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Gas Transfer
Preeti Birwal
Ph.D (DE)
ICAR-NDRI
1st Year
DEFINITION AND TERMS
Gas transfer: a physical phenomenon, by which gas molecules are exchanged
between a liquid and a gas at a gas-liquid interface.
This leads to:
 An increase of the concentration of the gas in the liquid phase as long as this phase
is not saturated with the gas under the given conditions of e.g. pressure,
temperature (absorption of gas).
 A decrease when the liquid phase is over saturated (desorption
or stripping of gas).
DEFINITION AND TERMS
Important natural phenomena of gas transfer: the reaeration of surface water:
I. The transfer of oxygen into surface water.
II. Release of oxygen produced by algal activities up to a concentration above the
saturation concentration.
III. Release of taste and odor-producing substances.
IV. Release of methane, hydrogen sulfide under anaerobic conditions of surface
water or of the bottom deposits.
•Exchange of gases between aqueous/solid and gaseous phases is an
essential element of many environmental processes.
•Wastewater treatment plants require enhanced transfer of oxygen into
activated sludge tanks to maintain aerobic degradation.
•Water treatment plants require gas transfer to dissolve chlorine gas or
ozone.
•Gas transfer can also be used to remove unwanted volatile chemicals
Some important examples of gas transfer in water and wastewater treatment.
1. Oxygen transfer to biological processes.
2. Stripping of volatile toxic organics (solvents).
3. CO2 exchange as it relates to pH control.
4. Ammonia removal by stripping.
5. Odor removal – volatile sulfur compounds.
6. Chlorination, ozonation for disinfection and odor control.
The materials of interest are soluble in water and volatile (i.e. they exert a
significant vapor pressure).
Exchange of a dissolved compound with the atmosphere is controlled by the:
I. extent of mixing in the aqueous and gaseous phase,
II. the surface area of the interface,
III. Temperature of mixture
IV. the concentration of the compound in the two phases, and
V. the equilibrium distribution of the compound.
A distinction
Volatilization - Stripping due to natural phenomenon.
Stripping - Stripping due to a mechanical device - aeration.
ELEMENTS OF AERATION AND GAS TRANSFER
OPERATIONS
The diffused aeration systems are categorized as
(a) Porous or fine-pore diffusers
(b) Nonporous diffusers
(c) Jet aerators, aspirating aerators and U-tube aerators.
Mechanical aerators are commonly divided into two groups based on major design and
operating features: aerators with vertical axis of operation and aerators with horizontal axis.
Both groups are further subdivided into surface and submerged aerators. In surface aerators,
gas is entrained from the surrounding atmosphere while in submerged aerators, gas is
entrained from the atmosphere or introduced in the tank bottom.
Gravity aerators
(a) cascades  the available difference head is subdivided into several steps
(b) inclined planes  equipped with riffle plates to break up the sheet of water for
surface renewal
(c) vertical stacks  droplets fall and updrafts of air ascend in counter current flow
ELEMENTS -- CASCADES
ELEMENTS – INCLINED PLANES
ELEMENTS –
VERTICAL STACKS
ELEMENTS OF AERATION AND GAS TRANSFER
OPERATIONS
(2) Spray aerators: the water is sprayed in the form of fine droplets into the air 
creating a large gas-liquid interface for gas transfer
ELEMENTS OF AERATION AND GAS TRANSFER
OPERATIONS
(3) Air diffusers (bubble aeration)
 air is injected into water
(a) through orifices or nozzles in the air piping system
(b) through spargers
(c) through porous tubes, plates, boxes or domes
 to produce bubbles of various size with different interfacial areas
per m3 of air.
ELEMENTS OF AERATION AND GAS TRANSFER
OPERATIONS
(4) Mechanical aerators
 create new gas-liquid interfaces by different means and constructions 
two types of construction:
(a) various construction of brushes  a horizontal revolving shaft with combs, blades
or angles
(b) turbine or cone aerators with vertical shaft
Impeller Designs:
Henry’s law
Water contains dissolved gases. In a closed vessel containing both gas (e.g., air
and water), the concentration of a volatile component in the gas -phase will be in
equilibrium with the concentration in the water phase, accordingto Henry’s law.
The equilibrium concentration can be calculated using the following form of
Henry’s law:
cw= equilibrium concentration of a gas in water [g/m3]
KH= Henry’s constant or distribution coefficient
= concentration of the gas in air[g/m3]
.w H gc k c
gc
Diffusivity
O2 has lower MW than CO2
Solubility of CO2 is 24x that of O2
CO2 diffuses 20x more rapidly through the alveolar capillary barrier
than O2
D  Solubility/MW
The solubility of a gas (mg/L) in water depends
on its temperature, salinity, gas composition,
and total pressure.
The solubility of a gas is also proportional to its
absolute pressure. Increasing the gas pressure
will also increase gas solubility proportionately,
i.e., doubling the gas pressure will double that
gases solubility. Higher gas pressures occur in
water injected into a pressurized system, or in
water obtained from a deep well.
SOLUBILITY OF GASES
The solubility of gases in water (and also in other liquids) depends upon:
(1) the nature of the gas generally expressed by a gas specific coefficient
 the distribution coefficient, kD
(2) the concentration of the respective gas in the gaseous phase 
related to the partial pressure of the respective gas in the gas phase
(3) the temperature of the water
(4) impurities contained in the water
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY
The higher the gas concentration in the gaseous phase  the greater will be the
saturation concentration in the liquid phase
The relation between the saturation concentration cs (g/m3) and the gas
concentration in the gas phase cg (g/m3):
cs = kD . cg
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY
The molar gas concentration in the gas phase (according to the universal
gas law):
(n/V) = p / (RT) (moles/m3)
Hence the corresponding mass concentration cg is obtained by
multiplication with the molecular weight (MW) of the gas:
cg = (p . MW)/ (RT) (g/m3)
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY
The combination yields:
cs = (kD . MW . p)/ (RT)
Henry’s law is generally written as:
cs = kH . p
The relation between distribution coefficient kD and Henry’s constant:
kH = (kD . MW)/ (RT)
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY
Bunsen absorption coefficient, kb  how much gas volume (m3), reduced to standard
temperature (0oC) and pressure (101,3 kPa), can be absorbed per unit volume (m3) of
water at a partial pressure of pO = 101,3 kPa of the gas in the gas phase :
cs (m3
STP gas/m3 water) = kb
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY
And any other partial pressure p:
cs = kb . (p/p0) (m3
STP/m3)
Since 1 m3
STP contains p0/R.T0 moles of gas and a mass of gas equal to MW. p0/R.T0 :
cs = (kb . MW)/(R.T0 ) p (g/m3)
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY
The relation between kD and kb:
kb = kD T0/T
The interrelationship between the three coefficients:
kD = kH .R.T/MW = kb .T/T0
INFLUENCE OF TEMPERATURE ON SOLUBILITY
Gases dissolved in water  accompanied by liberation of heat H
Le Chatelier principle  increase of temperature results in a decrease of
solubility  van’t Hoff’s equation:
[d(ln kD)/dT] = H/(RT2)
where R = universal gas constant
T = absolute temperature K
H = change of heat content accompanying by the absorption of 1
mole of gas (J/mole)
INFLUENCE OF TEMPERATURE ON SOLUBILITY
By integrating between the limits T1 and T2:
ln[(kD)2/(kD)1]= (H/R)(T2-T1)/(T1.T2)
The product T1 .T2 does not change significantly within the temperature range
encountered in gas transfer operations:
(kD)2= (kD)1. econst (T2 – T1)
INFLUENCE OF IMPURITIES ON SOLUBILITY
Other constituent that may be contained in water influence the solubility
of gases  expressed by an activity coefficient  :
cs = (kD/).cg
For pure water  = 1
  generally increases as the concentration of substances dissolved in
water rises  lowering the solubility
INFLUENCE OF IMPURITIES ON
SOLUBILITY
The influence of concentration of impurities cimp on the activity coefficient:
for non-electrolytes
log  = f . Cimp
for electrolytes
log  = f . I
where f = a constant depending on the matter dissolved in water
I = ionic strength of electrolyte
Time of Contact
DIFFUSION
The phenomenon of diffusion  the tendency any substance the spread uniformly
throughout the space available to it  in environmental engineering  diffusion
phenomena the liquid phase in gas transfer operations
DIFFUSION
For a body of water of unlimited depth contacting the gas by an area of A  the rate
of mass transfer dM/dt as a consequence of diffusion of the gas molecules in the
liquid phase  Fick’s Law
(dM/dt) = -D.A (dc/dx) (g/s)
where
D = coefficient of molecular diffusion (m2/s)
x = the distance from the interfacial area A
dc/dx = concentration gradient
DIFFUSION
The total amount of gas M (g) that has been absorbed through the surface area A
during the time t  independent of x 
under conditions of unlimited depth of water body

DtccAM s )(2 0
DIFFUSION
If the depth is not too small  the time of diffusion is not too
long  diffusion is very slow process and only very little gas is
brought into deeper layers of the water body:
t
DccA
dt
dM
s )( 0
Mechanism of mass transfer
The path of gaseous substrate from a gas bubble to bulk liquid can be divided into
several steps as follows:
1. Transfer from bulk gas in a bubble to a relatively unmixed gas layer
2. Diffusion through the relatively unmixed gas layer
3. Diffusion through the relatively unmixed liquid layer surrounding the bubble
4. Transfer from the relatively unmixed liquid layer to the bulk liquid
Theories
We can derive the three theories, but the overall difference and conclusions will relate to the impact of D upon kL, as
follows,
Two Film :
kL≈ D (molecular diffusivity)
Penetration:
where tc= contact time
Note that transfer is greatest for the shortest contact time. kL tends to zero for long contact times.
Surface removal:
where rc is a surface renewal rate, related to the rate of production of fresh surface.
We can derive the theories as follows, beginning with two film
The concept of gas transfer coefficients
FILM THEORY
Gas transfer rates
Gas transfer rate can be modeled as the product of a driving force (the difference
between the equilibrium concentration and the actual concentration) and an
overall volumetric gas transfer coefficient (a function of the geometry, mixing levels
of the system and the solubility of the compound). In equation form
where C is the dissolved gas concentration, C* is the equilibrium dissolved gas
concentration.
.
ˆ ( * )v l
dC
K C C
dt
 
Two Flim Theory
Assumptions:
1. Linear concentration profile through stagnant film
2. Steady state conditions
3. Instantaneous equilibrium
4. Transport by bulk diffusion is not limiting
5. Dilute solutions
A is transferred from the gas
phase into the liquid.
The concentration of A in the
liquid is CAL, in the bulk and CALi
at the
interface.
In the gas, the concentration is
CAG in the bulk and CAGi at the
interface.
Rate of mass transfer of A through the gas boundary layer is:
Rate of mass transfer of A through the liquid boundary layer is:
Where, k G is the gas-phase mass-transfer coefficient and k L is the liquid-
phase mass-transfer coefficient.
If we assume that equilibrium exists at the interface, C AG I and CALi can be related.
( )AG G AG AGiN k a C C 
( )AL L ALi ALN k a C C 
AG
AG AGi
G
N
C C
k a
 
AL
ALi AL
L
N
C C
k a
 
………………………………………………………………..1
…………………………………………………………..2
AG
AG Ali
G
N
C mC
k a
 
AGi
ALi
C
m
C

AL
ALi AL
L
N
m mC mC
k a
 
AG AL AN N N 
A A
AG AL
G L
N N
m C mC
k a k a
  
AGiA
AL
L
CN
C
k a m
 
AG AGiA
G
C CN
mk a m m
 
AGA A
AL
L G
CN N
C
k a mk a m
  
( )1 1
AG
AL
AL G
C
C
m
Nk a mk a

 
( )
1/
AG
AL
G
A
C
C
m k a
N


1 1 1
L G Gk a mk a K a
 
1 1
G L L
m
k a k a K a
 
………………………………………………………….3
Where, m is the distribution factor
Multiplying eq 2 with m Dividing eq 1 with m
Adding eq 4 and 6
………….4 ……………….5
………….6
………….7
Adding eq 5 and 7
We can define the overall gas-phase
mass-transfer coefficient KG as
the overall liquid-phase mass-transfer
coefficient K L as
The rate of mass transfer in gas-liquid systems can therefore be expressed using either of two
equations:
Equilibrium Concentrations:
mCAL is equal to C*AG, the gas-phase concentration of A in equilibrium with CAL and (CAG/m) is
equal to C*AL, the liquid-phase concentration of A in equilibrium with CAG.
However, as in liquid-liquid mass-transfer systems, it is generally difficult to
evaluate the interfacial area a – f (size and number of bubbles present)
(medium composition, stirrer speed and gas flow rate)
*( )A G AG AGN K a C C  *( )A L AL ALN K a C C 
( )A G AG ALN K a C mC  ( )AG
A L AL
C
N K a C
m
 
Case – 1
When solute A is very soluble in the liquid, for example in transfer of
ammonia to water, the liquid-side resistance is small compared with that
posed by the gas interfacial film. kLa is relatively large
K Ga ≈ k Ga
Case -2
Conversely, if A is poorly soluble in the liquid, e.g. oxygen in aqueous
solution, the liquid-phase mass-transfer resistance dominates and kGa is
much larger than k La.
KL a ≈ k La
*( )A G AG AGN k a C C 
*( )A L AL ALN k a C C 
1 1 1
L G Gk a mk a K a
 
1 1
G L L
m
k a k a K a
 
PENETRATION THEORY(Higbie, 1935)
During the time of exposure the gas diffuses into the fluid element  penetrates into liquid.
In contrast to the film theory, the penetration process is described by unsteady diffusion. This
theory assumes that turbulent eddies travel from the bulk of the phase to the interface
where they remain for a constant exposure time te. The solute is assumed to penetrate into a
given eddy during its stay at the interface by a process of unsteady-state molecular diffusion.
During this time the solute diffuses into the fluid element as a transient process, in the same
manner as transient heat conduction into a solid block. Such a transient diffusion process of
fixed contact time is not difficult to visualize in the situation where a liquid trickles down over
the surface of a piece of packing in a packed column. This model predicts that the mass-
transfer coefficient is directly proportional to the square root of molecular diffusivity (DAB).
1/2
2 AB
La
e
D
K
t
 
  
 
PENETRATION THEORY
. .PX Dt
. . . . .( ). .S L
S L
P
C CdM C
D A D A A C C D t
dt X X


    

Put Xp value
PENETRATION THEORY
During the time of the liquid the interface to the gas, the gases penetrate
into the liquid at a diminishing rate. The total mass of gas absorbed during
this time:

Dt
cckAM LgD )(2 
PENETRATION THEORY
Hence the average absorption rate m (g/s) during the time t is defined
by
The penetration assumes
t =tc
for a gas transfer process operated under steady state condition
t
D
cckAm
t
M
LgD

)(2 
PENETRATION THEORY
The final form of the rate expression for gas absorption as proposed by
the penetration theory:
)(2 LgD
c
cckA
t
D
m 

PENETRATION THEORY
According to the penetration theory:
stating that the coefficient of gas transfer is proportional to the root of
the coefficient diffusion.
c
L
t
D
k

2
PENETRATION THEORY
Assumption of a constant time of exposure of fluid elements to the gas phase  a
constant rate rc (s-1)
Taking rc instead of tc
c
c t
r 1

c
L
Dr
k 2
SURFACE RENEWAL THEORY (Danckwerts,
1951)
The model underlying the surface renewal theory is equal to that of the
penetration theory  unsteady diffusion of the gas into liquid elements
exposed to the gas phase.
However, this theory does not assume that the time to be constant 
follow a frequency distribution f(t) with ages of the fluid elements (= time
of exposure) ranging from zero to infinity.
SURFACE RENEWAL THEORY
The chance of an element of the surface being replaced with fresh liquid was independent of
the length of time for which it has been exposed. The surface age distribution function can
be expressed as
The theory is based on the assumption  the fraction of the surface having ages between t
and t+dt is given by:
where ‘s’ fraction of the area of surface which is replaced with fresh liquid in unit time. This
theory predicts that the mass transfer coefficient is proportional to the square root of the
molecular diffusivity
 if the surface element of any age always has chance of s.dt of being replaced  if each
surface element is being renewed with a frequency s, independent of its age
dtsedttf st
)(
 
1/2
.La ABK s D
SURFACE RENEWAL THEORY
the surface renewal approach seems closer to reality in such a case where the surface of
liquid in an agitated tank is in contact with the gas phase above, or with the surface of a
liquid flowing through an open channel. The average rate of gas transfer is
The surface renewal theory forecasts
DskL 
0
.( . ). . . st
D g l
D
m A k C C S e dt
t


 
. . .( . )D g lD S A k C C 
FILM-SURFACE-RENEWAL THEORY
This theory attempts a combination of the film theory
and the surface renewal theory in principle  a
combination of steady and unsteady diffusion.
The gas transfer coefficient as a function of the rate of
surface renewal s and max x = dL
FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
The effects of temperature on the rate gas transfer
(effects on kL and A)
The temperature coefficient  for oxygenation of
sewage  in the range of 1,016 to 1,047.
12
12
.)()( TT
TLTL
V
A
k
V
A
k 
 
FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
The influence of hydrophobic constituents and surface active agents on the rate of
gas transfer  Gibbs adsorption equation
c = concentration of hydrophobic substance in the bulk of the solution (g/m3)
S = excess concentration of hydrophobic substance at the surface (g/m3) as
compared with that of the bulk solution
R = universal gas constant
d/dc = rate of increase of surface tension with increasing the
concentration of the hydrophobic substance
dc
d
RT
c
S


FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
THE OVERALLGASTRANSFERCOEFFICIENTORAERATIONCOEFFICIENT
Under steady state conditions of gas transfer operation
 the coefficient diffusion and the time of exposure
may be assumed constant :
where k2 or kL.a is the overall gas transfer coefficient.
LL
c
kak
V
A
t
D
V
A
k .22 

THE OVERALLGASTRANSFERCOEFFICIENTORAERATIONCOEFFICIENT
The rate of gas transfer can be expressed as the rate
of concentration change
which integrates with c0 at t=0 to
or
 cck
dt
dc
V
m
s  2
  tk
ss ecccc 2
0


tk
s
s
e
cc
cc 2
0




THE OVERALLGASTRANSFERCOEFFICIENTORAERATIONCOEFFICIENT
The overall gas transfer coefficient k2 can easily
determined experimentally by measuring the change
of concentration as a function of time and by plotting
log (cs-c)/(cs-c0) versus time :
etke
cc
cc tk
s
s
log.loglog 2
0
2


 
tk2.4343,0
Liquid-Phase Mass Transfer with Chemical
Reactions
Occasionally, however, gas absorption is accompanied by chemical or biological
reactions in the liquid phase. For example, when CO2 gas is absorbed into an aqueous
solution of Na2CO3, the following reaction takes place in the liquid phase:
Na2CO3 +CO2 +H2O = 2NaHCO3
In general, the rates of the mass transfer increase when it is accompanied by
reactions. For example, if K*
La indicates the liquid-phase coefficient, including the
effects of the reaction, then the ratio E can be defined as:
E = K*
La/KLa
and is referred to as the ‘‘enhancement’’ (reaction) factor. Values of E are always
greater than unity.
Figure shows the idealized sketch of concentration profiles near the interface, for the
case of gas absorption with a very rapid second order reaction. The gas component A,
when absorbed at the interface, diffuses to the reaction zone where it reacts with B,
which is derived from the bulk of the liquid by diffusion. The reaction is so rapid that
it is completed within a very thin reaction zone; this can be regarded as a plane
parallel to the interface. The reaction product diffuses to the liquid main body. The
absorption of CO2 into a strong aqueous KOH solution is close to such a case.

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Gas transfer

  • 1. Gas Transfer Preeti Birwal Ph.D (DE) ICAR-NDRI 1st Year
  • 2. DEFINITION AND TERMS Gas transfer: a physical phenomenon, by which gas molecules are exchanged between a liquid and a gas at a gas-liquid interface. This leads to:  An increase of the concentration of the gas in the liquid phase as long as this phase is not saturated with the gas under the given conditions of e.g. pressure, temperature (absorption of gas).  A decrease when the liquid phase is over saturated (desorption or stripping of gas).
  • 3. DEFINITION AND TERMS Important natural phenomena of gas transfer: the reaeration of surface water: I. The transfer of oxygen into surface water. II. Release of oxygen produced by algal activities up to a concentration above the saturation concentration. III. Release of taste and odor-producing substances. IV. Release of methane, hydrogen sulfide under anaerobic conditions of surface water or of the bottom deposits.
  • 4. •Exchange of gases between aqueous/solid and gaseous phases is an essential element of many environmental processes. •Wastewater treatment plants require enhanced transfer of oxygen into activated sludge tanks to maintain aerobic degradation. •Water treatment plants require gas transfer to dissolve chlorine gas or ozone. •Gas transfer can also be used to remove unwanted volatile chemicals
  • 5. Some important examples of gas transfer in water and wastewater treatment. 1. Oxygen transfer to biological processes. 2. Stripping of volatile toxic organics (solvents). 3. CO2 exchange as it relates to pH control. 4. Ammonia removal by stripping. 5. Odor removal – volatile sulfur compounds. 6. Chlorination, ozonation for disinfection and odor control. The materials of interest are soluble in water and volatile (i.e. they exert a significant vapor pressure).
  • 6. Exchange of a dissolved compound with the atmosphere is controlled by the: I. extent of mixing in the aqueous and gaseous phase, II. the surface area of the interface, III. Temperature of mixture IV. the concentration of the compound in the two phases, and V. the equilibrium distribution of the compound.
  • 7. A distinction Volatilization - Stripping due to natural phenomenon. Stripping - Stripping due to a mechanical device - aeration.
  • 8. ELEMENTS OF AERATION AND GAS TRANSFER OPERATIONS The diffused aeration systems are categorized as (a) Porous or fine-pore diffusers (b) Nonporous diffusers (c) Jet aerators, aspirating aerators and U-tube aerators. Mechanical aerators are commonly divided into two groups based on major design and operating features: aerators with vertical axis of operation and aerators with horizontal axis. Both groups are further subdivided into surface and submerged aerators. In surface aerators, gas is entrained from the surrounding atmosphere while in submerged aerators, gas is entrained from the atmosphere or introduced in the tank bottom. Gravity aerators (a) cascades  the available difference head is subdivided into several steps (b) inclined planes  equipped with riffle plates to break up the sheet of water for surface renewal (c) vertical stacks  droplets fall and updrafts of air ascend in counter current flow
  • 12. ELEMENTS OF AERATION AND GAS TRANSFER OPERATIONS (2) Spray aerators: the water is sprayed in the form of fine droplets into the air  creating a large gas-liquid interface for gas transfer
  • 13. ELEMENTS OF AERATION AND GAS TRANSFER OPERATIONS (3) Air diffusers (bubble aeration)  air is injected into water (a) through orifices or nozzles in the air piping system (b) through spargers (c) through porous tubes, plates, boxes or domes  to produce bubbles of various size with different interfacial areas per m3 of air.
  • 14. ELEMENTS OF AERATION AND GAS TRANSFER OPERATIONS (4) Mechanical aerators  create new gas-liquid interfaces by different means and constructions  two types of construction: (a) various construction of brushes  a horizontal revolving shaft with combs, blades or angles (b) turbine or cone aerators with vertical shaft
  • 16. Henry’s law Water contains dissolved gases. In a closed vessel containing both gas (e.g., air and water), the concentration of a volatile component in the gas -phase will be in equilibrium with the concentration in the water phase, accordingto Henry’s law. The equilibrium concentration can be calculated using the following form of Henry’s law: cw= equilibrium concentration of a gas in water [g/m3] KH= Henry’s constant or distribution coefficient = concentration of the gas in air[g/m3] .w H gc k c gc
  • 17. Diffusivity O2 has lower MW than CO2 Solubility of CO2 is 24x that of O2 CO2 diffuses 20x more rapidly through the alveolar capillary barrier than O2 D  Solubility/MW
  • 18. The solubility of a gas (mg/L) in water depends on its temperature, salinity, gas composition, and total pressure. The solubility of a gas is also proportional to its absolute pressure. Increasing the gas pressure will also increase gas solubility proportionately, i.e., doubling the gas pressure will double that gases solubility. Higher gas pressures occur in water injected into a pressurized system, or in water obtained from a deep well.
  • 19. SOLUBILITY OF GASES The solubility of gases in water (and also in other liquids) depends upon: (1) the nature of the gas generally expressed by a gas specific coefficient  the distribution coefficient, kD (2) the concentration of the respective gas in the gaseous phase  related to the partial pressure of the respective gas in the gas phase (3) the temperature of the water (4) impurities contained in the water
  • 20. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY The higher the gas concentration in the gaseous phase  the greater will be the saturation concentration in the liquid phase The relation between the saturation concentration cs (g/m3) and the gas concentration in the gas phase cg (g/m3): cs = kD . cg
  • 21. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY The molar gas concentration in the gas phase (according to the universal gas law): (n/V) = p / (RT) (moles/m3) Hence the corresponding mass concentration cg is obtained by multiplication with the molecular weight (MW) of the gas: cg = (p . MW)/ (RT) (g/m3)
  • 22. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY The combination yields: cs = (kD . MW . p)/ (RT) Henry’s law is generally written as: cs = kH . p The relation between distribution coefficient kD and Henry’s constant: kH = (kD . MW)/ (RT)
  • 23. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY Bunsen absorption coefficient, kb  how much gas volume (m3), reduced to standard temperature (0oC) and pressure (101,3 kPa), can be absorbed per unit volume (m3) of water at a partial pressure of pO = 101,3 kPa of the gas in the gas phase : cs (m3 STP gas/m3 water) = kb
  • 24. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY And any other partial pressure p: cs = kb . (p/p0) (m3 STP/m3) Since 1 m3 STP contains p0/R.T0 moles of gas and a mass of gas equal to MW. p0/R.T0 : cs = (kb . MW)/(R.T0 ) p (g/m3)
  • 25. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY The relation between kD and kb: kb = kD T0/T The interrelationship between the three coefficients: kD = kH .R.T/MW = kb .T/T0
  • 26. INFLUENCE OF TEMPERATURE ON SOLUBILITY Gases dissolved in water  accompanied by liberation of heat H Le Chatelier principle  increase of temperature results in a decrease of solubility  van’t Hoff’s equation: [d(ln kD)/dT] = H/(RT2) where R = universal gas constant T = absolute temperature K H = change of heat content accompanying by the absorption of 1 mole of gas (J/mole)
  • 27. INFLUENCE OF TEMPERATURE ON SOLUBILITY By integrating between the limits T1 and T2: ln[(kD)2/(kD)1]= (H/R)(T2-T1)/(T1.T2) The product T1 .T2 does not change significantly within the temperature range encountered in gas transfer operations: (kD)2= (kD)1. econst (T2 – T1)
  • 28. INFLUENCE OF IMPURITIES ON SOLUBILITY Other constituent that may be contained in water influence the solubility of gases  expressed by an activity coefficient  : cs = (kD/).cg For pure water  = 1   generally increases as the concentration of substances dissolved in water rises  lowering the solubility
  • 29. INFLUENCE OF IMPURITIES ON SOLUBILITY The influence of concentration of impurities cimp on the activity coefficient: for non-electrolytes log  = f . Cimp for electrolytes log  = f . I where f = a constant depending on the matter dissolved in water I = ionic strength of electrolyte
  • 31. DIFFUSION The phenomenon of diffusion  the tendency any substance the spread uniformly throughout the space available to it  in environmental engineering  diffusion phenomena the liquid phase in gas transfer operations
  • 32. DIFFUSION For a body of water of unlimited depth contacting the gas by an area of A  the rate of mass transfer dM/dt as a consequence of diffusion of the gas molecules in the liquid phase  Fick’s Law (dM/dt) = -D.A (dc/dx) (g/s) where D = coefficient of molecular diffusion (m2/s) x = the distance from the interfacial area A dc/dx = concentration gradient
  • 33. DIFFUSION The total amount of gas M (g) that has been absorbed through the surface area A during the time t  independent of x  under conditions of unlimited depth of water body  DtccAM s )(2 0
  • 34. DIFFUSION If the depth is not too small  the time of diffusion is not too long  diffusion is very slow process and only very little gas is brought into deeper layers of the water body: t DccA dt dM s )( 0
  • 35. Mechanism of mass transfer The path of gaseous substrate from a gas bubble to bulk liquid can be divided into several steps as follows: 1. Transfer from bulk gas in a bubble to a relatively unmixed gas layer 2. Diffusion through the relatively unmixed gas layer 3. Diffusion through the relatively unmixed liquid layer surrounding the bubble 4. Transfer from the relatively unmixed liquid layer to the bulk liquid
  • 36. Theories We can derive the three theories, but the overall difference and conclusions will relate to the impact of D upon kL, as follows, Two Film : kL≈ D (molecular diffusivity) Penetration: where tc= contact time Note that transfer is greatest for the shortest contact time. kL tends to zero for long contact times. Surface removal: where rc is a surface renewal rate, related to the rate of production of fresh surface. We can derive the theories as follows, beginning with two film
  • 37. The concept of gas transfer coefficients
  • 39. Gas transfer rates Gas transfer rate can be modeled as the product of a driving force (the difference between the equilibrium concentration and the actual concentration) and an overall volumetric gas transfer coefficient (a function of the geometry, mixing levels of the system and the solubility of the compound). In equation form where C is the dissolved gas concentration, C* is the equilibrium dissolved gas concentration. . ˆ ( * )v l dC K C C dt  
  • 40. Two Flim Theory Assumptions: 1. Linear concentration profile through stagnant film 2. Steady state conditions 3. Instantaneous equilibrium 4. Transport by bulk diffusion is not limiting 5. Dilute solutions
  • 41. A is transferred from the gas phase into the liquid. The concentration of A in the liquid is CAL, in the bulk and CALi at the interface. In the gas, the concentration is CAG in the bulk and CAGi at the interface.
  • 42. Rate of mass transfer of A through the gas boundary layer is: Rate of mass transfer of A through the liquid boundary layer is: Where, k G is the gas-phase mass-transfer coefficient and k L is the liquid- phase mass-transfer coefficient. If we assume that equilibrium exists at the interface, C AG I and CALi can be related. ( )AG G AG AGiN k a C C  ( )AL L ALi ALN k a C C  AG AG AGi G N C C k a   AL ALi AL L N C C k a   ………………………………………………………………..1 …………………………………………………………..2
  • 43. AG AG Ali G N C mC k a   AGi ALi C m C  AL ALi AL L N m mC mC k a   AG AL AN N N  A A AG AL G L N N m C mC k a k a    AGiA AL L CN C k a m   AG AGiA G C CN mk a m m   AGA A AL L G CN N C k a mk a m    ( )1 1 AG AL AL G C C m Nk a mk a    ( ) 1/ AG AL G A C C m k a N   1 1 1 L G Gk a mk a K a   1 1 G L L m k a k a K a   ………………………………………………………….3 Where, m is the distribution factor Multiplying eq 2 with m Dividing eq 1 with m Adding eq 4 and 6 ………….4 ……………….5 ………….6 ………….7 Adding eq 5 and 7 We can define the overall gas-phase mass-transfer coefficient KG as the overall liquid-phase mass-transfer coefficient K L as
  • 44. The rate of mass transfer in gas-liquid systems can therefore be expressed using either of two equations: Equilibrium Concentrations: mCAL is equal to C*AG, the gas-phase concentration of A in equilibrium with CAL and (CAG/m) is equal to C*AL, the liquid-phase concentration of A in equilibrium with CAG. However, as in liquid-liquid mass-transfer systems, it is generally difficult to evaluate the interfacial area a – f (size and number of bubbles present) (medium composition, stirrer speed and gas flow rate) *( )A G AG AGN K a C C  *( )A L AL ALN K a C C  ( )A G AG ALN K a C mC  ( )AG A L AL C N K a C m  
  • 45. Case – 1 When solute A is very soluble in the liquid, for example in transfer of ammonia to water, the liquid-side resistance is small compared with that posed by the gas interfacial film. kLa is relatively large K Ga ≈ k Ga Case -2 Conversely, if A is poorly soluble in the liquid, e.g. oxygen in aqueous solution, the liquid-phase mass-transfer resistance dominates and kGa is much larger than k La. KL a ≈ k La *( )A G AG AGN k a C C  *( )A L AL ALN k a C C  1 1 1 L G Gk a mk a K a   1 1 G L L m k a k a K a  
  • 46. PENETRATION THEORY(Higbie, 1935) During the time of exposure the gas diffuses into the fluid element  penetrates into liquid. In contrast to the film theory, the penetration process is described by unsteady diffusion. This theory assumes that turbulent eddies travel from the bulk of the phase to the interface where they remain for a constant exposure time te. The solute is assumed to penetrate into a given eddy during its stay at the interface by a process of unsteady-state molecular diffusion. During this time the solute diffuses into the fluid element as a transient process, in the same manner as transient heat conduction into a solid block. Such a transient diffusion process of fixed contact time is not difficult to visualize in the situation where a liquid trickles down over the surface of a piece of packing in a packed column. This model predicts that the mass- transfer coefficient is directly proportional to the square root of molecular diffusivity (DAB). 1/2 2 AB La e D K t       
  • 47. PENETRATION THEORY . .PX Dt . . . . .( ). .S L S L P C CdM C D A D A A C C D t dt X X         Put Xp value
  • 48. PENETRATION THEORY During the time of the liquid the interface to the gas, the gases penetrate into the liquid at a diminishing rate. The total mass of gas absorbed during this time:  Dt cckAM LgD )(2 
  • 49. PENETRATION THEORY Hence the average absorption rate m (g/s) during the time t is defined by The penetration assumes t =tc for a gas transfer process operated under steady state condition t D cckAm t M LgD  )(2 
  • 50. PENETRATION THEORY The final form of the rate expression for gas absorption as proposed by the penetration theory: )(2 LgD c cckA t D m  
  • 51. PENETRATION THEORY According to the penetration theory: stating that the coefficient of gas transfer is proportional to the root of the coefficient diffusion. c L t D k  2
  • 52. PENETRATION THEORY Assumption of a constant time of exposure of fluid elements to the gas phase  a constant rate rc (s-1) Taking rc instead of tc c c t r 1  c L Dr k 2
  • 53. SURFACE RENEWAL THEORY (Danckwerts, 1951) The model underlying the surface renewal theory is equal to that of the penetration theory  unsteady diffusion of the gas into liquid elements exposed to the gas phase. However, this theory does not assume that the time to be constant  follow a frequency distribution f(t) with ages of the fluid elements (= time of exposure) ranging from zero to infinity.
  • 54. SURFACE RENEWAL THEORY The chance of an element of the surface being replaced with fresh liquid was independent of the length of time for which it has been exposed. The surface age distribution function can be expressed as The theory is based on the assumption  the fraction of the surface having ages between t and t+dt is given by: where ‘s’ fraction of the area of surface which is replaced with fresh liquid in unit time. This theory predicts that the mass transfer coefficient is proportional to the square root of the molecular diffusivity  if the surface element of any age always has chance of s.dt of being replaced  if each surface element is being renewed with a frequency s, independent of its age dtsedttf st )(   1/2 .La ABK s D
  • 55. SURFACE RENEWAL THEORY the surface renewal approach seems closer to reality in such a case where the surface of liquid in an agitated tank is in contact with the gas phase above, or with the surface of a liquid flowing through an open channel. The average rate of gas transfer is The surface renewal theory forecasts DskL  0 .( . ). . . st D g l D m A k C C S e dt t     . . .( . )D g lD S A k C C 
  • 56. FILM-SURFACE-RENEWAL THEORY This theory attempts a combination of the film theory and the surface renewal theory in principle  a combination of steady and unsteady diffusion. The gas transfer coefficient as a function of the rate of surface renewal s and max x = dL
  • 57. FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS The effects of temperature on the rate gas transfer (effects on kL and A) The temperature coefficient  for oxygenation of sewage  in the range of 1,016 to 1,047. 12 12 .)()( TT TLTL V A k V A k   
  • 58. FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS The influence of hydrophobic constituents and surface active agents on the rate of gas transfer  Gibbs adsorption equation c = concentration of hydrophobic substance in the bulk of the solution (g/m3) S = excess concentration of hydrophobic substance at the surface (g/m3) as compared with that of the bulk solution R = universal gas constant d/dc = rate of increase of surface tension with increasing the concentration of the hydrophobic substance dc d RT c S  
  • 59. FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
  • 60. FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
  • 61. THE OVERALLGASTRANSFERCOEFFICIENTORAERATIONCOEFFICIENT Under steady state conditions of gas transfer operation  the coefficient diffusion and the time of exposure may be assumed constant : where k2 or kL.a is the overall gas transfer coefficient. LL c kak V A t D V A k .22  
  • 62. THE OVERALLGASTRANSFERCOEFFICIENTORAERATIONCOEFFICIENT The rate of gas transfer can be expressed as the rate of concentration change which integrates with c0 at t=0 to or  cck dt dc V m s  2   tk ss ecccc 2 0   tk s s e cc cc 2 0    
  • 63. THE OVERALLGASTRANSFERCOEFFICIENTORAERATIONCOEFFICIENT The overall gas transfer coefficient k2 can easily determined experimentally by measuring the change of concentration as a function of time and by plotting log (cs-c)/(cs-c0) versus time : etke cc cc tk s s log.loglog 2 0 2     tk2.4343,0
  • 64. Liquid-Phase Mass Transfer with Chemical Reactions Occasionally, however, gas absorption is accompanied by chemical or biological reactions in the liquid phase. For example, when CO2 gas is absorbed into an aqueous solution of Na2CO3, the following reaction takes place in the liquid phase: Na2CO3 +CO2 +H2O = 2NaHCO3 In general, the rates of the mass transfer increase when it is accompanied by reactions. For example, if K* La indicates the liquid-phase coefficient, including the effects of the reaction, then the ratio E can be defined as: E = K* La/KLa and is referred to as the ‘‘enhancement’’ (reaction) factor. Values of E are always greater than unity.
  • 65. Figure shows the idealized sketch of concentration profiles near the interface, for the case of gas absorption with a very rapid second order reaction. The gas component A, when absorbed at the interface, diffuses to the reaction zone where it reacts with B, which is derived from the bulk of the liquid by diffusion. The reaction is so rapid that it is completed within a very thin reaction zone; this can be regarded as a plane parallel to the interface. The reaction product diffuses to the liquid main body. The absorption of CO2 into a strong aqueous KOH solution is close to such a case.