Chapter 6. Gas–Liquid Processes: Principles and Applications

6.2



CHAPTER Six



reactive gases for water stabilization and disinfection, precipitation of inorganic contaminants, and air stripping of volatile organic compounds (VOCs) and nuisance-causing dissolved gases. The diffused aeration (or bubble) systems are primarily used for the absorption

of reactive gases such as oxygen (O2), ozone (O3), and chlorine (Cl2). For example, ozone is

used for disinfection, oxidation of VOCs and pesticides, taste and odor control, disinfection

by-products control, as a coagulant aid, and for some other uses. Chlorine is primarily used

for disinfection and sometimes as a preoxidant for the oxidation of iron and manganese and

for other purposes. Diffused aeration systems have also been used for stripping of odorcausing compounds and VOCs. Surface aeration systems are primarily used for removal

of gases and VOCs. The packed tower and spray nozzle systems are primarily used for the

removal of NH3, CO2, H2S, and VOCs. The packed tower systems include countercurrent

flow, cocurrent flow, and cross-flow configurations. Spray nozzle systems include tower

and fountain-type configurations.

Another application is the dissolution of air into recycled water under pressure in packed

towers called saturators and subsequent production of air bubbles when the pressurized

recycle water is injected into an open tank for water clarification. This application is called

dissolved air flotation and is covered in Chap. 9.

A fundamental understanding of the theory of gas transfer is first discussed, followed

by a description of the various unit operations, development of the governing equations,

and example design calculations.



THEORY OF GAS TRANSFER

Proper design and operation of aeration and air stripping devices require a fundamental

understanding of equilibrium partitioning of chemicals between air and water as well as an

understanding of the mass transfer rate across the air-water interface is required. Equilibrium

is the final state that the system is moving towards. The displacement of the system from

equilibrium dictates how much fluid (air) is required for stripping or aeration and defines

the driving force that governs mass transfer, i.e., the rate at which chemicals move from one

phase to another, which in turn determines the vessel size required for stripping or aeration.

Both equilibrium and mass transfer concepts are incorporated into mass balance equations to

formulate the governing equations. Consequently, these concepts are reviewed first.

Equilibrium

Component A

water vapor

air

A(air)



A(aq)

Component A

water

Figure 6-1  Schematic of

equilibrium conditions for component A in air and water.



For most aeration and air stripping applications in water treatment, equilibrium partitioning of a gas or organic contaminant between air and water can be described by Henry’s law.

The Henry’s law equilibrium description can be derived by

considering the closed vessel shown in Fig. 6-1. If the vessel

contains both water and air and component A is in equilibrium with both phases at a constant temperature, equilibrium

can be described by the following expression:





K eq =



aair



aaq



(6-1)



where Keq is the equilibrium constant, aair is the activity of

component A in the gas phase, and aaq is the activity of component A in the aqueous phase.







GAS–LIQUID PROCESSES: PRINCIPLES AND APPLICATIONS



6.3



At a pressure of 1 atm, the gas behaves ideally, and Eq. 6-1 reduces to:





H = K eq =



PA



gA A



(6-2)



where H is the Henry’s law constant (atm-L/mole) of component A, PA is the pressure A

exerts in the gas phase (atm), gA is the activity coefficient of A in the aqueous phase, and A

is the aqueous-phase molar concentration of A (mole/L).

The presence of air does not affect the Henry’s law constant for organic chemicals or

gases. For low ionic strength, Henry’s law may be written as follows:







PA = H [ A]



(6-3)



When other dissolved organic and inorganic species are present at concentrations less than

0.01 mole/L, the equilibrium partitioning according to Eq. 6-3 is not affected and is generally valid. Further, it has been shown in some cases to be valid for concentrations as high

as 0.1 mole/L (Rogers, 1994). The units of H in Eq. 6-3 are atm-L/mole, but H has other

units. Figure 6-2 displays the three most commonly used unit measures of H. H is reported

in units of atm when the gas-phase concentration of component A is expressed in atm and

the aqueous-phase concentration of component A is expressed in terms of mole fraction. H

is reported in units of liters of water times atm per mole of gas (L ⋅ atm/mole) when the gasphase concentration of component A is expressed in atm and the aqueous-phase concentration of component A is expressed in terms moles of component A per liter of water. H is

also reported in dimensionless units when both the gas and aqueous phases are expressed in

the same concentration units. Because the reported units of H vary, it is necessary to convert

from one system of units to another. Table 6-1 displays various unit conversions that can

be used to perform this conversion. Dimensionless units are convenient for mass balances;

consequently, dimensionless units are preferred and are used in this chapter.

Estimating Henry’s Constant.  When the Henry’s law constant for a component of interest

is not readily available, it can be estimated if the component’s vapor pressure and aqueous

solubility are known. There are two situations in which it is possible to estimate the Henry’s

constant of component A: (1) when component A is perfectly miscible in the aqueous phase

and (2) when component A is immiscible in the aqueous phase. When component A is

perfectly miscible and the mole fraction of A is equal to 1 ( x H2O = 0), the pressure exerted

by A is equal to the vapor pressure of pure A at a given temperature. In this case H, can be

expressed as:





H = Pv , A



(6-4)



in which Pv , A is the vapor pressure of pure component A at a given temperature (atm).

When component A is immiscible in the aqueous phase, a third or separate phase of

component A is formed within the aqueous phase once the solubility of A is exceeded.

If this third phase contains water, then H cannot be determined from vapor pressure and

solubility data because the partitioning in the third phase is unknown. However, if the third

phase contains only pure component A, then the following expression can be used:







H=



Pv , A



Cs , A



(6-5)



in which Cs , A is the aqueous solubility of component A (mg/L). Equations 6-4 and 6-5

are estimation techniques that give H values within ±50 to 100 percent of experimentally

reported values and should therefore only be used when measured values of the constants

are not available.



6.4



CHAPTER Six



(a)



H (atm)



PA



moles A

XA moles A + moles H O

2

(b)



PA

(atm)



H (L-atm/mol)



CA



mol

L



(c)

YA

M

LAir

H



CA



L H 2O

LAir



M

LH 2O



Figure 6-2  (a) plot of H displayed in atm, (b) plot of H displayed

in liters of water ⋅ atm/mol, (c) plot of H displayed in liters of water

per liter of air.







GAS–LIQUID PROCESSES: PRINCIPLES AND APPLICATIONS



6.5



Table 6-1  Unit Conversions for

Henry’s Law Constants

H (LH2 O / LAir ) =



⋅atm

H (Lmol )

RT



L ⋅ atm

H

 = H ( LH2 O / LAir ) × RT

 mol 

H (atm )

H ( LH2 O / LAir ) =

2

RT × 55 . 6 mol HOO

L H2

L ⋅ atm

H (atm)

H

=

mol H 2 O

 mol  55 . 6 L H2 O

⋅atm

2

H (atm ) = H (Lmol ) × 55 . 6 mol HOO

L H2

2

H (atm ) = H (L H2 O /L Air ) × RT × 55 . 6 mol HOO

L H2



atm L

R = 0 . 08205 mol ⋅°K



T =K



Effects of Temperature and Solution Properties.  Temperature, pressure, ionic strength,

surfactants, and solution pH (for ionizable species such as NH3 and CO2) can influence the

equilibrium partitioning between air and water.

Pressure.  The impact of total system pressure on H is negligible because most aeration and stripping devices operate at atmospheric pressure.

Temperature.  For the range of temperatures encountered in water treatment, H tends

to increase with increasing temperature because the aqueous solubility of the component

decreases while its vapor pressure increases. Values of H for several organic compounds at

different temperatures are given in Table 6-2. Table 6-3 displays H values for gases at 20°C.

Assuming the standard enthalpy change (∆H°) for the dissolution of a component in water

is constant over the temperature range of interest, the change in H with temperature can be

estimated using the following van’t Hoff-type equation:





−∆ H o  1 1 

H 2 = H1 × exp 

 R T − T 



 2 1 





(6-6)



in which ∆H° is the standard enthalpy change in water due to the dissolution of a component in water (kcal/kmol), R is the universal gas constant (1.987 kcal/kmol-K), H1 is a

known value of Henry’s constant at temperature T1 (K), H2 is the calculated Henry’s law

constant at the desired temperature T2 (K), and C is a constant.

Equation 6-6 can be simplified to Eq. 6-7, and values of ∆H° and C for selected compounds are summarized in Table 6-4.





 ∆H o 

H = C × exp −



 RT 



(6-7)



Another common method of expressing the temperature dependence of H is to treat

∆H°, R, and C as fitting parameters A and B using the following equation:







B

H = exp  A − 



T



(6-8)



Table 6-5 lists values of A and B for several compounds. These are valid for temperatures ranging from 283 to 303 K (Ashworth et al., 1988).



Table 6-2  Henry’s Law Constants in atm m3/mole and the H Values in Liters of Water per Liter of Air Are Given in Parentheses for 45 Organic Compounds

(Ashworth et al., 1988).

Henry’s law constants, H

Component



6.6



Nonane

n-Hexane

2-Methylpentane

Cyclohexane

Chlorobenzene

1,2-Dichlorobenzene

1,3-Dichlorobenzene

1,4-Dichlorobenzene

o-Xylene

p-Xylene

m-Xylene

Propylbenzene

Ethylbenzene

Toluene

Benzene

Methyl ethylbenzene

1,1-Dichloroethane

1,2-Dichloroethane

1,1,1-Trichloroethane

1,1,2-Trichloroethane

cis-1,2-Dichloroethylene

trans-1,2-Dichloroethylene

Tetrachloroethylene



10°C

0.400 (17.2)

0.238 (10.3)

0.697 (30.0)

0.103 (4.44)

0.00244 (0.105)

0.00163 (0.0702)

0.00221 (0.0952)

0.00212 (0.0913)

0.00285 (0.123)

0.00420 (0.181)

0.00411 (0.177)

0.00568 (0.245)

0.00326 (0.140)

0.00381 (0.164)

0.00330 (0.142)

0.00351 (0.151)

0.00368 (0.158)

0.00117 (0.0504)

0.00965 (0.416)

0.000390 (0.0168)

0.00270 (0.116)

0.000590 (0.0254)

0.00846 (0.364)



15°C

0.496 (21.0)

0.413 (17.5)

0.694 (29.4)

0.126 (5.33)

0.00281 (0.119)

0.00143 (0.0605)

0.00231 (0.0978)

0.00217 (0.0918)

0.00361 (0.153)

0.00483 (0.204)

0.00496 (0.210)

0.00731 (0.309)

0.00451 (0.191)

0.00492 (0.210)

0.00388 (0.164)

0.00420 (0.178)

0.00454 (0.192)

0.00130 (0.0550)

0.0115 (0.487)

0.000630 (0.0267)

0.00326 (0.138)

0.00705 (0.298)

0.0111 (0.467)



20°C

0.332 (13.8)

0.883 (36.7)

0.633 (26.3)

0.140 (5.82)

0.00341 (0.142)

0.00168 (0.0699)

0.00294 (0.122)

0.00259 (0.108)

0.00474 (0.197)

0.00645 (0.268)

0.00598 (0.249)

0.00881 (0.366)

0.00601 (0.250)

0.00555 (0.231)

0.00452 (0.188)

0.00503 (0.209)

0.00563 (0.234)

0.00147 (0.0612)

0.0146 (0.607)

0.000740 (0.0308)

0.00360 (0.150)

0.00857 (0.356)

0.0141 (0.587)



25°C

0.414 (16.9)

0.768 (31.4)

0.825 (33.7)

0.177 (7.24)

0.00360 (0.147)

0.00157 (0.0642)

0.00285 (0.117)

0.00317 (0.130)

0.00487 (0.199)

0.00744 (0.304)

0.00744 (0.304)

0.0108 (0.442)

0.00788 (0.322)

0.00642 (0.263)

0.00528 (0.216)

0.00558 (0.228)

0.00625 (0.256)

0.00141 (0.0577)

0.0174 (0.712)

0.000910 (0.0372)

0.00454 (0.186)

0.00945 (0.386)

0.0171 (0.699)



30°C

0.465 (18.7)

1.56 (62.7)

0.848 (34.1)

0.223 (8.97)

0.00473 (0.190)

0.00237 (0.0953)

0.00422 (0.170)

0.00389 (0.156)

0.00626 (0.252)

0.00945 (0.380)

0.00887 (0.357)

0.0137 (0.551)

0.0105 (0.422)

0.00808 (0.325)

0.00720 (0.290)

0.00770 (0.310)

0.00776 (0.312)

0.00174 (0.0700)

0.0211 (0.849)

0.00133 (0.0535)

0.00575 (0.231)

0.0121 (0.469)

0.0245 (0.985)



6.7



Trichloroethylene

Tetralin

Decalin

Vinyl chloride

Chloroethane

Hexachloroethane

Carbon tetrachloride

1,3,5-Trimethylbenzene

Ethylene dibromide

1,1-Dichloroethylene

Methylene chloride

Chloroform

1,1,2,2-Tetrachloroethane

1,2-Dichloropropane

Dibromochloromethane

1,2,4-Trichlorobenzene

2,4-Dimethylphenol

1,1,2-Trichlorotrifluoroethane

Methyl ethyl ketone

Methyl isobutyl ketone

Methyl cellosolve

Methyl t-butyl ether*

Trichlorofluoromethane

*Fischer, Muller, and Klasmeier (2004).



0.00538 (0.237)

0.000750 (0.0323)

0.0700 (3.015)

0.0150 (0.646)

0.00759 (0.327)

0.00593 (0.255)

0.0148 (0.637)

0.00403 (0.174)

0.000300 (0.0129)

0.0154 (0.663)

0.00140 (0.0603)

0.00172 (0.0741)

0.000330 (0.0142)

0.00122 (0.0525)

0.000380 (0.0164)

0.00129 (0.0556)

0.00829 (0.357)

0.154 (6.63)

0.000280 (0.0121)

0.000660 (0.0284)

0.0441 (1.90)

0.5039 (0.0117)

0.0536 (2.31)



0.00667 (0.282)

0.00105 (0.0444)

0.0837 (3.54)

0.0168 (0.711)

0.00958 (0.405)

0.00559 (0.237)

0.0191 (0.808)

0.00460 (0.195)

0.000480 (0.0203)

0.203 (8.59)

0.00169 (0.0715)

0.00233 (0.986)

0.000200 (0.00846)

0.00126 (0.0533)

0.000450 (0.0190)

0.00105 (0.0444)

0.00674 (0.285)

0.215 (9.10)

0.000390 (0.0165)

0.000370 (0.0157)

0.0363 (1.54)

0.7490 (0.0177)

0.0680 (2.88)



0.00842 (0.350)

0.00136 (0.0566)

0.106 (4.41)

0.0217 (0.903)

0.0110 (0.458)

0.00591 (0.246)

0.0232 (0.965)

0.00571 (0.238)

0.000610 (0.0254)

0.0218 (0.907)

0.00244 (0.102)

0.00332 (0.138)

0.000730 (0.0304)

0.00190 (0.0790)

0.00103 (0.0428)

0.00183 (0.0761)

0.0101 (0.420)

0.245 (10.2)

0.000190 (0.00790)

0.000290 (0.0121)

0.116 (4.83)

0.9317 (0.0224)

0.0804 (3.34)



0.0102 (0.417)

0.00187 (0.0765)

0.117 (4.79)

0.0265 (1.08)

0.0121 (0.495)

0.00835 (0.342)

0.0295 (1.21)

0.00673 (0.275)

0.00065(00266)

0.0259 (1.06)

0.00296 (0.121)

0.00421 (0.172)

0.00025(0.0102)

0.00357 (0.146)

0.00118 (0.0483)

0.00192 (0.0785)

0.00493 (0.202)

0.319 (13.0)

0.00013(0.0053)

0.00039(0.0160)

0.0309 (1.26)

1.194 (0.0292)

0.101 (4.13)



0.0128 (0.515)

0.00268 (0108)

0.199 (8.00)

0.028 (1.13)

0.0143 (0.575)

0.0103 (0.414)

0.0378 (1.52)

0.00963 (0.387)

0.000800 (0.0322)

0.0318 (1.28)

0.00361 (0.145)

0.00554 (0.223)

0.000700 (0.0282)

0.00286 (0.115)

0.00152 (0.0611)

0.00297 (0.119)

0.00375 (0.151)

0.321 (12.9)

0.000110 (0.00443)

0.000680 (0.0274)

0.0381 (1.53)

1.557 (0.0387)

0.122 (4.91)



6.8



CHAPTER Six



Table 6-3  Henry’s Law

Constants at 20°C for Gases in Water

Compounds (Crittenden et al., 2005)

Compound



Table 6-4  Temperature Correction

Factors for H in atm (Crittenden et al.,

2005)



2



Ammonia

Carbon dioxide

Chlorine

Chlorine dioxide

Hydrogen sulfide

Methane

Oxygen

Ozone

Radon*

Sulfur dioxide



DH × 10–3



Compound



H, ( LH O / LAir )



Oxygen

Methane

Carbon dioxide

Hydrogen sulfide

Carbon tetrachloride

Trichloroethylene

Benzene

Chloroform

Ozone

Ammonia

Sulfur dioxide

Chlorine



0.000574

0.114

0.442

0.0408

0.389

28.7

32.5

3.77

4.08

0.0287



*Clever (1980).



Table 6-5  Parameters for Calculating Henry’s Law Constants

(in atm m3/mole) as a Function of Temperature (Ashworth et al.,

1988)

Component

Nonane

n-Hexane

2-Methylpentane

Cyclohexane

Chlorobenzene

1,2-Dichlorobenzene

1,3-Dichlorobenzene

1,4-Dichlorobenzene

o-Xylene

p-Xylene

m-Xylene

Propylbenzene

Ethylbenzene

Toluene

Benzene

Methyl ethylbenzene

1,1-Dichloroethane

1,2-Dichloroethane

1,1,1-Trichloroethane

1,1,2-Trichloroethane

cis-1,2-Dichloroethylene

trans-1,2-Dichloroethylene

Tetrachloroethylene

Trichloroethylene

Tetralin

Decalin

Vinyl chloride



A



B



r2



–0.1847

25.25

2.959

9.141

3.469

–1.518

2.882

3.373

5.541

6.931

6.280

7.835

11.92

5.133

5.534

5.557

5.484

–1.371

7.351

9.320

5.164

5.333

10.65

7.845

11.83

11.85

6.138



202.1

7530

957.2

3238

2689

1422

2564

2720

3220

3520

3337

3681

4994

3024

3194

3179

3137

1522

3399

4843

3143

2964

4368

3702

5392

4125

2931



0.013

0.917

0.497

0.982

0.965

0.464

0.850

0.941

0.966

0.989

0.998

0.997

0.999

0.982

0.968

0.968

0.993

0.878

0.998

0.968

0.974

0.985

0.987

0.998

0.996

0.919

0.970



(Continued)



C



1.45

1.54

2.07

1.85

4.05

3.41

3.68

4.00

2.52

3.75

2.40

1.74



7.11

7.22

6.73

5.88

10.06

8.59

8.68

9.10

8.05

6.31

5.68

5.75







GAS–LIQUID PROCESSES: PRINCIPLES AND APPLICATIONS



6.9



Table 6-5  Parameters for Calculating Henry’s Law Constants

(in atm m3/mole) as a Function of Temperature (Ashworth et al.,

1988) (Continued)

Component



A



Chloroethane

4.265

Hexachloroethane

3.744

Carbon tetrachloride

9.739

1,3,5-Trimethylbenzene

7.241

Ethylene dibromide

5.703

1,1-Dichloroethylene

6.123

Methylene chloride

8.483

Chloroform

11.41

1,1,2,2-Tetrachloroethane

1.726

1,2-Dichloropropane

9.843

Dibromochloromethane

14.62

1,2,4-Trichlorobenzene

7.361

2,4-Dimethylphenol

–16.34

1,1,2-Trichlorotrifluoroethane

9.649

Methyl ethyl ketone

–26.32

Methyl isobutyl ketone

–7.157

Methyl cellosolve

–6.050

Trichlorofluoromethane

9.480



B

2580

2550

3951

3628

3876

2907

4268

5030

2810

4708

6373

4028

–3307

3243

–5214

160.6

–873.8

3513



r2

0.984

0.768

0.997

0.962

0.928

0.974

0.988

0.997

0.194

0.820

0.914

0.819

0.555

0.932

0.797

0.002

0.023

0.998



Ionic Strength.  In water supplies, gases or VOCs that are high in dissolved solids have

higher volatility (or have a higher apparent Henry’s law constant) than those with low dissolved solids. This results in a decrease in the solubility of the volatile component, i.e., a

“salting-out effect,” that can be represented mathematically as an increase in the activity

coefficient of component A, γA in aqueous solution. γA will increase (γA > 1) with increasing

ionic strength; this in turn causes the apparent Henry’s law constant, Happ, to be greater than

the thermodynamic value of H. The following equation can be used to calculate Happ:

P

H app = g A H = A

(6-9)



[ A]

in which γA is a function of ionic strength and can be calculated using the following empirical equation:







log10 g A = K s × I



(6-10)



where K s is the Setschenow, or “salting-out,” constant (L/mole) and I is the ionic strength

of the water (mole/L).

Ionic strength (I ), which is discussed in Chap. 3, is defined as follows:





I=



1

∑ (Ci Zi2 )

2 i



(6-11)



in which Ci is the molar concentration of ionic species i (mole/L) and Z i is the charge of

species i. The values of Ks need to be determined by experimental methods because there

is no general theory for predicting them. Table 6-6 displays the salting-out coefficients for

several compounds at 20°C. For most water supplies, the ionic strength is less than 10 mM

and the activity coefficient is equal to 1. Significant increases in volatility and the apparent

Henry’s constant are only observed for high ionic strength waters, such as seawater.

pH.  pH does not affect the Henry’s constant per se but it does affect the distribution of

species between ionized and unionized forms. This, in turn, influences the overall gas-liquid



6.10



CHAPTER Six



Table 6-6  Setschenow or Salting-Out Coefficients, Ks at (20°C)

Compound

Tetrachloroethylene

Trichloroethylene

1,1,1-Trichloroethane

1,1-Dichloroethane

Chloroform

Dichloromethane

Benzene

Toluene

Naphthalene



Ks (L · mol–1)

0.213

0.186

0.193

0.145

0.140

0.107

0.195

0.208

0.220



Reference

Gossett 1987

–

–

–

–

–

Schwarzenbach et al. 1992

–

–



distribution of the compound because only the unionized species are volatile. For example,

ammonia is present as ammonium ion at neutral pH and is not strippable. However, at high

pH (greater than 10), ammonia is not an ion and may be stripped. To predict the effect of

pH on solubility, one must consider the value of the appropriate acidity constant pKa. If

the acid is uncharged, such as HCN or H2S, and the pH is much less than the pKa (2 units

lower), then equilibrium partitioning can be described using the Henry’s law constant for

+

the uncharged species. If the acid is charged, such as NH4 , and the pH is much higher than

the pKa (2 units higher), then the compound will be volatile and its equilibrium partitioning

can be described using Henry’s law constant for the uncharged species. See Chap. 3 for a

presentation of acid-base chemistry.

Surfactants.  Surfactants can also affect the volatility of compounds. Most natural waters

do not have high concentrations of surfactants; consequently, they do not affect the design of

most stripping devices. However, surfactants, if present, lower the volatility of compounds

by several mechanisms. The most important factor is that they tend to collect at the air-water

interface, diminishing the mole fraction of the compound at the interfacial area, thereby

lowering its apparent Henry’s law constant. In untreated wastewater, for example, the solubility of oxygen can be lowered by 30 to 50 percent due to the presence of surfactants.

Another effect for hydrophobic organics is the incorporation of the dissolved organics into

micelles in solution (this would occur only above the critical micelle concentration) that,

in turn, decreases the concentration of the organic compound at the air-water interface and

lowers the compound’s volatility (Vane and Giroux, 2000). O’Haver et al. (2004) provide a

more detailed discussion of the impact of surfactants on air stripping of VOCs.

Mass Transfer

The driving force for mass transfer between one phase and another derives from the displacement of the system from equilibrium. Figure 6-3 displays two situations where mass

transfer is occurring between the air and water. Figure 6-3a displays the situation where

mass is being transferred from the water to the air, and Fig. 6-3b displays the situation

where mass is being transferred from the air to the water. Because the mechanisms and

assumptions for mass transfer are essentially the same for both cases, a detailed explanation

of only one is warranted. Consider the case where a volatile contaminant is being stripped

from water to air (Fig. 6-3a). The contaminant concentration in the water is high relative to

the equilibrium concentration between the air and water. The tendency to achieve equilibrium is sufficient to cause diffusion of the aqueous-phase contaminant molecules from the

bulk solution at some concentration, Cb (µg/L), to the air-water interface, where the aqueous phase concentration is Cs (µg/L). Because Cb is larger than Cs, the difference between







6.11



GAS–LIQUID PROCESSES: PRINCIPLES AND APPLICATIONS



Bulk Air Phase



Air Film



Water Film



Bulk Water Phase



ys*



ys

Cb

yb

Cs



Cs*

Air-Water

Interface

(a) Striping



Bulk Air Phase



Air Film



Water Film



Bulk Water Phase



Cs*



Cs

yb

Cb

ys



ys*



Air-Water

Interface

(b) Absorption

Figure 6-3  Diagram describing the equilibrium partitioning of a contaminant between the air and

water phases using two film theory.



6.12



CHAPTER Six



them provides the aqueous-phase driving force for stripping. Similarly, the contaminant

concentration in the air at the air-water interface, ys, is larger than the contaminant concentration in the bulk air, yb, and diffusion causes the molecules to migrate from the air-water

interface to the bulk air. The difference between ys and yb is the driving force for stripping

in the gas phase.

Mass Flux.  Local equilibrium occurs at the air-water interface because on a local scale

of tens of Angstroms random molecular movement causes the contaminant to dissolve in

the aqueous phase and volatilize into the air. (On a larger scale, these motions equalize the

displacement of the system from equilibrium and cause diffusion.) Accordingly, Henry’s

law can be used to relate ys to Cs (Lewis and Whitman, 1924).

ys = HCs







(6-12)



Fick’s law can be simplified to a linear driving force approximation whereby the flux

(the mass transferred per unit of time per unit of interfacial area) across the air-water interface is proportional to the concentration gradient. Mathematically, the flux of A across the

air-water interface, J A, is given by:

J A = kl (Cb − Cs ) = kg ( ys − yb )







(6-13)



in which kl is the liquid-phase mass transfer coefficient that describes the rate at which

contaminant A is transferred from the bulk aqueous phase to the air-water interface (L/t)

and kg is the gas-phase mass transfer coefficient that describes the rate at which contaminant A is transferred from the air-water interface to the bulk gas phase (m/s). Both kl and kg

are sometimes called local mass transfer coefficients for the liquid and gas phases because

they depend upon the conditions at or near the air-water interface in their particular phase.

Because the interfacial concentrations ys and Cs cannot be measured and are unknown, the

flux cannot be determined from Eq. 6-13. Consequently, it is necessary to define another

flux equation in terms of hypothetical concentrations, which are easy to determine and

describe the displacement of the system from equilibrium. If it is hypothesized that all the

resistance to mass transfer is on the liquid side, then there is no concentration gradient on

the gas side and a hypothetical concentration Cs* can be defined as shown in Fig. 6-3a.

yb = HCs*







(6-14)



in which Cs* is the aqueous-phase concentration of A at the air-water interface assuming

no concentration gradient in the air phase (µg/L), i.e., equilibrium exists between the bulk

gas-phase concentration and the aqueous phase at the interface.

Alternatively, if it is hypothesized that all the resistance to mass transfer is on the gas

side, there is no concentration gradient on the liquid side and a hypothetical concentration

*

ys can be defined as shown in Fig. 6-3a.

*

ys = HCb







(6-15)



*

s



in which y is the equilibrium gas-phase concentration of A at the air-water interface assuming no concentration gradient in the liquid phase (µg/L); it can be calculated from the bulk

liquid-phase concentration.

Mass Flux Based on Water Side.  For stripping operations, mass balances are normally

written based on the liquid phase. It is convenient to calculate the mass transfer rate using

the hypothetical concentration, Cs* , and an overall mass transfer coefficient, K L, as shown

in the following equation:





J A = K L (Cb − Cs* )



(6-16)