Greenhouse gases from membrane bioreactors: Mathematical modelling, sensitivity and uncertainty analysis

Accepted Manuscript Greenhouse gases from membrane bioreactors: mathematical modelling, sensitivity and uncertainty analysis Giorgio Mannina, Alida Cosenza, George A. Ekama PII: DOI: Reference:

S0960-8524(17)30657-0 http://dx.doi.org/10.1016/j.biortech.2017.05.018 BITE 18044

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Bioresource Technology

Received Date: Revised Date: Accepted Date:

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Please cite this article as: Mannina, G., Cosenza, A., Ekama, G.A., Greenhouse gases from membrane bioreactors: mathematical modelling, sensitivity and uncertainty analysis, Bioresource Technology (2017), doi: http://dx.doi.org/ 10.1016/j.biortech.2017.05.018

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1

Greenhouse gases from membrane bioreactors: mathematical

2

modelling, sensitivity and uncertainty analysis

3 4 5

Giorgio Mannina1, Alida Cosenza*1, George A. Ekama2

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Palermo, Viale delle Scienze, Ed.8, 90100, Palermo, Italy (e-mail: [email protected];

Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, dei Materiali, Università di

10

[email protected])

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2

12

Rondebosch, 7700 Cape, South Africa

Water Research Group, Department of Civil Engineering, University of Cape Town,

13 14 15 16

*

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[email protected] (Alida Cosenza)

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Corresponding

Author

phone:

+3909123896514;

Fax:

+3909123860810;

e-mail:

19

Abstract

20

In this study a new mathematical model to quantify greenhouse gas emissions

21

(namely, carbon dioxide and nitrous oxide) from membrane bioreactors (MBRs)

22

is presented. The model has been adopted to predict the key processes of a

23

pilot plant with pre-denitrification MBR scheme, filled with domestic and saline

24

wastewater. The model was calibrated by adopting an advanced protocol based

25

on an extensive dataset. In terms of nitrous oxide, the results show that an

26

important role is played by the half saturation coefficients related to nitrogen

27

removal processes and the model factors affecting the oxygen transfer rate in

28

the aerobic and MBR tanks. Uncertainty analysis showed that for the gaseous

29

model outputs 88-93% of the measured data lays inside the confidence bands

30

showing an accurate model prediction.

31 32 33

Keywords: Uncertainty; greenhouse gases; wastewater; membrane; modelling.

34

1. Introduction

35

Wastewater treatment plants (WWTPs) can emit greenhouse gases (GHGs)

36

(such as carbon dioxide, CO2, nitrous oxide, N2O and methane, CH4). Among

37

the potential GHGs produced from a WWTPs, N2O is the most environmentally

38

hazardous due to its strong global warming potential (GWP) (298 higher that

39

CO2) and its capacity to deplete the stratospheric ozone layer (IPCC, 2013). An

40

accurate quantification and mitigation of GHG emissions from WWTP is

41

imperative

42

mathematical models can be useful and powerful tools.

43

In the past, several efforts have been performed for establishing the best tool to

44

predict/quantify GHG (Ni and Yuan, 2015; Mannina et al., 2016; Hiatt and

45

Grady, 2008, Ni et al., 2013; Peng et al., 2015; Spérandio et al., 2016; Pocquet

46

et al., 2016). These efforts are based on the modifications of the Activated

47

Sludge Models (ASMs) (Henze et al., 2000) to include GHG formation/emission

48

processes (Ni and Yuan, 2015; Mannina et al., 2016).

49

Corominas and co-workers demonstrated that mechanistic process-based

50

dynamic models represent the best way to predict GHG emissions (Corominas

51

et al., 2012). Ni et al. (2013) compared four mathematical models describing the

52

N2O production by means of ammonia oxidizing bacteria (AOB) as the final

53

product of nitrifier denitrification or as a product of incomplete oxidation of

54

hydroxylamine (NH2OH). They found that none of the tested models was able to

55

fully simulate the measured data. Very recently, Spérandio et al. (2016)

56

compared the results of five ASM family-like models describing N2O production

57

by AOB. Similarly to previous studies (i.e., Ni et al., 2013), Spérandio et al.

for

improved

environmental

protection.

With

this

respect,

58

(2016) found that, despite at least one of the investigated models being able to

59

reproduce the measured data, none of the tested models were able to simulate

60

measured data using the same parameter data set.

61

A new model which combines two N2O emission pathways due to AOB was

62

recently proposed and calibrated (Pocquet et al., 2016). This model showed

63

good correlation between measured and modelled data in long-term simulation

64

periods.

65

The aforementioned studies mainly refer to conventional activated systems with

66

solid-liquid separation with secondary settling tanks (CASs). However, there is

67

limited research on modelling GHG emissions from advanced wastewater

68

treatment systems such as membrane bioreactors (MBR). MBRs have some

69

specific peculiarities (i.e., membrane fouling, biomass selection; intensive

70

aeration for membrane fouling mitigation), which can influence GHG emissions

71

and hamper a straightforward transferability of CAS models to MBR systems.

72

For example, the Soluble Microbial Product (SMP) formation/degradation

73

processes and the role played by membrane aeration on GHG stripping are

74

generally not considered in CAS models but can be of paramount importance

75

for MBR system modelling.

76

A first attempt to GHG modelling from MBRs was recently presented (Mannina

77

and Cosenza, 2015). In particular, Mannina and Cosenza (2015) developed a

78

model able to estimate CO2 and N2O emissions from an MBR system with

79

University Cape Town (UCT) –MBR scheme. An extensive sensitivity analysis

80

was presented aimed at identifying the key influencing factors. Despite the

81

promising performance of the model, it was not calibrated using real MBR

82

system data.

83

Recent studies on the estimation of the uncertainty in GHG modelling confirmed

84

the relevant role played by such an analysis (Sweetapple et al., 2013). Indeed,

85

the assessment of the uncertainty may improve the calibration process.

86

Sensitivity and uncertainty analyses help the modeller identify the key constants

87

affecting model outputs (Sweetapple et al., 2013). However, despite the

88

usefulness of uncertainty analysis, only few such studies have been performed

89

(Mannina ad Cosenza, 2015; Sweetapple et al., 2013). Sensitivity and

90

uncertainty analysis may have a relevant role in MBR modelling, because, as

91

recently demonstrated by Mannina and Cosenza (2015), model constants

92

related to the physical processes of the membrane solid-liquid separation can

93

also affect GHG production.

94

In this paper a new mathematical model for GHG emission evaluation from

95

MBRs is presented. The model takes into account the main physical and

96

biological processes: solid/liquid separation, membrane fouling and SMP

97

formation/degradation. The mathematical model has been adopted to predict

98

the key biological processes of a sequential batch (SB) MBR pilot plant fed with

99

real saline wastewater. A long-term data base (for dissolved and gaseous N2O),

100

acquired during an extensive measurement campaign, was adopted for the

101

model calibration. Model uncertainty was quantified to better assess model

102

features.

103 104

2.

Material and methods

105

2.1 The mathematical model

106

The mathematical model proposed in this work couples the ASM1 model

107

(Henze et al., 2000) and the N2O modelling approach of Hiatt and Grady (2008).

108

The mathematical model consists of two sub-models (Figure 1): a biological

109

sub-model and a physical sub-model. All biological model (stoichiometric,

110

kinetic and fractionation) and physical model factors are reported in Table A.1.

111 112

[INSERT FIGURE 1 HERE]

113 114

The biological sub-model couples the ASM1, the SMP formation/degradation

115

processes, the N2O formation during the denitrification and the CO 2 production

116

during the biological metabolism (Figure 1). The biological sub-model involves:

117

16 biological processes (aerobic and anoxic); 19 state variables, which include

118

dissolved N2O and CO2 (SN2O and SCO2, respectively) and 63 model factors. In

119

Tables A.2 and A.3 of the Appendix the Gujer Matrix and the process rate

120

equations of the biological model are reported, respectively.

121

In order to consider the SMP formation/degradation processes two new state

122

variables have been included: (i) soluble utilization-associated products (SUAP)

123

and (ii) soluble biomass-associated products (SBAP). Furthermore, the aerobic

124

and anoxic hydrolysis processes of SUAP and SBAP have been added in the

125

ASM1 (see processes 1-4 of Table A.3). Thus, four new model parameters

126

have been introduced in the model according to Jiang et al. (2008): the

127

hydrolysis rate coefficient for SBAP and SUAP (kh,BAP and kh,UAP, respectively) in

128

the kinetics rate expressions (Table A.3) and the production of SUAP and SBAP in

129

the biomass growth and endogenous decay process stoichiometry via the (fBAP

130

and fUAP) coefficients. The SBAP and SUAP reduction follows a first order kinetics.

131

For example, the rate of the anoxic hydrolysis of SBAP is shown in Equation 1.

132

 K O 2,HYD    S NO3 k h ,BAP   NO3,HYD      S BAP  X H [1]  K O 2,HYD  SO 2   K NO3,HYD  S NO3 

133 134

Moreover, the aerobic and anoxic kinetic hydrolysis processes of Xs have been

135

modified in the model (see processes 5-6 of Table A.3) to include the

136

production of unbiodegradable soluble organics (SI). The model has been

137

expanded to describe the nitrification and denitrification processes according in

138

two step (see processes 13-14 of Table A.3) and four step (see processes 8-11

139

of Table A.3) processes respectively as described by Hiatt and Grady (2008).

140

So the autotrophic biomass is modelled with an ammonia-oxidising biomass

141

(XAOB) and and a nitrite oxidising biomass (XNOB). The denitrification is modelled

142

with a single ordinary heterotrophic organism (OHO) biomass (XOHO) utilizing

143

soluble biodegradable organics (SS) in four sequential steps of electron transfer

144

in the electron acceptor from nitrate to nitrite, to nitric oxide (NO) to nitrous

145

oxide (N2O) to nitrogen gas (N2). Specifically, each step has its own η specific

146

growth rate reduction factor for anoxic denitrification relative to the aerobic OHO

147

maximum specific growth rate (μOHO or μH). Specifically, SNO3 to SNO2 (ηg2), SNO2

148

to SNO (ηg3), SNO to SN2O (ηg4) and SN2O to SN2 (ηg5) have been introduced.. This

149

is equivalent to giving the OHO a different and independent maximum specific

150

growth rate for each of the four steps in the denitrification from nitrate to N 2 all

151

utilizing soluble biodegradable organics (SS) as electron donor. For example,

152

the kinetic rate related to the anoxic growth of heterotrophic biomass on soluble

153

biodegradable organics (SS) reducing SNO to SN2O (Bioprocess 10 in Table A3)

154

is reported in Equation 1. In Equation 1 both the switching functions related to

155

the alkalinity (

156

according to the corrections of the ASM1 as proposed by Hauduc et al. (2011).

157

Also added are two NO terms, one inhibition term, which decreases the rate

158

when the NO concentration gets high relative to the KI4NO inhibition

159

concentration and one switching term, which decreases the specific growth rate

160

when the NO concentration gets low relative to KI3NO. The kinetic rate equations

161

of the 16 bioprocesses in the biological sub-model are shown in Table A3. The

162

internal consistence of the Gujer matrix was checked and found to conform to

163

mass balance continuity.

S ALK K ALK  S ALK

) and the ammonia (

S NH 4 K NH 4, H  S NH 4

) have been introduced

164 165

  K O 2, H   S NO  H  g 4    2  K  S  K  S  S NO O2   O 2, H  NO NO K I 4 NO 

        K I 3 NO S NH 4 S ALK    SS     X    K S  S S   K NH 4, H  S NH 4   K ALK  S ALK   K I 3 NO  S NO  H  

166 167 168

[2]

169

N2O and CO2 emission, namely SGHG,N2O and SGHG,CO2 respectively. The

170

stripping processes for both N2O and CO2 is modelled including in the mass

171

balance the term of Equation 3 (Sabba et al., 2016).

The model includes the stripping processes for N2O and CO2 gases to evaluate

172 173 174 175

Where KLa [h-1] is the gas-liquid mass transfer coefficient, SGHG,N2O [mol m-3] is

176

the gaseous N2O concentration in the off-gas, HN2O [mol mol-1] is the Henry gas-

177

liquid coefficient of N2O at 25 ºC and SN2O [mol m-3] is the dissolved N2O

178

concentration in the mixed liquor. The stripping process for CO 2 has been

[3]

179

similarly described. For N2O and CO2 the KLa was estimated according to

180

Mampaey et al. (2015).

181

The biological model includes the influence of the influent salinity both for the

182

autotrophic and heterotrophic biomass (Park and Marchland, 2006). More

183

precisely, the maximum growth rate of both autotrophic and heterotrophic

184

biomass is modelled considering a reduction coefficient (i.e., Is coefficient),

185

assessed as:

186 187 188 189

Where I*s is the inhibition factor evaluated and %NaCl is the percentage of

190

salinity expressed as NaCl content. Equation 4 is valid in the range of 0-4%

191

NaCl as indicated by Park and Marchland (2006). Therefore, under 0% NaCl

192

condition Is is equal to zero. Conversely, Is has a constant value at higher

193

salinity levels (each constant value for each influent %NaCl). In this work two

194

inhibition factors have been considered one for heterotrophic and another for

195

autotrophic biomass (IS,H and IS,A, respectively).

196

The physical sub-model takes into account the main physical processes of an

197

MBR which interact with the biological sub-model (Figure 1). The key algorithms

198

of the physical sub-model are reported in Table A.4.

199

The physical sub-model involves 6 model factors. Specifically, the following six

200

processes are taken into account: (i) solids deposition and detachment on/from

201

membrane surface during the filtration and backwashing, respectively (cake

202

layer formation); (ii) carbon removal due to cake layer which acts as a filter; (iii)

203

carbon removal due to physical membrane; (iv) solute deposition within

204

membrane pore (pore fouling); (v) pore blocking and (vi) influence of SMP on

[4]

205

pore fouling. The same sectional method of Li and Wang (2006) was used to

206

model membrane; according to this method membrane surface is divided into N

207

areal fractions. In order to take into account the influence of the distance of the

208

aeration system on the membrane fouling, a different value of shear intensity of

209

the fluid turbulence (G) is considered on the basis of this distance. Both

210

reversible and irreversible fouling mechanisms are considered. Reversible

211

fouling is modeled as a continuous cake layer formation/removal during

212

filtration/backwashing phases. Irreversible fouling modelling is performed by

213

considering two mechanisms: pore fouling, due to the solute deposition within

214

the membrane pores, and stable cake fouling due to the particle deposition on

215

membrane surface that cannot be removed by means of the backwashing. The

216

physical and biological sub-models interact by means of: TSS, which influence

217

the cake layer; COD which is partially retained within the cake layer; SMP,

218

which influence membrane fouling.

219

For a detailed description of the physical sub-model reader is referred to the

220

literature (Mannina and Cosenza, 2013).

221 222

2.2 The case study

223

The SB-MBR pilot plant taken into account has a pre-denitrification scheme

224

(Figure 2).

225

The solid/liquid separation occurred by means of an hollow fiber ultrafiltration

226

membrane module in Polyvinylidene fluoride (PVDF) (Zenon Zeeweed, ZW10)

227

submerged into an aerated tank (MBR). The hollow fibre membrane has a width

228

specific area equal to 0.98 m2 and a nominal porosity of 0.04 m. In order to

229

ensure anoxic conditions, inside the anoxic reactor, an oxygen depletion reactor

230

(ODR) was inserted within the recycle line between the anoxic reactor and

231

MBR. Each reactor (aerobic, anoxic and MBR) was covered in order to ensure

232

the gas accumulation and the subsequent sampling.

233

[INSERT FIGURE 2 HERE]

234 235

The real domestic wastewater was stored inside a feeding tank and

236

discontinuously fed into the pilot plant by using the fill-draw-batch approach.

237

The pilot plant filling occurred according to 8 cycles per day, each of 3 hours

238

duration. During each cycle 40 L of wastewater (VIN) previously mixed with salt

239

were fed and treated. Each cycle was divided into two phases: i. biological

240

reaction (1 hour); ii. filtration (2 hours). During the biological reaction phase no

241

permeate extraction occurred, therefore the permeate flow rate (QOUT) was

242

equal to zero. Conversely, during the filtration phase Q OUT was set to 20 L h-1

243

and the permeate flux was equal to 21 L m 2 h-1. During the filtration phase, the

244

membrane was backwashed every 9 min for a period of 1 min; the backwashing

245

has been performed by reintroducing a fraction of the permeate back into the

246

internal lumen of the hollow fiber.

247

Mixed liquor was continuously recycled from the aerobic to MRR (Q R1 equal to

248

80 L h-1) and from the MBR to the anoxic reactor (QRAS, equal to 80 L h-1 during

249

the biological reaction phase and 60 L h-1 during the filtration phase).

250

The pilot plant was monitored for three months. The 84 day experimental

251

campaign was divided into six phases each characterized by a specific salt

252

concentration from 0 up to 10 g NaCl L-1. The NaCl concentration in the influent

253

was increased at steps of 2 g NaCl L-1 on a weekly basis. The last Phase VI

254

had a duration of 26 days. No sludge was wasted from the system during the

255

investigation making the sludge age indeterminate. During the experimental

256

campaign liquid samples withdrawn (every 15 min and 60 min for the gas and

257

liquid samples, respectively) from the aerobic and anoxic tank were analysed in

258

order to evaluate gaseous and dissolved N2O. With this regards a Gas

259

Chromatograph (Thermo Scientific™ TRACE GC) equipped with an Electron

260

Capture Detector was used. Both aerobic and anoxic tanks were covered and

261

sealed in order to allow gas samples. Furthermore, the N2O-N fluxes (gN2O-N

262

m-2 h-1) from aerobic and anoxic tanks were quantified by measuring the gas

263

flow rates, QGAS (L min-1 ). During plant operations, the influent wastewater, the

264

mixed liquor inside the anoxic and aerobic tank and the effluent permeate were

265

sampled and analyzed for total and volatile suspended solids (TSS and VSS),

266

total chemical oxygen demand (CODTOT), supernatant COD (CODsol),

267

ammonium nitrogen (NH4-N), nitrite nitrogen (NO2-N), nitrate nitrogen (NO3-N),

268

total dissolved nitrogen (TN), ortho-phosphate (PO4-P), total dissolved organic

269

carbon (TOC) and inorganic carbon (IC). Further, transmembrane pressure

270

(TMP) [bar] data were measured by means of an analogue data logger every 1

271

minute. Moreover, instantaneous permeate flow rate (QOUT,i) was measured

272

every day in order to evaluate the total membrane resistance R T [m-1] according

273

to Equation 5. Further details on the experimental campaign can be drawn from

274

previous studies (Mannina et al., 2016b).

275 276 277

RT 

Q

TMP OUT ,i A 

[5]

278

Where: A [m2] represents the membrane surface,  [Pa s] is the permeate

279

viscosity; the unit of the TMP is Pascal [Pa], QOUT,i is expressed as cubic meter

280

per second [m3 s-1].

281 282

2.3 Model calibration

283

The model calibration has been performed by adopting a calibration protocol

284

developed during previous studies (Mannina et al., 2011b). According to this

285

protocol model factors are calibrated on the basis of a calibration hierarchy

286

(Mannina et al., 2011b). To set up the hierarchy, a global sensitivity analysis

287

(GSA) is performed choosing the widest literature range of model factors.

288

The standardized regression coefficient (SRC) method has been adopted to

289

select important model factors (Saltelli et al., 2004). The SRC method allows to

290

define a multivariate linear regression model (established for each model output

291

on the basis of the randomly sampled value of the model factors).

292

The slope of the regression (SRC or βi) provides information on the influence of

293

each model factor on the model output variation (sensitivity). The sign of βi

294

indicates if the model factor “i” has positive (+) or negative (-) influence on the

295

considered model output. In case of linear model (regression R2 = 1) βi allows

296

to discriminate between important and non-influential model factors. The SRC

297

method can be applied also to non-linear models for identifying the important

298

model factors (Vanrolleghem et al., 2015). To apply the SRC method, at least

299

500 to 1000 simulations are required as suggested in the literature

300

(Vanrolleghem et al., 2015).

301

Apart the GSA, the calibration protocol considers the generalized likelihood

302

uncertainty estimation (GLUE) methodology based on Monte Carlo simulations

303

(Mannina et al., 2011b; Beven and Binley, 1992). For each Monte Carlo

304

simulation model outputs are compared with the observed and a likelihood

305

measure/efficiency is quantified. On the basis of the value of the likelihood

306

measure/efficiency the results are considered acceptable or not acceptable. In

307

this study the same likelihood measure as adopted by Mannina et al. (2011b)

308

was used.

309 310

2.3.1 Uncertainty analysis

311 312

Regarding the uncertainty analysis, non important factors have been fixed to

313

their default or trial and error calibration value. Only important model factors

314

have been considered during the uncertainty analysis. Specifically, important

315

model factors were varied within an uncertainty range according to a random

316

sampling. The results of the Monte Carlo simulations were analyzed on the

317

basis of cumulative distribution function (CDF) for each model output. The 5 th

318

and 95th percentiles were also evaluated.

319 320

2.4 Model application and numerical settings

321

Input time series established on the basis of the influent wastewater measured

322

data was adopted as model input data. Simulation period has the duration of 84

323

days. Four different sections of the SB-MBR plant were considered, in

324

particular, the anoxic tank (section 1), aerobic tank (section 2), MBR tank

325

(section 3) and permeate tank (section 4). The average values of the simulated

326

time series for each model output were considered for the SRC application.

327

Nineteen model outputs of the biological sub-model were considered for the

328

GSA: CODTOT for all the four sections; CODsol for sections 1, 2, and 3; SNO3 for

329

sections 1, 3 and 4; ammonia (SNH4) for sections 3 and 4; total nitrogen (TN) for

330

the section 4; total suspended solids (XTSS) for sections 1 and 2; SN2O for

331

sections 1 and 2 and SGHG,N2O for sections 1 and 2. Further, one model output of

332

the physical sub-model was also considered: membrane total resistance (RT).

333

To apply the SRC method, 1200 model simulations were performed. According

334

to the literature suggestion, a threshold value of 0.1 was chosen for the

335

absolute value of i to discriminate between important and non important model

336

factors (Varolleghem et al., 2015; Cosenza et al., 2013). Model calibration has

337

been performed by running for each calibration step, 8,000 Monte Carlo

338

simulations. This number was established by increasing the sample dimension

339

from 100 to 8,000 and verifying that the maximum efficiency was constant. The

340

same number of Monte Carlo simulations was adopted for each calibration step.

341

Uncertainty bands have been performed by employing 1000 Monte Carlo runs

342

by varying only the most important model factors for all the model outputs taken

343

into account. This number of Model Carlo runs was selected after verifying

344

(sample dimensions between 100 and 1000) that the uncertainty analysis was

345

not affected by any bias caused by the number of Monte Carlo simulations

346

(Bertrand-Krajewski et al., 2002; Dotto et al., 2012). The uncertainty bands were

347

calculated by adopting the likelihood distributions for each simulation time step

348

and for each model output were then used for calculating uncertainty bands (5%

349

percentile and 95% percentile of the 1000 runs for each model outputs).

350 351

3.

Results and discussion

352 353

3.1 Sensitivity analysis

354

Table 1 summarizes the parameters selected as important at least for one

355

model output. The application of the SRC method yielded for each model output

356

taken into account an R2 value around to 0.5 (Table 1).

357 358

[INSERT TABLE 1 HERE]

359 360

By applying the SRC method 33 model factors have been selected to be

361

important for at least one of the model output taken into account. For sake of

362

conciseness only the key model outputs for each plant section are discussed

363

below.

364

Figure 3 shows the results related to the important model factors at least for one

365

of the model outputs considered: SN2O,1 (a), SGHG,N2O,1 (b), SN2O,2 (c) and

366

SGHG,N2O,2 (d). For the meaning of the symbols reported in Figure 3 the reader is

367

referred to Table A.1. Among the important model factors, some deserve to be

368

discussed. The group of half saturation coefficients (kN2O, kNO3, kALK) (related

369

with the SN2O, SNO3 and SALK) have a great influence on all the model outputs

370

considered. Such a result corroborates the literature findings, which suggest to

371

focus the attention on the half-saturation coefficients of the biological processes

372

involving nitrogen due to their high uncertain degree (Sweetapple et al., 2013).

373

Therefore, it is advisable to experimentally quantify these factors. The model

374

factorsAUT,AOB and AUT,NOB mostly affect (positively) the SN2O,1 and SGHG,N2O,2.

375

Such a result shows an indirect effect for SN2O,1. Indeed, with the increasing of

376

the autotrophic maximum specific growth rate the availability of nitrate inside the

377

aerobic tank increases with a consequent increase of SN2O,1 produced during

378

the denitrification for example due to the scares availability of substrate. The

379

importance of the factors g3 and g4 for SGHG,N2O,1 is of relevant interest.

380

Indeed, these latter factors control the rate of the heterotrophic anoxic

381

processes on the substrate (SS) when SNO2 (nitrite) is reduced to SNO (g3) and

382

when SNO (g4) is reduced into SN2O. Thus, consequently g3 and g4 influence

383

the amount of gaseous N2O emitted from the anoxic tank (SGHG,N2O,1). Both k2,2

384

and k2,3 (coefficients for oxygen transfer of the aerobic tank and MBR tank,

385

respectively) have positive effect on SN2O,1. This result is due to the increase of

386

mainly debited to the increase of the amount of nitrate and dissolved oxygen

387

recycled into the anoxic tank with the increasing of the oxygen concentration

388

inside the aerobic and MBR tanks. Therefore, the N2O can be also produced

389

due to the AOB contribution inside the anoxic tank (in case the environment

390

become aerobic).

391

Thus, the role of k2,2 and k2,3 on SN2O,1 is mainly indirect. Indeed, with the

392

increase of k2,3 the amount of the available oxygen inside the aerobic tank

393

increases with a consequent complete nitrification. Therefore, the amount of

394

nitrate to be denitrified in the anoxic tank increases; nitrate could not be

395

completely denitrified due to the poor availability of carbon. On the other hand,

396

with the increase of k2,3 the amount of mass oxygen recycled from the MBR to

397

the anoxic tank (through the ODR) increases. The importance of the factors

398

affecting the oxygen transfer rate in the aerated tank suggests that in order to

399

better predict N2O emissions of a WWTP a detailed knowledge on the oxygen

400

transfer has to be acquired.

401

As can be additionally noted from Figure 3, the autotrophic salinity inhibition

402

coefficient (Is,H) positively influences the N2O production inside the aerobic tank.

403

Indeed, several studies have demonstrated that the salinity could promote the

404

N2O production during the nitrification (Zhao et al., 2014). It is interesting to note

405

that factors related to the physical model ( and , representing the stickiness

406

of the biomass particles and the screening parameter, respectively) affect both

407

SN2O,1 (Figure 3). Such a result is mainly debited to the role of the membrane in

408

retaining the substrate that will be or not available for the nitrate denitrification.

409

[INSERT FIGURE 3 HERE]

410 411

Model factors mostly affecting the model output CODTOT,1 and CODSOL2 isH

412

(Table 1). Indeed, the i value of H for both CODTOT,1 and CODSOL,2 is equal to

413

1; having a positive influence. Indeed, with the increasing of the maximum

414

growth rate of heterotrophic bacteria the increase of the particle fraction of COD

415

takes place. Further, CODTOT,1 is also affected by g3 and g4 which respectively

416

control the rate of the heterotrophic anoxic growth when S NO2 (nitrite) is reduced

417

to SNO (g3) and SNO (g4) is reduced into SN2O. The model output SNO3,1 is

418

mostly influenced by the half saturation coefficients for free ammonia (K FA) for

419

nitrous oxide-nitrogen (KN2O). Such a results is due to the fact that these

420

coefficients control the amount of nitrate that can be produced inside the

421

aerobic tank and consequently recycled inside the anoxic one. Similarly,

422

AUT,NOB and iN,Ss influence the amount of nitrate that can be produced inside the

423

aerobic tank and consequently SNO3,1 (Table 1). Indeed, AUT,NOB is the most

424

important model factor for SNO3,2 (Table 1). In terms of resistance, the set of the

425

following model factors has been selected as important: fUAP (fraction of SUAP

426

generated in biomass decay), KH,UAP (hydrolysis rate coefficient for SUAP), 

427

(screening parameter) and CE (efficiency of backwashing) (Table 1). Among

428

these factors fUAP and KH,UAP are related to the biological sub-model; fUAP and

429

KH,UAP positively influence RT due to the fact that with their increase, the

430

increase of the SUAP production takes place. Thus influencing the membrane

431

fouling. Such a result has paramount interest because suggests by reducing the

432

SMP production a substantial reduction of the membrane resistance (which

433

means a reduction of operational costs) can occur. Model factors  and CE are

434

directly connected with the physical sub-model. The negative influence of CE is

435

due to the fact that with the increase of the backwashing efficiency the amount

436

of the cake layer deposited on the membrane surface decreases thus reducing

437

the TMP value at fixed permeate flux.

438 439

3.2 Model calibration results

440

Model calibration has been performed by varying all the important model factors

441

selected during the sensitivity analysis. All the other model factors have been

442

fixed at their default value or at the value obtained during the initial trial and

443

error calibration according to the calibration protocol (Mannina et al., 2011b).

444

The model calibration has been performed by comparing simulated with

445

measured

446

characterized by a model efficiency greater than 0.2 were selected as

447

behavioral (Mannina et al., 2011b; Vanrolleghem et al., 2015). The selection of

448

the calibrated factor values have been performed on the basis of the maximum

449

model efficiency value.

450

In Table A.1, the final calibrated factor values are summarized along with the

451

literature range. More precisely, only factors selected as influential have been

452

calibrated (letter “C” in the line related to the source of Table A.1). Some model

453

factors have been evaluated on the basis of mass balance continuity check as

454

suggested by Vanrolleghem et al. (2005) (letter “M” in the line related to the

455

source of Table A.1). All the other factors have been fixed at the literature value

456

(letter “L” in the line related to the source of Table A.1).

457

Some calibrated factors merit to be further discussed. More precisely, regarding

458

the salinity inhibition factors one can observe that the inhibition factors related

459

to the heterotrophic biomass (IS,H) is lower than that related to the autotrophic

460

biomass (IS,A). Indeed, salinity has a inhibition effect on autotrophic biomass

461

growth than on the heterotrophic biomass (Luo et al., 2005; Mannina et al.,

462

2016b). More precisely, the salinity increase causes the cell plasmolysis and/or

463

the loss of metabolic activity for autotrophic biomass (Johir et al., 2013).

464

Therefore, the values of the maximum specific growth rate of XAOB and XNOB

465

were lower when adjusted for salt concentration IS,A. For example, the final

466

value related to the XAOB was equal to 0.68 d-1, which decreases to 0.48 d-1 due

467

to salt inhibition. This result is of particular interest to N2O modeling, because

data

acquired

during

the

sampling

campaign.

Simulations

468

salinity has been identified as one of the most influencing factors for the N2O

469

emission during nitrification (Kampschreur et al., 2009). In terms of

470

heterotrophic biomass the value of H obtained (0.9 d-1) is lower than literature

471

rates (Jiang et al., 2008; Mannina and Cosenza, 2015). Such low value is likely

472

due to the high sludge retention time (SRT); indeed, the pilot plant was

473

operated at indefinite SRT value. Such an operational condition could lead to

474

the accumulation of inert biomass and to the slowly biomass growth (Judd and

475

Judd, 2010).

476

Regarding the physical model factors they have some differences with respect

477

to the literature. For example the value of the backwashing efficiency coefficient

478

(CE) resulted lower than previous literature; the value obtained here is equal to

479

0.986 while in previous studies the value of 0.996 (Mannina and Cosenza,

480

2013; Mannina and Cosenza, 2015) was obtained. This lower value for CE

481

suggests a potential increase of the membrane resistance caused by the cake

482

layer, likely due to the mixed liquor features. Furthermore, the screening

483

parameter () has here a value of 1487 m-1 against the value of 1520.29 m-1 of

484

previous studies (Mannina and Cosenza, 2013; Mannina and Cosenza, 2015).

485

Such result suggested that the different features of biomass due to the

486

presence of salinity also influence the membrane fouling. Indeed, the factors

487

related to the SMP still have different value if compared with literature. In

488

particular, the fraction of SUAP due to the biomass decay (fUAP) obtained here

489

was higher compared with that observed in literature (Jiang et al., 2008) likely

490

due to the stress effect on the heterotrophic biomass grow due to the salinity

491

and to the high SRT. Furthermore, the worsening of membrane fouling can be

492

also due to the increase of the mixed liquor viscosity and to the reduction of the

493

oxygen solubility with the increasing of the salinity (Lay et al., 2010).

494

For sake of completeness in Figure 4 the calibrated and measured pattern for

495

CODTOT,1 (a), SNO3,1 (b), CODsol,2 (c), RT (d), SN2O,2 (e) and SGHG,N2O,2 (f) are

496

reported. Despite the salinity increase, a good prediction of COD model outputs

497

occurred (Figure 4a and Figure 4c). Such result has peculiar interest because

498

since these model outputs (CODTOT,1 of Figure 4a and CODsol,2 of Figure 4c) are

499

the sum of different model outputs. Further, from the results of Figure 4d one

500

can observe that the model allows to describe the increase of RT occurred with

501

the increase of salinity.

502

[INSERT FIGURE 4 HERE]

503 504

However, during Phase VI (specifically between days 62 and 78) occurred

505

some technical problems, not implemented in the model algorithms. When the

506

technical problems were resolved, the model was again able to reproduce the

507

measured RT values. In terms of N2O, the model shows an acceptable adaption

508

between simulated values and measured values (data reported for each

509

replicate) (Figure 5a-b). Specifically, the increase of N2O emission from aerobic

510

tank with the salinity is reproduced by the model. Details on the model efficiency

511

will be provided below.

512 513 514

[INSERT FIGURE 5 HERE]

515

Table 2 summarizes the results related to the model efficiencies. By analyzing

516

data of Table 2 one can observe that acceptable efficiencies were obtained for

517

the model outputs of sections 1, 2 and 4 (namely, anoxic, aerobic and MBR,

518

respectively). More precisely, the average efficiency of the model outputs of the

519

anoxic tank (section 1) was equal to 0.42. For the model output of the aerobic

520

tank (section 2) the average efficiency was equal to 0.41.

521

model outputs of the MBR (section 4). Conversely, the lowest efficiency value

522

was obtained for the model outputs of the section 3 (0.28 on average). Such a

523

result is mainly debited to the lower number of measured data for the section 3

524

with respect to the other sections. Regarding the total resistance (RT), the

525

model provided a quite high efficiency

526

suggests a good model ability to reproduce membrane fouling mechanisms.

While, 0.33 for the

value (0.79) (Table 2). This result

527 528

[INSERT TABLE 2 HERE]

529 530

3.3

531

Figure 6 shows the uncertainty analysis results for CODTOT,1 (a), SNO3,1 (b),

532

SNO3,3 (c), RT(d), SGHG,N2O,1 (e), SN2O,1 (f), SGHG,N2O,2 (g) and SN2O,2 (h).

533

By analysing the data reported in Figure 6 one can observe that the uncertainty

534

band widths (quantified as average difference between 95% and 5% uncertainty

535

band value) changes with the model outputs through the different plant sections

536

(e.g., greater for CODTOT,1) (Figure 6a). This is due to the different role that the

537

key processes occurring inside each plant section have on the model outputs

538

variation and on the interlinkage among model outputs. Indeed, for example the

539

variation of the total COD involves the combination of the variation of different

Uncertainty analysis

540

state variables of the model: XS, Xi, XH, XAOB, XNOB. Similarly, the variation of

541

supernatant COD involves the variation of SBAP, SUAP, SI, SS. A larger band

542

width was obtained for CODTOT,1. This result is likely due to the large number of

543

model factors, important for COD, varied during the uncertainty analysis.

544

Regarding RT, a very narrow band width was obtained (Figure 6d); this result

545

demonstrates the high accuracy of the model in reproducing the membrane

546

fouling. Globally, 90% of measured data for the model output shown in Figure 6

547

lies inside the uncertainty band.

548

The uncertainty band width (as average difference between 95% and 5%

549

percentile) of the model outputs related to GHG changes with the model outputs

550

in the different plant sections (e.g., greater for S GHG,N2O,1 and SN2O,2) (Figure 6e-

551

h). Indeed, variation of some factors could make more uncertain the N 2O

552

production in a certain section due to the overlapping effects among different

553

processes. For example, the increase of k2,2 and k2,3 could favour aerobic

554

conditions inside the anoxic tank due to the recycled oxygen mass. Therefore,

555

N2O formation due to the heterotrophic and autotrophic pathways could occur

556

inside the anoxic tank.

557

By analysing data of Figure 6e-h it is possible to observe that for the GHG

558

model outputs for which a greater number of measured data was available

559

(SGHG,N2O,1 and SGHG,N2O,2) a more accurate prediction was obtained. Indeed, for

560

SGHG,N2O,1 and SGHG,N2O,2 only the 7% and the 12% of the measured data lie

561

outside the band width. This result is important, suggesting that long extensive

562

databases are required to set up accurate models and reduce model

563

uncertainty. Indeed, 60% and 46% of the measured data lie outside the band

564

width for SN2O,1 and SN2O,2, respectively.

565 566

[INSERT FIGURE 6 HERE]

567 568

More precisely, the measured data lower than 0.01 mgN L -1 and 0.025 mgN L-1

569

lie outside the band for SN2O,1 and SN2O,2, respectively.

570 571

4.

572

A new integrated MBR mathematical model was presented. The main

573

contribution of the model is to consider (1) GHG emissions, (2) the influence of

574

salinity on the process rate, (3) the SMP formation/degradation processes. The

575

model has been calibrated by employing an innovative protocol and using an

576

extensive data set. Results derived by the model application have improved the

577

knowledge on N2O emissions from MBRs; for example, model factors that

578

require to be measured for improving N2O predictions have been selected (half

579

saturation coefficients related to the nitrogen processes or factors related to the

580

oxygen transfer). Further future investigations could demonstrate the predictive

581

capability

582

systems/conditions different to those in the calibrating data set.

583 584 585 586

Conclusions

of

the

integrated

model

presented

here

for

simulating

587

ACKNOWLEDGMENTS

588

This work forms part of a research project supported by grant of the Italian

589

Ministry of Education, University and Research (MIUR) through the Research

590

project of national interest PRIN2012 (D.M. 28 dicembre 2012 n. 957/Ric – Prot.

591

2012PTZAMC) entitled “Energy consumption and GreenHouse Gas (GHG)

592

emissions in the wastewater treatment plants: a decision support system for

593

planning and management – http://ghgfromwwtp.unipa.it” in which the first

594

author is the Principal Investigator.

595 596

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597

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717

718

FIGURE CAPTIONS

719

Figure 1. Conceptual structure of the mathematical model; SMP = soluble

720

microbial product; XTSS = total suspended solids

721 722

Figure 2. Layout of the SB-MBR pilot plant; stored tank volume = 320 L; anoxic

723

reactor volume = 45 L; aerobic reactor volume = 224 L; MBR reactor volume =

724

50 L (where VIN = 40 L = influent wastewater volume; ODR = Oxygen Depletion

725

Reactor; MBR = membrane Bioreactor; QRAS = 80 L h-1 = recycled sludge from

726

MBR to ODR; QR1 = 80 L h-1 = sludge feeding from aerobic tank to MBR; QOUT =

727

20 L h-1 (only during the MBR filtration phase = effluent flow rate)

728 729

Figure 3. Results related to the SRC application for SGHG,N2O,1 (a), SN2O,1 (b),

730

SGHG,N2O,2 (c), SN2O,2 (d) model outputs.

731 732 733

Figure 4. Calibrated and measured pattern for CODTOT,1 (a), SNO3,1 (b), CODsol,2

734

(c), RT (d), SN2O,2 (e) and SGHG,N2O,2 (f)

735 736

Figure 5. Calibrated and measured pattern for SN2O,2 (a) and SGHG,N2O,2 (b)

737

(aerobic tank)

738 739

Figure 6. CDF related to the measured data, calibrated model, 5% and 95%

740

percentiles for CODTOT,1 (a), SNO3,1 (b), SNO3,3 (c), RT(d), SGHG,N2O,1 (e), SN2O,1 (f),

741

SGHG,N2O,2 (g) and SN2O,2 (h).

742

743

TABLE CAPTIONS

744

Table 1. Summary of the value of SRC (or i) resulted important at least for one

745

of the model output taken into account. In grey important model factors; the two

746

model factors for each model outputs having the highest i value.

747 748

Table 2. Synthesis of efficiency for each measured state variable

749 750

APPENDIX CAPTIONS

751

Table A.1 Model factors. Where: C = calibrated value; M = value obtained by

752

using the mass balance continuity check proposed by Vanrolleghem et al.

753

(2005); L = value obtained from technical literature.

754 755

Table A.2 Gujer Matrix of the SB-MBR biological sub-model; in grey the new

756

processes added with respect to ASM1.

757 758

Table A.3 Process rate equations of the biological sub-model; in grey the rate

759

related to the new hydrolysis processes.

760 761 762 763 764

Table A.4 Key processes taken into account in the physical sub-model.

Figure_1

Physical sub-model

Biological sub-model  ASM1  SMP formation/degradation  N2O production during denitrification  CO2 as state variable

Influent

(63 model factors, 19 state variables)

XTSS, SMP

   

Cake layer formation Pre-filter effect Physical membrane effect Membrane fouling

(6 model factors, 2 state variables)

Integrated mathematical model

Effluent

Figure_2

VIN

Feeding tank

ODR

QRAS

Salt dosing QOUT

MBR

Aerobic Mixing tank

Anoxic

QR1

Figure_3

1.00

0.50

(d)

bi

0.00

SGHG,N2O,2

-0.50

-1.00 1.00

0.50

(c)

bi

0.00

SN2O,1

-0.50

-1.00 1.00

0.50

(b)

bi

0.00

SGHG,N2O,1

-0.50

-1.00 1.00

0.50

CE fxi

(a)

0.00

kNO3,HYDR iTSS,BM mH hg3 hg4 kNO3 kNO2 kN2O kI3NO kALK,H KH,UAP m AUT,AOB m AUT,NOB KFA Ki9FA kfna Ki10FA ki10fna f a l FXi I S,H k2,2 k2,3

-0.50

-1.00 fUAP iN,Ss iN,XS iTSS,Xi YA,NOB ko,HYDR

bi

SN2O,2

Figure_4

Anoxic tank

80

(a)

CODTOT,1

Concentration [mg L-1]

Concentration [g L-1]

10

8 6 4 2 Measured

Simulated

50 40 30 20 10 0

0

10

20

30

40 50 Time [d]

60

70

80

90

0

120 Aerobic tank

CODsol,2

100 80

60 40 20

0 0 0.16

10

20

30

Aerobic tank

60

70

SN2O,2

80

20

30

40 50 Time [d]

60

70

Technical failure

8

0.1 0.08 0.06 0.04 0.02 0

(d)

2 0

0.14

0.12

90

4

0

(e)

80

6

90

Concentration [mg L-1]

0.14

40 50 Time [d]

10

10

(c)

Resistance, RT [1012 m-1]

Concentration [mg L-1]

(b)

SNO3,1

60

0

Concentration [mg L-1]

Anoxic tank

70

10

20

30

Aerobic tank

0.12

40 50 Time [d]

60

70

SGHG,N2O,2

80

90 (f)

0.1 0.08 0.06 0.04 0.02 0

0

10

20

30

40 50 Time [d]

60

70

80

90

0

10

20

30

40 50 Time [d]

60

70

80

90

Figure_5

60 Aerobic tank 20 Concentration [mg L-1]

Concentration [mg L-1]

50

(a)

SN2O,2

15 10

40

5 0 56.3

30

56.35

56.4 56.45 Time [d]

56.5

20 10

0 0

10

20

30

40 50 Time [d]

60

70

80

90

50

SGHG,N2O,2

Aerobic tank Concentration [mg L-1]

Concentration [mg L-1]

40

30

12 10 8 6 4 2 0 56.3

56.35

56.4 56.45 Time [d]

(b)

56.5

20

10

0 0

10

20

30

40 50 Time [d]

60

70

80

90

Figure_6

1

1

(b)

(a)

0.8

0.6

Measured data Calibrated data 5% percentile 95% percentile

0.4 0.2

CDF

CDF

0.8

0.6 0.4 0.2

SNO3,1

CODTOT,1

0

0 0

2

4 6 8 Concentration [gCOD L-1]

0

10

1

20 40 60 Concentration [mgN L-1]

80

1 (d)

0.8

0.8

0.6

0.6

CDF

CDF

(c)

0.4

0.4

0.2

0.2

SNO3,3

RT

0

0 0

20 40 60 Concentration [mgN L-1]

80

0

1

4 6 Resistance [m-1 1012]

8

(e)

(f)

0.8

CDF

0.6

0.6

0.4

0.4

0.2

0.2

SGHG,N2O,1

SN2O,1

0

0 0

0.02

0.04 0.06 0.08 Concentration [mgN L-1]

0

0.1

1

0.05

0.1 0.15 0.2 Concentration [mgN L-1]

0.25

1

(g)

0.8

(h)

0.8

0.6

0.6

CDF

CDF

10

1

0.8

CDF

2

0.4

0.4

0.2

0.2

SGHG,N2O,2

0

SN2O,2

0 0

0.02

0.04 0.06 0.08 Concentration [mgN L-1]

0.1

0

0.05 0.1 0.15 Concentration [mgN L-1]

0.2

Table_1

ANOXIC - SECTION 1

R

2

AEROBIC- SECTION 2

CODTOT,1

CODSOL,1

SNO3,1

MLSS,1

SGHG,N2O,1

0.46

0.55

0.48

0.45

0.48

factor

SN2O,1 CODTOT,2 0.42

0.44

CODSOL,2

MLSS,2

0.52

0.46

SRC

MBR - SECTION 3

SGHG,N2O,2 SN2O,2 0.55

0.48

PERMEATE - SECTION 4

CODTOT,3

CODSOL,3

SNH3,3

SNO3,3

SGHG,N2O,3

SN2O,3

CODSOL,4

TN,4

SNO3,4

RT

0.45

0.58

0.44

0.42

0.52

0.48

0.48

0.55

0.44

0.62

SRC

SRC

SRC

fUAP

0.02

-0.12

0.56

-0.08

-0.09

0.46

0.06

-0.13

-0.07

0.39

-0.20

0.05

-0.16

0.19

0.75

0.01

0.05

0.28

0.63

0.75

0.47

iN,Ss

0.03

0.65

0.79

-0.33

-0.01

0.04

0.10

0.65

-0.33

-0.02

0.00

0.09

0.62

0.74

0.70

-0.05

0.00

0.07

-0.16

0.70

0.03

iN,XS

0.08

0.29

-0.19

0.13

0.15

0.31

0.25

0.30

0.13

0.14

0.99

0.24

0.26

-0.23

-0.23

0.00

0.02

0.70

-0.17

-0.23

0.03

iTSS,Xi

0.01

-0.03

-0.03

0.01

0.15

-0.28

0.01

-0.03

0.01

-0.50

-0.89

0.01

-0.03

-0.02

-0.03

0.05

0.02

-0.01

-0.02

-0.03

-0.01

YA,NOB

-0.02

0.03

0.03

-0.02

-0.41

0.92

-0.02

0.02

-0.02

0.11

-0.15

-0.02

0.03

0.03

0.04

0.02

0.01

0.00

-0.06

0.04

0.00

ko,HYDR

0.02

0.00

-0.05

0.02

0.28

-0.56

0.02

0.00

0.02

0.19

0.77

0.02

0.00

-0.04

-0.05

0.02

0.03

0.00

0.02

-0.05

0.00

kNO3,HYDR

0.00

0.00

0.00

0.01

0.13

0.37

0.00

0.00

0.01

-0.15

0.24

0.00

0.00

0.02

-0.01

0.01

0.01

0.01

0.03

-0.01

0.01

iTSS,BM

-0.06

-0.24

-0.28

-0.20

-0.01

-0.03

-0.18

-0.22

-0.21

0.00

0.00

-0.17

-0.20

-0.16

-0.37

0.02

0.00

-0.34

0.82

-0.37

-0.02

H

1.00

0.05

-0.29

-0.32

-0.02

-0.01

-0.50

1.00

-0.31

-0.02

-0.01

-0.50

0.04

-0.17

-0.32

0.02

-0.02

0.25

-0.58

-0.32

0.12

g3

0.33

-0.39

0.50

0.90

0.95

0.60

0.97

-0.37

0.90

-0.49

-0.09

0.97

-0.37

0.37

0.45

0.02

0.01

-0.15

-0.21

0.45

-0.07

g4

0.33

0.29

-0.08

0.84

0.86

0.16

0.99

0.30

0.84

-0.17

-0.29

0.99

0.32

-0.21

-0.10

0.01

0.00

-0.08

-0.09

-0.10

-0.04

kNO3

0.01

0.02

-0.05

0.03

0.50

-0.76

0.01

0.02

0.03

0.01

1.00

0.01

0.02

-0.04

-0.05

0.01

0.01

0.02

-0.01

-0.05

0.02

kNO2

0.11

1.00

0.07

0.14

0.15

0.00

0.34

0.10

0.13

0.25

-0.14

0.34

1.00

0.04

-0.03

0.01

0.05

0.48

0.04

-0.03

0.02

kN2O

0.23

0.77

0.78

0.30

0.36

1.00

0.69

0.78

0.29

1.00

0.39

0.67

0.75

0.93

0.53

0.04

0.03

0.15

0.02

0.53

0.05

kI3NO

0.00

0.03

-0.02

0.00

-0.12

-0.20

0.00

0.03

0.00

0.44

0.12

0.00

0.03

0.00

-0.04

0.02

0.00

0.01

-0.03

-0.04

0.01

kALK,H

0.30

-0.34

-0.74

1.00

1.00

-1.25

0.89

-0.32

1.00

0.70

0.55

0.89

-0.31

-0.44

-0.78

0.04

0.01

-0.09

0.25

-0.78

-0.04

KH,UAP

0.07

0.01

0.34

0.08

0.01

0.00

0.20

0.85

0.07

-0.01

0.03

0.20

0.02

0.48

0.18

0.00

-0.02

0.36

0.82

0.18

0.59

AUT,AOB

0.01

-0.01

0.03

0.01

0.24

0.34

0.01

-0.01

0.01

0.71

0.00

0.01

-0.01

0.03

0.03

0.03

0.01

0.01

0.03

0.03

0.01

AUT,NOB

0.16

0.40

0.54

0.07

0.09

0.64

0.47

0.41

0.07

0.31

-0.08

0.46

0.39

0.74

1.00

1.00

1.00

0.69

-0.06

0.39

0.33

KFA

-0.28

0.88

1.00

-0.69

-0.04

0.01

-0.82

0.83

-0.69

-0.03

-0.01

-0.82

0.85

-0.22

-0.04

0.01

0.00

0.04

0.38

-0.04

0.02

Ki9FA

-0.01

-0.87

-0.26

0.16

0.01

-0.02

-0.02

-0.83

0.16

-0.01

0.01

-0.02

-0.88

-0.27

-0.23

-0.01

-0.04

0.40

1.00

-0.23

0.02

kfna

-0.24

0.88

-0.20

-0.45

-0.52

0.73

-0.72

0.09

-0.45

-0.12

0.40

-0.72

0.85

-0.18

-0.15

0.04

0.00

0.33

0.72

-0.15

0.02

Ki10FA

-0.18

-0.32

-0.24

-0.05

-0.02

-0.01

-0.53

-0.28

-0.05

-0.07

-0.04

-0.53

-0.28

-0.17

-0.76

-0.02

-0.01

0.05

0.79

-0.76

0.03

ki10fna

-0.02

-0.02

-0.04

0.00

-0.09

-0.82

-0.02

-0.02

0.00

-0.23

-0.46

-0.02

-0.02

-0.03

-0.05

0.05

0.02

1.00

0.88

-0.54

0.07

f

0.11

-0.07

-0.48

0.23

0.01

-0.01

0.33

-0.07

0.23

-0.01

-0.01

0.33

-0.08

-0.54

-0.54

0.01

0.03

0.01

0.05

-0.03

0.01



0.00

0.01

-0.01

0.00

-0.11

0.58

0.00

0.01

0.00

-0.39

-0.23

0.00

0.01

-0.02

0.00

0.01

0.05

0.02

0.01

0.00

0.02



0.16

0.24

0.10

0.07

0.15

0.86

0.48

0.27

0.06

0.16

-0.44

0.47

0.23

1.00

0.17

0.06

0.01

0.74

-0.25

1.00

0.35

FXi

0.04

0.01

-0.01

0.03

0.63

-0.70

0.04

0.01

0.03

0.19

-0.71

0.04

0.01

-0.03

0.00

0.02

0.04

0.00

0.02

0.00

0.00

IS,H

-0.02

-0.01

-0.06

-0.01

-0.28

-0.16

-0.02

-0.01

-0.01

-0.14

0.70

-0.02

-0.01

-0.07

-0.06

0.05

0.03

0.00

-0.01

-0.06

0.00

k2,2

0.00

0.03

-0.02

0.00

-0.10

0.39

0.00

0.03

0.00

-0.45

0.79

0.00

0.03

-0.02

-0.02

0.04

0.02

0.01

-0.05

-0.02

0.01

k2,3

0.03

-0.02

0.00

0.03

0.60

0.53

0.03

-0.02

0.03

0.48

-0.44

0.03

-0.02

0.00

0.00

0.03

0.04

0.02

-0.01

0.00

0.02

CE

0.15

-0.15

0.03

0.28

0.01

0.00

0.45

-0.13

0.28

0.02

-0.03

0.44

-0.15

-0.01

-0.07

0.03

0.01

0.36

0.75

-0.07

-1.00

fxi

0.34

0.13

-0.22

0.60

0.00

0.01

1.00

0.14

0.60

0.00

0.01

1.00

0.14

-0.53

-0.03

-0.02

-0.03

-0.07

0.37

-0.03

-0.03

Table_2

Section Model output CODTOT,1 Efficiency 0.42 # data 14 Section Model output CODTOT,2 Efficiency 0.46 # data 14 Section Model output CODTOT,3 Efficiency 0.25 # data 8 Section Model output CODTOT,4 Efficiency 0.35 # data 15

CODsol,1 0.52 14

Anoxic tank XTSS,1 SNO3,1

0.31 0.44 16 17 Aerobic tank CODsol,2 XTSS,2 SGHG,N2O,2 0.52 0.46 0.49 14 14 65 MBR tank CODsol,3 SNH4,3 SNO3,3 0.29 0.31 0.28 8 8 8 Permeate SNH4,4 SNO3,4 TN,4 0.34 0.36 0.3 17 17 12

SGHG,N2O,1 SN2O,1 0.47 65 SN2O,2 0.39 15

RT 0.79 55

0.34 15

Table_A1

Symbol

Unit

Range

Reference

Value T=20°C

Source

Fraction of SI generated in biomass decay

fSI

g SI.g XH-1

0÷0.01

Hauduc et al. (2010)

0

L

Yield for XH growth

YH

g XH.g XS-1

0.38÷0.75

Hauduc et al. (2010)

0.39

L

fXI

XH-1

Description

Fraction of XI generated in biomass decay

fBAP

-

Fraction of SUAP generated in biomass decay

fUAP

-

Stoichiometric

N content of Ss

iN,Ss

Ss-1

g N.g

0.005÷0.150

Mannina and Cosenza, 2015

0.149

C

0.025÷0.035

Hauduc et al. (2010)

0.025

L

0.015÷0.025

Hauduc et al. (2010)

0.015

L

0.03÷0.05

Hauduc et al. (2010)

0.047

C

g N.g XI-1

iN,XS

XS-1

g N.g XBM

-1

0.0665÷0.0735

Hauduc et al. (2010)

0.068

L

-1

0.7125÷0.7875

Hauduc et al. (2010)

0.74

C

0.7125÷0.7875

Hauduc et al. (2010)

0.75

L

0.855÷0.945

Hauduc et al. (2010)

0.89

C

0.5÷0.99

Hauduc et al. (2010) Mannina and Cosenza (2015) Mannina and Cosenza (2015)

0.9

L

0.18

L

0.052

C

Conversion factor XI in TSS

iTSS,XI

g TSS.g XI

Conversion factor XS in TSS

iTSS,XS

g TSS.g XS-1

Conversion factor biomass in TSS

iTSS,BM

g TSS.g XBM

Anoxic yield factor for heterotrophs

ηy_H

-

-1

-1

0.165÷0.195 0.045÷0.075

Yield of XAOB growth

YAOB

g XAOB.g SNH4

Yield of XNOB growth

YNOB

g XNOB.g SNO2-1

iCOD_NO3

L

C

g N.g SI

iN,BM

C

0.007

0.082

iN,XI

N content of biomass

0.055

Hauduc et al. (2010)

iN,SI

g N.g

Hauduc et al. (2010) Mannina and Cosenza, 2015

0.08÷0.12

N content of XI N content of XS

0.05÷0.15 0.020÷0.023

-1

N content of SI

Conversion factor for NO3 in COD

-1

-

Vanrolleghem et al. (2005)

-4.571

M

-1

g COD.g N

Conversion factor for NO2 in COD

iCOD_NO2

g COD.g N

-

Vanrolleghem et al. (2005)

-3.429

M

Conversion factor for NO in COD

iCOD_NO

g COD.g N-1

-

Vanrolleghem et al. (2005)

-2.857

M

iCOD_N2O

-2

-

Vanrolleghem et al. (2005)

-2.286

M

-1

Conversion factor for N2O in COD Conversion factor for N2 in COD Maximum specific hydrolysis rate Half saturation parameter for XS/XH

iCOD_N2 kh KX

g COD.g N g COD.g N g XSg

-

Vanrolleghem et al. (2005)

-1.714

M

XH-1d-1

1.5÷4.5

Hauduc et al. (2010)

1.72

L

XH-1

0.03÷0.12

Hauduc et al. (2010)

0.1

L

0.55÷0.65

Hauduc et al. (2010)

0.65

L

0.15÷0.25

Hauduc et al. (2010)

0.23

C

0.4÷0.6

Hauduc et al. (2010)

0.44

C

0.9

C

g XS.g

Correction factor for hydrolysis under anoxic conditions

ηNO3,HYD

-

Half saturation/inhibition parameter for SO2

KO2,HYD

g SO2.m-3

Half saturation/inhibition parameter for SNO3

KNO3,HYD

g N.m

-3

Maximum growth rate of XH

μH

d

0.5÷5

Mannina and Cosenza (2015)

Correction factor for heterotrophic anoxic growth reducing NO3 to NO2

ηg2

-

0.25÷0.35

Mannina and Cosenza (2015)

0.28

L

Correction factor for heterotrophic anoxic growth reducing NO2 to NO

ηg3

-

0.1÷0.2

Mannina and Cosenza (2015)

0.18

C

Correction factor for heterotrophic anoxic growth reducing NO to N2O

ηg4

-

0.3÷0.4

Mannina and Cosenza (2015)

0.36

C

Correction factor for heterotrophic anoxic growth reducing N2O to N2

ηg5

-

0.3÷0.4

Mannina and Cosenza (2015)

0.35

L

Decay rate for XH

bH

d-1

0.2÷0.6

Mannina and Cosenza (2015)

0.6

L

Half saturation parameter for SO2 for XH Half saturation parameter for SNO3 Half saturation parameter for SNO2 Half saturation parameter for SNO

Kinetic

g XI.g

Fraction of SBAP generated in biomass decay

KO2,H KNO3 KNO2 KNO

-1

g SO2.m

-3

0.1÷0.5

Jeppsson et al (2007)

0.5

L

-3

0.2÷0.7

Hiatt and Grady (2008)

0.3

C

-3

0.18÷0.22

Hiatt and Grady (2008)

0.21

C

-3

0.045÷0.055

Hiatt and Grady (2008)

0.05

L

0.052

C

0.48

C

0.3

L

g SNO3.m g SNO2.m g SNO.m

Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015)

Half saturation parameter for SN2O

KN2O

g SN2O.m-3

0.045÷0.055

NO inhibition coefficient (reducing NO2 to NO)

KI3NO

g SNO.m-3

0.45÷0.55

NO inhibition coefficient (reducing NO to N2O)

KI4NO

g SNO.m-3

0.27÷0.33

NO inhibition coefficient (reducing N2O to NO)

KI5NO

g SNO.m-3

0.0675÷0.0825

Hiatt and Grady (2008)

0.075

L

0.025÷0.1

Mannina and Cosenza (2015)

0.095

L

0.08÷0.12

Hiatt and Grady (2008)

0.09

C

Mannina and Cosenza (2015) Mannina and Cosenza (2015)

8 10-7

C

0.0102

L

Half saturation parameter for SNH4 for XH

KNH4,H

g SNH4.m

HCO3-.m-3

Half saturation parameter for SALK for XH

KALK,H

Hydrolysis rate coefficient for SUAP

kh,UAP

d-1

5.93 10-7÷8.89 10-7

Hydrolysis rate coefficient for SBAP

kh,BAP

d-1

0.00816÷0.01224

Maximum specific growth rate of XAOB Maximum specific growth rate of XNOB

μAUT,AOB μAUT,NOB

mol

-3

d

-1

0.4÷0.7

Hiatt and Grady (2008)

0.68

C

d

-1

0.4÷0.7

Hiatt and Grady (2008)

0.55

C

0.096

L

0.096

L

0.6

L

1.2

L

0.0071

C

0.95

C

0.21

C

0.000099

C

Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015)

Decay coefficient of XAOB

bAUT,AOB

d-1

0.077÷0.115

Decay coefficient of XNOB

bAUT,NOB

d-1

0.077÷0.115

Half saturation parameter for SO2 (related to XAOB)

KO,AOB

g SO2.m-3

0.3÷1

Half saturation parameter for SO2 (related to XNOB)

KO,NOB

g SO2.m-3

0.9÷1.3

Half saturation coefficient for free ammonia

KFA

g SFA.m-3

0.00675÷0.00825

Free ammonia inhibition coefficient (related to XAOB)

KI9FA

g SFA.m-3

0.9÷1

Free ammonia inhibition coefficient (related to XNOB)

KI10FA

g SFA.m-3

0.18÷0.22

Half saturation coefficient for free nitrous acid

KFNA

g SFNA.m-3

0.00009÷0.00011

Free nitrous acid inhibition coefficient (related to XAOB)

KI9FNA

g SFNA.m-3

0.09÷0.11

Mannina and Cosenza (2015)

0.1

L

Free nitrous acid inhibition coefficient (related to XNOB)

KI10FNA

g SFNA.m-3

0.036÷0.044

Mannina and Cosenza (2015)

0.038

C

KALK,AUT

mol HCO3-.m-3

0.4÷0.6

Mannina and Cosenza (2015)

0.5

L

Oxygen transfer coefficient for aerobic tank to evaluate the overall kLaT

k1,2

d-1

240÷360

Jeppsson et al (2007)

300

L

Oxygen transfer coefficient for aerobic tank to evaluate the overall kLaT

k2,2

d m-3

-1.82÷-1

Jeppsson et al (2007)

-0.42

C

Oxygen transfer coefficient for MBR tank to evaluate the overall kLaT

k1,3

d-1

80÷120

Jeppsson et al (2007)

90

L

Oxygen transfer coefficient for MBR tank to evaluate the overall kLaT

k2,3

d m-3

-1.82÷-1

Jeppsson et al (2007)

-0.55

C

Overall kLaT for N2O

kLaT_N2O

d-1

108

Mampaey et al. (2015)

108

L

Overall kLaT for CO2

kLaT_CO2

Half saturation parameter for SALK for XAUT

Salinity inhibition factor for heterotrophs

Fractionation

Physical

Salinity inhibition factor for autotrophics

IS,H

97

Mampaey et al. (2015)

87

L

-1

0.24÷0.36

Park and Marchand (2005)

0.288

C

-1

d

IS,A

d

0.24÷0.6

Park and Marchand (2005)

0.48

L

Erosion rate coefficient of the dynamic sludge



-

0.00001÷0.001

Mannina et al. (2011b)

0.0138

L

Stickiness of the biomass particles



-

Mannina et al. (2011b)

0.32

C

Compressibility of cake



Kg m s

1.75 10 ÷3,25 10

Substrate fraction below the critical molecular weight

f

-

Screening parameter



m

Efficiency of backwashing

CE

-

0÷1 -3

-1

-5

-5

-5

Mannina et al. (2011b)

1.75 10

0.001÷0.99

Mannina et al. (2011b)

0.86

C

1000÷2000

Mannina et al. (2011b)

1487

C

0.986÷0.999

Mannina et al. (2011b)

9.86E-01

C

0.3

L

0.12

L

0.12

C

0.1

L

0.36

C

Fraction of influent Ss

FSs

-

0.1÷0.3

Fraction of influent SI

FSI

-

0.114÷0.126

Fraction of influent XI

FXI

-

0.05÷0.15

Fraction of influent XH

FXH

-

0.06÷0.18

Fraction of influent XS*

FXS

-

0.244÷0.676

Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015) Mannina and Cosenza (2015)

L

Table_A2

Process

SO2

1 2 3 4 5 6 7

1,7

SS

SBAP

1-fSI 1-fSI 1-fSI 1-fSI 1-fSI 1-fSI

-1 -1

SUAP

2,8 2,9 2,10

4,8 4,9 4,10

5,9 5,10

11

2,11

4,11

5,11

14

5,8

fUAP YAOB

1,13

 iN , BM 

1,14

i

COD _ NO3

6,8

SI

SALK

fSI fSI fSI fSI fSI fSI

iCharge_NH4*5,5 iCharge_NH4*5,6

7,8 7,9

8,9 8,10

9,10 9,11

fUAP YAOB

1 YAOB

-iN,BM



XI

XS

iCharge_NH4*5,8+iCharge_NO3*6,8+iCharge_NO2*7,8 iCharge_NH4*5,9+ iCharge_NO2*7,9 iCharge_NH4*5,10

13,8 13,9 13,10

1 1 1

iTSS,BM iTSS,BM iTSS,BM

iCharge_NH4*5,11

13,11

1

iTSS,BM

iCharge_NH4*5,12

13,12

5,13*iCharge_NH4+

1

5,14*iCharge_NH4+

1 YNOB

1 i YAOB Charge_NO2

iCharge_NO3 

1 YNOB

fXI

1-fXI-fBAP

13,13

iTSS,BM

13,14

*iCharge_NO2

fBAP

5,16

iCharge_NH4*5,16

13,16

fXI

1-fXI-fBAP

fXI*iTSS,XI+(1-fXI)*iTSS,XS-iTSS,BM

-1

1  YH  Y _ H 

 i COD _ NO2  YH  Y _ H

 7 ,9  8,9  8,10 

i



1  YH   Y _ H   f UAP COD _ NO 2

 i COD _ NO  YH  Y _ H

; 9,11 

i



1  YH  Y _ H   f UAP COD _ N 2 O

 i COD _ N 2   YH  Y _ H

; 10,11  

i

1  YH  Y _ H  COD _ N 2 O

 i COD _ N 2   YH  Y _ H

fXI*iTSS,XI+(1-fXI)*iTSS,XS-iTSS,BM

-1

 16     i COD _ NO3  YAOB  f UAP  i  i COD _ NO3  YNOB  f UAP f UAP 1 14  ;    COD _ NO2 ; 2,812   ; 4,811  ;  5,7  i N , BM ;  5,1811  i N ,BM ; 5,12  5,1516   f XI  i N ,XI  1  f XI   i N ,XS  i N ,BM  1,14 YNOB YH Y _ H YH Y _ H YAOB



iTSS,BM

1

16

COD _ NO3

fXI*iTSS,BM+(1fXI)*iTSS,XSiTSS,BM

-1 1

1-fXI-fBAP

i

-iTSS,XS -iTSS,XS iTSS,BM

fXI

 i COD _ NO2  YH   Y _ H

XTSS

1

13,15

;  7 ,8  

XNOB

13,7

iCharge_NH4*5,15

  Y _ H  f UAP 

XAOB

-1 -1

5,15

YH

XH

iCharge_NH4*5,7

10,11

YAOB

SCO2

fBAP



H

SN2

15



1  Y

SN2O

5,12

fBAP

5,56   1  f SI   i N ,SS  f SI  i N ,SI  i N ,XS ; 1,7   1  YH  f UAP  ; 1,13

 6 ,8 

SNO

5,7

8 9 10

13

SNO2

5,5 5,6 fUAP YH

12

SNO3

-1 -1

1 YH



SNH4



Table_A3

No.

Process

Process rate equation j

1

Aerobic hydrolysis of BAP

  SO 2 k h ,BAP     S BAP  X H  K O 2,HYD  SO 2 

2

Anoxic hydrolysis of BAP

 K O 2,HYD    S NO3 k h ,BAP   NO3, HYD      S BAP  X H  K O 2,HYD  SO 2   K NO3,HYD  S NO3 

3

Aerobic hydrolysis of UAP

  SO 2 k h , UAP     S UAP  X H  K O 2,HYD  SO 2 

4

Anoxic hydrolysis of UAP

5

Aerobic hydrolysis

6

Anoxic hydrolysis

7

Aerobic growth on SS

8

Anoxic growth on SS reducing NO3 to NO2

9

Anoxic growth on SS reducing NO2 to NO

10

Anoxic growth on SS reducing NO to N2O

11

Anoxic growth on SS reducing N2O to N2

12

Lysis of XH

 K O 2,HYD    S NO3 k h , UAP   NO3,HYD      S UAP  X H  K O 2,HYD  SO 2   K NO3,HYD  S NO3   XS      SO 2 XH    XH k h     K O 2, HYD  S O 2   K  X S   X X  H    XS  K O 2, HYD     XH S NO3 k h   NO3, HYD      K O 2, HYD  S O 2   K NO3, HYD  S NO3   K  X S  X X H 

    XH   



  Ss      SO 2 S NH 4 S ALK         XH  K O 2, H  S O 2   K s  S S   K NH 4, H  S NH 4   K ALK  S ALK 

H   

 K O 2, H



      Ss    S NO 3 S NH 4 S ALK            XH  S O 2   K NO 3  S NO 3   K s  S s   K NH 4, H  S NH 4   K ALK  S ALK 

K O 2, H

 H  g 2  

      SS      K I 3 NO S NO 2 S NH 4 S ALK      XH   K O 2, H  S O 2   K NO 2  S NO 2   K S  S s   K NH 4, H  S NH 4   K ALK  S ALK   K I 3 NO  S NO        K O 2, H        K I 3 NO S NO S NH 4 S ALK     S S     H  g 4       XH  2  K O 2, H  S O 2   K  S  S NO   K S  S S   K NH 4, H  S NH 4   K ALK  S ALK   K I 3 NO  S NO  NO  NO  K I 4 NO  

 H  g 3  



 H  g 5  

K O 2, H

      SS     K I 5 NO  S N 2O S NH 4 S ALK      XH   S O 2   K N 2O  S N 2O   K S  S S   K NH 4, H  S NH 4   K ALK  S ALK   K I 5 NO  S NO 

K O 2, H

 K O 2, H

bH  XH

          SO 2 S S ALK FA    K I 9 FNA  AUT , AOB        X AOB  2   K  S K  S K  S S FA  K S   ALK , AUT  O2  FNA   ALK   I 9 FNA  O , AOB FA  FA  K I 9 FA             SO 2 S S ALK FNA    K I 10 FA     AUT , NOB      X NOB 2   K  S K  S K  S S FNA  K S   ALK , AUT  O2  FA   ALK   I 10 FA  O , NOB FNA  FNA  K I 10 FNA  

13

Aerobic growth of XAOB

14

Aerobic growth of XNOB

15

Lysis XAOB

b AUT,AOB  X AOB

16

Lysis XNOB

b AUT, NOB  X NOB

Table_A4

Description Drag force Lifting force Probability of particle deposition on membrane surface Rate of biomass attachment

Equations

Fa  3s dp J d2 p 8 Fa 24J E  Fl  Fa 24J  C d dp G Fl  Cddp sG

24CSSJ2  dMdc     ECSSJ  24J  CddpG  dt a

Deep-bed filtration

1   GM2 dc  dMdc     Vf t  Mdc  dt d dMsc 24CSSJ2 1   GM2 dc   dt 24J  CddpG Vf t  Mdc dMsc  cMsc dt C s m  CS e  

ith total resistance

RtS,i  Rm  Rp,i  Rc,i  Rm  Rp,i  Rdc,i  Rsc,i 

Total resistance

Rt 

Rate of sludge detachment Net cake deposition Detachment rate during backwashing

R N

tS,i

i1

Trans-membrane pressure

TMP  JR t

Where: s = sludge viscosity; dp= particle diameter; J = permeate flux; Cd = lifting force coefficient; Css = suspended solid concentration of biomass sludge; = compression coefficient for dynamic sludge layer; Vf = volume of permeate produced;= erosion rate coefficient of dynamic sludge film= stickiness of biomass; c = efficiency of backwashing; Csm = concentration of COD at the physical membrane surface ; Cs = concentration of COD in the mixed liquor at the physical membrane surface; RtS,i = total resistance of fouling in the section i,; Rm = intrinsic resistance of the membrane; Rp,i = the pore fouling resistance caused by solute deposition inside the membrane pores in the section i; RC,i = resistance of cake layer in the section i; Rdc,i = resistance of dynamic sludge film in the section i; Rsc,i = resistance of stable sludge cake in the section i; Rt = total fouling resistances

Graphical Abstract (for review)