Page 618 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Gas Transfer 573

18.1.3.6 Grid Diffusers Equation H.28, that is, p*(A) ¼ H(A) X*(A), is the form
In the 1980s, the issue of diffused (bubble) aerationwas revisited used most commonly in physical chemistry and in chemical
and re-evaluated in terms of newer designs of diffusers and a engineering; it says that the equilibrium pressure of the adja-
grid layout (vis-à-vis spiral flow), and motivated by the signifi- cent atmosphere is proportional to the mass fraction of ‘‘A’’ in
cant energy reduction as compared with turbine aeration and the aqueous phase and is called here the ‘‘volatility relation.’’
coarse-bubble diffusers (see Boyle, 1985; Boyle et al., 1989).
Example 18.1 Illustration of Calculation of
18.1.3.7 Air Stripping
Dissolved Oxygen Concentration by Henry’s Law
Another strand of gas transfer was the issue of air stripping,
which has been around as an empirical practice in water Given
treatment since the 1920s, to remove odors, and in wastewater Elevation ¼ sea-level; T ¼ 208C; p(O 2 ) ¼ 0.209 atm.
treatment since the mid-1960s when the Lake Tahoe tertiary Required
treatment plant was designed to remove ammonia. Then, in Determine C(O 2 , sea level, 208C), that is, the aqueous
the 1980’s, VOCs were an issue as hazardous waste sites were concentration of oxygen at sea level at 208C.
identified and the 1986 Safe Drinking Water Act had as one of
Solution
its objectives the removal of certain VOCs (volatile organic s
From Table H.5, H (O 2 ,208C) ¼ 43.39 mg=L=atm. Appli-
compounds) from drinking water; air stripping was one of the cation of Equation 18.1, the solubility form of Henry’s law
treatment technologies used for their removal. gives,
C(O 2 ) ¼ (43:39 mg=L=atm) (0:209 atm)
18.2 GAS TRANSFER THEORY
¼ 9:07 mg=L
In-a-nutshell, gas transfer is limited by the rate of diffusion
across a gas–water interface and the rate of surface renewal. Discussion
The latter is related to the rate of advection to the gas–water C(O 2 ) ¼ 9.07 mg=L is about the concentration measured in
interface and turbulence. Overall, the gas-transfer rate is pro- a water sample at sea level by the well-known Winkler
portional to the departure from equilibrium between a surface titration.
‘‘film’’ and the interior of the reactor.
18.2.2 KINETICS
18.2.1 EQUILIBRIA
The rate of a process is described by its ‘‘kinetics.’’ As noted,
Most gas-transfer reactor systems are ‘‘open,’’ which means for the case of gas transfer, such rate is dependent upon the gas
that mass and=or energy flux may cross the boundaries. Any diffusion flux in the gas phase and aqueous phase and the rate of
open system is striving toward equilibrium. The relative creation of interfacial surface area. The diffusion is sequential,
departure from equilibrium ‘‘drives’’ the reaction, that is, gas either gas-phase-then-aqueous-phase or aqueous-phase-then-
transfer, and controls the rate of the mass transfer. gas-phase. For the sequence of gas-phase-then-aqueous-phase,
as interfacial surface area is created, a gas-deficient surface
18.2.1.1 Henry’s Law film becomes instantaneously ‘‘saturated’’ with a given gas, for
The equilibrium between a gas at a given pressure and its example, oxygen, which is then advected away from the gas–
aqueous phase concentration is given by Henry’s law, which water interface. The opposite occurs in ‘‘gas stripping,’’ that is,
has several forms (see Appendix H). The form favored here is removal of dissolved gas from the aqueous phase.
the ‘‘solubility relation,’’ which says merely that the aqueous-
18.2.2.1 Diffusion
phase concentration of a gas, ‘‘A,’’ is proportional to the
partial pressure of ‘‘A’’ above the gas–water interface, that is, The diffusion flux is due to the random thermal motion of
molecules. Fick’s law is the basis for the working equations.
S
C(A) ¼ H (A) p(A) (18:1)
18.2.2.1.1 Kinetic Energy of Gases
Molecules in a gas have a thermal kinetic energy,
where
C(A) is the concentration of gas in aqueous phase in 1
2
equilibrium with p(A) (mg=L) KE(thermal) ¼ mv ¼ kT (18:2)
S
H (A) is Henry’s constant, a proportionality constant 2
(mg=L=atm) where
p(A) is the partial pressure of gas ‘‘A’’ above the gas–water KE(thermal) is the kinetic energy due to thermal motion
interface (atm) (J=molecule)
m is the mass of molecule (g)
Table H.5 gives values of H S for different gases and v is the velocity of molecule (cm=s)
for different temperatures. It is simple since for p(A) ¼ 1.0 k is the Boltzman constant (1.38 10 23 J=molecule=K)
atm, C(A) ¼ H(A). T is the absolute temperature (K)