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Global sensitivity analysis of an in-sewer process model for the study of sulfide-induced corrosion of concrete B. M. R. Donckels, S. Kroll, M. Van Dorpe and M. Weemaes

ABSTRACT The presence of high concentrations of hydrogen sulfide in the sewer system can result in corrosion of the concrete sewer pipes. The formation and fate of hydrogen sulfide in the sewer system is governed by a complex system of biological, chemical and physical processes. Therefore, mechanistic models have been developed to describe the underlying processes. In this work, global sensitivity analysis was applied to an in-sewer process model (aqua3S) to determine the most important model input factors with regard to sulfide formation in rising mains and the concrete

B. M. R. Donckels (corresponding author) S. Kroll M. Van Dorpe M. Weemaes Research Department, Aquafin NV, Dijkstraat 8, B-2630 Aartselaar, Belgium E-mail: brecht.donckels@aquafin.be

corrosion rate downstream of a rising main. The results of the sensitivity analysis revealed the most influential model parameters, but also the importance of the characteristics of the organic matter, the alkalinity of the concrete and the movement of the sewer gas phase. Key words

| aqua3S, concrete corrosion, dynamic modeling, global sensitivity analysis, hydrogen sulfide, in-sewer processes

INTRODUCTION High concentrations of hydrogen sulfide in the sewer system can drastically decrease the service lifetime of concrete sewer pipes (Hvitved-Jacobsen et al. ). Hydrogen sulfide is formed under anaerobic conditions by sulfate-reducing bacteria. These bacteria grow in the anaerobic layers of the biofilms that cover the wetted surface of sewer pipes (Jiang et al. ). As long as oxygen is present in the sewage, the hydrogen sulfide molecules that are formed in the biofilm will be oxidized in the outer layers of the biofilm, either biologically or chemically (Nielsen et al. ). However, if dissolved oxygen concentrations are too low, hydrogen sulfide will accumulate in the sewage. This is typically the case in pressurized rising mains, where an oxygencontaining sewer gas phase is absent. When hydrogen sulfide rich sewage is discharged in the receiving gravity sewer, a fraction of the dissolved hydrogen sulfides will be released to the sewer atmosphere, where it causes socalled biogenic sulfuric acid corrosion. Indeed, emitted hydrogen sulfide adsorb on the unsubmerged concrete surface of the sewer pipes, where it is oxidized to sulfuric acid by sulfide-oxidizing bacteria ( Jensen et al. a). Sulfuric acid acidifies the concrete surface and reacts with the alkaline components of the concrete matrix to form a hydrated cement paste. With time, the cementing properties doi: 10.2166/wst.2013.763

of the concrete diminish and the thickness of the concrete pipe decreases. Corrosion rates of several mm/year have been reported in literature (Vincke et al. (); Hudon et al. ()). In many research disciplines, mechanistic models have proven to be useful tools for both scientists and engineers. Because the formation and fate of hydrogen sulfide in sewers are governed by a complex system of biological, chemical and physical processes (Hvitved-Jacobsen et al. ), mechanistic models have also been used in this context and have already resulted in an increased insight into the underlying processes (Nielsen et al. ). In addition, the models have also been used to identify potential or unknown problems (Vollertsen et al. a), to evaluate the effect and cost of possible sulfide control measures (Sharma et al. ) and to quantify processes that are difficult to measure, such as the corrosion rate (Vollertsen et al. b). A conceptual in-sewer process model was described in Hvitved-Jacobsen et al. (). The model was named the WATS model, which stands for Wastewater Aerobic– anaerobic Transformations in Sewers. The WATS model was originally developed to simulate changes in the dissolved oxygen concentration and the concentrations of

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two or three carbon fractions of the sewage with different biodegradability. For this, the WATS model adapts the methodology of the activated sludge models, where the carbon fractions of the organic matter are derived from dedicated respirometric experiments (Spanjers & Vanrolleghem ; Vollertsen & Hvitved-Jacobsen ). The model was later extended to include the sulfur cycle (Nielsen et al. ) and the concrete corrosion process ( Jensen et al. a, b; Jensen et al. ; Vollertsen et al. b). Recently, the WATS model was further extended to allow prediction of the pH (Vollertsen et al. ). The WATS model served as a starting point for the development of other models, such as the SeweX model (Sharma et al. ). The SeweX model uses different kinetic equations for sulfide formation and oxidation and includes key equilibrium processes for the prediction of pH and concentrations of carbonate, phosphate, sulfide and iron. The carbon fractions are estimated from the concentrations of volatile fatty acids, and soluble, flocculated soluble and total chemical oxygen demand (COD). This work focuses on the application of global sensitivity analysis to a dynamic, mechanistic model that resembles the WATS model and that was developed to describe the in-sewer processes that instigate sulfideinduced corrosion. The main objective of (global) sensitivity analysis was to discriminate among the model input factors according to their importance with regard to welldefined model outputs of interest (Saltelli et al. ). However, sensitivity analysis also contributes to a better understanding of the model behavior and, thus, of the interactions between the modeled processes. It also assists in the design of measurement campaigns and research programs by focusing on the most important sources of uncertainty.

the biofilm. In gravity sewers, the interactions between sewer gas phase, sewage, biofilm and unsubmerged concrete pipe are important and have to be taken into account. For this reason, separate models were developed for rising mains (named aqua3S1) and gravity sewers (named aqua3S2). These models are basically implementations of the WATS model, but the stoichiometric and kinetic equations for sulfide formation and oxidation of the SeweX model were used because the WATS model assumes that no organic substrate is consumed when hydrogen sulfide is formed (although the proposed kinetic equation does include a strong dependence on the substrate concentrations). Also, another approach was followed for incorporating endogenous respiration (similar to ASM3, Henze et al. ()) because this simplified the extension of the model to include for instance nitrate-consuming processes (not discussed in this paper). The resulting model library was named aqua3S, which is an acronym for Aquafin’s model library for Simulating Sulfide-related processes in Sewers. Below, both models are briefly described and the differences to the WATS model, which served as a starting point, are listed.

MATERIALS AND METHODS

Dynamic model for gravity sewers (aqua3S2)

Aqua3s: model library for simulating sulfides in sewers

The interactions between the sewer gas phase, sewage and unsubmerged concrete pipe are very important for describing the processes that occur in gravity sewers. From a modeling perspective, this implies that both the gas and water phase have to be included in the model. Although one can no longer assume a constant volume for the tanks in the tanks-in-series approximation, it is still possible to reasonably describe the wastewater hydraulics (Meirlaen ). For this purpose, a permanent flow is assumed at every time step, and the flow velocity is determined from the volume of wastewater present in the pipe segment

Beside the conventional gravity sewer pipes, sewer networks also involve pumping stations and pressurized rising mains. Rising mains can be considered as full-flowing pipes, whereas gravity sewers are partly filled. From a modeling perspective, this has consequences not only for the hydraulic part of the model, but also for the processes that have to be included in the model. The lack of a sewer gas phase in rising mains implies that the model should only consider processes that occur in the sewage and

Dynamic model for rising mains (aqua3S1) Because it is reasonable to assume that there is no sewer gas phase in pressurized rising mains, they are considered as full-flowing pipes. The implementation of the hydraulic part of the model is based on the tanks-in-series approach and is straightforward, since the volume of the tanks can be assumed constant. Although the biological processes take place in both the sewage and the biofilm, the biofilm itself is not included in the model but its influence on the concentrations in the water phase is included.

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using Manning’s equation (Hager ): u¼

1 2=3 1=2  R  is : n h

(1)

Here, u represents the flow velocity (in m/s), Rh represents the hydraulic radius (in m), is represents the slope (in m/m) and n represents Manning’s roughness coefficient (in s/m1/3). A detailed description of gas phase movement in partly filled sewer pipes is difficult and was not addressed in this work. Nevertheless, it is important to include at least a basic description of the longitudinal gas flow and the aqua3S2 model assumes that the sewer gas moves in the same direction as the sewage and with a velocity equal to a fixed fraction of the water flow velocity. As stated by Vollertsen et al. (), a typical ratio between both velocities lies between 0.05 and 0.20. The processes that occur in both rising mains and gravity sewers are modeled in the same way as in the aqua3S1 model and, hence, the aqua3S2 model can be seen as an extension of the aqua3S1 model. Compared to the aqua3S1 model, the aqua3S2 model includes kinetic equations to describe the mass-transfer between sewer gas phase and sewage (both for oxygen and hydrogen sulfide) and a kinetic equation for the adsorption of emitted sulfide on the unsubmerged concrete pipe. The kinetic equation for these processes were respectively taken from Jensen (), Yongsiri et al. () and Vollertsen et al. (). For sulfide adsorption in sewer pipes that were constructed using a corrosion-proof material (such as coated concrete or vitrified clay pipes), the parameter values reported for plastic pipes were used (Nielsen et al. ). For reaeration at sewer drops, the empirical equation of Pomeroy & Lofy () was incorporated in the model. Further, a simplified approach to estimate the concrete corrosion rate (Vollertsen et al. ) was added to the aqua3S2 model. Global sensitivity analysis Sensitivity analysis is performed to investigate to what extent variations of the model input factors are transferred to the model outputs. The term ‘model input factors’ not only includes model parameters, but also assumptions about the quantity and quality of the sewage (flow rate, total COD concentration and its fractionation, …) and the characteristics of the sewer systems (diameters and slopes of the sewer pipes, drop heights, …). Model output factors are the predicted variables of interest, such as corrosion rates and dissolved sulfide concentrations.

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Generally, a distinction is made between methods for local and global sensitivity analysis (GSA) (Saltelli et al. ). Methods for local sensitivity analysis investigate to what extent the model output is affected by small perturbations of nominal values of the individual model input factors. As a result, interactions between the model input factors are not considered and, at least for non-linear models, the interpretation of the calculated sensitivities is only valid in the vicinity of the nominal model input factor values. Because these methods only require a limited number of model evaluations, they were very popular in early studies (van Griensven et al. ). Methods for GSA, on the other hand, are more computationally demanding because they explore the entire space of feasible model input factor values and evaluate the sensitivities by varying all input factors simultaneously. As a result, the interactions between the model input factors are accounted for and the calculated sensitivities can be interpreted in a more general manner. A number of methods have been described in literature for performing GSA. Saltelli et al. () classified these methods into three categories: (i) regression and correlation based methods, (ii) global screening methods and (iii) variance decomposition based methods. In this work, GSA was performed using a correlation based method through the calculation of partial rank correlation coefficients (PRCC) (as described, for instance, in Marino et al. ()) and a variance decomposition based method (the eFAST method of Saltelli et al. ()). Description of the modeled sewer system In order not to complicate the interpretation of the results, the aqua3S models were used to describe the processes that occur in a simple, fictitious sewer system (Figure 1) that is comprised of a rising main (4 km, 400 mm) and the receiving gravity sewer (1 km, 500 mm, 5 mm/m). The pumping station that feeds the rising main receives the wastewater of 7,500 person equivalents. A characteristic diurnal profile is assumed for the wastewater flow rate and one person equivalent is assumed to produce 150 L of wastewater per day on average. The first 500 m of the gravity sewer is made of corrosion-proof material (such as vitrified clay or coated concrete) and the downstream part is made of concrete. The drop height at the rising main outlet is 0.2 m and the sewer gas phase is assumed to move in the same direction as the wastewater with a velocity equal to 20% of the velocity of the water phase. The characteristics of the wastewater are known to vary considerably with

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Figure 1

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Schematic representation of the modeled sewer system.

time (Vollertsen et al. ), but for reasons of simplicity the total COD concentration and the fractionation coefficients were assumed to be constant in time during the course of the simulation. Only dry-weather conditions are considered and the total COD concentration was set to 300 mg/L, which corresponds with the average COD concentrations measured in Flanders (Belgium). The temperature of the wastewater was assumed to be 20 C, which is a typical temperature in the summer months. As shown in Figure 1, the complete model of the sewer system is comprised of a sub-model for the rising main, a sub-model for the gravity sewer with corrosion-proof pipes and one for the gravity sewer with concrete pipes.

factors was equal to 45 (on a total of 106). For each of these, a uniform probability distribution was assumed from which values were sampled to perform the GSA. Because the eFAST method requires that the number of simulations is an odd multiple of the number of model input factors (Saltelli et al. ), a total of 11,295 (¼45 × 251) simulations were performed in each GSA method.

W

RESULTS AND DISCUSSION Below, the results obtained for the average sulfide formation in the rising main and the corrosion rate in the concrete part of the gravity sewer will be discussed.

Set-up of global sensitivity analysis The aim of the global sensitivity analysis was to identify the model input factors that are most influential with regard to the model outputs of interest. The model input factors can be grouped in four categories: (i) sewer properties – length, slope and diameter, (ii) hydraulic parameters, (iii) wastewater composition (mainly COD fractionation) and (iv) model parameters describing the process kinetics. Different levels of uncertainty are involved in each category. Sewer properties are well known (uncertainty class 1, or ±10% of default value), hydraulic inputs and wastewater characteristics typically have low uncertainty levels (uncertainty class 2, or ±25% of default value) and kinetics parameters have relatively high levels of uncertainty (uncertainty class 3, or ±50% of default value). The default values for the model input factors as well as the upper and lower bounds used in this work are shown in Table 1. The model parameters that characterize the kinetics of the processes that are shared among the sub-models were assumed to be equal. As a result, the total number of independent model input

Sensitivity analysis for sulfide formation in the rising main The results of the sensitivity analysis for the average sulfide concentration at the rising main discharge point are shown in Figure 2. The PRCC are depicted on the left-hand plot and the sensitivity indices (eFAST) are shown on the right-hand plot. Because even small PRCC values can be significant, their significance was determined with the two-tailed t-test described in Marino et al. (), with a significance level of 5%. The sensitivity indices include the direct effect of the model input factors (black bars), as well as the effect of its interaction with the other model input factors (white bars). Both methods identified the maximum surface-specific sulfide formation rate as the most important model parameter. The positive correlation coefficient and the observation that a large part of the variance can be explained by a first-order or direct effect of this model parameter are within expectation, as they dictate the sulfide

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Table 1

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Default values of the model input factors, as well as the upper and lower bounds that were assumed when performing the global sensitivity analysis. Note that the default values were taken from (a) Hvitved-Jacobsen et al. (2013) and (b) Nielsen et al. (2005) Default

Min.

Max.

Notation

Model input factor

value

value

value

Unit

Uncertainty class

Drm

Diameter of rising main

400

360

440

mm

1

Lrm

Length of rising main

4,000

3,600

4,400

m

1

Dgs

Diameter of gravity sewer

500

450

550

mm

1

sgs

Slope of gravity sewer

5

4.5

5.5

mm/m

1

dh

Drop height at rising main outlet

0.2

0

2

m



Alk

Alkalinity of concrete

0.181

0.0905

0.2715

gCaCO3 =gconcrete

3

n

Manning’s roughness coefficient

0.013

0.0117

0.0143

s × m1=3

1

ug/w

Ratio between gas and water flow velocity

0.20

0.05

0.25





COD

Total COD

300

225

375

gCOD =m3

2

fSA

Fraction of total COD present as fermentation product

0.05

0

0.10





fSF

Fraction of total COD present as fermentable substrate

0.05

0

0.10





fXB

Fraction of total COD present as heterotrophic biomass

0.05

0

0.10





fXS1

Fraction of total COD present as fast hydrolysable particulate substrate

0.10

0

0.25





ϑw

Temperature coefficient for processes that occur in water phase (except biological sulfide oxidation)

1.07

0.963

1.177



1

ϑf

Temperature coefficient for processes that occur in biofilm

1.05

0.945

1.155



1

ϑs

Temperature coefficient for sulfide formation

1.03

0.927

1.133



1

ϑb

Temperature coefficient for biological sulfide oxidation in water phase

1.10(b)

0.990

1.210



1

YH,Ow

Yield coefficient for aerobic growth of suspended heterotrophic biomass

0.55

0.275

0.825

gCOD =gCOD

3

YH,Of

Yield coefficient for aerobic growth of heterotrophic biomass in the biofilm

0.55

0.275

0.825

gCOD =gCOD

3

fXI

Production of inert organic matter during endogenous respiration

0.2(a)

0.1

0.3



3

μH

Maximum specific growth rate for heterotrophic biomass

6.7

5.0

8.4

L/d

3

bH

Maximum aerobic endogenous respiration rate

1.0

0.75

1.25

L/d

3 1

k1=2

Half-order rate constant for aerobic biofilm growth

4.0

3.0

5.0

1=2 gO2

kh1

Hydrolysis rate constant, fraction 1 (fast)

5.0

2.5

7.5

L/d

kh2

Hydrolysis rate constant, fraction 2 (slow)

0.5

0.25

0.75

L/d

3

kfe

Maximum fermentation rate

3.0

1.5

4.5

L/d

3

kH2 S

Maximum surface specific rate of sulfide formation

1.2(b)

0.5

2.5

gS2 m2 d1



0.13

0.93

1 m3 g1 O2 h

3

kH2 S,ox,c

Maximum chemical sulfide oxidation rate (at pH ¼ 7)

(b)

0.26

1=2

m

d

3 3

kH2 S,ox,b

Maximum biological sulfide oxidation rate

0.50

0.25

0.75

kH2 S,ox,f

Maximum biofilm sulfide oxidation rate

0.1(b)

0.05

0.15

KO

Saturation coefficient for dissolved oxygen

0.05

0.025

0.075

1 m g1 O2 h 1=2 1=2 m gO2 gS2 gO2 =m3

KF,w

Saturation coefficient for fermentable substrate in water phase

1.0

0.5

1.5

gCOD =m3

3

KA,w

Saturation coefficient for fermentable substrate in water phase

1.0

0.5

1.5

gCOD =m3

3

KF,f

Saturation coefficient for fermentable substrate in biofilm

5.0

2.5

7.5

gCOD =m3

3

(b)

3

3 h1

3 3

(continued)

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Table 1

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continued

Notation

Model input factor

Default value

Min. value

Max. value

Unit

Uncertainty class

KA,f

Saturation coefficient for fermentation products in biofilm

5.0

2.5

7.5

gCOD =m3

3

KF,fe

Saturation coefficient for fermentable substrate in fermentation

20

10

30

gCOD =m3

3

KX1

Saturation coefficient for hydrolysis, fraction 1 (fast)

1.5

0.75

2.25

gCOD =m3

3

KX2

Saturation coefficient for hydrolysis, fraction 2 (slow)

0.5

0.25

0.75

gCOD =m

3

ε

Efficiency reduction factor for the biofilm biomass

0.15

0.075

0.225



3

ηfe

Anaerobic hydrolysis reduction factor

0.14

0.07

0.21



3

XBf

Heterotrophic active biomass in biofilm

10

5

15

gCOD =m2

3

Figure 2

|

3

The PRCC for the average dissolved sulfide concentration at the rising main discharge point are shown in the left-hand plot. The black bars represent partial rank correlation coefficients that were significant at a significance level of 5%. The right plot shows the first-order (black) and the total-order (black and white) sensitivity indices calculated using the eFAST method.

formation rate in non-limiting conditions. Both methods also confirmed the importance of the total COD concentration, and especially the fractions present as fermentation product and fermentable substrate. This is in line with previous studies (for instance, Nielsen et al. () and Hvitved-Jacobsen et al. ()), where measurement campaigns clearly showed the importance of both the quantity and the quality of the organic matter in the wastewater. The different fractions of the COD are determined from respirometric experiments, which are time consuming and not standardized, or derived from directly measurable quantities such as the soluble, flocculated and

total COD concentration (Sharma et al. ). In many applications, however, the fractions are defined based on an educated guess taking into account the wastewater sources, BOD (biochemical oxygen demand) to COD ratios and/or soluble COD to total COD ratios. The relatively high sensitivity of these model input factors advocates for a careful evaluation of uncertainties introduced by doing so, as applied in Vollertsen et al. (, a). The results obtained with the eFAST method suggest that the use of the well-known empirical models (as discussed, for instance, in Hvitved-Jacobsen et al. ()) may be sufficient for describing sulfide formation in rising main

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in many cases, since the sensitivity indices of all other model input factors are small or negligible. Contrary to the eFAST method, the PRCC values indicate that also the saturation constants of the soluble fractions for biofilm processes had a significant influence on the sulfide concentrations, as well as the hydrolysis rate constant for rapidly hydrolysable particulate organic matter, the yield coefficient of the heterotrophic biomass in the water phase, the concentration of heterotrophic biomass in the biofilm and the maximum specific growth rate of the heterotrophic biomass. These results are not surprising, since the soluble COD fractions are replenished by hydrolysis and the hydrolysis rate will thus influence sulfide formation to some extent. In addition, the heterotrophic biomass will consume fermentation products and will compete with the sulfate-reducing bacteria in the biofilm. Finally, the model parameters that are used to describe the reduced rates of anaerobic and biofilm processes (such as sulfide formation) were found to be important by the correlation based method. Sensitivity analysis for the concrete corrosion rate The results obtained with the correlation based method and the eFAST method are depicted in Figure 3. Also here, the correlation based method identifies more model input

Figure 3

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factor as important compared to the eFAST method. As expected, the corrosion rate 550 m downstream of the rising main outlet (that is, the first part of the concrete gravity sewer) is to a large extent determined by the same model input factors as the formation of sulfide in the rising main outlet. In addition, the alkalinity of the concrete and the velocity of the sewer gas phase appear to be important, as well as the model parameters that are used to characterize the kinetics of the adsorption of sulfides on the unsubmerged sewer pipes. Little is known about the alkalinity of the concrete sewer pipes (at least in Flanders), and variations in the alkalinity of the concrete sewer pipes are likely to exist (for instance because the sewer infrastructure was developed over several decades). In addition, one can question the approach of lumping the complex reaction mechanisms that take place when concrete comes into contact with acids (Hudon et al. ) into one parameter (namely, the alkalinity). The movement of the sewer gas phase is difficult to model and the assumption that it moves with a velocity that is proportional to the wastewater velocity is an oversimplification. The results of the sensitivity analysis indicate that this has to be investigated further as it has a high impact on the predictions. The results also confirm the importance of the work of Nielsen et al. (), who investigated sulfide adsorption in concrete and plastic pipes.

The PRCC for the corrosion rate at 550 m downstream of the rising main outlet are shown in the left-hand plot. The black bars represent partial rank correlation coefficients that were significant at a significance level of 5%. The right plot shows the first-order (black) and the total-order (black and white) sensitivity indices calculated using the eFAST method.

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CONCLUSIONS The results of the GSA showed that the in-sewer process models are over-parameterized and that the maximum surface-specific sulfide formation rate is the most sensitive model parameter for predicting sulfide-related processes, including concrete corrosion rates. The characteristics of the organic matter of the sewage (that is, the total COD concentration and its fractions) highly influenced the model outputs as well, and the results highlighted the need to further investigate the movement of the sewer gas phase that is currently oversimplified in the published insewer models. In addition, the corrosion rate appeared to be highly sensitive to the assumed alkalinity of the concrete. In general, the task of interpreting the sensitivity analysis outcome resulted in an increased insight into the underlying processes and indicated the relative importance of the different processes.

REFERENCES Hager, W. H.  Wastewater Hydraulics: Theory and Practice. Springer-Verlag, Berlin, Germany. Henze, M., Gujer, W., Mino, T. & van Loosdrecht, M.  Activated Sludge Models ASM1, ASM2, ASM2d and ASM3 – Scientific and Technical Report No 9. IWA Publishing, London, UK. Hudon, E., Mirza, S., Asce, M. & Frigon, D.  Biodegradation of concrete sewer pipes: state of the art and research needs. Journal of Pipeline Systems Engineering and Practice 2 (2), 42–52. Hvitved-Jacobsen, T., Raunkjær, K. & Nielsen, P. H.  Volatile fatty acids and sulfide in pressure mains. Water Science and Technology 31 (7), 169–179. Hvitved-Jacobsen, T., Vollertsen, J. & Tanaka, N.  A process and model concept for microbial wastewater transformations in gravity sewers. Water Science and Technology 37 (1), 233–241. Hvitved-Jacobsen, T., Vollertsen, J. & Nielsen, A. H.  Sewer Processes – Microbial and Chemical Process Engineering of Sewer Networks, 2nd edn. CRC Press, Boca Raton, Florida, USA. Jensen, N. A.  Empirical modeling of air-to-water oxygen transfer in gravity sewers. Water Environment Research 67 (6), 979–991. Jensen, H. S., Nielsen, A. H., Lens, P. N. L., Hvitved-Jacobsen, T. & Vollertsen, J. a Hydrogen sulphide removal from corroding concrete: comparison between surface removal rates and biomass activity. Environmental Technology 30 (12), 1291–1296.

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First received 8 July 2013; accepted in revised form 12 November 2013. Available online 25 November 2013

Global sensitivity analysis of an in-sewer process model for the study of sulfide-induced corrosion of concrete.

The presence of high concentrations of hydrogen sulfide in the sewer system can result in corrosion of the concrete sewer pipes. The formation and fat...
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