Ind. Eng. Chem. Res. 2011, 50, 1127–1137
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Simulation of a Membrane Bioreactor System for Wastewater Organic Removal: Biological Treatment and Cake Layer-Membrane Filtration Yu Tian,*,†,‡ Lin Chen,‡ and Tian-Ling Jiang‡ State Key Laboratory of Urban Water Resource and EnVironment and School of Municipal and EnVironmental Engineering, Harbin Institute of Technology, Harbin 150090, China
This study was focused on providing an integrated model that could be used as an effective prediction tool for nutrient removal performance of membrane bioreactor (MBR) with emphasis on the interception of organic matter during cake layer-membrane filtration. The developed model was divided into two submodels for biological process and cake layer-membrane filtration process, respectively. With respect to the biological process, it was based on the platform of activated sludge model 3 (ASM3) with two main improvements: (i) adopting the concept of simultaneous growth and storage of organic substrates; (ii) introducing the formation and degradation of soluble microbial products. The removal of organic substances during cake layer-membrane filtration was simulated on the basis of mass balance, force balance, and first-order transport principle. The integrated model could offer a technique for the characterization of MBR operation and provide a valuable tool for operation improvement. 1. Introduction Submerged membrane bioreactor (MBR) is considered a promising biological treatment technology that uses a to replace the conventional sedimentation basin for the solid-liquid separation of mixed liquor.1 Compared to the conventional activated sludge (CAS) system, MBR offers numerous advantages, such as high-quality treatment of water, a compact footprint, a more concentrated mixed-liquor suspended solid (MLSS), and a reduced sludge yield.2 However, the use of a membrane and a higher MLSS concentration creates differences compared to traditional CAS;3 for instance, the complete sludge retention in MBR may change the selection pressure on the biomass population from sludge settling properties to growth kinetics. Additionally, membrane fouling is still a major problem that hinders MBR’s more widespread and large-scale application, which is strongly affected by the characteristics of the mixed liquor. Comprehension of the inherent mechanisms and subsequent integrated modeling of the process seems greatly helpful for optimization of the MBR behavior. Previously, modified activated sludge models (ASMs) have been applied for the biological modeling of MBR as reported in various studies, where the concept of soluble microbial products (SMP) was introduced into the models development.4-7 Generally, SMP are typically classified into two groups on the basis of the bacterial phase: utilized-associated products (UAP), associated with substrate uptake and biomass growth, and biomass-associated products (BAP), associated with biomass decay.6 The use of an ASM expansion with the SMP concept was encouraged if the following modeling objectives were pursued: linking biology with fouling, soluble chemical oxygen demanded (SCOD) predictions, and modeling high sludge retention time (SRT) processes.7 It should be noted here that the MBR biological conditions generally possessed high biomass concentration, high SRT, and low food to microorganism ratio (F/M) and, thereby, more chances for microorganisms to face the feast and famine periods.8 The concepts of conventional * To whom correspondence should be addressed. E-mail:
[email protected]. † State Key Laboratory of Urban Water Resource and Environment. ‡ School of Municipal and Environmental Engineering.
ASMs have been prone to skepticism for the MBR simulation as the ability of microorganisms to accumulate internal storage polymers was not documented in ASM1 and the growth on direct substrate uptake was not considered in ASM3. Thus, the modifications of ASM3, e.g., incorporation of the SMP concept and, recently, simultaneous growth and storage phenomena, mechanistically described by Sin et al.,9 provided other alternative model options for the biological process in the MBR system. Such a modified ASM3-SMP model was not available for the MBR system. During the membrane filtration process, the successive blocking of membrane pores gradually increased local flux, and the subsequent fouling occurred due to the formation of a cake layer over initially blocked regions. However, it should be noted that both the primary membrane and the cake layer helped to reduce the effluent concentration; particularly, the interception ability of the cake layer also helped to alleviate the evolution of pore fouling. The cake layer deposit on the membrane surface acted as a secondary or dynamic membrane which screened the primary membrane from the more strongly fouling species of the smaller of the large and small particles.10 It was also reported that the removal of organic substance in an MBR during the pass through the membrane could not be explained by the effect of a clean membrane with no cake.11 In previous simulation studies, a fixed coefficient was directly adopted to account for the interception efficiency of the cake layer and membrane on the COD removal, leading to a constant proportion between supernatant COD and effluent COD. The thickness of the cake layer had a direct influence on the removal of COD; comparatively, few models took into account the effect of the fouling phenomenon to evaluate the MBR effluent concentration. In this paper, an aerobic MBR process treating synthetic wastewater has been investigated; especially, the role of cake layer-membrane filtration in the physical removal of the pollutants has been surveyed. With the aim toward further advancement of MBR technology, an integrated model was developed and included two parts: simulation of the biological process and simulation of the cake layer-membrane filtration. The models for the biological process, which were developed on the template of improved ASM3 by using the concept of simultaneous storage and utilization and including the production
10.1021/ie101827y 2011 American Chemical Society Published on Web 12/02/2010
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and degradation of SMP, provided an effective interpretation for the biological nutrient removal and MLSS production in the MBR. With the incorporation of force balance, mass balance, and first-order transport principals, mechanistic models were established to simulate and describe the formation of cake layer and the function of cake layer-membrane during filtration of a multicomponent mixture. Finally, with use of the integrated model, the MBR process in terms of supernatant concentration and MLSS production could be characterized, and the cake layer-membrane filtration mechanism could be understood better.
Two different submodels were developed for simulation of the biological process and the cake layer-membrane filtration process, respectively, in order to evaluate the performance of the biological process and to assess the cake layer-membrane filtration on the COD removal. 2.1. Simulation of the Biological Process. The biological processes have been built on the basis of ASM3 with two main modifications: (i) adopting the concept of simultaneous growth and storage of organic substrates by heterotrophic bacteria; (ii) incorporating the formation and degradation of soluble microbial products into the biological processes. The related process stoichiometry and composition describing the interactions and transformations among model components are outlined in a matrix format, as shown in Table 2 of the Appendix. The concept of simultaneous microbial storage and growth12 could be explained in such a way that the heterotrophs were capable of simultaneously storing the external substrate within the cell in a polymeric form and growing on the external substrate. These stored materials were then consumed for growth when the external substrate became depleted. Noticeably, the degradation of stored materials by microorganisms was the rate-limiting step for the famine conditions;8 thus, the kinetic expression describing the degradation of storage products was developed on the basis of a Monod type model. Additionally, an inverse switch function was incorporated in order to activate XSTO consumption when SS was exhausted. The kinetic rates for storage on SS, growth on SS, and XSTO under aerobic conditions are formulated by the following expressions: SS SO X SS + KS SO + KOH H
)
The production of BAP can be described as being proportional to the biomass decay with a stoichiometric parameter (fBAP) as depicted in
SS SNH SO SHCO X SS + KS SNH + KNH SO + KOH SHCO + KHCO H
(5)
On the basis of previous experimental studies, both UAP and BAP exhibited biodegradability and had a large fraction of molecular weight greater than 20 kDa, suggesting that SMP would be unlikely to pass the cell membrane and utilized by cell directly. Thus, two distinctive, independent hydrolysis coefficients were used for UAP (kh,UAP) and BAP hydrolysis (kh,BAP), respectively. Switch functions were included in order to avoid the occurrence of negative values for the concentrations of the compounds in the liquid phase. A Monod type reaction was developed to describe the hydrolysis of SMP under aerobic conditions as shown in rSMPhydrolysis ) kh,UAP
SUAP SO X + SUAP + KUAP SO + KOH H SBAP SO X kh,BAP SBAP + KBAP SO + KOH H
(6)
2.2. Simulation of Cake Layer-Membrane Filtration. In cross-flow membrane filtration, the sludge particles either attached onto the membrane or stayed in the bulk phase, heavily dependent on the force that acted upon the sludge particle. To simulate the cake formation, the forces, including tangential force (Ft), friction force (Ff), drag force (Fd), van der Wals forces (Fv), electrostatic double layer repulsion force (Fr), shearinduced diffusion force (Fs), and lateral inertial lift fore (FI), were employed (Figure 1). The condition for particles to stick to the membrane surface is Ft - F f e 0
(7)
(1)
In the following, eq 7 was solved in order to determine the maximum particle diameter dcritical of particles adhering to the cake layer or the membrane surface. And the forces, including Ft, Ff, Fd, Fv, Fr, Fs, and FI, are computed from13-15
(2)
Ft ) 10.2πµsGdp2
(8)
Ff ) µmax(Fd + Fv - FI - Fr - Fs)
(9)
Fd ) 3πσµsdpJ
(10)
γgrowth on SS ) µH,S
(
rBAPproduction ) fBAP(bSTOXSTO + bAXA + bHXH)
2. Model Development
γstorage on SS ) kSTO
SNH SO SHCO SNH + KNH,H SO + KOH SHCO + KHCO XSTO /XH KS SS µH,STO + µH,S X + XSTO /XH + KSTO KS + SS KS + SS H SNH SO SHCO X (4) γUAP,AµA SNH + KNH,A SO + KOA SHCO + KA,HCO A
rUAPproduction ) γUAP,H
γgrowth on XSTO ) SNH SO KS XSTO /XH SHCO µH,STO X SNH + KNH SO + KOH KS + SS XSTO /XH + KSTO SHCO + KHCO H
(3) Fv ) Additionally, the SMP (including UAP and BAP) were produced by the active biomass during the cell proliferation phase and the decay phase as mentioned above. Two distinctive, independent yield coefficients were used for UAP production during heterotrophy growth (γUAP,H) and autotrophy growth (γUAP,A), respectively. The rate for UAP production under aerobic conditions is expressed by the following expression.
Hdp 12S2
(11)
Fr ) pdp
(12)
Fs ) 0.09πµsdp2G
(13)
FI ) CdµsG
πdp2 8
(14)
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In particular, the cake layer formation during membrane filtration basically became a sort of secondary filter to capture some of the small matter and to prevent them from fouling the primary membrane.5 The removal of clogging materials by the effect of the cake layer was assumed as a first-order transport process with respect to the removed concentration in the cake media: dC' dC' ) -J - kC' dt dLc
(21)
where C′ is the concentration of COD and k is the first-order removal coefficient. It was suggested that the filtration through the cake was a fast reaction. And a steady state could be obtained: Figure 1. Schematic illustration of the forces exerted on the particle and the cake formation on the membrane surface.
where µs is the apparent viscosity of mixed liquor, G is shear intensity, dp is particle diameter, µ is the friction coefficient, σ is Happel’s correction factor, J is membrane flux, H is the Hamaker constant, S is the separation distance, p is a systemdependent constant of electrostatic repulsion forces, and Cd is the coefficient of the lifting force of sludge particles. According to theoretical approach and assuming that apparent viscosity can be described by the Ostwald model,13 the shear intensity linked to air-sparging is expressed as G)
( ) FS gqa m
1/(n+1)
(15)
where Fs is the sludge density, qa ) Qa/A is the aeration intensity, Qa is the air flow rate, A is the cross-sectional air sparging area, and m and n are the biomass concentration function, according to m ) exp(1.7MLSS0.45)
(16)
n ) 1 - 0.068MLSS0.81
(17)
J
dC' ) kC' dLc
Cm ′ ) Cb′e-kLc/J
Ce ) imCm ′
where the constant of im is the interception coefficient of primary membrane and Ce is the concentration of COD in the effluent. 2.3. Model Calculation. A temperature correction was applied through Arrhenius type equation (eq 25) for the kinetic parameters corresponding to heterotrophic biomass (i.e., kSTO, µH,S, µH,STO, bH, and bSTO) as proposed by Henze.17 ◦
µ(3πσµs J + k ) 10.2πµsG + µ 0.09πµsG + CdµsG
π 8
) (18)
where k ) H/(12S ) - p is the coefficient of adhesion force (sum of Fv and Fr). Equation 18 calculated the maximum diameter dcritical of particles adhering to the cake layer or the membrane surface. A mass balance for the cake formation around the membrane surface yielded the following differential equations: FA
2
dLc ) JξMLSS Cc dt
∫ ∫
dcritical
ξ)
0
+∞
0
(24)
k(T) ) k(20◦C)e0.07(T-20 C)
FA
(
(23)
’ and Cb’ are the concentrations of COD in the where Cm membrane surface and bulk phase, respectively. Once the COD at the physical membrane surface was estimated, the model predicted the effluent COD considering the COD removal by physical membrane. This step was accomplished straightforwardly by adopting a modeling approach derived by Di Bella et al.5 and Jang et al.,16 as shown in the following:
Substituting eqs 8-14 into eq 7 yields dp e dcritical )
(22)
(25)
Modeling, simulation, and some parameter estimations were conducted using Matlab 7.6. The differential equations were solved using the fourth-order Runge-Kutta method. The parameter estimation and calibration were performed with the Levenberg-Marquart algorithm, where the sum of least-squares of deviations between the measured and the modeled data was used as an objective function.
∑ n
F(m) )
(xe,i - xs,i)2
(26)
i)1
(19)
g(x) dx
(20) g(x) dx
where Lc is the thickness of the cake layer, Cc is the particle concentration of the cake layer, ξ is the fraction of MLSS that attaches to the membrane, and g(x) is the distribution of bulk particle sizes.
where xe,i is the experimental results, xs,i is the simulated results, and n is the number of observations. Finally, two statistical indices were used to evaluate statistically accurate and valid predictions: root-mean-square error (RMSE) representing the scatter of errors between simulated series and measured data, and correlation coefficients (r) as a measure of the strength of linear dependence between simulated and measured data. These two indices are defined by eqs 27 and 28, respectively.
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RMSE )
r)
n
∑ (x
e,i
- xs,i)2
i)1
(27)
n-1
∑ (x - x )(x - x ) √ ∑ (x - x ) ∑ (x - x e,i
e,av
s,i
s,av
2
e,i
e,av
s,i
(28)
2 s,av)
where xe,av and xs,av are the experimental and simulated average values, respectively. 3. Material and Methods
Figure 2. Schematic diagram of MBR.
3.1. Experiment Setup. As shown in Figure 2, experiments were performed in a laboratory-scale submerged MBR with an effective volume of 150 L. Three hollow-fiber microfiltration membrane modules were mounted in the reactor, which were made of poly(vinylidene fluoride) (PVDF) with a surface area of 1 m2 and a normal pore size of 0.2 µm. Synthetic wastewater (glucose, 171 mg L-1; starch, 171 mg L-1; NaHCO3, 254 mg L-1; urea, 63 mg L-1; KH2PO4, 15.4 mg L-1; K2HPO4, 19.6 mg L-1; trace elements) was continuously introduced at an influent flow rate controlled by the liquid level in the reactor. The MBR was fixed at 30 days SRT, and the membrane flux was kept constant at 8 L m-2 h-1 with a suction cycle of 8 min followed by 2 min relaxation. The reactor was operated at room temperature 18-24 °C, and the pH was not controlled and ranged from 6.5 to 7.4. Gas was diffused into the reactor with an intensity of 0.8 m3 h-1 to maintain the desired dissolved oxygen (DO) concentration and to control membrane fouling. When the transmembrane pressure (TMP) exceeded 45 kPa, the membrane modules were cleaned by tap water to remove the cake layer followed by submerging in 0.5% sodium hypochlorite solution for 2-8 h. 3.2. Influent Characterization. Wastewater characteristics had a great impact on system performance, particularly for nutrient removal systems. Typically, influent wastewater was characterized (Table 1) using the protocol recommended by the Water Environment Research Foundation.18 A synthetic wastewater was used to maintain the stability of the influent characteristics in this study; therefore, no heterotrophs and autotrophs existed in the wastewater. The organic substrate in the influent was divided into four subcomponents, including unbiodegradable soluble COD (SI), readily biodegradable soluble COD (SS), unbiodegradable particulate COD (XI), and slowly biodegradable particulate COD (XS). The influent ammonium concentration (SNH) and nitrate/nitrite concentration (SNO) were measured directly. The main nitrogen source of the synthetic wastewater was urea. However, because soluble organic nitrogen is not defined in ASM3-SMP, the urea nitrogen was included in SNH. 3.3. Analytical Methods. Analysis of the influent flow, sludge, supernatant, and effluent was conducted twice per week. The MLSS, COD, SNH, SNO, and total nitrogen (TN) concentrations were measured according to standard methods.19 Particle size distribution (PSD) of the mixed liquor was detected by a laser granulometer (Mastersizer 2000, Malvern Instruments). The thickness of the cake layer was determined by laser displacement sensor (Banner L-GAGE LG10). Analysis of SMP in biomass suspensions collected from the MBR was carried out after suspensions had been filtered with a 0.45 µm filter.6 Proteins were measured using the Lowry method,20 and polysaccharides were measured using the phenol methods.21
Table 1. Summary of Influent Characterization Based on ASM3-SMP Modela COD fraction
nitrogen fraction
component
concentration
component
concentration
SS (mg of COD/L) SI (mg of COD/L) XS (mg of COD/L) XI (mg of COD/L)
321.7 (14.9) 13.1 (1.4) 24.4 (1.9) 66.1 (6.5)
SNH (mg of N/L) SNO (mg of N/L) iN,SI (g of N/(g of COD)) iN,XI (g of N/(g of COD)) iN,XS (g of N/(g of COD))
28.9 (1.8) 1.7 (0.8) 0.01 0.02 0.035
a
Standard deviations given in parentheses.
3.4. Parameter Determination. A respiromenter (3 L) controlled for temperature (20 °C), DO (3-6 mg L-1), and pH (7.1 ( 0.2) was used to determine the sludge oxygen uptake rate (OUR), which was equipped with a DO meter (E+H Liquisys M COM 253F). A magnetic stirring bar and a stirring plate provided internal mixing of the liquor and sludge. Prototype software was used for automated data acquisition and process control. Prior to the OUR test, the sludge taken from the MBR system was washed three times with dilution water (prepared by using distilled water and having the same inorganic contents as the influent: NaHCO3, 254 mg L-1; MgSO4, 23 mg L-1; CaCl2, 5.1 mg L-1). The endogenous-decay coefficient (bH) and maximum heterotrophic growth rate (µH,S) in independent OUR batch experiments were estimated as described by Henze.17 To estimate bH, the OUR profiles were measured over a period of 8 days without substrate addition, and then a plot of the logarithm of the respiration rate versus time gave a straight line with a slope of bH. The OUR data (F/M ) 5 mg of COD (mg of VSS)-1)) were primarily used to calculate µH,S after correction with the corresponding bH value. Respirometric tests on hetertrophic biomass,9 including the heterotrophic storage yield coefficient (YSTO), the yield coefficient for growth on SS (YH,S), the yield coefficient for growth on XSTO (YH,STO), the maximum storage rate of biomass (kSTO), and the maximum growth rate of biomass on XSTO (µH,STO), were carried out by dosing acetate as pulse readily biodegradable COD and keeping an initial F/M ranging between 0.15 and 0.25 mg of COD (mg of VSS)-1; allylthiourea (ATU) was added to inhibit the nitrification. The three distinct yield coefficients, including YSTO, YH,S, and YH,STO, were related to each through the efficiency of the oxidative phosphorylation representing the efficiency of conversion of NADH2 (dihydronicotinamide adenine dinucleotide) to ATP (adenosine-triphosphate) and would be estimated by fitting the model prediction with the OUR results as reported by Sin et al.9 The µH,STO was assumed to be on the same order of magnitude as the µH,S and estimated from the phase of storage material utilization. Additionally, the maximum specific growth rate of autotrophs (µA) was determined by a high F/M batch test (F/M ) 4 mg of N (mg of VSS)-1) as described by Melcer.18 The parameters
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associated with SMP formation and degradation were estimated form independent batch experiments,22 which were conducted under three initial known conditions: starvation, acetate spiking (MLSS ) 9240 mg L-1; COD ) 823 mg L-1; SNH ) 70 mg L-1; SPO43--P ) 15 mg L-1; MgSO4 ) 15 mg L-1; CaCl2 ) 10 mg L-1; ATU ) 15 mg L-1), and NH4Cl spiking (MLSS ) 9310 mg L-1; SNH ) 100 mg L-1; SPO43--P ) 20 mg L-1; MgSO4 ) 20 mg L-1; CaCl2 ) 10 mg L-1), respectively. A set of values for the model coefficients and parameters for the cake layer-membrane filtration are selected on the basis of previous reports, laboratory tests, and assumptions (Table 3 of the Appendix). The density (Fs) and viscosity (µs) of the sludge suspension were 1.0 × 103 kg m-3 and 2.69 × 10-3 Pa s, respectively. The lifting coefficient Cd ) (24/Re) + (3/Re) + 0.34 was believed to be smaller than 0.39, where the Reynolds number (Re) was considered to be greater than 5000 in the turbulence of an MBR. Drawing on previous investigation,23 the value of µ for the sludge particle used in this study was expected to be around 0.03, and the Happel’s coefficient σ with a value of 120 was applied into the determination of drag force. The adhesion coefficient kFA ) 3.5 × 10-6 N m-1 was estimated from atomic force microscopy analysis.24 The interception coefficient im ) 0.52 was used to fit the results of eq 24 through supernatant filtration experiments when no cake was assumed to have formed on the membrane surface. The COD concentra’ ) was calculated by dividing tion on the membrane surface (Cm the effluent COD concentration by (1 - im); thus, the first-order coefficient k ) 5 × 10-5 s-1 would be easily obtained to fit the ’ . results of eq 23 to the calculated Cm 4. Results and Discussion 4.1. ASM3-SMP Model for the Biological Process in MBR. 4.1.1. Kinetic Studies of ASM3-SMP Model. The stoichiometric and kinetic parameters estimated from OUR and batch experiments are summarized in Table 3 of the Appendix. Since the biomass was washed and the initial concentration of SMP was set to zero, the initial concentration for active biomass (XH(0)) could be estimated by using the baseline endogenous OUR level prior to substrate addition.9 The heterotrophic decay rate (bH) through long-term (8 days) monitoring of endogenous OUR was 0.25 day-1; simultaneously, the endogenous rate of XSTO(bSTO) was taken the same as the bH.25 The maximum growth rate for autotrophy (µA) was 0.85 day-1, maintaining the capacity of increasing nitrification rate due to the elevated ammonium concentration. Respirometric measurements with the biomass obtained after pulse addition of a certain amount of acetate to endogenously respiring activated sludge are shown in Figure 3. After the pulse addition of acetate, the OUR of biomass increased to a maximum level in a fast transient under the feast conditions. The biomass activity continued at this maximum level until all external substrate was taken up for storage and growth. In the famine phase, the OUR of the biomass dropped from the maximum level to a level higher than the endogenous OUR level, which resulted from the utilization of previous internal storage products. On the basis of the efficiency of oxidative phosphorylation with a value of 1.7508 molp molo-1, the respective kinetic coefficients for YH,S, YSTO, and YH,STO were 0.45, 0.71, and 0.59 g of COD (g of COD)-1, which were estimated by minimizing the sum of squares of the deviations between the measured OUR data and the model predictions. Concerning the calculated parameters, the yield coefficient YH,S for direct biomass growth can be compared with the biomass growth through storage, which resulted from the product of YSTO
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Figure 3. Experimental and modeled OUR profile for heterotrophic biomass. The total OUR is calculated as the sum of OUR growth on XSTO, OUR growth on SS, and OUR conversion of SS into XSTO.
and YH,STO: the ratio of (YSTOYH,STO)/YH,S actually indicated the reduction in biomass formation which can be achieved with storage and subsequent biomass growth. On average, the ratio has been quantified as 0.93, which meant that there was negligible reduction of the overall yield and the result was in good agreement with literature values provided by Sin et al.9 The heterotrophic maximum specific growth rate through utilization of storage polymers (µH,STO) is 0.6 day-1, which was the same as that through utilization of the external substrate (µH,S ) 0.6 day-1). Thus, growth through utilization of storage products was commensurate with growth on external substrate. The BAP, UAP, acetate, and NH4Cl profiles simulated with the established model are shown in Figure 4, where the simulation results are in good agreement with the measured data. The BAP built up slowly and continuously in the entire process (Figure 4a), whereas the UAP profiles induced by acetate and NH4Cl exhibited a peak followed by a declining curve (Figure 4b,c). On the basis of the definitions in the developed models, the production rates for BAP, UAP during autotrophy growth, and UAP during heterotrophy growth were 0.055, 0.45, and 0.12, respectively. The hydrolysis rate for UAP (0.03 day-1) was appropriately six times larger than that for BAP (0.005 day-1), suggesting that UAP were biodegradable and probably more readily biodegradable than BAP. The half-saturation coefficients for the UAP (1.3 g of COD L-1) and BAP (1 g of COD L-1) had the same order of magnitude as the KS, indicating biodegradation kinetics in the MBR system. 4.1.2. Sensitivity Analysis of ASM3-SMP. Prior to model calibration, a model parameter sensitivity analysis was carried out to determine the kinetic and stoichiometric parameters which had the largest effect on model outputs. Regarding the sensitivity coefficient, it was performed by perturbing each individual parameter one at a time according to the following: δi, j )
θj ∂yi yi ∂θj
(29)
where the vector y ) (y1, y2, ..., yn) represents the n modeling output variables and the vector θ ) (θ1, θ2, ..., θn) represents the m independent parameters of the model. The sensitivity analysis involved all the kinetic and stoichiometric parameters in the established ASM3-SMP model for the biological process. According to the adopted methods, Figure 5 shows the results of this analysis for the most significant parameters which at their maximum deviation of 60% changed the output by over 10%. The most significant parameters
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Figure 4. Simulated and measured (a) BAP concentration under starvation conditions; (b) net UAP concentration with acetate spiking; (c) net UAP concentration with ammonia nitrogen spiking.
Figure 5. Model sensitivity analysis, respectively, for (a) MLSS, (b) COD, (c) SMP, (d) SNH, and (e) SNO.
influencing the MLSS production were as follows: YSTO, YH,STO, YH,S, fXI, and bH. The parameters of YSTO, YH,S, YH,STO, bH, fBAP, γUAP,H, and kh,UAP demonstrated a strong influence on the output variable of COD. SMP kinetics were affected mostly by the following parameters: γUAP,H, YSTO, bH, fBAP, YH,S, YH,STO, γUAP,A, and kh,UAP. The parameters of µA, KNH,A, bA, and KOA had decisive influence on SNH and kSTO, YH,S, bH, KOH, YH,STO, µH,S, and YSTO on SNO. Clearly, it could be seen that both kinetic and stoichiometric parameters related to the biomass growth, includingYSTO, YH,S, YH,STO, and bH, had a considerable effect on the variability of
the model, especially on the simulation of the biomass content and substrate consumption. Additionally, the sensitive parameters for COD were almost the same as that for SMP except γUAP,A, which might be explained from the view of the supernatant SCOD component. On the basis of the concept of the ASM3-SMP model, the supernatant SCOD can be divided into three parts: SS, SI, and SMP. SS was not a determining factor to the supernatant COD, which accounted for a negligible part for its complete decomposition in the reactor. The SI in the supernatant had two main origins: wastewater influent and SMP hydrolysis. The SI concentration in the influent could be
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Figure 6. Measured and predicted results of the laboratory-scaled MBR in its 3 month operation: (a) MLSS concentration; (b) supernatant COD and SMP; (c) supernatant SNH; (d) supernatant SNO.
quantitatively determined; hence, the right prediction of SMP had a direct bearing on SI and further on the supernatant SCOD. A trial and error procedure adjusting manually ASM3-SMP sensitive parameters was conducted to seek the best fit between measured and simulated values, including MLSS, supernatant COD, SNH, and SNO. The parameter values in the model, which are used to generate the model outputs, are summarized in Table 3. The parameters of KOA and KNH,A were reduced 0.2 mg of O2 L-1 and 0.2 mg of N L-1, respectively, indicating an improved nitrification. Manser et al.26 also reported KO,AOB ) 0.18 ( 0.04 mg of O2 L-1, KO,NOB ) 0.13 ( 0.06 mg of O2 L-1, KNH4 ) 0.13 ( 0.05 mg of N L-1, and KNO2) 0.17 ( 0.02 mg of N L-1 in a pilot MBR. 4.1.3. Model Evaluation: Simulation of the Biological Process. As an application of ASM3-SMP, the developed model was validated using independent experimental results of the laboratory-scale MBR monitored under steady-state conditions. Figure 6 shows the model results in terms of MLSS, supernatant COD, SMP, SNH, and SNO. To assess the model performance quantitatively, two statistical indices, including RMSE and r, were used to evaluate statistically accurate and valid predictions for MLSS, COD, SNH, and SNO obtained from the independent experimental results. It came out that the model showed an acceptable agreement with MLSS, COD, SMP, and SNO, and the correlation coefficients between measured and simulated data were 0.83, 0.51, 0.58, and 0.74, respectively. With respect to SNH, the model showed a low correlation between the experimental and modeled data (r ) 0.15), while the correspondent RMSE was 0.12 mg L-1. This result might be related with low values for supernatant SNH in a range of 0.1-0.3 mg L-1, where a small deviation of simulation data from the measured data would heavily influence the calculation results of statistical indices.
The MLSS was the central parameter that embodied and reflected the fate of all particulate model components in the reactor, including active biomass and residual particulate organics and influent solids. Figure 6a gives the observed and simulated MLSS profiles throughout the study. The steady state of the MLSS concentration was around 8560-9679 mg L-1, which followed the variation trend of the influent COD. Considering the MLSS component, the proportion of XI, XH, XSTO, XA, and XS accounted for 72.7, 18.2, 5.5, 2.1, and 1.3%, respectively. Since the MBR process under 30 days SRT was decay dominant, the XI was the main component mainly resulting from biomass degradation and influent unbiodegradable particulate. The internal storage material and autotrophs had no significant effect on the total biomass content. Collected experimental data on influent total COD and supernatant soluble COD together with corresponding model simulation are shown in Figure 6b. The average of the COD removal efficiency was 88%, increasing to 92% independent of the COD loading in the influent and the DO concentration in the reactor. The values of supernatant soluble COD were in the range of 40-60 mg L-1, significantly higher than the soluble inert COD level of the influent (8-15 mg L-1). The adopted model characterized the measured supernatant COD efficiently by means of SMP generation, also indicating that the SMP was hydrolyzed into SS and SI, where the SS was utilized by the heterotrophy within the MBR system. Model simulation of the nitrification performance (SNH and SNO in the supernatant) of the MBR is presented in Figure 6c,d, together with the corresponding influent TN. The nitrifying biomass (XA) fraction was in the range of 2-3% (XA ) 183-220 mg of COD L-1), which could be explained by the relative abundance of total nitrifying community decreasing with elevated SRT.27 However, the collected data provided a clear
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Figure 7. (a) Particle size distribution and resulting cutoff diameters; (b) cake layer thickness increase during membrane operation.
indication that the MBR system showed good and stable nitrification efficiency and, conversely, a weak denitrification one; in fact, the system was capable only for organic removal since no anoxic reactor was installed. The average ammonia oxidation observed throughout the operation time was more than 90%, even if the DO concentration in the reactor was as low as 0.7 mg L-1. This result might be partially contributed to the adjustment of KOA and KNH,A, which indicated improved oxygen and nitrogen transformation into bioflocs. In the CAS system, 58% particles were in the size range of 50-200 µm, and 23% particles had a diameter larger than 200 µm.28 On the contrary, in the MBR system, the floc size lower than 100 µm accounted for 88.5% (Figure 7a) due to the violent current turbulence, which justified the low diffusion limitations for the biomass. 4.2. Cake Layer-Membrane Filtration for Organic Removal. 4.2.1. Experimental Observation. In the steadystate period (90-120 days), a survey of the laboratory-scale MBR operation was conducted. With regard to the system performance, the COD removal efficiency was excellent with an average of 93% removal and a stable nitrification was obtained with the effluent SNH lower than 0.5 mg L-1. The COD concentration in the effluent was relative;y stable in the range of 12.3-28.7 mg L-1 and had a much lower value than that in the bulk phase (in the range of 44.7-55.6 mg L-1), suggesting that all of the organic matter was intercepted by the membrane and only a fraction of SCOD was filtered through the membrane. Conversely, with nitrogen removal, comparing the concentration of different N species between the supernatant and effluent, it came up that there was no significant difference between the supernatant and effluent in terms of SNH and SNO. Thus, in this study, only COD reduction was taken into account from two points of views: cake layer interception and membrane filtration. 4.2.2. Model Evaluation: Simulation of the Cake Layer-Membrane Filtration Process. The PSD of the mixed liquors in the MBR was monitored as shown in Figure 7a, and 34.7 µm was the critical diameter for sludge particles that would be attached onto the membrane surface according to eq 18. Figure 7b presents the cake layer formation during the membrane filtration, where the formation rate of the cake layer was 6.17 × 10-4 m day-1 and the cleaning cycle of the membrane modules was 32 days. Considering the respective effect of cake layer and membrane interception, Figure 8 shows the removal of COD during cake layer-membrane filtration (121-210 days), including the concentration of organic matter in the bulk phase ′ ), and in the effluent (Ce). (Cb′), on the membrane surface (Cm The effect of membrane interception on the removal of organic matter played an important role in the initial filtration stage where a thin cake layer was formed on the membrane surface.
Figure 8. Effect of cake layer-membrane filtration on the COD effluent concentration in its 3 month operation.
The difference between Cb and Cm ′ became wider with the increase of the cake layer thickness. For instance, the difference increased from 0 to 17.3 mg L-1 at the end of the first filtration cycle. Conversely, the difference of the organic substance ′ and Ce decreased, such as from 24.9 to 14.5 between the Cm mg L-1 at the end of the first filtration cycle. Such difference was basically due to the formation of the cake layer that acted as an extra barrier reducing the COD concentration over time. Several groups have observed a significant difference between the concentration of COD in the MLSS and the effluent. Trussell et al.29 observed a difference of 30-50 mg/L in the COD concentration of an MBR permeate and the COD of the MLSS after filtering over a 0.45 µm membrane. The simulation results also basically led to take into account the rate of membrane pore blocking, which could be used as the basis for pore fouling observation. At the initial stage of membrane operation, the pore fouling of the cleaned membrane was relatively fast due to adsorption and convection of foulants. With the operation time increase, the lower cross-flow velocity enabled the formation of the sludge cake layer which protected the primary membrane from the fouling agents, such as proteins and polysaccharides, leading to a decrease of pore fouling rate. Conclusively, the removal of organic substance in the MBR system was due to in-series phenomena: biological degradation with biomass, interception in the cake layer, and filtration of the primary membrane. 4.2.3. Model Limitations. The formation of the cake layer was of benefit for organic substance removal and pore blocking alleviation. By varying the aeration intensity and the filtrate flux, it is possible to improve the filtration performance and generate
fBAP
fSI fSI
MX(t) ) (XS/XH)/(KX + XS/XH); MO,H(t) ) SO/(SO + KOH); MAO,H(t) ) [KOH/(SO + KOH)][SNO/(SNO + KNO)]; MBAP(t) ) SBAP/(KBAP + SBAP); MUAP(t) ) SUAP/(KUAP + SUAP); MS(t) ) SS/(KS + SS); MS,O(t) ) SS/ (KOH + SS); MNH,H(t) ) SNH)/(SNH + KNH,H); MHCO,H(t) ) SHCO/(SHCO + KHCO); MSTO,H(t) ) (XSTO/XH)/(XSTO/XH + KSTO); MKS(t) ) KS/(SS + KS); MO,A(t) ) SO/(KOA + SO); MNH,A ) SNH)/(SNH + KNH,A); MHCO,A(t) ) SHCO/(SHCO + KHCO,A).
1 - fXI - fBAP 1/YA
fBAP γUAP,A
γUAP,H γUAP,H
lysis of XSTO nitrification lysis of XA
iN,SM - iN,XIfXI - iN,SMPfBAP iN,XS(1 - fXI - fBAP) iN,BM - iN,SMPfBAP - iN,XS(1 - fBAP) -iXB - 1/YA - iN,SMPγUAP,A iN,SM - iN,XIfXI - iN,SMPfBAP iN,XS(1 - fXI - fBAP)
-iN,BM - iN,SMPγUAP,H -iN,BM - iN,SMPγUAP,H
-(1 - YH,STO)/ (2.86YH,STO)
fXI
fXI
1 - fBAP
-1 1 - fXI - fBAP
1 1
1 1 -(1 - YH,S)/ (2.86YH,S) - iN,BM - iN,SMPγUAP,H -iN,BM - iN,SMPγUAP,H γUAP,H γUAP,H
-1 -1
fBAP
a
-1
bSTOXSTO µAMO,A(t) MNH,A(t) MHCO,A(t)XA bAXA
bHXH
1 -1
YSTO YSTO
-1/YH,STO -1/YH,STO
rate XSTO XA XS
-1
XI SNO SNH SUAP
SBAP
iN,XS iN,SMP - iN,SIfSI iN,SMP - iN,SIfSI
1 1 - fSI 1 - fSI -1 -1 -1/YH,S -1/YH,S
SS SI process
lysis of XH
Additional information is given in Tables 2 and 3.
aerobic growth on XSTO anoxic growth on XSTO
Appendix
hydrolysis of XS hydrolysis of BAP hydrolysis of UAP aerobic storage of SS anoxic storage of SS aerobic growth on SS anoxic growth on SS
This study was supported by State Key Laboratory of Urban Water Resource and Environment, Harbin Institute of Technology, and the Special Project of the National Water Pollution Control and Management of China (Grant No.2008ZX0731702).
Table 2. Stoichiometric and Composition Matrices for the Modified ASM3-SMP Modela
Acknowledgment
XH
5. Conclusions An integrated model to simulate the MBR process was developed that considered a biological process and cake layer-membrane filtration simultaneously. The concluding remarks of this study are outlined as follows: (1) The modeling concept developed and involved basically regarded MBR as CAS, properly accounting, however, for its characteristics differentiating it from the conventional systems. The adopted model was based on extended ASM3 with two improvements: (i) including simultaneous storage and utilization and (ii) introducing formation and degradation of SMP. This ASM3-SMP model could be easily and successfully applied to describe the biological status of MBR, such as organic removal, simultaneous storage, and growth process. (2) The sensitivities of variables (MLSS, COD, SMP, SNH, and SNO) to changes in key model parameters were analyzed. Four parameters (YSTO, YH,S, YH,STO, and bH) were obtained from the analysis on the basis of their significant impact on the model output. The prediction of SMP had a direct bearing on SI and, further, on the supernatant SCOD, confirming the important role of SMP in the biological processes. In view of facilitating the application of the model, batch experiments and OUR experiments were conducted and applied successfully to estimate the model parameters, providing some insights into mechanisms involving in the biological process. (3) The sludge particles formed an external cake on the surface of the primary membrane, which then acted as a filter to prevent them from fouling the primary membrane. A mechanistic model was developed to demonstrate the formation of the dynamic cake layer by sludge lower than critical diameter, and the modeling results showed that the external cake layer of rejected sludge particles played an important role in COD removal before the physical membrane filtration.
khMX(t)XH kh,BAP(MO,H(t) + ηhMAO,H(t))MBAP(t)XH kh,UAP(MO,H(t) + ηhMAO,H(t))MUAP(t)XH kSTOMO,H(t) MS(t)XH ηgkSTOMAO,H(t) MS(t)XH µH,SMO,H(t) MS,O(t) MNH,H(t) MHCO,H(t)XH ηgµH,SMAO,H(t) MS,O(t) MNH,H(t) MHCO,H(t)XH
a sludge cake layer with low hydraulic resistance, which might be another key point worth further study. The model developed in this study might serve as a basis for further development of a more comprehensive membrane fouling model and control of membrane operation. However, it was necessary to point out the model limitations. The parameter of G was not only dependent on the aeration intensity, sludge concentration, and density but also closely related with the configuration of the reactor and the arrangement of the membrane module in the MBR system. For models’ simplicity, the uneven distribution of G along the membrane axial was neglected in this study. Hence, there should be a certain degree of errors in the simulation, which adopted eq 15 to calculate the value of G. Additionally, there has to be concern for further model development with respect to the primary membrane filtration, especially considering a variation of the parameter im which should take the characteristics of membrane pore (such as pore diameter, membrane porosity) and the molecular weight of organic matters into account.
µH,STOMO,H(t) MSTO(t) MNH,H(t) MHCO,H(t)MKSXH ηgµH,STOMAO,H(t) MSTO(t) NH,H(t) MKS(t) MHCO,H(t)XH
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Table 3. Main Model Parameter symbol bA bH bSTO fBAP fSI fXI iN,MB iN,SMP kh kh,BAP kh,UAP kSTO KBAP KHCO KHCO,A KNH,A KNH,H KNO KOA KOH KS KSTO KUAP KX YH,S YH,STO YSTO ηg ηh µA µH,S µH,STO γUAP,A γUAP,H Cd k kFA im Fs µ µs σ
definition decay rate coefficient for autotrophy decay rate coefficient for heterotrophy decay rate coefficient for storage material fraction of BAP produced during cell lysis fraction of SI in SMP hydrolysis fraction of XI in biomass lysis nitrogen content of biomass nitrogen content of biomass hydrolysis rate for XS hydrolysis rate for BAP hydrolysis rate for UAP maximum storage rate of biomass biomass affinity constant for BAP bicarbonate saturation for heterotrophy bicarbonate saturation for autotrophy nitrogen affinity constant for autotrophy nitrogen affinity constant for heterotrophy saturation constant for SNO saturation coefficient for oxygen dissolve oxygen affinity constant substrate affinity constant biomass affinity constant for XSTO UAP affinity constant hydrolysis saturation constant yield coefficient for growth on SS yield coefficient for growth on XSTO yield coefficient for storage correction factor for anoxic growth of XH correction factor for anoxic hydrolysis maximum growth rate on of autotrophy maximum growth rate on of heterotrophy SS maximum growth rate of heterotrophy on XSTO fraction of UAP produced during XA growth fraction of UAP produced during XH growth coefficient of lifting force first-order removal coefficient coefficient of adhesion force coefficient of membrane interception density of sludge suspension fraction coefficient apparent viscosity of sludge suspension Happel’s correction factor
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value -1
0.1 day 0.25 day-1 0.25 day-1 0.055 0.15 0.2 0.07 g of N (g of COD)-1 0.07 g of N (g of COD)-1 3.0 day-1 5 × 10-3 day-1 0.03 day-1 2.0 day-1 1.0 mg of COD L-1 0.1 mol of HCO3- m-3 0.5 mol of HCO3- m-3 0.2 mg of N L-1 0.01 mg of N L-1 0.5 mg of NO3--N L-1 0.2 mg of O2 L-1 0.2 mg of O2 L-1 2.0 mg of COD L-1 1.0 g of COD (g of COD)-1 1.3 mg of COD L-1 1.0 g of COD (g of COD)-1 0.45 g of COD (g of COD)-1 0.59 g of COD (g of COD)-1 0.71 g of COD (g of COD)-1 0.6 0.4 0.85 day-1 0.6 day-1 0.6 day-1 0.45 0.12 0.38 5 × 10-5 s-1 3.5 × 10-6 N m-1 0.52 1.0 × 10-3 g L-1 0.03 2.69 × 10-3 Pa S 120
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ReceiVed for reView August 31, 2010 ReVised manuscript receiVed November 1, 2010 Accepted November 16, 2010 IE101827Y
