S = N c 1 − 1m
F K
FRpoN

©2020 NCEES 362

Chapter 7: Mass Transfer

For multistage countercurrent extraction, the solute reduction factor is

cEpoN − 1 m
c1 − E
FR =
1
E m

For countercurrent extraction without discrete stages, the solute reduction factor is

exp <NTUor c1 − 1 mF − 1
E E
FR =
1 − 1
E

7.5.4 Liquid-Liquid Extraction Equipment

7.5.4.1 Spray Columns

Liquid Dispersion

For liquid distributors, the liquid should issue from the hole as a jet that breaks up into drops. As a general guideline, the
maximum recommended design velocity corresponds to a Weber number (We) of about 12. The minimum Weber number that
ensures jetting in all the holes is about 2. It is common practice to specify a Weber number between 8 and 12 for a new design.

uo,max . d We c 0.5
do td
n

where

uo,max = maximum velocity through an orifice or nozzle
We = Weber number

g = surface tension

do = orifice or nozzle diameter
rd = density of the dispersed phase

RAG LIGHT LIQUID OUT
REMOVAL HEAVY
LIQUID IN COLUMN
INTERFACE

LARGE-DIAMETER
ELGIN HEAD

LIGHT–PHASE
DISTRIBUTOR

HEAVY LIQUID OUT
LIGHT LIQUID IN

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 363

Chapter 7: Mass Transfer

Drop Size, Dispersed-Phase Holdup, and Interfacial Area

For the general case where the dispersed phase travels through the column as drops, an average liquid-liquid interfacial area can
be calculated from the Sauter mean drop diameter and dispersed-phase holdup.

The drop diameter is

dP = 1.15h c
Dt g

where

dp = Sauter mean drop diameter
Dr = density difference between the raffinate and the extract

h = parameter, specifically:

h = 1.0 for no mass transfer

h = 1.0 for transfer from continuous to dispersed phase

h = 1.4 for transfer from dispersed to continuous phase

The dispersed-phase holdup is

ud=cos c rg −2 apdp
4 2
mG

zd = − 6zd uc , g =
r −
f>uso exp d n − f`1 zdjH

where

zd = volume fraction of the dispersed phase (holdup)
z = tortuosity factor

ud = liquid velocity of the dispersed phase
uc = liquid velocity of the continuous phase
uso = slip velocity at low dispersed-phase flow rate
e = void fraction

aP = interfacial area

The interfacial area is

ap = 6f zd
dp

Drop Velocity

The average velocity of a dispersed drop udrop is

udrop = ud
fzd

Interstitial Velocity of Continuous Phase

The interstitial velocity of the continuous phase uic is

uic = uc
f`1 − zdj

©2020 NCEES 364

Chapter 7: Mass Transfer

Slip Velocity and Characteristic Slip Velocity
The relative velocity between the counterflowing phases is referred to as the slip velocity us:

us = udrop + uic

The characteristic slip velocity uso obtained at low dispersed-phase flow rate is

ReStokes = tc Dt g dP3
18 nc2

where

Re = Reynolds Number

rc = density of the continuous phase
Dr = density difference between the two phases

mc = viscosity of the continuous phase
For ReStokes < 2:

uso = Dt g dp2
18nc

For ReStokes > 2:

uso = Re nc
dp tc

where

Re = 0.94H0.757 − 0.857 H # 59.3
P0.149

Re = 3.42H0.441 − 0.857 H 2 59.3
P0.149

P = tc2 c3
nc4 g Dt

H = f 4d 2 g Dt p d nw 0.14 P0.149
p nc
n
3c

P, H = dimensionless groups
mw = reference viscosity equal to 0.9 cP or 9 × 10–4 Pas
The slip velocity at higher holdup is estimated from:
us . uso `1 − zdj

©2020 NCEES 365

Chapter 7: Mass Transfer

Flooding Velocity

It is generally recommended that flow velocities be limited to 50 percent of the calculated flooding velocities.

ucf = 0.178uso

1 + 0.925d udf n
ucf

where

ucf = continuous-phase flooding velocity
udf = dispersed-phase flooding velocity

Drop Coalescence Rate
Problems with coalescence are most likely when the superficial dispersed-phase flooding velocity udf is greater than about 12
percent of the characteristic slip velocity.

Mass-Transfer Coefficients and Efficiency

zd `1 − zdj f g3 Dt3 1/4
c tc2
p

koc a = mdvcol kod a = 0.08 # nc 1/2 nd 1/2
tc Dc td Dd
e o + d 1 n e o
mdc

where

Dc = solute diffusion coefficient for the continuous phase

Dd = solute diffusion coefficient for the dispersed phase

koc = overall mass-transfer coefficient based on the continuous phase

kod = overall mass-transfer coefficient based on the dispersed phase

mdc = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase
concentration

m vol = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase
dc

concentration on volumetric concentration basis

γ = interfacial tension

μc = viscosity of continuous phase

μd = viscosity of dispersed phase

ρc = density of continuous phase

ρd = density of dispersed phase

φd = volume fraction of dispersed phase (holdup)

With the height of one transfer unit (based on the continuous phase):

HTUqc = uc
koc a

©2020 NCEES 366

Chapter 7: Mass Transfer

7.5.4.2 Packed Columns
Liquid Redistribution
Little benefit is gained from a packed height greater than 10 ft (3 m). Redistributing the dispersed phase about every 5 to 10 ft
(1.5 to 3 m) is recommended to generate new droplets and constrain backmixing.

Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-64.

Minimum Packing Size

For a given application, a minimum packing size or dimension exists below which random packing is too small for good extrac-

tion performance. The critical packing dimension dc is

dc = 2.4 c
Dt g

where
γ = interfacial tension

Packing Holdup

For standard commercial packings of 0.5 in (1.27 cm) and larger, fd varies linearly with the liquid velocity of the dispersed phase
(ud) up to values of fd = 0.10 (for low values of ud). As ud increases further, fd increases sharply up to a "lower transition point"
resembling loading in gas-liquid contact. At still higher values of ud, an upper transition point occurs, the drops of dispersed phase
tend to coalesce, and ud can increase without a corresponding increase in fd. This regime ends in flooding. Below the upper transi-
tion point, the dispersed-phase holdup is

ud + 1 uc = f uso `1 − zdj
zd − zd

Packing Flooding: Siebert, Reeves, and Fair Correlation

ucf = 0.925d0uu.1dcff7n8]Z][]]\]]]]f=ucsoos 1 `_abbbbbbbb g = ap dp
2

1 + c rg 2
4
mG

©2020 NCEES 367

Chapter 7: Mass Transfer

Packing Flooding: Modified Crawford-Wilke Correlation2ρ
Flooding VelocitiesC

1040.5
6 LIQUID – LIQUID PACKED TOWERS0.5
4
VD αC
A MODIFIED CRAWFORD-WILKE CORRELATIONVC

2+

103l

6Vc
4
=

2ρ 2
C

VC 0.5 102

+ αC 6
4
VD0.5

2

10 46 10 2 4 6 102 2 4 6 103
12

'c γ 0.2 2 1.5

ρ ρc F

V = ft./hr. (SUPERFICIAL VELOCITY) µ'c = VISCOSITY IN (CENTIPOISE)
C = CONTINUOUS PHASE
D = DISPERSE PHASE ρ = DENSITY (POUNDS PER / CUBIC FOOT)

α = sq. ft. AREA OF PACKING/ c ft. γ = INTERFACIAL SURFACE TENSION (DYNES / cm)

= DIFFERENCE F = PACKING FACTOR (DIMENSIONLESS)

= VOID FRACTION IN PACKING

Pressure Drop

In general, the pressure drop through a packed extractor is due to the hydrostatic head pressure. The resistance to flow caused by
the packing itself normally is negligible; typical packings are large and flooding velocities are much lower than those needed to
develop significant DP from resistance to flow between the packing elements.

Mass-Transfer Coefficients
1
nd 2
e td Dd
o

U = nd
nc
d1 + n

For Φ < 6:

kd = 0.00375us
d1 + nndc n

©2020 NCEES 368

Chapter 7: Mass Transfer

For Φ > 6:

kd = 0.023use nd − 1
td Dd 2
o

kc dp = 0.698e nc 2 e dp us tc 1 `1 − zdj
Dc tc Dc 5 nc 2

o o

1 = 1 + mdvcol
kod kd kc

where

kc = continuous-phase mass-transfer coefficient
kd = dispersed-phase mass-transfer coefficient

Packing Data

Random and Structured Packings Used in Packed Extractors

Packing Surface Area ap1 m2 Void Fraction1 (e)
m3

Metal Random Packing

Koch-Glitsch IMTP® 25 224 0.964
Koch-Glitsch IMTP® 40 151 0.980
Koch-Glitsch IMTP® 50 102 0.979
Koch-Glitsch IMTP® 60 84 0.983
Sulzer I-Ring #25 224 0.964
Sulzer I-Ring #40 151 0.980
Sulzer I-Ring #50 102 0.979
Nutter Ring® NR 0.7 226 0.977
Nutter Ring® NR 1 168 0.977
Nutter Ring® NR 1.5 124 0.976
Nutter Ring® NR 2 96 0.982
Nutter Ring® NR 2.5 83 0.984
HY-PAK® #1 in. 172 0.965
HY-PAK® #1-1/2 in. 118 0.976
HY-PAK® #2 in. 84 0.979
FLEXIRING® 1 in. 200 0.959
FLEXIRING® 1-1/2 in. 128 0.974
FLEXIRING® 2 in. 97 0.975
CMR® 1 246 0.973
CMR® 2 157 0.970
CMR® 3 102 0.980
BETARING® #1 186 0.963
BETARING® #2 136 0.973
FLEXIMAX® 200 189 0.973
FLEXIMAX® 300 148 0.979
FLEXIMAX® 400 92 0.983

©2020 NCEES 369

Chapter 7: Mass Transfer

Random and Structured Packings Used in Packed Extractors (cont'd)

Packing Surface Area ap1 m2 Void Fraction1 (e)
m3

Plastic Random Packing

Super INTALOX® Saddles #1 204 0.896
Super INTALOX® Saddles #2 105 0.934
BETARING® #1 167 0.942
BETARING® #2 114 0.940
SNOWFLAKE® 93 0.949
FLEXIRING® 1 in. 205 0.922
FLEXIRING® 1-1/2 in. 119 0.925
FLEXIRING® 2 in. 99 0.932

Ceramic Random Packing

INTALOX® Saddles 1 in. 256 0.730
INTALOX® Saddles 1-1/2 in. 195 0.750
INTALOX® Saddles 2 in. 118 0.760

Ceramic Structured Packing

FLEXERAMIC® 28 282 0.720
FLEXERAMIC® 48 157 0.770
FLEXERAMIC® 88 102 0.850

Metal Structured Packing2

Koch-Glitsch SMV-8 417 0.978
Koch-Glitsch SMV-10 292 0.985
Koch-Glitsch SMV-16 223 0.989
Koch-Glitsch SMV-32 112 0.989
Sulzer SMV 2Y 205 0.990
Sulzer SMV 250Y 256 0.988
Sulzer SMV 350Y 353 0.983
INTALOX® 2T 214 0.989
INTALOX® 3T 170 0.989
INTALOX® 4T 133 0.987

Plastic Structured Packing2

Koch-Glitsch SMV-8 330 0.802
Koch-Glitsch SMV-16 209 0.875
Koch-Glitsch SMV-32 93 0.944
Sulzer SMV 250Y 256 0.875

1. Typical value for standard wall thickness. Values will vary depending upon thickness.

2. SMV structured packings also are available with horizontal dual-flow perforated plates
installed between elements (typically designated SMVP packing). These plates generally
reduce backmixing and improve mass-transfer performance at the expense of a reduction
in the open cross-sectional area and somewhat reduced capacity.

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

©2020 NCEES 370

Chapter 7: Mass Transfer

7.5.4.3 Sieve Tray Columns

Sieve Tray Perforated Area

Perforations usually are in the range of 0.125 to 0.25 in (0.32 to 0.64 cm) in diameter, set 0.5 to 0.75 in (1.27 to 1.81 cm) apart, on

square or triangular pitch. Hole size appears to have relatively little effect on the mass-transfer rate except that, in systems of high

interfacial tension, smaller holes produce somewhat better mass transfer. The entire hole area is normally set at 15 to 25 percent

of the column cross-section, although adjustments may be needed. It is common practice to set the velocity of liquid exiting the
ft
holes to correspond to a Weber number between 8 and 12. This normally gives velocities in the range of 0.5 to 1.0 sec
cm
(15 to 30 s ).

The velocity of the continuous phase in the downcomer (or upcomer) udow, which sets the downcomer cross-sectional area, should
be set lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, such as a diameter of 1/32 or 1/16

in (0.08 or 0.16 cm). Otherwise, recirculation of entrained dispersed phase around a tray will result in flooding. The terminal

velocity ut of these small drops can be calculated using Stokes' Law:

ut = g d 2 Dt
p

18nc

Downcomer area typically is in the range of 5 to 20 percent of the total cross-sectional area, depending upon the ratio of continu-
ous- to dispersed-phase volumetric flow rates.

For large columns, tray spacing between 18 and 24 in. (45 and 60 cm) is generally recommended.

LIGHT LIQUID OUT

HEAVY OPERATING
LIQUID IN INTERFACE

PERFORATED PLATE
DOWNCOMER

COALESCED
DISPERSED

LIGHT LIQUID IN

HEAVY LIQUID OUT

Source: Republished with permission of McGraw-Hill, Inc., from Perry's Chemical Engineers' Handbook, 8th ed.,
Don W. Green and Robert H. Perry, New York, 2008; permission conveyed through Copyright Clearance Center, Inc.

The height of the coalesced layer at each tray, h, is

h = DPo + DPdow − zd g Dt L
`1 − zdj g Dt

where

DPo = orifice pressure drop
DPdow = pressure drop for flow through a downcomer (or upcomer)
L = downcomer (or upcomer) length

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Chapter 7: Mass Transfer

The orifice pressure drop DPo is

DPo = 1 d1 − 0.71 −2 uo2 + 3.2 e do2 g Dt 0.2 c for Re = uo ndodtd
2 log Re c do
n td o

where do = diameter of orifice in ft
The pressure drop through the downcomer is

DPdow = 4.5ud2ow tc
2

where udow = velocity in downcomer (or upcomer)

For large columns, the design should specify that the height of the coalesced layer is at least 1 in. (2.5 cm) to ensure that all holes
are adequately covered.

For segmental downcomers, the area of the downcomer is

A = H _3H2 + 4S2i
6S

where

A = area of segmental downcomer (or upcomer)

H = height of segmental downcomer (or upcomer)

S = chord length of segmental downcomer (or upcomer)

Chord length S is

1
Dcol 2
S = =8H d 2 − H
2 nG

where Dcol = column diameter

Sieve Tray Flooding Velocity

Velocity of the continuous phase at the flood point is

STSSSSSSSR L−A C XWVWWWWWWW0.5
2
ucf = Bd udf +
ucf n

where

A = 6c B = 1.11td C = 2.7tc
do Dt g 2g Dt fd2a
g Dt f 2
ha

where

fha = fractional hole area

fda = fractional downcomer area

The cross-flow velocity of the continuous phase uc flow is
Lfp
ucflow . z−h uc

where

Lfp = length of flow path
z = sieve tray spacing

©2020 NCEES 372

Chapter 7: Mass Transfer

Sieve Tray Efficiency
The sieve tray efficiency is approximated by

po = 0.21f z0.5 pd ud 0.42
c do0.35 uc
n

7.6 Adsorption

7.6.1 Adsorption Equilibrium

For a single adsorbate in a gas stream, the equilibrium capacity of the adsorbent may be related to the concentration of the
adsorbate in the bulk stream by the Freundlich equation:

W = a p1/n

where

W = mass qf adsqrbate
unit mass of adsorbent

p = partial pressure of adsorbate in the bulk gas stream

a, n = empirical coefficients derived from log-log plot of data for W vs. p

Both coefficients are a function of temperature.

The Freundlich equation can be used for liquid-solid adsorption by entering concentration instead of partial pressure.
TyTYpPiIcCaALl AADdSOsRoPrTpIOtNioISnOTIHsEoRtMhSerms

MASS ADSORBATE/MASS ADSORBANT INCREASING
TEMPERATURE

LOG PARTIAL PRESSURE OF ADSORBATE

7.6.2 Adsorption Operation

Adsorption in typical commercial operations is conducted by passing the gas or liquid stream through a usually vertical fixed bed of
adsorbent particles. Adsorption beds are usually oriented vertically.
Adsorption beds have three zones that characterize the operation:

1. Equilibrium zone where adsorbate is in equilibrium with inlet concentration
2. Mass transfer zone where adsorbate is diffusing into adsorbent
3. Active zone where no adsorption has occurred
The length of the mass transfer zone (MTZ) is a function of the fluid velocity along with adsorbent porosity and uniformity of pore size.

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Chapter 7: Mass Transfer

Adsorption Concentration Profiles Across Bed

EQUILIBRIUM MASS- ACTIVE
ZONE TRANSFER ZONE

y IN ZONE

VAPOR-PHASE CONCENTRATION

y OUT BED LENGTH L
O CONCENTRATION PROFILE AT A GIVEN TIME DURING ADSORPTION OPERATION

Three performance regimes for adsorption beds characterize the operation. Considering a given point in a bed:
1. Dry, when the mass transfer zone is below the point in the bed and the concentration has a low value
2. Break-through, when the mass transfer zone reaches the point in the bed and the concentration increases
3. Saturated, when the concentration at the point in the bed increases to the value of the inlet concentration

Adsorption Outlet Composition Versus Time

LIGHT LIQUID OUT
DRY BREAK-THROUGH SATURATED

y IN HEAVY INTERFACE
LIQUID IN

VAPOR-PHASE CONCENTRATION REDISTRIBUTOR
PACKING

LIGHT
LIQUID IN

HEAVY LIQUID OUT

y OUT
0

TIME

CONCENTRATION PROFILE AS A FUNCTION OF TIME AT A GIVEN POINT IN THE BED. ADSORPTION STEP.

©2020 NCEES 374

Chapter 7: Mass Transfer

7.6.3 Adsorption Regeneration

Adsorption processes can be nonregenerative or regenerative. Nonregenerative adsorption is a batch process. For regenerative
adsorption, adsorbent beds are cycled between adsorption and desorption (regeneration) modes and multiple beds are required for
continuous operation.

During regeneration, stripping the adsorbate is accomplished by passing a pure fluid through the bed at a lower pressure for
pressure swing adsorption (PSA) or at a higher temperature for temperature swing adsorption (TSA). For TSA, the pressure may
be slightly lowered in addition to the temperature increase. Often a split stream from the fluid exiting the adsorbing bed is used as
the pure fluid for regenerating adsorption beds.

The regeneration of adsorption beds leaves a residual concentration of adsorbate in the adsorbent. This reduces the working
capacity of regenerated adsorbent in comparison with the capacity of fresh adsorbent.

Working capacity W l = Wsat − Wregen
where

Wsat = amount adsorbed on the bed at break-through
Wregen = amount of adsorbate remaining on the bed after regeneration

Characteristics of Typical Adsorption Systems

Adsorption System Characteristics

System Type: TSA PSA
Configuration of system Gas Phase
Number of beds Gas Phase Liquid Phase
Time on adsorption
Flow direction on adsorption 2 to 4 2 to 4 2 to 16
Flow direction on regeneration 4 to 8 hours 4 to 8 hours Minutes to hours
Common adsorbents Down Up Up
Down; treated vaporized
Hydrophobic Up liquid when feasible Down

Hydrophilic Activated carbons for re- Activated carbons for Activated carbon for
moving VOCs from gas water purification air separations; heavy
hydrocarbons from light
hydrocarbons

Silica gel, activated alumina, mol sieve for
dehydration and removing slightly polar organics

©2020 NCEES 375

Chapter 7: Mass Transfer

7.7 Humidification and Drying

7.7.1 Adiabatic Humidification and Cooling

Adiabatic Humidification and Cooling

FLOW MODEL LENGTH OR HEIGHT Z
O dZ
MATERIAL BALANCE
G 's1 G 's1 G 's1
GY''1s1 Y' Y '+ dY ' Y '2 dL' = G'sdY'
TG2 L'2 – L'1 = G's (Y '2 – Y '1)
TG1 TG TG + dTG

L'1 L' L'+ dL' L'2 INTERFACIAL SERVICE
Tas Tas Tas Tas ds = adz

ABS HUMIDITYMASS TRANSFER Y 'as RATE OF MASS TRANSFER
Y 'as GAS INTERFACE G'sdY ' = kYa (Y 'as – Y ')dz
Y '2
BULK GAS Y' dY '
Y '1

TEMPERATURESENSIBLE HEAT TRANSFER dTG SENSIBLE RATE OF TRANSFER
TG1 BULK GAS G's Cs1 dTG = hg a (TG – Tas) dz
TG
TG2
Tas INTERFACE AND BULK LIQUID Tas

O dz z

PSYCHOMETRIC RELATIONS
SATURATION HUMIDITY

ABS HUMIDITY Y 'as ADIABATIC SATURATION
Y '2
Y '1

Tas TG2 TG1
TEMPERATURE

©2020 NCEES 376

Chapter 7: Mass Transfer

where
Ll = solute-free liquid flow rate
Gls = dry-gas mass flow rate
Y 1l = initial humidity
Y l2 = final humidity
Y las = saturation humidity at liquid-gas interface
TG = temperature of bulk gas
Tas = temperature at liquid-gas interface
Cs1 = specific heat capacity at the liquid-gas interface
hg = gas heat-transfer coefficient

Since Y las is constant:

ln f Y las − Y 1l p = ky a z
Y las − Y l2 Gls

where

ky = overall mass-transfer coefficient

a = interstitial surface per unit volume, in ft 2
ft 3

z = height, in ft

Gls _Y l2 − Y 1l i = ky a z ^DY lhlm

where ^DY lhlm = logarithmic mean of humidity difference

or NTUtG = Y l2 − Y 1l = ln >YY las − Y 1l H
and ^DY lhlm las − Y l2
where
HTU=tG kG=y las z
NTUtG

NTUtG = number of gas-phase transfer units
HTUtG = height of transfer unit

Air-Water Systems
yw = mole fraction of water

ya = mole fraction of air

Yw = yw = 1 yw = 1 ya = molal humidity = mole water vapor/mole dry air
ya − yw − ya

=Yw 12=89 : Yw mass humidity = mass water vapor/mass dry air

©2020 NCEES 377

Chapter 7: Mass Transfer

Relative humidity = 100 Pw
Pw

where P w = partial pressure of water at a given temperature

Pw = vapor pressure of water at a given temperature

Yw = Pw Y ws = Pw
Patm − P w Patm − Pw

where Y ws = saturation humidity

Patm = atmospheric pressure (14.696 psia or 0.1013 MPa)

% saturation = 100 Y w = P w `Patm − Pwj (100) at total pressure of one atmosphere
Y ws Pw `Patm − P wj

Humid heat CPH = 0.24 + 0.46Yw

where

CPH = humid heat capacity, Btu/lb

Adiabatic Saturation Temperature

tAS = ty0 − mR `YwS − Yw0j
CPH

where

tAS = adiabatic saturation temperature
ty0 = initial inlet temperature
lR = latent heat of vaporization at reference temperature
Yw0 = initial inlet humidity
CPH = humid heat capacity
YwS = humidity at saturation

tWB = ty − mR `YWB − Ywj
CPH

where

YWB = humidity at wet bulb temperature
tWB = wet bulb temperature

©2020 NCEES 378

Chapter 7: Mass Transfer

Humidity Chart for the Air-Water System at One Atmosphere

HUMID HEAT, BTU/LB DRY AIR (°F)

22 0.22 0.24 0.26 0.28 0.30 0.15
0.14
21 14104°0°AADDRIABATIC SITUATION LINES
20 135° 0.12
VOLUME, CU FT/LB DRY AIR
19 HUMID HEAT VS HUMIDITY
SATPEURRACTEINOTN
91000%%
7800%%
60%
50%
40%
30%
20%
10%

HUMIDITY, LB WATER VAPOR/LB DRY AIR
18 130°

17 125° 0.10
0.08
16 0.06

15 SSAPTEUCRIAFTICEDVOVOLULUMMEEVVSST.ETMEPMEPREARTAUTRUERE 120°
14
13 115°
12 110°
105°

100° 0.04

95°

55° 60° 90° 0.02
45° 50° 85°
80° 0
65°70° 75° 180 200 220 240 250

25 40 60 80 100 120 140 160
TEMPERATURE, F°

Source: Brown, G.G., et. al., Unit Operations, New York: John Wiley & Sons, Inc., 1950.

Cooling Tower Operating Diagram

Hy8 vs t4

80 Hy vs tx
60
H, BTU/LB DRY AIR 40 CpxL Hy0
20 GB max TOP OF TOWER
0
tx0
50 CpxL
SLOPE = GB

HY1 tx 1
BOTTOM OF

TOWER

60 70 80 90 100 110
t, °F

Hy = e CPx L o : _t x − t x0 j + Hy0
GB

©2020 NCEES 379

Chapter 7: Mass Transfer

where

Hy = enthalpy of vapor phase
CPx = specific heat of liquid phase
L = liquid-phase mass velocity
GB = dry air mass velocity
tx = liquid-phase temperature
Hy0 = initial enthalpy of vapor phase
tx0 = liquid-phase inlet temperature

7.7.2 Drying of Solids

Moisture (Solvent) Percentage Content

Typically calculated on a dry solid/dry air basis:

X = % moisture in solid = mw
ms

where

X = moisture (solvent) content in solid, moisture mass/dry solid mass

mw = moisture (solvent) content, mass of water or solvent, in lbm

ms = mass of dry solid, in lbm

Y = % moisture in air = mw
ma

where

Y = moisture (solvent) content in air, moisture mass/dry air mass

mw = moisture (solvent) content, mass of water or solvent, in lbm
ma = mass of dry air, in lbm

Rate of Drying
Rate of drying is dictated by the state of the solvent, such as:

• "Free" solvent on surface of solids

• "Bound" solvent, which must reach the surface through diffusion or capillary action

• "Solvated" solvent, which is chemically bound to the solids (sometimes labile to removal, sometimes not) that are not gener-
ally considered in drying analyses

©2020 NCEES 380

Chapter 7: Mass Transfer

FALLING Drying Curve
RATE II
FALLING CONSTANT RATE
RATE I

N, DRYING RATE

X * XC
X, MOISTURE (SOLVENT) CONTENT lb/lb DRY SOLID

where
X* = equilibrium moisture content: the moisture content of the solid when it reaches equilibrium with the surrounding air;
depending upon the specific conditions of the surrounding air

Xc = critical moisture content: the moisture content that marks the instant when the liquid content on the surface of the solid
is no longer sufficient to maintain a continuous liquid film on the surface

Constant Rate: Rate of drying independent of moisture content. During this period the solid is so wet that the entire surface
of the solid is covered with a continuous film of liquid.

Falling Rate I: Only part of the solid surface is saturated as the entire solid surface can no longer be maintained at saturation
conditions by the movement of moisture within the solid. The rate of drying is linear with regard to X.

Falling Rate II: The entire solid surface is unsaturated and the drying rate is limited by the rate of internal moisture
movement.

Source: McCabe, Warren L., and Julian C. Smith, Unit Operations of Chemical Engineering, 3rd ed.,
New York: McGraw-Hill, 1976.

Specific Drying Applications
Drying of slab using gas from one side only:

1. For drying during the constant rate period

Rate of drying can be determined based on the balance between the heat transfer to the material and the rate of vapor
removal from the surface.

=NC h=t mDT kg Dp

where

DT = gas dry bulb temperature—temperature at surface of solid

Dp = vapor pressure of water at surface temperature—partial pressure of water vapor in the gas

kg = mass-transfer coefficient, in lbm
hr-ft 2-atm

NC = constant drying rate, in lbm
ft 2- hr

©2020 NCEES 381