Environmental Engineering Reference
In-Depth Information
4.6 MODELS OF PATHOGENS
the total depth of the stream (m),
f
p
is the fraction of
bacteria that are attached to suspended sediment
(dimensionless), and
v
s
is the settling velocity (m/d).
Under usual circumstances,
α
is approximately equal to
unity;
k
e
can be estimated by
Pathogens are generally tracked via indicator organ-
isms, and the most widely used indicator organisms in
(freshwater) streams are fecal coliform (FC) and
Esch-
erichia coli
. In cases of significant salinity, such as river-
ine estuaries, enterococci are the preferred indicator
organisms. Pathogen contamination is sometimes
referred to simply as
bacteria contamination
, and is the
leading cause of water-quality impairment of streams in
the United States (USEPA, 2008). Models of FCs in
streams can be classified as either deductive or induc-
tive. Deductive models are based on defined process
equations that are solved either analytically or numeri-
cally, while inductive models relate FC levels using
either regression or artificial intelligence-based rela-
tionships. Inductive models typically relate the average
daily FC levels to variables that include flow rate and
turbidity (Tufail et al., 2008).
The dieoff of indicator organisms is typically
described as a first-order process of the form
1.8
k
=
or
k
=
0.55
c
(4.154)
e
e
ss
SD
where SD is the Secchi disk depth (m) and
c
ss
is the
suspended solids concentration (mg/L); and
f
p
can be
estimated using the relation
K c
K c
d
ss
f
=
(4.155)
p
1
+
d
ss
where
K
d
is the partition coefficient for bacteria on
suspended sediment (m
3
/g).
EXAMPLE 4.22
dc
dt
Secondary-treated wastewater is discharged into a
freshwater stream, and on exiting the mixing zone, the
river water has a suspended solids concentration of
80 mg/L and a temperature of 15°C. Laboratory tests on
the mixed river water indicate that the suspended solids
have an average settling velocity of 0.3 m/d, and the
indicator bacteria have a distribution coefficient of
0.8 L/mg on the suspended solids. The average light
energy on the water surface is 400 Ly/d, the depth of the
stream is 3.0 m, and the average flow velocity is 2 cm/s.
Estimate the distance required for 90% attenuation of
the indicator bacteria.
= −
k c
(4.149)
b
where
c
is the bacteria concentration (ML
−3
),
t
is time
(T), and
k
b
is the loss rate (T
−1
). Typical units used for
bacteria concentration are CFU/100 mL or CFU/dL,
where “CFU” is an acronym for “colony forming units.”
Key factors affecting the value of
k
b
are temperature,
salinity, light, and sedimentation. The influence of these
factors on
k
b
can be separated by expressing
k
b
as
k
=
k
+
k
+
k
(4.150)
b
b1
b
2
b3
where
k
b1
,
k
b2
, and
k
b3
are the baseline mortality rate, the
loss rate due to light, and the loss rate due to settling,
respectively. These parameters in units of d
−1
can be
estimated as follows (Chapra, 1997)
Solution
From the given data:
S
= 0 ppt (freshwater),
c
ss
= 80 mg/L,
T
= 15°C,
v
s
= 0.3 m/d,
K
d
= 0.8 L/mg,
I
0
= 400 Ly/d =
16.67 Ly/h,
H
= 3.0 m, and
V
= 2 cm/s = 1728 m/d. It
will be assumed that
α
= 1, which is typical. The follow-
ing parameters can be derived from the given data:
T
−
20
k
=
(0.8 0.02 )1.07
+
S
(4.151)
b1
I
k H
α
0
(
)
k
=
1
−
e
k H
−
(4.152)
e
b2
−
1
e
k
=
0.55
c
=
0.55(80)
=
44.0
m
e
ss
v
H
s
k
=
f
(4.153)
K c
K c
(0.8)(80)
1 (0.8)(80)
b3
p
d
ss
f
=
=
=
0.9846
p
1
+
+
d
ss
where
S
is the salinity (ppt or g/L),
T
is the temperature
(°C),
α
is a proportionality constant (dimensionless),
I
0
is the average light energy incident on the water surface
(Ly*/h),
k
e
is the light extinction coefficient (m
−1
),
H
is
k
=
[0.8 0.02 ]1.07
+
S
T
−
20
=
[0.8 0.02(0)]1.07
+
15 20
−
b1
−
1
=
0.5704
d
I
k H
α
0
(1)(16.67)
(44)(3.0)
(
)
=
(
)
k
=
1
−
e
−
k H
e
1
−
e
−
(44)(3.0)
b2
e
=
0.1263
d
−
1
*
1 langley (Ly) = 1 J/m
2
.
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