Environmental Engineering Reference
In-Depth Information
There are a wide variety of expressions relating changes in solubility to temperature, salinity,
and other factors, from modiications to Henry's law constant to experimentally derived equations.
For example, a relatively large number of equations have been developed to predict the saturation
concentrations of oxygen, since oxygen is a critical environmental and regulatory parameter. Bowie
et al. (1985) reviewed a number of these formulations and compared their predictions, noting dis-
crepancies as high as 11% between formulations, particularly for highly saline conditions.
14.1.5 I
MpactS
of
b
aroMetrIc
p
reSSure
, e
LeVatIon
,
and
d
eptH
The equilibrium water solubility of gases is a function of pressure. For air solubility, that pres-
sure is due to the weight of the atmospheric gases (the sum of the partial pressures), which is the
atmospheric or barometric pressure. The normal sea-level barometric pressure is 760 mmHg (about
15 psi). That atmospheric pressure decreases as a function of altitude or due to changes in meteo-
rological conditions. For example, a storm may change the atmospheric pressure by 20 mmHg.
Similarly, the pressure of pure gases also impacts gas solubility, whether in a closed or an open
vessel (or at depth).
Altitude decreases the partial pressure by about 1.0% /100 m of elevation above sea level. So,
the partial pressure in Denver, Colorado, the “mile high city,” would only be about 82% of what it
would be at sea level. The relationship is slightly nonlinear; for example, the
p
alt
for Mount Everest
(8850 m) is about 31%, rather less than zero, which would result from a constant 1.0%/100 m.
Henry's relationship indicates that liquid saturation concentrations are a function of pressure.
Since water is relatively incompressible, the hydrostatic pressure due to the weight of water is a
linear function of the speciic weight of water and the water depth (
P
= γ
z
, where
z
is the depth in
meters and γ is the speciic weight of water, about 9.81 kN m
-3
at 4°C). The speciic weight can also
be computed from the product of density and gravitational acceleration.
For example, the hydrostatic pressure at 1 m depth would be 9.81 kN m
-2
. Standard atmospheric
pressure is 1 atm = 101325 Pa = 1.01325 bar = 101.325 kN m
-2
= 760 mmHg. Therefore, there is
an increase in pressure of about 1 atm for each 10.33 m depth of water. For example, at a depth of
200 m, the pressure would be about 20.4 atm.
Some of the consequences of the increases in pressure are well known. One well-known impact
occurs for divers who would have elevated gas levels in their blood as a consequence of the increased
pressure and depths. If that pressure is reduced too rapidly for the excess gas to be expelled safely,
bubble formation would cause the “bends”, which could be fatal. Similarly, gas bubble disease can
occur in ish below dams where, rather than depth, the momentum of falling water results in pressure
increases. The increase in pressure and the resulting gas concentrations are also of importance for
some of the practices used to increase the oxygen concentration in reservoir releases, such as through
the injection of oxygen into the hypolimnion near the dam. The increased pressure will also cause
gases to be rapidly lost to the atmosphere when reservoir releases are from deep in the reservoir, such
as hypolimnetic releases from hydropower operations. The hypolimnetic waters are often devoid of
oxygen during summer and fall, and have high concentrations of anaerobic materials, such as meth-
ane, hydrogen sulide, and ammonia, which can cause odor or toxicity problems in the tailwaters.
One extreme case of degassing from deep gas-saturated waters is known as a limnetic eruption.
The equilibrium solubility of a gas bubble at a speciied depth can be computed from the sum of
the air and hydrostatic pressures:
P
t
=+
BP
k gz
ρ
(14.4)
where
P
t
is the total pressure (mmHg)
BP is the air (barometric) pressure at the water surface (760 mmHg)
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