H2S emission dynamics in sewers are conditioned by the mass transfer coefficient at the interface. This work aims at measuring the variation of the mass transfer coefficient with the hydraulic characteristics, with the objective of estimating H2S emission in gravity pipes, and collecting data to establish models independent of the system geometry. The ratio between the H2S and O2 mass transfer coefficient was assessed in an 8 L mixed reactor under different experimental conditions. Then, oxygen mass transfer measurements were performed in a 10 m long gravity pipe. The following ranges of experimental conditions were investigated: velocity flow [0–0.61 m.s−1], Reynolds number [0–23,333]. The hydrodynamic parameters at the liquid/gas interface were calculated by computational fluid dynamics (CFD). In the laboratory-scale reactor, the O2 mass transfer coefficient was found to depend on the stirring rate (rph) as follows: KL,O2 = 0.016 + 0.025 N3.85. A KL,H2S/KL,O2 ratio of 0.64 ± 0.24 was found, in accordance with previously published data. CFD results helped in refining this correlation: the mass transfer coefficient depends on the local interface velocity ui (m.h−1): KL,O2 = 0.016 + 1.02 × 10−5ui3.85 In the gravity pipe device, KL,O2 also exponentially increased with the mean flow velocity. These trends were found to be consistent with the increasing level of turbulence.

correlation, gravity pipe, H2S emission, local turbulence intensity, numerical simulation, reaeration
a

specific interfacial area (m2.m−3)

ax

correlation coefficient (m.h−1)

bx, cx

correlation coefficients (–)

CL,i

concentration in liquid phase of component i (mg.L−1)

CS,i

saturation concentration of component i (mg.L−1)

d

stirrer diameter (m)

Dm,i

diffusivity coefficient of component i (m2.s−1)

dm

hydraulic mean depth (m)

dh

hydraulic diameter (m)

Fr1

Froude number for agitation (–)

Fr2

Froude number for flow (–)

g

standard gravity (m.s−2)

h

the vortex deformation (height h = hmax–hmin) (m)

k

turbulent kinetic energy (m2.s−2)

KL,i

overall mass-transfer coefficient of component i (m.h–1)

N

stirring rate (s−1)

n

coefficient

Re1

Reynolds number for mixing (–)

Re2

Reynolds number for flow (–)

Rei

interface Reynolds number (–)

Rh

hydraulic radius (m)

s

slope (m.m−1)

S

wetted surface (m2)

t

time (t)

u

flow velocity (m.s−1)

ui

weighted velocity at the interface (m.h−1)

z

distance (m)

ɛ

turbulent energy dissipation (m2.s−3)

μL

viscosity of water (Pa.s−1)

ρL

density of the continuous phase (kg.m−3)

The relation between concrete corrosion and hydrogen sulfide emission was identified more than a century ago. Sulfide is produced by sulfate-reducing bacteria under the form of dissolved H2S, which can be emitted into the atmosphere. Accumulation of H2S in the sewer atmosphere in gravity sewer systems is a detrimental phenomenon for several reasons. First, in the presence of oxygen, sulfide is oxidized in sulfuric acid, which is corrosive and causes the disintegration of cement materials. This phenomenon is a real economic loss for communities, because it requires an accelerated rehabilitation and pipe replacement frequency. Second, inhalation of H2S, even at relatively low concentrations, is toxic to humans. Many deaths during routine maintenance in sewers have been attributed to H2S toxicity. The sulfide problem will be accentuated in the future because of the temperature increase and the need to expand the cities. Consequently, understanding the fate of sulfide is a major challenge for better management of sewer systems. If the mechanism of sulfide production is quite known, its emission into the atmosphere is less described and deserves more attention (Carrera et al. 2015). Since H2S is produced in anaerobic conditions, the sulfuric cycle is linked to oxygenation. The oxygen concentration in wastewaters and hydrogen sulfide emission both depend on liquid-gas transfer phenomena in sewers (USEPA 1974).

The dynamics of H2S emission are conditioned by the liquid-gas mass transfer flux. This flux depends, on the one hand, on the difference between the concentration of H2S in the bulk liquid and the concentration at saturation (given by Henry's law) and, on the other hand, on the mass transfer coefficient and the exchange area. The mass transfer coefficient is, among others, responsible for the dynamics of H2S concentrations in the sewer atmosphere and has received growing attention; it is now commonly accounted for in dedicated models such as the WATS model (Yongsiri et al. 2003). The study of the sulfide liquid-gas mass transfer at laboratory scale and in situ is complex due to the hazardous properties of this gas and the lack of sensitive on-line analytical procedures. In addition, accurate methods have to be developed since many phenomena occur simultaneously in real systems, such as H2S build-up, H2S biological oxidation, oxygen uptake by microorganisms, etc. As a consequence, the direct determination of mass transfer coefficients in a real sewer is a very difficult task. Two main approaches have been developed in the literature: (i) empirical or theoretical connections between oxygen and hydrogen sulfide transfer coefficients; (ii) empirical models linking the sulfide emission to flow parameters.

The measurement of the mass-transfer coefficient for H2S is more difficult than for oxygen, because the available measurement methodologies are: (i) the methylene blue method, a sensitive off-line analytical procedure that restrains the sampling frequency and the data acquisition possibilities; (ii) on-line probe, which still lacks data feedback in literature. Consequently, the mass-transfer for H2S has not been studied in the field and barely at laboratory scale. Therefore, one of the objectives of the present work was to measure the H2S mass transfer coefficient with an on-line sensor, and to compare it with the O2 mass transfer coefficient. Theoretically, mass transfer limitations are localized at the liquid side in the laminar diffusion layer, and are related to the diffusivity of the species in water according to Equation (1) (Perry & Green 1985):
formula
1
Nevertheless, the exponent 0.5 may not be fully representative of all the hydrodynamic conditions encountered in real sewer networks, and an alternative relation was proposed (Equation (2)), where n is comprised between 0.5 and 1.
formula
2

Yongsiri et al. (2004a, 2004b) experimentally found a constant ratio KL,H2S to KL,O2 of 0.86 ± 0.08 at 20 °C. According to the literature, the gas-liquid oxygen mass transfer is strongly influenced by the flow conditions (Table 1). The models gathered in Table 1 were established based on indirect field measurements. These correlations account for the flow, the slope, the pipe geometry and the turbulence level of the system.

Table 1

Empirical models for gas-water oxygen mass transfer coefficients

Reaeration Estimation Model
Authors a expression  
Krenkel & Orlob (1962)   (3) 
Owens et al.(1964)   (4) 
Parkhurst & Pomeroy (1972)   (5) 
Taghizadeh-Nasser (1986)   (6) 
Jensen (1995)   (7) 
Reaeration Estimation Model
Authors a expression  
Krenkel & Orlob (1962)   (3) 
Owens et al.(1964)   (4) 
Parkhurst & Pomeroy (1972)   (5) 
Taghizadeh-Nasser (1986)   (6) 
Jensen (1995)   (7) 
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Since the available models (Table 1) estimate global transfer coefficients and refer to parameters depending on the system geometry (dm, Rh), it would be useful to dispose of models independent of the geometric dimensions of the system. For this purpose, the main idea was to establish a link between the local mass transfer coefficient and local data, collected at the interface, which is basically not related to the size of the system. The objectives of this work were thus:

  • to measure the KL of H2S and O2 in the same experimental device in order to estimate the ratio between the two components;

  • to compute the local liquid velocities near the interface by computational fluid dynamics (CFD) in order to correlate the measured KL to the local hydrodynamic parameters;

  • to perform a similar analysis in a gravity pipe device by investigating the O2 mass transfer coefficient and derive a correlation based on local hydrodynamic parameters.

Mass transfer coefficient KL in a small reactor

Experimental approach

Batch experiments were performed in an 8 L capacity cylindrical reactor. The temperature was fixed at 20 °C (±0.5 °C) and regulated by water circulation in a water jacket. Stirring was ensured by a Rushton turbine made of four symmetric blades. For all experiments, the stirring velocity N was set between 50 and 140 rpm and controlled by a tachymeter. The calculated dimensionless numbers for stirring were:
formula
8
formula
9
The range of values for the stirring velocity corresponds to Reynolds numbers [8,333–23,333] and Froude numbers [0.007–0.015]. Those mixing conditions were chosen to fall in the turbulent flow regime, which intensifies the mass transfer. The vessel had an interfacial area to volume a comprised between 4.73 and 5.11 m−1 depending on the surface deformation, which was accounted for by considering the shape of the vortex as a truncated cone. The O2 mass transfer coefficient was measured according to the conventional re-oxygenation method (American Society of Civil Engineers 2003; Capela et al. 2004). The experimental procedure consisted of depleting the O2 content in the liquid phase by adding an adequate amount of sulfite (Na2SO3, CAS 7757-83-7) and 1 mg/L of cobalt as a catalyzer (CoSO4, CAS 10026-24-1). O2 was monitored with an oximeter installed 6 cm under the liquid/gas interface (Mettler-Toledo easySense O2 21 Oxygen Sensor) and plugged to a computer device and software. The response time of the dissolved oxygen (DO) probe was experimentally checked: during the experimental period it ranged from 25 to 35 seconds, which is far below the duration of the experiment (several hours). The reactor headspace was open to the atmosphere, in order to keep the oxygen concentration constant in the gaseous phase. Based on the two film theory, the oxygen concentration during re-oxygenation varied according to Equation (10):
formula
10
The model was fitted to the experimental data with EXCEL solver. The adjusted parameters were and Cs,O2.
For H2S experiments, the experimental device was isolated from the atmosphere and purged with N2 to avoid any chemical reaction between O2 and H2S, and H2S accumulation. The determination of the mass transfer coefficient was made on the basis of a degassing technique. The principle was: (i) to create oversaturated conditions by adding a solution of sodium sulfide (Na2S, 9H2O, CAS 1313-84-4) in the liquid phase. The sulfide is mostly in the form of HS− (at pH >8); (ii) to inject a small HCl drop in order to decrease the pH and to turn HS− into H2S, (iii) to measure the decrease in H2S concentration with the AQUA-MS probe MS-08, composed of an amperometric sulfide probe combined with pH and temperature measurements; (iv) to model the H2S concentration decrease to determine the mass transfer coefficient. A typical degassing curve for H2S is shown in Figure 1.
Figure 1
Figure 1. Typical experimental result for H2S mass-transfer coefficient determination.
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Typical experimental result for H2S mass-transfer coefficient determination.

Figure 1
Figure 1. Typical experimental result for H2S mass-transfer coefficient determination.
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Typical experimental result for H2S mass-transfer coefficient determination.

Close modal
The variation of concentration was supposed to follow an equation similar to Equation (10):
formula
11
where CL,0 is the concentration at t=t0.
The model was fitted to the experimental results with EXCEL solver, by adjusting and Cs,H2S. Indeed, the theoretical Cs for H2S should be 0 since the reactor headspace was continuously purged with N2. Nevertheless, in practice the value of 0 did not give consistent results and had to be fitted (fitted values lower than 0.2 mg/L). The aim of this experimental part was to establish an empirical correlation between KL (m.h−1) and the mixing velocity (rph) by means of the ordinary least squares (OLS) method, in the form of:
formula
12
with a1, b1 and c1 being three distinct constants for O2 and H2S. The ratio was then determined according to the different hydrodynamic conditions investigated. The results were obtained in clear water (tap water), but could be transferable to real sewers since the ratio between KL between clear water and wastewater is expected to be known from previous work (Yongsiri et al. 2004a, 2004b).

Numerical approach

CFD was used to describe the hydrodynamic conditions near the liquid – gas interface where the mass transfer mainly occurs (Yang & Mao 2014). The ICEM CFD™ was used as a mesh generator, and FLUENT™ v.14 software was used for modeling the flow pattern and the distribution of the liquid and the gas phases along the flow. A two-fluid model with the volume of fluid (VOF) method was used in order to characterize the free water surface. The kε-RNG model was chosen to simulate the gas-liquid turbulence. This model is usually employed to simulate multiphase flow (Paul et al. 2004): the kε-RNG model is based on transport equations for the turbulent kinetic energy k and its dissipation rate ɛ. Furthermore, the effect of swirl on turbulence was included in the RNG model. In the present study, the kɛ-RNG model was chosen to strike a balance between predictive accuracy and computational economy (CFD On line 2016). The simulation was validated by: (i) the y+ dimensionless number (between 20 and 100), which accounts for the flow velocity and the turbulent quantities at the nodes adjacent to the solid wall; (ii) the comparison of the experimental free surface deformation with the numerical description of the interface. A difference below 15% would validate our modeling results.

Many meshes had to be envisaged to improve the grid quality and to check that the simulation results were independent of the grid design (Celik et al. 2008). The mesh was refined near the impeller blades, the interface and the reactor walls (Figure 2). The mesh quality was specified with an aspect ratio of 22 and an orthogonal quality of 0.69 (Hirsch & Tartinville 2009). The whole 8 L tank was meshed with 4.1 × 105 hexahedral elements. Finally, the O-grid mesh type chosen to model the reactor is presented in Figure 2 in its bottom section.
Figure 2
Figure 2. Computational grid used for the simulations (bottom view at the left and lateral view at the right).
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Computational grid used for the simulations (bottom view at the left and lateral view at the right).

Figure 2
Figure 2. Computational grid used for the simulations (bottom view at the left and lateral view at the right).
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Computational grid used for the simulations (bottom view at the left and lateral view at the right).

Close modal
The numerical model was simulated in steady flow with a RANS turbulence model. The major purpose was to extract the fluid velocity ui (m.h−1) and the Reynolds number Rei at the interface:
formula
13
The Reynolds number appeared as the most likely to be extrapolated in a real sewerage system. To represent the interface with accuracy, the vortex deformation (height h = hmax–hmin) was selected to be the characteristic dimension, since it is directly governed by the stirring rate and the interfacial conditions. The local velocity used for the Reynolds number calculation was obtained with numerical results.
Then, it was possible to link KL to the interface parameters to improve Equation (12) by including the modeling data to obtain Equations (14) and (15) as follows:
formula
14
formula
15
with ui the fluid velocity per surface unit (m.h−1) at the interface, Rei the Reynolds number (–), a2, a3, b2, b3, c2 and c3 constants determined by a best-fit regression approach (OLS method). Equations (14) and (15) enable the mass transfer coefficient to be deduced from local parameters describing the interface.

Mass transfer coefficient KL in a gravity pipe pilot

Empirical approach

The aim of this part was to measure the mass transfer coefficient in a free-flowing pipe system. Oxygen was chosen to investigate the mass transfer coefficient. Experiments were carried out in a 10 m long PVC pipe with an internal diameter of 0.2 m (Figure 3). The slope was adjusted between 0 and 2%. Tap water was pumped from a 2 m3 tank and the pumping flow was measured by a flow meter (Rosemount 8732 E).
Figure 3
Figure 3. Gravity pipe device.
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Gravity pipe device.

Figure 3
Figure 3. Gravity pipe device.
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Gravity pipe device.

Close modal
For each experiment, the slope and a constant flow rate was adjusted. Oxygen was depleted below the saturation level in the tank by addition of sodium sulfite. The oxygen concentration (due to reaeration of the liquid phase in the pipe) was measured at steady-state by six oxygen probes (Mettler Toledo easySense O2 21 Oxygen Sensor) located along the pipe length. The controlled and monitored initial parameters were the water flow rate and the initial dissolved oxygen concentration in the tank. Under each flow condition, the height h and the flow width B were measured. These parameters are sufficient to determine the wetted surface S, the hydraulic diameter dh and the interfacial area a (Lahav et al. 2004). The turbulence is commonly characterized via Reynolds and Froude numbers following these equations:
formula
16
and
formula
17
In this present work, the flow velocities varied between 0.27 and 0.61 m/s, corresponding to Reynolds number values of [4,332–46,130] and Froude numbers [0.70–0.71].
In steady-state conditions, the mass balance equation reduces to:
formula
18
where the saturated concentration Cs,i is taken from the Winkler table. This equation can then be integrated to calculate the mass transfer coefficient knowing the dissolved concentration CL,i. All experiments, in the reactor and in the pipe, were performed at least in triplicate. Within the replicates, outliers were excluded from the dataset by the statistical method of Thompson (Cimbala 2011).

Numerical approach

The system geometry was numerically reproduced. The picturing mesh was refined in the water height value (0.55 to 3.55 cm). The mesh quality was specified by an aspect ratio of 19.9 and an orthogonal quality of 0.66. Two meters of the long pipe were meshed with 1.33 × 105 hexahedral elements (Figure 4). The y+ value and the orthogonal quality validated the mesh design.
Figure 4
Figure 4. Computational grid used for the simulations (bottom view at left and lateral view at right) in the pipe.
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Computational grid used for the simulations (bottom view at left and lateral view at right) in the pipe.

Figure 4
Figure 4. Computational grid used for the simulations (bottom view at left and lateral view at right) in the pipe.
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Computational grid used for the simulations (bottom view at left and lateral view at right) in the pipe.

Close modal

For numerical calculations, the kε-RNG model was chosen to strike a balance between the predictive accuracy and the computational economy. The velocity and the Reynolds number at the interface were obtained with numerical results, in each cell center. The experimental and the numerical oxygen mass transfer coefficient values were compared to validate the modeling results: a difference inferior to 15% would validate our modeling results. Once the numerical description of the flow were obtained, the interface fluid velocity ui and the Reynolds number Rei were extracted from the simulated data.

Study of the mass transfer coefficient KL (O2 and H2S) in a small reactor

Experimental approach: link between H2S and O2 mass transfer coefficient

Figure 5 plots the hydrogen sulfide mass transfer coefficient (m.h−1) as a function of the stirring rate (rpm) for the dataset obtained in the 8 L reactor (35 experiments). exponentially increased with the stirring rate. A similar trend was observed for (36 experiments) (results not shown). The exponential evolution of the mass transfer coefficient with the stirring velocity is consistent with the increasing level of turbulence. Indeed, the depth of the liquid film diffusion layer (or the renewal rate of the concentration near the interface) in strongly influenced by the fluid velocity.
Figure 5
Figure 5. Influence of the stirring rate mass transfer coefficient of the H2S (m.h−1).
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Influence of the stirring rate mass transfer coefficient of the H2S (m.h−1).

Figure 5
Figure 5. Influence of the stirring rate mass transfer coefficient of the H2S (m.h−1).
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Influence of the stirring rate mass transfer coefficient of the H2S (m.h−1).

Close modal
The following empirical correlations fitted the experimental results:
formula
19
formula
20
The same tendency was observed by Wu (1995), Vasel (2003) and Parkhurst & Pomeroy (1972). Wu (1995) found in aerated bioreactors an exponential trend for the KLa as a function of the stirring velocity, where KLa is proportional to N1.95. In rivers and canals, Vasel (2003) found that the mass transfer coefficient was proportional to the square root of the velocity. In sewers, the mass transfer coefficient would be proportional to u3/8 (Parkhurst & Pomeroy 1972). Lahav et al. (2006) found that the mass transfer coefficient was proportional to the velocity gradient in a sewer pipe. The following step was to study and compare the mass transfer coefficient between the oxygen and the hydrogen sulfide. Figure 6 plots the experimental mean ratio as a function of the stirring rate.
Figure 6
Figure 6. Influence of the stirring rate on the ratio between the hydrogen sulfide mass transfer coefficient (m.h−1) and the oxygen mass transfer coefficient (m.h−1).
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Influence of the stirring rate on the ratio between the hydrogen sulfide mass transfer coefficient (m.h−1) and the oxygen mass transfer coefficient (m.h−1).

Figure 6
Figure 6. Influence of the stirring rate on the ratio between the hydrogen sulfide mass transfer coefficient (m.h−1) and the oxygen mass transfer coefficient (m.h−1).
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Influence of the stirring rate on the ratio between the hydrogen sulfide mass transfer coefficient (m.h−1) and the oxygen mass transfer coefficient (m.h−1).

Close modal
The experimental error was symbolized in the figure. The mean ratio was calculated:
formula
21

Given the uncertainty, this value falls in the range of the diffusivity ratio (DH2S/DO2 = 0.86). The rate of the H2S transfer was generally lower than the reaeration process and exhibits a similar behavior. In 1974, USEPA suggested that the KL,H2Sa/KL,O2a ratio was 0.72, which is consistent with our conclusions.

Numerical approach

The modeling results of the flow characteristics in the stirred reactor highlighted no dead zone, and the velocity fields evidenced a homogeneous mixing in the liquid volume (Figure 7). Therefore, the system description is consistent with the basic assumptions needed to apply the two film theory. For the lowest stirring velocity (50 rpm), the local velocities ranged between 0.006 and 0.130 m.s−1 (mean value of 0.112). For the highest stirring velocity (140 rpm), the local velocities were modeled in the range of values [0.018–0.341] (mean value of 0.310 m.s−1). The mean velocity modeled in the liquid film was found to be proportional to the stirring rate, with a good accuracy:
formula
22
This correlation is fully dependent on the experimental set-up, and therefore extrapolation to other systems is impossible. Nevertheless, it was of interest from a methodological viewpoint. A correlation made from the numerical modeling results may be similarly written involving the interface Reynolds number. Those results were then added to the experimental measurements of KL. For instance, merging Equation (22) with Equation (20) enables the oxygen transfer coefficient to be expressed as a function of the flow conditions at the interface:
formula
23
with the OLS method, Equation (24) was also edited:
formula
24
Those results make the estimation of the oxygen transfer mass coefficients possible in systems of different geometries, provided that the hydrodynamic conditions are in the same range of values and that local hydrodynamic conditions are accessible with numerical modeling tools as CFD.
Figure 7
Figure 7. Velocity fields at 50 rpm and 140 rpm stirring rates (median transverse section).
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Velocity fields at 50 rpm and 140 rpm stirring rates (median transverse section).

Figure 7
Figure 7. Velocity fields at 50 rpm and 140 rpm stirring rates (median transverse section).
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Velocity fields at 50 rpm and 140 rpm stirring rates (median transverse section).

Close modal

Study of KLa in gravity pipe with oxygen

Experimental approach

The hydrodynamic conditions in the gravity pipe were determined as follows: (i) subcritical flow, i.e. a flow controlled from a downstream point and transmitted in the upstream (Fr2 < 1); (ii) turbulent flow (Re2> 4,000); (iii) no axial dispersion (plug flow). Figure 8 shows that the oxygen mass transfer coefficient KL,O2 (m.h−1) exponentially increased with the mean water velocity (m.s−1). This evolution of the mass transfer coefficient is consistent with the increasing level of turbulence, similarly to what was obtained in the reactor. The KL,O2 can thus be derived from the average water velocity (Equation (25)):
formula
25
Figure 8
Figure 8. Flow velocity (m.h−1) effect on the oxygen transfer coefficient (m.h−1).
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Flow velocity (m.h−1) effect on the oxygen transfer coefficient (m.h−1).

Figure 8
Figure 8. Flow velocity (m.h−1) effect on the oxygen transfer coefficient (m.h−1).
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Flow velocity (m.h−1) effect on the oxygen transfer coefficient (m.h−1).

Close modal

The advantage of this kind of correlation is that it depends on a single parameter, and is easily usable in the field. The values estimated by Equation (25) were in agreement with Parkhurst & Pomeroy (1972), Krenkel & Orlob (1962) and Jensen (1995), with observed mean differences of 42%, 37% and 48%, respectively. Equation (25) can be used for predicting by applying a coefficient of 0.64 (Equation (21)) in the same range of hydraulic conditions.

Numerical approach

In the gravity pipe device, the simulation results enabled the extraction of the hydraulic conditions at the interface. As in the small reactor, once the simulation grid was designed and approved, and the accuracy of the modeling results verified, the flow was simulated in the pipe. The overall hydraulic patterns were examined. The hydraulic conditions in the liquid-gas boundary layer, the local velocity and the Reynolds number were extracted from the modeling results. The interfacial liquid velocity ui (averaged over the whole section of the pipe) was found to be proportional to the average velocity (ui=0.92 u). Using this result by injecting it in Equation (25) makes the KL in the pipe predictable from the interfacial velocity:
formula
26

This predictive correlation is however different from Equation (23), which means that our comparative approach between the two systems (mixed reactor and pipe) needs some refinements in order to obtain a transposable correlation independent of the geometry. Very probably, in free flowing systems another parameter than the average interfacial velocity will have to be accounted for.

The dynamics of hydrogen sulfide emission in sewer systems are strongly influenced by the mass transfer coefficient at the interface KL. This coefficient is known to depend on the flow conditions. The purpose of this work was to collect more data in order to establish a predictive model that could be independent of the system geometry. For this purpose, several scales were investigated: an 8 L mixed batch reactor and a 10 meter gravity pipe device with continuous water flow were set up.

  • In the batch reactor, the behavior of the H2S mass transfer was studied using a new technique based on an on-line sulfide probe as a function of the turbulent conditions (Reynolds range values [0–23,333] and Froude range values [0.70–0.71]). The results were then compared to the O2 mass transfer coefficient.

  • The mean ratio was 0.64 ± 0.24, which is consistent with previously reported data.

  • as well as increased exponentially with the flow velocity, in accordance with the increasing level of turbulence near the interface.

  • CFD simulations of both systems enabled the proposal of correlations between the mass transfer coefficient and the local interface conditions (Reynolds number at the interface or fluid velocity), so as to make the equations independent of the averaged hydraulic parameters of the system.

  • These results were applied to a gravity pipe. The discrepancy between the measured and the predicted mass transfer coefficients was discussed and the correlations were refined. These equations are expected to be valid in the field and to simplify the modeling and the prediction of the phenomena linked to O2 and H2S mass transfer in sewer networks.

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