Mechanisms of SMP production in membrane bioreactors: Choosing an appropriate mathematical model structure

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Mechanisms of SMP production in membrane bioreactors: Choosing an appropriate mathematical model structure Adrienne Menniti a,1, Eberhard Morgenroth a,b,* a b

Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Department of Animal Sciences, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

article info

abstract

Article history:

Being able to predict the soluble microbial product (SMP) concentration, an important

Received 7 September 2009

foulant in membrane bioreactors (MBRs), with mathematical models provides the oppor-

Received in revised form

tunity to use foulant production as an MBR design and optimization parameter. This study

8 June 2010

examined the ability of three mathematical model structures to describe two distinct

Accepted 16 June 2010

mechanisms of SMP production. The production mechanisms evaluated are (1) the erosion

Available online 23 June 2010

or hydrolysis of floc-associated extracellular polymeric substance (EPS) and (2) decay of active cells. The models were compared based on their ability to predict SMP concentra-

Keywords:

tions observed in an MBR system during a period of increased SMP and floc-associated EPS

Membrane bioreactor

production due to increased predation. Predation was an important contributor to overall

Extracellular polymeric substances

biomass decay. Short-term batch experiments were also preformed to examine model

(EPS)

assumptions related to the (1) production of SMP due to decay of active cells, (2) production

Soluble microbial products (SMP)

of SMP due to erosion of floc-associated EPS, (3) degradability of SMP present in the MBR

Modeling

mixed liquor during increased predation and (4) degradability of eroded floc-associated EPS. Both erosion of floc-associated EPS and decay of active cells were shown to be important independent mechanisms of SMP production. Therefore, a mathematical model used to predict SMP concentrations should provide the ability to capture both mechanisms independently. SMP produced during increased predation were slowly degradable while eroded floc-associated EPS was rapidly degradable. Model results demonstrate that the slowly biodegradable SMP fraction will dominate the bulk phase SMP concentration. ª 2010 Elsevier Ltd. All rights reserved.

1.

Introduction

The effective application of membrane bioreactors (MBRs) is limited by membrane fouling and the associated cost and energy burdens. Biologically produced soluble compounds such as proteins and carbohydrates are widely acknowledged

as key MBR membrane foulants and these compounds are called soluble extracellular polymeric substances (soluble EPS) or soluble microbial products (SMPs) (Laspidou and Rittmann, 2002a). Additionally, floc-associated EPS is an important contributor to membrane fouling in MBRs as the concentration of floc-associated EPS influences the cake fouling

* Corresponding author. Present address: Swiss Federal Institute of Technology Zu¨rich (ETH) and Swiss Federal Institute of Aquatic ¨ berlandstrasse 133, P.O. Box 611, CH-8600 Du¨bendorf, Switzerland. Tel.: þ41 (0)44 823 5539; fax: þ41 (0) Science and Technology (Eawag), U 44 823 5028. E-mail address: [email protected] (E. Morgenroth). 1 Present address: CH2M HILL, Portland, OR 97201, USA. 0043-1354/$ e see front matter ª 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.watres.2010.06.040

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qSEPS

Nomenclature b fSMP k1 k2 KBAP kXEPS khyd KS KSEPS KUAP mmax qBAP

1

first order biomass decay coefficient, day fraction of SMP retained by the membrane, dimensionless SUAP formation rate constant, mg CODSMP mg COD1 S SBAP formation rate constant, 1 mg CODSMP mg COD1 VSS day half-saturation coefficient for SBAP, mg CODSMP L1 XEPS formation constant, mg CODVSS mg COD1 S first order hydrolysis rate coefficient, day1 half-saturation coefficient for acetate, mg CODS L1 half-saturation coefficient for SEPS, mg CODSMP L1 half-saturation coefficient for SUAP, mg CODSMP L1 maximum specific growth rate, day1 maximum specific utilization rate of SBAP, 1 mg CODSMP mg COD1 VSS day

properties of the biomass (Le-Clech et al., 2006). Floc-associated EPS plays an essential role in the aggregation of microorganisms into flocs and biofilms (Flemming and Wingender, 2001) and is a complex matrix of proteins, polysaccharides, lipids and nucleic acids (Liu and Fang, 2003). The terms SMP and soluble EPS evolved from differing research areas e one focusing on the origins of residual wastewater organic matter (Namkung and Rittmann, 1986) and the other focusing on flocculation of microorganisms (Nielsen et al., 1997). Laspidou and Rittmann (2002a) reconciled the divergent but parallel frameworks and argued that SMP and soluble EPS refer to the same set of biologically produced soluble compounds. These compounds originate from flocassociated EPS that is released into solution, lysis products from biomass decay, hydrolysis products from particulate substrate degradation, and other byproducts of substrate degradation (Laspidou and Rittmann, 2002a; Nielsen et al., 1997). The pool of SMP has been divided into classes based on the source but the classification depends on the researcher’s frame of reference. Utilization associated products (UAPs) are generally classified as compounds produced during substrate metabolism (Namkung and Rittmann, 1986; Laspidou and Rittmann, 2002a). Namkung and Rittmann (1986) classified biomass associated products (BAPs) as byproducts of biomass decay. Laspidou and Rittmann (2002a) differentiated the overall biomass into active cells and floc-associated EPS and suggest that BAP is produced from the hydrolysis of flocassociated EPS. Aquino and Stuckey (2008) argued that BAP is produced by two distinct processes, from the decay of active cells and from the hydrolysis of floc-associated EPS, that should be modeled separately. The current study attempts to differentiate between the different mechanisms of SMP production, therefore the terminology of Aquino and Stuckey (2008) has been adopted. In the current manuscript, SBAP,Xa is used to describe the soluble byproducts of decay of active cells while SBAP,EPS describes SMP produced by the erosion or

qUAP S SBAP,Xa SSMP SUAP Xa XEPS XVSS YS YSMP

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maximum specific utilization rate of SEPS, 1 mg CODSMP mg COD1 VSS day maximum specific utilization rate of SUAP, 1 mg CODSMP mg COD1 VSS day concentration of acetate, mg CODS L1 concentration of BAP produced from the hydrolysis of XEPS, mg CODSMP L1 SUAP þ SBAP,Xa þ SBAP,EPS, concentration of all soluble microbial products, mg CODSMP L1 concentration of utilization associated products (UAP), mg CODSMP L1 concentration of active biomass, mg CODVSS L1 concentration of floc-associated extracellular polymeric substances (EPS), mg CODVSS L1 Xa þ XEPS, concentration of all biomass components, mg CODVSS L1 yield for acetate utilization, mg CODVSS mg COD1 S yield for SMP utilization, mg CODVSS mg COD1 SMP

hydrolysis of floc-associated EPS. UAP continues to represent byproducts of substrate metabolism. Three different structures used in mathematical modeling to describe the production of SMP are presented in Fig. 1. While the models do not specifically exclude other mechanisms of SMP production in their conceptual development, their model structures emphasize differing BAP production mechanisms. All models have terms describing UAP production. Model A (de Silva and Rittmann, 2000) suggests overall biomass decay as an BMP production mechanism while Model B (Laspidou and Rittmann, 2002b) describes the overall biomass as a combination of active cells and floc-associated EPS and suggests erosion or hydrolysis of floc-associated EPS to produce BMP. Model C (Aquino and Stuckey, 2008) introduced a third model that is the direct combination of the active cell decay and hydrolysis of floc-associated EPS. The kinetic and stoichiometric matrices for the three mathematical models are provided in Table 1. Other variances of these three approaches have been described in the literature (e.g., Lu et al., 2001 is a variance of Model A). This paper uses experimental data to examine the ability of three different model structures to describe SMP production in an MBR system. The purpose is to understand how the mathematical structure of the three models presented in Fig. 1 influences their ability to capture the experimental data. The models were compared based on their ability to predict SMP concentrations observed in an MBR system both during steady-state operation and during a period of increased soluble and floc-associated EPS production due to increased predation (Menniti and Morgenroth, 2010). Short-term batch experiments were also performed to examine the production of SMP due to starvation, and the production of SMP due to erosion of floc-associated EPS. The degradability of SMP compounds present in the MBR mixed liquor during increased predation and the degradability of eroded soluble EPS was also examined.

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was aerated with an air flow rate of 45 L h1. Floc-associated EPS and SMP were quantified in both reactors. Floc-associated EPS was extracted using a cation exchange resin (CER) following Frolund et al. (1996). Floc-associated EPS was quantified as the total mass of extracted floc-associated EPS COD per gram of MLVSS and converted to the total mass of EPS COD per liter of reactor volume based on the MLVSS concentration. Reactor operation resulted in average total solids concentrations of 2,703  113 mg/L in the low shear reactor and 2,783  94 mg/L in the high shear reactor. On average, the mixed liquor in both MBRs had a volatile fraction of 90%. SMP was separated from the mixed liquor using a Whatman 934AH glass fiber filter with a nominal pore size of 1.2 mm. The permeate from the glass fiber filter was then further filtered using a 0.2 mm cellulose acetate filter. SMP was quantified by measuring the COD concentration. All COD measurements of floc-associated EPS and SMP were performed on the day of sampling. Further details on the reactor system and reactor performance monitoring are provided in Menniti and Morgenroth (2010).

2.1.2.

Fig. 1 e Summary of mathematical models describing SMP production. State variables are boxed, processes are labeled in bold, and process rates are shown in italics. rS is the rate of substrate utilization, k1 is a stoichiometric factor describing SUAP production, and k2 is a stoichiometric factor describing SBAP,Xa production, kEPS is a stoichiometric factor describing floc-associated EPS production, and khyd is a stoichiometric factor describing SBAP,EPS production, Xa is the concentration of active biomass, XEPS is the concentration of floc-associated EPS and XVSS is the sum of XEPS and Xa. BAP is the sum of SBAP,Xa and SBAP,EPS and SSMP is the sum of SUAP, SBAP,Xa and SBAP,EPS. Note that the original publications of Models AeC do not differentiate between BAP produced from XEPS or from Xa. Active biomass has different meanings in Model A (overall biomass including active cells and floc-associated EPS) and in Models B and C (only the active cell fraction of the overall biomass).

2.

Materials and methods

2.1.

Long-term MBR experiments

2.1.1. Reactor operation and quantification of floc-associated EPS and SMP Two 20 L MBRs were operated identically except for the aeration rate. One reactor was aerated with an air flow rate of 15 L h1 and is called the low shear MBR. The high shear MBR

Arbitrary worm index

Brightfield images of MBR mixed liquor were captured approximately weekly using a Zeiss Axioskop (Carl Zeiss, Oberkochen, Germany) optical microscope. A 20 mL drop of mixed liquor, collected from the reactor immediately before image capture, was placed on a microscope slide and covered with a cover slip. A series of 30e60 randomly selected images was collected using 5 magnification Plan-Neofluar objective (Carl Zeiss, Oberkochen, Germany). The 1388  1040 pixel resolution images are collected using an Axiocam MRm camera and the AxioVision software (Carl Zeiss, Oberkochen, Germany). The number of aquatic earthworms, Aeolosoma hemprichi, in all images in a set was counted and divided by the total number of images in the set to determine the arbitrary worm index. The arbitrary worm index is intended to provide a qualitative estimation of the abundance of aquatic earthworms in the low shear MBR over time.

2.2. Mathematical modeling of floc-associated EPS and SMP production All simulations were performed using AQUASIM (Reichert, 1994). All state variables for organic matter in the mathematical models are based on COD units. Floc-associated EPS and SMP were measured in COD units directly. MLVSS measurements were converted to COD units assuming a conversion factor of 1.42 g COD/g VSS. The MBR system was modeled with fSMP ¼ 80% retention of SMP (SUAP, SBAP,Xa, SBAP, EPS) based on the average measured soluble COD retention across the membrane. The MBR system was also modeled with complete retention of particulate matter (Xa, XEPS), and no retention of influent substrate (S ). Active biomass (Xa) in Model A represents the combination of active cells and flocassociated EPS while in Models B and C active cells (Xa) and floc-associated EPS (XEPS) are modeled separately. Model stoichiometries and kinetics are presented in Table 1. Nomenclature for state variables is chosen to highlight similarities and differences between modeling approaches and differ slightly from the original publications. In Aquino and

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Table 1 e Process matrices for the mathematical models evaluated here. For explanation of processes and state variables see Section 2 and Fig. 1. Process

Component Xa

XEPS

(Model A) de Silva and Rittmann (2000) (A1) Growth on acetate Ys

S

SUAP

1

k1

Rate SBAP,Xa

SBAP,EPS 1 S Xa m YS max KS þ S

b

k2

Xa

(A3) Growth on SBAP

YSMP

1

qBAP

(A4) Growth on SUAP

YSMP

(A2) Decay

(Model B) Laspidou and Rittmann (2002b) (B1) Growth on acetate Ys(1 k1  kXEPS) (B2) Decay

1

YSMP

(B5) Growth on SUAP

YSMP

(Model C) Aquino and Stuckey (2008) (C1) Growth on acetate Ys(1 k1 kXEPS)

k1

1 S Xa m YS max KS þ S Xa 1 1

kXEPS

1

YSMP

(C5) Growth on SUAP

YSMP

(C6) Growth on SBAP

YSMP

Parameter estimation

The parameters describing SMP and floc-associated EPS production in each model evaluated here were estimated based on the measured SMP and floc-associated EPS concentrations in the high shear MBR. It was previously shown that there is no difference in SMP and floc-associated EPS production between the high and low shear MBR when aquatic earthworms were not present (Menniti and Morgenroth, 2010). The data from the high shear MBR were therefore used to estimate parameters because aquatic earthworms were never observed in this reactor. Parameter estimations were performed using AQUASIM (Reichert, 1994) and the parameter estimation algorithm was run with multiple initial parameter values and for several iterations to ensure the true least squares values were determined for each parameter or parameter set.

SBAP;EPS Xa KSEPS þ SBAP;EPS

SUAP Xa KUAP þ SUAP

k1

1 S Xa m YS max KS þ S k2

Stuckey (2008), BAP had been modeled as a single state variable while in the current study we separate BAP into SBAP,Xa and SBAP,EPS. For simplicity the same default parameters (Table 2) were used for the three models.

qSEPS

qUAP

1

(C4) Growth on SEPS

khyd XEPS

1

b

(C3) Hydrolysis of XEPS

2.3.

qUAP

1

(B4) Growth on SEPS

SUAP Xa KUAP þ SUAP

1

b

(B3) Hydrolysis of XEPS

(C2) Decay

kXEPS

SBAP;Xa Xa KBAP þ SBAP;Xa

Xa 1 1

1

khyd XEPS qSEPS qUAP

1

qBAP

SBAP;EPS Xa KSEPS þ SBAP;EPS

SUAP Xa KUAP þ SUAP

SBAP;Xa Xa KBAP þ SBAP;Xa

Parameter estimation based on least squares analysis was performed twice: once to determine Model A parameters and once to determine Model B parameters. The decay rate, k2, was estimated for Model A using only the SMP data. The parameter set khyd and kEPS in Model B was estimated using both the SMP and floc-associated EPS data. The estimated k2, khyd and kEPS values were directly used to predict the SMP and floc-associated EPS concentrations in Model C. The SMP data for the high shear MBR are shown with the steady-state model predictions for both Model A and Model B in Fig. 2(a). The floc-associated EPS data for the high shear MBR are shown together with the steady-state model prediction for Model B and Model C in Fig. 2(b). Parameter values estimated in the current study are provided in Table 2 together with other parameter values used in the current analysis. Not all parameters were identifiable from the experimental data due to parameter correlation therefore, a constant value was assumed for k1 during all parameter estimations. A constant value for k1 means that the rate of substrate utilization and therefore UAP production remained constant and observed changes in SMP production were due to the other mechanisms.

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Table 2 e Parameter values describing the MBR system in the current study. See Table 1 and the Nomenclature for explanation of parameters. Parameter

Value

Source

Parameters describing SMP production k1 k2 khyd kXEPS

0.05 mg CODSMP mg COD1 S 1 0.065 mg CODSMP mg COD1 VSS day 1 0.115 mg CODSMP mg COD1 day EPS 0.044 mg CODEPS mg COD1 S

Laspidou and Rittmann (2002b) Estimated in current study Estimated in current study Estimated in current study

Parameters describing SMP degradation YSMP KUAP qUAP KBAP qBAP KSEPS qSEPS

0.45 mg CODVSS mg COD1 SMP 100 mg CODSMP L1 1 1.27 mg CODSMP mg COD1 VSS day 1 85 mg CODSMP L 1 0.07 mg CODSMP mg COD1 VSS day 85 mg CODSMP L1 1 0.07 mg CODSMP mg COD1 VSS day

Laspidou Laspidou Laspidou Laspidou Laspidou Laspidou Laspidou

Parameters describing acetate degradation YS mmax KS

0.34 mg CODVSS mg COD1 S 9.7 day1 0.7 mg CODS L1

Laspidou and Rittmann (2002b) Laspidou and Rittmann (2002b) Laspidou and Rittmann (2002b)

Other parameters b fSMP

0.74 day1 0.8

Laspidou and Rittmann (2002b) Measured in the current study

Once the steady-state parameter values were determined for each model, the parameters were manually adjusted to capture the dynamic increase in SMP and floc-associated EPS concentrations observed in the low shear MBR. The parameters chosen for manual dynamic adjustment were based on the mechanistic assumptions behind each model structure. The appropriate parameters were manually adjusted to capture the trends in the experimental data such that the models approximately predicted the timing and magnitude of the concentration changes as closely as possible.

2.4.

Short-term batch experiments

2.4.1.

Batch SMP production experiments

Short-term batch experiments were performed with mixed liquor wasted from each of the lab-scale MBRs. A volume of biomass was placed in a beaker and aerated for 4 h while a separate volume of biomass was sheared for the same time. The DO concentration in both samples was above 6 mg/L for the duration of the experiment. The tank used for shearing the biomass had the standard reactor geometry defined by Holland and Chapman (1966). Therefore the average velocity gradient in the reactor, G, can be determined based on the mixing intensity. The MBR biomass was sheared by vigorous mixing with a 2-inch (5.08 cm) Rushton mixing impellor at 1000 revolutions per minute (rpm) resulting in G equal to 1800 s1. Changes in the SMP concentration were measured as changes in the soluble COD concentration using the methods described above.

2.4.2. OUR using acetate, SMP, and floc-associated EPS as substrate The oxygen utilization rate (OUR) was measured using a commercial respirometer (Challenge Environmental Systems, Model MS8-300 S.N. 0310, Fayetteville AR-USA). Closed bottles with working volumes of 250 mL are connected to a gas cylinder containing 99.95% oxygen. The respirometer counts oxygen

and Rittmann (2002b) and Rittmann (2002b) and Rittmann (2002b) and Rittmann (2002b) and Rittmann (2002b) and Rittmann (2002b) and Rittmann (2002b)

bubbles that enter the bottles as oxygen is depleted through microbial respiration. The bubbles are a fixed size and therefore contain a known amount of oxygen allowing the oxygen uptake rate to be calculated based on the number of bubbles counted in a fixed time interval. Temperature was controlled using a recirculating water bath (PolyScience Recirculator, Niles, CA). The pH was monitored at the beginning and the end of the batch experiments but not controlled. Test tubes containing 4 mL of 30 weight percent potassium hydroxide were suspended in the bottles to scrub carbon dioxide produced during respiration. Fresh MBR sludge was aerobically starved for 12e24 h in each batch test until OUR reached endogenous respiration levels. After the aeration period, the sludge was fed the substrate solution to be tested (concentrated SMP, extracted floc-associated EPS or concentrated acetate solution). The OUR was measured until all of the added substrate was consumed by the sludge and respiration rates decreased back to endogenous levels. Allyl-thiourea (ATU) was added at a concentration of 20 mg L1 to the fresh sludge to inhibit nitrification. The SMP present in the reactor was sampled by filtering freshly wasted MBR sludge with a solids filter as described previously. This SMP was then concentrated by membrane filtration to avoid dilution of the biomass during OUR measurements. Approximately 1 L of permeate from the solids filter was further filtered with a 10 kDa cellulose acetate membrane until only 100e200 mL of retentate ( ¼ concentrated SMP) remained. The COD of this retentate was then measured and 10e30 mL was added to each respirometer bottle resulting in an SMP concentration of 60e100 mg L1 COD. Thirty millilitres of extracted floc-associated EPS were added directly after harvesting the solution (described previously), resulting in an EPS concentration of 60e100 mg L1 COD. A concentrated solution of acetate was prepared so the addition of 30 mL contained 100 mg of COD. The MBR biomass was diluted with effluent for each experiment so that the resulting MLVSS concentration of all respirometer experiments was 500e1000 mg L1.

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High shear MBR 400

a

300 250 200 150 100

300 250 200 150 100 50

50

0

0 0

10

20

30

40

50

0

60

1,200

1,200

b

Floc EPS (mg COD L )

1,000

-1

Floc EPS (mg COD L-1)

c

350

SMP (mg COD L-1)

350

SMP (mg COD L-1)

Low shear MBR 400

800 600 400 200 0

10

20

30

40

50

60

10

20

30

40

50

60

20

30

40

d

1,000 800 600 400 200 0

0

10

20

30

40

50

60

0

Day of Reactor Operation

1.2

e

Worm Index

1.0 0.8 0.6 0.4 0.2 0.0 0

10

50

60

Day of Reactor Operation

Fig. 2 e Change in (a) SMP and (b) floc-associated EPS with time in the high shear MBR. The dashed line represents the steady-state model result that minimizes the error between prediction and data. Change in (c) SMP, (d) floc-associated EPS and (c) arbitrary worm index with time in the low shear MBR. Note that no worms were observed in the high shear MBR.

2.4.3. Degradation of floc-associated EPS under starvation conditions The concentration of floc-associated EPS in freshly wasted high shear MBR sludge was characterized with duplicate extractions on day 54 of reactor operation. One liter of this high shear biomass was then starved aerobically overnight. The change in floc-associated EPS concentration after starvation was characterized the following day with duplicate extractions. The change in the volatile solids concentration was also characterized.

3.

Results and discussion

3.1. The influence of predation on SMP and flocassociated EPS production Changes in SMP and floc-associated EPS over time during MBR operation in the low shear MBR are shown in Fig. 2(c) and (d),

respectively. As discussed in Menniti and Morgenroth (2010), these earthworms were identified as A. hemprichi based on their red color and the presence of red oil globules within their structure. A. hemprichi was first observed on day 30 of low shear reactor operation and started to strongly proliferate on day 37. Predation by A. hemprichi resulted in an increase in the production of both floc-associated EPS (Fig. 2(d)). A. hemprichi was never observed in the high shear reactor throughout the experiment. OUR was measured in batch experiments where acetate was added to biomass from the high and the low shear MBRs (Fig. 3). The biomass was sampled on day 52 of reactor operation, during a time when A. hemprichi were abundant in the low shear MBR. The OUR profiles of acetate consumption are very different between the two reactors. The respiration rate of the high shear biomass increased to a high plateau immediately after acetate addition and remained relatively constant until all the acetate is degraded. The low shear biomass, on the other hand, increases to a much lower level upon acetate addition. The respiration rate then increases gradually until all the

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80 Low shear MBR High shear MBR

OUR (mg L-1hr-1)

70 60

100 mg L COD

50

-1

-1

67 mg L COD

40 30 20 10 0 0

20

40

60

80

100

Time (hr) Fig. 3 e Batch respirometry results for acetate degradation in the high and low shear MBR biomass. The initial COD concentrations in the respirometer bottle after substrate addition are also provided. The respirometry experiments were performed in duplicate for each MBR and both measured OUR curves are presented here.

acetate is degraded. These characteristic OUR profile shapes are reproduced after a second acetate addition. The plateau shape of the OUR profile in the high shear reactor suggests that the acetate degrading population of organisms was already present and ready to degrade added substrate immediately upon addition. The gradual increase in the OUR of low shear biomass during acetate degradation can be explained with the growth of acetate degraders during the experiment. It is unlikely that this increase in rates is due to the biomass needing to produce the enzymes necessary for acetate degradation as acetate was the sole carbon source fed to the reactor. Thus, the shape of the low shear OUR curve suggests a larger decay rate in the low shear acetate degrading biomass, which was likely caused by severe predation by A. hemprichi. The increased decay of acetate degraders due to predation is consistent with the assertion of van Loosdrecht and Henze (1999) that predation is an important contributor to overall biomass decay in activated sludge systems. The increased predation and therefore increased decay had a profound effect on the production of both floc-associated EPS and SMP, as shown in Fig. 2(d) and (c), respectively.

3.2.

Evaluation of mathematical models

The three mathematical models in Table 1 were evaluated based on their ability to capture the observed floc-associated EPS and SMP results presented in Fig. 2(d) and (c), respectively. The dynamic increase of floc-associated EPS and SMP concentrations instigated by A. hemprichi predation were reproduced in each model by fitting time dependent parameters for SMP and EPS related processes until the model output (XEPS, SMP) matched the experimental data. This variation of model parameters over time was necessary to capture the effect of changes in the extent of predation where predation is only indirectly included in the three models. The choice of appropriate parameters to adjust, discussed in greater detail below,

was made based on the conceptual SMP production mechanisms underlying the mathematical structure of each model. For Model A, the parameter k2 was increased such that the observed SMP dynamics were captured in the mathematical model prediction by an increase in BAP concentration. This choice is consistent with the observation that predation and therefore biomass decay caused the increased in SMP production. For Model B, the parameter kEPS was chosen for dynamic adjustment. The structure of Model B forces the increase in SMP production to be a function of the dynamic increase in floc-associated EPS concentration. The parameter kEPS was adjusted such that the predicted floc-associated EPS concentrations match the experimental observations. The time dependent variation of the parameter values is shown in Fig. 4 together with the corresponding model output for XEPS and each SMP fraction. The increase in predation by A. hemprichi and therefore the increase in biomass decay can be translated to an increase in BAP production in Model A (Table 1). Increasing the decay rate is consistent with the batch respirometry experiments on acetate degradation, which suggests increased decay of acetate degraders due to predation. Predicting the observed experimental SMP results using Model A (Table 1) was achieved by increasing the decay rate (k2) during the predation event as shown in Fig. 4(a) and (c). The SMP prediction matches very well with the experimental data. The de Silva and Rittmann (2000) model structure, however, does not contain a term describing floc-associated EPS production and, therefore, cannot describe these experimental data (Fig. 4(b)). The inability to predict floc-associated EPS production is a shortcoming of Model A in MBR applications because flocassociated EPS may play a major role in controlling the concentration of SMP and because the concentration of flocassociated EPS influences the fouling properties of MBR biomass (Menniti et al., 2009). There is no direct active cell decay-related SMP production term in Model B (Table 1). Increased SBAP,EPS production could be achieved by two possible mechanisms: (1) by an increase in the rate of microbial hydrolysis or erosion of floc-associated EPS (khyd) (Process B3 in Table 1) and/or (2) by an increase in the production rate of floc-associated EPS (kEPS) (Process B1 in Table 1). Increased microbial hydrolysis or erosion of flocassociated EPS decreases the concentration of floc-associated EPS, which is not consistent with the experimental observations (Fig. 2(c)). Thus, within the context of the mathematical structure of Model B, increased SBAP,EPS production is best represented with an increased rate of production of flocassociated EPS. The predicted floc-associated EPS concentrations shown in Fig. 4(d) match the observed experimental trend very well. The first order nature of the SBAP,EPS production within Model B forces the SMP concentration to follow changes in the flocassociated EPS concentration. However, the SMP prediction based on this model structure (Fig. 4(e)) does not approximate the experimental observations. Model C is a direct combination of the Model A and Model B (Table 1). The time dependent parameters from Models A and B were used without further adjustment in the combined Model C (Fig. 4(i)). The SMP and floc-associated EPS concentrations predicted by Model C are provided in Fig. 4(g) and (h),

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Fig. 4 e Experimental results (symbols) and model predictions (lines) for SMP and floc-associated EPS in the low shear MBR (a, b, d, e, g, h, j, k). Modification in parameter values used to approximate the observed experimental results within each model (c, f, i, l). Model predictions of SMP for Model C are provided either assuming parameters from Models A and B (Table 2) (g) or assuming that SBAP,EPS is readily degradable (j).

respectively. Although the concentration of SMP is over-predicted due to the additive nature of the two SMP fractions in Model C, this model is able to capture the observed experimental trends for both SMP and floc-associated EPS, which neither previous model is able to accomplish. Combining a decay-related SMP (SBAP,XA) production term with a term to predict SMP production by erosion or hydrolysis of floc-associated EPS (SBAP,EP) is necessary to explain the experimental results in the current study.

3.3. Batch experiments on the production and degradation of SMP 3.3.1.

SMP production

Even with a dramatic increase in floc-associated EPS, the increase in SMP production could not be explained without the inclusion of a decay-related term. This result suggests that, when predicting the overall SMP concentration, the hydrolysis or erosion mechanisms of SMP production may not

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be important relative to the decay-related mechanisms in MBR systems. However, the importance of shear-induced erosion as a mechanism of SMP production has previously been demonstrated (Menniti et al., 2009; Rosenberger and Kraume, 2002; Wisniewski and Grasmick, 1998) and the level of shear is likely to drive the relative contribution of each SMP fraction. Batch experiments provide the opportunity to quantify the relative importance of shear-induced erosion due to short-term changes in shear (SBAP,EPS) compared to shortterm starvation conditions (SBAP,Xa) with respect to SMP production. The results of these short-term batch experiments are shown in Fig. 5. The soluble COD of the aerated mixed liquor increased over the soluble COD at the beginning of the batch experiment. Increased shear further increased the soluble COD. Aerating the biomass without an external carbon source results in starvation where the observed increase in soluble COD can be attributed to biomass decay (van Loosdrecht and Henze, 1999) while the additional COD released with high shear conditions is interpreted as floc-associated EPS released into solution due to erosion. Starvation increased the SMP (SBAP,Xa) concentration by 8.5 and 10.4 mg COD L1 for low and high shear MBR biomass, respectively. Increased shear resulted in an additional increase in SMP (SBAP,EPS) of 5.6 or 16.2 mg COD L1 for low and high shear MBR biomass, respectively. The increase of soluble COD due to starvation is included in Model A as decay of active cells resulting in SMP production but this mechanism is not directly included in Model B. Shearinduced erosion is included in Model B but not in Model A. Only Model C, which is combination of Model A and Model B, can reproduce the observed increase of SMP due to starvation and due to shear. Similar amounts of SBAP,Xa and SBAP,EPS were produced in the batch experiments indicating both mechanisms have equal importance under the conditions studied here. Thus, both mechanisms should be included in the mathematical model used to predict SMP concentrations, especially in systems having dynamics conditions of substrate availability or levels of shear.

b

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Fig. 5 e Soluble COD production due to decay and erosion during short-term experiments with high shear and low shear MBR biomass. The error bars represent that standard deviation of three COD measurements for each data point.

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Time (hr) Fig. 6 e Batch respirometry results for (a) concentrated SMP and (b) extracted floc-associated EPS with biomass from both the low shear and high shear MBRs. The initial concentrations of SMP or EPS in the respirometer bottle are provided.

3.3.2.

SMP degradation

Net SMP production is the result of SMP production and degradation. However, the results of reactor operation do not allow the separation of these two processes. Therefore, batch experiments specifically evaluating the degradability of individual SMP fractions were performed. The degradability of concentrated SMP sampled from the mixed liquor of the MBR and of extracted floc-associated EPS was evaluated using batch respirometry (Fig. 6(a) and (b)). Addition of SMP resulted in a very minor increase of OUR over the endogenous level (Fig. 6(a)). This small increase indicates that only a very small fraction of the SMP added was readily degradable and that the majority of the concentrated SMP was very slowly degradable. Noguera et al. (1994), Aquino and Stuckey (2004), and Jarusutthirak and Amy (2007) all confirmed the presence of a slowly degradable, high molecular weight SMP fraction. During MBR operation, high molecular weight soluble compounds are retained by the membrane. The concentration of these retained compounds is dependent on their degradability because readily degradable SMP compounds produced during reactor operation would be quickly consumed within the MBR while the slowly degradable compounds would build up to a higher level because they take longer to be degraded. This is demonstrated by the model results for SMP shown in Fig. 4(h),

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where the concentration of readily degradable UAP compounds is very low compared to the concentrations of slowly degradable BAP and soluble EPS. Thus, slowly degradable compounds constitute the majority of the soluble COD present in the reactor during operation and therefore in the SMP that was sampled, concentrated, and added as substrate to the batch experiment. The assumptions of Model C would suggest that these slowly degradable compounds represent both SBAP,EPS and SBAP,Xa. Therefore, a second batch experiment was performed in an effort to independently evaluate the degradability of SBAP,EPS. Models B and C define a fraction of SMP as floc-associated EPS that enters solution through microbial hydrolysis or erosion. While there is uncertainty associated with the similarity of SMP produced by microbial hydrolysis and shearinduced erosion, it was assumed that SMP produced by both mechanisms have the same chemical nature with respect to degradability because both mechanisms serve to generate smaller, soluble or colloid pieces of a larger solid material. It was further assumed that this SMP retains the same properties of the solid floc-associated EPS. Thus, extracted floc-associated EPS can be used to independently evaluate the degradability of soluble EPS. The results are shown in Fig. 6(b). In contrast to the results for concentrated reactor SMP, the floc-associated EPS generated a strong OUR response indicating that floc-associated EPS is readily degradable. The readily degradable nature of the floc-associated EPS studied here does not agree with the assumptions of Model B and Model C, where soluble EPS that is produced by the erosion or hydrolysis of floc-associated EPS is defined as slowly degradable. However, these results are consistent with those of Zhang and Bishop (2003) for biofilm EPS and Wang et al. (2007) for EPS extracted from granular sludge. There exists, however, the possibility that the extraction process changed the floc-associated EPS properties, making it more degradable. So, an additional experiment was performed to assess the degradability of floc-associated EPS without extracting it from the floc structure. The concentration of flocassociated EPS decreased from 284.7  1.7 mg COD g VSS1 (average  standard deviation) to 228.2  5.2 mg COD g VSS1 when the MBR biomass was aerobically starved overnight. This decrease is consistent with the results of Park et al. (2006), who showed that waste activated sludge degrades its own EPS during aerobic digestion and with Nielsen et al. (1997) and Horn et al. (2001), who asserted that organisms consume their own EPS as a food source during times of starvation. The result also confirms that the respirometer results are not an artifact of the extraction procedure and that floc-associated EPS eroded or hydrolyzed into solution to become SMP may be more readily degradable than previously assumed.

3.4. Re-evaluation of model predictions based on batch experiment results Based on the results of the batch experiments on SMP degradation, the parameters of Model C were adjusted such that the SBAP,EPS fraction was modeled as readily degradable rather than slowly degradable. This assumption was achieved by adjusting the kinetic parameters (KSEPS, qSEPS) for SBAP,EPS presented in Table 2 (which made them slowly degradable) to be equal to the parameters that describe UAP degradation (KUAP, qUAP) (which

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are readily degradable). No overall parameter estimation for all SMP related parameters was attempted as parameters are not uniquely identifiable based on the available data. Only the experimental observation that SBAP,EPS is readily degradable rather than slowly degradable was implemented. The concentrations of all the SMP fractions were predicted using Model C with SBAP,EPS assumed to be readily degradable and the results are shown in Fig. 4(j). All other parameters were kept the same as in Fig. 4(g)e(i). Assuming SBAP,EPS is readily degradable reduces its contribution to the overall SMP concentration dramatically. In Fig. 4(g), SBAP,EPS represents almost half of the total SMP concentration. In Fig. 4(j), the relative contribution of SBAP,EPS to the overall SMP concentration is small compared to SBAP,Xa, even during the time of increased floc-associated EPS production. The modeling results presented in Fig. 4(g) demonstrate the significance of having a complete understanding of the degradability of all SMP fractions in MBR systems. While all high molecular weight SMP fractions (meaning those larger than the membrane pore size) are retained by the membrane in MBRs, slowly degradable SMP builds up to a higher level than readily degradable compounds. Thus, processes producing slowly degradable SMP have the greatest impact on SMP concentration. The batch experiment results presented here suggest that SBAP,EPS is readily degradable while SBAP,Xa is slowly degradable.

3.5.

Practical implications

The ability to predict SMP, a key foulant in MBR systems, provides an opportunity to use foulant production as a process design and optimization parameter. However, there exists a tradeoff between model complexity and parameter identifiability. Often, more complex mathematical models more closely represent the processes the model is meant to capture but if the parameters in the model are not identifiable, the complex model losses its practical usefulness to predict accurately across a wide range of process conditions. On the other hand, over-simplification can also lead to the poor prediction of relevant parameters. All of the mathematical models presented here can successfully capture steady-state data when gross parameters like soluble COD are used to quantify SMP. Dynamic data coupled with an understanding of the triggers causing the changes provide opportunities to evaluate the relevance of mathematical models to successfully predict these dynamic changes. In the case of the current paper, the best model structure is the most complex but this was required to accurately capture SMP and EPS concentrations resulting from a dynamic increase in biomass decay. The structure of the de Silva and Rittmann (2000) or Laspidou and Rittmann (2002b) models (Models A and B, respectively) were not flexible enough to capture the data set analyzed here. While the mathematical models developed by de Silva and Rittmann (2000) and Laspidou and Rittmann (2002b) do not specifically exclude SMP production mechanisms, their model structures inherently emphasize one mechanism over another. The combined version of these models (Model C, Aquino and Stuckey, 2008) was required to predict the dynamic changes in floc-associated and SMP production.

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While complex, this model may also be necessary to capture the relevant SMP production mechanisms across a wide range of process conditions. For instance, the solid retention time (SRT), a key parameter in all activated sludge processes, is known to influence the concentration and properties of SMP and floc-associated EPS. The total concentration of soluble and floc-associated EPS tends to decrease with increasing SRT (Ahmed et al., 2007; Al-Halbouni et al., 2008) and low food to microorganism ratios at long SRT also promote biomass decay. These differences suggest that production of SMP by the erosion or hydrolysis of floc-associated EPS may be more important at lower SRT while production by decay of active cells could dominate at longer SRTs. Further research on the relative importance of the mechanisms of SMP production under various process conditions could provide a more detailed overview of the physiology of SMP production in MBR systems, and provide insight into how to appropriately capture the production of SMP with a mathematical model. Furthermore, while the dynamic reactor data and batch experiments presented here provide strong evidence of the importance of the SMP production mechanisms evaluated, additional research to determine model parameters describing the production and degradation of each SMP fraction is required. The universal application of parameters determined for chemostat (Laspidou and Rittmann, 2002b) or anaerobic (Aquino and Stuckey, 2008) conditions are unlikely to represent the production and degradation rates in other systems such as MBRs.

4.

Conclusions

Three mathematical models describing SMP production and degradation were compared based on their ability to predict SMP concentrations observed in an MBR system during a period of increased SMP and floc-associated EPS production due to increased predation. The SMP production mechanisms evaluated here were that SMP is produced either by (1) the erosion of floc-associated EPS, (2) decay of active cells, or (3) a combination of erosion of floc-associated EPS and decay of active cells. Mathematical model structures that emphasize SMP production either by erosion of floc-associated EPS or decay of active cells individually were not able to reproduce system performance under dynamic operating conditions. To accurately describe experimental results, a mathematical model structure that predicts SMP production by both erosion of floc-associated EPS and decay of active cells was required. SMP produced by the erosion of floc-associated EPS was shown to be readily degradable while SMP produced by predation or biomass decay was shown to be slowly degradable. Incorporating these degradability results into the mathematical modeling of SMP production and degradation in MBR systems showed that SMP produced by biomass decay is the SMP fraction with the highest concentration in MBR systems because it is slowly degradable.

Acknowledgements The authors gratefully acknowledge Dr. Mike Dempsey and Dr. Hilde Lemmer for their help in identifying the aquatic earthworms in the low shear MBR. We also acknowledge very

helpful comments provided by three anonymous reviewers. This manuscript is based upon work supported by the Center of Advanced Materials for the Purification of Water with Systems, a National Science Foundation Science and Technology Center, under Award No. CTS-0120978.

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