Modelling SMP and EPS formation and degradation kinetics with an extended ASM3 model

Desalination 261 (2010) 117–125

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Modelling SMP and EPS formation and degradation kinetics with an extended ASM3 model T. Janus ⁎, B. Ulanicki Process Control-Water Software Systems, De Montfort University, The Gateway, Leicester, LE1 9BH, United Kingdom

a r t i c l e

i n f o

Article history: Received 24 November 2009 Received in revised form 10 May 2010 Accepted 11 May 2010 Available online 16 June 2010 Keywords: Activated Sludge Model No. 1 (ASM1) Activated Sludge Model No. 3 (ASM3) EPS Mathematical modelling Membrane bioreactor (MBR) SMP

a b s t r a c t This paper presents a dynamic mathematical model of activated sludge which is able to predict the formation and degradation kinetics of SMP and EPS in a bacterial biocenosis. The model is based on a calibrated version of ASM3 [1] and an extended unified theory of production and degradation of SMP and EPS as proposed by Laspidou and Rittmann [2,3]. The model was calibrated on the published experimental data from batch and continuous flow laboratory and pilot plant experiments [4–6] and proved to be in good agreement with the measurements. A standard set of parameters was then chosen for the model as a combination of the calibrated values and literature data. The CES-ASM3 was then used to predict SMP and EPS production in an activated sludge system under various operating conditions. The simulations indicated an increased production of SMP and EPS at higher MLSS, lower temperatures and lower SRT. The model also predicted a slight increase in SMP and EPS with increased DO. © 2010 Elsevier B.V. All rights reserved.

1. Introduction EPS and SMP are by-products of the metabolic activity of bacterial cultures and are excreted by these microorganisms during their growth, decay or in a response to changing environmental conditions [7–9]. An extensive review of SMP has been provided by Barker and Stuckey [10]. EPS are a mixture of complex high molecular-weight polymers forming a three-dimensional matrix which envelop bacterial cells and protect them against environmental stress and toxicity [8,11–13]. SMP are made of different organic compounds, such as humic and fulvic acids, polysaccharides, proteins, amino acids and exocellular enzymes [10] and together with EPS have been found to play an important role in the formation of flocs and biofilms [8,11–13]. Ability to predict SMP and EPS in activated sludge systems is important for the following reasons: SMP and EPS contents in the mixed liquor have been found to correlate with floc strength and resistance to shear and to influence various properties of activated sludge such as floc size distribution, dewaterability, settleability and compressibility, non-settleable solids fraction, SSVI, cake filtration properties such as CST and filtration resistance, hydrophobicity, viscosity, and surface charge. In MBR systems, bound EPS co-deposit together with bacterial cells on filtration membranes filling voids between cells and forming a potentially compressible cake with high hydraulic resistance [14,15] thus attributing to membrane fouling. SMP was found to lead to a

⁎ Corresponding author. E-mail addresses: [email protected] (T. Janus), [email protected] (B. Ulanicki). 0011-9164/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2010.05.021

decrease in membrane filterability [16–18] and cause so-called ‘irreversible fouling’, although not under all operating conditions [19]. SMP have also been found to comprise the majority of soluble organic material in the effluents from biological WWTPs and their presence is, therefore, of particular interest in terms of achieving effluent BOD and COD standards [10]. As bound and free EPS and SMP have been reported to be major fouling components in MBR process it is crucial to establish optimum operating conditions for activated sludge systems under which the production of these organic substances is minimal. Many experimental and modelling studies have led to developments of several SMP production and degradation models which have been briefly outlined in Barker and co-workers [10,20,21]. From the modelling perspective SMP can be subdivided into two groups, either from the point of view of kinetic origin or based on their chemical composition. In most models SMP are subdivided into UAP which are produced during substrate metabolism and into BAP which originate directly from biomass, presumably as part of decay. If we looked into chemical composition of SMP which has a direct impact on such properties as molecular size distribution or hydrophobicity, we could quantify the amounts of PP and PS in SMP. It was found that depending on their composition SMP and EPS exhibit different fouling properties [22,23]. Most of the models developed to date however did not look into the chemical composition of SMP and so does the model proposed in this article. The authors believe that a biological model for predicting SMP and EPS concentrations together with their PS and PP fractions would need to be developed at some point of time in order to describe SMP and EPS production in greater detail and provide better links to fouling models.

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Among the newest developments in SMP modelling, Lu et al. [24] created an ASM1 modification which included two additional states: UAP and BAP. However, during an analysis of their paper, some defects of the model have been found such as negative BAP output concentrations and COD, N and charge imbalances in the Petersen matrix. OliveiraEsquerre et al. [25] produced a modified ASM3 model which included MP as an additional state. The model was however unable to predict the measured SMP concentrations without compromising the prediction accuracy of original ASM3 state variables. Jiang et al. [21] produced a very well calibrated SMP model capable of predicting UAP and BAP and based on ASM2d. Laspidou and Rittmann [3] created a dynamic model based on their unified theory of SMP and EPS production [2] which in addition to UAP and BAP also included EPS, but which was not based on any of the activated sludge models developed by IAWQ [26]. Jang et al. [27] created an SMP and EPS model very similar to Laspidou and Rittmann [3] but extended with several additional equations describing filtration and fouling. Ahn et al. [28] created an ASM1 extension with both SMP and EPS. This model was however fitted to only three points for three different SRTs. Model comparison studies performed by the authors of this article for various published SMP models with their default parameter sets revealed that in the work of Lu et al. [24] and Oliveira-Esquerre et al. [25], the stoichiometric parameters for SMP kinetics have a very large impact on other reaction terms in their base activated sludge models. As a result, the accuracy of predicting the original ASM1 and ASM3 state variables is sacrificed to such a degree that model outputs such as O2 demand or sludge production vary up to 100% from the outputs of ASM1 and ASM3 models. The main task of this study was to develop an SMP and EPS formation model based on an extended version of the unified theory by Laspidou and Rittmann [2], to include this model in the ASM3 matrix form and then obtain a standard parameter set for this model extension. The model should be able to accurately predict SMP and EPS concentrations in activated sludge systems without compromising the prediction accuracy of other states. The importance of modelling SMP and EPS together comes from the fact that formation and utilisation kinetics of these two components are inter-related and that both of these groups of chemical substances have an impact on membrane fouling. As the basis for this model, ASM3 rather than ASM1 was chosen as from the authors' experiences ASM3 is easier to calibrate for long sludge age systems, possibly as a result of replacing the ‘death-regeneration’ concept with an endogenous respiration process. Additionally ASM3 solves several wellknown limitations of ASM1 as reported in Gujer et al. [1] and with some add-ons it can be used to simulate for example a two-stage nitrification process [29,30] or EBPR [31]. For comparison purposes the authors implemented the same SMP and EPS kinetics into the ASM1 model. Due to space limitations this model will however not be described in this article but references to it are included in some of the figures. 2. Model definition The purpose of this section is to describe only the components and processes relating to SMP and EPS production and utilisation. Hydrolysis and heterotrophic and autotrophic processes are modelled exactly as in ASM3 [1,26] and will not be discussed here. 2.1. Definition of components

3. XEPS [M(COD) ⋅ L − 3]: Extracellular polymeric substrates. In most experimental studies, it is assumed that EPS and SMP (UAP and BAP) are composed of only PP and PS. For comparison with modelling outcomes, PP and PS measurements need to be converted to COD using Eq. (1) first introduced in Jiang et al. [21]. The equation assumes that PP and PS have been determined with colorimetric methods. SCOD = ð1:5⋅SPT + 1:07⋅SPS Þ = 0:65

ð1Þ

2.2. Definition of new processes and process kinetics The new model (CES-ASM3) assumes that production of EPS in activated sludge systems obeys the Leudeking–Piret equation [32] with a reformulated non-growth associated term and an additional reaction for EPS hydrolysis/dissolution: rEPS = fEPS ⋅μ⋅X + fEPS;d ⋅b⋅X−kh;EPS ⋅XEPS

ð2Þ

where μ is the microbial growth rate (T − 1), X is the biomass concentration (MXL − 3), XEPS is the EPS concentration (MEPSL − 3), fEPS is the growth associated EPS formation coefficient (MEPS MX− 1), fEPS, d is the non-growth associated EPS formation coefficient (MEPSMX− 1), b is the microbial decay rate (T − 1), and kh, EPS is the rate of EPS hydrolysis/ dissolution (T − 1). Production of UAP is associated with biomass growth and substrate utilisation and can be expressed with a reformulated equation of [33]: rUAP = ðγUAP = Y Þ⋅μ ⋅X

ð3Þ

where γUAP is the UAP formation coefficient (−) and Y is the biomass −1 yield (MXMSMP ). BAP is assumed to originate from biomass decay and hydrolysis/ dissolution of EPS and its production follows the reactions described in Eq. (4): rBAP = fBAP ⋅b⋅X + ð1−fS Þ⋅kh;EPS ⋅XEPS ⋅YBAP

ð4Þ

where fBAP is the BAP formation coefficient (MSMPMX− 1), fS is the fraction of SS produced from EPS hydrolysis/dissolution (−), and YBAP −1 is a unit conversion between EPS and SMP (MSMPMEPS ) and is equal to 1 as all modelled carbonaceous substrates including EPS and SMP have the same unit (COD). According to this equation part of BAP is biomass associated SMP whereas the rest can be regarded soluble EPS as it's originating from hydrolysis/dissolution of EPS. The kinetic pathways of SMP and EPS in the model are presented in Fig. 1. As shown, UAP as well as BAP are taken up by heterotrophic biomass for storage, growth and respiration. The above described three processes have been incorporated in ASM3. This led to a model extension by 5 new kinetic equations, 3 kinetic parameters and 14 stoichiometric parameters. The new kinetic rate expressions are listed in Table 1. Values of the new kinetic parameters at the temperature of 20 °C are shown in Table 3 together with the new stoichiometric parameters. The temperature dependency coefficients for BAP and UAP storage rates are equal to the one for SS storage. The EPS hydrolysis rate temperature dependency coefficient has the same value as the one for hydrolysis of XS.

Three new components are added to the base model (ASM3) 2.3. Stoichiometry 1. SUAP [M(COD) ⋅ L − 3]: Utilisation associated products. This is a fraction of SMP which is produced as a by-product of substrate utilisation and cell growth. 2. SBAP [M(COD) ⋅ L − 3]: Biomass associated products. This is a fraction of SMP which is independent of cell growth rate and is a byproduct of cell lysis and decay as well as EPS hydrolysis/dissolution.

The stoichiometric matrix for the new model is shown in Table 2. All new stoichiometric parameters together with their definitions are listed in Table 3. Values of these parameters have been taken from literature or calibrated. All unknown stoichiometric coefficients: xj, yj, zj, and tj in the Petersen matrix can be calculated from mass and charge conservation

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Fig. 1. EPS and SMP formation and utilisation processes in the model.

equations using the parameters listed in the Composition matrix included in Table 2. 3. Model calibration The new model has been calibrated on the experimental data from two different sources in order to obtain an initial set of kinetic and stoichiometric parameters for simulations of activated sludge systems. The first calibration was based on the data obtained by Hsieh et al. [4,5] who had measured the production of biopolymers in a pure bacterial culture of Pseudomonas atlantica cultivated in a glucose medium under different, well-defined environmental conditions in a continuous flow and a batch reactor. The second calibration was based on a set of EPS, SMP, MLSS, and MLVSS data at various SRTs obtained by Yigit et al. [6]. The measurements were taken under steady-state conditions during long-term operation of a hollow fibre MBR pilot plant fed with raw domestic wastewater. The kinetic and stoichiometric parameters obtained from both calibration tasks are listed in Table 3. 3.1. Calibration on the data set from Hsieh et al. [4,5] The experiments carried out and published by Hsieh et al. [5] have been modelled in the MATLAB® environment with operating and initial conditions conforming to the experiments. The bacterial culture was cultivated in a 2.0 g/l glucose medium, therefore it has been assumed in the model that the influent COD is composed of only SS with a concentration of 2000 mgO2/l. Influent SNH was set at 125 mgN/ l which corresponds to 0.5 g/l NH4CL as defined in Hsieh et al. [5]. Based on other information provided in Hsieh et al. [5] the influent (continuous flow reactor) and initial (batch experiment) XEPS concentrations were set to 10 mgCOD/l. All other COD and N influent fractions are set to zero. DO concentration in the mixed liquor was assumed to be 1.5 mgO2/l. Reactor volumes and flow-rates were taken from the original article.

Table 1 Process rate expressions for SMP and EPS kinetics. No.

Process

Process rate equation

p2, b

Aerobic storage of SBAP

kSTO;BAP ⋅

p2, c

Aerobic storage of SUAP

p3, b

Anoxic storage of SBAP

p3, c

Anoxic storage of SUAP

p13

Hydrolysis of XEPS

SBAP SO ⋅X KBAP + SBAP KO + SO H SUAP SO kSTO;UAP ⋅ ⋅X KUAP + SUAP KO + SO H SBAP KO SNO kSTO;BAP ⋅ηNO ⋅ ⋅X KBAP + SBAP KO + SO KNO + SNO H SUAP KO SNO kSTO;UAP ⋅ηNO ⋅ ⋅X KUAP + SUAP KO + SO KNO + SNO H

kh, EPS ⋅ XEPS

As the modelled reactors were inoculated with pure heterotrophic bacterial culture, the autotrophic biomass activity in the mathematical model had to be switched off by setting μA to zero. Thus, only the parameters responsible for SMP and EPS kinetics in the heterotrophic biomass could be estimated in this calibration exercise. It was then assumed that the unidentified SMP and EPS kinetic and stoichiometric parameters for the autotrophic biomass are equal to the corresponding ones for the heterotrophic biomass. Although this is very likely not be true, the relative error this assumption may cause on mixed liquor EPS and SMP concentrations is very small as the autotrophic mass fraction in the activated sludge is roughly only 2 to 5%. This low impact of autotrophic activity on mixed liquor SMP and EPS concentrations was later confirmed by the results of the parameter sensitivity study. The selected kinetic and stoichiometric parameters have been calibrated in order to generate model responses closest to the measurements. The list of estimated parameter values is shown in Table 3 and the results of the calibration are presented in Figs. 2 and 3. For the readers' information, the graphs also show the results of the simulations obtained from a different, ASM1-based model which was also developed by the authors and which was subsequently replaced with the current ASM3-based one. SMP concentrations on the plots correspond to a sum of SUAP an SBAP, total biomass is a sum of XH and XEPS and S depicts the concentration of a readily biodegradable substrate SS. The graphs show a good quality of fit for both models with small differences between ASM1-based model and CES-ASM3 which result from different growth and decay formulations in ASM1 and ASM3. Death regeneration concept in ASM1 has been replaced in ASM3 with endogeneous respiration. These different approaches to modelling decay have an effect on substrate utilisation kinetics and necessitated slightly different mathematical formulations of SMP and EPS kinetics. Additionally, both models have been manually calibrated in two separate calibration studies which itself would lead to slightly different calibration results. Manual adjustment of the parameters was based on the authors' previous experiences with calibrating activated sludge models. During numerous simulations with different parameter sets, the authors observed that because the model attempts to model all possible SMP and EPS metabolic paths which have been observed by various researchers, the mathematical model became overparameterised leading to identifiability problems already present in ASM1 and ASM3. As a result of this overparameterisation, it is possible to obtain different parameter sets which will produce the same or very similar SMP and EPS concentrations — especially when adjusting parameters in the opposing processes such as production/ utilisation. Exact identification of the model parameters would require several separate and appropriately designed batch test experiments, but for the time being the parameters listed in Table 3

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Table 2 Stoichiometric and composition matrices for CES-ASM3 model, j: process, i: component.

j

Model components i

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Processes

SO

SI

SS

SNH

SN2

SNO

SHCO

SBAP

SUAP

XI

XS

XH

XSTO

XA

XEPS

XTSS

fSI

1− fSI −1

y1

z1

y2a

z2a

Heterotrophic organisms p1 Hydrolysis p2,a

Aerobic storage of SS

x2a

p2,b

Aerobic storage of SBAP

x2b

y2b

z2b

p2,c

Aerobic storage of SUAP

x2c

y2c

z2c

p3,a

Anoxic storage of SS

p3,b

−1 −1

− x3a

x3a

z3a

Anoxic storage of SBAP

y3b

− x3b

x3b

z3b

p3,b

Anoxic storage of SUAP

y3c

− x3c

x3c

z3c

−1

p4

Aerobic growth

z4

γH YH;O2

p5 p6 p7 p8 p9

Anoxic growth Aerobic endog. respiration Anoxic endog. respiration Aerobic respiration of XSTO Anoxic respiration of XSTO Autotrophic organisms Nitrification

p11 p12

p13

Aerobic endogenous respiration Anoxic endogenous respiration EPS hydrolysis Hydrolysis of XEPS

Composition matrix 1 ThOD g ThOD 2 Nitrogen g N 3 Ionic charge Mole + 4 TSS g TSS +

x4

y4

x6

y5 y6 y7

− x5

x5

− x7

x7

z5 z6 z7

− x9

x9

z9

1/YA

z10

t1 YSTO,O2 − fEPS,STO YSTO,SMP,O2 − fEPS,STO

y3a

p10

−1

−1

YSTO,SMP,O2 − fEPS,STO YSTO,NO − fEPS,STO YSTO,SMP,NO − fEPS,STO

−1

fBAP fBAP

γH YH;NO

YSTO,SMP,NO − fEPS,STO 1 − fEPS,h 1 − fEPS,h −1 −1

fXI fXI

y10

x11

y11 y12

− x12

x12

1 iNSI

1 iNSS

− 24/14 1

− 64/14 1 − 1/14

t2b

t2c fEPS,STO

t3a

fEPS,STO

t3b

t3c fEPS,h

t4

− 1/YH,NO

fEPS,h fEPS,d fEPS,d

t5 t6 t7 t8 t9

γA/YA

z11

fBAP

fXI

z12

fBAP

fXI

−1

1 − fS

1 1/14

fEPS,STO

− 1/YH,O2

1− fEPS,a −1

fS

−1

fEPS,STO

t2a

−1 −1

x8

x10

fEPS,STO

fEPS,STO

1 iNSBAP

1

fEPS,a

t10

fEPS,d

t11

fEPS,d

t12

−1

t13

1 iNXI

1 iNXS

1 iNBM

1

1 iNBM

1 iNXEPS

iTSSXI

iTSSXS

iTSSBM

iTSSSTO

iTSSBM

iTSSEPS

−1 1

This model assumes that ThOD is identical to the measured COD. 1 gSO = − 1 gThOD, 1 gSNH = 0 gThOD, 1 gSNO = − 64/14 gThOD, 1 gSN2 = − 24/14 gThOD.

need to be used as a starting point for further investigations. It was very difficult for this particular experimental data set to obtain a good fit for SMP for both reactors (batch and continuous flow). By raising the parameters responsible for BAP production, we were able to increase the effluent SMP concentrations in the continuous flow process up to the measured values but at the same time this caused the SMP to gradually increase in time in the batch process, in contrast to the measurements. Unsure of the accuracy of the measurements and the methodology used, the model was calibrated in such a way as to provide a compromise between the accuracy of SMP predictions in the continuous flow and the batch process. In the process of fitting the substrate (S) and the biomass curves, three ASM3 parameters: μH, kSTO, and bH, O2 had to be increased and YH, O2 had to be lowered from the default ASM3 values. These changes had to be made in order to describe the kinetics of P. atlantica which differ significantly from the kinetics of a mixed population biocenosis of an activated sludge. Additionally, it was assumed that the decay rates under anoxic conditions are, similarly to ASM3, half of the decay rates under aerobic conditions and that respiration rates of XSTO are equal to the respiration rates of XH. YH, NO was adjusted together with YH, O2 to obtain the same anoxic to aerobic sludge yield ratio as in the original ASM3 model. This adjustment was only of cosmetic relevance as the experiments were performed under completely aerobic conditions. It has been assumed that storage yields for SMP are equal to those for the SS, N contents of SBAP and XEPS are equal to those of the biomass and unit production of XEPS remains the same during the growth and

the storage of internal substrates. The Monod constants for the storage of SBAP and SUAP have been adopted from the growth kinetics on SMP as a substrate, published by Noguera et al. [7]. All other SMP and EPS kinetic and stoichiometric parameters have been obtained through parameter estimation. 3.2. Calibration on the data set from Yigit et al. [6] In order to test how the new mathematical model would simulate a wastewater treatment process, it was calibrated using a second set of experimental data, this time obtained from a submerged MBR pilot plant fed with raw domestic sewage and operated at five different MLSS concentrations (4600; 6600; 8600; 10,100 and 12,600 mg/l). The experiment was simulated to follow the procedures described in Yigit et al. [6]. First, a steady-state condition was attained by running the model for 200 days at a MLSS setpoint of 4600 mg/l. The next MLSS setpoints were achieved by setting biomass wastage to zero and running the model until the next MLSS setpoint is reached. Results of the calibration are shown in Fig. 4. Values of the calibrated parameter are listed in Table 3. Similarly to the previous calibration exercise, the predictions of CES-ASM1 were also included in the plots. The experimental data shows a linear relationship between SMP and EPS concentrations and MLSS. Both models were able to reproduce EPS concentrations very accurately although it could not exactly follow the SMP measurements if the kinetic and stoichiometric parameters were to be kept at similar values to those reported in the literature. For the purpose of calibration, it was assumed that all parameters of the ASM3

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Table 3 Kinetic and stoichiometric parameters for SMP and EPS kinetics of CES-ASM3 model. Parameter

Symbol

Unit

Calibration 1

Calibration 2

Value

Method

Value

Method

Data set for simulations

Reported values/range

References

2.0 1.0 5 0.2–0.74 0.1 0.2 0.1 0.63 0.54 0.85 0.80

[1] [1] [1] [1,5] [1] [1] [1] [1] [1] [1] [1]

0.03 (anaerobic)– 0.17

[3,34]

0.017–0.096

[3,21]

30-85-500 (anaerobic) 30-100-500 (anaerobic)

[7,24,34]

0.0215 0.03 (anaerobic)– 0.18

[21] [3,34]

0.07

[21]

ASM3 parameters Heterotrophic maximum growth rate Autotrophic maximum growth rate Storage rate constant Aerobic endogenous respiration rate of XH Anoxic endogenous respiration rate of XH Aerobic respiration rate of XSTO Anoxic respiration rate of XSTO Aerobic yield of heterotrophic biomass Anoxic yield of heterotrophic biomass Aerobic yield of stored product per SS Anoxic yield of stored product per SS

μH μA kSTO bH, O2 bH, NO bSTO, O2 bSTO, NO YH, O2 YH, NO YSTO, O2 YSTO, NO

d−1 d−1 gSSg − 1XHd − 1 d−1 d−1 d−1 d−1 gXHg − 1XSTO gXHg − 1XSTO gXSTOg − 1SS gXSTOg − 1SS

12 0 30 0.60 0.30 0.60 0.30 0.43 0.40 0.80 0.70

Fitted Assumed Fitted Fitted Assumed Assumed Assumed Fitted* Assumed Literature Literature

2.0 1.0 5 0.2 0.1 0.2 0.1 0.80/(1+γH) 0.65/(1+γH) 0.80/(1+γH) 0.70/(1+γH)

Literature Literature Literature Literature Literature Literature Literature Calculated Calculated Calculated Calculated

2.0 1.0 5 0.2 0.1 0.2 0.1 0.80/(1+γH) 0.65/(1+γH) 0.80/(1+γH) 0.70/(1+γH)

CES-ASM3 kinetic parameters BAP storage rate constant UAP storage rate constant EPS hydrolysis rate constant

kSTO, BAP kSTO, UAP kH, EPS

gSBAPg − 1XHd − 1 gSUAPg − 1XHd − 1 gXEPSg − 1XHd − 1

1 0.1 0.4

Fitted Fitted Fitted

0 0 0.055

Fitted Fitted Fitted

0.1 0.1 0.17

γH

gSUAPg − 1XH

0.04

Fitted**

0.0193

Fitted

0.0193

γA

gSUAPg − 1XA

CES-ASM3 stoichiometric parameters Fraction of SUAP produced during heterotrophic cell growth Fraction of SUAP produced during autotrophic cell growth Saturation constant for SBAP

KBAP

0.04

Assumed

0

Assumed

0***

gSBAPm

−3

85

Literature

85

Literature

85

−3

100

Literature

100

Literature

100

Saturation constant for SUAP

KUAP

gSUAPm

Aerobic yield of stored product per SBAP and SUAP (SMP) Anoxic yield of stored product per SBAP and SUAP (SMP) Fraction of SBAP produced during cell lysis Fraction of XEPS produced during cell growth of XH

YSTO, SMP, O2

gXSTOg − 1SMP

Fraction of XEPS produced during cell growth of XA Fraction of XEPS produced during storage of internal substrates Fraction of XEPS produced during cell decay of XH Fraction of XEPS produced during cell decay of XA Fraction of SS produced during XEPS hydrolysis N content of SBAP N content of XEPS

YSTO, SMP, NO

gXSTOg

0.80

Assumed

0.80

Assumed

0.80

−1

0.70

Assumed

0.70

Assumed

0.70

−1

SMP

fBAP fEPS, h

gSBAPg (XHorXA) gXEPSg − 1XH

0.05 0.12

Fitted Fitted

0.0215 0

Literature Fitted

0.0215 0.12

fEPS, a

gXEPSg − 1XA

0.12

Assumed

0

Assumed

0***

gXEPSg

−1

XH

0.12

Assumed

0

Fitted

0.12

fEPS, dh

gXEPSg

−1

XH

0.05

Fitted

0.175

Fitted

0.05

fEPS, da

gXEPSg − 1XA

0.05

Assumed

0.175

Assumed

0***

fS

gSSg − 1XEPS

0.4

Fitted

0.4

Assumed

0.4

0.07 0.07

Literature Literature

0.07 0.07

Literature Literature

0.07 0.07

fEPS, STO

iNSBAP iNXEPS

−1

gNg SBAP gNg− 1XEPS

[7,24,34]

⁎Biomass net yield: YH,O2 ⋅ YSTO,O2 = 0.43 ⋅ 0.85 = 0.37. [3] − 0.34. **γH/(YH,O2 ⋅ YSTO,O2 = 0.04/0.43 = 0.093). ***EPS and SMP formation kinetic parameters for autotrophic biomass are set to zero as they have been found not to affect SMP and EPS concentrations. Parameter fitting was performed manually (parameters adjusted by hand) during the two described calibration exercises. Some of the parameters have been calculated as a function of other parameters which had been fitted, assumed or taken from the literature.

model would be left at their default values except the heterotrophic yields which were modified accordingly to the formulas written in Table 3. In order to obtain a sufficiently large SMP vs. MLSS gradient close to the one produced by the experimental results, the storage constants for SUAP and SBAP (kSTO, BAP and kSTO, UAP) had to be set to zero, meaning that BAP and UAP are assumed to be non-biodegradable. Similarly, the EPS production constants: fEPS, h, fEPS, a, and fEPS, STO had to be set to zero which means that EPS originates only from biomass decay, not from substrate utilisation. Other adjusted SMP and EPS kinetic and stoichiometric parameters are shown in Table 3.

to 0.1 d− 1 and XEPS hydrolysis constant kH, EPS was set to 0.17 d− 1 [3]. Like in the second calibration study and based on the outcomes of the results of the sensitivity analysis, stoichiometric parameters for SMP and EPS kinetics for the autotrophic biomass have been set to zero. The stoichiometric parameters for EPS: fEPS, h, fEPS, STO, and fEPS, d have been assigned the same values as in the first calibration exercise. The values of γH and fBAP were carried forward from the second calibration. This parameter set was used to carry out the simulations described in Section 5.

3.3. Default parameter set for CES-ASM3

The sensitivity analysis was carried out in order to determine which of the new kinetic and stoichiometric parameters have the largest effect on the output SMP and EPS concentrations. Figs. 5 and 6 show the results of this analysis for the most significant parameters which at their maximum deviation of 60% changed the output by over 10%. As shown in Fig. 5, the most significant parameters influencing the EPS production were: fraction

For further simulation studies, we have attempted to select a default parameter set for the CES-ASM3 model. These parameters are shown in Table 3. All ASM3 parameters were carried forward from the first calibration. The SUAP and SBAP storage constants were assumed to be equal

4. Sensitivity analysis

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Fig. 2. Results of CES-ASM3 calibration on a batch reactor data from Hsieh et al. [4,5].

of XEPS produced during storage of internal substrates ( fEPS, STO), EPS hydrolysis rate constant (kH, EPS), fraction of XEPS produced during cell growth of XH ( fEPS, h), and fraction of XEPS produced during heterotrophic cell decay ( fEPS, d). EPS is not affected by parameters fEPS, a and fEPS, da due to very small fraction of autotrophic organisms in the total biomass. SMP kinetics were affected mostly by the following parameters: BAP storage rate constant (kSTO, BAP), fraction of SS produced during XEPS hydrolysis ( fS), fraction of XEPS produced during the storage of internal substrates (fEPS, STO), saturation constant for SBAP (KBAP), EPS hydrolysis rate constant (kH, EPS), and fraction of XEPS produced during cell growth of XH (fEPS, h). The results show that SMP concentrations are very dependent on EPS kinetics and as a result, BAP is the dominant fraction of SMP. In this simulation study, SMP concentrations did not depend on any UAP formation processes. This was most likely due to the fact that after each parameter change, the system with high SRT was brought to a steady state, under which biomass decay dominates over substrate utilisation and growth processes. UAP production is going to play a more important role under time varying conditions and when a surplus of organic substrates is present in the reactor. 5. Simulation results The CES-ASM3 model with its default parameter set has been simulated in a single completely stirred aerobic tank treatment plant configuration with an ideal separation clarifier used to simulate the

separation membrane. Simulations have been performed under steadystate conditions for different DO, SRT, MLSS and temperatures in order to investigate the SMP and EPS outputs under various operating conditions. The ranges of variability for the operational parameters were as follows: DO: 0.5–6.0 mgO2/l, SRT: 12–250 d, MLSS: 3000–30,000 mg/l, and temperature: 8–26 °C. The simulation results are shown in Fig. 7. SMP predictions from Jiang's model [21] have also been included for comparison purposes. SMP concentrations produced by CES-ASM3 are a bit higher from those predicted by Jiang's model. This discrepancy originates from differences in default parameter sets of both models. SMP in both models is expected to increase with MLSS and decrease with SRT. The first relation is supported by the experimental results of Yigit et al. [6]. If we agree with the wide-spread and well supported hypothesis that SMP is one of the major foulants in MBR system then the second relationship is presumably correct as most of the authors claims that fouling propensity decreases with increasing SRT [19]. Jiang's model tends to predict an increase in SMP concentration with temperature whether in CES-ASM3 this trend is slightly negative, i.e. decrease in SMP with increasing temperature. Relation between SMP and temperature in CES-ASM3 is however weaker than in Jiang's model. Literature findings such as in Drews and co-workers [35,36] tend to agree qualitatively with the results obtained from CES-ASM3. Higher ambient temperature leads to higher bacterial metabolism and higher SMP elimination rates. The effects of temperature have been found to be higher during temperature transients rather than for difference in temperature under steady-state

Fig. 3. Results of CES-ASM3 calibration on a continuous flow reactor data from Hsieh et al. [4,5].

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Fig. 4. Results of model calibration on the experimental data from Yigit et al. [6].

conditions [35]. As earlier mentioned these simulations have been performed for steady-state conditions, thus the relationship between SMP concentration and temperature is weak. The models also differ in predicting SMP as a function of DO. CES-ASM3 showed increased SMP production at higher DO concentrations whereas Jiang's model predicted a slight decrease. It has been reported in some literature that higher DO concentrations lead to lower elimination of SMP in MBR systems [35], but at the same time the results of other experimental studies show that mixed liquor SMP concentrations increase with DO [37]. It is generally accepted that higher DO concentrations reduce the amount of fouling but this can be attributed as well to better sludge filterability which changes not only with SMP but can also be related to floc size distribution and floc geometry. When it comes to EPS, CES-ASM3 predicts that its concentrations will increase with MLSS, although the content of EPS in sludge will decrease, just as observed in Yigit et al. [6]. EPS was also found to be in negative proportion to SRT and temperature. For intermediate sludge ages, EPS was found to be unrelated to SRT [38], however the authors are in opinion that EPS concentrations would decrease for systems with older sludges where endogenous respiration plays a more important role [38,39]. The relation between EPS concentration and temperature is controlled by the EPS hydrolysis temperature dependency coefficient which has been initially set equal to the temperature dependency

coefficient for XS hydrolysis. Due to the lack of strong literature evidence for the exact character of the relation between EPS and temperature, these two coefficients have been set to an equal value of θ=1.0408. A slight increase in EPS with DO can be observed but this relationship is much weaker than for SMP. 6. Conclusion EPS and SMP production in bacterial cultures has been a subject of research for at least a decade, but despite of the efforts of various research groups a fully comprehensive model capable of accurately predicting SMP and EPS in activated sludge systems has not yet been developed, due to a highly complicated nature of SMP and EPS kinetics. SMP and EPS kinetics are dependent on many different factors which are currently not accounted for in the activated sludge models and thus it is difficult to include them in any of the current ASM model formulations. Additionally, SMP and EPS are produced and utilised as a result of different, often opposing metabolic mechanisms making identification of model parameters very difficult. The model presented here does not offer a final solution to modelling SMP and EPS in activated sludge systems but rather tries to encapsulate the knowledge obtained by various researchers within a single ASM-based model which can be used as a starting point for

Fig. 5. Sensitivity of EPS to most influencing new kinetic and stoichiometric parameters.

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Fig. 6. Sensitivity of SMP to most influencing new kinetic and stoichiometric parameters.

simulations of various activated sludge systems. The model is based on the kinetics postulated in Laspidou and co-workers [2,3,32–34] and has been calibrated with good results on two experimental data sets. It is intended for use in projects where accurate predictions of effluent COD are required, for modelling MBR reactors or in research projects looking at finding relationships between SMP and EPS production and various activated sludge parameters such as specific cake resistance, SSVI, sludge cake dewaterability and others, as outlined in Section 1. As a result of the assumptions made during formulation of the equations, the model has several limitations when it comes to modelling SMP and EPS. These limitations have been listed below: • SMP are subdivided from the point of view of their metabolic origin into UAP and BAP without considering their chemical composition. It has been found that SMP displays different fouling strengths depending on their molecular-weight distribution which varies with the polysaccharide and protein content. • Apart from SMP and EPS, membrane fouling is greatly affected by the floc size distribution of activated sludge which depends on

flocculation rate, shear stresses, floc density and resistance to shear. None of these processes are included in this model. • SMP and EPS production were found to increase under highly time varying conditions such as large temperature changes, variations in influent salinity or toxic effects which this model does not address. • As the new model is based on ASM3, it inherits all its deficiencies such as the inability to vary process kinetics with influent substrate composition which was found to affect many different processes including SMP and EPS production. • The kinetic and stoichiometric parameter sets for the model are combinations of literature data and the results of two calibration procedures. Due to identifiability issues, in order to identify all unknown parameters, appropriately designed batch tests would need to be carried out. Such tests were not performed here and therefore the parameter set in this article is just indicative and can be used as an initial step for further investigations. Ever increasing popularity of MBR systems creates the need for development of mechanistic models which could be used for design and

Fig. 7. CES-ASM3 predictions of SMP and EPS under various operating conditions.

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