Chemosphere 339 (2023) 139605 Contents lists available at ScienceDirect Chemosphere journal homepage: www.elsevier.com/locate/chemosphere Integrating thermodynamics and mathematical modelling to investigate the stoichiometry and kinetics of sulphide oxidation-nitrate reduction with a special focus on partial autotrophic denitrification Eric Valdés a, David Gabriel a, *, Daniel González a, Giulio Munz b, Cecilia Polizzi b a GENOCOV Research Group, Department of Chemical, Biological and Environmental Engineering, Escola d’Enginyeria, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain b Department of Civil and Environmental Engineering, University of Florence, Via di S. Marta, 3, 50139, Firenze, Italy H I G H L I G H T S G R A P H I C A L A B S T R A C T • Thermodynamics agree with theory under the high energy dissipation hypothesis. • Five kinetic models on SO-NR processes were compared to describe PAD performance. • Satisfactory capacity to simulate nitrite accumulation for 3 out of the 5 models. • NO−2 accumulation well modelled through Monod and Haldane kinetics for NO−2 uptake. • Haldane showed higher parametric identifiability allowing for further model simplification. A R T I C L E I N F O A B S T R A C T Handling Editor: Y Liu In the present study, the stoichiometry of the Sulphur Oxidizing-Nitrate Reducing (SO-NR) process, with a focus on Partial Autotrophic Denitrification (PAD), has been evaluated through a thermodynamic-based study whereas Keywords: a model-based approach has been adopted to assess process kinetics. Experimental data on process performance Partial autotrophic denitrification and biomass yields were available from a previous work achieving efficient PAD, where a biomass yield of 0.113 Nitrite accumulation gVSS/gS was estimated. First, the free Gibbs energy dissipation method has been implemented, in order to SOB provide a theoretical framework exploring the boundaries for sulphur oxidizing biomass yields. Second, a Thermodynamics Modelling screening of available mathematical models describing SO-NR process was conducted and five published models were selected, in order to assess the most suitable model structure for describing the observed PAD kinetics. To the best of our knowledge, none of reported biomass yields are estimated in systems operating PAD as the main process and, analogously, none of the proposed models have been applied to case studies aiming at partial denitrification only. The work showed that the very low biomass yield of 0.117 ± 0.007 gVSS/gS, observed in a PAD system in our previous work, suggests that the conditions applied to achieve partial denitrification resulted * Corresponding author. Escola d’Enginyeria, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain. E-mail address: David.Gabriel@uab.cat (D. Gabriel). https://doi.org/10.1016/j.chemosphere.2023.139605 Received 24 April 2023; Received in revised form 18 July 2023; Accepted 19 July 2023 Available online 22 July 2023 0045-6535/© 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by- nc/4.0/). E. Valdés et al. Chemosphere 339 (2023) 139605 in a high energy-dissipating metabolism compared to complete denitrification applications. Models’ analysis revealed that nitrite accumulation can be described by a classical Monod kinetics if different μmax are adopted for each intermediate reaction, with Theil Inequality Coefficient values lower than 0.21 for both NO−3 and NO−2 . Nonetheless, adopting Haldane-type kinetics for nitrite uptake inferred higher identifiability to the model structure, resulting in confidence intervals below ±10% for all the parametric estimations. The thermodynamic and modelling outcomes support the experimental results obtained in the reference study and the critical comparison of model suitability to represent PAD process is believed pivotal to pave the way to its real-scale implementation. 1. Introduction ratio) and biomass adaptation also affect observed uptake rates and stoichiometry. SOB biomass yields are reported in the range of 0.1–0.4 Sulphur Oxidation-Nitrate Reduction (SO-NR) is a complex process gVSS/gS (see Polizzi et al., 2022). Due to the complexity of the possible carried out by Sulphur Oxidizing Bacteria (SOB) and characterized by reaction combinations, solving the full stoichiometry is not a trivial peculiar aspects such as: (i) multistep reactions involved both for elec­ exercise (Klatt and Polerecky, 2015). When dealing with complex pro­ tron acceptor reduction and electron donor oxidation; (ii) high chemical cesses, mathematical models are an effective tool for gaining insight into reactivity of reduced sulphur compounds, such as sulphide and thio­ the mechanisms underlying processes’ response under different opera­ sulphate; (iii) variety in microbial population able to mediate SO-NR tional conditions. The models proposed in the literature for the reactions, from strictly to facultative anaerobic and from chemo­ description of SO-NR process mainly differ for the following character­ lithotrophic to mixotrophic cultures (Madigan et al., 2019), being Thi­ istics: (1) one or two-step reactions are presented for the oxidation and obacillus and Sulfurimonas the most abundant and dominant genera in reduction semi-reactions; (2) Monod kinetics are typically assumed for aerobic and anoxic sulphur oxidation applications (Mora et al., 2014). NO−3 and S0 uptake while both Monod or Haldane kinetics are encoun­ Both sulphide oxidation and nitrate reduction are typically described as tered for HS− and NO−2 uptake; (3) switch functions are sometimes two-step processes, resulting in the possible combination of electron included in order to elicit the preferred uptake of one electron acceptor acceptor/electron donors described in equations (1)–(4) (see Table S2 (or donor) or the other, in case multistep reactions; (4) kinetic param­ for the solved catabolic reactions) even though the actual reactions eters, in terms of maximum growth rate and/or half saturation co­ involve several other intermediates. efficients, are either assumed having the same value in all reaction steps or different values for each reaction step. As a consequence, the Eq. (1) − HS− + NO−3 + H + → S0 + NO2 + H2 O complexity and the consequent number of parameters required by models can vary significantly. HS− + 0.67 NO−2 + 1.67 H + → S0 + 0.335N2 + 1.335H2 O Eq. (2) In the present work, an integrated approach based on a thermody­ namic study and mathematical modelling is proposed to gain insight, Eq. (3) − S0 + 3 NO3 + H2 O → SO2−4 + 3 NO−2 + 2 H + respectively, on the stoichiometry and kinetics of SO-NR, with special focus on the novel process of PAD. The work by (Polizzi et al., 2022) is Eq. (4) − S0 + 2 NO2 → SO2−4 + N2 selected as the reference study for successful PAD implementation. The first aim of the work is to present a theoretical framework for the In the last decades, the SO-NR process has received increasing attention biomass yields through a thermodynamic study, offering a critical as a sustainable solution to effectively remove nitrogen from streams comparison with experimental stoichiometric values observed in the with a low C/N ratio. Thus, it has been successfully applied in treating literature on SO-NR systems as well as those estimated in the reference groundwater, secondary effluent of municipal wastewater, drinking study on PAD. The second purpose is to achieve a mathematical repre­ water, mariculture wastewater (Wang et al., 2023), municipal tailwater sentation of the observed nitrite accumulation kinetics: five models (Li et al., 2023) and landfill leachate (Zhang et al., 2023). Furthermore, available in the literature were selected and studied through a sensitivity the coupling of this process with C removal has been successfully and identifiability analyses, in order to assess their suitability for the implemented in full scale facilities (SANI® process, Wu et al., 2016), as representation of the observed data. To the best of our knowledge, none well as H2S removal from gaseous streams such as biogas (Baspinar of the reported biomass yield is estimated in a system operating PAD as et al., 2011). More recently, innovative solutions are promoting the the main process and, analogously, none of the proposed models have integration of gaseous and wastewater biological treatments, such as the been applied to case studies aiming at representing partial denitrifica­ integrated nitrogen and sulphur removal combining the anammox pro­ tion only. cess and the sulphide-driven partial autotrophic denitrification, PAD (Chen et al., 2019). Such an integrated process can offer an appealing 2. Material and methods application in the treatment of wastewater side-streams generated by anaerobic digestion, typically highly rich in reduced forms of nitrogen, 2.1. Experimental dataset as well as in the H2S removal from biogas. Even though successful PAD has been presented in recent studies using elemental sulphur, thio­ Data from (Polizzi et al., 2022) were considered both for the ther­ sulphate or sulphide as electron donor (Chen et al., 2018; Deng et al., modynamics and modelling tasks. In the mentioned publication, suc­ 2022; Polizzi et al., 2022), the comprehension of the mechanism un­ cessful partial denitrification (i.e., nitrite accumulation) was achieved in derlying successful nitrite accumulation and the consequent operational a chemostat under sulphide-limiting conditions. During stable opera­ strategies to be applied are still object of discussion. tion, three operational phases were tests adopting SRT values in the The complexity of SO-NR process is reflected in the different, and range of 13–44 h and influent S/N within 0.65 and 0.95 gS/gN. Nitrite sometimes contradictory, results that can be found in the literature on conversion rate, calculated as the nitrite production over the removed the favoured electron acceptor between nitrate and nitrite as well as the nitrate, was above 70% at all the applied conditions, with peaks close to observed biomass yields. For instance, some authors indicate nitrate as 100%. The observed biomass yield was estimated at 0.117 ± 0.007 the preferred electron acceptor when coupled with sulphide oxidation mgVSS/mgS. Microbial community analysis revealed that a clear pop­ (Campos et al., 2008; Guo et al., 2016), whereas other works report ulation shift occurred: Sulfurimonas was the dominant genus in the nitrite instead (Cui et al., 2019). Biomass cultivation mode (e.g., sus­ inoculum (97% of relative abundance) and was almost completely pended or granular systems), operational conditions (e.g. SRT, S/N 2 E. Valdés et al. Chemosphere 339 (2023) 139605 replaced by Thiobacillus (83% of relative abundance) after 80 days of 2.3. Model selection operation. As reported in the work, S0 was not measured but rather estimated, with a 10–30% error on S mass balance, depending on the A bibliographical research was conducted in order to screen out the operational phase. In Table S1 of the supplementary material, the main various approaches adopted in mathematical modeling of autotrophic operational conditions are summarized for each phase. For the model­ denitrification rates, with the final aim of assessing their capability of ling purpose, phase 1a was removed from the experimental dataset since simulating the experimental data on nitrite accumulation presented by the system had not reached stable conditions. (Polizzi et al., 2022). In order to establish a common ground among the available publi­ cations, only the works matching the following criteria were considered: 2.2. Thermodynamic study 1) processes were modelled through rate-limited reactions, i.e. no mass transport limitations; 2) SO-NR was modelled through the four main The free Gibbs energy dissipation method formulated by (Heijnen steps presented in equations (1)–(4), referred to as process 1, 2, 3 and 4, et al., 1992a) and further generalized by (Kleerebezem and Loosdrecht, herein; 3) one single biomass was considered for all the reactions; 3) 2010), was used to estimate theoretical biomass yields for the different operational conditions were in the typical/optimal ranges of pH and reaction steps involved in SO-NR, based on sulphide and elemental temperature for autotrophic denitrification processes (7–8 and sulphur as electron donor and nitrate/nitrite as electron acceptor. 22–30 ◦ C, respectively, according to (Deng et al., 2021)). Five models Catabolic stoichiometry was solved for all the intermediate steps were selected, and special attention was devoted to the kinetic functions involved in SO-NR: both oxidation and reduction reactions were and parameters regulating uptake rates among the different reactions, in simplified in a 2-step reaction and no other intermediary products were each model structure. Specifically, the following aspects were analyzed: considered except sulphur and nitrite, respectively. According to (Heijnen et al., 1992a), energy dissipation (ΔGdis) in autotrophic - Substrate uptake kinetics: Monod-type vs Haldane-type; metabolism appears strongly dependent on the fact that bacteria utilizes - Half-saturation coefficients: same value assumed for a given sub­ or not the reverse electron transport (RET) mechanism. Chemo­ strate in all the processes vs different values depending on the lithotrophic SOB are reported to adopt RET for C fixation but defining if process; and how efficiently bacteria adopt RET is not always straightforward - Maximum growth rates: same value assumed for all the processes vs since many metabolic mechanisms remain unclear (Klatt and Polerecky, different values for each process. 2015; Lin et al., 2018; Madigan et al., 2019; Yavuz et al., 2007) have - Switch functions for the competition among electron acceptors/do­ applied the free Gibbs energy method to estimate the theoretical nors: adopted vs not adopted. biomass yield of SOB, under the assumption that a highly energy-requiring RET mechanism was required for biomass synthesis, A summary of the main assumptions of the selected mathematical assuming ΔGdis = 3500 kJ/C-mol. Results from (Yavuz et al., 2007) have models is shown in Table 1; complete growth rate formulations of each been used by (Can-dogan et al., 2010; Mora et al., 2015a) to support model is reported in Table S5 of the supplementary material. their experimental results. On the other hand, (Kleerebezem and Men­ Each model was solved using the Gear numerical method in Matlab dez, 2002) have compared the biomass yield obtained in their R2020B software (toolbox ode15s). Experimental biomass yields avail­ SOB-based work with values reported in literature. A total of 8 studies able in (Polizzi et al., 2022) were used in all the models instead of the were reviewed, adopting mainly thiosulphate as electron donor but also default values, with further assumptions derived in the thermodynamic sulphide and elemental sulphur; literature biomass yields were then study and described in section 3.1. Table S4 reports the stoichiometric used to derive overall metabolic energy dissipation, by applying the free matrix applied to all the models. Gibbs energy method in a bottom-up approach, and energy dissipation was estimated to be around 1500 ± 600 kJ/C-mol. Even though the standard deviation was as high as the 40%, the confidential interval falls 2.4. Model comparison procedure below the value of 3500 kJ/C-mol, suggesting a more efficient energy uptake. The multi-step procedure shown in Fig. 1 and described in the next In the present work, full stoichiometry has been solved for all the sections was implemented in order to evaluate models’ suitability to possible reaction steps occurring in SO-NR, under the following two represent the observed data. scenarios: - STEP 1. First, a sensitivity analysis was performed in order to assess Energy dissipation, EDiss the three most sensitive parameters of each model. The sensitivity analysis was a local analysis, i.e., the effect of each parameter over the 1. EDiss_1 ΔGdis = 3500 kJ/C-mol; simulated output variables was assessed varying each parameter by a 2. EDiss_2 ΔGdis = 1500 kJ/C-mol (average value from Kleerebezem 10% increase and decrease, one at a time. The analysis was performed and Mendez, 2002) three times for every model, one for each experimental phase (see Table S1), to reach steady-state simulated outputs. Thus, the relative Another aspect discussed in this section is the biomass formulation sensitivity (Sij) of a steady-state output θi with respect to a parameter γ j used in the stoichiometries available in literature. Some studies report a was calculated according to Equation (5) (Reichert and Vanrolleghem, C-mol formulation of CH1,8O0,5N0,2 as reported by Roels (1983); some 2001): others a 5C-mol formulation of C5H7O2N (Rittmann and McCarty, θi dγ j 2001). Normalizing the second formulation to one C-mol, biomass Sij = Eq. (5) γj dθi stoichiometry results in CH1,4O0,4N0,2, slightly different for H and O fractions. The presented methods and hypotheses have been applied to The two output variables used for this analysis were nitrate NO−3 both of the biomass composition (BC): BC_1: CH1,8O0,5N0,2 (Roels, (mgN/L) and nitrite NO−2 (mgN/L). Due to the uncertainties on the 1983) and BC_2: CH1,4O0,4N0,2 (normalized to 1 C-mol from Rittmann experimental data on the sulphur species (see section 2.1), the latter and McCarty, 2001). were not included in the sensitivity analysis nor in the objective function As general assumptions, one single SO-NR biomass is assumed for all of the calibration procedure, but rather used for a qualitative validation the possible reactions, CO2 (as HCO3-) and NH4+ are considered as C of the calibrated models. The average of both sensitivity absolute values and N source, respectively. The derived theoretical biomass yield was (±10%) was first calculated for each parameter and output. Then, the conducted and compared with literature values. average of the values obtained per each of the two output variables was 3 E. Valdés et al. Chemosphere 339 (2023) 139605 Table 1 Summary of the mathematical models considered in this study. Default stoichiometric parameters were not used in the present study, see section 2.3. Model No. of Substrate Substrate Switch No. of Experimental data kinetic uptake kinetics affinities among functions stoichiometric parameters processes parameters Tot μmax Monod Haldane Constant Non- Non- value constant competitive value inhibition (Xu et al., 18 4 S0, S2− , – S2− , S0, NO−3 over 1 Batch tests with autotrophic and/or heterotrophic a 2014) NO−3 , NO−2 NO−3 , NO−2 NO−2 denitrification. NO−2 a NO−2 over NO−3 b Mora et al. 12 4 S0, S2− , S2− , S0, – S2− over S0 1 Autotrophic denitrification in respirometric batch (2015a) NO−3 NO−2 NO−3 , tests. NO−2 (Hauduc 11 2c S0, S2− , S2− , S0 NO−3 , NO−2 S2− over S0 d 1 Literature review. et al., NO−3 NO−2 2019) (Xu et al., 5 1 S2− , None S2− , S0, – – 4 Autotrophic denitrification in a sequential batch 2016) NO−3 , NO−3 , reactor NO−2 NO−2 (Huo et al., 11 4 S2− , S0, None S2− , S0 NO−3 , NO−2 – 2 Autotrophic denitrification in batch tests from Cui. 2022) NO−3 , et al. (2019), and coupled autotrophic denitrification- NO−2 Anammox in batch tests from Deng et al. (2021). a The Monod term for nitrite is only present in process 4. The Haldane term for nitrite is only present in process 2. Both Haldane terms use different inhibition constants for processes 1 and 2, and 2 and 4, for S2− and NO−2 ,respectively. b The switch term accounting for outcompetition of nitrate over nitrite is only present in process 3. The switch term for outcompetition of nitrite over nitrate is only present in process 1. c Each μmax and biomass/substrate yield value for each electron donor – uptake processes (S2− and S0). d The switch term accounting for outcompetition of sulphide over sulphur is only present in process 3. Fig. 1. Flow chart of the model comparison procedure. FIM refers to the Fisher Information Matrix while TIC refers to the Thiel Inequality Coefficient. calculated to obtain a single sensitivity value for each parameter and - STEP 2. After performing the sensitivity analysis, the 3 most sen­ phase. Therefore, in each case a p x r sensitivity matrix was obtained, sitive parameters (i.e., the parameters with the highest relative sensi­ where p is the number of parameters analyzed and r is the number of tivities) were selected for calibration. Parameter calibration was carried experimental phases considered. out by using the simplex search method of (Lagarias et al., 1998), which 4 E. Valdés et al. Chemosphere 339 (2023) 139605 is included in Matlab by using the toolbox fminsearch. The fitting of the process have been solved and results are presented in Table S2, experimental data considered NO−3 (mgN/L) and NO−2 (mgN/L) to whereas the full metabolic reactions are reported in tables S3a-b. Table 2 minimize the objective function (F) (Eq. (6)). Function F was defined as reports a synthesis of the biomass yields derived for each catabolic step, the sum of the norm of the differences between model predictions and under the two assumptions on energy dissipation and biomass compo­ the experimental data for each output variable y: sition. Biomass yields (herein referred as Y) are reported both as C-mol/ √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ S-mol and C-mol/e-mol (i.e. C-mole production per electron mole √∑ √ m ∑ released during the ED oxidation). At each ED oxidation reaction, n [ ]2 F=√ yexp,i− ymod,i Eq. (6) j=1 i=1 biomass yield, either as C-mol/S-mol or C-mol/e-mol, varies by 27–29%, depending on the TEA reduction reaction that is used in catabolism. where m is the number of output variables, n is the number of experi­ Such a wide range is to be ascribed to the fact that 2 to 5 electrons can be mental data, yexp,i is the experimental value and ymod,i is the predicted accepted in the TEA reduction steps, thereby affecting the free Gibbs value. In order to avoid inconsistency of calibrated parameter values energy available from catabolism and, ultimately, the λCat determining with empirical evidenced, the calibration was limited within an “con­ the full metabolism stoichiometry (Kleerebezem and Loosdrecht, 2010). sistency range”, whose upper and lower values were set according to The last three rows of Table 2 summarize the Y values for each ED literature. The assumed range for each parameter can be found in the oxidation step, reporting average value and standard deviation, calcu­ supplementary material (Table S8). lated over the three possible TEA reduction cases. Considering biomass The fit of each calibrated model was quantitatively assessed through yields expressed as C-mol/S-mol, the values from the oxidation reaction the Thiel Inequality Coefficient (TIC). This index is specifically appro­ HS− →S0 is almost half of the one obtained from the reaction S0→SO42− priate to compare different models and was calculated according to and almost one third of the one from reaction HS− →SO42− , consistently Equation (7) (Huiliñir et al., 2010): with the fact that 2, 4 and 6 electrons are released in each reaction, √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ respectively, as well as with previous results presented in the literature ∑m ( )2 (Deng et al., 2021b; Mannucci et al., 2012a). Such an evidence is in line yexp,i− ymod,i with the results of biomass yields normalized to the electron released at Eq. (7) i TIC = √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ ̅ ∑m ∑m each corresponding ED oxidation step. All the yields as C-mol/e-mol, in yexp,i 2 + ymod,i 2 i i fact, exhibit values of 0.23 and 0.47 C-mol/e-mol, for the assumption of 3500 and 1500 kJ/C-mol, respectively. TIC values range between 0 and 1, being 0 a model output with no It can be easily observed that the hypothesis on the overall energy differences with the experimental data (i.e., a model with no errors in its dissipation is much more relevant than the one on the biomass compo­ predictions) and 1 the limit value when differences tend to be infinite. It sition, resulting in 50% of variation, if the two values of 3500 or 1500 is generally accepted to consider a maximum TIC of 0.3 as the threshold kJ/C-mol are considered. Indeed, only 1–2% variation is observed for a good fit of the modeling results (Hvala et al., 2005). comparing the results from the two biomass compositions. In the Model identifiability was evaluated through the FIM (Fisher Infor­ biomass composition from (Savageau, 1984), CH1,8O0,5N0,2, the mation Matrix) methodology (Guisasola et al., 2006) in order to calcu­ oxidation state of carbon is 0.2 and 4.2 e-mol/C-mol are required to the late the confidence intervals of the calibrated parameters. The FIM is a reduction of CO2 to biomass. In the biomass composition from Rittmann pxp matrix, where p is the number of parameters, that incorporates the and McCarty (2001), CH1,4O0,4N0,2, the oxidation state of carbon is sensitivity functions of the calibrated parameters and the error of the 0 and 4 e-mol/C-mol are required instead. Thereby, it is reasonable that experimental measurements. It is particularly useful to evaluate model such a minor difference in electron requirement (0.2 e-mol/C-mol) im­ structures and their capacity to reduce uncertainty in their predictive plies a comparable requirement of electron donor in anabolism. responses, since the presence of misspecifications in a given model (e.g., Biomass yields available in literature have been evaluated and inclusion of extraneous variables or omission of relevant variables) gathered according to the corresponding catabolic reaction considered might lead to incorrect parameter estimations (Guisasola et al., 2006a; in each work. Only works where sulphide or sulphur were used as Quaglio et al., 2018). electron donor were considered and results are summarized in Table 3. Nevertheless, the values reported by (Kleerebezem and Mendez, 2002) - STEP 3: The performance of the calibrated models was compared are considered as representative also of the experimental values using considering the goodness of fit of the modelled N species dynamics thiosulphate as electron donor, since the literature review presented by throughout the three experimental phases, in light of the results of the authors encompasses works based on thiosulphate, sulphur and step 2. sulphide oxidation (coupled with denitrification) and anaerobic cellular - STEP 4. After evaluating the best-fitting models for this study, one yields on sulphide consumption are reported to be comparable with that last effort was done in order to evaluate whether further structure on thiosulphate for T. denitrificans (Hoor and Cell, 1981). When the in­ simplification was possible without hampering the stability of the formation reported was sufficient, biomass yield unit conversion has model output. To do that, the methodology of Fig. 1 was applied been calculated for each study. Note that the use of granular or again to the new simplified model versions. biofilm-based biomass in UASB-like reactors are often reported, but biomass concentration is rarely assessed. Thereby, many studies on Moreover, beyond the analyzed models, an alternative 2-population denitrifying SOB could not be used in this literature review due to the modelling approach was investigated and results are presented in the lack of information on biomass growth. supplementary material (see section S4). This parallel modelling effort As presented in Tables 2 and 3, the biomass yields observed by falls out of the main scope of this study, but it is presented as an illus­ (Polizzi et al., 2022) is among the lowest reported in literature. The trative and complementary approach that can be applied to simulate the theoretical yields derived under the two assumptions of energy dissi­ population shift observed in Polizzi et al., 2022). pation, at all the SO-NR catabolic steps, are reported in tables S3a-b; it can be observed that the experimental yield of the reference study is 3. Results and discussion close to the values obtained with the assumption of high energy dissi­ pation. To the best of our knowledge, no other works report on biomass 3.1. Thermodynamic theoretical framework: exploring the boundaries of yields in process operating mainly (or exclusively) the denitratation SOB yield factor step. (Klatt and Polerecky, 2015) report a study on SOB proposing a new theoretical approach to estimate microbial bioenergetics efficiency, Catabolic reactions for the possible intermediate steps in SO-NR based on the factorization of the metabolic aspects involved in energy 5 E. Valdés et al. Chemosphere 339 (2023) 139605 Table 2 Main results from biomass yield study. ΔG01_met = 3500 kJ/Cmol ΔG01_met = 1500 kJ/Cmol C-mol_biom/S-mol C-mol_biom/e-mol C-mol_biom/S-mol C-mol_biom/e-mol CH1,8O0,5N0,2 CH1,4O0,4N0,2 CH1,8O0,5N0,2 CH1,4O0,4N0,2 CH1,8O0,5N0,2 CH1,4O0,4N0,2 CH1,8O0,5N0,2 CH1,4O0,4N0,2 HS− → SO2- 4 0.189 0.191 0.024 0.024 0.383 0.392 0.048 0.049 NO−3 → N2 HS → SO2- − 4 0.228 0.231 0.028 0.029 0.452 0.463 0.056 0.058 NO−2 → N2 HS → SO2- − 4 0,126 0,128 0,016 0,016 0.266 0.272 0.033 0.034 NO−3 → NO−2 0 HS → S − 0.050 0.050 0.025 0.025 0.101 0.103 0.050 0.052 NO−3 → N2 HS− → S0 0.060 0.060 0.030 0.030 0.118 0.121 0.059 0.060 NO−2 → N2 HS− → S0 0.034 0.035 0.017 0.017 0.072 0.074 0.036 0.037 NO−3 → NO−2 S0 → SO2- 4 0.139 0.141 0.023 0.023 0.282 0.289 0.047 0.048 NO−3 → N2 S0 → SO2- 4 0.168 0.171 0.028 0.028 0.334 0.342 0.056 0.057 NO−2 → N2 0 S → SO2−4 NO3 → NO2 − − 0.092 0.093 0.015 0.015 0.194 0.198 0.032 0.033 HS− → SO2- 4 0.181 0.183 0.023 0.023 0.367 0.376 0.046 0.047 HS− → S0 0.048 0.048 0.024 0.024 0.097 0.099 0.049 0.050 S0 → SO−4 - 0.133 0.135 0.022 0.022 0.270 0.276 0.045 0.046 HS¡ → SO2- 4 0.18 ± 0.05 0.023 ± 0.006 0.37 ± 0.09 0.046 ± 0.012 HS¡ → S 0.05 ± 0.01 0.024 ± 0.006 0.10 ± 0.02 0.049 ± 0.012 S → SO2- 4 0.13 ± 0.04 0.022 ± 0.006 0.27 ± 0.07 0.046 ± 0.012 Table 3 Literature and theoretical values for SOB yield factor. Y Reference Method 1C-mol/ 1C-mol/ g_biom/gS g_biom/gN S-mol e-mol HS¡→ SO2- 4 0.512 0.064 0.378 0.635 (Sublette and Sylvester, 1987) Experimental NO¡3 → N2 0.333 0.042 0.256 0.451 Kleerebezem and Mendez, Review/Thermodynamics calculations 2002 0.511 0.064 0.361 0.694 Campos et al. (2008) – 0.184 0.023 0.130 0.208 Can-Dogan et al. (2010) Thermodynamic calculationsb confirmed by experimental evidence 0.465 0.058 0.328 0.610 Mora et al., 2014 Experimental 0.156 0.019 0.118 0.149 Polizzi et al., 2022a Experimental 0.189–0.383 0.023–.046 0.145–0.294 0.230–0.526 This studyc Thermodynamic calculations HS¡ →S0 0.159 0.08 0.562 (Gadekar et al., 2006) Experimental and modelling NO¡3 → N2 0.046 0.023 0.032 Can-Dogan et al. (2010) Thermodynamic calculationsb confirmed by experimental evidence 0.13–0.37 Xu et al., 2016 Experimental and modelling 0.065 0.033 0.046 0.300 Mora et al., 2014c Experimental 0.050–0.1 0.025–0.05 0.038–0.077 0.244–0.563 This studyc Thermodynamic calculations S0 → SO2- 4 0.364 0.061 0.257 0.646 (Sahinkaya et al., 2011) – NO¡3 → N2 0.400 0.067 0.283 0.737 Mora et al., 2014c Experimental 0.364 0.061 0.257 0.646 (Batchelor and Alonzo, 1978) Experimental 0.21–0.38 Xu et al., 2014 Calibration on continuous experiment modelling a Estimated in a system performing PAD as the main reaction. b Free Gibbs energy method, under the hypothesis of ΔGDISS of 3500 kJ/C-mol. c Theoretical yield according to the free Gibbs energy change method, under the hypothesis of ΔGDISS of 3500 kJ/C-mol (lower limit) and 1500 kJ/C-mol (upper limit). conversion and production. Specifically, for SOB bacteria, the energetic observed in the reference work, where energy-limiting conditions were efficiency of the following aspects is considered: (i) energy production in determined by steady electron donor limitation. In line with such a the catabolic reaction, depending on the Sulphur metabolic pathway consideration is the observed outcompetition of the more used by the microorganism; (ii) CO2 fixation cycles and (iii) electron energy-efficient Thiobacillus genus over the Sulphurimnas genus (Klatt donor consumption in RET for the reducing power to be produced (NAD and Polerecky, 2015; Polizzi et al., 2022). (P)H, FADH2 or reduced Ferredoxin). Even though, such a new method is not implemented in the present study, it is of interest to highlight the 3.2. Model implementation, sensitivity analysis and calibration results underlying assumptions and conclusions proposed by the authors, since they clarify how the actual microbial bioenergetics also depends on the According to the study on the electron availability in the first and specific bacteria involved and the metabolic pathways adopted. It is second step of HS− oxidation, the experimental biomass yield of 0.117 remarkable to highlight that, in the reference study, energy optimization g_biom/gS, observed over the complete HS− oxidation to SO−4 -, was mechanisms are speculated to have promoted the population shift proportionally recalculated for each oxidation step; such an approach is 6 E. Valdés et al. Chemosphere 339 (2023) 139605 in line with yields reported in other works (Deng et al., 2021; Mannucci of how well the simulated data fits with the experimental dataset for et al., 2012). The yields resulted in 0.029 g_biom/gS, for process 1 and 3, nitrite and nitrate, respectively. Consistently, as shown in Table 4, the and 0.088 g_biom/gS, for process 2 and 4, and were adopted in each of higher the F value of a given model, the higher the TIC values. The the five model instead of their default value. highest F and TIC values are observed by the models from (Hauduc et al., 2019; Xu et al., 2016), both showing TICNO2 above the critical threshold. 3.2.1. Sensitivity analysis On the contrary, the lowest F and TIC values are observed for the models The results of the sensitivity analysis for each model are shown in from (Mora et al., 2015a; Huo et al., 2022). In terms of F and TIC values, Table S7. The parameters that showed higher sensitivities are directly the model proposed by (Xu et al., 2014) showed intermediate values involved in nitrate and nitrite reduction: maximum specific growth rates compared to the above-mentioned models, with the TICNO3 slightly (μmax), semisaturation coefficients (ksNO3 and ksNO2) and inhibition below the critical threshold. Also noteworthy, optimized parameters constants (kiNO2 and kswitch). In the simulations related to the sensitivity with extreme values close to the limits set during calibration were ob­ analysis, simulated sulphide and elemental sulphur were barely tained in those models where the goodness-of-fit was not satisfying (see observable throughout phases 1b and 2 (data not shown); thereby, semi- Table S6), i.e., models by (Xu et al., 2016; Hauduc et al., 2019; Xu et al., saturation coefficients and inhibition constants referring to sulphide and 2014). Regarding parameter identifiability, the models from (Mora sulphur did not show any significant impact. Nevertheless, in phase 3 a et al., 2015a; Huo et al., 2022) showed the narrower range for the general increase of parameter sensitivity was observed. According to confidence interval for the three optimized parameters. (Polizzi et al., 2022), S0 accumulation probably occurred at this last phase and was likely related to the higher and less stable influent S/N, 3.2.3. Model assessment: analysis of fit, parameter identifiability and compared to the other phases. Consistently, the sensitivity of the pa­ process rates rameters involved in processes 3 and 4, such as semi-saturation co­ Fig. 2 shows the N species profiles of each model, after calibration. A efficients for S0, is higher in the 3rd phase (see Table S7). discussion on the outcomes on parameters’ calibration, goodness-of-fit Noticeably some models showed, on average, higher sensitivity in and parametric identifiability is presented as a baseline for models’ their parameters than others. For instance (Hauduc et al., 2019), was the comparison. least sensitive model to its kinetic parameters, as a general behaviour. Results on models’ accuracy were in agreement with the outcomes When looking at the default performance of this model, it was noticeable described in the previous section. Indeed, the calibrated models from how steady-state values for nitrite were approaching a value of 0 under (Xu et al., 2014; Mora et al., 2015a; Huo et al., 2022) were generally all three experimental phases. As a consequence of such limitation, most capable to represent NO−2 accumulation with good accuracy under the parameters did not show any significant effect over the simulated three experimental conditions (TICNO2 >0.14 all three models). On the values; in fact, only 1 parameter displayed a sensitivity higher than 0.25 contrary, the calibrated models from (Hauduc et al., 2019)) and of (Xu in any of the 3 phases – which is considered the threshold for significant et al., 2016)) resulted in poorer fits for NO−2 (TICNO2 = 0.32 and TICNO2 influence of a parameter over a variable (Cao et al., 2021). On the other = 0.49, respectively), in all the three phases. Remarkably, all models hand (Xu et al., 2016), showed very high sensitivity (>3, on average) to showed a good representation of the volatile suspended solids (VSS) its kinetic parameters and (Mora et al., 2015a) had a total of 9 param­ dynamics (see Fig. S2), which demonstrated the adequacy of the eters with values higher than the 0.25 threshold in, at least, one phase, experimental biomass/substrate yields from (Polizzi et al., 2022). Also which suggested that the model was more sensitive to its parameters sulphate and elemental sulphur concentrations were in line with the under the applied conditions. experimental data (see Figs. S2 and S3). Specifically, elemental sulphur accumulation during phase 3 was predicted by the five models, in 3.2.2. Parameter calibration and identifiability accordance with the experimental findings by (Polizzi et al., 2022). Dynamic calibration comprised the optimization of the three most An in-depth analysis of the biomass growth rates, in process 1 to 4, relevant parameters of each model, using the experimental dataset from has been conducted in order to better discern the reasons underlaying the full-operation of the reference study. Parameters’ calibrated values models’ outcomes discrepancies. Fig. 3 reports the average biomass are shown in Table 4 along with their confidence regions calculated with growth rates from the 5 calibrated models, for processes 1 to 4, at each the FIM. Results on the objective function and the TIC criteria are also operational phase (Hauduc et al., 2019; Xu et al., 2016). showed high provided in Table 4. rates in the reduction step NO−2 →N2 (involved in processes 2 and 4), As presented in Table 4, the goodness-of-fit among the different which appeared to limit NO−2 accumulation; the rate of process 4 was, on models was quite different as suggested by the wide range of the F average, 4.6 and 6 times higher in (Hauduc et al., 2019; Xu et al., 2016), values, from a value of 230–621. TICNO2 and TICNO3 are also a measure respectively, compared to the other three calibrated models. Process 4 Table 4 Models’ calibration outcomes: Optimum parameters’ value and their confidence regions, calculated with the FIM and presented in parenthesis, as absolute and relative value (%); objective functions values and the TIC values for NO−2 and NO−3 fits. Model Optimized parameters F value TICNO2 TICNO3 − 1 − 1 (Xu et al., 2014) μmax,1 = 7.68 d μmax,3 = 0.72 d kswitch, NO2 = 190.41 mgN/L 314 0.13 0.27 (±11.08) (±0.002) (±682.50) (±144.35%) (±0.3%) (±358.44%) Mora et al. (2015a) μmax,3 = 2.17 d− 1 μmax,4 = 0.67 d− 1 kiNO2 = 102.43 mgN/L 225 0.10 0.18 (±0.01) (±0.06) (±1.53) (±0.67%) (±9.58%) (±1.49%) (Hauduc et al., 2019) μmax,2 = 1.64 d− 1 ksNO2, S0 = 110.00 mgN/L ksNO2, HS = 110.00 mgN/L 458 0.32 0.16 (±0.003) (±8.25) (±41.38) (±0.19%) (±7.51%) (±37.61%) (Xu et al., 2016) ksNO2 = 109.93 mgN/L μmax,1 = 6.78 d− 1 nS = 0.176 621 0.49 0.31 (±1.29) (±9.77) (±10.03) (±1.2%) (±144.1%) (±5700%) (Huo et al., 2022) KsS0 = 3.68 mgS/L μmax,3 = 1.58 d− 1 μmax,4 = 0.09 d− 1 230 0.11 0.20 (±0.64) (±0.03) (±0.003) (±17.46%) (±2.30%) (±3.70%) 7 E. Valdés et al. Chemosphere 339 (2023) 139605 Fig. 2. Data fitting of the calibrated models on nitrate and nitrite: A) (Xu et al., 2014), B) (Mora et al., 2015a), C) (Hauduc et al., 2019), D) (Xu et al., 2016), E) (Huo et al., 2022). Vertical lines in bold delineate the three experimental phases (1, 2 and 3). was, overall, much slower than process 3 in all models that could result; in this model, the rate of process 1 was 29% higher than the other effectively predict nitrite accumulation. This suggests a better capacity models (see Fig. 3). Also, low NO−2 reduction rates led to its excessive of nitrate to oxidize S0, which is in line with the findings of (Cai et al., accumulation in phase 1 (see Fig. 2). Furthermore, the wide confidence 2022; Li et al., 2021). In (Xu et al., 2016), the source of this limitation intervals for two out of three of the optimized parameters indicated a comes from the calibrated maximum specific growth rate (one single very high uncertainty of the calibrated parameters (Table 4). The cause value, according to model structure), whose value was as high as μmax,1 of this misestimation was attributed to the different kinetic terms and = 6.78 d− 1 (2.26 and 6 times higher than the average calibrated values parameters of the model. For instance, substrate inhibitions play a for processes 2 and 4, respectively, see Table S6). The optimization different role in the different processes: in the case of nitrite inhibition, a procedure was likely constrained by a deficient capacity of the model to Haldane term is present in the growth rate formulation of process 2 but simulate NO−3 reduction, as a consequence of the low affinity for nitrite not in process 4, whereas in the case of sulphide inhibition, it is reported in that study (ksNO3 = 109 mgN/L, 2–3 orders of magnitude considerably stronger in process 2 than in process 1 (ki, HS,1 = 2053.2 higher than the average reported values, see Table S6). It is worth mgSL− 1 and ki, HS,2 = 1.38 mgSL− 1, see Table S6). Therefore, process 2 mentioning that the uncertainty analysis performed in (Xu et al., 2016) was completely hindered (as can be seen in Fig. 3), consequently revealed large confidence intervals (±95%) for the paired set of pa­ affecting the calibration outcomes. Nevertheless, the model was able to rameters ksNO2-ksNO3 and ksNO3-ksHS. predict NO−2 accumulation under the experimental conditions of phases In the case of (Hauduc et al., 2019), the high affinity for S0 and the 2 and 3, as confirmed by low values of TICNO2 and TICNO3. lack of a non-competitive terms for HS- over S0 resulted in a high rate of Both models from (Mora et al., 2015a; Huo et al., 2022) properly fit process 4 throughout all phases, as it can be observed in Fig. 3. As a nitrate and nitrite profiles in the three experimental conditions, and the result, the calibration phase in both models led to high values for the resulting confidence intervals of the estimated parameters were signif­ optimized values for ksNO2: 1–3 orders of magnitude higher than the icantly lower than in the other models (see Table 4). (Mora et al., 2015a) average literature values (approaching the upper limit of 110 mgN/L). confidence intervals were all below ±10% while in (Huo et al., 2022), The model from (Xu et al., 2014) properly fits experimental data in the confidence region for KsS0 was ±17.5%, which suggests a slightly phases 2 and 3, whereas in phase 1 all NO−3 was reduced to NO−2 , i.e., no worse parametric identifiability. The latter might be a consequence of NO−3 was observed as shown in Fig. 2. The reason of that comes from the two peculiarities of the model structure: (1) no inhibition is represented calibrated μmax,1, with an optimized value 3 times higher than the for any substrate, unlike (Mora et al., 2015a) where Haldane inhibitions average reported values (see Table S6), over-enhancing process 1 as a are formulated for nitrite and sulphide; (2) the semi-saturation 8 E. Valdés et al. Chemosphere 339 (2023) 139605 Fig. 3. Average biomass growth rates for the different SO-NR processes (1–4), for each model and experimental phase. coefficients for N species were not sensitive because their default values model achieved the best fit with the experimental data, along with (Huo are very low – between 0.1 and 0.21 mgN/L (Table S6) – and the varying et al., 2022); the goodness-of-fit was very similar in both models ac­ affinities among processes are not relevant when using the model under cording to the obtained TIC values for NO−3 and NO−2 , but it is considered this specific experimental dataset, where the concentration of both NO−3 that the model from (Mora et al., 2015a) holds a more rigorous structure and NO−2 in the system are far above the semi-saturation coefficients. As since it accounts for substrates’ inhibition and uptake competition, a result, the model is highly dependent on a limited set of parameters, widely observed and reported in literature. Indeed, both nitrite and mainly the maximum specific growth rates (see Table S7), and it is not as sulphide have been described as an inhibitor for denitrifying SOB cul­ identifiable as (Mora et al., 2015a). The importance of calibrating pa­ tures at different concentration ranges (Mora et al., 2015b). reported rameters in high-sensitivity regions is highlighted by the fact that, nitrite inhibition concentrations as low as 11.5 mgN/L in a among the optimized parameters of these two models, the ones that non-acclimated culture, and as high as 75.4 mgN/L in were less sensitive in phase 3 were also less identifiable (higher confi­ previously-acclimated to nitrite biomass (Wang et al., 2022; Cai et al., dence regions). Therefore, a different selection procedure for parameter 2022). found nitrite to be inhibiting between 36 and 60 mgN/L (Fajardo calibration with a stronger focus on phase 3 could have possibly et al., 2014), reported a Haldane nitrite inhibition constant of 34.7 improved both the goodness-of-fit and the parametric estimations. mgN/L and (Claus and Kutzner, 1985) observed nitrite inhibition at In light of the presented model-specific discussion (Mora et al., concentrations over 200 mgN/L. The calibrated inhibition constant for 2015a), is suggested as the most suitable model structure to describe nitrite obtained in this work was kiNO2 = 102.43 mgN/L, which is about nitrite accumulation observed in (Polizzi et al., 2022). Specifically, this 50% higher than the values generally reported in the literature. Possibly, 9 E. Valdés et al. Chemosphere 339 (2023) 139605 biomass acclimation to the substrate hindered the inhibitory effect of through different modelling approaches. Sensitivity analysis of the nitrite. Moreover, the use of slightly basic conditions in the experimental selected models showed specific growth rates to be crucial parameters, setup (pH = 7.6) could have led to lower concentrations of free nitrous especially under S/N ratios close to 1 gS/gN. Nitrite accumulation could acid (FNA), generally accepted as the actual inhibitory form of nitrite be accurately predicted either by Haldane-type and Monod-type kinetics (Zhou et al., 2011). High concentrations of sulphide – over 80 mgS/L – for its uptake in biomass growth rates. Nevertheless, a more thorough have also been reported to be inhibitory on autotrophic denitrification analysis on models’ performance and parameters’ identifiability by many authors (Lan et al., 2019; An et al., 2010; Li et al., 2021; Lu revealed that the model including non-competitive inhibition for nitrite et al., 2018; Fajardo et al., 2014); even though this Haldane term has uptake, i.e., Haldane saturation function, showed higher accuracy and little relevance in this specific case, since there is no sulphide accumu­ identifiability. Furthermore, the latter approach was found to be lation, its inclusion is deemed relevant to simulate other experimental consistent enough to withstand model simplification, remaining able to studies with a higher sulphide loading rate and/or S/N ratio. represent the experimental dataset preserving parametric identifiability. In conclusion, including substrate inhibition is considered a plus for The reported results are considered a relevant contribution on the the accuracy of the model, but the experimental data could be properly stoichiometry and kinetics governing the PAD process, especially in the represented by means of standard Monod terms in the growth rate ex­ perspective of process upscale and control. A better understanding of the pressions, as demonstrated by the calibration results of (Huo et al., PAD process, encompassing process bioenergetics and kinetics, allows to 2022). move step forwards its implementation in synergy with other innovative processes such as anammox or biogas biological removal of sulphide in 3.2.4. Exploring possible model simplifications innovative anoxic bioscrubbers. An effort to simplify the ultimately selected model was performed. A sensitivity analysis and calibration procedure were again performed on Authors’ contributions (Mora et al., 2015; Huo et al., 2022). The following modification to the models were arbitrarily selected and implemented: the four μmax were E. Valdes: modelling work, writing, discussion. D. Gabriel: supervi­ grouped into two μmax; one for processes 1 and 2, and another one for sion, discussion and conceptualization, fund acquisition. D. Gonzalez: processes 3 and 4, using the default μmax,1 and μmax,3, respectively. The supervision, discussion. G. Munz: supervision, discussion and concep­ results of this approach are shown in Table S9, and the obtained rep­ tualization, fund acquisition. C. Polizzi thermodynamic analysis, resentation of NO−2 , and NO−3 by the calibrated modified models is writing, supervision, discussion and conceptualization. shown in Fig. S1. All the authors contributed to the revision of the work and agreed Results show that (Mora et al., 2015), even with less parameters, with the final version of the article. could still represent the experimental data with good accuracy accord­ ing to the resulting TIC for nitrite and nitrate, as well as the objective Declaration of competing interest function. On the contrary, the modified version of (Huo et al., 2022) could not withstand the model simplification, and was not able to The authors declare that there is no competing interest to disclose. simulate experimental data properly, as can be observed in Fig. 4. Indeed, according to the sensitivity analysis (Table S7), the Data availability non-modified model from (Huo et al., 2022) relied strongly on μmax,3 and μmax,4 and the applied modifications strongly hampered its ability to Data will be made available on request. represent nitrite accumulation. Moreover, the confidence regions ob­ tained indicated a huge difference regarding parametric identifiability Acknowledgements between the two models. Optimized parameters from (Huo et al., 2022) could not be accurately estimated because the model was remarkably This project has received funding from the European Union’s Hori­ depending on having 4 different μmax values in order to simulate this zon 2020 research and innovation programme under the Marie Skło­ data, whereas (Mora et al., 2015) was still identifiable. This evidence dowska-Curie grant agreement No 872053. further indicates that a more complete and robust structure in the latter made it more adequate to simulate the observed nitrite accumulation. Appendix A. Supplementary data Results obtained also demonstrate the feasibility of developing simpler models to describe the PAD process. Supplementary data to this article can be found online at https://doi. org/10.1016/j.chemosphere.2023.139605. 4. Conclusions References This work provides a theoretical framework on the biomass yields as well as a comprehensive study comparing and analysing available ki­ An, S., Tang, K., Nemati, M., 2010. Simultaneous biodesulphurization and denitrification using an oil reservoir microbial culture: effects of sulphide loading rate and sulphide netic models of SO-NR systems, with a specific focus on partial auto­ to nitrate loading ratio. Water Res. 44, 1531–1541. https://doi.org/10.1016/j. trophic denitrification supported by experimental evidences. watres.2009.10.037. The theoretical framework on the biomass yield confirms that Baspinar, A.B., Turker, M., Hocalar, A., Ozturk, I., 2011. Biogas desulphurization at technical scale by lithotrophic denitrification: integration of sulphide and nitrogen experimental values should be critically considered together with the removal. Process Biochem. 46, 916–922. https://doi.org/10.1016/j. specific conditions of the studied systems, due to the high variety of the procbio.2011.01.001. involved SOB population and the strong influence of the operational Batchelor, Bill, Alonzo, W Lawrence, 1978. Autotrophic Denitrification Using Elemental Sulfur. Water Pollution Control Federation (50 (8):), 1986–2001. conditions. Specifically, the low biomass yield estimated in the reference Cai, J., Sun, Y., Qaisar, M., Wang, K., Chen, B., 2022. Revealing the effect of multiple study on PAD is in line with the lower energy delivered in the catabolic nitrogen sources on sulfide oxidation by progressively changing nitrate to nitrite. reaction of partial nitrate reduction to nitrite (denitratation), and the Sep. Purif. Technol. 283 https://doi.org/10.1016/j.seppur.2021.120226. Campos, J.L., Carvalho, S., Portela, R., Me, R., 2008. Kinetics of Denitrification using comparison with theoretical values suggests that a high energy dissi­ Sulphur Compounds: Effects of S/N Ratio, Endogenous and Exogenous Compounds, pation was involved. Moreover, it is speculated that energy constraints 99, pp. 1293–1299. https://doi.org/10.1016/j.biortech.2007.02.007. and energy optimization mechanisms are possibly behind the clear Can-dogan, E., Turker, M., Dagasan, L., Arslan, A., 2010. Sulfide removal from industrial population shift observed. wastewaters by lithotrophic denitrification using nitrate as an electron acceptor. Water Resour. Ind. 2286–2293. https://doi.org/10.2166/wst.2010.545. The critical application, calibration and comparison of 5 published Chen, F., Li, X., Gu, C., Huang, Y., Yuan, Y., 2018. Selectivity control of nitrite and nitrate models showed that PAD dynamics can be successfully described with the reaction of S0 and achieved nitrite accumulation in the sulfur autotrophic 10 E. Valdés et al. Chemosphere 339 (2023) 139605 denitrification process. Bioresour. Technol. 266, 211–219. https://doi.org/10.1016/ Lin, S., Mackey, H.R., Hao, T., Guo, G., Loosdrecht, M.C.M., Chen, G., 2018. Biological j.biortech.2018.06.062. sulfur oxidation in wastewater treatment: a review of emerging opportunities. Water Chen, F., Li, X., Yuan, Y., Huang, Y., 2019. An efficient way to enhance the total nitrogen Res. https://doi.org/10.1016/j.watres.2018.06.051. removal efficiency of the Anammox process by S0-based short-cut autotrophic Lu, H., Huang, H., Yang, W., Mackey, H.R., Khanal, S.K., Wu, D., Chen, G.H., 2018. denitrification. J. Environ. Sci. 81, 214–224. https://doi.org/10.1016/j. Elucidating the stimulatory and inhibitory effects of dissolved sulfide on sulfur- jes.2019.01.010. oxidizing bacteria (SOB) driven autotrophic denitrification. Water Res. 133, Claus, G., Kutzner, H., 1985. Physiology and kinetics of autotrophic denitrification by 165–172. https://doi.org/10.1016/j.watres.2018.01.022. Thiobacillus denitrificans. Appl. Microbiol. Biotechnol. 22 https://doi.org/10.1007/ Madigan, M.T., Bender, K.S., Buckley, D.H., Sattley, W.M., Stail, D.A., 2019. Brock BF00252031. Biology of Microorganisms, fifteenth ed. Pearson Education Limited. Cui, Y., Guo, G., Ekama, G.A., Deng, Y., Chui, H., Chen, G., Wu, D., 2019. Elucidating the Mannucci, A., Munz, G., Mori, G., Lubello, C., 2012. Biomass accumulation modelling in Bio Fi Lm Properties and Biokinetics of a Sulfur-Oxidizing Moving-Bed Bio Fi Lm for a highly loaded biotrickling filter for hydrogen sulphide removal. Chemosphere 88, Mainstream Nitrogen Removal 162, pp. 246–257. https://doi.org/10.1016/j. 712–717. https://doi.org/10.1016/j.chemosphere.2012.04.026. watres.2019.02.061. Mora, M., Dorado, A.D., Gamisans, X., Gabriel, D., 2015a. Investigating the kinetics of Deng, Y., Tang, W., Huang, H., Qian, J., Wu, D., 2021. Development of a Kinetic Model to autotrophic denitrification with thiosulfate: modeling the denitritation mechanisms Evaluate Thiosulfate-Driven Denitrification and Anammox (TDDA) Process 198. and the effect of the acclimation of SO-NR cultures to nitrite. Chem. Eng. J. 262, https://doi.org/10.1016/j.watres.2021.117155. 235–241. https://doi.org/10.1016/j.cej.2014.09.101. Deng, Y.-F., Zan, F., Huang, H., Wu, D., Tang, W., Chen, G.-H., 2022. Coupling sulfur- Mora, M., Fernández, M., Gómez, J.M., Cantero, D., Lafuente, J., Gamisans, X., 2015b. based denitrification with anammox for effective and stable nitrogen removal: a Kinetic and Stoichiometric Characterization of Anoxic Sulfide Oxidation by SO-NR review. Water Res. 224, 119051 https://doi.org/10.1016/j.watres.2022.119051. Mixed Cultures from Anoxic Biotrickling Filters 77–87. https://doi.org/10.1007/ Fajardo, C., Mora, M., Fernández, I., Mosquera-Corral, A., Campos, J.L., Méndez, R., s00253-014-5688-5. 2014. Cross effect of temperature, pH and free ammonia on autotrophic Mora, M., Guisasola, A., Gamisans, X., Gabriel, D., 2014. Examining thiosulfate-driven denitrification process with sulphide as electron donor. Chemosphere 97, 10–15. autotrophic denitrification through respirometry. Chemosphere 113, 1–8. https:// https://doi.org/10.1016/j.chemosphere.2013.10.028. doi.org/10.1016/J.CHEMOSPHERE.2014.03.083. Gadekar, S, Nemati, M Ã, Hill, G A, 2006. Batch and continuous biooxidation of sulphide Polizzi, C., Gabriel, D., Munz, G., 2022. Successful sulphide-driven partial denitrification by Thiomicrospira Sp . CVO : reaction kinetics and stoichiometry. Water Res. 40, : efficiency , stability and resilience in SRT-controlled conditions. Chemosphere 295, 2436–2446. https://doi.org/10.1016/j.watres.2006.04.007. 133936. https://doi.org/10.1016/j.chemosphere.2022.133936. Guisasola, A., Baeza, J.A., Carrera, J., Sin, G., Vanrolleghem, P.A., Lafuente, J., Matrix, F. Quaglio, M., Fraga, E.S., Galvanin, F., 2018. Chemical Engineering Research and Design I., 2006. The influence of experimental data quality and quantity on parameter Model-based design of experiments in the presence of structural model uncertainty : estimation accuracy Andrews inhibition model as a case study. Educ. Chem. Eng. 1, an extended information matrix approach. Chem. Eng. Res. Des. 136, 129–143. 139–145. https://doi.org/10.1016/j.cherd.2018.04.041. Guo, Q., Hu, H.Y., Shi, Z.J., Yang, C.C., Li, P., Huang, M., Ni, W.M., Shi, M.L., Jin, R.C., Reichert, P., Vanrolleghem, P., 2001. Identifiability and uncertainty analysis of the river 2016. Towards simultaneously removing nitrogen and sulfur by a novel process: water quality model No. 1 (RWQM1). Water Sci. Technol. 43 https://doi.org/ anammox and autotrophic desulfurization-denitrification (AADD). Chem. Eng. J. 10.2166/wst.2001.0442. 297, 207–216. https://doi.org/10.1016/j.cej.2016.03.138. Rittmann, B.E., McCarty, P.L., 2001. Environmental Biotechnology: Principles and Hauduc, H., Wadhawan, T., Bruce, J., Bott, C., Ward, M., Takács, I., 2019a. Incorporating Applications, first ed. McGraw-Hill Education, New York. sulfur reactions and interactions with iron and phosphorus into a general plant-wide Roels, J.A., 1983. Energetics and Kinetics in Biotechnology. Elsevier Biomedical Press, model Hélène Hauduc , Tanush Wadhawan , Bruce Johnson , Charles Bott. Water Sci. Amsterdam. Technol. 79 (1), 26–34. https://doi.org/10.2166/wst.2018.482. Sahinkaya, Erkan., Dursun, Nesrin., Kilic, Adem., Demirel, Sevgi., Uyanik, Sinan., Heijnen, J.J., Loosdrecht, M.C.M., Tijhuis, L., 1992a. A black box mathematical model to Cinar, Ozer., 2011. Simultaneous heterotrophic and sulfur-oxidizing autotrophic calculate auto- and heterot rophic biomass yields based on Gibbs energy dissipation. denitrification process for drinking water treatment : control of sulfate production. Biotechnol. Bioeng. 40, 1139–1154. Water Res. 45 (20), 6661–6667. https://doi.org/10.1016/j.watres.2011.09.056. Hoor, T., Cell, A., 1981. c o m p a r e d w i t h Thiobacillus denitrificans Netherlands. Savageau, M.A., 1984. Energetics and kinetics in biotechnology. J. A. Roels. Q Rev Biol Institute for Sea Research , Texel. The Netherlands ’ 47. 59, 179. https://doi.org/10.1086/413814. Huiliñir, C., Romero, R., Muñoz, C., Bornhardt, C., Roeckel, M., Antileo, C., 2010. Sublette, Kerry L., Sylvester, Nicholas D., 1987. Of natural gas. Biotechnol. Bioeng. XXIX: Dynamic modeling of partial nitrification in a rotating disk biofilm reactor: , 57–249. calibration, validation and simulation. Biochem. Eng. J. 52, 7–18. https://doi.org/ Wang, K., Qaisar, M., Chen, B., Liu, S., Wu, Y., Zheng, Z., Cai, J., 2022. Strategy for rapid 10.1016/j.bej.2010.06.012. recovery of simultaneous sulfide and nitrite removal under high substrate inhibition. Huo, P., Chen, X., Yang, L., Wei, W., Ni, B., 2022a. Modeling of sulfur-driven autotrophic Biochem. Eng. J. 180 https://doi.org/10.1016/j.bej.2022.108368. denitrification coupled with Anammox process. Bioresour. Technol. 349, 126887 Wang, L., Liu, J., Li, Y., Liu, Z., Zhang, L., Che, H., Cui, H., Zhang, Y., 2023. Elemental https://doi.org/10.1016/j.biortech.2022.126887. sulfur-driven autotrophic denitrification process for effective removal of nitrate in Hvala, N., Strmcnik, S., Sel, D., Milanic, S., Banko, B., 2005. Influence of model mariculture wastewater: performance, kinetics and microbial community. validation on proper selection of process models — an industrial case study. Comput. Chemosphere 337, 139354. https://doi.org/10.1016/j.chemosphere.2023.139354. Chem. Eng. 29, 1507–1522. https://doi.org/10.1016/j.compchemeng.2004.11.013. Wu, D., Ekama, G.A., Chui, H.K., Wang, B., Cui, Y.X., Hao, T.W., van Loosdrecht, M.C.M., Klatt, Judith M., Polerecky, L., 2015. Assessment of the stoichiometry and efficiency of Chen, G.H., 2016. Large-scale demonstration of the sulfate reduction autotrophic CO 2 fixation coupled to reduced sulfur oxidation. Front. Microbiol. 6 https://doi. denitrification nitrification integrated (SANI®) process in saline sewage treatment. org/10.3389/fmicb.2015.00484. Water Res. 100, 496–507. https://doi.org/10.1016/j.watres.2016.05.052. Kleerebezem, R., Loosdrecht, M.C.M., 2010. A Generalized Method for Thermodynamic Xu, X., Chen, C., Wang, A., Guo, W., Zhou, X., Lee, D., Ren, N., Chang, J., 2014. State Analysis of Environmental Systems A Generalized Method for Thermodynamic Simultaneous removal of sulfide , nitrate and acetate under denitrifying sulfide 37–41. https://doi.org/10.1080/10643380802000974. removal condition : modeling and experimental validation. J. Hazard Mater. 264, Kleerebezem, R., Mendez, R., 2002. Autotrophic denitrification for combined hydrogen 16–24. https://doi.org/10.1016/j.jhazmat.2013.10.056. sulfide removal from biogas and post-denitrification. Water Sci. Technol. 45, Xu, G., Yin, F., Chen, S., Xu, Y., Yu, H.Q., 2016. Mathematical modeling of autotrophic 349–356. denitrification (AD) process with sulphide as electron donor. Water Res. 91, Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E., 1998. Convergence properties of 225–234. https://doi.org/10.1016/j.watres.2016.01.011. the nelder–mead simplex method in low dimensions. SIAM J. Optim. 9 https://doi. Yavuz, B., Türker, M., Engin, G.Ö., 2007. Autotrophic removal of sulphide from org/10.1137/S1052623496303470. industrial wastewaters using oxygen and nitrate as electron acceptors. Environ. Eng. Lan, L., Zhao, J., Wang, S., Li, X., Qiu, L., Liu, S., Bin Nasry, A.A.N., 2019. NO and N2O Sci. 24 https://doi.org/10.1089/ees.2006.0068. accumulation during nitrite-based sulfide-oxidizing autotrophic denitrification. Zhang, D., Cheng, L., Zhang, S., Zheng, J., 2023. Denitrification performance and Bioresour Technol Rep 7. https://doi.org/10.1016/j.biteb.2019.100190. microbial community analysis of sulfur autotrophic denitrification filter for low- Li, W., Liu, J., Sui, X., Lin, M., Zhao, W., Zhen, Y., Bing, X., Lin, J., 2021. Response of the temperature treatment of landfill leachate. J. Environ. Chem. Eng. 11 https://doi. reactor performances and bacterial communities to the evolution of sulfide-based org/10.1016/j.jece.2023.109314. mixotrophic denitrification processes from nitrate-type to nitrite-type. Biochem. Zhou, Y., Oehmen, A., Lim, M., Vadivelu, V., Ng, W.J., 2011. The role of nitrite and free Eng. J. 173 https://doi.org/10.1016/j.bej.2021.108069. nitrous acid (FNA) in wastewater treatment plants. Water Res. 45, 4672–4682. Li, Y., Han, Q., Li, B., 2023. Engineering-scale application of sulfur-driven autotrophic https://doi.org/10.1016/j.watres.2011.06.025. denitrification wetland for advanced treatment of municipal tailwater. Bioresour. Technol. 379 https://doi.org/10.1016/j.biortech.2023.129035. 11