Environ. Sci. Technol. 2006, 40, 4703-4708
A Generalized Model for Aerobic Granule-based Sequencing Batch Reactor. 1. Model Development KUI-ZU SU AND HAN-QING YU* School of Chemistry, University of Science & Technology of China, Hefei, Anhui, 230026 China
A generalized model was established for simulating an aerobic granule-based sequencing batch reactor (SBR) with considerations of biological processes, reactor hydrodynamics, mass transfer, and diffusion. Methodology of discretization was effectively used for the model development and calculations. The activated sludge model no.1 was modified to describe the biological processes within the granules. Based on the difference between the calculated and measured results, the model structure was further improved through introducing simultaneous consumption of soluble substrates by storage and heterotrophs growth with a changeable reaction rate. Model calculations were conducted using a MATLAB program. The calculation results show the respective contributions of granules in different size fractions and slices to the overall change of model component concentrations. Moreover, oxygen concentration profiles within granules and oxygen consumption rate varied in one operating cycle. This confirms the applicability and validity of the discretization method and the model structure.
Introduction Sequencing batch reactor (SBR) has been widely used for wastewater treatment all over the world since its invention by Irvine and co-workers in 1980s (1). In most of the SBR units biomass grows in flocs. However, in recent years the use of granule SBR systems has attracted increasing research interest (2). Granules have good settling properties and present high biomass activity. Aerobic granule-based SBR has been proven to be applicable for treating various industrial wastewaters, such as dairy (3), malting (4), and soybean-processing wastewaters (5). Moreover, granule SBR operated under low oxygen saturation (20%) may be capable to simultaneously treat chemical oxygen demand (COD), nitrogen, and phosphate (6). For a biological wastewater treatment system, its optimization requires a lot of experimental input. Therefore, a simulation model is desirable for such an optimization (7-9). The model simulation and prediction can provide a solid foundation for design and operation of the biological treatment systems. Thus, a mathematical model for describing the aerobic granule-based SBR is essential. For the conventional floc-based activated sludge systems, activated sludge model (ASM) established by the International Water Association provides a consistent framework for the description of biological processes, including carbon oxidation, nitrification, and denitrification (10, 11). These model series * Corresponding author fax: +86 551 3601592; e-mail: hqyu@ ustc.edu.cn. 10.1021/es060141m CCC: $33.50 Published on Web 06/21/2006
2006 American Chemical Society
have been extensively employed for the conventional flocbased activated sludge systems (12-14). On the other hand, information on mathematical modeling of aerobic granule-based SBRs is still limited. Based on activated sludge model no. 1 (ASM1), a simulation model was developed to describe nitrification and denitrification processes in a sequencing batch airlift reactor (SBAR) with aerobic granules (8). This model was successfully used to evaluate the effects of decreased dissolved oxygen (DO) levels in the SBAR and to predict the effect of several process parameters on N removal. However, an aerobic-granulebased SBR is a complex biological system with numerous internal interactions among process variables and sludge characteristics. In addition to the biological reactions, mass transfer, hydrodynamic of reactors, and the characteristics of granules have been proven to be influential to the overall performance of the aerobic granule-based SBR (15). However, a model with full considerations of all these factors has not been developed for granule-based SBRs yet. Therefore, in this work a generalized model for aerobicgranule-based SBRs was established, taking all biological processes, reactor hydrodynamics, oxygen transfer, and diffusion into account. The ASM1 was modified and applied for describing the biological reactions. Parameter sensitivity analysis, model calibration, and verification are presented in the accompanying paper (16). The main aim of this research is to present a model that could be useful to simulate the conversion of nitrogen and organic compounds in aerobic-granule-based SBRs.
Materials and Methods Reactor Operation. The SBR used in this study had a working volume of 3.8 L with an internal diameter of 7.0 cm and a height of 100 cm. It was operated sequentially as 5 min of influent filling, 345 min of aeration, 5 min of settling, and 5 min of effluent withdrawal. Half of the liquid was drawn at the end of one cycle. An air velocity of 0.4 m3/h was applied to the SBR, equivalent to a superficial upflow velocity of 2.8 cm/s. The reactor was supplied with an influent COD of 3000 mg/L and was operated at 20°C. The synthetic wastewater consisted of sucrose (3000 mg COD/L), NH4Cl (200 mg N/L), Na2HPO4 (30 mg P/L), and elements as described elsewhere (17). After one-month of operation, the granules matured. The radii of matured granules varied from 0.1 mm to 1.1 mm with an average of 0.52 mm. The granules had a settling velocity of 31.8 ( 8.2 m/h, sludge volume index (SVI) of 29.8 ( 3.2 mL/g and a specific gravity of 1.019 ( 0.002, respectively. Determination of Kinetic and Stoichiometric Parameters. For the aerobic granules, diffusion resistance could mask the intrinsic properties of substrate utilization. Therefore, determination of kinetic and stoichiometric parameters was performed using fine floc particles ( 1, the ith component is completely penetrated, i.e., δim ) 0. The granule of the mth size fraction is taken as N slices (N ) 50 in this study). Assuming that the concentrations of component within each slice are uniform, they could be
calculated by solving eq 8. Concentrations and their gradients of component i in the nth slice of the mth size-fractioni i and ∂Sm,n /∂r, respectively. granule can be expressed as Sm,n If eq 8 is used in its original form, it can be calculated only using the Runge-Kutta method, attributed to its nonlinearity. To apply this method, the second-order differential equation describing the diffusion-reaction phenomena should be transformed into an equivalent system of two first-order differential equations, which must be solved simultaneously. The fourth-order Runge-Kutta numerical integration scheme can be implemented if both boundary conditions are known at the same value of the independent variables, either at the center of the granule or on its external surface. However, for a fully penetrated granule, a 0/0 mathematical error arises in one of the equations when the method is used for the center of the particle. Thus, in this work, this problem is solved by starting the numerical integration at a point very near the center, i.e., r ≈ 10-6. Since the substrate concentration in the center of the particle (SG, 0) is unknown, the method consists of guessing this concentration and integrating the equation system from r ) 0 to r ) R, thus obtaining the value of SG at the surface (SG, R). The value of (SG, R) obtained is then compared with the known value. If the desired precision is not achieved, another guess should be made for the SG value in the center this time. This new guess could be given with the following expression:
) Si(old) + δ[Si(known) - Si(calculated) ] Si(new) 0 0 sur sur
(11)
where δ > 0 is a factor that accelerates or retards the convergence. Sub-Model for Biological Reactions. The ASM1 was used to describe the biological reaction processes in this work. Substrate degradation, nitrification, denitrification, and hydrolysis were taken into account with seven components and seven processes shown in the Supporting Information (C1-C8 and R1-R7 in Table S1). The reaction rates are also shown in the Supporting Information (R1-R7 in Table S2). Products of cell decay and particle organic nitrogen were integrated into the slowly degradable substrate and they were assumed to have an identical hydrolysis rate. The inert matters were omitted in the model and could be readily added when needed. Moreover, considering the characteristics of SBRs and difference between the granules and sludge flocs, several modifications were made to the ASM1 to describe the biological reactions within the aerobic granules.
Results and Discussion Modifications to the ASM1. Basic Modifications. Both heterotrophs and autotrophs utilize oxygen as their terminal electron acceptors. When oxygen diffusion is limited in the aerobic granules, the competition for oxygen will give the heterotrophs a selective advantage over the slow-growing autotrophs. This results in a limitation of nitrification because of the shortage of oxygen. To obtain a lower specific growth rate at a higher substrate concentration, a modification to the autotrophic maximum specific growth rate was performed through substituting µmax,A with µmax,A(t), which can be expressed as follows:
µmax,A(t) ) µmax,Ae-P1SS(t)
(12)
where P1 is a constant. Modification of Model Structure. For the modified ASM1, parameter values were calibrated using the following objective function:
Objective function )
(ymeasured - ysimulated)2
∑
2 ymeasured
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growth on SS” and “polymer storage on SS” competed for the available readily degradable substrates. When a sufficient amount of substrate was supplied to the famine biomass at the beginning of an operating cycle in the SBR, storage prevailed against the heterotrophic growth due to its greater substrate utilization rate. Afterward, storage gradually gave way to the heterotrophic growth on the storage polymers and substrates. Both maximum storage rate and growth rate were considered to be changeable with operating time (indicated by COD concentration), and experiential coefficients with exponential form were proposed as follows:
FIGURE 1. Measured (dot) and predicted (line) concentration profiles of COD, NH4+-N and VSS. where ymeasured and ysimulated are the measured and simulated values of parameters, respectively. The concentrations of COD, NH4+-N, and VSS were used in the calibration process. During the calibration with eq 13, the lowest value of objective function was calculated to be 1.027. As shown in Figure 1, an inconsistence between the measured and predicted results was found. A very rapid consumption of ammonia accompanying the initial growth of biomass was simulated. The simulated rates of COD degradation and biomass growth were lower in the initial 2 h and became higher in the subsequent 2 h (Figure 1). This might result from the accumulation of biomass without ammonia consumption. In the simulation of activated sludge systems, a simultaneous heterotrophic growth on soluble substrates and storage of polymers are observed (12, 26). Considering the difference between the predicted and measured results, processes of polymer storage and heterotrophic biomass growth on the storage polymers under both aerobic and anoxic conditions were included in this modified model as shown in the Supporting Information (C9, R8-11 in Table S1 and R8-11 in Table S2). To simplify the model structure, storage polymers (XSTO) were incorporated into the heterotrophic biomass (XH) and considered as a part of the biomass, instead of an individual component in the subsequent calculations. The processes “heterotrophic
µmax,H-SS(t) ) (1 - eP2*(SS(t)-SS(0)))µmax,H-SS
(14)
kSTO(t) ) eP2*(SS(t)-SS(0))kSTO
(15)
where P2 is a constant, SS(0) is the initial substrate concentration. Model Calculations. A program was written using the software of MATLAB for calculation. Because the model for the aerobic-granule-based SBR is complex and cannot be expressed using an integrated equation, the model calculation must be conducted step by step. As shown in the Supporting Information (Figure S3), after parameter initiation, profiles of each component within the granules for different radii were initially determined by solving eqs 1-11. Thereafter, the biological reaction kinetics in each slice for different size fractions were calculated, with which the total reaction rates of model components were determined. Concentration of the model component at time t + ∆t was then calculated by adding its production (negative for consumption) to the concentration at time t. Then, the variation of the model component as a function of time could be determined. Table 1 lists the parameter values of the modified ASM1 either defaulted or measured. Values of other parameters were defaulted in ASM1 (10). These parameter values will be calibrated in the accompanying paper and applied for model verification (16). Granule characteristics and mass transfer coefficients are summarized in Table 2. For the models established, calculation was carried out through categorizing granules by size and slicing one granule of a given size fraction. The contributions of the granules in
TABLE 1. Parameters Values for Model Simulation parameter
unit
definition
value
YH
g COD/g COD
0.58
measured
YSTO
g COD/g COD
0.75
defaulted
YH,STO
g COD/g COD
0.53
defaulted
kSTO
1/d
25.0
defaulted
µmax,H-STO
1/d
25.0
defaulted
µmax,H-SS
1/d
4.98
measured
KS
g COD/m3
26.1
measured
bH
1/d
heterotrophs yield coefficient storage yield coefficient yield coefficient by storage maximum specific storage rate maximum specific growth by storage maximum specific growth by SS substrate half-saturation coefficient heterotrophs decay coefficient anoxic correction coefficient maximum specific hydrolysis rate organic nitrogen hydrolysis coefficient constant in eq 12 constant in eq 14 and eq 15
0.92
measured
0.46
measured
1.50
defaulted
0.07
measured
0.003 0.002
defaulted defaulted
ηH,NO3
kh
1/d
R
g N/g COD
P1 P2
4706
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FIGURE 2. Contributions of different size fractions and slices to the reaction rates: (A) size fraction; and (B) slice (R ) 0.5 mm).
TABLE 2. Granule and Mass Transfer Parameters parameter granules minimum radius maximum radius mean radius variance of radius constant of size distribution wet density mass transfer effective diffusivity of O2 effective diffusivity of sucrose effective diffusivity of NH+4 superficial gas velocity
symbol
unit
Rmin Rmax Rmean Rvar A
mm mm mm mm
Fw
g/m3 1.03
DeO
m2/s
DeS DeNH4
m2/s 3.30 × 10-10 polakovic et al. (27) m2/s 1.52 × 10-9 wik (28)
Ug
cm/s 1.10
2
value 0.10 1.10 0.52 0.18 4.78
1.58 ×
reference measured measured measured measured measured measured
10-9
measured
measured
different size fractions and numerous slices to the overall change of concentrations of the model components (SS, NH4+-N and NO3--N) were different. Therefore, calculations were conducted to evaluate the ratios of reaction rates of different size fractions to the overall reaction rates (Figure 2A), and the reaction rates of different slices to those of the entire granule (Figure 2B) using the parameter values shown in Tables 1 and 2. As illustrated in Figure 2A, the kinetic rates for SS, SNH, and SNO3 had peak curves with increasing radius of size fraction. This was mainly associated with the peakcurve size distribution of the granules. More granules had radius around the mean value, and accordingly, the corresponding size fraction had a greater reaction rate. For the granules larger than 0.8 mm, negative values of reaction rates of NO3--N were found, suggesting that the NO3- concentration was decreased due to the higher denitrification rate within the larger granules. For the 0.5 mm-granules, the reaction rates of different slices are shown in Figure 2B. For the slices near the granule center (r < 0.65 R), the denitrification rate was greater than that of nitrification due to the low DO concentration. For the entire granule, nitrification was predominant and the NO3- concentration increased. The increase in SS, SNH, and SNO3 was accelerated by increasing the distance of slice to the granule center, mainly associated with the high DO concentration and the presence of more microorganisms for the slices in outer layers. The calculation results confirmed the possibility of simultaneous nitrification and denitrification observed for the SBAR (8). Because an SBR was taken as a series of CSTRs in time sequence, oxygen consumption rates within the granules should be calculated for each CSTR. As shown in Figure 3, the oxygen consumption rate decreased with a decrease in
FIGURE 3. Oxygen consumption rate as a function of operating time.
FIGURE 4. (A) Oxygen concentration profiles; and (B) oxygen flux at the surface for 0.75-mm-radius granules in a cycle of operation. substrate concentration in an operating cycle. When the oxygen consumption rate was higher than that of diffusion, oxygen was consumed before diffusing into the inner granules. This led to a partial penetration of oxygen at the initial time of operation (Figure 4A). However, with the increasing consumption of substrates, the oxygen consumption rate decreased and diffusion prevailed, resulting in a full oxygen penetration (Figure 4A). This implies that, at the VOL. 40, NO. 15, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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beginning of an operating cycle, the microorganisms in the center of granules stored soluble substrates as polymers under anoxic conditions. As oxygen concentration increased with operating time, oxygen became available to the microorganisms and these polymers could be used for the aerobic growth of the heterotrophs. Oxygen diffusion flux into the granules also decreased with cycle time (Figure 4B). Although the oxygen diffusion flux was greater at the beginning of a cycle, the oxygen concentration within the granules was lower, resulting from a higher oxygen consumption rate (Figure 4). On the contrary, at a low substrate concentration, oxygen could penetrate into the granule center even when the diffusion flux was low. As one of the main limited components, oxygen concentration was proven to be significantly influenced by the biological reaction rates in an operating cycle. Model calculations based on a series of CSTR in time sequence and granule classifications and slices were proven to be precise and reliable. The model predicted different behaviors of the granules with various sizes and numerous slices within one granule. The oxygen consumption rates and concentration profiles for a certain granule during an operating cycle could also be calculated.
Acknowledgments The authors wish to thank the Natural Science Foundation (NSFC) of China (grant no. 20577048), and the NSFC-RGC joint project (50418009) for the partial support of this study. We also greatly appreciate the valuable suggestions of Dr. Raymond Zeng at Technical University of Denmark.
Supporting Information Available Tables of stoichiometric matrix for the heterotrophs and autotrophs and the kinetics rate expressions for the reaction processes based on ASM1 and some modifications are presented; Internal interactions, calculating process of the model, and the schematics of the sliced aerobic granules are also shown. This material is available free of charge via the Internet at http://pubs.acs.org.
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Received for review January 22, 2006. Revised manuscript received May 16, 2006. Accepted May 19, 2006. ES060141M
