Page 214 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Flotation 169

they may be dislodged from low-elevation lake or river muds (by mass-spectrograph analyses) to comprise a mixture
during summer months. of gases, e.g., N 2 ,CH 4 , and CO 2 (Hendricks, 1966). Most
A dissolved gas, e.g., N 2 , will precipitate if its concentra- likely, the mixture of gases observed in bubbles is due to
tion exceeds that which would be in equilibrium with a collisions.
pseudo-pure-N 2 -gas, which is at the pressure of the water
at the particular point in question. For a flotation system,
using nitrogen gas to illustrate, the idea may be expressed as Example 8.4 Saturation Concentration
follows:
Given
The nozzles of a flotation tank are located at a depth of
C(N 2 , nozzle contraction) > H(N 2 ) P(pseudo-pure-N 2 -gas
4.0 m at a sea-level location, T ¼ 208C.
at depth of flotation tank-at-nozzle) (8:8) Required
Determine the critical concentration at which gas precipi-
in which tation will occur.
C(N 2 , nozzle contraction) is the actual concentration of Solution
dissolved N 2 in the nozzle contraction, i.e., just before Apply the principle that the concentration of a gas
the throat and immediately preceding bubble formation cannot exceed that which would be at pseudo equi-
that occurs in the nozzle expansion (mg dissolved N 2 =L librium with the local pressure of the water being con-
3
water) or (kg dissolved N 2 =m water) sidered, i.e.,
H(N 2 ) is the Henry’s coefficient for N 2 at a specified
temperature as given in Table H.5 (19.01 mg dissolved lim C(dissolved O 2 ) ¼ H(O 2 ) X(O 2 ) P(Nozzles)
N 2 =L water=atm N 2 ) or (0.0001876 kg dissolved N 2 =m 3 ¼ (43:39 mg=L=atm)
water=kPa N 2 )
(1:0 mol O 2 =mol pure O 2 )
[1:0 atm þ (4:0m=10:33 m) atm]
P(pseudo-pure-N 2 -gas at depth of flotation tank-at-nozzle)
¼ 56:0mg=L
¼ P(atm) þ g D(flotation-tank-depth) (kPa)
w
Comments
The concentration of dissolved oxygen must exceed
P(atm) is the pressure of atmosphere at elevation of water
56 mg=L in order for gas precipitation to occur.
surface (kPa); for reference, P(atm at sea level) ¼
101.325 kPa
D(flotation-tank-depth) is the depth of nozzles in flotation Example 8.5 Saturation Concentration—Bubbles
tank (m) Adjacent to Algae Mats
3
g w is the specific weight of water (N=m )
g w ¼ r w g, r w is the mass density of water (998.2063 Given
3
kg=m at 208C, Table B.9) and g is the acceleration of Bubbles are sometimes observed adjacent to ‘‘mats’’ of
2
gravity (9.806650 m=s ) floating algae sometimes found in summer in quiescent
natural waters. Assume this occurs at sea level and at or
near the water surface.
In other words, if the left side of Equation 8.8 exceeds the
quantity on the right side, gas precipitation occurs. The left Required
Determine the maximum concentration of dissolved oxy-
side is the actual dissolved gas concentration from the satura-
gen in the vicinity of the algae.
tor while the right side is that calculated by Henry’s law and is
the maximum dissolved gas concentration that can exist. The Solution
difference between the left side and the right side is the The gas will precipitate at concentration.
‘‘released gas’’ (also called ‘‘excess gas’’) that becomes bub-
bles. The dissolved gas concentration in the ‘‘contact zone,’’ lim C(dissolved O 2 ) ¼ H(O 2 ) X(O 2 ) P(atmosphere)
and at the nozzle elevation (after gas precipitation), is at
¼ (43:39 mg=L=atm)
‘‘equilibrium’’ with the gas bubbles, and is designated, C a ,
(1:0 mol O 2 =mol pure O 2 )
where, by Henry’s law, C a ¼ H(N 2 ) P(pure-N 2 -gas at depth
[1:0 atm þ (0:0m=10:33 m) atm]
of flotation tank-at-nozzle).
¼ 43:4mg=L
It is not known whether the bubbles formed are pure gas of
a single species, e.g., N 2 , or a mixture, e.g., N 2 and O 2 . Based
on theory, it is assumed here that a bubble of pure gas will Comments
form initially, but the gas–water interface formed would The dissolved oxygen (a reaction product of photosyn-
facilitate another gas species diffusing into the bubble. Gas thesis) concentration cannot exceed 43.4 mg=L since gas
bubbles collected from primary clarifier sludge were found precipitation will preclude higher levels.