H_{2}S 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 H_{2}S emission in gravity pipes, and collecting data to establish models independent of the system geometry. The ratio between the H_{2}S and O_{2} 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 O_{2} mass transfer coefficient was found to depend on the stirring rate (rph) as follows: *K*_{L,O2} = 0.016 + 0.025 *N*^{3.85}. A *K*_{L,H2S}/*K*_{L,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 *u _{i}* (m.h

^{−1}):

*K*

_{L,O2}= 0.016 + 1.02 × 10

^{−5}

*u*

_{i}

^{3.85}In the gravity pipe device,

*K*

_{L,O2}also exponentially increased with the mean flow velocity. These trends were found to be consistent with the increasing level of turbulence.

## SYMBOL

*a*specific interfacial area (m

^{2}.m^{−3})*a*_{x}correlation coefficient (m.h

^{−1})*b*_{x}, c_{x}correlation coefficients (–)

*C*_{L,i}concentration in liquid phase of component i (mg.L

^{−1})*C*_{S,i}saturation concentration of component i (mg.L

^{−1})*d*stirrer diameter (m)

*D*_{m,i}diffusivity coefficient of component i (m

^{2}.s^{−1})*d*_{m}hydraulic mean depth (m)

*d*_{h}hydraulic diameter (m)

*Fr*_{1}Froude number for agitation (–)

*Fr*_{2}Froude number for flow (–)

*g*standard gravity (m.s

^{−2})*h*the vortex deformation (height h = h

_{max}–h_{min}) (m)- k
turbulent kinetic energy (m

^{2}.s^{−2})*K*_{L,i}overall mass-transfer coefficient of component i (m.h

^{–1})*N*stirring rate (s

^{−1})- n
coefficient

*Re*_{1}Reynolds number for mixing (–)

*Re*_{2}Reynolds number for flow (–)

*Re*_{i}interface Reynolds number (–)

*R*_{h}hydraulic radius (m)

*s*slope (m.m

^{−1})*S*wetted surface (m

^{2})*t*time (t)

*u*flow velocity (m.s

^{−1})*u*_{i}weighted velocity at the interface (m.h

^{−1})*z*distance (m)

## Greek symbols

## INTRODUCTION

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 H_{2}S, which can be emitted into the atmosphere. Accumulation of H_{2}S 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 H_{2}S, even at relatively low concentrations, is toxic to humans. Many deaths during routine maintenance in sewers have been attributed to H_{2}S 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 H_{2}S 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 H_{2}S emission are conditioned by the liquid-gas mass transfer flux. This flux depends, on the one hand, on the difference between the concentration of H_{2}S 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 H_{2}S 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 H_{2}S build-up, H_{2}S 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.

_{2}S 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 H

_{2}S 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 H

_{2}S mass transfer coefficient with an on-line sensor, and to compare it with the O

_{2}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):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.

Yongsiri *et al.* (2004a, 2004b) experimentally found a constant ratio *K*_{L,H2S} to *K*_{L,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.

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) |

Since the available models (Table 1) estimate global transfer coefficients and refer to parameters depending on the system geometry (*d _{m}, R_{h}*), 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

*K*of H_{L}_{2}S and O_{2}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

*K*to the local hydrodynamic parameters;_{L}to perform a similar analysis in a gravity pipe device by investigating the O

_{2}mass transfer coefficient and derive a correlation based on local hydrodynamic parameters.

## MATERIALS AND METHODS

### Mass transfer coefficient K_{L} in a small reactor

#### Experimental approach

*N*was set between 50 and 140 rpm and controlled by a tachymeter. The calculated dimensionless numbers for stirring were: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 O

_{2}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 O

_{2}content in the liquid phase by adding an adequate amount of sulfite (Na

_{2}SO

_{3}, CAS 7757-83-7) and 1 mg/L of cobalt as a catalyzer (CoSO

_{4}, CAS 10026-24-1). O

_{2}was monitored with an oximeter installed 6 cm under the liquid/gas interface (Mettler-Toledo easySense O

_{2}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):The model was fitted to the experimental data with EXCEL solver. The adjusted parameters were and

*C*.

_{s,O2}_{2}S experiments, the experimental device was isolated from the atmosphere and purged with N

_{2}to avoid any chemical reaction between O

_{2}and H

_{2}S, and H

_{2}S 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 (Na

_{2}S, 9H

_{2}O, 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 H

_{2}S, (iii) to measure the decrease in H

_{2}S concentration with the AQUA-MS probe MS-08, composed of an amperometric sulfide probe combined with pH and temperature measurements; (iv) to model the H

_{2}S concentration decrease to determine the mass transfer coefficient. A typical degassing curve for H

_{2}S is shown in Figure 1.

*C*is the concentration at

_{L,0}*t*

*=*

*t*

_{0}_{.}

*C*. Indeed, the theoretical

_{s,H2S}*Cs*for H

_{2}S should be 0 since the reactor headspace was continuously purged with N

_{2}. 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

*K*(m.h

_{L}^{−1}) and the mixing velocity (rph) by means of the ordinary least squares (OLS) method, in the form of:with a

_{1}, b

_{1}and c

_{1}being three distinct constants for O

_{2}and H

_{2}S. 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

*K*between clear water and wastewater is expected to be known from previous work (Yongsiri

_{L}*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.

*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 × 10

^{5}hexahedral elements. Finally, the O-grid mesh type chosen to model the reactor is presented in Figure 2 in its bottom section.

_{i}(m.h

^{−1}) and the Reynolds number Re

_{i}at the interface: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 = h

_{max}–h

_{min}) 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.

*K*to the interface parameters to improve Equation (12) by including the modeling data to obtain Equations (14) and (15) as follows:with

_{L}*u*the fluid velocity per surface unit (m.h

_{i}^{−1}) at the interface,

*Re*the Reynolds number (–), a

_{i}_{2,}a

_{3}, b

_{2,}b

_{3}, c

_{2}and c

_{3}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 *K*_{L} in a gravity pipe pilot

_{L}

#### Empirical approach

^{3}tank and the pumping flow was measured by a flow meter (Rosemount 8732 E).

_{2}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

*d*and the interfacial area

_{h}*a*(Lahav

*et al.*2004). The turbulence is commonly characterized via Reynolds and Froude numbers following these equations:andIn 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].

*C*is taken from the Winkler table. This equation can then be integrated to calculate the mass transfer coefficient knowing the dissolved concentration

_{s,i}*C*. 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).

_{L,i}#### Numerical approach

^{5}hexahedral elements (Figure 4). The y

^{+}value and the orthogonal quality validated the mesh design.

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 *u _{i}* and the Reynolds number

*Re*were extracted from the simulated data.

_{i}## RESULTS AND DISCUSSION

### Study of the mass transfer coefficient K_{L} (O_{2} and H_{2}S) in a small reactor

#### Experimental approach: link between H_{2}S and O_{2} mass transfer coefficient

^{−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.

*as a function of the stirring velocity, where*

_{L}a*K*is proportional to

_{L}a*N*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

^{1.95}.*u*(Parkhurst & Pomeroy 1972). Lahav

^{3/8}*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.

Given the uncertainty, this value falls in the range of the diffusivity ratio (*D _{H2S}/D_{O2}* = 0.86). The rate of the H

_{2}S transfer was generally lower than the reaeration process and exhibits a similar behavior. In 1974, USEPA suggested that the

*K*ratio was 0.72, which is consistent with our conclusions.

_{L,H2S}a/K_{L,O2}a#### Numerical approach

^{−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:

*K*. 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:with the OLS method, Equation (24) was also edited: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.

_{L}### Study of *K*_{L}a in gravity pipe with oxygen

_{L}a

#### Experimental approach

*i.e.*a flow controlled from a downstream point and transmitted in the upstream (

*Fr*< 1); (ii) turbulent flow (

_{2}*Re*> 4,000); (iii) no axial dispersion (plug flow). Figure 8 shows that the oxygen mass transfer coefficient

_{2}*K*(m.h

_{L,O2}^{−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

*K*can thus be derived from the average water velocity (Equation (25)):

_{L,O2}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

*u*(averaged over the whole section of the pipe) was found to be proportional to the average velocity (

_{i}*u*). Using this result by injecting it in Equation (25) makes the

_{i=}0.92 u*K*in the pipe predictable from the interfacial velocity:

_{L}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.

## CONCLUSION

The dynamics of hydrogen sulfide emission in sewer systems are strongly influenced by the mass transfer coefficient at the interface *K _{L}*. 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 H

_{2}S 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 O_{2}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 O

_{2}and H_{2}S mass transfer in sewer networks.