Gas transfer

Gas Transfer

Preeti BirwalPh.D (DE)ICAR-NDRI1st 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 mixtureIV. 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 OPERATIONSThe 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

Watercontains dissolved gases. In aclosed 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, according to 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) (m3STP/m3)

Since 1 m3STP 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

DIFFUSIONThe 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:

tDccA

dt

dMs )( 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

dCK 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

AGAG AGi

G

NC C

k a

ALALi AL

L

NC C

k a

………………………………………………………………..1

…………………………………………………………..2

AGAG Ali

G

NC mC

k a

AGi

ALi

Cm

C

ALALi AL

L

Nm mC mCk a

AG AL AN N N

A AAG AL

G L

N Nm C mC

k a k a

AGiAAL

L

CNC

k a m

AG AGiA

G

C CN

mk a m m

AGA AAL

L G

CN NC

k a mk a m

( )1 1AG

AL

AL G

CC

mNk a mk a

( )1/

AGAL

GA

CC

m k aN

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 mDividing 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 ( )AGA L AL

CN 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 ABLa

e

DK

t

PENETRATION THEORY

. .PX D t

. . . . .( ). .S LS L

P

C CdM CD 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

DcckAm

t

MLgD )(2

PENETRATION THEORY The final form of the rate expression for gas absorption as proposed by the penetration theory:

)(2 LgDc

cckAt

Dm

PENETRATION THEORY According to the penetration theory:

stating that the coefficient of gas transfer is proportional to the root of the coefficient diffusion.

cL t

Dk

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

cc tr 1

c

L

Drk 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

.( . ). . . stD g l

Dm 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

Ak

V

Ak


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

cS



THE OVERALL GAS TRANSFER COEFFICIENT OR AERATION COEFFICIENT

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.

LLc

kakV

A

t

D

V

Ak .22


The rate of gas transfer can be expressed as the rate of concentration change

which integrates with c0 at t=0 to

or

cckdt

dc

V

ms 2

tkss ecccc 2

0

tk

s

s ecc

cc2

0


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 :

etkecc

cc tk

s

s log.loglog 20

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.

Food

Gas transfer