Page 636 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Gas Transfer 591

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g w is the specific weight of water, that is, g w ¼ r w g(N=m ) Calculation of C*(ST) is in accordance with Henry’s law,
d(water) is the depth of water used for calculation of that is, Equation H.60, that is,
bubble pressure (m)
C*(O 2 , ST) ¼ H(O 2 ,20 C) X(O 2 ) p(sea-level) (18:69)

Since the pressure in the bubble decreases as the bubble rises,
the average depth is used for the pressure argument in Henry’s
where
law, Equation H.60. In principle, the calculation of K L a for
H(O 2 ,208C) is Henry’s constant for oxygen at 208C
bubble aeration is the same as for turbine aeration or air
(mg O 2 =L=atm O 2 )
stripping. The gas concentration in the aqueous phase is
X(O 2 ) is the mole fraction of oxygen in atmosphere
calculated by Henry’s law, Equation 18.1.
(0.2095 per Table B.7)
p(sea-level) is the atmospheric pressure at sea-level
18.3.1.1.4 Convert K L a(T) to K L a(ST)
(1.00 atm or 101.325 kPa)
A traditional equation for temperature conversion (Ecken-
felder and O’Connor, 1961; Boyle, 1989) is
The reactor volume, V, is a part of the activated sludge reactor
design. For the purpose of this illustration, however, V can be
K L a(T) taken as the volume for a 6 h detention time using average
T 20
u ¼ (18:67)
K L a(ST) daily flow at the end of the design period (which is a common
assumption).
where
K L a(T) is the gas transfer coefficient at any temperature, 18.3.1.2 Oxygen Transferred per Unit of Energy
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T (s ) Expenditure
K L a(ST) is the gas transfer coefficient for standard tem- To compare aeration systems, a parameter that has been used
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perature, that is, 208C(s ) (during the 1960s) is mass of oxygen transferred per unit of
T is the temperature (8C)
energy required under standard conditions, for example kg O 2
u ¼ temperature conversion coefficient (dimensionless) transferred=kwh (lb O 2 transferred=hp-h). To evaluate a sys-
¼ 1.024 is a common assumption (Boyle, 1989) tem, the test is done under whatever conditions exist to
determine K L a(T, p, W) and is then converted to K L a(clean
As to the source of Equation 18.67, Eckenfelder and water, sea level, 208C), that is, K L a(ST), which permits cal-
O’Connor (1961, p. 68) show a derivation based on the culation of the equivalent J(ST), that is, Equation 18.68.
van’t Hoff–Arrhenius relations, Equation H.54. Looking at Measurement of the power consumed permits calculation of
the definition of K L a, however, as seen in Equation 18.20, the mass of oxygen transferred per unit of energy expended,
that is, K L a ¼ DA=dV, and by the Wilke–Chang relation, that is,
Equation 18.9, K L a should be directly proportional to T.
This has not been ascertained, however, and so Equation J(O 2 , ST)
18.67 remains as the means for taking temperature into W(O 2 , ST) ¼ (18:70)
E n
account.
where
18.3.1.1.5 Calculate Equivalent J(ST)
W(O 2 , ST) is the mass of oxygen transferred per unit of
In oxygen uptake, the mass flux of oxygen for a given reactor
energy expended under equivalent standard conditions,
and given conditions is commonly converted to standard that is, 208C and sea level pressure (kg O 2 transferred=
conditions, that is, W ¼ clean water, T ¼ 208C, sea level pres- kwh or lb O 2 transferred=hp-h).
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sure, and C(reactor) ¼ 0kg=m . The key is that K L a(ST) is
E n is the energy expended (specified wire or impeller) over
determined as outlined in the preceding steps. Thus, J(ST) is
adefined time period (kwh or hph)
calculated as
As seen in Equation (18.68), J(O 2 , ST) depends on the
J(O 2 , ST) ¼ K L a(ST) C*(O 2 , ST) V(reactor) (18:68) volume of the reactor. Therefore, W(O 2 , ST) is not a valid
indicator of the impeller efficiency in transferring oxygen.
where The term is referred to only because of its past use, mostly
J(O 2 , ST) is the mass flux of dissolved oxygen from gas in the 1960s.
phase to solution phase due to aeration for clean water at
208C (kg O 2 =s)
18.3.2 EQUIPMENT
C*(ST) is the dissolved oxygen saturation concentration
for clean water at temperature, T ¼ 208C, and sea level A variety of aeration equipment and gas stripping equipment
atmospheric pressure, that is, p(sea level) ¼ 101.325 has been manufactured over the years, for example, surface
kPa, and at partial pressure of oxygen in atmosphere, aerators, submerged diffusers, packed towers, etc. Activated
that is, X(O 2 ) ¼ 0.0209 sludge aeration equipment has included surface units, for