GAS TRANSFER

1
GAS TRANSFER
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 ?
• (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)

3
DEFINITION 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

4
ELEMENTS OF AERATION AND GAS 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).

5
ELEMENTS OF AERATION AND GAS TRANSFER OPERATIONS

• Four different types of aerators
• 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

6
ELEMENTS -- CASCADES
7
ELEMENTS INCLINED PLANES
8
ELEMENTS VERTICAL STACKS
9
ELEMENTS VERTICAL STACKS
10
ELEMENTS VERTICAL STACKS
11
ELEMENTS AMMONIA STRIPPING
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 SPRAY AERATORS
14
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.

15
ELEMENTS AIR DIFFUSERS
16
ELEMENTS AIR DIFFUSERS (POROUS TUBES)
17
ELEMENTS AIR DIFFUSERS
18
ELEMENTS AIR DIFFUSERS
19
ELEMENTS AIR DIFFUSERS
20
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

21
Boyles Law
22
Charles Law
23
Gay-Lussacs Law
24
Ideal 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.
25
Absolute Zero and the Kelvin Scale
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.
26
Kinetic 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

27
(No Transcript)
28
Kinetic Theory of Gases Basic Assumptions

• 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.

29
(No Transcript)
30
(No Transcript)
31
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

32
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

33
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)

34
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY

• The combination yields
• cs (kD . MW . p)/ (RT)
• Henrys law is generally written as
• cs kH . p
• The relation between distribution coefficient kD
  and Henrys constant
• kH (kD . MW)/ (RT)

35
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

36
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)

37
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

38
INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY

• 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

39
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 ? vant
  Hoffs equation
• d(ln kD)/dT ?H/(RT2)
• where R universal gas constant
• T absolute temperature K
• ?H change of heat content
  accompanying by the absorp- tion of 1 mole
  of gas (J/mole)

40
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)

41
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

42
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

43
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

44
DIFFUSION

• 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 ? Ficks
  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
• dx/dt concentration gradient

45
DIFFUSION
46
DIFFUSION
47
DIFFUSION
48
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

49
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

50
THE CONCEPT OF GAS TRANSFER COEFFICIENTS
51
THE CONCEPT OF GAS TRANSFER COEFFICIENTS

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

52
THE CONCEPT OF GAS TRANSFER COEFFICIENTS

• 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
• ?

53
THE CONCEPT OF GAS TRANSFER COEFFICIENTS

• The total gas transfer coefficient KL is composed
  of both the partial coefficients and the
  distribution coefficient
• then
• m A KL (kDcg cL)

54
THE CONCEPT OF GAS TRANSFER COEFFICIENTS

• 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)

55
FILM THEORY
56
FILM THEORY
57
FILM THEORY
58
FILM THEORY
59
FILM THEORY
60
PENETRATION 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

61
PENETRATION THEORY
62
PENETRATION THEORY
63
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

64
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

65
PENETRATION THEORY

• The final form of the rate expression for gas
  absorption as proposed by the penetration theory

66
PENETRATION THEORY

• According to the penetration theory
• stating that the coefficient of gas transfer is
  proportional to the root of the coefficient
  diffusion.

67
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

68
SURFACE 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.

69
SURFACE RENEWAL THEORY

• The theory is based on the assumption ? the
  fraction of the surface having ages between t and
  tdt 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

70
SURFACE RENEWAL THEORY

• The average rate of gas transfer is
• The surface renewal theory forecasts

71
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

72
COMPARISON OF THE THEORIES
73
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.

74
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

75
FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
76
FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS
77
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.

78
THE OVERALL GAS TRANSFER COEFFICIENT OR AERATION
COEFFICIENT

• The rate of gas transfer can be expressed as the
  rate of concentration change
• which integrates with c0 at t0 to
• or

79
THE OVERALL GAS TRANSFER COEFFICIENT OR AERATION
COEFFICIENT

• 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

80
THE EFFICIENCY COEFFICIENT

• 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

81
THE EFFICIENCY COEFFICIENT
82
THE EFFICIENCY COEFFICIENT
83
THE OXYGENATION CAPACITY
84
THE OXYGENATION CAPACITY
85
THE OXYGENATION CAPACITY
86
AIR STRIPPING
87
AIR STRIPPING
88
AIR STRIPPING
89
AIR STRIPPING
90
AIR STRIPPING
91
AIR STRIPPING
92
AIR STRIPPING
93
AIR STRIPPING
94
AIR STRIPPING
95
AIR STRIPPING
96
AIR STRIPPING
97
AIR STRIPPING
98
AIR STRIPPING
99
AIR STRIPPING