ARTICLE IN PRESS
WAT E R R E S E A R C H
40 (2006) 259 – 266
Available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/watres
A different approach for predicting H2S(g) emission rates in
gravity sewers
Ori Lahav, Amitai Sagiv, Eran Friedler
Faculty of Civil and Environmental Engineering, Technion, Haifa 32000, Israel
art i cle info
ab st rac t
Article history:
All detrimental phenomena (malodors, metal corrosion, concrete disintegration, health
Received 28 December 2004
hazard) associated with hydrogen sulfide in gravity sewers depend on the rate of H2S
Received in revised form
emission from the aqueous phase to the gas phase of the pipe. In this paper a different
23 September 2005
Accepted 26 October 2005
approach for predicting H2S(g) emission rates from gravity sewers is presented, using
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
g S V=m; S is the
concepts adapted from mixing theory. The mean velocity gradient (G ¼
Available online 15 December 2005
slope, V the mean velocity), representing mixing conditions in gravity flow, was used to
Keywords:
quantify the rate of H2S(g) emission in part-full gravity sewers. Based on this approach an
H2S emission
emission equation was developed. The equation was verified and calibrated by performing
Gravity sewers
20 experiments in a 27-m gravity-flow experimental-sewer (D ¼ 0:16 m) at various hydraulic
Gas transfer
Mean velocity gradient
conditions. Results indicate a clear dependency of the sulfide stripping-rate on G1
(R2 ¼ 0:94) with the following overall emission equation:
!
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w
d½ST ST
1:024ðT20Þ
P
K
¼ 8 107 g S V=m
p H2 S H ,
Ks1
K Ks2
dt
Acs
1 þ 10pH
þ 10s12pH
where ST is the total sulfide concentration in the aqueous phase, mg/L; w the flow surface
width, m; Acs the cross-sectional area, m2; T the temperature, 1C; KH the Henry’s constant,
mol L1 atm1; and PpH2S the partial pressure of H2S(g) in the sewer atmosphere, atm.
& 2005 Elsevier Ltd. All rights reserved.
1.
Introduction
The sulfide cycle in sewers has been investigated and
modeled extensively in recent years because of the welldocumented detrimental effects associated with sulfides: the
release of rotten-egg odors, health hazard to maintenance
personnel, and the enhancement of metal corrosion and
concrete disintegration. All these phenomena, invariably
occurring in gravity sewage collection systems, are related
directly to the accumulation (and/or subsequent oxidation) of
H2S(g) in the gas space above the flow surface. While bad odors
and toxicity are caused directly by H2S(g), the enhancement of
metal corrosion and cement dissolution is a two-step process:
Corresponding author. Tel.: +972 4 8292191; fax: +972 4 8228898.
E-mail address: [email protected] (O. Lahav).
0043-1354/$ - see front matter & 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.watres.2005.10.026
H2S(g) diffuses from the gas phase and is absorbed into the
slime layer on the sewer wall and crest, where it is aerobically
oxidized to (mainly) sulfate releasing two equivalents of H+.
The flux of H2S(g) into the slime layer and the acidity released
due to its oxidation typically exceed the buffering capacity of
the minimal volume of liquid present in the biofilm, resulting
in a sharp pH drop that expedites both metal corrosion and
cement dissolution. In contrast, sulfides that are oxidized in
the aqueous phase normally cause no harm because of the
high buffering capacity of the bulk sewage.
Since H2S in sewers is generated in the aqueous phase
(mainly by biological sulfate reduction), but has to be released
to the gas phase in order to become harmful, the conditions
ARTICLE IN PRESS
260
WA T E R R E S E A R C H
that enhance its transfer, and the associated emission
kinetics, are of obvious importance. Consequently, prediction
of hydrogen sulfide emission rates into the sewer gas phase is
a prerequisite for a better control over sulfide-related
problems in sewer collection systems.
Despite the significance of H2S emission kinetics only a
handful of publications are found in the literature on this
matter. These are divided, by and large, between two main
approaches: (i) empiric models that link sulfide stripping with
parameters that describe flow conditions (mean flow velocity,
sewer slope) or turbulence (Reynolds or Froude numbers), and
(ii) adaptation of sewer reaeration models in which the gas
transfer coefficient of sulfide replaces the gas transfer
coefficient of oxygen.
Representing the first group of models, the Pomeroy–Parkhurst empiric equation (Pomeroy and Parkhurst, 1977) is by
far the most widely used for predicting sulfide buildup in the
aqueous phase of gravity sewers (Delgado et al., 1998;
Gostelow et al., 2001; Tanaka and Hvitved-Jacobsen, 2001).
The equation, developed using field data gathered from
gravity sewers in the Los Angeles county sanitation district,
consists of two terms: the first predicts the rate of sulfide
generation in the sewer and the second represents the rate of
sulfide disappearance from the aqueous phase (i.e. the
combined effect of biological sulfide oxidation, sulfide stripping, and indirectly, the effect of natural ventilation and
sulfide oxidation in the gas phase of the sewer):
d½ST ¼ 0:32 103 ½BODð1:07ÞðT20Þ
dt
1
0:64ðS VÞð3=8Þ ½ST dm ,
ð1Þ
where [ST] is the total sulfide concentration (mg/L), S the
sewer’s slope (m/m), V the mean flow velocity in the sewer
(m/s), dm the ‘‘hydraulic depth’’; cross-sectional area of the
flow divided by the flow width (m), t the time (h), T
the temperature (1C), BOD the biochemical oxygen demand
(mg/L).
Out of the three processes described by their second term,
Pomeroy and Parkhurst (1977) explicitly stated that the
oxidation of sulfide in the aqueous phase is the dominant
process, and that stripping from the aqueous phase to the gas
phase was ‘‘minimal’’.
Citing Pomeroy, the EPA Design Manual for Odor and
Corrosion Control (1985) suggested a similar approach to
specifically quantify sulfide emission rates. In contrast with
the original approach the sulfide removal rate is proportional
to the H2S(aq) concentration rather than to the total sulfide
concentration:
d½ST 1
¼ 0:69ðS VÞð3=8Þ ½H2 SðaqÞ dm .
dt
(2)
More recently, a modified sewer reaeration model has been
used to describe H2S emission rates in sewers, and the
emission component was incorporated into a comprehensive
model that describes the overall sulfide cycle in sewers
(Yongsiri et al., 2003, 2004a, b). This approach first quantifies
the overall mass transfer coefficient for H2S (KL aH2 S ) at varying
turbulence levels (as represented by Froude number), temperatures, ionic strengths and pH values, and links it with the
overall mass transfer coefficient of oxygen (Yongsiri et al.,
40 (2006) 259– 266
2003):
KL aH2 S ¼ ð1:736 0:196 pHÞKL aO2
ðat 4:5opHo8:0Þ.
ð3Þ
Subsequently, a previously developed oxygen-transfer equation (Parkhurst and Pomeroy, 1972), developed to predict
sewer reaeration rates (Eq. (4)), was transformed to represent
the sulfide emission rate by incorporating Eq. (3) into Eq. (4),
to yield Eq. (5).
1
,
KL aO2 ¼ 0:86 1 þ 0:2 Fr2 ðS VÞ3=8 dm yðT20Þ
r
(4)
1
KL aH2 S ¼ 0:86 1 þ 0:2 Fr2 ðS VÞ3=8 dm yðT20Þ
r
ð1:736 0:196 pHÞ,
ð5Þ
pffiffiffiffiffiffiffiffiffiffi
where Fr ¼ V= g dm , yr is the temperature coefficient for
reaeration ¼ 1.024, and T the temperature (1C).
The current paper aims at developing a new H2S emission
equation that is not based on either of the two approaches.
The incentive was two-fold: first, the Pomeroy–Parkhurst
equation (Pomeroy and Parkhurst, 1977) was developed under
conditions where sulfide stripping was not the dominant
phenomenon controlling the elimination of sulfide from the
aqueous phase, and second, it was observed in previous
works (Lahav et al., 2004, in press) that gas transfer
coefficients derived from completely stirred vessels somewhat over-predict the emission rates observed under the
typical flow conditions that develop in gravity sewers. This
empirical observation may be explained as follows: Because
the vertical mixing in gravity flow is less than complete (for
the G values normally encountered in gravity flow in sewers),
a vertical H2S(aq) concentration gradient builds up. Therefore,
a below-average concentration of H2S(aq) is typically present
at the liquid–gas interface, resulting in low gas transfer rates.
Conversely, in completely mixed containers, no such gradient
occurs, and H2S(aq) concentration close to the liquid–gas
interface is (practically) the average bulk concentration,
resulting in higher experimental KL values. Therefore, it is
doubtful, in our opinion, that KL a values derived in stirred
batch experiments, as in the approach presented by Yongsiri
et al. (2003), are readily suitable for predicting gas emissions
in gravity sewers.
The current paper seeks to develop a term that specifically
deals with the stripping phenomenon. Preliminary results
obtained from emission experiments in an artificial gravity
sewer operated at relatively high slopes (1–3%) with no
biological activity indicated that the prediction of the
Pomeroy—Parkhurst equation and its derivatives, and other
approaches, considerably underestimate the actual emission
rates.
The hypothesis of the current work was that sulfide
emission rate is proportional to the head loss in gravity
sewers. To represent the head loss, a parameter, G, adapted
from mixing theory was used. A theoretical equation was
developed, verified and calibrated in an artificial sewer, where
controlled experiments could be conducted at conditions
where sulfide stripping was the only process affecting the
concentration of sulfide in the aqueous phase.
ARTICLE IN PRESS
WAT E R R E S E A R C H
261
40 (20 06) 25 9 – 266
2.
Materials and methods
above 1.5 h before oxidation begins was reported at pH values
lower than 7.2 (Chen and Morris, 1972).
2.1.
Experimental sewer
2.3.
Materials
Experiments were carried out in a 27 m long PVC sewer pipe,
with internal diameter of 0.16 m. Schematic of the experimental sewer is given in Figure 1. The pipe consisted of 3 m
long sections joined by rubber seals. The sewer pipe was
placed on a rig with an adjustable incline that enabled varying
the slope between 0% and 3%. It was estimated that the actual
slope did not deviate by more than 0.018% from the desired
average slope (i.e. not more than an error of 0.005 m over
27 m). In order to enable appropriate ventilation of the
gaseous phase in the pipe, ventilation ‘‘windows’’ were cut
in the PVC pipes in eight out of nine pipe sections, leading to
60% of the total pipe length being fully open to the atmosphere. In addition, a powerful air-suction pump was
operated during the experiments to ensure that the H2S(g)
partial pressure in the gas phase of the pipe would be
negligible. Other parts of the system included auxiliaries
utilized for circulating the simulative sewage solution: 2 HDPE
water tanks, the lower with an operational volume of 0.85 m3
and the upper with an operational volume of 0.27 m3. Both
tanks were sealed at the top at the beginning of each
experiment, and the water surface in the tanks was covered
with a floating plastic sheet.
The sulfide chemical that was used was always a fresh can of
non-hydrated Na2S of technical grade. H2S was first added to
the downstream container as 10-L concentrated solution to
make up for a concentration of 20 mg S/L (in the whole
system). Following this, the pumps were switched on and the
sulfide-containing water (at pH48.5) was recycled in the
whole system for a few minutes until steady flow was
attained. Because of the high pH, H2S losses during this short
stage were minimal. When steady flow was attained, a precalculated amount of HCl (32%) was added to the downstream
container in order to lower pH to 7.170.03. Once the pH was
stable sulfide measurements commenced. Using this technique, only an insignificant amount of sulfide escaped the
system before the start of the experiment, and in any event,
data was collected only when both pH and flow characteristics were steady. Tap water (pH around 7.8, alkalinity of
180–200 mg/L as CaCO3, negligible TOC, SS, iron and heavy
metals concentration, DO of about 6 mg/L and sulfate of about
20 mg S/L), to which phosphate buffer at 100 mg P/L was
added, was used in all experiments.
2.2.
Dissolved sulfide was sampled consistently at 20 m downstream (simultaneous sulfide measurements revealed that
the change in concentration of sulfide along the pipe at a
given time was negligible). A 2.3 ml water sample was
pipetted and inserted directly into a test tube containing
0.2 ml of a reagent mixture (N,N-dimethyl-p-phenylenediamine+FeCl3 6H2O+HCl)) according to the colorimetric method
proposed by Cline (1969). Special care was exercised to insert
the sulfide-containing sample below the water surface of the
test tube, so that sulfide would not be lost in the procedure.
Once the sulfide is mixed with the reagents it is immediately
oxidized to sulfate/elemental sulfur and thus cannot be
further lost. The time required for full color development is
20 min and thereafter color is stable for many hours.
Wavelength for spectrophotometer reading is 670 nm. The
colorimetric method was calibrated using the iodometric
method (Standard Methods, 1998).
2.4.
Methods
Minimization of possible biological activity: Twenty experiments,
each lasting between 1 and 4 h, were conducted over a period
of about 6 months. Thus, normally there would be a gap of at
least 1 week between experiments. After each experiment the
water was drained and the system was let to stand dry. Every
second run, the system was cleaned by passing it through
fresh tap water, and draining it. Since sulfide-oxidizing
bacteria are autotrophic, having low yield and slow growth
kinetics, these measures ensured practically no biofilm
formation, and thus absolutely negligible biological activity.
Heterotrophic sulfate reduction did not occur due to lack of
organic electron donor. Chemical sulfide oxidation by oxygen
was also not considered, as at pH 7.1, and in the absence of
catalysts, the rate constants in tap water are in the order of
days (Millero et al., 1987). Moreover, an induction period of
Sampling and analysis
27 m
ow
Aeration Wind
ow
ow
Aeration Wind
ow
Aeration Wind
ow
t
eigh
le h
stab
Adju
Adjustable height
Aeration Wind
Aeration Wind
Figure 1 – Schematic layout of the PVC experimental sewer and auxiliary systems.
ARTICLE IN PRESS
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WA T E R R E S E A R C H
40 (2006) 259– 266
Based on Eq. (7) the following general equation was
proposed to represent H2S emission rates as function of G:
3.
Development of the basic emission
equation
d½ST =dt ¼ K Gx
Conventionally, the rate of exchange of species between the
aqueous and gas phases is considered to be equal to the
product of the reaction’s driving force and a mass transfer
rate constant:
d½H2 Saq
As ½H2 Saq KH PH2 S ,
¼ KL
dt
8
(6)
where ½H2 Saq is the hydrogen sulfide concentration in the
aqueous phase (mol L1), t the time (s), KL the overall liquid–gas
transfer rate coefficient (s1), As the surface area between the
aqueous and gas phases (m2), 8 the aqueous phase volume
(m3), KH the Henry’s constant (mol L1 atm1), and PH2 S ¼ H2 S
the partial pressure in the sewer gas phase (atm).
Gas transfer models hinge round accurate prediction of the
transfer rate-coefficient, KL . Several theories were developed
to quantify KL, the most widely used being the so-called twofilm theory of Lewis and Whitman (1924). Regardless of the
theory used, it is accepted that (i) under turbulent conditions
the hydrodynamic film controls the transfer rate from the
liquid phase to the gas phase, i.e. the two-film reduces to a
one-film approach, and (ii) the gas transfer coefficient (KL )
increases when the liquid phase is agitated because the
thickness of the hydrodynamic film is reduced.
In engineering practice, the concept of ‘‘agitation’’ can be
replaced by controlled mixing (Peng et al., 1995). In a sewer
environment, mixing conditions depend on the hydraulic
flow characteristics, which have been linked to the head loss
along the line of flow (Camp, 1969).
In water treatment practice (particularly in theory developed for mixing conditions associated with the flocculation–
coagulation process) such head loss has been linked to a
mean velocity gradient parameter, G, that can be empirically
linked to flow characteristics. The parameter G reflects the
mixing conditions in a system; the higher the G value, the
better the mixing rate in the system (Camp, 1969). In simple
terms, G is a measure of the power imparted to a unit of
volume of water to effect mixing. In the approach presented
here it is hypothesized that linking G with the mass transfer
coefficient KL would allow predicting sulfide emission rates
simply by knowing the hydraulic and geometric characteristics of a sewer. The concept of using G as a measure of the
turbulence intensity and thus linking it with gas-transfer
rates is not new: Smith (1981) used this approach to predict
the volatilization rates of high-volatility chemicals from
water, and Peng et al. (1995) used it for determining the effect
of turbulence on volatilization rates of selected VOCs from
water.
By definition, the mean velocity gradient G depends on the
net power dissipated in the water (P) divided by the sample
volume (8) and the dynamic viscosity of the mixed liquid
(Bratby, 1980; Droste, 1997):
0:5
G ¼ P=ðm8Þ ,
(7)
where P is the net power dissipated in the water (N m s1), 8
the volume of mixed water sample (m3), m the dynamic
viscosity (N s m2).
As ½H2 Saq Pp H2 S KH ,
8
(8)
where K and x are the constants.
Using a standard flocculator with known G-to-mixingspeed characteristics, the rate of H2S(aq) emission from batch
reactors was measured in the laboratory and plotted against
time (Lahav et al., 2004). A regression procedure was then
used to fit a variety of possible equations to the experimental
data. It was found that for T ¼ 22 2 1C an excellent fit (as
attained by applying a least-square technique) between H2S
emission rate and all G values in a batch test was attained
when using the following equation (Lahav et al., 2004):
d½ST =dt ¼ K G2
As ½H2 Saq Pp H2 S KH .
8
(9)
In the same paper (Lahav et al., 2004) it was theoretically
hypothesized that Eq. (9) could be also used, after geometrical
adjustment, for predicting H2S emission rates from gravity
sewers. This hypothesis, i.e. that the stripping rate in gravity
sewers is a function of G2 , was refuted in the current work,
where a series of emission experiments were conducted in an
experimental sewer with the purpose of establishing the
dependency of the stripping rate on G, and determining the
rate constant.
3.1.
Applying the laboratory-derived reaeration rate
equation to a sewer system
To apply Eq. (8) in gravity sewers a term for G in straight flow
has to be developed. Droste (1997) states that the integral
dissipation function in a straight-line sewer system is
W ¼ P =8 ¼ ðg DHx Þ=t,
(10)
1
2
where W is the dissipation function (N s m ), g the unit
weight of liquid (N m3), t the retention time corresponding to
the mixing period (s), DHx the head loss in a straight pipe of
length x (m).
Combining Eq. (10) and Eq. (7), the expression for G
commonly used for static mixing devices can be derived:
0:5
(11)
G ¼ ðg DHx Þ=ðt mÞ .
Using a Lagrangian frame of reference, the retention time t
can be described as the length of the section, x, divided by the
flow mean velocity, V.
0:5
(12)
G ¼ ðg DHx VÞ=ðx mÞ ,
where G is now defined as a function of distance. In the case
of a uniform steady channel flow, DHx =x is equal to the sewer
slope, S. Hence, Eq. (12) becomes:
0:5 0:5
¼ g S V=m .
(13)
G ¼ ðg DHx VÞ=ðx mÞ
Combining Eqs. (8) and (13), and incorporating geometrical
considerations, the theoretical equation describing the stripping rate of H2S to the gas phase of a sewer can be written as
follows:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix
g S V=m
d½ST =dt ¼ K
w ½H2 Saq Pp H2 S KH ,
ð14Þ
Acs
ARTICLE IN PRESS
WAT E R R E S E A R C H
strength, and pH on the emission rate.
where w is the width of water flow at the inter-phase
water–air (m); Acs the cross-sectional area of flow (m2 ).
4.
Results and discussion
4.1.
Effect of temperature
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix w
d½ST ¼K
g S V=m
1:024ðT20Þ
dt
Acs
A series of batch experiments were conducted with two G
values (239 and 355 s1) and temperatures varying from 8 to
38.5 1C in order to quantify the effect of temperature on the
stripping rate. Statistical analysis (not shown) revealed that
the differences between emission rates as function of the
temperature can be largely eliminated by the addition of the
following term, suggested by EPA Design Manual for Odor and
Corrosion Control (1985), and frequently used in sulfide
emission equations (e.g. Yongsiri et al., 2003), to Eq. (14):
Temperature effect term ¼ 1:024ðT20Þ .
4.2.
4.3.
(15)
Based on equilibrium and mass balance considerations, the
equation for H2S(aq) concentration as function of ST and pH is
ST
,
1 þ Ks1 =10pH þ Ks1 Ks2 =102pH
!
ST
P
K
p H2 S H . ð17Þ
1 þ Ks1 =10pH þ Ks1 Ks2 =102pH
H2S emission experiments in the experimental sewer
Twenty experiments were conducted to find the dependency
of the stripping rate on G and to determine the value of the
rate constant, K. In all runs H2S(g) concentration was
assumed (and verified) negligible (see Materials and methods). The experimental conditions in all the runs are
summarized in Table 1. In all experiments the slope varied
between 1% and 3%, and average water velocity between 0.65
and 1.55 m/s, all parameters typical to hydraulic conditions
prevailing in medium to fast flowing sewers. The normalized
sulfide concentration in the aqueous phase in all the
experiments, as a function of the time, is summarized in
Figure 2. In order to find the best overall fit for the data
obtained from all the experimental sewer runs, Eq. (17) was
rearranged as follows:
Effect of pH
½H2 Saq ¼
263
40 (20 06) 25 9 – 266
(16)
Z
St
d½ST t
¼
½S T St¼0
where Ks1, Ks2 are the thermodynamic equilibrium constants
for the sulfide weak-acid system adjusted for Debye–Huckel
effects.
Thus, adding the term in Eqs. (15) and (16) to Eq. (14) will
incorporate the effects of both the temperature, ionic
Z
t
K
0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix w
g S V=m
1:024ðT20Þ
Acs
1
dt,
1 þ Ks1 =10pH þ Ks1 Ks2 =102pH
ð18Þ
where [ST]t is the total sulfide concentration at time t.
Table 1 – Hydraulic condition in the experimental-sewer runs
Exp. no.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
a
Calculateda G
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
g S V=m
m s1
Exposed
volume/total
vol. (8exp/8T)
m3 m3
0.65
0.85
0.90
0.96
1.29
0.98
1.08
1.13
1.21
1.35
1.01
1.12
1.24
1.33
1.46
0.96
1.14
1.31
1.38
1.55
0.036
0.064
0.074
0.088
0.183
0.040
0.051
0.057
0.066
0.086
0.034
0.043
0.054
0.064
0.080
0.024
0.036
0.050
0.056
0.073
238.4
271.1
279.1
289.5
334.4
412.0
433.3
443.5
458.3
485.2
469.2
494.0
519.8
538.6
564.4
499.9
544.8
585.3
600.6
635.7
Temp.
Slope (S)
Flow rate (Q)
Hydraulic
depth (Acs/w)
Average
velocity (V)
(1C)
(%)
m3 s1
m
23
27.3
27.7
30.2
24.5
16.8
21.6
22.9
30.8
25.2
24.2
31.3
24.6
29.6
29.6
28.1
30.3
27.4
30.1
28.7
1
1
1
1
1
2
2
2
2
2
2.5
2.5
2.5
2.5
2.5
3
3
3
3
3
0.0015
0.0036
0.0044
0.0057
0.075
0.0025
0.0036
0.0042
0.0052
0.0078
0.0021
0.0032
0.0044
0.0056
0.0078
0.0014
0.0026
0.0042
0.0051
0.0075
0.019
0.030
0.033
0.039
0.089
0.021
0.025
0.027
0.031
0.038
0.018
0.022
0.026
0.030
0.036
0.014
0.019
0.024
0.027
0.033
G is calculated at 20 1C. Temperature effects were incorporated into the model as shown in Eq. (20).
s1
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WA T E R R E S E A R C H
a
all expll exp
(1%,G=290 1/s)
(2%,G=411 1/s)
(2.5%,G=564 1/s)
(3%,G=544 1/s)
(3%,G=585 1/s)
40 (2006) 259– 266
1%,G=238 1/s)
(1%,G=334 1/s)
(2%,G=443 1/s)
(2.5%,G=493 1/s)
(3%,G=635 1/s)
Linear (all exp)
(1%,G=271 1/s)
(2%,G=485 1/s)
(2%,G=458 1/s)
(2.5%,G=519 1/s)
(3%,G=500 1/s)
(1%,G=279 1/s)
(2%,G=433 1/s)
(2.5%,G=469 1/s)
(2.5%,G=538 1/s)
(3%,G=600 1/s)
5.0
4.5
4.0
ln So/STt
3.5
3.0
2.5
y = 8E-07x
R2 = 0.9389
2.0
1.5
1.0
0.5
0.0
0.E+00
2.E+06
4.E+06
6.E+06
∀
1
w
⋅1.024(T−20)
. exp t
( ⋅ S ⋅ V / )
Ks1 Ks1Ks2 ∀T
Acs
+
1+
10−pH 10−2pH
Figure 2 – Linear regression of all data collected in the 20 experimental sewer runs, under the assumption that sulfide
emission rate is proportional to G1 (K ¼ 8 07).
Integration of Eq. (18) yields:
ln
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix w
½ST t
¼K
g S V=m
1:024ðT20Þ
½ST 0
Acs
1
t,
1 þ Ks1 =10pH þ Ks1 Ks2 =102pH
ð19Þ
where [ST]0 is the total sulfide concentration at t ¼ 0.
In the experimental sewer the water was exposed to the gas
phase (where H2S transfer occurs) only a small fraction of the
total time (between 3.4% and 18.3% in the various experiments). The exposure time can be expressed as the ratio
between the water volume present at any given time in the
gravity pipe (8exp) and the total volume of water in the system
(8T). In order to compensate for this phenomenon and to
calculate the stripping rate as in an infinite sewage pipe, this
fraction was calculated in each of the experiments and added
to Eq. (19) as follows:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix w
½ST t
¼K
g S V=m
1:024ðT20Þ
ln
½ST 0
Acs
8exp
1
t,
1 þ Ks1 =10pH þ Ks1 Ks2 =102pH 8T
ð20Þ
where 8exp is the volume of water in the gravity pipe, in a
particular experiment (m3), and 8T the total volume of water
in the system (m3).
To plot Figure 2 the raw data was manipulated in the
following manner: the measured H2S(aq) concentration at any
given time was inserted into the left-hand side of Eq. (20) to
yield the Y-axis value, while the time was inserted into the
right-hand side to form the X-axis. The slope (S), velocity (V),
flow width (w), and flow cross-sectional area (Acs ) were
calculated individually (and verified empirically) for each
run. The initial sulfide concentration [ST]0 aimed at was 20 mg
S/L, and pH was maintained at 7.170.03.
The best fit (R2 ¼ 0:94) with the data was attained for x ¼ 1,
suggesting that the sulfide emission rate is proportional to G1
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(or to g S V=m), with a constant K ¼ 8 107 . The calibrated
emission equation is thus:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w
d½ST ¼ 8 107 g S V=m
1:024ðT20Þ
dt
Acs
0
1
ST
1þðKs1 =10pH ÞþðKs1 Ks2 =102pH Þ
@
A.
Pp H2 S KH
ð21Þ
Considering the inherent inaccuracy associated with such
complex experiments and analyses, the minor scattering of
data points shown in Figure 2 is satisfactory. The accuracy of
the prediction is even better as demonstrated in Figures 3A–D,
which show the raw data of four representative experiments
plotted vs. the prediction curves of the current model, the
Pomeroy and Parkhurst (1977) approach, and the approach of
Yongsiri et al. (2003). Figure 3 shows that Eq. (21) fits the
experimental data exceptionally well, and that the other
approaches show considerably slower emission rates, which
result in much higher-than-observed sulfide concentrations
in the aqueous phase. This trend was consistent in all the
ARTICLE IN PRESS
WAT E R R E S E A R C H
25
(A)
20
PP
(B)
25
PP
20
15
15
10
10
Yongsiri
5
ST (mg S L-1)
265
40 (20 06) 25 9 – 266
Yongsiri
5
Eq. (21)
Eq. (21)
0
0
0
130
260
25
390
(C)
20
0
80
25
15
PP
15
Yongsiri
10
Yongsiri
10
5
5
Eq. (21)
Eq. (21)
0
0
0
240
(D)
20
PP
160
60
120
0
180
Time (min)
50
100
150
Figure 3 – (A–D). Measured and predicted H2S(aq) concentration vs. time in four selected experiments (experiments no. 1, 7, 15,
and 20 in Table 1). PP ¼ Pomeroy and Parkhurst (1977), Yongsiri ¼ Yongsiri et al. (2003).
experiments performed, regardless of the hydraulic conditions (in all experiments Yongsiri’s prediction was closer to
the actual observation than the prediction of the Pomeroy–
Parkhurst equation). For example, in experiment 20 (Table 1),
a drop in sulfide concentration from 22 to 5 mg S L1 that
lasted in reality 46 min, was predicted to be completed in
136 min by the Yongsiri equation. According to Pomeroy and
Parkhurst’s approach such drop in sulfide concentration
should have taken 468 min, i.e. about 10 times more than
the actual stripping period.
Note: In order to account for the difference between tap
water and sewage, two well-known correction factors should
be empirically measured and incorporated into Eq. (21)
(Droste, 1997): a—to compensate for the difference in TDS
and surface tension; and b—to compensate for the difference
in the saturation concentration of H2S, resulting from
different TDS concentration, presence of particulates, and
surface-active substances.
5.
Conclusions
A new equation aimed at predicting sulfide emission rates
from gravity sewers, as function of the hydraulic conditions,
was developed. The equation was tested, verified, and
calibrated in an artificial sewer, under tightly controlled
conditions. It would appear that the new equation, that is
neither based on the traditional Pomeroy and Parkhurst (1977)
sulfide equation, nor on the Parkhurst and Pomeroy reaeration equation (1972) or its modifications, could be considered
a realistically accurate tool for predicting the flux of H2S(g)
released to the gas phase of gravity sewers. It is noted that in
order to implement the model equation in real sewers, Eq. (21)
should be incorporated into a comprehensive model that
includes all other phenomena affecting the sulfide concentration in sewers. However, we believe that in certain
circumstances, where stripping is by far the most dominant
mechanism, (such as in fast flowing, very turbulent flow
patterns, with low d/D ratio, and relatively low pH) Eq. (21)
might yield reasonable results even when used as a standalone model.
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