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: (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

6. ELEMENTS -- CASCADES

7. ELEMENTS – INCLINED PLANES

8. 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 m 3 of air.

15. ELEMENTS – AIR DIFFUSERS

16. ELEMENTS – AIR DIFFUSERS (POROUS TUBES)

17. 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. Boyle’s Law

22. Charles’ Law

23. Gay-Lussac’s 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

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.

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, k D (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 c s (g/m 3 ) and the gas concentration in the gas phase c g (g/m 3 ): c s = k D. c g

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/m 3 ) Hence the corresponding mass concentration c g is obtained by multiplication with the molecular weight (MW) of the gas: c g = (p. MW)/ (RT) (g/m 3 )

34. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY The combination yields: c s = (k D. MW. p)/ (RT) Henry’s law is generally written as: c s = k H. p The relation between distribution coefficient k D and Henry’s constant: k H = (k D. MW)/ (RT)

35. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY Bunsen absorption coefficient, k b  how much gas volume (m 3 ), reduced to standard temperature (0 o C) and pressure (101,3 kPa), can be absorbed per unit volume (m 3 ) of water at a partial pressure of p O = 101,3 kPa of the gas in the gas phase : c s (m 3 STP gas/m 3 water) = k b

36. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY And any other partial pressure p: c s = k b. (p/p 0 ) (m 3 STP /m 3 ) Since 1 m 3 STP contains p 0 /R.T 0 moles of gas and a mass of gas equal to MW. p 0 /R.T 0 : c s = (k b. MW)/(R.T 0 ) p (g/m 3 )

37. INFLUENCE OF THE GAS CONCENTRATION ON SOLUBILITY The relation between k D and k b : k b = k D T 0 /T The interrelationship between the three coefficients: k D = k H.R.T/MW = k b.T/T 0

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 p w  the partial pressure p of the other gases are reduced  p’ = p. (P – p w )/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  van’t Hoff’s equation: [d(ln k D )/dT] = H/(RT 2 ) 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 T 1 and T 2 : ln[(k D ) 2 /(k D ) 1 ]= (H/R)(T 2 - T 1 )/(T 1.T 2 ) The product T 1.T 2 does not change significantly within the temperature range encountered in gas transfer operations: (k D ) 2 = (k D ) 1. e const (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  : c s = (k D /).c g 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 c imp on the activity coefficient: for non-electrolytes log  = f. C imp 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  Fick’s Law (dM/dt) = -D.A (dc/dx) (g/s) where D = coefficient of molecular diffusion (m 2 /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. 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

52. THE CONCEPT OF GAS TRANSFER COEFFICIENTS where k g = partial gas transfer coefficient for the gas phase k L = partial gas transfer coefficient for the liquid phase c gi and c Li  generally not known  c Li = k D. c gi 

53. THE CONCEPT OF GAS TRANSFER COEFFICIENTS The total gas transfer coefficient K L is composed of both the partial coefficients and the distribution coefficient: then m = A K L (k D c g – c L )

54. THE CONCEPT OF GAS TRANSFER COEFFICIENTS The value of k D /k g will be very small with respect to 1/k L  the influence of the gas transfer coefficient of the gas phase may be neglected  K L = k L and consequently m = A k L (k D c g – c L )

55. 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

63. 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 =t c 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 r c (s -1 ) Taking r c instead of t c

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 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

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 = d L

72. COMPARISON OF THE THEORIES

73. FACTORS AFFECTING THE GAS TRANSFER COEFFICIENTS The effects of temperature on the rate gas transfer (effects on k L 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/m 3 ) S = excess concentration of hydrophobic substance at the surface (g/m 3 ) 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

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 k 2 or k L.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 c 0 at t=0 to or

79. THE OVERALL GAS TRANSFER COEFFICIENT OR AERATION COEFFICIENT The overall gas transfer coefficient k 2 can easily determined experimentally by measuring the change of concentration as a function of time and by plotting log (c s -c)/(c s -c 0 ) 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 t k is assumed for the aeration step under steady state conditions:

81. THE EFFICIENCY COEFFICIENT

83. THE OXYGENATION CAPACITY

86. AIR STRIPPING