Environmental Technology iFirst, 2012, 1–8

Development of a simple model for anaerobic digestion based on preliminary measurements of the bacterial sulphur activity in wastewater stabilization ponds
Casimir Harerimanaa , Chéma Keffalab∗ , Hugues Jupsinb and Jean-Luc Vaselb a Centre b Département

Universitaire de Recherche Multidisciplinaire en Environnement (CURME), Université du Burundi, Bujumbura, Burundi; des Sciences et Gestion de l’Environnement, Unité ‘Assainissement et Environnement’, Université de Liège, Arlon, Belgium (Received 12 March 2012; final version received 26 August 2012 )

The present study was undertaken to develop a simple and practical model for anaerobic digestion, encompassing sulphate reduction and sulphur oxidation, in a waste stabilization pond. The basic microbiological phases of the model consisted of four processes, namely acidogenesis, methanogenesis, sulphate reduction and sulphur oxidation. It also incorporated multiple reaction stoichiometry and substrate utilization kinetics. The study also aimed to investigate the mutual interaction between sulphate-reducing bacteria (SRB) and photosynthetic sulphur bacteria (PSB) in an anaerobic sludge consortia using batch reactors. The results revealed that for an initial concentration of sulphate ranging between 250 and 2800 mg.l−1 , SRB activity ranged between 20 and 190 mgSO2− reduced . The gVSS−1 .d−1 and PSB activity varied between 60 and 4 320 mgSO2− produced .gVSS−1 .d−1 , and PSB activity was noted to be twice as high as that of SRB. PSB can, therefore, 4 be used effectively in the fight against odors. The most important environmental factors affecting the sulphur cycle in the waste stabilization pond were likely to be the availability of sulphate and light for SRB and PSB, respectively. Keywords: modelling; sulphate-reducing bacteria; photosynthetic sulphur bacteria; stoichiometry; odour

Introduction Wastewater stabilization ponds have been commonly used as a means of wastewater treatment because of their low cost, simplicity of operation and ease of maintenance. The efficiency of this technique has, however, often been limited by a number of inadequacies, particularly the release of offensive odours, often associated with the presence of hydrogen sulphide (H2 S), which is itself generated by the sulphate-reduction process [1–3]. In fact, sulphate stimulates the growth of sulphate-reducing bacteria (SRB), which out-compete methane-producing bacteria (MPB) for H2 and acetate substrates [4]. The optimum oxidation-reduction potential (ORP) for the growth of SRB ranges between −100 and −300 mV at pH 7.0 [5]. No growth was previously observed at potentials of more than +27 mV [6]. The main problems associated with the sulphate-reduction process arise from the generation of hydrogen sulphide, a phenomenon that not only creates troublesome odour and corrosion problems [7], but also is fatally toxic to humans, causing death within 30 min at gaseous concentrations of only 800–1000 ppm, and instant death at higher concentrations [8,9]. The sulphides in a stabilization pond can be oxidized by coloured photosynthetic bacteria in the presence of light [5].

A large number of photosynthetic sulphur bacteria (PSB) are found in stabilization ponds, particularly during the summer and autumn, imparting a characteristic brown or red colour to the pond. The appearance of PSB is often accompanied by a reduction in the odours generated by hydrogen sulphide, a phenomenon that earned them the name of ‘biological deodorizers’ in the literature. Both types of bacteria (phototrophic and sulphatereducing) contribute to the turnover of the sulphur cycle in waste stabilization ponds [10]. The development of a simple model that simulates and predicts anaerobic digestion based on the determination of bacterial sulphur activity in wastewater stabilization ponds would, therefore, help improve and optimize current wastewater treatment systems. In fact, modelling is one of the most important tools for the simulation, prediction and optimization of water and ecological systems [11]. This technique was previously applied by an International Water Association (IWA) expert group who developed a model for anaerobic digestion, ADM1 [12], that consisted of 19 biochemical processes, including 3 kinetic processes of gas-liquid transfer and 7 different bacterial populations. Although efficient, this model is quite sophisticated and demanding, for it requires a relatively good knowledge of the kinetic and stoichiometric parameters of

∗ Corresponding

authors. Emails: harecasimir@yahoo.fr; keffalachema@yahoo.fr

ISSN 0959-3330 print/ISSN 1479-487X online © 2012 Taylor & Francis http://dx.doi.org/10.1080/09593330.2012.725773 http://www.tandfonline.com

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H2 Xc
Complex organic material Proteins, carbohydrates, lipids

Xh2 Xac VFA

Xh2,so4 CH4, CO2 Xac,so4 H2S, CO2

Xh2,so4 Xpsb

Sulfate

Xc

Figure 1.

Schematic biochemical process stages of anaerobic digestion with sulphate-containing waste waters. Main trophic group bacteria used in the model. Trophic group Symbol Xc Xac Xh2 Xac,so4 Xh2,so4 Xpsb Substrate Complex organic matter VFA (acetate equivalent) H2 and CO2 Acetate and sulphate H2 and sulphate Sulphur and CO2 Product Volatile fatty acid (VFA) and H2 Methane, CO2 Methane Sulphur and CO2 Sulphur Sulphate

Table 1.

1 2 3 4 5 6

Acidogenic bacteria Acetotrophic methanogenic bacteria Hydrogenotrophic methanogenic bacteria Acetotrophic SRB Hydrogenotrophic SRB Phototrophic sulphur oxidizing Bacteria

the bioreactor to modelize [13]. Others authors [14] modified and extended the ADM1 model, through adding a sulphato-reduction process, which improved its predictive power but added to its complexity. Considering the troublesome limitations associated with wastewater stabilization ponds and the promising opportunities that modelling could offer with regards to their alleviation and/or prevention, this study was undertaken to develop a simple model of anaerobic digestion, including the sulphate-reducing and sulphur-oxidizing processes in waste stabilization ponds. To achieve this aim, a stoichiometric and kinetic model was developed, and the results were synthesized in a Petersen Matrix. The reduction of sulphate by SRB and the oxidation of sulphur by PSB in batch reactors were then submitted to kinetic investigation. Model description Figure 1 illustrates the basic microbiological phases of the model presented in this work. The model consists of four stages, namely acidogenesis, methanogenesis, sulphate reduction and sulphur oxidation. It describes an anaerobic reaction sequence in which substrates are transformed by the six trophic groups of bacteria presented in Table 1. The principles underlying the extension of the anaerobic digestion model, including sulphate reduction and sulphur oxidation processes, are basically stoichiometric and kinetic in nature. Stoichiometry According to [15], microorganisms obtain their energy for growth and maintenance from oxidation-reduction reactions, which always involve an electron donor and an electron acceptor. Under anaerobic conditions, some microorganisms can use other electron acceptors in energy metabolism, including nitrate, sulphate and carbon dioxide. In some cases, organic matter is used as the electron

acceptor as well as the electron donor, and the reaction is termed ‘fermentation’. Table 2 summarizes half-reactions, written as one-electron oxidation, for a series of oxidation reductions of interest to the present study [3]. The complex organic material is represented by C8 H16 O6 N, and the bacterial population is represented by C5 H7 O2 N. The nitrogen required for bacterial synthesis is obtained from the release of NH3 in reaction. When microorganisms use an electron-donor substrate for synthesis, a portion of its electrons (fe0 ) is initially transferred to the electron acceptor to provide energy for the conversion of the other portion of electrons (fs0 ) into microbial cells. The sum of (fs0 ) and (fe0 ) is 1 [11]: fe0 + fs0 = 1 (1)

where fs0 is a portion of the electron equivalent in the electron-donor substrate used for synthesis and fe0 is a portion of the electron equivalent in the electron-donor substrate used for energy. The fraction fs0 is similar to the true yield Y if it is expressed as gCOD_cell produced/gCOD_consumed. Equation (2) is a general equation that can be used for the establishment of a wide variety of accurate stoichiometric equations describing microbial processes, such as synthesis and growth [15]. The result is an equation written on an electron-equivalent basis that represents the net consumption of reactants and the production of products when the microorganisms consume one-electron equivalent of electron donor: R = fe0 Ra + fs0 Rc − Rd (2)

where R is the general equation, Ra is the acceptor halfreaction, Rd is the donor half-reaction and Rc is the cell half-reaction. The selecting of the appropriate half-reactions from Table 2 and the use of Equation (2) give the following overall biological reaction (Table 3).

Environmental Technology
Table 2. The oxidation and reduction half-reaction of the model main compound. Component COM Acetate H2 Sulphate Microorganisms Half-reaction 1 10 8 1 C8 H16 O6 N + H2 O → CO2 + NH3 + H+ + e− 33 33 33 33 1 1 1 7 CH3 COO− + H2 O → CO2 + H− + e− 8 4 4 8 1 H2 → H + + e− 2 1 2− 10 + 1 4 SO + H + e− → H2 S + H2 O 8 4 8 8 8 1 1 2 1 CO2 + NH3 + H+ + e− → C 5 H7 O2 N + H 2 O 4 20 20 5

3

Table 3. Overall reactions for biological growth and substrate uptake involved in the model. Uptake of complex organic material by X c 17 − 33YC 33YC H2 O → C5 H7 O2 N + (3.3 − 3.3YC )CH3 COOH+ 5 20 28 − 33YC 20 − 33YC (3.3 − 3.3YC )H2 + CO2 + NH3 20 20 C8 H16 O6 N + Uptake of acetate by X ac CH3 COOH + 2Yac 2Yac 6Yac NH3 → C5 H7 O2 N + (1 − Yac )CH4 + H2 O + (1 − Yac )CO2 5 5 5

Uptake of H2 by X h2 H2 + Yh2 1 + Yh2 Yh2 1 5 + 3Yh2 NH3 + CO2 → C5 H7 O2 N + (1 − Yh2 ) CH4 + H2 O 10 4 10 4 10 2Yac,so4 5 10 − 12Yac,so4 5

Uptake of acetate by X ac,so4 CH3 COOH + (1 − Yac,so4 )SO2− + 4 2Yac,so4 5 NH+ + 4 H+ → H2 O

C5 H7 O2 N + (1 − Yac,so4 )H2 S + (2 − 2Yac,so4 )CO2 +

10 − 12Yac,so4 5

Uptake of H2 by X h2,so4 H2 + (1 − Yh2,so4 )SO2− + 4 2Yh2,so4 5 2Yh2,so4 5 NH+ + 4 10 − 12Yh2,so4 5 20 − 4Yh2,so4 5 H+ + (2Yh2,so4 )CO2 →

C5 H7 O2 N + (1 − Yh2,so4 )H2 S +

H2 O

Uptake of H2 S by X psb 10CO2 + 5H2 S + 2NH3 + 4H2 O → 2C5 H7 O2 N + 5SO2− + 10H+ 4

Kinetics Cellular kinetics is described by three expressions (uptake, growth and decay; see Appendices 1 and 2). The key rate equation is substrate uptake, which is based on the substrate level of a Monod-type kinetics or multiplicative Monod approach when both the electron donor and electron acceptor are rate limiting. Considering that the present study is interested in substrate removal (sulphur and sulphate), the rate of substrate consumption was selected as the basic rate, while cell growth was derived from substrate

utilization. Bacterial decay was described by first-order kinetics [4]. The growth parameters for SRB and substrate consumption cannot be taken as ‘random variables’. They have specific units and ranges of values (Tables 4 and 5). In several cases, the values are constrained by cell stoichiometry and energetics [15]. The five growth parameters for PSB reported by [13] are μmax = 4.12 h−1 , KS = 1.48 mM, KI = 850 lx, Ki = 3.90 × 10−5 lx and YS = 2.9 g_cell. mol_H2 S−1 , where μmax refers to the maximum

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Table 4. Kinetics parameters and rates used in the model. Symbol μmax km, process Ys KS, process KSO4, process kdec KI , inhibit, substrate Iinhibitor, process kprocess ρj YSO4 Description Monod maximum specific growth rate Monod maximum specific uptake rate Yield of biomass on substrate Half-saturation value of substrate Half-saturation value of sulphate First-order decay rate 50% inhibitory concentration Inhibition function First-order parameter (hydrolysis) Kinetic rate of process j Yield of biomass on sulphate Units d−1 gCOD_S.gCOD_X−1 .d−1 gCOD_X.gCOD_S−1 gCOD_S.l−1 gSO2− .l−1 4 d−1 gCOD.l−1 (see KI ) d−1 gCOD_S.l−1 .d−1 gCOD_X.gSO2− 4

Table 5. Values of bacterial parameters used in some models. Ref 1 2 3 4 2 3 4 3 4 3 4 Trophic group Xc Xac μmax d−1 0.91 0.24 0.29 0.30 1.0 2.6 0.98 0.51 0.24 5.0 0.98 km gCOD/gCOD.d 6.51 6.50 8 9.62 40 35 24.24 8.8 7.1 7.0 26.7 Ks gCOD/l 0.4 0.056 0.150 0.210 0.00013 0.00003 0.0001 0.024 0.220 0.00005 0.0001 KSO4 gS04/l Y gCOD/gCOD 0.140 0.037 0.050 0.032 0.025 0.060 0.040 0.058 0.034 0.109 0.037 kdec d−1 0.016 0.010 0.018 0.050 0.009 0.010 0.025 0.015 0.030 0.010 ki gCOD/l 2.285 – 0.690 0.215 – 0.600 0.285 0.750 0.550 0.750

Xh2

Xac,so4 Xh2,so4

0.019 0.010 0.001 0.010

Notes: 1. estimated with thermodynamic method; 2. according to [4]; 3. according to [12]; 4. according to [14].

specific growth rate, KS to the saturation constant for dissolved H2 S concentration, KI to the saturation constant for light intensity and Ki to the light inhibition constant. Model presentation (Appendices 1 and 2) According to the literature [16], the Petersen matrix forms a succinct summary of the complex interactions between compounds and processes. It allows alterations in processes, compounds, stoichiometry and kinetics to be readily incorporated. The matrix shows two important process aspects, namely that the reaction equation for each process is represented on the different rows and that one can observe in which conversions the compound is involved directly from the columns of each compound. By multiplying the stoichiometric factors with their respective rate equations, one gets the total conversion equation for each compound. For convenience, two extra aspects can be added to the matrix description. The first aspect relates to composition matrix in terms of conserved balances. Accordingly, it covers the chemical oxygen demand (COD), N, S and charge balance. In this respect, biomass is expressed in the stoichiometric matrix in terms of COD, but also contains

nitrogen. This is included in the composition matrix, since the composition matrix and the stoichiometry matrix effectively contain all the conserved balances. The second aspect pertains to the observed matrix, since the present work is interested not only in the compounds expressed in the dimensions as used in the model, but also in their measured or observed units. For instance, the sludge amount is usually measured as gVSS and not gCOD. The observed matrix contains these conversion values between, for example, gCOD and gVSS. Other potentially interesting observed quantities include Kjeldahl nitrogen, sulphur, volatile suspended solids (VSS) and biochemical oxygen demand (BOD).

Materials and methods The batch assay study was used to assess the sulphidogenic activity of sulphur bacteria. The biomass inoculum was obtained from an anaerobic municipal wastewater treatment lagoon located at El Jem, Tunisia. Twenty litres of anaerobic pond sewage were centrifuged at 3500 rpm for 10 min to obtain concentrated biomass. At the onset of the experiment, between 13 and 17 g/litre VSS of bacterial

Environmental Technology biomass was added to the reactors. For all experiments, a basal medium was used in such a way that the C/N/P ratio did not constitute a nutrient limitation for bacterial growth. The enriched basal medium consisted of (in mg.l−1 ): NaHCO3 (1000), NaCl (1000), K2 HPO4 (500), NH4 Cl (1000), MgCl2 .6H2 O (300), CaCl2 .6H2 O (1000), yeast extract (1000), ascorbic acid (1000), resazurin (1) and a trace element solution (1 ml.l−1 ) consisting of (in mg.l−1 ): HCl (25%; 7.7 M) (10 ml.l−1 ), FeCl2 .4H2 O (1500), ZnCl2 (70), MnCl2 .4H2 O (100), H3 BO3 (6), CoCl2 .6H2 O (190), CuCl2 .2H2 O (2), NiCl2 .6H2 O (24), Na2 MoO4 .2H2 O (36) and cysteine-HCl (560). Six reactors were fed with the same level of acetate (2000 mg.l−1 ), but different levels of sulphate, that is, 260 mg.l−1 for reactor A, 480 mg.l−1 for reactor B, 535 mg.l−1 for reactor C, 1335 mg.l−1 for reactor D, 1860 mg.l−1 for reactor E and 2775 mg.l−1 for reactor F. Serum vials (125 ml) were filled with 100 ml of the sample, leaving a headspace of 25 ml. The pH of all media (basal media with sulphate and acetate) was set to a value of above 8. Nitrogen was bubbled throughout the sample for at least 5 min after the addition of sodium acetate and potassium sulphate to ensure that the wastewater sample and headspace were free from oxygen, which would otherwise inhibit the sulphate reduction processes. The water samples in the reactors were continuously stirred, and syringes were used to withdraw 4 ml of liquid samples that were immediately filtered through a 0.45 μm membrane filter. The entire study was conducted at 30◦ C, and sulphate was analysed by ion chromatography. The VSS and COD were determined according to standard methods.
Test 2 1200 1000
[SO42-] (mg/l)

5

Results and discussion The sulphate concentrations in each reactor were determined at regular intervals throughout the experimental assays. The typical variation of the concentration is illustrated in Figure 2. The results from the series of tests revealed that the concentration of sulphate decreased and increased alternatively. The decrease observed for the sulphate concentration was due to the sulphate reduction processes induced by SRB [17]. The increase was, on the other hand, attributed to the oxidation of sulphide by phototrophic sulphur bacteria, without oxygen and in the presence of light. Both kinds of bacteria (phototrophic and sulphate-reducing) contributed to the turnover of the sulphur cycle in each reactor. The average activities of SRB and PSB were calculated by Equations (3) and (4) and expressed as mgSO2− reduced .gVSS−1 .d−1 and 4 mgSO2− produced .gVSS−1 .d−1 , respectively: 4 υSRB = − υPSB = 1 XSRB 1 XPSB t
2− SSO4

t
2− SSO4

(3) (4)

2− where SSO4 refers to the sulphate concentration reduced or produced, at fixed time intervals t, assuming that the biomass concentrations of SRB (XSRB ) and PSB (XPSB ) are constant. The activities determined for SRB and PSB in each reactor during the whole experimental period are summarized in Table 6.

2500 2000
[SO42-] (mg/l)

Test 5

800 600 400 200 0

1500 1000 500 0

0

10

20 Time (h)

30

40

50

0

10

20 Time (h)

30

40

50

Figure 2.

Sulphate reduction and production curves for calculation of SRB and PSB activity. Specific rate of sulphate reduction and sulphate production. Reactor A Reactor B 1075 164,42 535 94,66 Reactor C 1470 188,78 480 149,46 Reactor D 1335 125,26 490 83,00 Reactor E 2375 128,80 1860 60,64 Reactor F 2775 145,16 1675 230,94 mg.l−1 mgSO2− reduced . gVSS−1 .d−1 4 mg.l−1 mgSO2− produced . gVSS−1 .d−1 4

Table 6.

[SO2− ] initial 4 SRB activity [SO2− ] initial 4 PSB activity

260 19,42 135 315,44

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[2] J. Paing, Bilan du carbone et du soufre dans le lagunage anaérobie. Contrôle de l’émission d’H 2 S pour la réduction des nuisances olfactives, thèse de doctorat, Université de Montpellier I, France, 2001, p. 218. [3] C. Harerimana, B. Harbi, and J.L. Vasel, Développement d’un modèle stœchiométrique de la sulfato-réduction par des bactéries sulfato-réductrices en lagunage anaérobie, Biotechnol. Agron. Soc. Environ. 14(S2) (2011), pp. 577–582. [4] S.V. Kalyuzhnyi and V. Fedorovich, Mathematical modelling of competition between sulphate reduction and methanogenesis in anaerobic reactors, Bioresour. Technol. 65 (1998), pp. 227–242. [5] E.F. Gloyna, Bassins de stabilisation des eaux usées, Organisation mondiale de la Santé, Génève, 1972, p. 187. [6] S. H. Chuang, T. Y. Pai, and R. Y. Horng, Biotreatment of sulfate_reach wastewater in an anaerobic/micro aerobic bioreactor system, Environ. Technol. 26 (2005), pp. 993–1002. [7] A. Rinzema, Anaerobic treatment of wastewater with high concentrations of lipid or sulphate, PhD thesis, Wageningen Agricultural University, Netherlands, 1988. [8] P.N.L. Lens and L.P. Hulshoff, Environmental Technologies to treat Sulfur Pollution, Principles and Engineering, IWA Publishing, London, 2000, p. 547. [9] R.E. Speece, Anaerobic Biotechnology for Industrial Wastewaters, Archae Press, Nashville, TN, USA, 1996. [10] C. Caumette, Ecology and physiology of phototrophic bacteria and sulfate-reducing bacteria in marine salterns, Experientia 49 (1993), pp. 473–481. [11] B.K. Rajbhandari and C. Annachhatre, Modelling response of nitrifying biofilm to inhibitory shock loads, Water Sci. Technol. 50 (2004), pp. 53–60. [12] D.J. Bastone, J. Keller, S.V. Kalyuzhnyi, S.G. Pavlostathis, A. Rozzi, W.T.M. Sanders, H. Siegrist, and V.A. Vavilin, Anaerobic Digestion Model No.1 (ADM1), Scientific and Technical Report No.13, IWA, London, 2002. [13] O. Bernard, Mass Balance Modelling of Bioprocesses, Mathematical Control Theory, INRIA, Comore, France, 2001. [14] V. Fedorovich, P. Lens, and S.V. Kalyuzhnyi, Extension of anaerobic digestion model no.1 with processes of sulfate reduction, Applied Biochem. Biotechnol. 109 (2003), pp. 33–45. [15] B.E. Rittman and P.L. McCarty, Environmental Biotechnology, Principles and applications, McGraw-Hill International Editions, New York, 2001, p. 755. [16] M. Henze, M.C.N. van Loosdrecht, G.A. Ekama, and D. Brdjanovic, Biological Wastewater Treatment: Principles, Modelling and Design, IWA Publishing, London, 2008, p. 455. [17] N. J. Kim, M. Hirai, and M. Shoda, Comparison of organic and inorganic carriers in removal of hydrogen sulfide in biofilters. Environ. Technol. 19 (1998), pp. 1233– 1241. [18] S. K. Patidar and V. Tare, Effect of molybdate on methanogenic and sulfidogenic activity of biomass, Bioresour. Technol. 96 (2004), pp. 1215–1222.

As Table 6 illustrates, SRB activity ranged between 19.42 and 188.78 mgSO2− reduced .gVSS−1 .d−1 , correspond4 ing to the initial concentrations of sulphate, which ranged between 260 and 2775 mg.l−1 . These values are, in fact, comparable to those previously reported in the literature, such as those described by Patidar and Tare [18] where the bioreduction of sulphate was noted to vary between 40 and 190 mgSO4reduced .gVSS−1 .d−1 . The activity recorded for PSB was slightly higher than that of SRB, varying between 60.64 and 315.44 mgSO2− produced .gVSS−1 .d−1 . This suggested that 4 PSB were able to overcome SRB by oxidizing all sulphurs produced during the sulphate-reducing process. In fact, only a few studies are currently available in the literature on the kinetics of sulphur oxidation with PSB. These include the work by Harerimana et al. [3] where the oxidation of dissolved H2 S by PSB in fed-batch reactors and the specific oxidation rates of PSB in the fed-batch cultures were determined to be 301–767 mgH2 Soxidized .gVSS−1 .d−1 . Although slightly lower, the values recorded for PSB activity in the present study remain comparable to those previously reported in the literature. Conclusion Both sulphate-reducing and sulphur-oxidizing processes were studied in batch cultures at 30◦ C and pH 8 over a wide range of sulphate concentrations. The maximum specific rates of SRB and PSB contained in mixed culture were 188.78 mgSO4reduced .gVSS−1 .d−1 and 315.44 mgSO2− produced .gVSS−1 .d−1 , respectively. More4 over, the rate of PSB activity was noted to be twice as high as that of SRB. Accordingly, the findings indicate that PSB can be used effectively in fighting against odours. The most important environmental factors affecting the sulphur cycle in the waste stabilization pond are likely to be the availability of sulphate and light for SRB and PSB, respectively. Acknowledgements
The work was partially supported by CUD (Commission Universitaire pour le Dévéloppement) through the PIC (Projets interuniversitaires ciblés), Tunisia-Belgium.

References
[1] Y. Racault, Le lagunage naturel, les leçons tirées de 15 ans de pratique en France, Cemagref Editions, France, 1997.

Appendix 1. Petersen matrix of the anaerobic digestion model, including sulphate reduction and sulphur oxidation process in wastewater stabilization ponds (WSP). Component i j 1 2 Process Sc Disintegration Hydrolysis of 1 complex organic material Uptake of complex −1 organic material Uptake of acetate Uptake of hydrogen Uptake of acetate by SRB −1 1 Sac 2 Sh2 3 Sso4 4 SH 2S 5 Sch4 6 SIC 7 SIN 8 SH + Kdis Xc Khyd,c Xc 9 Rate (ρj , kg COD.m−3 .d−1 )

3 4 5 6

3.3 − 3.3Yc −1

3.3 − 3.3Yc 1 − Yac −1 Yac,so4 −1 1 − Yac,so4 0.25 − 0.25Yh2

1.4 − 1.65Yc 1 − Yac

1 − 1.65Yc −0.4Yac

km,c

Sc Xc kS,c + Sc

−(0.25 + −0.4Yh2 0.25Yh2 ) 2− 2Yac,so4 −0.4Yac,so4 2.4Yac,so4 − 2

Sac Xac I1 kS + Sac Sh2 Xh2 I2 km,h2 kS + Sh2 km,ac

Environmental Technology

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Uptake of hydrogen by SRB

−1

Yh2,so4 − 1 1 − Yh2,so4

−2Yh2,so4

−0.4Yh2,so4 2.4Yh2,so4 − 2

SSO4 KSO4 + SSO4 Sac × Xac,so4 Kac + Sac SSO4 km,SO4 KS,SO4 + SSO4 Sh2 × Xh2,so4 KS,h2 + Sh2 km,SO4 km,H 2S SH 2S KS,H 2S + SH 2S I × XPSB KI + I + Ki I 2

8

Growth of phototrophic sulphuroxidizing bacteria Decay of Xc Decay of Xac Decay of Xh2 Decay of Xac,SO4 Decay of Xh2,SO4 Decay of XPSB

1

−1

−2

−0.4

2

9 10 11 12 13 14

Complex Total Hydrogen Sulphates Total sul- Methane Inorganic organic acetate phides gas (kgCOD gas carbon material (kgCOD (kgCOD (kgCOD m−3 ) (kgCOD gas m−3 ) m−3 ) m−3 ) m−3 ) (kmoleC m−3 )

Inorganic Methane gas (kgCOD nitrogen m−3 ) (kmoleN m−3 )

Kdec,Xc Xc Kdec,Xac Xac Kdec,Xh2 Xh2 Kdec,Xac,so4 Xac,so4 Kdec,Xh2,so4 Xh2,so4 Kdec,Xpsb XPSB I1 and I2 : inhibition factor I1 = IpH IIN , lim I2 = IpH IIN , lim INH 3,Xac I = light intensity

7

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Appendix 2.

Petersen matrix of the anaerobic digestion model including sulphate reduction and sulphur oxidation process in WSP (suite). 1 Xac 2 Xh2 3 4 Xac,so4 5 Xh2,so4 Xpsb 6 Xi Kdis Xc Khyd,c Xc 7 Rate (ρj , kg COD.m−3 .d−1 )

Component i j Process Xc 1 Disintegration 2 Hydrolysis of complex organic material 3 Uptake of complex organic material 4 Uptake of acetate 5 Uptake of hydrogen 6 Uptake of acetate by SRB 7 Uptake of hydrogen by SRB 8 Growth of phototrophic sulphur oxidizing bacteria 9 10 11 12 13 14 Decay of Xcom Decay of Xac Decay of Xh2 Decay of Xac,SO4 Decay of Xh2,SO4 Decay of XPSB −1 1.65Yc

km,c 0.4Yac 0.1Yh2 0.4Yac,so4 0.4Yh2,so4 0.4

Sc Xc kS,c + Sc

Sac Xac I1 kS + Sac Sh2 km,h2 Xh2 I2 kS + Sh2 km,ac km,SO4 km,SO4 km,H 2S SSO4 Sac Xac,so4 KSO4 + SSO4 Kac + Sac SSO4 Sh2 Xh2,so4 KS,SO4 + SSO4 KS,h2 + Sh2 SH 2S I XPSB KS,H 2S + SH 2S KI + I + Ki I 2

C. Harerimana et al.

−1

−1

−1

−1 Sulphates reducing (kgCOD m−3 )

Complex organic Acetate Hydrogen Sulphates degraders degraders degraders reducing (KgCPD m−3 ) (kgCOD (kgCOD (kgCOD m−3 ) m−3 ) m−3 )

Kdec,Xc Xc Kdec,Xac Xac Kdec,Xh2 Xh2 Kdec,Xac,so4 Xac,so4 Kdec,Xh2,so4 Xh2,so4 −1 Kdec,Xsob Xpsb Sulphur Particulate inerts I1 and I2 : inhibition factor oxydation gas (kmoleC m−3 ) I1 = IpH IIN , lim I2 = IpH IIN , lim INH 3,Xac I = light intensity