gas transfer. definition and terms gas transfer a physical phenomenon, by which gas molecules are...

GAS TRANSFERGAS TRANSFER

DEFINITION AND TERMSDEFINITION AND TERMS• Gas transfer a physical phenomenon, by

which gas molecules are exchanged between a liquid and a gas at a gas-liquid interface (1) an increase of the concentration of the gas(es) 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)(2) a decrease when the liquid phase is over saturated (desorption, precipitation or stripping of gas)

DEFINITION AND TERMSDEFINITION AND TERMS• Important natural phenomena of gas transfer

the reaeration of surface water:(1) the transfer of oxygen into surface water(2) release of oxygen produced by algal activities up to a concentration above the saturation concentration(3) release of taste and odor-producing substances(4) release of methane, hydrogen sulfide under anaerobic conditions of surface water or of the bottom deposits

ELEMENTS OF AERATION AND ELEMENTS OF AERATION AND GAS TRANSFER OPERATIONSGAS TRANSFER OPERATIONS

• Gas transfer occurs only through the gas-liquid interface has to be carried out as to maximize the opportunity of interfacial contact between the two phases.

• The engineering goal to accomplish the gas transfer with a minimum expenditure of initial and operational cost (energy).


• Four different types of aerators:(1) Gravity aerators

(a) cascades the available difference head is subdivided into several steps(b) inclined planes eqipped 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 -- CASCADESELEMENTS -- CASCADES

ELEMENTS – INCLINED ELEMENTS – INCLINED PLANESPLANES

ELEMENTS – ELEMENTS – VERTICAL STACKSVERTICAL STACKS

ELEMENTS – ELEMENTS – AMMONIA STRIPPINGAMMONIA STRIPPING


(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 –ELEMENTS –SPRAY AERATORSSPRAY AERATORS


(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 –ELEMENTS –AIR DIFFUSERSAIR DIFFUSERS

ELEMENTS –ELEMENTS –AIR DIFFUSERS (POROUS TUBES)AIR DIFFUSERS (POROUS TUBES)

ELEMENTS –ELEMENTS –AIR DIFFUSERSAIR DIFFUSERS


(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

Boyle’s LawBoyle’s Law

Charles’ LawCharles’ Law

constant (constant pressure)V

T

Gay-Lussac’s LawGay-Lussac’s Law

constant (constant volume)p

T

Ideal Gas LawIdeal Gas Law

The ideal gas law is a special form of an equation of state,i.e., an equation relating the variables that characterize a gas(pressure, volume, temperature, density, ….).The ideal gas law is applicable to low-density gases.

constant (fixed mass of gas)

B

pV

TpV nRT

pV Nk T

p RT

Absolute Zero and the Kelvin Absolute Zero and the Kelvin ScaleScale

The pressure-temperature relation leads to the design of a constant-volume gas thermometer. Extrapolation of measurements made using different gases leads to the concept of absolute zero, when the pressure (or volume) is zero.

Kinetic Theory: ApplicationsKinetic Theory: Applications

Kinetic theory investigates (on a molecular scale) topics such as:•Change of phase (evaporation; vapour pressure; latent heat)•Pressure•Change of shape and volume (elasticity; Hooke's law)•Transport phenomena (diffusion - transport of mass; viscosity - transport of momentum; electrical conduction - transport of electric charge; thermal conduction - transport of heat)•Thermal expansion•Surface energy and surface tension

Kinetic Theory of Gases: Basic Kinetic Theory of Gases: Basic AssumptionsAssumptions

•The number of molecules is large, and the average separation between them is large compared with their dimensions. This means that the molecules occupy a negligible volume in the container.

•The molecules obey Newton's laws of motion, but as a whole they move randomly. 'Randomly' means that any molecule can move equally in any direction.

•The molecules undergo elastic collisions with each other and with the walls of the container. Thus, in the collisions both kinetic energy and momentum are constant.

•The forces between molecules are negligible except during a collision. The forces between a molecule are short-range, so the molecules interact with each other only during a collision.

•The gas is a pure substance. All molecules are identical.

SOLUBILITY OF GASESSOLUBILITY 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 INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITYCONCENTRATION 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


• 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)


• 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)


• 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


• And any other partial pressure p:cs = kb . (p/p0) (m3

STP/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)


• The relation between kD and kb:

kb = kD T0/T

• The interrelationship between the three coefficients:

kD = kH .R.T/MW = kb .T/T0


• In the practice of aeration the gas phase will always be saturated with water vapor exerting a certain partial pressure pw the partial pressure p of the other gases are reduced

p’ = p . (P – pw)/P

INFLUENCE OF TEMPERATURE INFLUENCE OF TEMPERATURE ON SOLUBILITYON 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 INFLUENCE OF TEMPERATURE ON SOLUBILITYON 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 INFLUENCE OF IMPURITIES ON SOLUBILITYON 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 INFLUENCE OF IMPURITIES ON SOLUBILITYON 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

DIFFUSIONDIFFUSION• 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

DIFFUSIONDIFFUSION• For a quiescent 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 Adx/dt = concentration gradient

DIFFUSIONDIFFUSION

DIFFUSIONDIFFUSION• 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

DIFFUSIONDIFFUSION• 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

THE CONCEPT OF GAS THE CONCEPT OF GAS TRANSFER COEFFICIENTSTRANSFER COEFFICIENTS


• In accordance with Fick’s Law the mass transport per unit time (g/s) is proportional to the concentration difference :for the gas phase

for the liquid phase

)( gigg ccAkm

)( LLiL ccAkm


where kg = partial gas transfer coefficient for

the gas phase kL = partial gas transfer coefficient for

the liquid phase cgi and cLi generally not known

cLi = kD . cgi

)()1

( 1LgD

g

D

L

cckAk

k

km


• The total gas transfer coefficient KL is composed of both the partial coefficients and the distribution coefficient:

then

m = A KL (kDcg – cL)

g

D

LL k

k

kK

11


• The value of kD/kg will be very small with respect to 1/kL the influence of the gas transfer coefficient of the gas phase may be neglected

KL = kL

and consequently

m = A kL (kDcg – cL)

FILM THEORYFILM THEORY

PENETRATION THEORYPENETRATION THEORY• 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

PENETRATION THEORYPENETRATION THEORY

PENETRATION THEORYPENETRATION 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 THEORYPENETRATION THEORY• Hence the average absorption rate m

(g/s) during the time t is defined by

The penetration assumest =tc

for a gas transfer process operated under steady state condition

t

DcckAm

t

MLgD )(2

PENETRATION THEORYPENETRATION THEORY• The final form of the rate expression for

gas absorption as proposed by the penetration theory:

)(2 LgDc

cckAt

Dm

PENETRATION THEORYPENETRATION 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 THEORYPENETRATION 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 THEORYSURFACE RENEWAL THEORY• 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 THEORYSURFACE RENEWAL THEORY• The theory is based on the assumption the

fraction of the surface having ages between t and t+dt is given by:

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)(

SURFACE RENEWAL THEORYSURFACE RENEWAL THEORY• The average rate of gas transfer is

• The surface renewal theory forecasts

DskL

FILM-SURFACE-RENEWAL FILM-SURFACE-RENEWAL THEORYTHEORY

• 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

D

dsDsk L

L

2.coth

COMPARISON OF THE COMPARISON OF THE THEORIESTHEORIES

FACTORS AFFECTING THE GAS FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTSTRANSFER 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

solutionR = universal gas constantd/dc = rate of increase of surface tension with increasing

the concentration of the hydrophobic substance

dc

d

RT

cS

THE OVERALL GAS TRANSFER THE OVERALL GAS TRANSFER COEFFICIENT OR AERATION COEFFICIENT OR AERATION

COEFFICIENTCOEFFICIENT

• 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

THE EFFICIENCY THE EFFICIENCY COEFFICIENTCOEFFICIENT

• With some transfer operations, e.g. cascades, weir aeration difficult or impossible to determine the parameter time t.

• If now a constant time tk is assumed for the aeration step under steady state conditions:

Kecc

ccktk

s

es 12

0

Kcc

cc

cc

cc

s

e

s

es

110

0

0

THE EFFICIENCY THE EFFICIENCY COEFFICIENTCOEFFICIENT

THE OXYGENATION THE OXYGENATION CAPACITYCAPACITY

AIR STRIPPINGAIR STRIPPING

gas transfer. definition and terms gas transfer a physical phenomenon, by which gas molecules are...

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